VOLTERRA BROCHURE ELECTRIC FIRE TRUCK REFERENCE GUIDE minimize fuel and produce less noise with no compromise on apparatus features functionality and safety with an electric fire truck The revolutionary Pierce® Volterra™ platform of electric vehicles meets the needs of your fire department while providing the operational performance you expect from your apparatus.  the operational benefits of the distinct power source solution provide transparent vehicle operational characteristics to the firefighter.  Oshkosh Patented Parallel-Electric Drive Train Industry-Leading Operational Range For Full-Shift Operation Fire Station-Based Charging Infrastructure an Oshkosh patented parallel-electric drivetrain featuring an EMIVT allows zero-emissions operation when powered by the integrated onboard batteries.  The electric fire truck chassis will operate independently in either the all-electric The EMIVT leverages either source of power to provide uninterrupted performance in extended emergency operations Standardized Pierce pumping configurations are driven through the EMIVT and are powered by either the integrated onboard batteries or the internal combustion engine The driveline allows for zero emissions during quick attack responses and has the ability to transition seamlessly to internal combustion power for extended pumping operations.  all encompassing vehicle charging infrastructure provides operational readiness for Volterra electric vehicles but it is not a one-size-fits-all solution Pierce works with departments to calculate optimal charging requirements helping to customize the right-sized solution based on typical run volume This ensures efficiency without unnecessary costs and fast charging solutions capable of supporting an electric fire truck in EV mode for your departments operational cadence 155 kWh hour battery pack to meet the City of Madison’s daily duty cycle Enforcer™ Volterra™ 155 kWh hour battery pack to meet Portland Fire and Rescue's daily duty cycle 244 kWh hour battery pack to meet Gilbert Fire and Rescue’s daily duty cycle We've made installing your electric fire engine infrastructure simple. The planning phase of adding an electric apparatus to your fleet starts with a discussion of the future you first need to consider the right investment Understanding how an electric fire truck can fit in your station and the charging capacity calculations are all items Pierce and your dealer discuss in the initial planning stages Pierce acts as the technical resource to help compliment your preferred power vendors We’ll take the time to meet and align with your local experts to support your goals so you can focus on your daily work and not on the technical details of your new apparatus As a subsidiary of Oshkosh Corporation our team has a long and successful history of developing electric vehicles moving the world closer to zero emissions.  Electrification Journey Q+A: How Does Electric Fire Truck and Pump Performance Compare to a Traditional Truck and Pump? Q+A: Electric Fire Truck High Voltage Overview Electric Fire Trucks in Cold Weather A Day in the Life of a Volterra Electric Fire Truck Electric Fire Truck Charging Infrastructure Pierce Volterra Platform of Electric Vehicles: The Story Behind the Technology San Diego (CA) Fire-Rescue’s $52M Order Includes 18 Custom Pierce Fire Apparatus Electric Fire Trucks are Coming to the Pacific Northwest Pierce Volterra Awarded ‘Coolest Thing Made In Wisconsin’ Growing Electrification Throughout Fleets The Best Emergency Services and Defense Innovations of 2022 Portland to Add Zero-Emissions Apparatus to Fleet Electric Vehicles are Gaining Traction Among Wisconsin Drivers and Businesses that Provide Support First Pierce Electric Fire Truck Already Responding in WI City Meeting the Demand for Electric Vehicles Wisconsin Municipality Reaches Milestone with 100th EV Wisconsin Manufacturer Releases Electric Fire Truck Pierce and Portland Fire and Rescue Secure Joint Development Agreement for Volterra Electric Pumper The Age of Electrification Future of Firefighting Madison, Wisconsin Department First to Add Pierce Volterra Electric Vehicle First Electric Fire Truck in North America Made by Pierce Manufacturing Now in Service at Madison (WI) Fire Department Pierce and Oshkosh Airport Products Introduce the Volterra Platform of Electric Vehicles Watch now: Madison Unveils Nation's First Electric Fire Engine Pierce and Oshkosh Airport Products Introduce the Volterra Platform of Electric Vehicles Pierce and Oshkosh Airport Products Introduce the Volterra Platform of Electric Vehicles Registered Trademark of Pierce Manufacturing Inc The City of Madison Fire Department and Pierce Manufacturing Inc. an Oshkosh Corporation (NYSE:OSK) business announce the first Pierce® Volterra™ electric pumper production unit ordered is now in service This milestone represents the culmination of years of collaboration and commitment to advancing zero-emissions technology in the fire service industry The City of Madison Fire Department became the first in North America to test and evaluate the Pierce Volterra platform in a live operational environment they celebrate the first production custom unit in their fleet—a significant achievement for both the department and the city’s broader sustainability agenda “We are proud to officially welcome the first Pierce Volterra electric pumper production unit,” said Fire Chief Chris Carbon of the City of Madison Fire Department “This vehicle is a testament to our department’s dedication to innovation The partnership with Pierce has enabled us to deliver the highest-quality apparatus to our firefighters and the community we serve.” The custom-built electric pumper is designed to align with the City of Madison’s environmental and operational goals offering zero-emissions pumping and driving in EV mode It features Pierce’s patented parallel-electric drivetrain and a comprehensive charging infrastructure supported by Madison Gas and Electric helping to ensure uninterrupted performance and seamless integration into the department’s fleet Assistant Fleet Superintendent for the City of Madison emphasized the significance of this delivery “Fire trucks are among the most challenging vehicles to electrify and seeing the first production unit delivered to Madison is a remarkable achievement,” she said “Adding this electric pumper to our fleet showcases Madison’s commitment to being at the forefront of clean energy innovation while supporting our first responders in their critical mission.” Key Features of the City of Madison’s Pierce Volterra Electric Pumper Include: The City of Madison Fire Department serves over 250,000 residents across nearly 100 square miles from 14 fire stations The Pierce Volterra electric pumper will respond to emergency calls from Fire Station 8 on Lien Road the department’s dedication to innovation and sustainability is now embodied in the Pierce Volterra electric pumper “This is an exciting milestone for the fire service industry and our valued partnership with the City of Madison,” said Jason Krueger “Integrating a Volterra electric pumper into their fleet is a testament to Madison’s leadership and Pierce’s commitment to pushing the boundaries of technology.” To learn more about Pierce Manufacturing and the revolutionary Pierce Volterra platform of electric vehicles, visit www.piercemfg.com ™ All brand names referred to in this news release are trademarks of Oshkosh Corporation or its subsidiary companies Subscribe to the City of Madison News Releases email list Wisconsin Public Records Laws may require us to provide your email address to third parties you are requesting that we treat your email as confidential and we will not release it to public records requests City-County Building210 Martin Luther King Jr Copyright © 1995 - 2025 City of Madison Thank you for completing the form, here is your download: "+jQuery("body").attr("docName")+" Thank you for completing the form, here is the link to your on-demand webinar: On-Demand Webinar Link The first Pierce Volterra Electric Pumper production unit ordered is now in service with the City of Madison Fire Department in Wisconsin The City of Madison Fire Department became the first in North America to test and evaluate the Pierce Volterra platform in a live operational environment Copyright © 2025 Lexipol. All rights reserved.Do Not Sell My Personal Information Thank you!We have emailed you a PDF version of the article you requested You can also addnewsletters@iflscience.comto your safe senders list to ensure you never miss a message from us IFLScience HomePopulation Growth Appears To Closely Follow The Lotka-Volterra Mathematical EquationsComplete the form below to listen to the audio version of this article IFLScience needs the contact information you provide to us to contact you about our products and services You may unsubscribe from these communications at any time For information on how to unsubscribe, as well as our privacy practices and commitment to protecting your privacy, check out ourPrivacy Policy IFLScience HomeJoin for Exclusive FacebookemailJames is a published author with four pop-history and science books to his name. He specializes in history, strange science, and anything out of the ordinary. FacebookemailEditedbyLaura SimmonsLaura Simmons emailLaura is an editor and staff writer at IFLScience She obtained her Master's in Experimental Neuroscience from Imperial College London Populations in predator-prey groups tend to oscillate two mathematicians working on separate continents proposed the same set of mathematical equations for describing population growth and decline in biological systems.  "In both systems, all processes could be reduced to two kinds of changes: those involving exchanges of matter between the components of the system, and those involving exchanges of energy," a review of the topic by science historian Dr Sharon Kingsland explains of Lotka's thinking "In the chemical system the components were molecules In the biological system the components were organisms plus the raw materials in their environment and the exchanges of matter and energy took place through the web of food relationships the Lotka-Volterra equations describe population growth with eerie levels of accuracy           The predator population meanwhile grows as the prey grows but then face more competition for their food as they reduce the abundant prey and the result is a reduced predator population "Periodic phenomena play an important role in nature, both organic and inorganic. In chemical reactions rhythmic effects have been observed experimentally, and have also been shown, by the writer and others, to follow, under certain conditions, from the laws of chemical dynamics," Lotka wrote in a 1920 paper in the cases hitherto considered on the basis of chemical dynamics the oscillations were found to be of the damped kind only transitory (unlike certain experimentally observed periodic reactions)." "It seemed that the occurrence of [...] permanent oscillations the occurrence of purely imaginary exponents in the exponential series solution presented would demand peculiar and very specific relations between the characteristic constants of the systems undergoing transformation; whereas in nature these constants would with considerable surprise that the writer on applying his method to certain special cases                  it shows how mathematical equations can appear to govern (or adequately describe) extremely complex and variable systems animalsFemale Bonobos Can Elevate Their Status By Teaming Up To Gain Power Over Males1 hour agolink to article VideoanimalsBiofluorescence vs Bioluminescence1 hour agolink to article Biofluorescence vs Bioluminescencelink to article T. Rex Leather, Glow-In-The-Dark Gas Clouds, And Musical Sea Lionslink to article © 2025 IFLScience. All Rights Reserved. RSS Metrics details As part of our special issue focused on glia we are having conversations with both established leaders in the field and those earlier in their careers to discuss how the field has evolved and where it is heading we speak with Andrea Volterra (visiting faculty at the Wyss Center and honorary professor at the Department of Fundamental Neuroscience who dedicated his research career to uncovering astrocyte–synapse communications in physiology and disease and a strong advocate of the Socratic method Prices may be subject to local taxes which are calculated during checkout Download references Nature Neuroscience https://www.nature.com/neuro/ Reprints and permissions Download citation DOI: https://doi.org/10.1038/s41593-024-01721-4 Anyone you share the following link with will be able to read this content: a shareable link is not currently available for this article Sign up for the Nature Briefing newsletter — what matters in science Republic Services Inc. has placed an order for 100 McNeilus Volterra ZSL electric refuse and recycling collection vehicles from Oshkosh Corporation This second order follows the successful operation of initial units into Republic Services’ residential collection fleet “Republic Services has made an industry-leading commitment to fleet electrification and we look forward to continuing our longstanding partnership with Oshkosh and McNeilus,” says Brett Rogers “Our latest order of Volterra EVs will help us provide cleaner quieter service to customers and help our municipal partners achieve their climate goals.” Republic Services first ordered 50 Volterra ZSL electric refuse and recycling collection vehicles from Oshkosh in 2023 Republic Services plans to have electric vehicles to comprise half of its new truck purchases over the next five years a fully integrated electric refuse and recycling collection vehicle is designed to meet the demands of waste and recycling collection while managing carbon emissions “Republic Services has been a valued partner for many years and we are thrilled to support their sustainability initiatives with our McNeilus Volterra electric refuse and recycling collection vehicles,” adds John Pfeifer president and chief executive officer of Oshkosh “This order is a testament to our shared vision of advancing environmental sustainability while delivering high-performance solutions for waste and recycling management.” The 100 McNeilus Volterra electric vehicles will be deployed across multiple states contributing to Republic Services’ goals to reduce greenhouse gas emissions 35% by 2030 Each vehicle is equipped with advanced safety features lane-departure sensors and automated braking systems The Volterra eRCV can operate a full day’s route on a single charge “In addition to helping advance environmental goals, the Volterra eRCV was thoughtfully designed with drivers, service technicians and business owners in mind,” says Lee Dreas, vice president and general manager of McNeilus Truck and Manufacturing. “We’re proud to offer this innovative solution, which transforms the driver experience while delivering outstanding total cost of ownership advantages.” The McNeilus Volterra electric refuse and recycling collection vehicles feature a purpose-built chassis and body, integrated as a single unit to maximize interior space and streamline operations. The vehicle has zero-emission certifications from the California Air Resources Board (CARB) and the U.S. Environmental Protection Agency (EPA). alongside groundbreaking technological innovations have enabled new and profound analyses of the mathematical sophistication behind these ancient architectural projects Courtesy of AutodeskA New Lens on Vitruvian Ideals When Professor Wladek Fuchs began his work with the Volterra-Detroit Foundation, he could not have anticipated the groundbreaking revelations the project would uncover. According to Fuchs, Vitruvius focused on general design principles (utilitas, firmitas, venustas) and aimed to make architectural language accessible to a broad audience, rather than detailing practical methods. This likely explains the discrepancies between his recommendations and actual Roman practices. Courtesy of AutodeskThe Intersection of Technology and Tradition Although the workflow was groundbreaking, it was not without its challenges. From precisely maneuvering drones at the sites to managing vast data sets, the project demanded innovation at every stage. Nevertheless, as Randall emphasizes, the effort paved the way for a scalable and replicable approach to heritage preservation worldwide. "These tools are more accessible and affordable than ever, making it possible to meet the needs of digital preservation across the globe." Courtesy of AutodeskLessons for the Present and Future The Volterra Project is more than an academic exercise; it serves as a bridge between the ancient and the modern. Fuchs emphasizes the potential of these discoveries to influence contemporary architectural education. "We often teach the history of architecture as a catalog of dramatic forms," he observes. "But understanding Roman design methods—how they optimized geometry and proportions—can make history more relevant and transformative for today's designers." Courtesy of Autodesk I would risk a statement that the geometry and mathematics of Roman structures are like a mix between the fingerprints of the architects and the mitochondrial DNA of all Roman architecture it will take a long time to fully understand them—if that is even possible—because much of the material must be re-studied I feel that I am merely laying the groundwork for future knowledge But this already offers a completely different perspective on ancient architecture: that it was not homogenous with much to be learned about its variations emphasizing the role of technology in preserving historical memory "What we've accomplished in Volterra can serve as a model and public groups to sustainably breathe life into these incredible places."  We have an almost insurmountable global need to protect and preserve these important sites What we've achieved collaboratively in Volterra can be used as a template to organize resources worldwide and unite experts and the public sector to safeguard these extraordinary locations Fuchs also notes that the principles of Roman design can inspire new approaches to solving architectural challenges today "Their proportional systems weren't just about aesthetics; they simplified logistics and construction offering a level of precision that minimized errors If today's architects can integrate that logic with modern materials and techniques The Volterra Project has illuminated a richer and more intricate tapestry of Roman architecture than Vitruvius's writings alone suggest "The geometry and mathematics in Roman structures are like the architects' fingerprints and the DNA of the architectural tradition They reveal a diversity and ingenuity that challenge our assumptions and invite deeper exploration." By blending advanced technologies with rigorous historical investigation the Volterra Project is not only preserving the past—it is redefining how we understand and utilize it it ensures that the wisdom of ancient architects continues to inspire future generations You'll now receive updates based on what you follow Personalize your stream and start following your favorite authors If you have done all of this and still can't find the email Portland Fire & Rescue has integrated a Pierce® Volterra™ electric fire truck into its fleet demonstrating their city’s commitment to innovation and sustainability we explore how Portland Fire & Rescue’s electric fire truck performs on the job meets daily demands and fits into their existing fleet Read on to learn more about the benefits and insights from their experience Portland Fire & Rescue serves over 630,000 citizens across approximately 150 square miles The department operates out of 31 fire stations with a diverse fleet Portland Fire & Rescue has several specialty teams marine and a land based shipboard firefighting team Portland Fire & Rescue’s Pierce Volterra electric fire truck has joined a busy fleet handling roughly 3,500 calls per year like its traditional diesel apparatus counterparts. The Pierce Volterra electric fire truck is tasked with maneuvering Portland’s busy city streets and managing both short and long runs with reliable and consistent performance managing the majority of calls in electric mode The fire truck is equipped with a backup internal combustion engine for prolonged emergency response scenarios but has yet to rely heavily upon this feature.  “Aside from the Pierce Volterra electric fire truck sticker on the side of the truck you’d never even know this is an electric vehicle It blends in seamlessly with the rest of our fleet.” Firefighters and community members alike remark that the Pierce Volterra EV looks just like a traditional diesel engine powered truck and complements the existing fleet's effectiveness and efficiency One of the key benefits of the Pierce Volterra Electric Vehicle is that it looks and operates like traditional Pierce fire trucks the vehicle can be configured to match existing fleet vehicles with ease This is a critical consideration for a new fire apparatus investment When a new fire truck configuration matches existing fleet apparatus with tools and equipment in similar compartments it reduces training requirements and improves firefighter efficiencies “Truck familiarity is very important to the way we work in Portland,” said Matt Fullerton “When our firefighters approach a high-rise fire the driver will often go up with the rest of the crew and another driver will step in to run the pumper and the standpipe system If we had a completely different form factor vehicle it would make it really difficult for anyone else to come and run the equipment.” "The Pierce Volterra EV uses common driveline components (axles etc) to match your current fleet,” said Matt Sauter Business Unit Director at Pierce Manufacturing “Our high voltage (HV) components are centrally located in a confined area allowing non-HV trained technicians to safely work on almost any component on the truck." Learn more about the benefits of fleet standardization in this blog. Electric vehicles are virtually silent without an engine powering the fire truck while in electric mode This added benefit makes for quieter operations around town and benefits firefighters in several ways there’s a big reduction in engine noise,” stated Fullerton I don’t have quite as much noise surrounding me.” Read more about the operational benefits of an electric fire truck from Gilbert Fire & Rescue Department. the Pierce Volterra electric fire truck at Portland Fire & Rescue is frequently in and out of the station But the battery’s performance has met the call requirements with ease I plug in the engine and it tops itself off at 100% it will be in electric mode until the engine hits the ICE threshold but other drivers have when they have longer drives to other parts of the city the engine automatically switches to the diesel engine—we don’t even notice it in the cab.” plugging in the electric vehicle is a simple step in the standard operating procedures It ensures the rig is ready for the next call maintaining its charge for optimal electric mode performance minimizing downtime and ensuring the truck can handle the call demands Whether the truck operates in electric mode or seamlessly switches to diesel for longer drives firefighters trust the system will support their needs without any interruptions in performance Portland Fire & Rescue's adoption of the Pierce Volterra electric fire truck demonstrates the department’s dedication to sustainable solutions without sacrificing performance The electric fire truck has seamlessly integrated into the fleet efficient and reliable service while reducing noise and emissions in the community the Pierce Volterra is already showing promising results with minimal disruptions and impressive operational benefits Is your department ready to explore electric fire trucks Find your local Pierce dealer today to learn how an electric fire truck can enhance your fleet’s efficiency and sustainability This news release contains statements that the Company believes to be “forward-looking statements” within the meaning of the Private Securities Litigation Reform Act of 1995 All statements other than statements of historical fact statements regarding the Company’s future financial position and plans and objectives of management for future operations words such as “may,” “will,” “expect,” “intend,” “estimate,” “anticipate,” “believe,” “should,” “project” or “plan” or the negative thereof or variations thereon or similar terminology are generally intended to identify forward-looking statements These forward-looking statements are not guarantees of future performance and are subject to risks some of which are beyond the Company’s control which could cause actual results to differ materially from those expressed or implied by such forward-looking statements These factors include the Company's ability to successfully integrate the AeroTech acquisition and to realize the anticipated benefits associated with the same; the risks associated with international operations and sales including compliance with the Foreign Corrupt Practices Act;  the Company’s ability to comply with complex laws and regulations applicable to U.S government contractors; cybersecurity risks and costs of defending against mitigating and responding to data security threats and breaches impacting the Company; the Company’s ability to successfully identify complete and integrate other acquisitions and to realize the anticipated benefits associated with the same; and risks related to the Company’s ability to successfully execute on its strategic road map and meet its long-term financial goals Additional information concerning these and other factors is contained in the Company’s filings with the Securities and Exchange Commission All forward-looking statements speak only as of the date of this news release to update information contained in this news release Investors should be aware that the Company may not update such information until the Company’s next quarterly earnings conference call Use this free guide as a tool to help your fire department and municipality understand electric fire truck features hbspt.cta._relativeUrls=true;hbspt.cta.load(1641088 As fire departments across the world consider procuring an electric fire truck many are curious about how other departments have navigated the process of ‘going electric.’ In fall of 2023, the Gilbert Fire & Rescue Department added a Pierce® Volterra™ electric fire truck to its fleet in one of the community’s busiest fire stations The department responds to a variety of emergency scenarios After using the Pierce Volterra electric fire truck to run more than 1,000 service calls The leadership team at Gilbert Fire & Rescue spoke with Pierce representatives to offer insights on why they chose the Pierce Volterra EV as well as advice the Assistant Fire Chief would offer to other fire departments considering electric fire apparatus Gilbert Fire & Rescue’s decision to pursue an electric fire truck was driven by a desire for innovation and improvement within their service delivery framework Department leadership recognized the importance of staying ahead in the evolving sustainability landscape aiming to enhance both their service delivery and the safety of their fire personnel By addressing the direct health risks associated with diesel emissions and improving on-scene communication through reduced noise levels Gilbert Fire & Rescue aims not only to keep pace with industry changes but to set a new standard for fire service operations in the modern era Gilbert Fire & Rescue applied their standard pumper specification as a baseline to ensure the new Pierce Volterra electric fire truck would seamlessly integrate into their operations without compromising on key functional Along with its innovative electric powertrain what makes the Pierce Volterra stand out is its remarkable resemblance to a traditional Pierce Manufacturing fire truck distinguishing between the Pierce Volterra and its conventional counterparts is a challenge aiming to maintain familiarity for the firefighters and ease the transition to electric vehicles “Other available electric fire truck options didn’t feel like a traditional North American fire truck,” stated Cory Gerard Assistant Fire Chief at Gilbert Fire & Rescue Department the crews who use it have to be familiar with it and understand how to use it effectively.” was also a key consideration from a maintenance perspective Notable features of Gilbert’s Pierce Volterra pumper include: This thoughtful integration of traditional features with innovative technology underscores Gilbert Fire & Rescue's commitment to advancing their service capability in a manner which prioritizes both the safety of their personnel and environmental responsibility How does electric fire truck and pump performance compare to a traditional truck and pump? This Q+A reviews the details. Recognizing change can challenge what is known the department placed a strong emphasis on training its crews on electric apparatus operation and functionality By engaging with firefighters early on—before the truck was even put into service—the department aimed to foster organizational support and smooth over the transition Members of the department who initially had reservations about electric vehicles began to see the electric fire truck in a new light The quiet operation during pumping became a point of appreciation particularly among engineers who were accustomed to the loud environments of diesel pumpers along with reduced exposure to diesel emissions in the bay contributed to a broader acceptance and interest in the truck The Pierce Volterra EV’s seamless integration into daily operations mirroring the start-up and operational procedures of traditional pumpers played a significant role in breaking down barriers of acceptance With the procurement of any new fire apparatus operations and maintenance planning required “Integrating an electric fire truck to an existing fleet does come with challenges,” stated Chief Gerard “Planning ahead and knowing the requirements of charging and maintenance are two key considerations.” “Pierce’s network of dealers across North America does offer electric fire truck maintenance services but planning ahead is critical to reduce downtime,” said the fire chief your station must be prepared to manage truck downtime effectively whether it’s an electric or traditional apparatus.” Can firefighters perform routine maintenance on trucks with high-voltage power? We answer this question and more in this Q+A with our engineering team The Pierce Volterra electric fire truck combines reliable and consistent power with the advantages of electrification This innovative fire truck is engineered to deliver optimal performance and robust firefighting capabilities across all modes of operation ensuring fire departments have a versatile and efficient solution Learn more about electric fire trucks, the Pierce Volterra platform of electrified vehicles or contact your local dealer today to hear more about why our power solution stands out from the competition ®, ™ All brand names referred to in this news release are trademarks of Oshkosh Corporation or its subsidiary companies. © 2025 Pierce Manufacturing, Inc. Registered Trademark of Pierce Manufacturing Inc. Appleton, WI, USA an Oshkosh Corporation Business Volume 2 - 2022 | https://doi.org/10.3389/fsysb.2022.1021897 This article is part of the Research TopicEducation in Systems Biology 2022View all 5 articles The Lotka-Volterra (LV) model was introduced in the early 20th Century to describe predator-prey systems the model has been expanded to capture the dynamics of numerous types of interacting populations and to include the effects of external factors from the environment the LV approach has proven to be a very valuable tool for gaining insights into the dynamics of diverse biological interaction systems recognizing the critical importance of microbiomes for human and environmental heath LV systems have become effective tools of analysis and the default for quantitatively assessing interactions within these large microbial communities Here we present an overview of parameter inference methods for LV systems specifically addressing individuals entering the field of biomathematical modeling who have a modest background in linear algebra and calculus The methods include traditional local and global strategies as well as a recently developed inference method based strictly on linear algebra We compare the different strategies using both lab-acquired and synthetic time series data We also address a recent debate within the scientific community of whether it is legitimate to compose large models from information inferred for the dynamics of subpopulations In addition to parameter estimation methods the overview includes preparatory aspects of the inference process and the choice of an adequate loss function Our comparisons demonstrate that traditional fitting strategies such as gradient descent optimization and differential evolution tend to yield low residuals but sometimes overfit noisy data and incur high computation costs The linear-algebra-based method produces a satisfactory solution much faster but requires the user to estimate slopes from the time series The results also suggest that composing large models from information regarding sub-models can be problematic there is no clear “always-best method” for inferring parameters from data and prudent combinations may be the best strategy LV models are considered old-fashioned and inferior to more modern methods of systems biology due to their simplicity and intuitive structure they are often excellent baseline models for potential comparisons with more sophisticated models One might add that LV models have been used in almost 500 PubMed-listed studies over the past decade alone The generic LV system for n populations or species xi takes the form: where the non-negative parameter αi is the growth rate of species i and each real-valued interaction parameter βij quantifies the type and strength of the effect of species j on species i βii reflects intraspecies interactions For the case of a single species (n = 1) the LV model simplifies to the logistic equation The two parameters are directly related to the carrying capacity (K) of the system which is the maximal size of the population that the environment can support over an extended period of time This carrying capacity term implicitly includes information about the spatial and nutritional environment of the species. For example, it has been shown that the amount of carbon initially available to a bacterial culture contributes to the species’ carrying capacity (Rattray et al., 2022) The two-variable case (n = 2) of the Lotka-Volterra model includes three terms for each species: one growth term (αi) one intraspecies term (βii) and one interspecies interaction term (βij): The sign of each interspecies interaction term represents the type of relationship between the two species, which can be categorized as presented in Table 1 The balances among all terms in these equations determine the dynamics of the community we provide a gentle introduction to parameter estimation for non-linear differential equation systems we review and compare the concepts of representative methods specifically for inferring the parameters of LV models from observational time series data using microbial communities as our central target We also discuss preparatory data management steps that facilitate the inference process Applying simple mathematical models to microbes faces challenges associated with critical assumptions that are not necessarily true in bacterial communities (Fort, 2020) regulatory shifts or evolutionary changes are taken into account); There are no higher-order interactions in a sense that Species three might alter the interactions between Species one and 2 In an experimental setting, a researcher can control for these issues to some degree, for instance, by constantly shaking the cultures during growth (assumption 1) or growing only two species together (assumption 3). The environmental changes in assumption two are potentially addressed by the use of a chemostat, which however still allows for adaptations and evolution (Gresham and Dunham, 2014) The synthetic dataset was created from a simulated LV system and consists of trajectories of four species, with or without superimposed noise. All parameters (growth rates, carrying capacities, and interaction terms) were selected to fall within the range of -2 to 2.5 (see Supplementary Table S5) The data were designed such that all species coexist in various scenarios aureus Expressing dsRed Fluorescent Protein Squares are 100 × 100 μm with a depth of 10 μm An average of four squares was used to calculate density in CFU/mL Experimental Results of de novo 3-Species System Column panels display different combinations of co-cultured species (e.g. with each panel showing proportions of species observed at different passages Each passage contains 25 hourly measurements (t = 0 to t = 24) Rows represent biological replicates of the experiment Black lines indicate the overall community size at different time points The y-axis on the left shows relative abundances while the y-axis on the right represents logarithms of community sizes Experimental and Simulated Growth Curves of Two Bacterial Populations with Passaging; from the de novo Dataset we passaged 2.5% of the cells at 24 h resulting in a 1/40 reduction in density at the 24-h time point we programed a callback: when the solver reached t = 24 This callback allowed us to use our normal parameter estimation methods despite the discontinuity one must choose a metric for deciding which of two sets of model parameters provides the better fit for the given dataset The main criterion is generally the value of a loss function which describes how different the estimated model predictions are from the true data the optimal solution of a parameter estimation problem is the set of parameters that correspond to a model instantiation with the smallest loss function Several loss functions are in common use. The most prevalent defaults are the sum of squared errors, SSE, the SSE divided by the number of parameters to be estimated, SSE/p, or the SSE divided by the number of data points, SSE/n. Frequent alternatives include the mean absolute error (MAE) and the coefficient of determination (R2), which measures the proportion of the dependent variable’s variance that can be explained by the independent variable. (Reid, 2010) which is the sum of the squared differences between each data point and the predicted model estimate at that point: but any level of noise will lead to a higher value we look to determine the set of parameters that results in the smallest residual error “Regularization” is a process where one or more penalty terms are added to the loss function in order to solve ill-posed problems or prevent overfitting of data (Neumaier, 1998) LASSO (“L1-norm”) regularization seeks to minimize SSE while also minimizing the number of non-zero parameters This task is set up by adding a regularization hyperparameter λ which is multiplied by the sum of the absolute values of all parameters (∑|P|): the LASSO approach tends to produce solutions with reasonable SSE and a quite small number of parameters This strategy can be useful for finding parameters with strong explanatory power or to create a model with minimal complexity An alternative regularization method is Ridge (“L2-norm”, or Tikhonov) regression (Tikhonov et al., 1995) where the objective of the optimization is to balance the data fit with the total magnitude of all parameters: LASSO regression tends to yield sparse sets of parameters and should therefore be used to fit large systems with minimally complex models while Ridge regression often uses every available parameter but tends to avoid extreme magnitudes of the parameter values The elastic net approach combines both L1 and L2 regularizations: While this method benefits from both, the LASSO and Ridge regression concepts, the elastic net regression obviously requires the optimization of two lambda hyperparameters (Zou and Hastie, 2005). Figure 5 and Table 2 illustrate the differences among the various alternative methods FIGURE 5. Comparison of Regularization Methods in the System of Piccardi et al. (Piccardi et al., 2019) While the estimation with no penalty is presumably overfitted the other three approaches produce much smoother solutions testosteroni from the 4-species experiment Three dots at each timepoint represent three biological replicates Results for additional species are shown in Supplements Here ∑|P| is the summed total of the magnitude of all parameters in the estimation In the example of Figure 5, all three methods using a penalty term have similar curves for one the species shown, but very different parameters, both in amount and magnitude (see Supplementary Table S1) The estimation with no penalty term has the lowest error but appears to be overfitting the data based on the biological assumption that the over- and undershoots between hours 50 and 150 are unlikely to be true and therefore the model fit is “chasing noise” in the data The LASSO and elastic net approaches shrink the number of parameters from 20 to seven or 9 while the elastic net additionally keeps the β22 and β34 parameters Ridge regression attempts to shrink the magnitude of parameters but does so only as well as the LASSO method showing that this particular approach is not optimal for this problem All three of the regularization methods avoid the overfitting that the non-penalized estimation displayed While the SSE, with or without regularization and normalization, is arguably the most important criterion, a minimal residual error should not be the only criterion, for several reasons (Voit, 2011). First, one should remember the extreme case of a high-dimensional polynomial, which can be constructed to fit any finite dataset perfectly (Camporeale, 2019) one problem with this approach is that its parameter values do not have much biological meaning The polynomial has two additional problems: First the removal or addition of even a single data point typically changes the entire parameter set (the coefficients of the polynomial) drastically extrapolations toward higher values of the independent variable tend to converge to ∞ or –∞ It happens quite often that the parameterization of systems yields many good solutions which consist of somewhat or even completely different parameter values as shown in the earlier regularization example The reason can be the existence of an entire solution domain with the same or very similar SSEs One scenario is an entire (one- or multi-dimensional) surface or domain of solutions with exactly the same SSEs in which a search algorithm determines all points to be optimal solutions It is also possible that different parameter sets yield SSE values that are so similar that the optimizer cannot distinguish them Yet another possibility is that each point (i.e. parameter set) within this domain corresponds to an isolated local minimum a point with a small loss function surrounded by (slightly) larger ones The smallest loss function value in the entire search space is found at the global minimum but this exact point can often be difficult to obtain but they usually only reveal the neighborhood of the global minimum by stopping before they find the exact value FIGURE 6. Density Plot of a Parameter with Values from All Combinations of Replicates. The four-species case with three replicates from the dataset of Piccardi et al. (Piccardi et al., 2019) permits three rank-four replicates and three replicates with each species removed giving a total of 3^4 different combinations The values of the same parameter inferred from each of the 81 combinations are displayed in orange and their mean is indicated with the green dot the mean value of the parameter is about -1.48*10–10 and the standard deviation is 3.96*10–10 The blue distribution curve is fitted by using kernel density estimation One interesting estimation issue particular to mixed community systems is the general strategy for inferring interactions Should one perform replicates of experiments with all populations of interest and then estimate all interactions at once (top-down) or should one instead (bottom-up) create monoculture experiments to estimate growth and saturation parameters for each species from which pairwise interaction parameters are inferred where the earlier parameter values are considered known from the previous experiments Both strategies present strong pros and cons and much of the answer is driven by the size of the system which becomes evident from a thought experiment for a moderately large system: To infer parameters for a system with n=10 species in a single experiment one would have to estimate n2+n = 110 L V parameters which would have to be fitted simultaneously the task would be woefully underdetermined and there would likely be numerous drastically different parameterizations with similar goodness of fit suppose the interaction parameters for co-cultures of two or three species at a time had been estimated from corresponding experiments and that new experiments with these species plus one or two new species were to be analyzed Given the quadratic increase in parameters characterizing a community (n2+n) it is tempting to build models up from smaller ones and insert the earlier estimates as allegedly known quantities into the larger model to estimate a ten-species community model up from the bottom up one would have to test every combination of species this means 10 monoculture experiments and (n2) = 45 different interaction experiments ideally with a sufficient number of replicates but each estimation task would be fairly simple as it involves only a few parameters the bottom-up approach offers a “pro” side by dissecting a large optimization task into smaller ones each having to deal with considerably fewer “free” parameters which would make the estimation problem much easier to solve requiring less computation time and minimizing redundancies among the parameters each solution space would have considerably fewer dimensions which increases the likelihood that a search algorithm is able to find the optimal solution Whether this finding is true in general is unknown The standard LV model is not equipped to handle these types of complex interactions directly and the question becomes how well the LV model which still reflects reality and at least permits reliable predictions of the signs of interactions As an illustration, we analyze again data from the earlier mentioned system with four species (Piccardi et al., 2019), but use a different example from the study. Figure 7 displays the results of an analysis where we inferred the parameters in four different ways: using a top-down approach with no previous assumptions regarding the parameter values where all parameters are fit simultaneously; adopting growth rates from single-species experiments and fitting all interaction parameters from data of the four-species experiment; adopting growth rates and carrying capacities from the single-species experiments; and using the growth rate and carrying capacity from each single-species experiment as well as the interaction parameters from two-species experiments; in this case all parameters were thus considered known and the four-species data were only used as validation because no parameter was left to be fitted The results in Figure 7 highlight several issues that may or may not emerge in the various estimation strategies it is clear that overfitting is reduced when some of the parameters are fixed The estimation without former knowledge (all parameters free; Top Down) and the estimation with fixed growth rates produce over- and undershoots caused by the algorithm attempting to fit all data points with the minimal SSE It is unlikely that this is the true dynamics of the system Regularization methods (above) would presumably tame these over- and undershoots FIGURE 7. Comparison of Top-Down vs Bottom-Up Methods. Shown here is growth of Ochrobactrum anthropi. Time is in hours and abundances are in CFU/mL on a logarithmic scale. The colors of dots represent three replicates. Data from (Piccardi et al., 2019) the estimation that exclusively uses single-species and two-species parameter values so that no parameters remain to be estimated (All Fixed; Bottom Up) overestimates the density at virtually all time points thus indicating that the growth of individual species is affected and/or that some of the interactions change in the transition from the two-species systems to the combined four-species system In this example, the estimation that adopts the growth parameters (Fixed Growth + Carrying Capacity) but leaves the interaction parameters free to be estimated displays a good tradeoff between accuracy and overfitting (Figure 7) It is not known whether this result is true with some generality FIGURE 8. Differences in Signs of Inferred Interaction Terms from the Bottom-up (A) and Top-down (B) Fits for Data from Four Co-cultured Bacterial Species (Piccardi et al., 2019). The species are (A) tumefaciens (AT), C. testosteroni (CT), M. saperdae (MS), and O. anthropi (OA). The interactions are colored positive (blue) or negative (red); cf. Table 1 80% of interactions in the bottom-up system and 60% of the top down system match the authors’ inferred interaction direction No significant direct influence was detected for MS and OA and vice versa in (A); more exactly the corresponding interaction terms were very close to 0 This is also the effect of OA on CT in (B) The overall conclusion from this example is two-fold: Caution is necessary when adopting parameter values from sub-models in combined community models There is no guarantee that the lower-level parameter values validly translate into the larger model because interaction parameters could possibly change in the presence of additional species thereby leading to higher-order interactions it is not possible to discern which interaction structure is most likely the different analyses indicate which interactions are presumably persistent among the alternative estimations and pose hypotheses regarding those interactions that are variable within an ensemble of candidate models Initially fixing some parameters may give reasonable initial estimates for fitting higher-dimensional systems because one might argue that the earlier parameter values are probably not totally wrong but simply become modulated by the addition of species it might be beneficial to pass the lower-level parameter values as initial guesses to the solver for the higher-level inference task the solver may more readily converge to the optimal solution it is advisable to vary the parameter values in the solution and re-estimate the system in order to see whether the solution is more or less unique or part of a larger ensemble As some aspect of validation, we can look at the simulated system, which we know adheres to the LV interaction structure, and where we have a defined ‘ground truth’ of user defined parameters. Table 3 suggests that both parameter sets from the bottom-up and the top-down estimations are reasonably good when compared to the ground truth parameters all parameters from the two-species bottom-up estimations roughly match the parameters obtained when estimating all four species together offer good initial guesses for a subsequent gradient optimization (see below) Signs of inferred interaction terms from the bottom-up and top-down fits for data from four simulated bacterial species If the system under consideration is linear and time series data are available, it is usually straightforward to estimate optimal parameter values per multivariate linear regression (Kutner et al., 2004). This approach is similarly feasible, if the system becomes linear through some equivalence transformation. Notably, this is possible for LV systems, at least under favorable conditions (Voit and Chou, 2010) The available classes of algorithms differ in the way new parameter sets are chosen and we focus here just on the basic concepts The general procedure of a search estimation consists of the following steps: Enter the model structure into a search algorithm of choice and choose a loss function The simplest choice consists of default values provided by the algorithm if any information regarding the parameters is known using this information can speed up the algorithm tremendously it is often known whether a parameter value must be positive or negative Enter the parameter values into the model and simulate Let the algorithm change the current parameter values This step allows tremendous variations and is the hallmark of each method Repeat steps 3-5 until an optimized solution is found or a predefined limit on the number of iterations is reached it may be a local—but not the global—minimum of SSE but there is still no silver bullet that successfully and effectively yields the optimal solution every time The various types of algorithms can be categorized as shown in the following sections Most methods directly–or with some coding–permit the setting of bounds for some or all parameters to be estimated Such bounds are a blessing and also a problem strong bounds can reduce the size of the search domain substantially whether a parameter value should be positive or negative the implementation of bounds in an algorithm is not always facilitated and may require specific coding Estimation Results for the Logistic Model with Grid Search and Five Gradient-descent Optimizations The grid search is within the parameter domain ([0,3] [-3,0]) for a and ß of a logistic equation Grid sizes Δx and Δy were set to 0.005 The true minimum of the system (star) is (0.7 the values of the loss function were interpolated between grid points to create a surface Five different initial guesses for the gradient-descent are labeled with numbers All sets of initial parameters allow the algorithm to converge at the global minimum (0.7 the systematic grid search actually returns the exact parameter values since their combination is located exactly on one of the grid points that were tested even if the true solution does not lie on the grid the search can provide a good estimate of the location where the optimal solution can be found relatively coarse grid searches are sometimes a good initial step for determining the approximate locations of local minima and thereby provide a good starting point for more refined types of optimizations including possibly a finer grid search within the neighborhood of the best local minimum determined in the previous step has a good chance of leading to a parameter set close to the global minimum within predefined bounds as it is theoretically possible that the coarse grid search determined locally the best solutions even though the true The most common direct search method is gradient descent a gradient-descent optimizer takes an initial set of parameters {P0} solves the model with these parameter values and approximates the gradient of this function at {P0} It then changes the parameters to a new set {P1} that is located in the negative direction of the gradient which is therefore expected to yield a lower SSE The distance of {P0} from {P1} is controlled by a hyperparameter The algorithm then solves the model with set {P1} This process of local improvement is iterated thousands of times Uncounted variations of gradient-descent based methods have been described in the literature While a very effective approach in principle, this type of approach is prone to getting stuck in local minima, each of which the algorithm considers a successful result, because all values close-by have a higher SSE, even though the global minimum, possibly far away, would have an even lower SSE. For more information, see Chapter 4 of (Goodfellow et al., 2016) Recent techniques have been designed to avoid this local-minimum problem, for instance, by using adaptive learning rates and momentum-based methods (Qian, 1999; Duchi et al., 2011) restarting the estimation with different sets of parameters may help to avoid allegedly optimal solutions at local minima these methods require that the model to be estimated is differentiable which complicates the methods for models with discontinuities or points without derivatives; an example is y=1/x Simulated annealing is an effective algorithm that adds an important twist on the direct search algorithm: the possibility of not strictly following the gradient towards the local minimum. The likelihood of proceeding into a different direction is determined by the parameter T. T stands for temperature, in reference to annealing in metallurgy, which inspired this method. This method often works well, but is generally computationally expensive (van Laarhoven and Aarts, 1987) Figure 9 visualizes the process of gradient-descent based parameter optimization with the same example of a logistic function as before. Here, the algorithm is set to start at five different points in the parameter space (initial guesses). In this simple case, they all converge quickly to the true minimum of the loss function, with the correct parameters. The optimizer used here is a variant of the ADAM optimizer (Kingma and Ba, 2014) which uses an adaptive learning rate based on the first and second moments of the gradient The generic steps of these types of algorithms are: It has turned out that it is advantageous to make the choice probabilistic thereby allowing some less-fit solutions to enter the next generation two parent solutions from the previous generation are combined stochastically to create a new candidate solution all parameter values are sequentially arranged into a string and the first portion of the offspring chromosome comes from one parent and the remainder from the other parent These candidate solutions are evaluated with respect to their SSEs and solutions with the lowest SSEs among parents and offspring will constitute the new generation of parameter sets These details vary depending on the algorithm Most parameter changes emerge in this step of the optimization Mutation–With a very small probability bits of candidate solutions can be mutated before they reach the new generation This option is meant to replicate biological mutation and maintain diversity in the population candidate solutions may become too similar and never approach the optimal solution For the purpose of comparison in a later section, we will use radius-limited differential evolution, as implemented in (Wang et al., 2014a) As an example, consider the tracking of an evolutionary parameter search for the logistic function whose global minimum is at (2.5, -2.0) (Figure 10) the solution quickly jumps to around (4.96 Generations three through seven do not find better solutions than what had been found in Generation 2 The solution of Generation eight holds for nearly 200 generations until a solution is found in Generation 195 that is considerably closer to the true minimum The solution is now slowly improved further with a solution at about (2.84 Additional minor improvements ensue successively until Generation 5314 which is the last generation where the solution improves and the algorithm terminates with a final solution of (2.502 FIGURE 10. Progression of an Evolutionary Optimization. This figure uses the same logistic function as in Figure 9 (A) The solution successively migrates from the first population of estimates with the minimum SSE for parameter set (4.96 to the cluster of points in the upper left where the solution is fine-tuned in generations 1486–5314 (B) The SSE is improving in distinct steps and converges to about 2.8·10–9 at generation 5314 Note that evolutionary methods are unlikely to find the precise minimum of the loss function since the parameters are randomly generated and a criterion for cutoff must be defined which is generally a set number of generations or a successive number of generations without solution improvement we do not really know if the algorithm has found a value close enough to the true solution One should however note that most modern algorithms usually do a good job avoiding local minima which is the Achilles heel of gradient-based methods it is often a good strategy to start with an evolutionary algorithm let it evolve to a reasonably good solution and then to use the result as a very good starting point for a direct search method All the above methods are directly applicable to LV systems in stark contrast to the direct and evolutionary search methods many other approaches have been proposed for general or specific LV inference tasks We present two methods here: ALVI-LR (Algebraic LV Inference by Linear Regression) and ALVI-MI (Matrix Inversion) Both can be used as stand-alone estimation algorithms or as tools for quickly determining candidate solutions that are to be subsequently fine-tuned with gradient-descent based methods can be rearranged by moving each xi to the left-hand side of the ODE If time series data of sufficient quantity and quality are available, both xi and dxidt can be estimated from the data, and the task of estimating all αi and βij becomes a straightforward multi-variate linear regression problem (Varah, 1982; Voit and Savageau, 1982; Voit and Almeida, 2004) Because values and slopes can only be estimated at discrete time points the regression problem is thus based on equations of the type: for each time point tk; k=1,…,K where Si(tk) is the slope of species i at time point k and approximately true for reasonably small ∆t An often-better approximation is the averaged slope in the “three-point formula” For data of exponentially changing populations it is furthermore possible to estimate slopes in terms of logarithms: Because one may perform the estimation of 1xiSi(tk) from data presented on a logarithmic y-axis and with reasonably small ∆t: Further information on slope estimation can be found in (Voit and Almeida, 2004) It should be noted that it is often advantageous to smooth the data and to compute slopes from this spline (see below) To summarize, if data are available at K time points, they may be used to estimate the slopes for the left side of Eq. (Mounier et al., 2007) at each time point and also to populate the xj’s on the right side resulting in K linear algebraic equations per variable Subsequent linear regression is used for each xi to calculate the αi and βij that minimize the square errors For ease of discussion of the inference task, we may collect the parameters into a vector p, which depends on the xi’s, and reformulate Eq. (Mounier et al., 2007) Written in matrix form (where S∼ is a vector of slopes each ln(xi(tk+∆t))−ln(xi(tk))) there is no strict criterion guiding the decision when smoothing is necessary or beneficial A somewhat vague rule is to smooth the data if the signal-to-noise ratio in the sample is so low that it is difficult to discern whether certain features in the data are biologically reasonable or due to randomness Smoothing should also be considered if slopes of the time trends are to be estimated and if the estimates of subsequent slopes vary much in magnitude Smoothing offers other important advantages beyond reducing the effects of outliers and noise values of xi and the corresponding slopes may be estimated at any points within the reported time interval thus increasing the base for performing regression slopes can be estimated algebraically from the spline function why is it even necessary to estimate an LV model The answer is that smoothing functions typically contain numerous parameters who have no biological meaning whatsoever they do not reveal anything about the nature of the interactions among the population in a mixed community an effective inference consists of the following steps: Estimate values of xi and of slopes S∼i at K time points and collect data into data matrices (A) and slope vectors (B); Minimize the loss function using Least-Squares Regression possibly with normalization and/or regularization consider a two-variable system and choose Δt = 1 For a dataset of 11 time points (t = 0 we thus obtain a vector (B) of 11 slope estimates for species x1 We also formulate a data matrix (A) of values of x1 at different time points: The result at each time point is B = A⋅P Δt is incorporated in the elements of the vector B This type of equation is established for each variable in a multi-species system but the A matrix is the same for all species Matrix A has an additional column of 1s for each species The optimal parameters correspond to the solution of the equation set A⋅P-B = 0 Due to noise or the fact that the smoothed trends are not exactly captured by the LV equations the task is now to minimize the function AP-B which is most easily accomplished with least-squares regression they are plugged into the LV equations to assess the goodness of fit While we have not used bounds on possible parameter values they may be imposed on some or all of the parameters in ALVI-LR estimation tasks The previous section has demonstrated that the inference task for LV models becomes linear if time series data are available from which values xi and slopes are estimated we assumed data at K time points and obtained the solution by linear regression Instead of using values at all K time points Assuming that the data and slopes at these points are linearly independent the matrices A and B lead to a system of linear equations that can be solved by simple matrix inversion The fact that only n+1 time points are used for each solution retaining all results with low SSEs naturally generates an ensemble of well-fitting models As an illustration, we revisit the simulated example of four variables with the following data points, with the average of three replicates, superimposed with 5% Gaussian noise (Table 4) Simulated data for the four species system First, we choose n+1 time points. We should select a representative (spread-out) sample, so we choose points 1, 2, 3, 8, and 9. We can use the LOESS method to smooth our slopes, as shown in (Olivença et al., 2021), which gives the matrix slightly different values than the data points in Table 4 This step is not necessary for the method to work but may yield slightly better inferences with A being the data matrix and Bi the vector for species i: six and nine produce the solution with the lowest SSE Some of these solutions may be discarded if they display over- or undershoots that do not appear reasonable on biological grounds (here How many parameter sets are to be included in the ensemble is a matter of choosing cut-offs within the set of SSEs and of biological judgment ALVI-MI Fits of Data Points from the Simulated Dataset with Noise and Replicates Nine different combinations of (n+1) time points yielding fits with the lowest SSEs are displayed along with the true solution (105)=252 combinations of points are possible Fits for all four variables are presented in the Supplements TABLE 5. Sample Point Sets for ALVI-MI inferences and corresponding SSE values for Data in Figure 11 Even though experimental conditions were the same in all three replicates experimental endpoints appeared with dominance of either E Fits for all four variables are in Supplements FIGURE 13. Comparison of Parameter Inference Methods for the Dataset of Piccardi et al. (Piccardi et al., 2019) Time is in hours and abundance is in CFU/mL on a logarithmic scale The data points are three replicates of the species TABLE 6. Comparison of Methods with the Simulated Dataset in Figure 12. The difference from true parameters is defined as ∑|Ptrue−Pinferred|. (A) and (B) refer to Figure 12. The two ALVI methods have higher errors but are obtained in a fraction of the time needed for the other methods and still generate reasonable fits (cf. Table 7) TABLE 7. Comparison of Parameter Inference Methods using the Dataset of Piccardi et al. (Piccardi et al., 2019). These values correspond to the fits from Figure 13 Time to solution does not include data processing the structure of such a system permits several stable steady states whose basins of attraction are delineated by separatrices different outcomes are possible if the initial states of two communities may be quite close to each other but are located on different sides of a separatrix but starting with slightly different initial values of the species within the community can lead to distinctly different steady states including extinction of one or more species but they do not make use of information about the growth of each species suppose the values of two different steady states are available for a two-species system but in the second experiment Species two does not survive suppose these two steady-state data points are: x1SS=1.094, x2SS=0.6235 and x1SS=1.25,x2SS=0 Suppose further that growth rates had been determined for both species with values of 2.5 and 0.7 for Species 1 and 2 These data permit setting up two steady-state equations with two unknowns and putting in the first steady-state profile gives Similarly for the second steady-state profile we can convert the equations into the matrix form: which can be solved with matrix inversion (or pseudo-inversion for undetermined equations) To compare the methods, we use the same simulated four-variable dataset that we discussed in the context of top-down/bottom-up estimation. For a fair comparison, we first identify the growth rates and fix them in each scenario.1 For the case published by Piccardi et al. (Piccardi et al., 2019) and discussed before we can compare the results to some aspects of the authors’ inferred interaction network As their inferred interactions came from comparing the area under mono- and co-culture growth curves they cannot be compared directly to our Lotka-Volterra analysis we can qualitatively compare at least the signs of interactions the linear regression method most closely matches the interactions that the authors of the paper concluded The gradient search method has the lowest SSE but introduces an overshoot in the second half of the curve The evolutionary method also produces some bumps compared to the linear algebra-based fits that yield relatively smooth trends One notes that the algebraic methods require a fraction of the computation time to find a solution although we did not include data preprocessing computation time becomes a practical criterion of substantial weight if the estimation task targets large models with dozens or even hundreds of parameters It is well possible that methods fail in these situations even if they perform well for small models including the algebraic algorithms mentioned here are better suited than others when it comes to speeding up the solution through parallel computing or the use of multi-threaded programming and it is impossible to declare winners and losers in a general manner It is also advisable to consider different metrics for the quality of data fits resulting from the parameter inference These methods do not always capture the transient dynamics as well as gradient methods which is likely due to imprecision when estimating slopes but they avoid overfitting and are computationally so cheap that numerous fits are readily computed either to select the solution with the lowest value of some loss function or to establish an entire ensemble of well-fitting solutions An unbiased overall comparison of all methods is difficult, as different metrics should be considered that are truly incomparable (Table 8) and parameter values that seem biologically doubtful it might be advisable to clean and smooth the data this procedure will generate good solutions but it can also be used as a quick method for generating good initial guesses for more refined methods Comparison of different aspects of the various fitting strategies uncounted methods are available but there is still no silver bullet and parameter estimation remains to be somewhat of an art this is so because the computational techniques are still not universally effective and all methods can boast with examples where they shine the proponents of these methods should also acknowledge situations where the algorithms become very slow the structure of model is such that many parameter sets yield similar because an “optimal” parameter set for a given dataset may fail drastically if the same parameters are used to model another dataset A positive interpretation of this situation leads to the acceptance of multiple solutions and the identification of ensembles of models by permitting higher-order interactions among species These fits with lower SSEs would likely necessitate a higher number of parameters raising the difficult question whether the increased model complexity is “worth it.” but many of them have at least been identified and subjected to scientific scrutiny the estimation of parameter values stands between the power of theoretical models and the biological reality of the actual world Simulations and optimization tasks were performed in the Julia programming language (v1.7) (Bezanson et al., 2017). Results were visualized with the ggplot2 package (v.3.3.6) in the R (v4.1.3) programming language or the Javascript version of the Plotly package (v2.14.0) (Wickham, 2016; Sievert, 2020). Network visualization was done with Cytoscape (v3.9.1) (Shannon et al., 2003) Differential equations were solved using different variants of Runge-Kutta (Tsitouras, 2011; Rackauckas and Nie, 2017) methods, depending on the type of problem to be solved. Simulations were executed in the Julia programming language (Bezanson et al., 2017) Grid search method: Each parameter was assessed over a predefined range (0–five for α and -5 to 0 for βii) and the model was simulated at Δ =0.005 increments in each dimension Gradient-descent based method: Parameters were tuned using the AdaMax (Kingma and Ba, 2014) method with a learning rate of 1e-3 with 0s as initial parameters using the Flux optimization package (v0.13.4) (Innes, 2018) Differential evolution method: Parameters were tuned with the bounds of -5 to five for α Parameters were tuned with the bounds of -5 to five for α The initial population size was 500 and 0s were used as initial parameters using the BlackBoxOptim package (v0.6.1) ALVI-LR method: Data were discretized as in (Mounier et al., 2007) and separated into a vector of abundances and estimated slopes. Each variable was optimized individually using an interior point optimization solver (Biegler and Zavala, 2009) in the JuMP package (v. 1.1.1) (Dunning et al., 2017). Smoothing was performed with the LOESS method as described in (Olivença et al., 2021) The ALVI-MI method was performed as described in (Olivença et al., 2021) The ALVI survivor profile method was performed as described in (Voit et al., 2021) conceived this project and performed the literature review DO contributed to the analysis and to the code required for the study All authors reviewed and edited the manuscript The authors acknowledge the following funding sources supporting this project: The Cystic Fibrosis Foundation (BROWN19I0 the Centers for Disease Control and Prevention (BAA 2016-N-17812 the National Institutes of Health (1R21AI143296 and 1R21AI156817) The authors would also like to acknowledge members of the Voit and Brown labs for their valuable contributions to the manuscript and the Partnership for Advanced Computing (PACE) at Georgia Tech for use of their computing nodes The authors declare that the research was conducted in the absence of any commercial or financial 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Volume 2 - 2022 | https://doi.org/10.3389/fbinf.2022.1021838 This article is part of the Research TopicExpert Opinions in Network bioinformatics: 2022View all 6 articles Networks are ubiquitous throughout biology spanning the entire range from molecules to food webs and global environmental systems despite substantial efforts by the scientific community the inference of these networks from data still presents a problem that is unsolved in general One frequent strategy of addressing the structure of networks is the assumption that the interactions among molecular or organismal populations are static and correlative They usually ignore the asymmetry of relationships between two species and inferences become more challenging if the network nodes represent dynamically changing quantities two very different network inference approaches have been proposed in the literature: Lotka-Volterra (LV) models and Multivariate Autoregressive (MAR) models These models are computational frameworks with different mathematical structures which have both been proposed for the same purpose of inferring the interactions within coexisting population networks from observed time-series data we assess these dynamic network inference methods for the first time in a side-by-side comparison using both synthetically generated and ecological datasets Multivariate Autoregressive and Lotka-Volterra models are mathematically equivalent at the steady state but the results of our comparison suggest that Lotka-Volterra models are generally superior in capturing the dynamics of networks with non-linear dynamics whereas Multivariate Autoregressive models are better suited for analyses of networks of populations with process noise and close-to linear behavior this is the first study comparing LV and MAR approaches Both frameworks are valuable tools that address slightly different aspects of dynamic networks “The exploding interest in network science during the first decade of the 21st century is rooted in the discovery that despite the obvious diversity of complex systems the structure and the evolution of the networks behind each system is driven by a common set of fundamental laws and principles notwithstanding the amazing differences in form most networks are driven by common organizing principles Once we disregard the nature of the components and the precise nature of the interactions between them the obtained networks are more similar than different from each other.” no clear guidelines or gold standards exist and none of the existing tools successfully addresses all issues of network inference many methods have problems with identifying spurious relations within microbial communities the selection of the most appropriate technique is often made in an ad hoc manner based on the characteristics of the available data and features like computational scalability whereas MAR systems are statistical models The former were designed to elucidate the long-term dynamics of interacting populations whereas the latter were conceived not only to study interacting population but also the stochastic structure of the supporting data two modeling frameworks with different mathematical structures have been proposed for essentially the same purpose of extracting key features of dynamic interactions among coexisting species from observed time series data but a direct comparison of the two approaches has never been reported Such a comparison is the subject of this article Our focus for their comparison is the ability of each model framework to produce an acceptable fit to observation data capture the process dynamics underlying the observed trends in population abundances and infer correct parameter sets as well as possible We begin with a description and comparison of the main features of LV and MAR models, subsequently analyze small synthetic systems, which offer the advantage of simplicity and full knowledge of all model features, and then assess several real-world systems. It is quite evident that it is impossible to compare distinct mathematical approaches with absolute objectivity and without bias (Rykiel, 1996) and it sometimes happens that inferior choices of models in specific cases outperform otherwise superior alternatives We will attempt to counteract these vagaries by selecting case studies we consider representative and by stating positive and negative facts and features as objectively as possible Lotka-Volterra (LV) models (Lotka, 1925; Volterra, 1926) are systems of first-order ordinary differential equations (ODEs) with the format The left side of Eq.1 represents the change in species Xi with respect to time With only the first term on the right side while the sum captures interactions between pairs of populations Most of these terms represent interactions between different species such as predation or competition for the same resources or cooperation accounts for interactions among the members of the same species and is sometimes interpreted as a crowding effect If time-dependent environmental inputs are to be considered, one may add one or more terms γikXiUk, where Uk is the kth element of a vector of these inputs and the coefficients γik are weights that quantify the effects of the factors on species Xi (Stein et al., 2013; Dam et al., 2016, 2020). This addition does not fundamentally alter the format of Eq. 1: In an effort to simplify the comparisons in this study these environmental factors will be omitted henceforth Background and further details regarding these models are presented in Supplementary Section S1.1 Because ODEs are natural representations of dynamic processes Splines have degrees of freedom and we will refer to a spline with 8 degrees of freedom as “8DF-spline” These slope values are equated to the right-hand side of the equation with values of the dependent variables at the same K time points This conversion of one ODE into K algebraic equations leaves the parameters as the only unknowns that are to be estimated In contrast to the ODEs of the LV format, Multivariate Autoregressive (MAR) models are discrete recursive linear models (Ives et al., 2003; Holmes et al., 2012) the quantities ug,t represent environmental variables and the noise wi,t is normally distributed the “state” of the system at time t+1 depends exclusively on the state of system one time unit earlier as well as on external inputs and stochastic effects is usual represented in the matrix form as α is the vector of intersects and β is the population interaction matrix The term γut describes how cofactors affect the dependent variables ut is a vector of external variables and γ is the matrix of weights associated with these external variables the term wt is a vector representing stochastic noise affecting the dependent variables Eq. 4 conveys that the state of the system at time t+1 depends on the state at t and possibly on temporary environmental and/or other stochastic input As an alternative to this modeling structure with “memory 1,” it is possible to extend MAR models to depend also on states farther in the past this strategy greatly increases the number of parameters to be estimated and the commonly used models depend only on the immediately prior state; they are sometimes called MAR(1) we only consider MAR(1) models and refer to them simply as MAR models but it is difficult to propose a general mathematical solution unless the nature and quantitative details of the alterations can be converted into fully characterized functions affecting the parameters even if a precise mathematical formulation is not feasible these considerations should not be ignored The software package MARSS, using an expectation maximization algorithm, greatly facilitates the estimation of MAR model parameters (Holmes et al., 2020, 2012). Some details of MARSS usage, and especially the setup we used, are discussed in Supplementary Section S1.5 Both LV and MAR models have been proposed as effective tools for characterizing the interactions among populations within dynamically changing mixed communities. At first glance, the two formats appear to be distinctly different and, in a strict sense, incomparable. However, they do exhibit fundamental mathematical similarities, which are sketched below and analyzed in more detailed in Supplementary Section S1.4 we focus on MAR models without environmental factors and noise (Dennis and Taper, 1994; Ives, 1995; Certain et al., 2018). Borrowing the principles of solving ODEs with Euler’s method, we discretize the LV model (Eq. 1) we employ Euler’s stepwise-linearized formulation of the system dynamics solely as a means of discretizing the ODE format of LV in order to compare it more directly with the MAR structure For simplicity of discussion, suppose h = 1. If the dynamics remains close to the steady state, then Xi,t+1−Xi,t≈0 for any given t. Furthermore, division of both sides of (6) by Xi,t, as long as it is greater than 0, yields approximately one on the left-hand side and a linear expression on the right-hand side. Thus, the results corresponding to Eqs 5, 6 MAR is linear and uses a log transformation to deal with some non-linearities multiplying Xi,t by the growth rate and sum of interaction terms allows for non-linearities and does not require any further remediation to handle them The comparison between LV and MAR models may be executed in two ways. A purely mathematical approach was sketched in Section 2.5 and expanded in Supplementary Section S1.4 An alternative approach focuses on practical considerations and actual results of inferences from data we omit environmental inputs (γik XiUk and γig ug,t respectively) and begin by testing several synthetic datasets with different types of representative dynamics We design these data as moderately sparse and noisy we test whether the LV inference from synthetic LV data returns the correct interaction parameters and whether the MAR inference from synthetic MAR data does the same we test to what degree LV inferences from MAR data yield reasonable results and vice versa we apply the inferences to several real datasets from the literature we compare the sums of squared errors (SSEs) and use a Wilcoxon rank test to assess the significance of the differences For a representative illustration of the parameter inference process in the presence of stochastic environmental variations the variables Xi and Xj represent the abundances of the different species ai the rate constants and bij the intra- and interspecies interaction parameters To account for stochastic environmental variations Here, Xi, Xj, ai and bij have the same meaning as in Eq. 9 and the ki represent the shape parameter for the gamma-distributed influences affecting the four variables The scale parameter is set to 1/ki−1 for the mode of the gamma to equal 1 Variable X4 was intentionally designed as a (decoupled) logistic function It is unaffected by the other variables and does not affect them either It was included to explore to what degree the methods to be tested can detect this detachment The fits for the noisy and replicate LV datasets, obtained per LV matrix inversion, are presented in Figures 1A,B, along with the inferred parameter estimates (Table in Figure 1) These generally possess the correct sign and could serve as the starting point for an additional for instance with a steepest-descent method The inferred and true values are quite similar for both datasets Because we usually obtain better results through matrix inversion we display those results here and present linear LV regression results in the Supplements Because MARSS yields parameter values for a discrete recursive system, they are not directly comparable to the true parameters of a LV system; nonetheless, their numerical values are recorded for completeness in Supplementary Tables S1.4, S1.5. For MARSS inferences from the replicate LV dataset, we had to average points with the same time value. Additional details are presented in Supplementary Section S2 In both LV datasets, the matrix inversion method produced parameters estimates closer to the true parameters (Supplementary Table S8) Here we reverse the set-up of Case Study one by creating synthetic data with an MAR model and test whether inferences with either model can achieve results corresponding to the original system One could argue that data in the real world very seldom result from truly linear processes but it is nevertheless important to analyze linear MAR models because practitioners within the ecological community have been using them Due to the different nature of the two modeling formats the LV parameters are not directly comparable to the MAR parameters For practical inference purposes in biology this requirement regarding the density of data can be a genuine concern TABLE 1. Sum of squared errors (SSE) of data fits for all experiments with ALVI-LR (linear regression), ALVI-MI (matrix inversion) and four variants of the MAR methods. We also include SSEs for the estimates obtained by Mühlbauer et al. (2020) for LV data presented in Figure 4 Bold values identify the lowest SSE score for each example Examples used in the Wilcoxon rank test are marked with asterisks For the noisy MAR dataset, the MAR parameter estimates without transformation or smoothing worked best and yielded the closest parameter estimates to the true parameters (Figure 2) ALVI also works for more complicated dynamics than analyzed so far, as can be seen in Figure 3 Here we are interested in determining if the methods can recover the dynamics which in some cases turns out to be challenging for sparse data even without the introduction of noise data for early time points (t ∈ [1 100]) were fitted and then extrapolated for a much longer time horizon of t ∈ [1 It uses data samples with points corresponding to timepoints t = 5 and 50 for all cases except for the chaotic oscillations where we used t = 4 one must recall that the original data were produced with LV models While the MAR model extrapolations are not always satisfactory it is nevertheless comforting that the inference method returns good results for the short initial time interval used for data fitting The SSEs concerning the differences between the data and estimates for t ϵ [1 500] are presented as labels to the Y-axis No smoothing was needed because the data were noise free ALVI-MI generally performed very well but did not adequately capture the deterministic chaos (chaos 1) which is understandable as chaotic systems are extremely sensitive to any type of numerical variation results with ALVI-LR are very similar to ALVI-MI results and therefore not displayed For the data in Figure 3B the MAR model performed well when log-abundances were used or these exploded by reaching amplitudes far bigger than in the dataset One also notes early discrepancies between the initial points used to create the estimates and the MAR estimates The overall result is that the inferred MAR models never outperform the results for the corresponding LV models One could argue that these examples had been used to test actual data for compatibility with the LV structure which may explain the superior performance of the LV model real-world data of the type that both LV and MAR are supposed to capture For the case in Figure 4A, matrix inversion with the LV model yields the same results as found in (Mühlbauer et al., 2020). In contrast, the MAR estimates are poor, with a very high estimate for the noise (Supplementary Table S4.3), especially if one does not use log-abundances; this problem occurs for all cases presented in Figure 4. The data in Figure 4A are close to a logistic function similar to X4 in the previous noisy dataset Figure 4B shows data from a competition experiment between the unicellular protists Paramecium caudatum and Paramecium aurelia that were co-cultured aurelia are similar for all methods but LV matrix inversion exhibits clear superiority for P but constitutes a considerable improvement over our initial fits using the solution from the matrix inversion as initial parameter values for a subsequent gradient-descent optimization the resulting solution reflected the data well it is difficult to choose degrees of freedom that capture both maxima High degrees of freedom capture the global maxima but overshoot the local maxima Low degrees of freedom capture the local but undershoot the global maxima We suspect this to be the cause for the initially poor performance of LV The data in Figure 4D are also complicated, in this case due to two aspects. First, they show a stark difference in absolute numbers, with the abundance values for moose being several magnitudes higher than the numbers of tree rings. As a potential remedy, we normalized the fitting error for each dependent variable by dividing it by its mean to balance the SSE. The result is shown in Figure 4D and MAR with log-abundances produces a better noise estimate than with the untransformed data Figure 4E describes yet another complicated example. According to the inference, the LV estimates fit the first peak well but the oscillations die down, in contrast to the data. Estimates from Mühlbauer et al. (2020) produce even poorer estimates suggesting that the data may not be compliant with the LV structure although MAR with log-abundances produces good noise estimates MAR with smoothing yields very poor fits to these data We repeated the analysis using linear regression instead of matrix inversion for the LV inference. The results were by and large similar and slightly inferior; they are shown in Supplementary Figure S7; Supplementary Table S4.2 One should note that Mühlbauer et al. (2020) used a steepest-descent method, while our method did not. Therefore, our results can be further improved by adding a refinement cycle of steepest-descent optimization. We present an example in Figure 4C where the fit of the steepest descent optimization over the algebraic LV solution is depicted with a red line The optimization reduces the error from 2,191 to 874 Figure 5A shows fits to the gray whale data (Gerber et al., 1999). LV noticeably outperforms MAR, even though the data came from a MAR demonstration. In particular, the MAR results (without transformation) suggest that the whales are close to regaining their carrying capacity, which seems to contradict the trend in the data. The SSEs can be seen in Table 1 It is unclear why the MAR method without transformation does not perform better the estimates are inadequate (with the highest SSE) and have a very high variance for the error An LV model with one variable is a logistic function and the LV fit represents initial quasi-exponential growth that starts to slow down after a while This behavior nicely reflects the fact that the whales were recovering from very small numbers due to overfishing but the population is apparently still much below the carrying capacity The results of the MAR model are identical with those published in, with the same log transformation and z-scoring of the data, and the same parameter values were inferred. The result consists of acceptable estimates, although we found a slightly better fit without the z-scoring. Still, for a direct comparison, we opted to present the example exactly as Holmes et al. (2020) did these fits miss all oscillatory behavior seen in the data The LV results do show oscillations but clearly suffer from the disruption in the wolf population in 1981 and 1982 Because we used in this example only MAR with log transformation we display the confidence intervals for the MAR model as dashed green lines Very few datapoints are outside the confidence intervals We decided to test the hypothesis that MAR might perform better if the simulations were initiated near the steady state, because the model then would not be affected much by the non-linearities in dynamics, which can strongly affect a simulation starting far from the steady state. For this purpose, we again used the artificial LV and MAR artificial systems utilized in Figures 1, 2 Both cases reveal an increase in SSEs as the simulations start further away from the steady state ALVI-MI performed better than MAR when the initial conditions were set further away from the steady state which was not the case in the MAR synthetic datasets This observation supports the claim that MAR will have difficulty obtaining a good fit to the data if extreme non-linear dynamics are present These results show that the LV models capture the interactions of the artificial LV system better as the MAR models better capture the artificial MAR system although it did not reveal any tendency directly associated with the initial conditions we found that MAR will have difficulty obtaining a good fit to the data if non-linear dynamics are present The data also suggest that both methods have greater SSEs as the starting point shifts away from the system’s steady state one should probably compare them to delay differential equations (DDEs) the decision for MAR(1) appears to provide the fairest comparison between MAR and LV This type of variation is natural for MAR systems but not straightforwardly accommodated by the LV format because we considered this type of noise as potentially more appropriate than static observational noise we mimicked it by simulating the system with a discretized version of the LV structure This decision pertained only to test data we created to compare the different models most likely contain a mixture of process and observational noise which can hardly be teased apart based on the data alone A smoothed representation of a dataset implicitly integrates information that is not explicit in the data This integration step is not entirely unbiased and requires prudent judgment because it must answer the following questions often without true knowledge of the system: Are the deviations between the data and the smoothing function due to (random) noise or are they part of a true signal do they belong to a trajectory exhibiting true oscillations if a few data points deviate much more than all others from the smoothing function are they true peaks or valleys or are they statistical outliers It is difficult to answer these questions objectively but two features of the data are of great benefit: First if the variation in noise amplitude is much smaller than the range of signal values (high signal-to-noise-ratio) the distinction between signal and noise is relatively straightforward they may support or refute the potential of true oscillations or peaks at certain time points in the data the biologist familiar with the phenomenon at hand usually has developed an expectation regarding signal and noise and if there is no biological rationale for expecting oscillations or strong deviations from some simple trend the smoothing strategies are flexible enough to allow the integration of the biologist’s knowledge and expectations The result of the smoothing process therefore is a synthesis of all relevant information constrained by external knowledge and reasonable expectations it is also feasible to create alternative models with different thresholds between signal and noise and to analyze them side by side Algebraic LV inference (ALVI) allows a choice between two variants (linear regression or matrix inversion). The former is simpler, because it uses all points available, and faster since no data samples need to be chosen. In most cases tested, it also produces good fits and estimates. However, the matrix inversion variant usually produces slightly better results and works well even in occasional cases where the regression solution fails (Table 1) It also offers a natural approach to inferring comprehensive ensembles of well-fitting model parameterizations it is of course possible that other parameter estimation methods could outperform both in some or even all cases of LV inferences our overall conclusions still stand; in fact the differences between LV and MAR would be even more pronounced steepest-descent methods tend to get trapped in local minima if the initial guesses are poor one would likely not encounter this problem as the solutions are already very good and could be used directly as initial guesses for the refinement step A second example of potential future improvement and automation is the adequate smoothing of the raw data with splines which requires the determination of a suitable number of degrees of freedom and may also suggest beneficial weights for different variables within a dataset It might be interesting in the future to study how well MARSS deals with non-normal process noise The algorithm used by MARSS assumes the noise nature to be normal it should be interesting to test what happens to the estimation of not only the noise itself Because the LV structure is continuous, solutions can directly be evaluated at any point or for any interval between the points in the numerical solution. MAR does not truly reveal a time resolution higher than its intrinsic interval between solution points but addressing this issue, Holmes et al. (2012) demonstrated with the MARSS R function that it is feasible to interpolate any number of missing values between the known datapoints and that this method can be used to decrease the time unit for stepping forward While this step does not make the MAR model as densely time-resolved as an ODE model it mitigates the apparent granularity disadvantage considerably It also increases the computational requirements of MARSS considerably Concerning the analysis of the effect of initial conditions the result may have been influenced by the particular model structure or the sampling Changing the initial conditions created quick but intense dynamics near the initial part of the simulation The sampling scheme may not have been able to capture these dynamics accurately causing the observed result that all methods yielded higher SSEs when the simulation started further away from the system’s steady state Estimation and inference methods typically do not scale well The algebraic LV inference bucks this trend as both the smoothing and estimation of slopes are performed one equation at a time The computing time for matrix inversion or linear regression is essentially the same for all realistically sized models the only time-consuming step within ALVI-MI is the choice of datapoints An exhaustive test for all combinations grows quickly in the number of analyses but it is always possible to opt for a much faster random search this method is so fast that many inferences can be obtained in a short period of time and the best solutions are retained while other solutions are discarded The result might not necessarily be the best possible solution but it can still provide an excellent fit or a valuable starting point for a steepest-descent refinement optimization a collection of good solutions can be collated to establish an ensemble of well-fitting models which will often yield more biologically meaningful insight than a single optimized solution Our overarching conclusion, with numerical results summarized in Table 1 is that LV outperforms MAR in the vast majority of analyzed cases by yielding often substantially lower SSE values one must note that while the two approaches have similar goals they are best suited in different situations MAR models are very useful for investigations where the quantification of noise is of importance because noise is characterized in MAR by a parameter that can be estimated together with the other parameters we noticed that MAR performed rather poorly for artificial LV datasets where the model had a fair number of zero-valued parameters although we do not completely understand the reasons our study suggests that MAR should not be used in cases where many parameters may have zero values MAR models proved to be very effective in dealing with process noise when there were no replicates This outcome was true for both the artificial LV and MAR data MAR appears appropriate for data that display non-linearities that align with the MAR model structure possibly upon a log transformation of the data LV models are better suited to capture the dynamics in many datasets because this architecture is able to deal with complex non-linearities. In fact, the LV structure was shown to be capable of modeling very complex non-linear dynamics (Peschel and Mende, 1986; Voit and Savageau, 1986; Vano et al., 2006) and has no problems with zero-values parameters as we encountered them with MAR Our experiments with the artificial LV and MAR data suggest that LV models should be used when replicates for the different time points are available or when the influence of process noise is moderate The datasets presented in this study can be found in online repositories. 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Olivença, ZG9saXZlbmNhM0BnYXRlY2guZWR1 Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher 94% of researchers rate our articles as excellent or goodLearn more about the work of our research integrity team to safeguard the quality of each article we publish Home/Technical Rescue Oshkosh Airport Products’ 2021 Road Rally will give aircraft rescue and fire fighting crews a chance to experience the revolutionary new Striker® Volterra™ ARFF hybrid electric vehicle OSHKOSH, WIS. (August 10, 2021) – Oshkosh Airport Products, LLC an Oshkosh Corporation (NYSE: OSK) Company announced today that its upcoming ‘Road Rally’ will offer aircraft rescue and fire fighting crews at airports throughout North America a hands-on and immersive experience to learn about the revolutionary new Striker®  Volterra™ performance Aircraft Rescue and Fire Fighting (ARFF) hybrid electric vehicle (HEV) Oshkosh Airport Products’ Road Rally will provide airport fire department representatives an opportunity to meet one-on-one with experts to learn about the Striker Volterra vehicle’s attributes and its ability to meet each location’s unique environmental and sustainability initiatives Featuring live demonstrations and Q&A sessions the Road Rally kicks off at Portland International Airport (PDX) August 9-12 we introduced the Striker Volterra ARFF hybrid electric vehicle which is designed around Oshkosh proprietary and patented technology,” said Jack Bermingham business unit director for Oshkosh Airport Products customer response to learning more about this fire apparatus has exceeded our expectations and we are eager to share more about the Striker Volterra ARFF vehicle in person during our North American Road Rally.”  Features of the Striker Volterra HEV Include: “Another key feature of the Striker Volterra hybrid electric vehicle is its ability to meet the growing emergency response and environmentally-conscious needs among airports of all sizes without compromising on operational performance or the traditional configurations and styling our customers expect.” The Striker Volterra performance HEV is custom-engineered and extensively tested to deliver rapid response while simultaneously managing its carbon footprint it is fully compliant to NFPA 414 and ICAO standards while being certified to off-highway EPA and EU regulations.  As Oshkosh Airport Products’ Road Rally takes place over the next several months on the west coast of the U.S. airport emergency response and fire fighting crews on the east coast of the U.S. and internationally will also have the opportunity to experience the new Striker Volterra ARFF in the months ahead at a location in their region the Road Rally featuring the Oshkosh Airport Products Striker Volterra HEV will take part in the Advanced Clean Transportation (ACT) Expo on August 29 – September 2 in Long Beach California at Oshkosh Corporation’s booth #246 and #1634 The ACT Expo is North America’s largest advanced transportation and clean fleet event where attendees learn about the most progressive fuels Individuals and teams interested in attending Oshkosh Airport Products’ Road Rally should contact their local Oshkosh Airport Products dealership or sales representative for more information To learn more about the Striker Volterra ARFF vehicle, visit www.oshkoshairport.com Jehad Mustafa has left his role as senior associate at Volterra Fietta to become partner in the dispute resolution practice at London-based law firm Farrer & Co Register for free to receive GAR’s daily briefing and access to GAR 100 expert analysis and essential resources from the Global Arbitration Review experts Copyright © Law Business ResearchCompany Number: 03281866 VAT: GB 160 7529 10 Get more from GARSign up to our daily email alert Unlock unlimited access to all Global Arbitration Review content Metlen Energy & Metals announced the conclusion of the agreement to acquire all the shares of electricity producer with the absorption of Volterra by the parent Metlen Energy & Metals which operates in the electricity retail market through the Protergia brand The merger is expected to be completed by the end of the year The acquisition and absorption of Watt+Volt preceded it in 2023 while the acquisition of EFA Energy was also completed earlier this year Enter your information below to receive our weekly newsletters with the latest insights opinion pieces and current events straight to your inbox This website is using a security service to protect itself from online attacks The action you just performed triggered the security solution There are several actions that could trigger this block including submitting a certain word or phrase You can email the site owner to let them know you were blocked Please include what you were doing when this page came up and the Cloudflare Ray ID found at the bottom of this page the Centro Studi Espositivo Santa Maria Maddalena in Volterra will host the exhibition Gianni Berengo Gardin an exhibition that brings together twenty-four photographs by Gianni Berengo Gardin (Santa Margherita Ligure each accompanied by a text written by a leading figure in culture The exhibition is sponsored by Anima di Volterra with the Fondazione Cassa di Risparmio di Volterra and the Cathedral Basilica of Volterra and produced by Opera Laboratori in collaboration with Contrasto The exhibition presents a sober and powerful layout that allows visitors to immerse themselves in more than eighty years of history filtered through the gaze of Gianni Berengo Gardin and reinterpreted by the words of personalities who have shared paths visions and friendships with him.Born in 1930 he has traversed entire decades with his camera recounting Italy and its changes with a direct and unartificial style He never pursued aesthetics as an end in itself A photographer by vocation rather than by trade he has been an attentive and passionate witness of everyday life but also of the elegance and beauty hidden in the details helping to build a shared visual memory of our country At the heart of the Volterra exhibition is precisely the relationship between images and words Each photograph selected from Berengo Gardin’s immense archive is flanked by an original text written by personalities from the worlds of art A chorus of voices that includes names such as Carlo Verdone who recount the photographer’s cinematic gaze; architects such as Renzo Piano who reflect on the urban and human landscape in his images; and artists such as Mimmo Paladino who read his works in a poetic and symbolic key There is no shortage of writers and critics such as Roberto Cotroneo who offer literary and historical interpretations; photographers such as Sebastião Salgado Ferdinando Scianna and Luca Nizzoli Toetti who reveal the secrets of the craft and respect for a colleague who set the standard The voice of science and social engagement also finds space with contributions from Domenico De Masi and psychiatrist Peppe Dell’Acqua as well as street artist Alice Pasquini complete the picture The exhibition is a tribute to the encounters that marked his life and career the decision to entrust the presentation of the images to friends colleagues and intellectuals represents a way to recount photography as a collective gesture the result of a glance but also of a network of relationships Each text thus becomes a second level of reading which does not explain but accompanies the image It is a project that combines photographic art with narrative transforming the exhibition into a reflective experience The commented photos is part of the larger exhibition Anima di Volterra a cultural initiative that unites different places in the city in a single itinerary visitors can continue their visit by discovering with a single free audio guide also Piazza San Giovanni home of the Centro Studi Espositivo Santa Maria Maddalena allowing the photographic exhibition to be contextualized in a very rich urban and cultural fabric making the experience even more complete and engaging Gianni Berengo Gardin is among the most influential Italian photographers where he started his professional career devoting himself mainly to reportage He collaborates with important Italian and international newspapers but finds his most accomplished expression in photographic books: he publishes more than 260 of them His first images appeared in 1954 in Mario Pannunzio’s Il Mondo From 1966 to 1983 he worked with the Touring Club Italiano on a vast series of volumes on Italy and Europe He also photographs for the Istituto Geografico De Agostini and for large companies such as Olivetti Between 1979 and 2012 he follows and documents Renzo Piano’s architectural projects His talent was recognized internationally: in 1972 Modern Photography included him among the “32 World’s Top Photographers”; three years later he was cited by Cecil Beaton in The Magic Image The Genius of Photography from 1839 to the Present Day selected by Bill Brandt for an exhibition at the Victoria and Albert Museum in London and in 1982 he is mentioned by Ernst Gombrich in The Image and the Eye Italo Zannier calls him “the most remarkable photographer of the postwar period.” In 2003 he is among the artists chosen for the exhibition Les choix d’Henri Cartier-Bresson while Hans-Michael Koetzle devotes ample space to him in the volume Eyes Wide Open and the exhibition The Italian Metamorphosis 1943-1968 at the Guggenheim in New York (1994) Among the most recent exhibitions: in 2016 True Photography Encounters at PalaExpo in Rome and in 2022 The Eye as a Craft at MAXXI Also notable is the reportage on the transit of large ships in Venice He has received numerous awards: the Scanno Prize (1981) the Lucie Award for Lifetime Achievement (2008) the Laurea Honoris Causa in Art History and Criticism (2009) the Kapuściński Prize (2014) and the Leica Hall of Fame Award (2017) His works are in the collections of prestigious international institutions such as MoMA in New York the Bibliothèque Nationale and the Maison Européenne de la Photographie in Paris the Musée de l’Elysée in Lausanne In alignment with the goals set out in The City of Calgary’s Climate Strategy the Calgary Fire Department (CFD) is proud to announce the introduction of our new electric fire engine pilot program and the Pierce® Volterra™ electric engine from Pierce Manufacturing The CFD anticipates the engine will enter service by the end of summer Mayor Jyoti Gondek commented on the engine’s arrival "The introduction of the electric fire engine marks a significant step forward in our commitment to a greener Calgary By reducing emissions and improving air quality this addition to the Calgary Fire Department not only enhances our emergency response capabilities it also demonstrates our dedication to building a sustainable future for our community." Calgary’s Pierce Volterra™ EV engine was custom made by Pierce Manufacturing to meet CFD specifications the engine will be tested and evaluated by both Pierce and the CFD against performance measures including the battery’s ability to operate in our varied climate This Pierce Volterra™ EV is the first of its kind in Canada and will operate out of the Mount Pleasant Fire Station which has been outfitted with the necessary charging infrastructure "The introduction of the Pierce Volterra™ electric engine into our fleet through this pilot program allows the CFD to test the functionality and performance of an electric engine without making a long-term financial commitment," said Acting Fire Chief Pete Steenaerts "Deployment of the Pierce Volterra™ engine in three cities in the United States has been successful which gives us confidence in the reliability and performance of this technology We look forward to evaluating the performance of the engine and providing feedback that could make future versions even better." One of the features of the Pierce Volterra™ electric engine is its backup diesel system which ensures continuous power to both the pumping and driving systems this dual-power setup allows the CFD to maintain operational readiness under all circumstances Reduced emissions and improved air quality: Electric engines produce zero tailpipe emissions and will help to reduce the carbon footprint of the CFD Minimized fuel use: While the engine is supported with a back-up diesel system if required it is anticipated the vehicle will use substantially less fuel Quieter operation: Electric engines operate more quietly than their diesel counterparts General Manager of Commercial Emergency Equipment the Pierce dealer and service provider for the Calgary Fire Department’s Pierce Volterra™ Pumper “We are proud to support Pierce Manufacturing’s first zero-emission emergency apparatus in Canada The Commercial Group of Companies has a long history of vehicle electrification and sustainability including the outfitting of fully electric work vehicles for The City of Calgary and this partnership is a testament to our commitment to a greener future Our certified technicians are ready to ensure the successful integration of this advanced vehicle into the Calgary Fire Department’s fleet.” About the Calgary Fire DepartmentThe Calgary Fire Department (CFD) is dedicated to serving Calgarians through excellence in fire prevention we are one of only seven accredited fire services in Canada Teamwork and Respect guide our actions and how we work with the communities we serve Learn more about the CFD at calgary.ca/fire McNeilus Truck and Manufacturing Inc., an Oshkosh Corp. business, has kicked off its Road Tour, showcasing the Volterra ZSL electric refuse collection vehicle (eRCV). As a fully integrated electric refuse vehicle, the Volterra ZSL eRCV delivers driver comfort, safety, sustainability and operational efficiency. The McNeilus Road Tour will offer customers and industry professionals an exclusive opportunity to experience the vehicle firsthand. The tour will include several locations throughout the United States. The Volterra ZSL eRCV is designed with the driver in mind, offering nearly 38% more cab space compared with the industry average. The vehicle features a low 15-inch step height, making it easy and safe for drivers to enter and exit. The fully integrated cab provides direct visibility, helping to minimize potential incidents and promoting a safe working environment. Equipped with advanced driver assistance systems, including blind-spot monitoring, a 360° camera view, forward and rear collision notifications, and lane departure warnings, the vehicle helps drivers operate safely and efficiently. The 12.3-inch digital gauge cluster display informs drivers with real-time data, enhancing their ability to manage routes safely and efficiently. The Volterra ZSL eRCV is certified zero emissions by both the U.S. Environmental Protection Agency (EPA) and the California Air Resources Board (CARB). Its advanced lithium-ion batteries and electric-axle system enable a full day’s collection on a single charge in many cases. The vehicle’s tight turning radius, smart battery system, and real-time vehicle monitoring contribute to its extended range and reduced downtime. Volume 9 - 2015 | https://doi.org/10.3389/fncom.2015.00112 Chemical synapses are comprised of a wide collection of intricate signaling pathways involving complex dynamics These mechanisms are often reduced to simple spikes or exponential representations in order to enable computer simulations at higher spatial levels of complexity these representations cannot capture important nonlinear dynamics found in synaptic transmission we propose an input-output (IO) synapse model capable of generating complex nonlinear dynamics while maintaining low computational complexity This IO synapse model is an extension of a detailed mechanistic glutamatergic synapse model capable of capturing the input-output relationships of the mechanistic model using the Volterra functional power series We demonstrate that the IO synapse model is able to successfully track the nonlinear dynamics of the synapse up to the third order with high accuracy We also evaluate the accuracy of the IO synapse model at different input frequencies and compared its performance with that of kinetic models in compartmental neuron models Our results demonstrate that the IO synapse model is capable of efficiently replicating complex nonlinear dynamics that were represented in the original mechanistic model and provide a method to replicate complex and diverse synaptic transmission within neuron network simulations If computational modeling is to help in better understanding the mechanisms underlying normal and pathological cases multi- and large-scale models are essential for taking into account relevant processes that take place at all levels Mathematical models that simulate physiological systems are developed to depict the system of interest, or at least provide a reasonable view of some of its inherent mechanisms and functions. Markov kinetic state models (MSM) represent a popular choice of model structure used to represent many dynamical physiological systems (Prinz et al., 2011) integration of a large number of kinetic models with varying temporal dynamics without simplification can increase the computational loads ultimately leading to prohibitively long simulation times despite significant advances in technology and computing the computational power required to simulate large-scale models comprising a large number of biomolecular details still exceeds the capabilities of today's most performant computers which thus inherently results in measurable errors between empirical (i.e. Synapse models can have various representations which differ in computational efficiency and model detail (A) The exponential synapse is a commonly used synapse model that produces a postsynaptic response from a simplistic equation The result is fast but lacks more complex dynamics typically seen in an actual synapse parametric model of a hippocampal glutamate synapse Markov kinetic state models and other additional mechanisms govern the overall postsynaptic response resulting in an accurate and nonlinear response more characteristic of the response that would be observed in an actual glutamatergic synapse (C) The IO synapse model uses the Volterra functional power series to faithfully reproduce the nonlinear details seen in the EONS/RHENOMS model As this IO synapse model characterizes the dynamic relationships between the input events and the corresponding output much of the computationally intensive calculations are waived through the use of this methodology (D) Schematic representation of the computation time required and the detailed accuracy of each model The IO synapse model can provide a much more accurate representation than the exponential synapse while computationally lighter than the parametric EONS synapse model the IO synapse model is provided with random interval train input with mean firing rates ranging from 2 to 10 Hz to determine the degree of nonlinearities that the model is capable of capturing to further evaluate the efficiency of the IO synapse model the kinetic receptor models were implemented directly in the NEURON simulation environment and simulation times between IO and kinetic models were compared The results clearly indicate that the IO synapse model is capable of replicating the complex functional dynamics of a detailed glutamatergic synapse model while significantly reducing computational complexity thereby enabling simulations on larger temporal (seconds to minutes) and spatial scales (large network of neurons containing highly elaborate functional synapses) each state representing a different conformation of the receptor (open vs The AMPAr current is calculated through the following equation: with currents returning to baseline in less than 30 ms the dynamics of AMPAr desensitization are much slower and the receptor can take up to approximately 500 ms to recover from desensitization The conductance gAMPA is used for estimations by the IO receptor model of the AMPA receptor model NMDAr is characterized by slower dynamics than the AMPA receptor (about 300 ms). The kinetic model used in the parametric modeling framework is the 8 states receptor model developed by Erreger et al. (2005) (alternative models were investigated as well—results not presented here) NMDAr current is defined in a similar manner as the AMPAr current: For NMDAr, the number of NMDA receptors (nbNMDA) is set to 20, which is in range of reported studies (Racca et al., 2000) is intrinsically different from the conductance of AMPAr because of the nonlinear response to voltage due to the magnesium block properties This feature was separately accounted for in the IO synapse model and is explained in more detail in the next section Because calculations of both AMPAr and NMDAr kinetic models are time-consuming constituting a potential bottleneck for larger scale simulations we propose to derive their corresponding Input-Output counterparts where g0 represents the total conductance in the absence of any magnesium g2 represent the open state conductances with one glutamate bound and 2 glutamate molecules bound g1is set at 40 pS while g2 is set at 247 pS represents the external magnesium concentration and is set The value α = 0.01 represents the steepness of the transition between g1 and g2 Mg02+represents the external magnesium concentration and is set at 1 mM K0 is the equilibrium constant for magnesium set at 3.57,F is Faraday's Constant (9.64867.104 C mol−1) R is the molecular gas constant (8.31434 J mol−1 K−1) The variable ψm represents the affinity between NMDAr and magnesium which is dependent on the postsynaptic potential of the synapse; the value is set to 0.8 Here we utilize the open state O(t) as the output data during training of the IO receptor model of the NMDA receptor; the estimated conductance is then calculated from the predicted open state value by the IO receptor model the EONS synapse calculates the probability of vesicle release based on past release events glutamate diffusion is calculated and depending on postsynaptic receptor location the result is used for deriving the open states in the kinetic models of the receptors (C) The IO synapse model accounts for both the diffusion and kinetic receptor dynamics to calculate the predicted open states of the receptors The open states are used to calculate conductances and resulting currents based on the postsynaptic potential The calculated response is then passed on to the NEURON model The Input-Output model for receptors uses the Volterra functional power series together with Laguerre basis functions (Berger et al., 2010) The general form of the Volterra functional power series is described by: where v represents the basis functions convolved with the input for a memory window length Mk and can are the scaling coefficients used to have the basis functions fitting the shape of the training data N denotes the number of basis function sets and L represents the number of basis functions for each set Each set is representative of basis functions of different decay constants which is further elaborated in the description of Laguerre basis functions Nonlinearities are captured through modeling higher model orders This corresponds to the baseline signal in the presence of no event Values for c1 and v1 represent the 1st order kernel and account for responses to a single event c2s and v2s represent 2nd order nonlinearities within an individual set of basis functions whereas c2x and v2x represent cross kernels Nonlinearities occur when multiple events interact with each other and represent the differences between the output of the system and the linear solution of the model given by only the 1st order kernels 2nd order consists of the basis functions cross multiplying with each other (basis functions within a set are multiplied with each other for 2s and basis functions are multiplied with outside sets for 2x) Higher orders involve more cross multiplications between basis functions For basis functions, the Laguerre equations are used for their orthogonality and convergence properties. Additionally, the signals reproduced using Laguerre basis functions have high resemblance to signals encountered in physiology and biology. More details of the methodology are described in Ghaderi et al. (2011) the Laguerre basis functions are derived from Laguerre polynomials The Laguerre polynomials are orthogonal from the interval of 0 to infinity with a weight function ex∕2 and thus the Laguerre functions can be defined as ln(x)=e−x∕2Ln(x) In the time domain,−x∕2 is replaced with p·t where p is a time scaling factor that corresponds to the decay of the basis functions With proper normalization the equations take the following form: A visualization of the Laguerre basis functions is shown in Figure 3 The basis functions are then scaled with coefficient values that are fitted to provide the appropriate response when all functions are convolved with the input signal and summed the basis functions are cross multiplied with each other as described previously These functions together correspond to one set of basis functions with one given decay value Because of the complexities of receptor responses two sets of basis functions are used with different decay values represented by p The first set covers the general response of the system within a short time frame to capture the overall waveform The other covers a much longer time frame and accounts for slower mechanisms We found that using two basis function sets yield better approximation of the dynamics seen in the original kinetic models The p-values were determined via gradient descent to find the optimal decay values with the lowest absolute error while fitting the data The fitting process is further elaborated later in the description on coefficient estimation Graphical representation of the first five Laguerre basis functions The basis functions are scaled with coefficients and summed to produce the first order response to the system these basis functions are multiplied with each other to produce the functions used for reproducing nonlinear responses Note that increasing the order exponentially increases the number of equations and coefficients used for the input-output model. Previous uses of the generalized Laguerre-Volterra model (Song et al., 2009b) have shown that models up to the 3rd order are generally sufficient for modeling most neural spiking activity In this study the model uses 3rd order for low frequency presynaptic activity and 4th order for higher input frequencies The IO receptor models were trained using a series of Poisson random interval train inputs and with the responses of the kinetic models of AMPA and NMDA receptors These responses are the total conductance gAMPA for the AMPA receptor and the open state of the receptor O(t) for the NMDA receptor The open state was chosen as the response to be modeled for the NMDA receptor to avoid complications that may arise with the Magnesium blockade; this blockade is thus factored in afterwards when calculating NMDA conductance The input frequency used for training was either 2 Hz for 3rd order models or a hybrid of 2 and 10 Hz frequency trains for both 3rd order and 4th order models Poisson random impulse trains (RIT) are used because they provide broadband input in order to highlight nonlinearities and dynamics for a wide range of input patterns rather than with events at fixed intervals A total of 1000 input events was used for training for 3rd order models and 2000 input events for order 4th models (this ensured a broad spectrum of input was covered for both 2 and 10 Hz mean input frequencies) The number of Laguerre basis functions used for each set is 4 for the AMPAr 3rd order IO receptor model The number of basis functions per set was reduced to 3 for the NMDAr model with cross terms and for 4th order models; for models with cross terms and higher order models the number of coefficients needed to be estimated is much larger therefore the number of basis functions per set was changed to reduce calculation time required The IO synapse model coefficients were estimated with the MATLAB simulation environment and the Control System toolbox Training the model involved iterating over various decay constants p for each set to find optimal values yielding the lowest absolute error between the actual response of the model and predicted response using the estimated coefficients and decay constants Estimation of the coefficients was done by taking the inverse function of the basis functions multiplied with the training data: V(t) represents the matrix of all the basis functions (including both sets of basis functions with their given p-values) and their cross terms convolved with the input This matrix is inverted using the pinv function in MATLAB then multiplied with the training data to estimate the best fit coefficients for the IO model The training estimate values are subtracted from the true training data set to determine the difference at each instant; these differences are then summed together to determine the absolute error of the training estimate given the p-values and the estimated coefficients p-values are determined by gradient descent choosing the p-values with the lowest absolute error when training to fit the data The optimal p-values we obtained were 0.52 and 0.03 for the basis function sets associated with AMPAr and 0.049 and 0.002 for the basis functions associated with NMDAr Validation of the optimal coefficients and decay constants was performed following the training procedure; it was done with a novel RIT input different from the input used for training The length of the input signal for validation was set to 20 s The average frequency of the input signal is generally 2 Hz unless otherwise specified the normalized root mean square error (NRMSE) was calculated as shown in the following manner: The IO synapse model structure was implemented in NEURON with the use of module (mod) files The module files accept the decay values and the coefficients as parameters Because the number of basis function equations and coefficients differs between models of different orders separate module files were made for different order models 3rd order models were used with 2 Hz Poisson random interval train events to simulate synaptic activity The 4th order model was tested when simulating with higher frequency inputs and compared to the 3rd order model the third order model requires 68 coefficient values whereas 4th order models use 209 coefficients—thus the number of inputs to the module files is different the basic structure of the IO synapse model the module file was set to have a memory window of 2 s keeping all input events triggered within the last 2 s of the current time point in memory for calculation of the IO synapse model responses The width of this 2 s memory window was chosen as there were no significant contributions to the responses for events that take place more than 2 s prior to the current time point To test the IO synapse model in a cell simulation, the CA1 pyramidal cell model proposed by Jarsky (Jarsky et al., 2005) is used as a template Synapse locations are randomly generated on the apical dendrite of the cell simulation input trains consist of Poisson random interval trains having a mean frequency of 2 Hz and the number of synapses is 16 NEURON simulations with the use of the EONS synapse model were run on cluster nodes with dual quad-core Intel Xeon 2.3 GHz processors with 16 Gb RAM IO synapse model simulations were conducted with a single Fedora-based computer with Intel quad-core 2.67 GHz processor and 8 Gb RAM All results were obtained with 20 s of simulated time the IO synapse model has more under-estimate error the error consisted in over-estimation of the output Such analysis shows that the IO synapse model is accurate not only according to the overall RMS error but even high order nonlinearities are well fitted in the model This results in some compensation from the lower order nonlinear interactions but in return responses that must consider up to 10 events in the past are still described accurately by the IO synapse model NRMSE comparison between the EONS synapse model and the IO synapse model Scatterplot on bottom right shows direct comparison of y-values (current) between the two models where each point represents a different time point in the results Results are shown to be nearly identical to each other with only minor differences as shown in the error comparison and scatterplot (B) Response from the EONS synapse model (blue) and the IO synapse model (red) when connected to a neuron model within the NEURON simulation environment (C) Somatic response in a neuron model using the EONS synapse model (blue) and the IO synapse model (Red dotted) within the NEURON simulation environment stochastic vesicle release was disabled for consistency and all synapses fired in response to a pre-synaptic event The minor differences noted in the synaptic current as shown in the other comparisons do not significantly affect the response of the postsynaptic cell The error for both simulations were compared with each other to assess whether there were discrepancies between fixed and variable time steps Accuracy of the IO synapse model with various input frequencies The normalized RMS error is plotted for the 3rd order IO synapse model simulated at fixed (blue) and variable (red) time step simulations and for the 4th order IO synapse model simulated at fixed (green) and variable (purple) time step simulations the error noticeably increases at higher frequencies The 4th order model yields constant error at all tested frequencies the normalized RMS error was plotted as a function of average input frequency rate for 3rd and 4th order IO synapse models the 3rd order IO synapse model was re-trained with a new set of input events in order to better capture the higher frequency nonlinearities The training input events consisted of a hybrid of 2 and 10 Hz Poisson randomized interval trains: the first 500 events averaged a mean frequency of 2 Hz and the second 500 events averaged a mean frequency of 10 Hz The IO synapse model was validated with simulations using input frequencies of 1 simulations at higher frequencies resulted in higher error for the 3rd order IO synapse model when compared with results from the EONS synapse model with normalized mean square error (NRMSE) of up to 35% in simulations with 10 Hz input frequency At lower frequencies (1–4 Hz) the error remained around 10% Higher frequencies are commonly associated with more nonlinear behavior In order to more accurately account for such nonlinearities we implemented an IO synapse model utilizing 4th order Volterra functional power series The 4th order IO synapse model was trained and validated similarly to the 3rd order IO synapse model; the only difference was the number of input events which was increased from 1000 to 2000 events to better estimate the large number of coefficients The 4th order model was found to have an error difference of 10% across the frequency spectrum when compared to the EONS synapse model and thus captures nonlinearities associated with higher frequencies more accurately (up to 25% more accurate with 10 Hz input) than the 3rd order IO synapse model Additional simulations were conducted with a single compartment Izhikevich model with similar results; these results were further analyzed in a manuscript yet to be published All simulations were run using adaptive time step methods and total number of steps are also presented to demonstrate difference in the number of steps required per simulation In the first condition, synapse weights were calibrated to reflect physiological conditions leading to postsynaptic neuron firing (Table 2) the IO synapse model required 617 s of simulation time with 67,319 simulation steps while the kinetic models required 1090 s and 107,640 steps This condition was chosen to investigate the simulation time required with minimal neuron model computation thus reflecting more of the contributions of the synapses to the simulation benchmarks Calculation of the compartments within the neuron model still take place however as the inputs to the neuron is set to 0 calculations by the neuron model should have minimal influence on the simulation time the neuron using IO synapse models required 3.7 s of simulation time with 417 steps while the one using kinetic models needed 589 s and 40,760 steps the IO synapse model outperforms the kinetic models and requires less steps for calculation the speedup is more significant in simulations in which the computational contribution of the neuron model is minimal (i.e. when simulation times are used to calculate synaptic models only) Simulation time and number of steps required to simulate the original kinetic models vs as well as the speedup between the two conditions Several points can be made about the results of these simulations regardless of whether the kinetic models or the IO synapse model was used the neuron model independently of the synaptic model used can take up a significant portion of simulation time depending on its complexity Reducing the synaptic weight to 0 minimizes the neuron model's computational weight to the simulation thereby emphasizing the synaptic component all simulations conducted in this part of the study were simulated within NEURON under adaptive time step conditions This results in a direct comparison between the kinetic models and the IO synapse model based on the Volterra functional power series Differences in simulation time and number of steps seen in the results are therefore directly indicative of the difference in modeling methodology the relative speedup between the IO synapse model and the kinetic models is shown to be significantly larger in simulations with the synaptic weights being set to 0 This result suggests that (1) calculation of the changes in potential in the neuron model compartments requires a significant amount of simulation time thus resulting in longer simulation times compared to the IO synapse model This is likely because kinetic models contain rate equations which require previous time points to calculate the state values the Volterra functional power series models the conductances of the receptors and accounts for the nonlinearities analytically—as a result the response of the IO synapse model does require past values to calculate present values For these simulations the computational contributions of the neuron model were minimized by reducing synaptic weight to 0 The results indicated that the neuron comprised of IO synapse model retains a total calculation time of less than 1 min even in simulations with up to 1000 synapses the calculation time required for the kinetic models ranges from 10 min with 10 synapses The number of steps remained almost constant for both models: 400 steps for the IO model Measuring the approximate speedup of the IO model in comparison to the kinetic model as a function of the number of synapses gives approximately a 150x speedup at 10 synapses number which decreases as the number of synapses increases to finally stabilize at about 50x speedup for 1000 synapses Additional tests performed at up to 5000 synapses confirm that beyond 1000 synapses the speedup of the IO synapse model remains around the same at around 50x Simulation Time varies as a function of the number of synapse instances simulation time is represented in logarithmic scale Computation time required for the kinetic synapse model is within the range of 10–20 min while the computation time required for the IO synapse model ranges between 3 and 30 s Dashed line represents the speedup of the IO synapse model against the kinetic synapse model based on number of synapses the speedup of the IO synapse model is highest at around 150x faster than the computation time required for the kinetic synapse model but stabilizes at around 50x speedup in later values such as Markov kinetic states receptor models reflect the inherent mechanistic properties of the system of interest Their utilization can shed some light on potential abnormalities and dysfunctions underlying pathological cases as well as identify possible solutions to re-establish normal receptor function thereby facilitating identification of new therapeutics Although these models are designed to be as mechanistically close as possible to the physiological structures they represent their computational complexity often restrict the extent of what may be simulated thereby making large-scale simulations impractical This consequently impedes the creation of a unified computational platform that bridges micro- to macroscale dynamics Yet function and dysfunctions that appear in pathological cases often stem from modifications at the molecular level giving rise to altered macroscopic levels of activity leading to the observed phenotype It is therefore essential to determine how changes propagate from the molecular and synaptic levels up to the network level we described the development and characteristics of an IO synapse model that extracts and successfully replicates the functional properties generated by detailed kinetic models while significantly reducing computational complexity thereby enabling simulations at a larger scale training and calibration of the IO synapse model was done on a local scale yielding parameters values for the Volterra functional power series to accurately describe the dynamics of the system with a low computational complexity We assessed the accuracy of the model compared to its parametric counterpart We then went on to demonstrate that large-scale simulations could be performed with a very large number of IO synapse models number unreachable using traditional parametric models Synapse models routinely used in large scale simulations typically consist of linear exponential synapses (Roth and Rossum, 2000; Hendrickson et al., 2012) while sufficient to replicate the global waveform of synaptic responses are not detailed enough to replicate nonlinear behaviors or to have any application for studying molecular-level modifications or drug-target interactions the IO synapse model may faithfully reproduce nonlinear dynamics under a wide range of conditions (e.g. with a computational cost nearly equivalent to the exponential synapse we used the EONS synapse model to develop two separate IO receptor models—the AMPAr and NMDAr models we first considered the implementation of a single IO synapse model for the postsynaptic component of the model (rather than one for each receptor type) Since an input-output model is based on input-output relationships it was presumed that all nonlinearities may be taken together This would then require only one overall IO synapse model to be implemented thus presumably becoming more computationally efficient several key factors influenced the choice of making the system more modular the different receptors have different rise and decay characteristics This had an impact on the overall estimation accuracy and the dynamics were not properly captured due to different decay rates (results not shown) the decision to use separate input-output models for each ionotropic receptor allowed for each of the models to be more adequately calibrated If the postsynaptic response was represented by a single input-output model the rise and decay rate of the input-output model would need to be averaged out between the two receptor models that it represents Another reason for separating receptor models is the existence of specific characteristics associated with different types of receptors The magnesium blockade is a clear example of such model-specific characteristics; here using a separate model allows for the magnesium blockade factor to be separately accounted for in the NMDAr IO model only If the entire synapse model was represented by only one input-output model it would not be possible to associate the magnesium blockade effect with only NMDAr a more complex multi-input model would be required The IO synapse model circumvents this issue by capturing the input-output relationships of the kinetic models This means that no matter how intricate the original model may be the IO synapse model will attempt to capture and replicate the outputs of the model using the same functional structure (sets of basis functions and coefficients) and consequently with the same computational complexity This can facilitate integration of a large number of microscopic components with less concern for growing complexities as would be the case for kinetic models with high numbers of states and rate equations input-output modeling can even be extended into macroscopic levels to reduce neuron models to a set of Volterra functions Such methods could provide a way to extend multi-scale modeling even further one limitation of our IO synapse model is that its input-output reference data is captured from a parametric model which may not capture the full dynamics of the biological element the IO synapse models would be trained using experimental results individual synapses and their dynamics are particularly difficult to measure kinetic models may be better suited for initial calibration which are based on experimental studies of individual synaptic components such as receptors isolated in expression systems (e.g. The results of the calibrated kinetic models can then be used to train the input-output models for multi-scale and large-scale application experimental techniques may be perfected in the future to allow direct calibration of the IO synapse models which can also be used to further refine mechanistic (kinetic) models to subsequently provide further insights into mechanistic functions Such dual mechanistic and non-parametric approach may be able to further refine simulation predictions at the single and multi-scale levels while further extending the range of complex nonlinear dynamics modeled all the way up to large-scale systems providing further insights into the complex physiological mechanisms taking place in the nervous system during normal function or pathological dysfunctions and consequently help identify efficacious therapies to alleviate them Work supported by NIBIB grant P41 EB001978-24 and U01 GM104604 to TB We thank Rhenovia Pharmaceuticals for providing kinetic receptor models to use within the NEURON simulation environment The Supplementary Material for this article can be found online at: http://journal.frontiersin.org/article/10.3389/fncom.2015.00112 Supplementary Figure 1. A linear representation of Figure 6 The left axis represents the simulation time range for the IO synapse model while the right axis presents the range for the kinetic synapse model for the overhead simulation time that is irrelevant to the number of synapses the kinetic synapse model has a much higher overhead than the IO synapse model A computational model to investigate astrocytic glutamate uptake influence on synaptic transmission and neuronal spiking Blue gene: a vision for protein science using a petaflop supercomputer Computational studies of NMDA receptors: differential effects of neuronal activity on efficacy of competitive and non-competitive antagonists Ananthanarayanan “The cat is out of the bag,” in Proceedings of the Conference on High Performance Computing Networking PubMed Abstract Nonlinear systems analysis of the hippocampal perforant path-dentate projection Effects of random impulse train stimulation Comparison of random train and paired impulse stimulation The neurobiological basis of cognition: identification by multi-input multioutput nonlinear dynamic modeling: a method is proposed for measuring and modeling human long-term memory formation by mathematical analysis and computer simulation of nerve-cell “An introduction to volterra series and its application on mechanical systems,” in Advanced Intelligent Computing Theories and Applications With Aspects of Contemporary Intelligent Computing Techniques Communications in Computer and Information Science CrossRef Full Text Integrated multiscale modeling of the nervous system: predicting changes in hippocampal network activity by a positive AMPA receptor modulator Modeling glutamatergic synapses: insights into mechanisms regulating synaptic efficacy Carnevale, N. T., and Hines, M. L. (2006). The NEURON Book. Cambridge University Press. Available online at: http://books.google.com/books?hl=ja&lr=&id=YzcOyjKBPHgC&pgis=1 Nonstationary modeling of neural population dynamics and residual calcium at three presynaptic terminals Inositol 1,4,5-Trisphosphate-Dependent Ca2+ threshold dynamics detect spike timing in cerebellar purkinje cells Multiscale coupling of transcranial direct current stimulation to neuron electrodynamics: modeling the influence of the transcranial electric field on neuronal depolarization Dyhrfjeld-Johnsen Topological determinants of epileptogenesis in large-scale structural and functional models of the dentate gyrus derived from experimental data Mechanism of partial agonism at NMDA receptors for a conformationally restricted glutamate analog The cholinergic hypothesis of Alzheimer's disease: a review of progress Modeling neuron-glia interactions: from parametric model to neuromorphic hardware Simulation of postsynaptic glutamate receptors reveals critical features of glutamatergic transmission Towards a large-scale biologically realistic model of the hippocampus The contribution of relative activation levels between populations of cells to network activity in a large-scale biologically realistic model of the hippocampus Large-scale model of mammalian thalamocortical systems Conditional dendritic spike propagation following distal synaptic activation of hippocampal CA1 pyramidal neurons A nonlinear model of cardiac autonomic control in obstructive sleep apnea syndrome PubMed Abstract | CrossRef Full Text | Google Scholar Analysis of Physiological Systems: The White-noise Approach Google Scholar Dendritic spine geometry is critical for AMPA receptor expression in hippocampal CA1 pyramidal neurons Integration of biochemical and electrical signaling-multiscale model of the medium spiny neuron of the striatum Megìas Total number and distribution of inhibitory and excitatory synapses on hippocampal CA1 pyramidal cells Requirement for hippocampal CA3 NMDA receptors in associative memory recall Markov models of molecular kinetics: generation and validation NMDA receptor content of synapses in stratum radiatum of the hippocampal CA1 area Studies on single neurons in dorsal hippocampal formation and septum in unrestrained rats Behavioral correlates and firing repertoires How AMPA receptor desensitization depends on receptor occupancy PubMed Abstract | Google Scholar AMPA receptors as a molecular target in epilepsy therapy Roth, A., and Rossum, M. C. W. (2000). “Modeling synapses,” in Computational Neuroscience: Realistic Modeling for Experimentalists, ed E. De Schutter (CRC Press). Available online at: http://books.google.com/books?hl=ja&lr=&id=Tk4BNxIjTBYC&pgis=1 PubMed Abstract Reduced hippocampal LTP and spatial learning in mice lacking NMDA receptor epsilon 1 subunit PubMed Abstract | CrossRef Full Text Parametric and non-parametric modeling of short-term synaptic plasticity Identification of sparse neural functional connectivity using penalized likelihood estimation and basis functions Etiology of infantile autism: a review of recent advances in genetic and neurobiological research “Functional model selection for sparse binary time series with multiple inputs,” in Economic Time Series: Modeling and Seasonality PubMed Abstract | Google Scholar Implementation of the excitatory Entorhinal-Dentate-CA3 topography in a large-scale computational model of the rat hippocampus Baudry M and Berger TW (2015) Volterra representation enables modeling of complex synaptic nonlinear dynamics in large-scale simulations Received: 28 April 2015; Accepted: 25 August 2015; Published: 17 September 2015 Copyright © 2015 Hu, Bouteiller, Song, Baudry and Berger. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) provided the original author(s) or licensor are credited and that the original publication in this journal is cited *Correspondence: Eric Y. Hu and Jean-Marie C. Bouteiller, University of Southern California, HNB 412, 3641 Watt Way, Los Angeles, CA 90089-2520, USA,ZWh1QHVzYy5lZHU=;amJvdXRlaWxAdXNjLmVkdQ== Volume 12 - 2018 | https://doi.org/10.3389/fncel.2018.00098 This article is part of the Research TopicNeuron-Astrocyte Communication at Synapses and CircuitsView all 9 articles Three programs are available: MultiROI_TZ_profiler for interactive graphing of several movable ROIs simultaneously Gaussian_Filter5D for Gaussian filtering in several dimensions and Correlation_Calculator for computing various cross-correlation parameters on voxel collections through time for which we here provide the detailed guide and the relevant software plugins In our study (Bindocci et al., 2017) we decided to apply 3D Ca2+ imaging to astrocytes One of the consequences was the generation of large microscopy datasets (the so-called “big data”) Big data production is an ongoing trend in neuroscience in general because by them one obtains unprecedented levels of information on the spatiotemporal positioning and interactions between the key brain cell components Large speed/scale functional Ca2+ imaging in particular is known to generate datasets of many gigabytes to terabytes which represents a practical challenge for both initial exploration and automated analysis of the experimental data manual identification and processing of each Region of Interest (ROI) is time consuming and therefore automated detection and analysis of individual functional units and signals is needed Some general assumptions are that: (1) a single well-defined unit such as a soma carries most of the relevant information (e.g. it becomes generally desirable that somatic ROI detection is optimized and activity of other sub-cellular components (dendrites axons) is instead minimized by subtraction; (2) constraints in terms of size and/or shape can be imposed to the ROI-defined structure; (3) each active pixel belonging to such structure follows the same time-course as the entire structure; (4) generally the ROI-defined structure is repeatedly and reproducibly activated multiple times throughout the recording; (5) Ca2+ events have stereotyped kinetics mostly dependent on the properties of the dye used (with certain rise/decay-time characteristics considered as genuine); (6) background noise can be accurately modeled and discarded be it coming from true noise sources or the surrounding neuro(glia)pil while independent units (or “microdomains”) within astrocytes may dynamically merge and split under some circumstances the dwell time of each voxel is greatly reduced leading to a significant increase in the total voxel scan rate with the final result of capturing multiple focal planes in the time it normally takes to acquire a single plane While the storage requirements for the 3D datasets are substantial a main difficulty is the lack of user-friendly analytical tools allowing for interactive exploration of the datasets such as a real-time display of Ca2+ traces from the volumes of interest interactively defined and moved by the user It is the kind of tools that we developed for our study and present here below tens to hundreds of ROIs should be in principle defined for each region of the cell typically at locations that are thought to themselves act as functional units including also the inactive or sparsely active structures a comprehensive look at the entire structure (volume) of the astrocyte is required in order to understand the properties of the astrocytic responses and ROI-based or SDV-related approaches face inherent limitation While this can be considered a conservative approach it is still useful to quantify activity throughout an astrocyte and does not incur in mistakes which are unavoidable when trying to arbitrarily merge active voxels from sub-resolved regions Advantages of 3D Ca2+ imaging in astrocytes over 2D-based techniques Applying 2D-based approaches to astrocytes is likely to produce artifacts such as incomplete and incorrect capture of the structural and functional information (A) An example of a 3D volume selected for imaging which contains several astrocytes expressing GCaMP6f calcium indicator Top: average projection of the morphological (SR101 dye labels astrocytes) and functional indicators (GCaMP6f Middle: an SR101-based reconstruction (mask) of the core borders of the two GCaMP6f expressing astrocytes present in the selected imaging volume Smaller processes and most of the “gliapil” are not included here A blood vessel is also labeled via the astrocytic end-feet (B) A representative example of GCaMP6f activity as seen in 3D (Top left) by monitoring the volume of an astrocyte (average of 2 s The regions segmented by the astrocytic core mask are faintly outlined magenta rectangle indicates the location of the selected focal plane A large Ca2+ event is apparent in a vertical process in the 3D 2D imaging in practice fragments the 3D structure of the astrocyte and misses most of it The majority of the large Ca2+ event apparent in 3D is likewise missed and fragmented into multiple smaller events generating artifacts in reporting the event frequency and spatial properties Bottom: A top-down projection of 30 individual focal planes (3D) recovers the astrocyte structure fragmentation and most of the missing Ca2+ event allowing correct reporting of its properties (1) Gaussian_Filter5D: a simple 5D Gaussian filter plugin for signal processing This was currently missing from the default ImageJ tools since the built-in 3D filter functionality does not fully support filtering higher-order stacks (such as combined z+t) The current plugin is natively capable of processing a 5-D stack and is able to filter in all dimensions (except across channels) A DC offset option is provided to blank arbitrary noise values below a selectable threshold (2) MultiROI_TZ_profiler: a multi-ROI trace plotter allowing for interactive, real-time exploration of the 5D data by the user. This expands the functionality of the built-in “Z-axis profiler” tool set up by the NIH developers (Baler and Rasband, 2003) which allows for plotting the average ROI signal through space or time Using the Z-axis profiler code as a starting base we added the multi-ROI (multi-trace) capability as well as the capability of adding an externally loaded trace (e.g. A number of other user-friendly options such as filtered trace overlay color-coding and various display normalization options are also provided via an extra interface window The plugin implements dynamic update capability and see the resulting trace changes in real time we provide a practical guide based on our experience as to how Ca2+ transients evoked in astrocytes by neuronal activity can be recorded via 3D two-photon Ca2+ imaging and subsequently analyzed the experimental procedures for expressing GECI in neurons and astrocytes for stimulating axons and for Ca2+ imaging in brain slices or in vivo in awake mice as well as the tools to be used for data storage deionized electrophysiology-grade water (18.2 MOhm-cm) prepared according to a number of possible recipes and methanol for coating the stimulation pipette Imaging system: in principle, this can be any system providing sufficient space-time resolution and sensitivity appropriate to the question at hand. In our case, for studying astrocytic Ca2+ responses to axonal stimulation in 3D (Bindocci et al., 2017) the system is a fast raster-scanning two-photon microscope equipped with an 8 kHz resonant galvanometer (for fast x-axis scan) and piezoelectric objective actuator (for fast z-axis positioning) volume imaging is accomplished by a consecutive raster scanning of every voxel (at a corresponding position x while the speed improvement is traded off for a greatly decreased voxel dwell time The resulting signal loss is partially compensated with the use of sensitive GaAsP detectors and space-time filters Synchronization of imaging and electrical stimulation via simultaneous capture of timing information from the two systems By concurrently recording the image frame counts and the electrical inputs one can later link analytically the imaging and electrophysiology data An electrophysiology computer is also simultaneously recording two signals for synchronization: a Y-galvanometer position feedback pin and a split-off of a stimulator TTL trigger (B) Low-zoom overview of the captured synchronization signals (light-blue highlight is magnified in next panel Vertical deflections in the Y-galvo trace correspond to individual Y-frame scans whereas spikes on the Stim TTL trace indicate the relative timings of axonal stimulation (C) A high-zoom version of the highlighted stretch in (B) showing the relationship between the imaging frame position and the stimulation signal timing Each Z-stack consumes an entire Y-scan frame per focal plane (here 21) plus any additional overhead depending on whether bi-directional z-scanning is implemented Microelectrode positioning system/micromanipulators: in our case we used a Luigs & Neumann SM-5 system equipped with an appropriate electrode holder rod The procedure for recording correlated electrical and visual data is described below Experiments involving axonal electrical stimulation are generally performed in brain slices. A slice is placed in the microscope slice chamber equipped with an appropriate aCSF perfusion system and environmental controls. The cells of interest are visually located, the stimulation electrodes placed, and the stimulation/acquisition performed according to the protocol. In our case, we chose to stimulate the axons over an interval of 15 min (see Figure 2B) The protocol consisted in three periods of sparse stimulation separated by intervals without any stimulation of similar duration (2–3 min) This protocol was chosen to reliably separate high background spontaneous Ca2+ activity from true evoked activity the electrophysiology and imaging systems used in these experiments need to be accurately synchronized for future data analysis offline notably for establishing the correct temporal sequence of neuronal activity and astrocytic responses such as paired whole-cell patch clamp experiments or optogenetic (ChR2 etc.) stimulation could be used to activate the axons in a more spatially restricted manner For analyzing the temporal relationship between electrical and Ca2+ activity recorded in the brain preparation the electrophysiological and imaging data streams need to be precisely synchronized The exact method of accomplishing the synchronization is highly hardware- and configuration-dependent and may even be provided out-of-box by the modern imaging systems (albeit generally not designed with electrophysiologists in mind More precise x-y coordinates of each voxel could be estimated within each frame by sampling the galvanometer position signals at a faster rate that corresponds to the pixel dwell time (variable on the order of 0.1 μs in our setup) or other related imaging system outputs could be captured for similar purposes but note the sub-sampling artifacts in ramping amplitudes in B) The min/max filter option provided the highest amplitude of peaks but also occasionally introduced some artifacts and therefore the analog filter option was chosen it would also be prudent to store a time-stamped copy of the electrophysiology signal on the imaging system the amplified traces can also be saved as a new image channel albeit with some data loss between frames and during the galvanometer/piezo fly-back intervals and with decreased fidelity or range (imaging cards typically have a lower ADC resolution of 8–12 bits vs 16+ bits typical for the standard electrophysiology equipment) drilled a small opening in the scull and used a pulled glass capillary to inject a small volume of the virus (0.5–1.0 μl at viral titer of ~1 × 1012 VG/ml) stereotaxically at the following coordinates (bregma: −4.5 mm; lateral: 2.85 mm; ventral: −3.30 mm adjusted slightly for different mouse strains and ages) over a period of 5–10 min After an additional 10 min in which the capillary was left in place to permit viral diffusion Analgesia was provided by paracetamol (500 mg/250 ml) in the drinking water starting 1 day prior to the surgery and for several days afterwards Good viral expression was apparent 4–5 weeks post-infection All procedures have received ethics approval and were conducted under license and according to the regulations of the cantonal Veterinary Offices of Vaud this procedure may require at least 6–8 weeks to produce a physiological Ca2+ activity in the astrocytes whereas at shorter timings the transients have distorted kinetics possibly due to a still reactive state of the astrocytes upon the injection the animals were anesthetized with isoflurane and decapitated placed into an ice slurry solution (regular aCSF with half of NaCl substituted by sucrose and glued to the stage of the microvibratome (Leica VT1000 or Microm 650) The slices were incubated in aCSF at 34°C for at least half an hour we added a brief incubation in low-concentration sulforhodamine 101 (5 min in 0.05 μM SR101) followed by a washout step of at least 15 min we describe the main steps of treatment of the data acquired during the experiments data handling involves conversion and storage of the data files (image series and electrophysiological recordings) for later Data can be safeguarded on external disks or network attached storage (NAS) computer systems data exploration typically involves loading and filtering the data and displaying them for the user in an on-line interactive manner Two of our plugins are designed to allow 5D filtering and interactive multi-ROI placement and associated signal display data analysis involves extracting signals from defined populations of cells One of our plugins is designed to automatically identify the size of reliably-responding regions that exhibit consistent increases in Ca2+ transients in response to axonal stimulations the 5D voxel data can be accessed via either a Macro script (user-friendly and very handy for chaining built-in commands and plugins but generally too slow for extensive voxel-wise analysis) or natively through Java plugins (requiring larger programmer participation but resulting in several orders of magnitude speed improvements during computations) extraction of the data for a voxel at coordinates (x c) is accomplished by locating and extracting a single 2d (X-Y) frame in the stack that corresponds to the desired z For ease of access (but at a cost of doubling memory requirements) two of our three plugins first transfer these data into a structured 5D memory array (e.g. The only practical limitation of such approach is when the data size exceeds the amount of RAM available to Java VM or when any of the five array dimensions exceeds the maximum value for the Java integer type (obtained via Integer.MAX_VALUE parameter) After the data stacks are converted and loaded the data can be processed with filtering as usual Because the built-in tools are unable to perform filtering over 2 dimensions on stacks containing both T and Z series we have generated a 5D filter plugin able to perform the filtering on 5D data in up to 4 dimensions (x The ability to pre-subtract a noise floor from the data (thresholding This is useful to remove low-level electrical noise pickup (e.g. Here below is shown the sample user interface for the Gaussian Filter 5D plugin: data can be manually explored by placing a user-generated ROI and displaying the corresponding Ca2+ trace Recent versions of ImageJ have added the ability to move interactively and resize the ROI while getting an instantaneous update of the trace graph We have further expanded this ability by adding the following capabilities: (1) simultaneous placement of multiple ROIs and display of the corresponding Ca2+ traces; (2) normalization of each trace to the min/max values; (3) overlay of the original trace with a filtered trace; and (4) simultaneous display of the externally loaded stimulus file on top of the Ca2+ traces (see section Expected Results below) Here below is shown the main interface for the MultiROI TZ profiler plugin: The resulting correlation coefficients were added up for all values of time lag between 0 and a pre-defined time window (corresponding to 2.5 or 5 s in our case) user-independent quantification of the estimated active volumes or responding regions the user can specify the time size of the correlation window used to detect the response (in t frames) and the size of an X-Y filter (averaging neighboring pixels) that can be applied to the data The time size of the correlation window will vary depending on the sampling rate the expected time delay between the stimulation and the response This window size also acts as a normalization window for the fluorescence trace Here below is shown the user interface for the Correlation Calculator plugin: neurons are expected to start expressing the selected fluorophores at quantities sufficient to visualize individual axons The exact mode of visualization will depend on the fluorophore and the imaging technique used it may be better to choose red-spectrum fluorophores (such as tdTomato as a morphological dye or jRCaMP as a Ca2+ indicator) due to a somewhat lower tissue autofluorescence in the red spectrum The figures below show the typical appearance of labeled axonal fibers in slices and a typical example of electrically-evoked Ca2+ transients recorded from the gliapil of GCaMP6f-expressing astrocytes allowing correct calculations of the events frequency and spatial-temporal properties The software provided here allows to optimize the analysis workflow on the multi-dimensional datasets high-resolution whole-volume imaging and voxel-by-voxel automated analysis provide a very promising venue for future understanding of astrocytic and neuronal computation during spontaneous conditions as well as during learning and behavioral tasks The three stimulation epochs are separated by quiescent intervals even when stimulating with very large current strength Astrocytes and neurons respond differently to information flow evoked Ca2+ transients are much less likely to follow a predictable stereotypical waveform and spatio-temporal distribution in astrocytes than in neurons Fewer a priori assumptions can be made for studying astrocytic compared to neuronal Ca2+ transients particularly regarding their size and location the astrocytic soma appears to be of little use for recapitulating astrocytic excitability as most of the Ca2+ activity in astrocytes is local and occurs 3D-based volumetric imaging approaches appear to be the most promising way to capture and study the full range of astrocytic Ca2+ activity Even though the resulting data complexity is challenging the 3D signals can nevertheless be amenable to interactive visualization including with the early tools released by this lab Because our tools are implemented natively in Java and take advantage of the multi-threading capability of modern CPUs generally exceeding that of other higher-level scripting approaches in writing this practical guide article on our 3D Ca2+ imaging approach and in releasing the related analysis tools we hope to have made a concrete step for convincing the scientific community to apply multidimensional approaches to the functional study of axon-astrocyte interactions in view of their superior quality of investigation IS: Wrote the plugins (software) and made the figures; GC: Established the original stereotaxic AV injection for transgenically labeling EC-DG projections; AV: Guided and supervised the study; IS and AV: Wrote the manuscript and Denise Becker for collaboration and helpful discussions We are grateful to Nicolas Toni for his large initial assistance with establishing the stereotaxic viral injection procedures for the entorhinal cortex projections and to Frank Kirchhoff for his generous gift of the GFAP-CreERT2 mice Transgenic Rosa26-lsl-GCaMP6f mice [Gt(ROSA)26Sortm95.1(CAGGCaMP6f)Hze] were purchased from Charles River under an MTA with the Jackson Laboratory Research in the Volterra lab is supported by the ERC Advanced grant Astromnesis (340368) as well as by the National Centers of Competence in Research (NCCR) Synapsy (51NF40-158776) and Transcure (51NF40-160620) The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fncel.2018.00098/full#supplementary-material Thin dendrites of cerebellar interneurons confer sublinear synaptic integration and a gradient of short-term plasticity Transient opening of the mitochondrial permeability transition pore induces microdomain calcium transients in astrocyte processes Quantum dot-based multiphoton fluorescent pipettes for targeted neuronal electrophysiology Baler, K., and Rasband, W. (2003). Z Profiler. [Computer Software: ImageJ plugin]. https://imagej.nih.gov/ij/plugins/z-profiler.html (NIH) Astrocyte calcium signaling: the third wave Three-dimensional Ca2+ imaging advances understanding of astrocyte biology Dendritic discrimination of temporal input sequences in cortical neurons “The synapse-astrocyte boundary: an anatomical basis for an integrative role of glia in synaptic transmission,” in The Tripartite Synapse: Glia in Synaptic Transmission Glutamate induces calcium waves in cultured astrocytes: long-range glial signaling Local Ca2+ detection and modulation of synaptic release by astrocytes Fernandez-Alfonso Monitoring synaptic and neuronal activity in 3D with synthetic and genetic indicators using a compact acousto-optic lens two-photon microscope Freeman, J., Sofroniew, N., Broxton, M., Grosenick, L., Trautmann, E., Kitch, L., et al. (2017). Codeneuro/Neurofinder, Benchmarking Challenge for Finding Neurons in Calcium Imaging Data. Available online at: http://neurofinder.codeneuro.org/ Cerebellar cortical molecular layer inhibition is organized in parasagittal zones Imaging cellular network dynamics in three dimensions using fast 3D laser scanning Neural ensemble dynamics underlying a long-term associative memory High-speed in vivo calcium imaging reveals neuronal network activity with near-millisecond precision Fast two-layer two-photon imaging of neuronal cell populations using an electrically tunable lens Microdomains for neuron-glia interaction: parallel fiber signaling to Bergmann glial cells Conditions and constraints for astrocyte calcium signaling in the hippocampal mossy fiber pathway Temporal control of gene recombination in astrocytes by transgenic expression of the tamoxifen-inducible DNA recombinase variant CreERT2 Astrocyte calcium signals at Schaffer collateral to CA1 pyramidal cell synapses correlate with the number of activated synapses but not with synaptic strength Dysfunctional calcium and glutamate signaling in striatal astrocytes from huntington's disease model mice Imaging intracellular Ca(2)(+) signals in striatal astrocytes from adult mice using genetically-encoded calcium indicators Measuring neuronal population activity using 3D laser scanning Fast two-photon in vivo imaging with three-dimensional random-access scanning in large tissue volumes Nitric oxide signals parallel fiber activity to Bergmann glial cells in the mouse cerebellar slice Automated analysis of cellular signals from large-scale calcium imaging data In vivo stimulus-induced vasodilation occurs without IP3 receptor activation and may precede astrocytic calcium increase Imaging extrasynaptic glutamate dynamics in the brain Astrocytes are endogenous regulators of basal transmission at central synapses Astrocytic neurotransmitter receptors in situ and in vivo Astrocytes regulate cortical state switching in vivo Disentangling calcium-driven astrocyte physiology Topological regulation of synaptic AMPA receptor expression by the RNA-binding protein CPEB3 Astrocyte Ca2+ waves trigger responses in microglial cells in brain slices NIH Image to ImageJ: 25 years of image analysis Imaging calcium microdomains within entire astrocyte territories and endfeet with GCaMPs expressed using adeno-associated viruses A tutorial on principal component analysis Google Scholar Synapse-specific plasticity and compartmentalized signaling in cerebellar stellate cells Ca(2+) signaling in astrocytes from Ip3r2(-/-) mice in brain slices and during startle responses in vivo In vivo calcium imaging of circuit activity in cerebellar cortex Astrocyte calcium microdomains are inhibited by bafilomycin A1 and cannot be replicated by low-level Schaffer collateral stimulation in situ Glutamate-dependent neuroglial calcium signaling differs between young and adult brain Calcium oscillations in neocortical astrocytes under epileptiform conditions Astrocyte Ca(2)(+) signalling: an unexpected complexity Astrocytic Ca2+ signaling evoked by sensory stimulation in vivo Spatiotemporal calcium dynamics in single astrocytes and its modulation by neuronal activity Carriero G and Volterra A (2018) Studying Axon-Astrocyte Functional Interactions by 3D Two-Photon Ca2+ Imaging: A Practical Guide to Experiments and “Big Data” Analysis Received: 24 January 2018; Accepted: 22 March 2018; Published: 13 April 2018 Copyright © 2018 Savtchouk, Carriero and Volterra. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited *Correspondence: Andrea Volterra, YW5kcmVhLnZvbHRlcnJhQHVuaWwuY2g= the Palazzo dei Priori in Volterra is hosting a major exhibition dedicated to Mino Trafeli (Volterra curated by Marco Tonelli: Mino Trafeli: Being Modern/Becoming Contemporary 1968-1947 is the third and concluding exhibition of a retrospective cycle that the City of Volterra with the support of the Committee for the Public Enjoyment of the Artistic Heritage of Mino Trafeli dedicates to the first sculptor from Volterra who made the decisive transition from figuration to modernity to postmodernism and the contemporaneity of plastic languages.The city of Volterra is inseparable from the private and professional history of Mino Trafeli the son and grandson of alabaster craftsmen and himself a workshop practitioner since childhood to transcend the artisanal and popular culture without ever forgetting it but rather using alabaster as a real sculptural material He had already sensed this bond of blood and deep roots between the city of Volterra and the artist Trafeli’s first gallery owner and founder of the historic Galleria delle Ore in Milan where Trafeli exhibited almost continuously from 1957 to 1966) introducing him in a catalog in 1966: “It is certain that Volterra this Etruscan city cut off (until when?) from the news where the echoes of the intellectualistic chatter of the great metropolises come muffled and distant like echoes from another planet .. allowing him to reflect on his own convictions with the same hard constancy of the roots that penetrating laboriously into the ancient walls that encircle Volterra to find nourishment there renew every year the miraculous birth of leaves Following the exhibitions held at Palazzo dei Priori between 2022 and 2024 entitled The Turning Years 2018-1980 and From Object to Space 1980-1968 the exhibition Mino Trafeli: Being Modern/Becoming Contemporary 1968-1947 traces the career of the Volterra sculptor back to his modern origins after years of “Renaissance Florentineism” and forcing “strapaese” suggestions (in Florence frequenting the likes of Carlo Ludovico Ragghianti and Alessandro Parronchi) he began to be inspired by Cubism and the sculpture of Boccioni and Mino Rosso gradually broadening his horizon first toward neo-naturalism Palazzo dei Priori thus hosts the concluding exhibition dedicated to his sculpture with works ranging from the first chine and wooden works of a Cubofuturist matrix of male and female figures from 1947 to sculptures in welded and “sewn” iron dedicated to female figures to the cycle Figure and Environment in bronze together with large temperas and paintings of the 1960s that in Trafeli would later convert over the decades into painted sculptures as foreshadowed by the work of later date in the exhibition curator of the exhibition together with Marta Trafeli the artist’s daughter and head of the Trafeli Archive what his sculptures “produced between 1947 and 1968 seem to anticipate will not be so much the concept and practice of the impossibility of the object nor the ’object use or the ironic a Duchampian valence nor the happy metaphysical mythological drift of the 1980s or even the drawing sculptures of the late work but erotic and visceral charge of the use of one’s own body starting with the theatrical actions and the agile sculptures of the 1970s.” It is from here that begins the disruptive at times even brutal and poetic adventure at the same time and always committed (to the 1950s and 1960s date several of his public monuments) of a sculptor who protected his own freedom working in the solitude of Volterra’s studios but not isolated from the world (just think of his political commitment as a councilman and town councillor between the 1940s and 1950s or the organizational role he had in the historic public art review Volterra 73) not to mention that between the 1950s and 1960s he took part in several Quadriennali in Rome and that in 1964 he was invited to his first International Biennale in Venice A catalog will be published for the occasion by Sillabe with contributions by Marco Tonelli the city where he began to receive his first rudiments of craftsmanship Few works are preserved from that early period He obtained his diploma at the Regia Scuola Artistica Industriale in Volterra in 1937 enrolled at the Regio Istituto d’Arte in Florence where he graduated in 1940 and was taught by the literary critic and art historian Alessandro Parronchi he refused to join the republican army and joined the Resistance thanks to a friend who had put him in touch with the underground movement he would militate in the Partito d’Azione where he met art critic and historian Carlo Ludovico Ragghianti Dating back to the years between 1940 and 1943 were his friendships with writer Carlo Cassola (whose funeral monument he would perform in the cemetery of Montecarlo di Lucca) and gallery owner Piero Santi a Volterra writer and founder of the L’Indiano Gallery in Florence He thus began his political activity as town councilor in Volterra right in the Partito d’Azione In 1965 he married Maria Masti (their daughter Marta would be born from their marriage in 1967) and the following year he was elected town councillor for public works and education and president of the commission for the study of the economic social problems of Volterra and its territory Also in 1956 he began his collaboration with Giovanni Fumagalli’s Galleria delle Ore in Milan where he would exhibit in several solo shows (1957 In the meantime he will also take part in several Quadrennial Exhibitions in Rome (1955 the International Sculpture Biennial in Carrara (1957) the São Paulo Biennial in Brazil (1963) and the Venice Biennial (1964) where he will be noticed by critics Gillo Dorfles and Enrico Crispolti with whom in the following decades and until his death he will hold deep and uninterrupted human and professional relationships) holding a solo exhibition at the Galleria L’Indiano in Florence in 1963 It was between the 1950s and 1960s that he made all his most representative public monuments including the one to the Fisherman in Livorno (1956) to the Fallen in the War in Lissone (1962) 1944 Memorial in Volterra (1966) and to the Freedom Monument in Pomarance (1950-1997) In 1964 the first monograph on his work came out an art critic originally from Florence and director of the Pinacoteca di Brera in Milan from 1957 to 1977 Electric fire trucks offer municipalities the opportunity to achieve zero emissions with no compromise on safety response or operational effectiveness.  This electric fire truck reference guide covers all of the information a fire department needs to understand about electric vehicles and how they integrate into an existing fleet also referred to as an electric fire engine is a fire truck powered by electric power.  There are several electric fire trucks on the market today each with its own list of attributes and unique design and manufacturing qualities The common factor between all brands is that while the majority of truck operations are fueled by electric energy Backup systems ensure lifesaving efforts are not delayed based on depletion of charge or lack of power supply.  a few manufacturers have introduced considerably different concepts in recent years The types of electric fire trucks fall within two main categories Range-extended electric vehicles run on battery power and utilize a generator or engine as backup power Once the battery’s state of charge drops below a specified threshold the generator or engine engages and the battery continues to power all operations while the ICE powers the batteries Unlike the parallel-electric drive train fire truck which bypasses the batteries completely a range-extended vehicle continues to use the battery at all times There are many inherent benefits that come with the use of an electric fire truck Pierce® Volterra™ electric fire truck technology consists of an Oshkosh patented parallel-electric drive train featuring an electro-mechanical infinitely variable transmission (EMIVT) which allows zero-emissions operation when powered by the integrated onboard batteries.  The integrated electric motors in the electro-mechanical infinitely variable transmission are always providing the output to the driven components whether it’s the pump or the drive axle.  Because the EMIVT can also be coupled to the internal combustion engine it will always provide continuous and uninterrupted power to the pumping system or drive system Learn more about fire truck electrification modes here From demanding environmental goals to reduced emissions a smaller carbon footprint and cost savings there are many reasons why fire departments across the world are seeking electric fire trucks.  Here’s a look at some of the reasons why the demand for electric fire trucks is growing Changing regulations and legislation. With each passing year, more and more local and state governments develop clean vehicle policies to reduce greenhouse gasses, improve air quality and increase sustainability. In the United States, over 170 cities, more than ten counties and eight states have goals in place to power their communities with 100% clean Electric fire trucks provide municipalities with a sustainable solution to help meet their local and state legislative requirements Environmental initiatives. Currently, emissions from vehicles contribute to about one-third of all U.S. air pollution. Tailpipe emissions have detrimental effects on the health More municipalities are taking the initiative to address constituents' concerns about the environment By prioritizing environmental programs and choosing electric vehicles municipalities are leading by example for the community at large Choosing electric vehicles for municipal fleets sets a standard for excellence with a focus on improving overall community health Municipal fleets operate routes that are aligned with range delivery and fire apparatus all leave and return to a common site on a daily or frequent cycle This allows them to leverage infrastructure which is more commonly available in urban environments Fire trucks represent a significant source of fuel consumption and can ultimately cause a detrimental environmental impact The adoption of electric fleet vehicles can help significantly cut both fuel costs and the negative impacts of fuel consumption municipalities and fleet managers can anticipate savings on preventive maintenance ongoing engine repairs and down time spent on re-fueling.  An all-electric fire truck with an internal combustion engine charges much like a typical home electric vehicle connected to an electric power source.  Choosing a zero-emission electric vehicle requires solutions to recharge or other municipal or community settings.  Fire departments are finding success with the installation of charging solutions at the station. When you partner with Pierce, charging solutions are easier than you may think to install. Pierce and its network of trusted energy partners manage all aspects of planning, charging installation and ongoing maintenance and support.  The integration of overhead charging stations for electric vehicles matches the infrastructure of most existing firehouses and is beneficial because it doesn’t take up valuable floor space an electric fire truck can regain full charge in one hour normal charging times are often quite less.  Learn more about the process in this blog post: Electric Fire Truck Charging Infrastructure Overview Electric fire truck manufacturers are committed to the safety of firefighters and their lifesaving work electric fire trucks are designed to maintain the high level of operational standards firefighters demand with no compromises.  Pierce electric fire trucks offer the same reliability and functionality as all traditional apparatus To learn more about integrating an electric fire truck into your fleet and how Pierce electric fire trucks are serving local communities now, reach out to your local dealer. must maintain reliable and responsive performance The Pierce Volterra electric fire truck is equipped with a sophisticated thermal management system to counteract the adverse effects of temperature on the battery supports immediate operational readiness and contributes to extending battery life expectancy Learn more about this process and see real-life examples in this blog article: Electric Fire Trucks in Cold Weather: Facts, Challenges and Examples Fire departments rely on mission-ready trucks ready at all times to support emergency response demands So how do electric fire trucks manage prolonged fire events requiring pump operations It depends on the type of vehicle and the architecture of the drivetrain A fire apparatus with a parallel-electric drivetrain operates in either all-electric mode or internal combustion mode Pierce Volterra can power all truck operations at full capacity, including the ability to drive the vehicle or pump up to 2000 gpm at a continuous rate of pressure and performance in both all-electric and internal combustion mode. In contrast to a parallel-electric drivetrain a range-extended series-electric drivetrain vehicle uses battery power until the batteries are depleted and then uses an engine driven generator to continue to power truck operations through the battery In certain series-electric configurations, the batteries are involved in the vehicle’s ability to provide power, and once the batteries become depleted, or faulted, the back-up power source may not be able to supply enough power through the batteries to manage pump operations. Additionally, some electric fire truck systems may not be sized large enough to meet the power requirements of a 2000 gpm pump, let alone be adequate to first charge the batteries and then run the pump at the rated capacity. A range-extended series-electric vehicle with depleted batteries may not even be able to move until the batteries are recharged Interested in diving deep into this topic? Review this article: Q+A: How Does Electric Fire Truck and Pump Performance Compare to a Traditional Truck and Pump? Electric fire truck service and maintenance largely follow traditional fire apparatus day-to-day service and maintenance the added bonus of an electric fire truck is that you should expect less frequent engine and engine-related component maintenance because they are not used as often therefore the intervals occur less frequently may also see less frequent repairs (depending on driving conditions) than a traditional apparatus due to regenerative braking from the electric drive line.  battery and high-voltage component maintenance will be required trained maintenance technicians will require high-voltage tools to complete service.  are completed following regular engine protocols because the engine is used less frequently standardized maintenance needs should decrease as well as the overall cost of preventative maintenance the vehicle will not be out of service as often because of the longer intervals between standardized maintenance In terms of servicing charging infrastructure There is not a lot of necessary maintenance because there are not a lot of moving parts Following basic intervals for inspection set by the charging solutions provider will ensure the infrastructure maintains its ready state.   High voltage systems on electric fire trucks are designed to be safe under normal operating conditions. However, the placement of high-voltage elements on fire apparatus can significantly affect firefighter functionality The Pierce Volterra electric fire truck consolidates and isolates electrical components to a single area on the fire truck body behind the cab The truck was specifically designed to keep all electrical elements in one place so firefighters could easily manage operations and maintenance with confidence they will not inadvertently encounter high-voltage wiring or components As fire departments consider adding an electric fire truck to their fleet, it’s important to ask electric fire truck manufacturers about high-voltage component and wiring placement because it can significantly impact operation and maintenance To learn more about how firefighters can effectively manage electric fire truck high voltage components and key considerations for placement, review this recent article: Q+A: Electric Fire Truck High Voltage Overview In the unlikely event that electric fire truck batteries are damaged, how the truck maintains operational capacity is again dependent on the type of truck A damaged or faulted battery which renders a truck unusable is not a reliable option for fire departments When you choose to purchase a Pierce Volterra electric fire truck you’re not just investing in a truck; you're investing in a complete electric vehicle solution Understanding how an electric fire truck can fit in your station on your power grid and into your service model are all items that Pierce and its energy partners help manage on your behalf Pierce representatives align experts to support your needs so you can focus on your daily work and not on the technical details of your new apparatus To appropriately power the Pierce Volterra™ platform of electric vehicles a fire station will need enough 480-volt three-phase power to support the charging infrastructure This is standard for any commercial power requirements this power requirement can be accomplished with a step-up transformer.  While smaller charging units may be used to provide support they will limit the ability for fast charge recovery and negatively impact response-readiness Full station energy planning is the optimal choice because it considers both short and long-term energy goals and provides solutions to ensure departments are aligned with operational expenses and budgeting Starting with an EV charging solution that can support future growth and long-term energy goals across all specialty vehicles is important and is often a better long-term investment.  Integrating the necessary electrification components in a fire station and getting an electric fire truck up and running is a straightforward and seamless process. Learn more about this six-step process in this blog post. The process of integrating an electric fire truck into your department fleet can run as seamlessly as adding any other type of apparatus—ultimately Adding an electric fire truck to a fleet doesn’t necessarily translate into more planning steps it may involve additional discussions around future energy objectives a municipality may look to add an electric ambulance or other electric utility vehicles to the fleet and thinking through future goals can help set up the department for success.  manufacturing and integrating any new fire truck into your fleet takes time Adding an electric fire engine is no different You can count on Pierce to help manage the process and support your fire truck needs before during and after you receive your new electric fire truck and provide service support for the lifespan of the apparatus Fire trucks come in all shapes and sizes and electric fire trucks are no different.  The Pierce Volterra™ platform of electric vehicles is designed to look like a traditional North American fire truck and match the style and operational configuration of the existing trucks in your fleet Each truck is equipped with the Oshkosh Patented Parallel-Electric Drive Train The parallel-electric drivetrain featuring an EMIVT allows zero-emissions operation when powered by the integrated onboard batteries.  The electric fire truck operates independently in either the all-electric or internal combustion engine modes; the EMIVT can leverage either source of power to provide uninterrupted performance in extended emergency operations this simplified solution allows traditional vehicle accessories to be powered by the EMIVT as well.  The driveline allows for zero-emissions during quick attack responses with the ability to transition seamlessly to internal combustion power for extended pumping operations Learn more about the design details of the electric fire truck now.  If you are interested in more information about electric fire trucks these resources may be of interest to you: Don't’ forget to download our Electric Fire Truck Reference Guide to send a copy of the information on this page directly to your inbox.  Volume 17 - 2023 | https://doi.org/10.3389/fncom.2023.1120516 This article is part of the Research TopicMathematical Treatment of Nanomaterials and Neural Networks Volume IIView all 10 articles we investigate a new neural network method to solve Volterra and Fredholm integral equations based on the sine-cosine basis function and extreme learning machine (ELM) algorithm The novel neural network model consists of an input layer in which the hidden layer is eliminated by utilizing the sine-cosine basis function by using the characteristics of the ELM algorithm that the hidden layer biases and the input weights of the input and hidden layers are fully automatically implemented without iterative tuning we can greatly reduce the model complexity and improve the calculation speed the problem of finding network parameters is converted into solving a set of linear equations One advantage of this method is that not only we can obtain good numerical solutions for the first- and second-kind Volterra integral equations but also we can obtain acceptable solutions for the first- and second-kind Fredholm integral equations and Volterra–Fredholm integral equations Another advantage is that the improved algorithm provides the approximate solution of several kinds of linear integral equations in closed form (i.e. Several numerical experiments are performed to solve various types of integral equations for illustrating the reliability and efficiency of the proposed method Experimental results verify that the proposed method can achieve a very high accuracy and strong generalization ability Volterra and Fredholm integral equations have many applications in natural sciences and engineering. A linear phenomenon appearing in many applications in scientific fields can be modeled by linear integral equations (Abdou, 2002; Isaacson and Kirby, 2011). For example, as mentioned by Lima and Buckwar (2015) describes the large-scale dynamics of spatially structured networks of neurons These equations are widely used in the field of neuroscience and robotics and they also play a crucial role in cognitive robotics The reason is that the architecture of autonomous robots which are able to interact with other agents in dealing with a mutual task is strongly inspired by the processing principles and the neuronal circuitry in the primate brain This study aims to consider several kinds of linear integral equations The general form of linear integral equations is defined as follows: but y(x) is the unknown function that will be determined; a and b are constants; and ϵ Equation (1) is called linear Fredholm integral equation of the first kind if ϵ Equation (1) is called linear Volterra integral equation of the first kind if ϵ Equation (1) is called linear Fredholm integral equation of the second kind if μ = 0 and ϵ Equation (1) is called linear Volterra integral equation of the second kind if λ = 0 and ϵ Equation (1) is called linear Volterra–Fredholm integral equation if μ most of these traditional methods have the following disadvantage: they provide the solution at specific preassigned mesh points in the domain and they need an additional interpolation procedure to yield the solution for the whole domain one either has to increase the order of the method or decrease the step size we propose a neural network method based on the sine-cosine basis function and the improved ELM algorithm to solve linear integral equations the hidden layer is eliminated by expanding the input pattern utilizing the sine-cosine basis function and this simplifies the calculation to some extent the improved ELM algorithm can automatically satisfy the boundary conditions and it transforms the problem into solving a linear system which provides great convenience for calculation the closed-form solution by utilizing this model can be obtained and the approximate solution of any point for linear integral equations can be provided from it The remainder of the article is organized as follows a brief review of the ELM algorithm is provided a novel neural network method based on the sine-cosine basis function and ELM algorithm for solving integral equations in the form of Equation (1) are discussed we show several numerical examples to demonstrate the accuracy and the efficiency of the improved neural network algorithm For a data set with N + 1 different training samples (xi gi) ∈ ℝ × ℝ(i = 0 the neural network with M+1 hidden neurons is expressed as follows: wj is the input weight of the j-th hidden layer node bj is the bias value of the j-th hidden layer node and βj is the output weight connecting the j-th hidden layer node and the output node Assuming the error between the output value oi of SLFN and the exact value gi is zero the relationship between xi and gi can be modeled as follows: Where both the input weight wj and the bias value bj are randomly generated The equations (4) can be rewritten in the following matrix form Where H is the output matrix of the hidden layer A common minimum norm least-squares solution of the linear system Equation (5) is calculated by The structure of sine-cosine neural network method for solving several kinds of linear integral equations The steps of the sine-cosine neural network method for solving several kinds of linear integral equations are as follows: b] into a series of collocation points Ω = {a = x0 < x1 < .. Step 2: Construct the approximate solution by using sine-cosine basis as an activation function Step 3: According to different problems and different data sets we substitute the trial solution ŷSC-ELM into the Equation (1) to be solved we convert this equation into a matrix form: Step 4: From the theory of Moore–Penrose generalized inverse of matrix H bj and the number of neurons M with the smallest MSE as the optimal value The corresponding optimal number of neurons M and output weights aj the optimal number of neurons M and optimal output weights β^ M into Equation (7) to get the new numerical solution Some advantages of the single-layer sine-cosine neural network method for solving integral equations are as follows: (i) The hidden layer is eliminated by expanding the input pattern using the sine-cosine basis function (ii) The sine-cosine neural network algorithm only needs to determine the weights of the output layer The problem could be transformed into a linear system and the output weights can be obtained by a simple generalized inverse matrix which greatly improves the calculation speed (iii) We can obtain the closed-form solution by using this model the approximate solution of any point for linear integral equations can be given from it It provides a good method for solving integral equations some numerical experiments are performed to demonstrate the reliability and powerfulness of the improved neural network algorithm The sine-cosine neural network method based on the sine-cosine basis function and ELM algorithm is applied to solve the linear Volterra integral equations of the first kind linear Volterra integral equations of the second kind linear Fredholm integral equations of the first kind linear Fredholm integral equations of the second kind and linear Volterra–Fredholm integral equations The algorithm is evaluated with MATLAB R2021a running in an Intel Xeon Gold 6226R CPU with 64.0GB RAM The training set is obtained by taking points at equal intervals The validation set is the set of midpoints V = {vi|vi = (xi+xi+1)/2 where {xi}i=0N are training points in the following studies mean absolute error (MAE) and root mean square error (RMSE) to measure the error of numerical solution Where y(xi) denote the exact solution and ŷ(xi) represent the approximate solution obtained by the proposed algorithm Note that wj = jπ/(b−a) and bj = −jπa/(b−a)(j = 0 the number M of hidden neurons that results in minimum mean squared error on the validation set can be selected Consider linear Volterra integral equation of the second kind (Guo et al., 2012) as We train our proposed neural network for 50 equidistant points in the given interval [0, 1] with the first 12 sine-cosine basis functions. Comparison between the exact solution and the approximate solution via our improved neural network algorithm is depicted in Figure 2A, and the plot of the error function between them is cited in Figure 2B the mean squared error is 1.3399 × 10−19 and the maximum absolute error is approximately 7.4910 × 10−10 (A) Comparison between exact and SC-ELM solutions for Example 1 Table 1 incorporates the results of the exact solution and the approximate solution via our proposed neural network algorithm for 11 testing points at unequal intervals in the domain [0, 1]. The absolute errors are listed in Table 1 in which we observe that the mean squared error is approximately 1.6789 × 10−19 These results imply that the proposed method has higher accuracy Comparison between the exact solution and approximate solution (Example 1) Table 2 compares the proposed method with the LS-SVR method. The maximum absolute error is approximately 6.8246 × 10−10. Note that in Guo et al. (2012), the maximum absolute error shown in Guo et al. (2012) Table 5 is approximately 2.4981 × 10−7 The solution accuracy of the proposed algorithm is higher Comparison between the SC-ELM method and the LS-SVR method (Example 2) Consider the linear Volterra integral equation of the first kind (Masouri et al., 2010) as The analytical solution is f(x) = e−x A total of 21 equidistant points in the given interval [0, 1] are used as the training points, and the neural network adapts the first 10 sine-cosine basis functions. Figures 3A, B shows that the exact solution and the approximate solution are highly consistent The maximum absolute error is approximately 1.3959 × 10−6 (A) Comparison between exact and SC-ELM solutions for Example 2 Table 3 lists the results of the exact solution and the approximate solution via our proposed neural network algorithm in the domain [0 The mean squared error is approximately 2.5781 × 10−16 These findings provide a strong support for the effectiveness of our proposed method Comparison between exact solution and approximate solution (Example 2) We consider linear Fredholm integral equation of the first kind (Rashed, 2003) as This problem is solved by utilizing our proposed neural network model in the given interval [0, 1]. We consider 21 equidistant points in the domain [0, 1] with the first six sine-cosine basis functions to train the model. Comparison between the exact solution and the approximate solution via our improved neural network algorithm is depicted in Figure 4A, and the error plot is depicted in Figure 4B Note that the mean squared error is 4.5915 × 10−8 for these training points (A) Comparison between exact and SC-ELM solutions for Example 3 Table 4 incorporates the results of the exact solution and the approximate solution via our proposed neural network algorithm for 11 testing points at unequal intervals in the domain [0 We observe that the maximum absolute error is approximately 2.7433 × 10−4 The results show that this new neural network has a good generalization ability Comparison between the exact solution and approximate solution (Example 3) We consider the linear Fredholm integral equation of the second kind (Golbabai and Seifollahi, 2006) as The improved neural network algorithm for the linear Fredholm integral equation of the second kind has been trained with 50 equidistant points in the given interval [0, 1] with the first 12 sine-cosine basis functions. The approximate solution obtained by the improved neural network algorithm and the exact solution are shown in Figure 5A, and the error function is displayed in Figure 5B the mean squared error is 2.3111 × 10−17 and the maximum absolute error is approximately 9.8998 × 10−9 which fully demonstrates the superiority of the improved neural network algorithm (A) Comparison between exact and SC-ELM solutions for Example 4 Finally, Table 5 provides the results of the exact solution and the approximate solution via our proposed neural network algorithm for 11 testing points at unequal intervals in the domain [0, 1]. As shown in Table 5 the mean squared error is approximately 3.1391 × 10−17 which undoubtedly shows the power and effectiveness of the proposed method Comparison between the exact solution and approximate solution (Example 4) Table 6 compares the proposed method with RBF networks. The maxmium absolute error by our proposed method is approximately 7.7601 × 10−9. Note that in Golbabai and Seifollahi (2006), the maxmium absolute error shown in Golbabai and Seifollahi (2006), as shown in Table 1 is approximately 6.7698 × 10−7 Comparison between the SC-ELM method and RBF method (Example 4) Consider the linear Volterra–Fredholm integral equation (Wang and Wang, 2014) as A total of 50 equidistant points in the given interval [0, 1] and the first 11 sine-cosine basis functions are considered to train the neural network model. The comparison images and error images of the exact solution and the approximate solution are listed in Figures 6A, B from which we can see that the mean squared error is 3.3499 × 10−18 (A) Comparison between exact and SC-ELM solutions for Example 5 Table 7 shows the results of the exact solution and the approximate solution via the improved ELM method for 11 testing points at unequal intervals in the domain [0 the maximum absolute error is approximately 2.6673 × 10−9 which reveals that the improved neural network algorithm has higher accuracy and excellent performance Comparison between the exact solution and approximate solution (Example 5) We compare the RMSE of our proposed method and the Taylor collocation method in Wang and Wang (2014). From Table 8, we can see clearly that our algorithm is more accurate than the algorithm in the Taylor collocation method. As can be seen from Table 8, when 5, 8, and 9 points are tested, the RMSEs shown by the Taylor collocation method in Wang and Wang (2014) are approximately 4.03 × 10−7 but the RMSEs shown by our proposed method are respectively 1.67 × 10−9 We consider linear the Volterra integral equation of the second kind (Saberi-Nadjafi et al., 2012) The analytical solution is f(x) = sin(2x)+cos(2x) A total of 21 equidistant discrete points and the first 11 sine-cosine basis functions are utilized to construct the neural network model. The comparison images and error images of the exact solution and the approximate solution are displayed in Figures 7A, B It ia not hard to find that the MSE is 4.2000 × 10−16 and this implies that the proposed algorithm has higher accuracy (A) Comparison between exact and SC-ELM solutions for Example 6 To verify the effectiveness of our proposed method, we provide the results of the exact solution and the approximate solution via the improved ELM method for 11 testing points at unequal intervals in the domain [0, 1], see Table 9 the maximum absolute error is approximately 2.9539 × 10−8 which shows that the proposed algorithm has good generalization ability Comparison between the exact solution and approximate solution (Example 6) Table 10 compares the MSE of the numerical solutions obtained by the SC-ELM model when more training points are added and different numbers of hidden layer neurons are configured. From these results, it can be seen that the proposed method can achieve good accuracy. The calculation time of different examples is listed in Table 11 These data suggest that our method is efficient and feasible Comparison of the different examples of MSE with different numbers of training points and hidden neurons the improved neural network algorithm based on the sine-cosine basis function and extreme learning machine algorithm has been developed for solving linear integral equations The accuracy of the improved neural network has been checked by solving a linear Volterra integral equation of the first kind a linear Volterra integral equation of the second kind a linear Fredholm integral equation of the first kind a linear Fredholm integral equation of the second kind and a linear Volterra-Fredholm integral equation The experimental results of the improved ELM approach with different types of integral equations show that the simulation results are close to the exact results the proposed model is very precise and could be a good tool for solving linear integral 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Received: 10 December 2022; Accepted: 13 February 2023; Published: 09 March 2023 Copyright © 2023 Lu, Zhang, Weng and Sun. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) *Correspondence: Hongli Sun, aG9uZ2xpc3VuQDEyNi5jb20= formerly known by the much cooler name "Project Volterra," and it's supposed to help solve that software problem Microsoft has tried doing Arm Windows developer boxes before—namely, the $219 ECS LIVA QC710 it began selling about a year ago (it's no longer for sale using it was like revisiting the bad old netbook days Maybe you could get some basic browsing done on it even for someone like me who primarily works with text and medium-resolution photos all day The Dev Kit 2023 is nearly three times as expensive but the hardware is powerful enough that it mostly just feels like a typical midrange mini-desktop in day-to-day use Freed from the limitations of cruddy hardware the machine makes it much easier to evaluate Windows-on-Arm's remaining software limitations but it does give us a good chance to evaluate where the Windows-on-Arm project is right now both in hardware and software—especially relative to the Mac the other hardware and software ecosystem that is making a much cleaner and more graceful transition from x86 software to Arm Microsoft isn't selling the Dev Kit as a Surface device because it's not meant to be a machine for everyday PC users It's a substantial-feeling hunk of black plastic over a metal frame with a Microsoft logo imprinted on the top; it's smaller than a Mac mini (which has had the same physical dimensions for 12 years) but if Microsoft had set out to make a Surface-branded Mac mini clone One reason the device is smaller is that it uses a 90 W external power brick whereas the Mac mini's power supply is inside the enclosure That flows from the way Microsoft seems to have put together the Dev Kit—the Mac mini's internals were designed specifically for their enclosure while the Dev Kit appears to be quite literally a Surface Pro 9 with 5G motherboard with a case built around it it's less like the Mac mini and more like the Apple Silicon "Developer Transition Kit," which adapted iPad Pro-ish innards for a Mac mini-shaped case The most obvious giveaway is a bunch of unused connectors that are visible at the top-right of the board when you remove the bottom of the Dev Kit—these would be used to drive a display and other internal peripherals in a Surface device but go unused in the Dev Kit with identical positioning and space between them) are the only ones built into the board and power jack on the back are all built into a separate board (That it's a Surface Pro clone also means that the Dev Kit has no headphone jack.) Firmware and driver updates pulled down from Windows Update are also Surface-branded The Dev Kit can connect to up to three monitors at once using its mini DisplayPort and USB-C ports and up to two of those can be 60 Hz 4K displays (refresh rates faster than 60 Hz are available at lower resolutions but 60 Hz does appear to be the hard cap at 4K) Microsoft says that the DisplayPort is the one you should use for the primary display and it's the only one that will display a signal when you're adjusting the box's UEFI firmware settings likely also a holdover from its Surface roots—the internal display in a Surface would likely be connected with an internal embedded DisplayPort connector (eDP) that worked the same way The only upgradeable component in the Dev Kit is the 512GB SSD which is a short M.2 2230 drive just like the ones Microsoft uses in other Surfaces A typical M.2 2280 SSD would definitely fit though you'd have to figure out how to hold it in place yourself since there's no built-in standoff for it The rationale for using a short little SSD in the first place is probably the same as for reusing a Surface motherboard—cheaper to reuse a thing than to design and pay for a whole different thing especially in what is likely to be a low-volume product To talk about the problem the Dev Kit seeks to fix it's instructive to take a look at the Windows-on-Arm experience "So close and yet so far" sums up the vibe We'll start with "so close." Windows-on-Arm looks and acts exactly the same way that Windows does on a regular x86 PC. The interface is the same, apps are the same, downloading and installing apps and running apps are all the same. We've come a long, long way from Windows RT which looked and acted kind of like Windows but couldn't run most of the third-party software Microsoft deserves credit for steadily improving Windows-on-Arm and improving the x86-to-Arm translation layer that makes it possible to run most Windows apps on Arm devices Windows 11 added the ability to translate 64-bit x86 code as well as 32-bit code greatly expanding the universe of apps that will run I can get most of my basic apps up and running on Arm Windows and the Dev Kit's performance is fast and responsive when running Arm-native apps I plugged the Dev Kit right into my dual-monitor setup and it did just fine driving both 4K displays fluidly and working properly with most of my connected accessories That starts with the x86-to-Arm app translation But x86 apps running on the Dev Kit regularly stutter or hesitate when rendering waiting on the translation to happen before responding to input The Slack and Discord apps were both good examples—you sometimes need to wait a second or so between clicking to a different server or channel or conversation and actually seeing the result of that click show up on-screen It's even more of a problem in the Audacity audio editor where scrubbing back and forth through multiple audio tracks requires fluid UI rendering that the Dev Kit can't quite manage even with a relatively quick processor Apple's Rosetta technology has some of these problems is noticeably jerkier than scrolling in an Apple Silicon-native app But that's mitigated somewhat by (1) the M1 and M2 chips' superior performance and (2) the fact that Intel-only apps on the Mac are currently the exception rather than the norm where Arm-native apps are only sometimes available The Windows ecosystem's core assumption that you're running the OS on an x86-compatible PC even causes problems when the Arm versions of software are available Some apps we installed (Firefox from Mozilla's website Zoom from the Microsoft Store) did download and install their Arm64 versions automatically but it lists an Arm64 version on its homepage right next to the 64-bit and 32-bit x86 versions (an approach some Mac apps take to advertise Apple Silicon support) But downloading Handbrake from its website and VLC from the Microsoft Store got us x86 versions of the apps even though Arm64 versions are available from other sources Still other software refuses to run on the Arm version of Windows at all Dropbox was the most notable of my typical app suite that simply refused to install kicking me to an inferior "S Mode" version of the product from the Microsoft Store And you may be out of luck for any hardware that requires specialized drivers like my Scarlett Solo mic preamp; Arm Windows drivers are even rarer than Arm Windows apps they can't be emulated or translated—no driver a preview of Visual Studio and many of its extensions and even things like PowerToys) are available in both x86 and Arm versions Adobe supports most of the features of Photoshop and Lightroom in the Arm-native versions of those apps Google doesn't offer an Arm version of Chrome and third-party app support is a crapshoot let's talk about where the Windows-on-Arm hardware ecosystem is right now The Dev Kit's Snapdragon 8cx Gen 3 is Qualcomm's fastest Arm chip to date and since Windows-on-Arm only officially runs on Qualcomm's chips right now that makes it the fastest Arm chip that can run Windows (The "SQ" branding that Microsoft uses in the Arm Surface devices is just another name for the exact same silicon though Microsoft may weigh in on the chip's clock speeds and power use and other performance-tuning settings) Qualcomm says the 8cx Gen 3 offers up to 85 percent better CPU performance and 60 percent better GPU performance than the 8cx Gen 2 and pulling numbers from the Geekbench online results database backs that up rips the Snapdragon 7c's guts out and wears them as a hat The issue for the ecosystem is that this best-of-the-best chip is significantly slower than the Apple M1; the 2-year-old versions of Apple's slowest Apple Silicon Macs still run circles around its performance The Dev Kit is a lot cheaper than a Mac mini once you take specs into account—both devices start at $600 that gets you 32GB of RAM and 512GB of storage but upgrading to 16GB of RAM and 512GB of storage adds another $400 to the price tag even before you take into account the Mac's smoother x86 emulation and superior Arm-native app library The higher power usage is also a problem when you're comparing it to Intel and AMD processors The 8cx Gen 3 in the Dev Kit uses an amount of power comparable to Core i5 and Ryzen 5-tier laptop chips from Intel and AMD processors you can get in mini PCs like Intel's NUC series It's hard to recommend an Arm-on-Windows box if its performance-per-watt is no better than the x86 systems it's striving to compete with the 8cx Gen 3 doesn't totally embarrass itself It's fast enough that when you have a bad experience with Arm Windows it's mostly Arm Windows' fault rather than underpowered hardware it's another reminder of how far there is to go It's undeniably good for the Arm Windows app ecosystem to have a viable decently specced PC that is usable as an everyday computer so there may be some developers who buy one just for the hell of it which might have some positive trickle-down effects for the rest of the ecosystem the Windows-on-Arm project will need to develop some tangible benefit for the people who choose to use it What you're getting with an Arm Windows device right now is essentially the worst of both x86 and Arm—compatibility problems without lower power use and heat to offset them and so-so performance to boot Apple has cracked all three of these things; Windows and Qualcomm are struggling to do any of them Or it could end up as just another interesting footnote in the annals of Microsoft's hardware division Ars Technica may earn compensation for sales from links on this post through affiliate programs The TimesWho needs a Tuscan castle hotel when you can have an entire village The hamlet (borgo) of Pignano was established in the early Middle Ages on top of a hill overlooking nearby Volterra Twelfth-century walls lead into a pint-sized piazza where everything from the main villa (the one-time home of local aristocracy) to old barns and workers’ cottages have been turned into accommodation With its spectacular views over the rippling landscape and an organic farm producing everything from the food to the natural toiletries this feels like your own private Tuscan idyll Become a subscriber and along with unlimited digital access to The Times and The Sunday Times you can enjoy a collection of travel offers and competitions curated by our trusted travel partners The San Bartolomeo suiteMR & MRS SMITHScore 8/10There’s a dizzying array so almost every room is booked individually there are three distinct types of accommodation The grand 18th-century villa houses 14 rooms and suites which pair original details such as frescoed ceilings and walls with jaw-dropping views of those dramatic hills repeating ad infinitum into the distance (some overlook the side hills rather than the luscious ones towards Volterra) Next up are the maisonettes — farm buildings within the borgo’s walls turned into smart little apartments with one to three bedrooms Farm workers lived here until after the Second World War and tiny bathrooms stuffed under the eaves with deliciously comfortable beds and modern kitchenettes (so you can brew your own pre-breakfast coffee in a traditional moka pot) but for a bit more independence these are a good choice The Artists’ House villaSTEFANO SCATAFor high rollers and families there are villas spread around the 750-acre estate (each comes with a golf buggy to get around easily) these have private pools and “villa service” — a cross between concierge and butler service the rooms are dressed in pastels and pair antique details with comfortable but calming furniture Livening things up are the artworks — there is always an artist in residence from London’s Royal Drawing School and the hotel buys much of what they produce to add to the in-house collection are produced using organic herbs grown on the estate Villa Pignano restaurantScore 7/10The main restaurant has a Michelin Green Star for its sustainability practices Many of the ingredients are grown on the organic estate The food is simpler than regular Michelin-starred places focusing on those ingredients: think a platter of homegrown veg drizzled in grape must such as plankton-infused pasta scattered with fresh fish for a true taste of the sea (which is around an hour from the hotel) with a wide buffet spread featuring eggs from the estate’s hens cooked to order Al Fresco is a summertime poolside restaurant with more laidback fare: pizza and steaks cooked in the garden There’s even an ice cream van beside it for dessert • Best hotels in Tuscany• Best vineyard hotels in Tuscany The Belvedere BarScore 8/10Life revolves around the belvedere on the lawn outside the main villa sofas and tables scattered around at intervals Two outdoor pools include one that is family-friendly in the garden beside the Al Fresco restaurant built within a former Etruscan quarry with blinding white stone providing a backdrop to the sun loungers A couples’ spa treatment roomSTEFANO SCATAA small spa has two treatment rooms and a relaxation area in an old wine cellar The latter provides a unique meditation area in an ancient cistern sculpted from the rock a concise gym with Technogym equipment was opened in a new building a quick walk down the hillside from the main house Nearby is a space filled with drying herbs and flowers a resident herbalist makes all the toiletries for the resort infusing them with homegrown essential oils where you can make your own from the estate’s organic olive oil and herbs where you set up your easel at the belvedere; cooking classes; wine tastings at the on-site winery; truffle hunts; bike and hiking routes; and horse riding (including romantic night-time rides) Inside the main villa is a TV room (bedrooms don’t have them) There’s also a games room and La Collezione Italiana a gorgeous collection of vintage Italian cars Score 8/10This is a brilliant base if you’re visiting Tuscany’s big hitters: Florence Siena and Pisa are all around an hour’s drive away Volterra and San Gimignano are easy drives across the hills so you can easily combine them with an afternoon by the pool A car is essential though — this is as rural as it gets — and if you don’t want to eat in-house Price B&B doubles from £296Restaurant mains from £29Family-friendly YAccessible N Julia Buckley was a guest of Borgo Pignano (borgopignano.com) • Best things to do in Tuscany• Best villas in Tuscany Sign up to the Times Travel newsletter for weekly inspiration, advice and deals here Home/FireRescue APPLETON, Wis. (May 23, 2024) – Pierce Manufacturing Inc., an Oshkosh Corporation (NYSE:OSK) business, is pleased to announce the Calgary Fire Department will receive the fourth placement of the Pierce® Volterra™ Electric Pumper in North America This is Pierce’s first in Canada and part of its ongoing commitment to optimizing and evaluating the Pierce Volterra Platform of Electric Vehicles in various environmental conditions The Calgary Fire Department’s winter operations provide an ideal environment for cold weather verification allowing Pierce to gather valuable data on the vehicle’s performance in extreme low temperatures much like the ongoing evaluation of performance in arid “We look forward to incorporating the Pierce Volterra electric fire truck into our fleet as it represents a significant advancement in our commitment to sustainable firefighting solutions and reduced emissions,” said Nigel Thorley Fleet and Equipment for the Calgary Fire Department “Pierce and Commercial Emergency Equipment have been trusted partners and their dedication to innovation and reliability ensures that this state-of-the-art vehicle will enhance our ability to serve Calgary’s diverse and growing community We will be working together to share performance data which will further contribute to the Pierce electric fire truck’s optimization.” The City of Calgary is dedicated to environmental sustainability through initiatives outlined in its 2023-2026 Climate Implementation Plan. The city’s Green Fleet Strategy aims to reduce greenhouse gas emissions by 60% by 2030 promoting the use of electric and low-carbon vehicle technologies Adding the Pierce Volterra Electric Pumper aligns with these goals supporting Calgary’s mission to be an environmentally sustainable and resilient city The Pierce Volterra Electric Pumper will be showcased in Commercial Emergency Equipment’s booth during the 2024 Alberta Fire Chiefs Association Tradeshow on May 26-27 and will be delivered to the Calgary Fire Department soon thereafter The electric fire apparatus is expected to be in service this summer will provide service support for the vehicle as it does with all Calgary Fire Department’s Pierce fire apparatus Commercial Emergency Equipment’s emergency vehicle technicians (EVTs) have undergone Volterra-specific high-voltage system service training at the manufacturer’s headquarters in Appleton “We are proud to support Pierce Manufacturing’s first zero-emission emergency apparatus in Canada,” said Carey Feduniw general manager of Commercial Emergency Equipment “The Commercial Group of Companies has a long history of vehicle electrification and sustainability including the outfitting of fully electric work vehicles for the City of Calgary Key Specifications of Calgary Fire Department’s Enforcer™ Volterra Pumper: Drivetrain: Several fire departments throughout North America have Pierce Volterra electric fire trucks on order and in production Fire departments interested in configuring a Pierce Volterra EV to meet their specific needs are encouraged to contact their local Pierce dealer for more information and to begin the customization process To learn more about Pierce Manufacturing and the revolutionary Pierce Volterra Platform of Electric Vehicles, visit www.piercemfg.com mission-critical equipment to help everyday heroes advance communities around the world Oshkosh Corporation employs approximately 17,000 team members worldwide all united behind a common purpose: to make a Oshkosh products can be found in more than 150 countries under the brands of JLG® These factors include the Company’s ability to successfully integrate the AeroTech acquisition and to realize the anticipated benefits associated with the same; the risks associated with international operations and sales including compliance with the Foreign Corrupt Practices Act; the Company’s ability to comply with complex laws and regulations applicable to U.S Find sanctuary city resources from the City of Portland's Immigrant & Refugee Program including free legal services and state resources for reporting hate crimes Please join Portland Fire & Rescue for a traditional “push-in” ceremony for our newest fire engine PF&R entered a Joint Development Agreement with Pierce Manufacturing a zero-emissions fire engine (also known as a pumper) into service in the downtown core of Portland at Fire Station 1 This is only the second Pierce Volterra fire engine placed into service thus far nationwide and run volume of Station 1’s Fire Management Area--along with the historical relationship between PF&R with this fire apparatus manufacturer--aligned well with Pierce’s goal of improving the development of this new technology and will be the first step toward PF&R placing an emergency response apparatus into service that assists in meeting the City of Portland’s Climate Action Plan The Pierce Volterra is a 42,000-pound GVW fire engine that has the capacity to seat 6 firefighters with an onboard 500-gallon water tank and a single stage For all intents and purposes in both appearance and operational capability this fire engine is identical to the rest of the diesel-powered fleet in service by PF&R The difference is the patented parallel-electric drivetrain-- featuring an electro-mechanical infinitely variable transmission which allows zero-emissions operation in most operational situations when powered by the integrated onboard batteries These batteries can be charged to full capacity by a fire station-based vehicle charging infrastructure that is capable of full electric fire engine recharge is less than 90 minutes This battery-powered system is coupled with an internal combustion engine which provides continuous and uninterrupted power to the pumping system or drive system as needed The internal combustion engine is leveraged only for back-up power during extended emergency operations Another benefit to this addition of the Volterra to our fleet of emergency response vehicles is reduced firefighter exposure to known carcinogenic toxins encountered in diesel exhaust fumes With too many firefighters succumbing to cancer because of exposures to carcinogens over the course of decades-long careers in the fire service the introduction of the Pierce Volterra is an important step taken by the City of Portland and Portland Fire & Rescue to reduce the incidences of cancer in all current and future members of PF&R.  The history of placing a new fire apparatus into service by pushing it backward into the apparatus bay has historical ties to the days when all apparatus were drawn to emergency scenes by teams of horses so returning an apparatus to the bay in the fire station was always the work of the crew of firefighters on duty This traditional push-in ceremony has continued within the fire service even with the advent of internal combustion powered rigs and the ability to reverse under power Come join Portland Fire & Rescue on Monday June 12 fire engine into service at our Headquarters Fire Station See something we could improve on this page? Give website feedback The City of Portland ensures meaningful access to City programs, services, and activities to comply with Civil Rights Title VI and ADA Title II laws and reasonably provides: translation, interpretation, modifications, accommodations, alternative formats, auxiliary aids and services. Request an ADA accommodation or call 503-823-4000, Relay Service: 711 503-823-4000  Traducción e Interpretación | Biên Dịch và Thông Dịch | 口笔译服务 | Устный и письменный перевод | Turjumaad iyo Fasiraad | Письмовий і усний переклад | Traducere și interpretariat | Chiaku me Awewen Kapas | अनुवादन तथा व्याख्या With the recent announcement of Pierce Manufacturing’s development of the Pierce Volterra™ platform of electric vehicles for the fire and emergency market there have been many questions about the demand for the technology how it works and how it supports municipalities’ environmental initiatives.Learn more about the story behind the electric fire truck technology below cities are taking increased responsibility for pollution As municipalities grapple with these challenges there are several key indicators that are helping to drive change environmental initiatives and cost saving opportunities Over 170 cities, more than ten counties and eight states across the U.S. have goals to power their communities with 100% clean Additionally, The Clean Air Act (CAA) requires every engine and motor vehicle in the United States to meet a set of emission standards and conformity requirements Environmental Protection Agency’s (EPA) emission regulations specify test procedures to measure engine or vehicle emission levels With increasing demand to meet environmental goals cities are seeking ways to reduce emissions and the carbon footprint of the community at large like the Pierce Volterra Platform of Electric Vehicles provide municipalities with a sustainable solution to help meet their local and state legislative requirements In addition to meeting legislative requirements, municipalities are also demanding electric vehicles to meet more broad environmental goals. Currently, emissions from vehicles contribute to about one-third of all U.S. air pollution and buses have profound detrimental effects on the health By making the decision to support electric vehicles municipalities are leading the charge for citizens to follow suit municipalities have a lot of decision-making power Environmentally focused initiatives can regulate taxis and ridesharing programs and include plans to purchase electric vehicles for large municipal fleets municipalities can develop the required charging infrastructure to support electric vehicles When a municipality chooses to purchase an electric fire truck it is helping to normalize new technology and set a high standard for environmental sustainability The overall growth of electric vehicle use in municipalities supports reduced emissions and environmental initiatives There are several cost-saving benefits that come with the use of electric vehicles and electric fire trucks represent a major source of fuel consumption and can ultimately cause a detrimental environmental impact Electric vehicles require significantly less maintenance because the main source of power is not the internal combustion engine The chassis operates under electric power in all normal operational situations and leverages the internal combustion engine only for backup power in extended emergency operations municipalities can anticipate savings on preventive maintenance and ongoing engine repairs.It’s important to factor these savings into long-term strategies to help offset potential concerns about the upfront capital costs The team at Pierce is continuously researching and developing technologies and products to improve firefighter safety and efficiency Pierce routinely partners with customers to prove these new concepts and technologies before they are released for sale to a broader customer base With the development of an electric vehicle in progress, Pierce approached the City of Madison to discuss the opportunity to partner on technology advancements for fire apparatus that aligned with the City’s Climate Forward initiative The City of Madison has been a pioneer in adopting new technologies to minimize its carbon footprint and has been purchasing fire apparatus from Pierce Manufacturing for many years Here are just some of the key characteristics of the Pierce Volterra pumper now in service in Madison Metrics details we identified a corresponding astrocyte subgroup that responds reliably to astrocyte-selective stimulations with subsecond glutamate release events at spatially precise hotspots which were suppressed by astrocyte-targeted deletion of vesicular glutamate transporter 1 (VGLUT1) deletion of this transporter or its isoform VGLUT2 revealed specific contributions of glutamatergic astrocytes in cortico-hippocampal and nigrostriatal circuits during normal behaviour and pathological processes By uncovering this atypical subpopulation of specialized astrocytes in the adult brain we provide insights into the complex roles of astrocytes in central nervous system (CNS) physiology and diseases and identify a potential therapeutic target magnified images of the DGML (indicated by the white rectangle 1 in the top images) showing expression of all of the astrocytic markers and glutamate exocytosis markers listed in the top images A glutamatergic astrocyte (yellow arrow) and a non-glutamatergic astrocyte (white arrow) are indicated Inset (left): magnified view of the glutamatergic astrocyte but from the CA1 stratum radiatum region (CA1 The proportion of glutamatergic (segmented in yellow) versus non-glutamatergic (azure) astrocytes along the dorsal–ventral axis of the hippocampus Glutamatergic astrocytes are more abundant in a dorsal slice (left) compared with in a ventral slice (right) the experimental data demonstrate a hippocampal subpopulation of cells with morphological immunohistochemical and transcriptional features typical of astrocytes that contain transcripts required for glutamatergic regulated secretion we refer to these cells as glutamatergic astrocytes Source data chemogenetic and endogenous Gq-GPCR stimulation in situ both evoke hotspots of fast glutamate release in a subpopulation of DGML astrocytes our data in brain slices and awake mice show that both chemogenetic and natural stimulations in the presence of synaptic blockers trigger local subsecond SF-iGluSnFR signal elevations in astrocytes The responses in situ were suppressed by astrocyte-selective deletion of P2y1r (2MeSADP-evoked responses) or Slc17a7 (CNO-evoked responses) indicating that glutamate release is from astrocytes occurs after astrocyte Gq-GPCR activation and involves a vesicular exocytosis pathway Glutamate release responses always took place at specific hotspots of an astrocyte and only subpopulations of astrocytes were responders These findings provide direct functional evidence for the existence of a specialized population of glutamatergic astrocytes predicted by transcriptomic studies These data indicate a robust correlation between our physiological and molecular identification of glutamatergic astrocytes Representative EEG traces of seizures recorded from a VGLUT1GFAP-WT and a VGLUT1GFAP-KO mouse after injection of kainic acid (KA Seizure parameters were analysed in VGLUT1GFAP-KO (n = 7) VGLUT1GFAP-WT (n = 6) and VGLUT1WT-TAM (n = 7) mice Analysis of the specific differences between VGLUT1GFAP-KO and the control mice on the basis of the time to the first seizure (l); the total seizure number per mouse (one-way ANOVA with Tukey’s test; **P = 0.0083 *P = 0.0120) (m); the time from first to last seizure (n); individual seizure length (o); and the inter-ictal duration (Kruskal–Wallis with Dunn’s test; *P = 0.0232) (p) Source data The contextual memory defect observed after astrocyte VGLUT1 deletion indicates that glutamatergic astrocytes have a function in physiological memory processing these data show that glutamatergic astrocytes have active roles not only in physiological processes but also in pathological processes they reveal a protective function of astrocyte VGLUT1-dependent signalling against kainate-induced acute seizures in vivo notably opposing the mechanisms causing seizure amplification This function is worth examining further in chronic epilepsy models for possible therapeutic perspectives a, The breeding scheme for generating astrocyte-specific conditional VGLUT2 mice and related controls (details as in Fig. 3a The experimental paradigm and timeline of mouse treatments for electrophysiology recordings (left) schematic of midbrain slices showing the STN SNpc and substantia nigra pars reticulata (SNpr) with the position of the stimulating and recording electrodes sEPSCs recorded in SNpc DA neurons of VGLUT2GFAP-KO (15 cells increased sEPSC frequency (middle; one-way ANOVA with Tukey’s test; **P = 0.00187 (bottom) **P = 0.00233 (top)) and unchanged amplitude compared with the controls (right) Group III mGluR agents differently affect sEPSCs in VGLUT2GFAP-KO mice compared with the control mice (two-tailed paired t-test) The histograms show the percentage change induced by group III mGluR agonist l-SOP (10 μM) and antagonist MSOP (10 μM) on the baseline sEPSC frequency (left) and amplitude (right) in VGLUT2GFAP-KO mice (l-SOP: 12 cells 3 mice) and VGLUT2GFAP-WT mice (l-SOP: 10 cells EPSCs evoked in SNpc DA neurons by STN stimulation in VGLUT2GFAP-KO (24 cells representative traces of paired pulse-evoked EPSCs histograms showing a reduced PPR in VGLUT2GFAP-KO mice compared with in the control mice (one-way ANOVA with Fisher’s test; *P = 0.020 (top) Differential effects (expressed as the percentage change versus the control) induced by group III mGluRs agents on PPR in VGLUT2GFAP-KO (l-SOP: 10 cells 4 mice) compared with in VGLUT2GFAP-WT (l-SOP: 10 cells Statistical analysis was performed using two-tailed paired t-tests The experimental paradigm and timeline of mouse treatments for in vivo microdialysis measures of DA levels in the dST The baseline DA levels in VGLUT2GFAP-KO mice (n = 12) compared with in VGLUT2GFAP-WT mice (n = 13; Kolmogorov–Smirnov test; *P = 0.039) the box limits show the 25th to 75th percentiles and the whiskers show the minimum to maximum values Time course of DA levels after amphetamine challenge (AMPH The DA levels were significantly (Friedman ANOVA with Wilcoxon signed rank test) increased only at 40 min in VGLUT2GFAP-WT mice (*P = 0.0175) whereas DA levels were significantly increased at 20 100 and 120 min in VGLUT2GFAP-KO mice (##P = 0.00253 The amphetamine-induced increase was higher in VGLUT2GFAP-KO mice compared with in VGLUT2GFAP-WT mice at any tested time (Kolmogorov–Smirnov test; ***P = 0.00049 Source data astrocyte VGLUT2-dependent signalling represents a potential therapeutic target for Parkinson’s disease suggesting that different groups of specialized astrocytes have distinct roles in brain function By using astrocyte-targeted genetic VGLUT deletion we revealed that glutamatergic astrocytes contribute to cortico-hippocampal and nigrostriatal circuit function during normal behaviour and pathological processes The identified actions—strengthening LTP and hippocampal memories opposing hyperexcitation during seizures and STN overactivation in Parkinson’s disease—testify to the functional relevance of these specialized astrocytes and highlight their potential as targets for CNS protective therapies Future studies are expected to generate CNS-wide maps that will help to define the overall distribution of glutamatergic astrocytes and their full range of actions and to better understand why this atypical astrocytic population exists and by which specific modalities it integrates anatomically and functionally into CNS circuits as well as if and how its altered properties contribute to defined pathological CNS conditions A list of the reagents used in this study is provided in Supplementary Table 3 from Janvier) mice and transgenic mouse lines were housed at two to five animals per cage under a 12 h–12 h light–dark cycle (lights on from 07:00 to 19:00) at a constant temperature (23 °C) and humidity (~50%) with ad libitum access to food and water All animal protocols in the present study were approved by the Swiss Federal and Cantonal authorities (VD1873.1 VD3115.1) or by the Council Directive of the European Communities (2010/63/EU) and the Animal Care Committee of Italian Ministry of Health (375/2018-PR) Mice were used at different postnatal (P) ages according to experimental type (specified in corresponding sections) cortices and midbrains were quickly and carefully dissected in cold Hanks’ balanced salt solution (HBSS) buffer without Ca2+ and Mg2+ to decrease the debris in the final cell suspension Each cell suspension was prepared starting from 5 animals Tissue dissociation was run using the neural tissue dissociation kit (P) (Miltenyi Biotec) supplemented with DNase I and then mechanically dissociated using three rounds of trituration with 5 ml serological pipettes The resulting suspension was filtered through a 20 μm strainer (RUAG) to remove any remaining clumps Contamination by myelin and cell debris was removed by equilibrium density centrifugation 90% Percoll PLUS (Life Sciences) in 1× HBSS with Ca2+ and Mg2+ (Sigma-Aldrich) was added to the suspension to produce a final concentration of 24% Percoll Further DNase I (Worthington) was added (125 U per 1 ml) before centrifugation of the cell suspension at 300g for 11 min at room temperature (with minimal centrifuge braking) The resulting cell pellet was resuspended in Dulbecco’s phosphate-buffered saline (dPBS) (without Ca2+ and Mg2+) containing 0.5% bovine serum albumin (BSA) (Sigma-Aldrich) The supernatants were centrifuged again at 300g for 10 min at room temperature Any pelleted cells were resuspended in 0.5% BSA/dPBS (without Ca2+ and Mg2+) The images were acquired using the Leica Axioplan stereomicroscope (×20 objective the images were acquired using the Leica SP5 confocal microscope (Leica Microsystems) confocal acquisition consisted of a z-stack (12–20 µm; step size Laser-excitation wavelength was set at 405 nm for DAPI; 488 nm with an argon laser for Alexa Fluor 488; and 543 nm and 633 nm with a He/Ne laser for tdTomato and Alexa Fluor 633 Images were visualized using the LAS X software (v.3.7.4. Leica Microsystems) and transformed into .tiff format To assess recombination in the hippocampus DG (molecular layer) cells expressing the reporter gene (tdTomato+ cells) were counted using ImageJ; the ROI was identified using the free hand selection tool and the cell counter plugin was used for manual counting The final cell density is expressed as cells per mm2 tdTomato+ cells double labelled with GS/s100β OLIG2 or IBA1 markers were also counted and expressed as cells per mm2 A minimum of 140 tdTomato+ cells for each category was counted 2–4 images of 620 × 500 µm from 2–4 slices from 2–3 animals per group were analysed Images in the figures are confocal image maximum projections with contrast adjusted for display purposes Registration results were assessed visually for correctness All of the blobs within a distance of 1.5× the radius of a cell from the cell centroid were assigned to that cell we consider 1.5× the radius as a conservative estimate of the true cell size We generated a cell x gene count matrix by counting the transcripts of each probe assigned to individual cells to identify glutamatergic astrocytes in the molecular region of the DG across the dorso-ventral axis The region was chosen for its optimal isolation between DAPI nuclei resulting in more accurate identification and quantification of individual cells The same approach used for the RNA counting was used to measure the fluorescence signal intensity for each protein (tdTomato and the combination of astrocyte markers GS/S100β) To improve the detection of positive cells we computed the background signal for each cell measurement for each channel We considered an annular region of 30 pixels (8.5 µm) around the cell mask and measured the fluorescence intensity in this background region We assigned for each cell a background intensity by computing the minimum background intensity over its three nearest neighbours This respective background signal was then removed in all protein measurements for each cell Acute hippocampal or midbrain slices from transgenic mouse lines or WT mice were prepared and used in patch-seq two-photon imaging and synaptic electrophysiology experiments Details of each preparation are provided under the related experimental description Transcriptomic analysis was performed as described in the ‘Single-cell RNA analysis’ section enhances sensitivity in detecting cell populations we also excluded genes detected in less than five cells the cells from mouse hippocampus that were retained for further analysis were: 1,086 from the Artegiani dataset; 1,536 from the Batiuk dataset; 18,693 from the Habib dataset; 9,101 from the Hochgerner dataset; 21,064 from the Zeisel-1 dataset; 49,859 from the Saunders hippocampus dataset; 2,626 from the Zeisel-2 dataset; 78,064 from the Yao dataset; 65 from our patch-seq dataset; and 20 from our combined glutamate imaging/patch-seq dataset cells retained were: 8,370 from the Habib human dataset; 120,842 from the Ayhan dataset; and 8,907 from the Tran dataset cells retained were: 39,684 from the Zipurski dataset; 123,312 from the Liu dataset and 18,079 from the Zhang dataset cells retained were: 16,526 from the Saunders substantia nigra dataset; 38,498 from the Welch dataset; and 5,257 from the Agarwal dataset The prediction and clustering results of the dataset were then consolidated to determine the accuracy This was done after each round of dataset removal Our results demonstrated the robust and consistent performance of the model We next applied this model to subset only the predicted astrocytes from all of the different hippocampal mouse databases 16,800 astrocytes were predicted: 216 from the Artegiani dataset; 1,368 from the Batiuk dataset; 2,893 from the Habib dataset; 1,054 from the Hochgerner dataset; 3,718 from the Zeisel-1 dataset; 7,002 from the Saunders hippocampus dataset; 176 from the Zeisel-2 dataset; and 373 from the Yao dataset On the basis of their genetic fate mapping physiological and morphological properties all of the patch-seq cells (85) were considered to be astrocytes The following software packages were used: Seurat v.4 All viral constructs were provided by the Viral Vector Facility and virally injected with AAV5-hGFAP-hM3D(Gq)-mCherry FOVs comprised whole individual astrocytes and we used a single CNO stimulation protocol through local puff as above we compared Ca2+ responses in the medial DGML of Slc17a7fl/fl mice injected with AAV5-hGFAP-GCaMP6f Ca2+ indicator and either AAV5-hGFAP-mCherry (controls) or AAV5-hGFAP-mCherry-iCre (VGLUT1GFAP-KO) viruses during medial perforant pathway (MPP) electrical stimulation periods (either single stimuli or ϴ-LTP protocols; for details see the ‘LTP of excitatory synapses in the hippocampal DG’ section below Mice were virally injected at 2 months of age and used experimentally at 4 months of age Two-photon imaging was performed in the same system as above but using the galvo mode at 0.3 Hz frame-rate and a low optical zoom (×1.5) to simultaneously monitor responses in multiple astrocytes The laser was tuned to 920 nm for GCaMP6f imaging and at 1,000 nm for mCherry imaging the effect of local applications of specific agents (CNO (100 µM–1 mM) or Ach (10–50 mM) both in ACSF containing 25 nM Alexa Fluor 594) during imaging was tested in small FOVs An electrode with 0.1 Ω resistance was filled with the agent solution carefully inserted into the cranial window and moved to the FOV under low magnification Release of microvolumes of solution in the glass pipette was then performed in a timed manner using air pressure controlled by a pneumatic PicoPump (PV820; WPI) 15–50 psi) spaced by 10 s intervals to allow tissue diffusion of the agent and avoid build-up of tissue pressure Effective delivery was confirmed by the appearance of Alexa Fluor 594 red fluorescence in the FOV pipette clogging during the experiment required a temporary change of the picopump settings until the red fluorescence appeared in the tissue around the pipette tip The start time of exposure to the agent in these cases was assigned to the puff on which Alexa Fluor 594 fluorescence first appeared in the tissue In experiments evaluating astrocyte Ca2+ dynamics during MPP stimulations we analysed FOVs containing several astrocytes in different stimulation conditions we generated mean time projections of the GCaMP6f signal over 70–80 frames (21–24 s) representing periods comprising either (1) spontaneous astrocyte Ca2+ activity with responses to a single stimulus or (2) peak astrocyte Ca2+ responses to ϴ-LTP stimulation Corresponding Ca2+ traces were extracted from representative single-astrocyte ROIs set in ImageJ and compared between astrocytes from control mice and from VGLUT1GFAP-KO mice blue light from a 473 nm ps-pulsed laser (at 50 MHz; pulse width 80 ps FWHM) was delivered through a single mode fibre Fluorescence emission from the tissue was collected by a multimode fibre with a sample frequency of 100 Hz The single mode and multimode fibres were arranged side by side in a ferrule that is connected to a detachable multimode fibre implant The emitted photons collected through the multimode fibre pass through a band-pass filter (FF01-550/88 Photons were recorded by the time-correlated single-photon counting (TCSPC) module (SPC-130EM Becker and Hickl) in the ChiSquare X2-200 system mice were habituated to the head-fixation system for 5 days for around 20 min connected to the recording apparatus and left waiting 5–10 min to allow the photon recording traces to stabilize A stable baseline of 5 min was recorded and a Hamilton syringe (500 nl) was carefully plugged in the head-implant cannula in which synaptic blockers were dissolved (5 mM NBQX 0.010 mM SNX-482) was administered at a constant flow rate of 1.6 nl s−1 The recording was stopped 10 min after the end of the infusion Mice were given 3 days for recovery from the first injection and all of the procedures were repeated administering CNO (2.5 mM) in the same synaptic blockers mixture Raw fibre photometry data were processed using the Spike2 v.8 software (Cambridge Electronic Design) Data were smoothened by a factor of 0.1 and downsampled to reach a final frequency of 2 Hz Data were finally normalized using the ∆F/F0 formula where F0 corresponds to the average photometry value during the 5 min recording before the cannula was plugged in male GFAPCreERT2Slc17a7fl/fltdTomatolsl/lsl mice (P21–25) were treated with TAM (2 i.p long protocol) to induce cell-specific Slc17a7 gene deletion coupled to tdTomato fluorescence expression in GFAP-expressing cells (VGLUT1GFAP-KO) littermate male GFAPcreERT2Slc17a7fl/fltdTomatolsl/lsl mice of the same age were treated with vehicle (corn oil The procedures for midbrain slice preparation and patch-clamp recordings of sEPSCs in SNpc DA neurons were performed as described above EEGs were continuously recorded at a sampling rate of 250 Hz in each experimental cage using an EEG-telemetry system with associated video monitoring of the movement of the animals (Pinnacle Technology) from 24 h before administration of KA to 48 h after its injection For detecting and analysing KA-induced seizures EEG traces and video recordings were evaluated by the experimenter through manual scoring with Sirenia seizure software v.1.7 (Pinnacle Technology) Artifacts in the raw EEG traces (electrical noise exploratory behaviour and grooming) were manually identified and excluded from analyses Quantitative analysis of seizures was performed in the first 4 h after KA injection Seizures were defined as EEG segments starting with low-amplitude high-frequency activity (tonic phase) and evolving into higher-amplitude and lower-frequency bursts (clonic phase) with a minimal duration of 30 s Parameters analysed and expressed as the mean value for each individual mouse were: (1) seizure latency (mean time to first seizure): the time between KA injection and the start of the first seizure; (2) the total number of seizures during the 4 h post-KA period defined as the time between the onset and the end of the seizure episode with the end defined as the time when the EEG returned to the mean baseline or (in the case of postictal depression) to a value lower than the mean baseline; (4) the time first-to-last seizure which is the time interval between the appearance of the first seizure and of the last seizure; (5) the inter-ictal activity duration The correctness of probe placement in the dST was confirmed after each experiment by brain dissection and slicing and through observation under a microscope Data shown from representative experiments were repeated with similar results in at least two independent biological replicates Sample sizes were estimated empirically on the basis of previous studies Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article may be addressed to andrea.volterra@unil.ch or 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D Sahlender for initial characterization of GFAPcreERT2Slc17a6fl/fltdTomatolsl/lsl mice; C Vivar Rios for developing the pipeline for glutamate imaging analysis in situ in the first part of the study; C Calvo from the CSR-UNIL team for developing an open source version of the same imaging pipeline; J Prados for sharing the torch prediction algorithm and for his general advice; E Magrinelli for performing initial bioinformatic analysis of patch-seq experiments and integration of the existing databases; B Xiong for contributing to image acquisition for the RNAscope HiPlex experiment; R Kirchhoff for sharing the Slc17a6fl/fl and GLASTcreERT2P2ry1fl/fl mouse lines Martirosyan for sharing unpublished data and methods Pryce for advice on protocols and analysis of behavioural experiments; N Liaudet for advice on imaging experiments and analysis and for reading parts of the manuscript; and D Jabaudon for advice on single-cell transcriptomics and for reading the manuscript Research in the Volterra laboratory was supported by Swiss National Science Foundation (SNSF) NCCR TransCure grant/award number 51NF40-160620; SNSF grants/award numbers 31003A-173124 and 31003B-201276; European Research Council (ERC) Advanced Grant 340368 “Astromnesis”; Stiftung Synapsis—Demenz Forschung Schweiz DFS grant/award number 2018-PI-01; and the Wyss Center for Bio and Neuroengineering Research in the Telley laboratory was supported by ERC starting grant CERDEV_759112 and a SNSF grant 31003A_182676/1 Present address: Department of Biomedical Sciences These authors contributed equally: Ada Ledonne Emanuele Claudio Latagliata & Nicola Mercuri David Gregory Litvin & Andrea Volterra Department of Life Sciences and UK Dementia Research Institute supervised most of the experimental and analytical part of the project designed and supervised breeding schemes of transgenic lines participated in single-cell transcriptomics RNAscope HiPlex and imaging experimental design and supervised some of the co-authors during experiments performed and analysed electrophysiological experiments in hippocampus designed experiments on the nigrostriatal DA circuit performed and analysed electrophysiological recordings in nigral DA neurons execution and analysis of in vivo microdialysis experiments and contributed to writing the corresponding sections of the manuscript performed and analysed SF-iGluSnFR imaging experiments in situ participated in the design and preparation of the ad hoc pipeline for SF-iGluSnFR image analysis in situ performed combined imaging and patch-seq experiments with A.L and wrote the corresponding sections of the manuscript performed and analysed SF-iGluSnFR imaging experiments in vivo designed and wrote the code for SF-iGluSnFR image analysis in vivo and wrote the corresponding sections of the manuscript developed the acute seizure and video EEG approach and performed the initial studies and performed viral injections performed and analysed in vivo microdialysis experiments performed two-photon Ca2+ imaging experiments and patch-seq videos with A.L performed electrophysiology experiments combined with two-photon Ca2+ imaging designed dual-recording LFP Θ-LTP hippocampal experiments and performed the initial studies developed analysis for RNAscope HiPlex experiments image analysis and cell counting experiments and collaborated in the behavioural experiments developed the Slc17a7fl/fl transgenic line and gave advice on its use in this project contributed to their analysis and to writing that part of the manuscript contributed to designing the substantia nigra electrophysiological experiments and supervised that part of the project designed and supervised the single-cell and spatial transcriptomics part of the project developed and used the bioinformatics approaches for generating all of the integrated databases and for their analysis as well as for analysis of patch-seq and RNAscope HiPlex experiment and participated in the overall writing and strategy of the project designed its different components and wrote the manuscript The authors declare no competing interests Nature thanks Alfonso Araque and the other, anonymous, peer reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations Accuracy and loss value after each epoch for training and validation data; Bottom confusion matrix showing cell prediction for validation data We performed cross-validation by removing each individual dataset one at a time and running the prediction and clustering using the others then calculated the overall prediction efficiency Data are shown as box plot (25–75 percentile with median) with min to max whiskers excluding outliers Expression levels for canonical astrocytic markers in the integrated hippocampus database Expression intensity per astrocyte cluster and corresponding dot plot for selected canonical astrocytic (d,e) regulated exocytosis and glutamatergic pre-synaptic function markers (f,g) Heatmap showing the percent of cells in each cell cycle phase for each astrocytic cluster Expression level per astrocyte cluster for Ifitm3 High-magnification images of examples of glutamatergic astrocytes in various regions of the hippocampus: DGML: molecular layer of the dentate gyrus; Hilus: Hilus region of the dentate gyrus CA3-RAD: stratum radiatum of the CA3 region CA3-OR: stratum oriens of the CA3 region; CA1-RAD: stratum radiatum of the CA1 region The visualization was achieved using a combination of immunohistochemistry for tdTomato (Tom and DAPI (white) and fluorescent in situ hybridization for Slc17a7 (yellow) The red dashed line indicates the threshold for significant enrichment in these gene ontologies Source data containing only active clusters (“hotspots”) with ≥4 neighbours was used to calculate hotspots number and areas CNO-dependent Gq-DREADD stimulation evokes Ca2+ elevations in all the tested astrocytes timeline of the experiments: TAM-inducible GFAPcreERT2GCaMP6ffl/fl mice were unilaterally injected with AAV5-hGFAP::hM3D(Gq)-mCherry virus After 3 days mice received TAM administration for 3 days and after 4 weeks two-photon Ca2+ imaging was performed representative fluorescence image of an astrocyte FOV (red: hM3D(Gq); green: GCaMP6f) Traces of cytosolic GCaMP6f Ca2+ responses in the ROI (whole astrocyte) for each tested astrocyte (n = 10 cells) in response to a single puff of CNO (100 µM) expressed in z-scores of the raw GCaMP6f signal Note large Ca2+ elevation in all CNO-stimulated astrocytes Each trace is accompanied by ROI display as perceptually uniform ‘magma’ colormap Stimulation with vehicle does not reproduce the glutamate-releasing effect of CNO in Gq-DREADD-expressing astrocytes: top wild-type mice (n = 2) were unilaterally injected in hippocampus with AAV5-hGFAP::SF.iGluSNFR(A184S) and AAV5-hGFAP::hM3D(Gq)-mCherry viruses Binarized functional maps of vehicle- and L-Glut-evoked SF-iGluSnFR responses of 5 individual astrocyte FOVs while in all of them L-glut elicited the usual large response CNO does not evoke glutamate release in astrocytes expressing an mCherry scrambled virus instead of Gq-DREADD wild-type mice (n = 2) were unilaterally injected in hippocampus with AAV5-hGFAP::SF.iGluSNFR(A184S) and AAV5-hGFAP::mCherry viruses binarized functional maps of CNO- and L-Glut-evoked SF-iGluSnFR responses of 5 individual astrocyte FOVs (azure halo) of 2MeSADP- and L-Glut-evoked SF-iGluSnFR responses in wild-type mice For 2MeSADP: rise-time10–90; 96.78 ± 17.53 ms; FWHM: 400.39 ± 42.98 ms; decay time: 303.61 ± 30.56 ms; ≥32 traces from 7 ± 1 grid locations from 6 FOVs) schematic of the viral treatments in GLASTcreERT2P2y1fl/fl mice; Middle and Bottom: matched 2MeSADP- and L-Glut-evoked SF-iGluSnFR fluorescence responses (light green) as in e but in P2Y1RGFAP-KO mice (20 FOVs of L-Glut-evoked SF-iGluSnFR responses as in f but in P2Y1RGFAP-KO mice (>100 traces from 10 FOVs) For 2MeSADP no kinetics of evoked responses are shown because no 2MeSADP-responder FOV was observed in P2Y1RGFAP-KO mice CNO or ACSF in all astrocytes investigated in vivo in the visual cortex in 37.5 x 37.5 µm FOVs in the presence of synaptic blockers Astrocytes are regrouped as responders or non-responders to the stimulus (Methods) For each astrocyte and for each stimulus is presented a colour-coded spatial map of the ROIs in the FOV displaying increased peak frequency upon stimulus application The colour scale represents intensity of frequency increase above baseline from 0 (pink) to 0.25 Hz (yellow); scale bar: 10 µm Source data corresponding histogram quantification showing statistical significance (two tails Fisher exact test P = 0.0320) for correct prediction of cluster 7 for “responder” astrocytes and of other clusters for “non responder” astrocytes 3 out of 4 responders were correctly attributed to cluster 7 14 were correctly attributed to non-glutamatergic clusters (9 to cluster 2; 3 to cluster 4 and 2 to cluster 5) and two to cluster 7 Representative fluorescence activated cell sorting (FACS) of tdTomato-positive (Tom+) astrocytes in cerebral cortex samples of VGLUT1GFAP-WT mice (sorted ≥2 x 105 Tom+ cells per experiment VGLUT1GFAP-KO mice (sorted ≥2 x 105 Tom+ cells per experiment 5 mice per experiment) and GFAPCreERT2tdTomlsl/lsl mice (sorted ≥2 x 105 Tom+ cells per experiment here acquired with confocal microscope (n = 2) confirming no leakage in the absence of TAM-induced cre recombination lack of any Tom+ cells (red) in the hippocampus of VGLUT1GFAP-WT and VGLUT1WT-TAM control mice also stained with the astrocyte markers GS and S100β (green) n = 8 images from 4 independent experiments table presenting the total number per mm2 of Tom+ cells and the relative numbers of the same Tom+ cells co-labelled with astrocyte (GS+S100β) oligodendrocyte (Olig2) or microglia (Iba1) markers counted in two hippocampal regions (CA1 and DG) and in the visual cortex of VGLUT1GFAP-KO mice upon TAM-induced cre recombination Confocal images confirming lack of any co-labelling of Tom+ cells with microglia (Iba1 green) markers in the DG of VGLUT1GFAP-KO mice ϴ-LTP recorded in DGML of wild-type mice by 3 local field potential (LFP) electrodes positioned along the same bundle of PP fibres at an average distance of 200 µm (electrode 1) 300 µm (electrode 2) and 400 µm (electrode 3) from the stimulation pipette (STIM) ϴ-LTP magnitude is the same at all tested locations (two-way ANOVA repeated measures (P = 0.78 Setting for ϴ-LTP induction and measure in GFAPcreERT2Slc17a7fl/fltdTomlsl/lsl mice undergone short TAM treatment (Methods) bright-field (BF) and fluorescence images (Tom) show positioning of the stimulation pipette (STIM) and of the two LFP recording electrodes in the DGML higher zoom images show the position of electrode 1 proximal to a non-fluorescent astrocyte (astro) proximal to a fluorescent astrocyte (astro Tom+) Basal input-output curves (left) and basal fEPSP amplitudes (right) recorded in two DGML fields containing a VGLUT1GFAP-WT (grey) and a VGLUT1GFAP-KO astrocyte (orange) show no significant differences (data mean ± s.e.m.; paired Student’s t test Thin lines connect individual LFP electrode pairs (n = 16 slices Astrocyte Ca2+ dynamics during low and high-frequency stimulation of MPP in VGLUTGFAP-WT and VGLUT1GFAP-KO mice Slc17a7fl/f mice are injected with AAV5-GFAP-mCherry virus (control virus) and AAV5-GFAP-GCaMP6f virus to report astrocyte Ca2+ dynamics multiple astrocytes present in the same FOV as in h and i display both mCherry (red) and GCaMP6f (green) fluorescence mean time projection over 70 frames (21 s) of the GCaMP6f signal in astrocytes in the period before ϴ-LTP induction (Pre) representative Ca2+ traces from selected single-cell ROIs during  the same Pre period Astrocytes show small asynchronous local Ca2+ activity and a few larger responses to single MPP stimulations mean time projection of the GCaMP6f signal in astrocytes as in h but during MMP stimulation inducing ϴ-LTP (ϴ-LTP) representative Ca2+ traces from single astrocyte ROIs during ϴ-LTP induction Multiple astrocytes show very large Ca2+ elevation (note the scale is 10-fold larger than in the Pre period) almost synchronously at the start of the ϴ-LTP protocol (red vertical line) Slc17a7fl/fl mice are injected with AAV5-GFAP-mCherry-iCre virus to delete VGLUT1 selectively in astrocytes and with AAV5-GFAP-GCaMP6f virus to report astrocyte Ca2+ dynamics display both mCherry fluorescence (red) indicating Cre recombination and GCaMP6f fluorescence (green) mean time projection over 80 frames (24 s) of the GCaMP6f signal in astrocytes in the Pre period representative Ca2+ traces from selected single-cell ROIs in the same Pre period Astrocyte Ca2+ dynamics in VGLUT1GFAP-KO mice in the Pre period are comparable to those in controls mice (h) Left: mean time projection of the GCaMP6f signal in astrocytes as in k but in the ϴ-LTP induction period representative Ca2+ traces from selected single-cell ROIs during ϴ-LTP induction The very large synchronous astrocyte Ca2+ responses in VGLUT1GFAP-KO mice are comparable to those in controls Open field (O.F.) and activity tests (A.T.) performed on VGLUT1GFAP-KO (orange histograms reporting parameters index of locomotor activity (total distance travelled P = 0.086) and anxiety (time spent immobile P = 0.28; and time in the inner zone of the arena example traces of locomotor activity in the three mouse groups placed in the O.F top: Histograms reporting parameters index of exploratory activity (total number of rearings measured during the 5 min activity test preceding fear conditioning) do not show group differences (P = 0.89) histograms reporting parameters index of pain sensitivity (mean total distance moved during 2s e-shocks repeated 6 times during the fear conditioning test) do not show group differences (P = 0.84) Source data lack of any Tom+ cells (red) in the SNpc of VGLUT2GFAP-WT and VGLUT2WT-TAM control mice also stained with the neuronal marker TH (green) the oligodendrocyte marker Olig2 (grey) or the microglia marker Iba1 (grey) confocal images confirming co-labelling of Tom+ cells (red) with the astrocyte marker S100β (grey) but not with the neuronal (TH grey) markers in the SNpc of VGLUT2GFAP-KO mice table presenting the total number of Tom+ cells and the relative numbers of the same Tom+ cells co-labelled with astrocyte (S100β) counted in SNpc of VGLUT2GFAP-KO mice after TAM-induced cre recombination Left: representative cell-attached firing traces and Right histograms of basal electrophysiological properties (firing frequency membrane resistance (Rm) and holding current at –60 mV) of SNpc DA neurons in midbrain slices from VGLUT2GFAP-KO 8 mice; Rm and Ihold at −60 mV: VGLUT2GFAP-KO No differences among groups were observed: one-way ANOVA: P = 0.7399 for firing frequency; P = 0.47 for Rm; P = 0.516 for holding current at −60 mV Plot of spontaneous firing frequency recorded in cell-attached mode in SNpc DA neurons of VGLUT1GFAP-KO (n = 18 cells No significant differences were found between the two groups: P = 0.228 Histograms of frequency and amplitude of spontaneous excitatory postsynaptic currents (sEPSCs) recorded in SNpc DA neurons of VGLUT1GFAP-KO (n = 17 cells and show no differences between the two groups P = 0.63 for sEPSC frequency and P = 0.64 for sEPSC amplitude Source data List of genes significantly enriched in astrocytes versus the other hippocampal cell types (data obtained from the integrated mouse hippocampus database) Differential expression analysis was performed using two-sided nonparametric Wilcoxon rank-sum tests and genes were ranked on average log2-transformed fold change Lists of significant type-enriched transcripts in each individual astrocyte cluster (data obtained from the integrated mouse hippocampus database) Differential expression analysis was performed using two-sided nonparametric Wilcoxon rank-sum test and genes were ranked on average log2-transformed fold change Representative example of SF-iGluSnFR glutamate imaging of a Gq-DREADD-expressing astrocyte in DGML of the hippocampus challenged with CNO The video shows raw acquisitions of aligned short periods before during and after each of the six consecutive puffs of CNO in Alexa 594 (red channel) onto a SF-iGluSnFR (green channel) fluorescent astrocyte expressing Gq-DREADD–mCherry in a hippocampal slice of a WT mouse virally injected with the appropriate viruses (Methods) The puffing pipette is positioned at the top edge of the FOV and aligned puffs start at ~8.7 s of the video The arrowheads indicate three representative small responding regions in the green channel the mean standard deviation map of the SF-iGluSnFR signal helps to visualize these  locations and a few others recurrently active on CNO puffs The video was downsampled to 10 Hz and slowed down five times to help with visualization of the responses Representative example of collection of a patch-seq astrocyte visualized thanks to expression of tdTomato fluorescence and differential interference contrast (DIC) in a two-photon microscope (Methods) A patch pipette was positioned onto a DGML red-fluorescent astrocyte in a hippocampal slice of a TAM-treated GFAPcreERT2tdTomlsl/lsl mouse and used in whole-cell configuration to aspirate the cell body content into the pipette The pipette was then removed from the tissue Download citation DOI: https://doi.org/10.1038/s41586-023-06502-w The firefighters in Madison, Wisconsin, have embarked on a journey with Pierce Manufacturing—to use, challenge and track the operations and performance of the Pierce® Volterra™ electric fire truck, the first electric fire truck ever put into service in North America Below, Assistant Fire Chief Scott Bavery from the City of Madison Fire Department provides an in-depth interview on a day in the life of Madison firefighters and the Pierce Volterra electric fire truck Follow along on a typical day to see how the Volterra integrates into station operations how it supports the local community and for an inside look at electric fire truck performance The Madison Fire Department is made up of 14 fire stations serving an area of nearly 100 square miles and a population of over 250,000 The Volterra electric fire truck is housed in Station 8 which has 10 firefighters on duty each day which is often the busiest ambulance in the city Most firefighters arrive between 6:30am and 6:45am for shift change This allows firefighters to relieve their colleagues and discuss any logistics to set the new day up for success They allow the teams to exchange pertinent insights regarding fleet vehicles and station- or task-specific information firefighters begin their day with a vehicle inspection and placing their personal protective equipment (PPE) on the truck in preparation for the first call Apparatus engineers walk around each rig with a checklist of items to review If firefighters notice any operational issues they put in a work order so items can be addressed as soon as possible the City of Madison Fire Department holds a department-wide briefing Led by the incident commander at Station 1 the briefing is held over Zoom and reviews the operational plan for the day planned protests or key developments that firefighters should prepare for and also review any training requirements or other department updates Many take the time to clean the trucks in the station and perform minor station tasks to ensure they are ready for the day sweeping and mopping to cleaning bathrooms station tasks are a way to kick start the day with a teamwork mentality Health and wellness are important to our firefighters Some firefighters use the quieter morning hours to get in a daily workout Each station is outfitted with a gym and each department prioritizes time for firefighters to get in a physical workout to stay in shape "What's great about the Pierce Volterra pumper is its ability to enter and exit the station without generating exhaust fumes providing a better environment for our firefighters." the morning hours are often used for housekeeping tasks firefighters pool their personal money together to purchase food for the day so the assigned chef for the shift can make an early morning run to the grocery store any incomplete tasks are resumed when firefighters return to the station.  Each day is designed to remain flexible as calls come in and as crew members leave from and return to the station Most mornings include some kind of drill or training exercise Some are based on requirements and certifications while others are hands-on initiatives to practice operational tactics and sequences The Madison Fire Department has priority dispatching which means the dispatcher determines the right rig to assign to each call based on the emergency type The closest unit with the appropriate support supplies is dispatched immediately and depending on the nature of the emergency other support vehicles are also dispatched the Volterra engine is on first response call All engines and ladder trucks are staffed with four personnel these men or women are either EMTs or paramedics After a call, the Volterra fire truck returns to the station and is plugged into an overhead charging unit The familiarity of overhead infrastructure makes it easy to integrate electric vehicle charging units into fire stations Overhead charging is beneficial because it doesn’t take up valuable floor space and it improves overall employee safety by reducing trip hazards in high traffic areas the crew takes time to remove any contaminated gear to ensure it gets washed or cleaned immediately to reduce carcinogens in the station Any EMS or firefighting supplies used on the call are replenished and any used equipment is cleaned and checked for readiness the cab interior or truck exterior becomes dirty or contaminated The goal is to ensure that the truck is mission-ready as soon as possible once it returns to station because another call could come at any moment The evening hours at the station follow a similar pattern to the early morning shift Firefighters wind down the day with a vehicle review to make sure each truck is ready to perform and the hours pass with workouts the Volterra electric fire truck has had some hurdles over its first two years in service Pierce’s unique approach to put a concept demonstrator in service to validate the design technology and performance is groundbreaking The overarching goal of learning and refining the truck using the power of data and real-life scenarios means the Pierce team can truly understand the metrics behind truck requirements and performance and adjust the new technology accordingly When operational or mechanical issues arise Pierce is often able to perform remote upgrades to address areas of concern The truck has been brought out of service to study performance and opportunities for improvement New technology comes with unanticipated obstacles and great opportunities for advancement Pierce has been able to gather valuable daily operations data and information to make significant improvements in the electric vehicle technology and battery operation In-depth discussions with each crew member daily reports and a continuous stream of real-time data have allowed the Pierce team to learn performance capabilities and opportunities based on weather Based on feedback from the station crew and Chief Bavery Pierce has already integrated design adjustments to the Volterra Pierce received feedback that firefighter ergonomics could be improved if the charging port on the side of the vehicle was moved higher Take a look at our additional resources on the electric fire truck to learn more: