scholarly journals Network Models Made by Dynamic Differential Equations

2017 ◽  
Vol 107 ◽  
pp. 466-471 ◽  
Author(s):  
Bing Yao ◽  
Jing Su ◽  
Fei Ma ◽  
Xiaomin Wang ◽  
Hui Sun ◽  
...  
Keyword(s):  
Differential Equations ◽  
Network Models

EVANS FUNCTIONS AND NONLINEAR STABILITY OF TRAVELING WAVES IN NEURONAL NETWORK MODELS

2007 ◽  
Vol 17 (08) ◽  
pp. 2693-2704 ◽  
Author(s):  
BJÖRN SANDSTEDE
Keyword(s):  
Differential Equations ◽  
Neuronal Network ◽  
Nonlinear Stability ◽  
Traveling Waves ◽  
Network Models ◽  
Function Spaces ◽  
Spectral Stability ◽  
Evans Function ◽  
Evans Functions

Modeling networks of synaptically coupled neurons often leads to systems of integro-differential equations. Particularly interesting solutions in this context are traveling waves. We prove here that spectral stability of traveling waves implies their nonlinear stability in appropriate function spaces, and compare several recent Evans-function constructions that are useful tools when analyzing spectral stability.

SIMPLIFIED DYNAMICS AND OPTIMIZATION OF LARGE SCALE TRAFFIC NETWORKS

2004 ◽  
Vol 14 (04) ◽  
pp. 579-601 ◽  
Author(s):  
MICHAEL HERTY ◽  
AXEL KLAR
Keyword(s):  
Differential Equations ◽  
Traffic Flow ◽  
Large Scale ◽  
Dynamic Models ◽  
Optimization Problems ◽  
Network Models ◽  
Traffic Networks ◽  
Algebraic Models ◽  
Simplified Models ◽  
Large Scale Networks

Simplified dynamic models for traffic flow on networks are derived from network models based on partial differential equations. We obtain simplified models of different complexity like models based on ordinary differential equations or algebraic models. Optimization problems for all models are investigated. Analytical and numerical properties are studied and comparisons are given for simple traffic situations. Finally, the simplified models are used to optimize large scale networks.

Synaptic integration of NMDA and non-NMDA receptors in large neuronal network models solved by means of differential equations

1994 ◽  
Vol 70 (3) ◽  
pp. 267-273
Author(s):  
C. Bernard ◽  
Y. C. Ge ◽  
E. Stockley ◽  
J. B. Willis ◽  
H. V. Wheal Not Available
Keyword(s):  
Differential Equations ◽  
Nmda Receptors ◽  
Neuronal Network ◽  
Network Models ◽  
Synaptic Integration

Synaptic integration of NMDA and non-NMDA receptors in large neuronal network models solved by means of differential equations

1994 ◽  
Vol 70 (3) ◽  
pp. 267-273 ◽  
Author(s):  
C. Bernard ◽  
Y. C. Ge ◽  
E. Stockley ◽  
J. B. Willis ◽  
H. V. Wheal
Keyword(s):  
Differential Equations ◽  
Nmda Receptors ◽  
Neuronal Network ◽  
Network Models ◽  
Synaptic Integration

scholarly journals Intelligent Control Systems in Urban Planning Conflicts: Social Media Users’ Perception

2021 ◽  
Vol 11 (14) ◽  
pp. 6579
Author(s):  
Nailia Gabdrakhmanova ◽  
Maria Pilgun
Keyword(s):  
Neural Network ◽  
Social Media ◽  
Urban Planning ◽  
Differential Equations ◽  
Instant Messaging ◽  
Network Models ◽  
Urban Systems ◽  
Neural Network Models ◽  
The North ◽  
North Eastern

The relevance of this study is determined by the need to develop technologies for effective urban systems management and resolution of urban planning conflicts. The paper presents an algorithm for analyzing urban planning conflicts. The material for the study was data from social networks, microblogging, blogs, instant messaging, forums, reviews, video hosting services, thematic portals, online media, print media and TV related to the construction of the North-Eastern Chord (NEC) in Moscow (RF). To analyze the content of social media, a multimodal approach was used. The paper presents the results of research on the development of methods and approaches for constructing mathematical and neural network models for analyzing the social media users’ perceptions based on their digital footprints. Artificial neural networks, differential equations, and mathematical statistics were involved in building the models. Differential equations of dynamic systems were based on observations enabled by machine learning. Mathematical models were developed to quickly detect, prevent, and address conflicts in urban planning in order to manage urban systems efficiently. In combination with mathematical and neural network model the developed approaches, made it possible to draw a conclusion about the tense situation around the construction of the NEC, identify complaints of residents to constructors and city authorities, and propose recommendations to resolve and prevent conflicts. Research data could be of use in solving similar problems in sociology, ecology, and economics.

scholarly journals Neural Ordinary Differential Equations and Recurrent Neural Networks for Predicting the State of Health of Batteries

2021 ◽  
Author(s):  
Simona Pepe ◽  
Jiapeng Liu ◽  
Emanuele Quattrocchi ◽  
Francesco Ciucci
Keyword(s):  
Neural Networks ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Short Term Memory ◽  
Network Models ◽  
The State ◽  
State Of Health ◽  
Neural Network Models ◽  
Efficient Operation ◽  
Ode Models

<p>Battery management systems require efficient battery prognostics so that failures can be prevented, and efficient operation guaranteed. In this work, we develop new models based on neural networks and ordinary differential equations (ODE) to forecast the state of health (SOH) of batteries and predict their end of life (EOL). Governing differential equations are discovered using measured capacities and voltage curves. In this context, discoveries and predictions made with neural ODEs, augmented neural ODEs, predictor-corrector recurrent ODEs are compared against established recurrent neural network models, including long short-term memory and gated recurrent units. The ODE models show good performance, achieving errors of 1% in SOH and 5% in EOL estimation when predicting 30% of the remaining battery’s cycle life. Variable cycling conditions and a range of prediction horizons are analyzed to evaluate the models’ characteristics. The results obtained are extremely promising for applications in SOH and EOL predictions.</p>

scholarly journals Neural Ordinary Differential Equations and Recurrent Neural Networks for Predicting the State of Health of Batteries

2021 ◽  
Author(s):  
Simona Pepe ◽  
Jiapeng Liu ◽  
Emanuele Quattrocchi ◽  
Francesco Ciucci
Keyword(s):  
Neural Networks ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Short Term Memory ◽  
Network Models ◽  
The State ◽  
State Of Health ◽  
Neural Network Models ◽  
Efficient Operation ◽  
Ode Models

<p>Battery management systems require efficient battery prognostics so that failures can be prevented, and efficient operation guaranteed. In this work, we develop new models based on neural networks and ordinary differential equations (ODE) to forecast the state of health (SOH) of batteries and predict their end of life (EOL). Governing differential equations are discovered using measured capacities and voltage curves. In this context, discoveries and predictions made with neural ODEs, augmented neural ODEs, predictor-corrector recurrent ODEs are compared against established recurrent neural network models, including long short-term memory and gated recurrent units. The ODE models show good performance, achieving errors of 1% in SOH and 5% in EOL estimation when predicting 30% of the remaining battery’s cycle life. Variable cycling conditions and a range of prediction horizons are analyzed to evaluate the models’ characteristics. The results obtained are extremely promising for applications in SOH and EOL predictions.</p>

What's in a model? Network models as tools instead of representations of what psychiatric disorders really are

2019 ◽  
Vol 42 ◽  
Author(s):  
Hanna M. van Loo ◽  
Jan-Willem Romeijn
Keyword(s):  
Psychiatric Disorders ◽  
Network Models ◽  
Model Network

AbstractNetwork models block reductionism about psychiatric disorders only if models are interpreted in a realist manner – that is, taken to represent “what psychiatric disorders really are.” A flexible and more instrumentalist view of models is needed to improve our understanding of the heterogeneity and multifactorial character of psychiatric disorders.

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