Analysis of open dynamical systems' models with the help of stochastic differential equations (based on the example of macroeconomic growth models)

2017 ◽  
Author(s):  
Nataliya Asanova ◽  
Irina Tarasova ◽  
Liana Sagatelova ◽  
Yaroslav Kalinin
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Growth Models ◽  
Systems Models ◽  
Macroeconomic Growth ◽  
Dynamical Systems Models

scholarly journals Multivariate dynamical systems models for estimating causal interactions in fMRI

NeuroImage ◽  
2011 ◽  
Vol 54 (2) ◽  
pp. 807-823 ◽  
Author(s):  
Srikanth Ryali ◽  
Kaustubh Supekar ◽  
Tianwen Chen ◽  
Vinod Menon
Keyword(s):  
Dynamical Systems ◽  
Systems Models ◽  
Dynamical Systems Models

scholarly journals Modeling Epidemics: A Primer and Numerus Software Implementation

2017 ◽  
Author(s):  
Wayne M. Getz ◽  
Richard Salter ◽  
Oliver Muellerklein ◽  
Hyun S. Yoon ◽  
Krti Tallam
Keyword(s):  
Dynamical Systems ◽  
Software Implementation ◽  
Epidemiological Models ◽  
Model Builder ◽  
Systems Models ◽  
Spatially Homogeneous ◽  
Dynamical Systems Models

AbstractEpidemiological models are dominated by SEIR (Susceptible, Exposed, Infected and Removed) dynamical systems formulations and their elaborations. These formulations can be continuous or discrete, deterministic or stochastic, or spatially homogeneous or heterogeneous, the latter often embracing a network formulation. Here we review the continuous and discrete deterministic and discrete stochastic formulations of the SEIR dynamical systems models, and we outline how they can be easily and rapidly constructed using the Numerus Model Builder, a graphically-driven coding platform. We also demonstrate how to extend these models to a metapopulation setting using both the Numerus Model Builder network and geographical mapping tools.

scholarly journals On Smoother Attributions using Neural Stochastic Differential Equations

2021 ◽  
Author(s):  
Sumit Jha ◽  
Rickard Ewetz ◽  
Alvaro Velasquez ◽  
Susmit Jha
Keyword(s):  
Neural Networks ◽  
Dynamical Systems ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Systems Theory ◽  
Dynamical Systems Theory ◽  
Small Perturbations

Several methods have recently been developed for computing attributions of a neural network's prediction over the input features. However, these existing approaches for computing attributions are noisy and not robust to small perturbations of the input. This paper uses the recently identified connection between dynamical systems and residual neural networks to show that the attributions computed over neural stochastic differential equations (SDEs) are less noisy, visually sharper, and quantitatively more robust. Using dynamical systems theory, we theoretically analyze the robustness of these attributions. We also experimentally demonstrate the efficacy of our approach in providing smoother, visually sharper and quantitatively robust attributions by computing attributions for ImageNet images using ResNet-50, WideResNet-101 models and ResNeXt-101 models.

Are dynamical systems the answer?

2001 ◽  
Vol 24 (1) ◽  
pp. 50-51 ◽  
Author(s):  
Arthur B. Markman
Keyword(s):  
Dynamical Systems ◽  
Embodied Cognition ◽  
Cognitive Processing ◽  
Systems Approach ◽  
Sensorimotor Coordination ◽  
Proposed Model ◽  
Systems Models ◽  
Dynamical Systems Models

The proposed model is put forward as a template for the dynamical systems approach to embodied cognition. In order to extend this view to cognitive processing in general, however, two limitations must be overcome. First, it must be demonstrated that sensorimotor coordination of the type evident in the A-not-B error is typical of other aspects of cognition. Second, the explanatory utility of dynamical systems models must be clarified.

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