scholarly journals Recurrent Switching Dynamical Systems Models for Multiple Interacting Neural Populations

2020 ◽  
Author(s):  
Joshua I. Glaser ◽  
Matthew Whiteway ◽  
John P. Cunningham ◽  
Liam Paninski ◽  
Scott W. Linderman
Keyword(s):  
Dynamical Systems ◽  
Latent Variables ◽  
Mean Field Approximation ◽  
Neural Population ◽  
High Dimensional ◽  
Discrete State ◽  
Linear Dynamical Systems ◽  
Neural Populations ◽  
Systems Models ◽  
Dynamical Systems Models

AbstractModern recording techniques can generate large-scale measurements of multiple neural populations over extended time periods. However, it remains a challenge to model non-stationary interactions between high-dimensional populations of neurons. To tackle this challenge, we develop recurrent switching linear dynamical systems models for multiple populations. Here, each high-dimensional neural population is represented by a unique set of latent variables, which evolve dynamically in time. Populations interact with each other through this low-dimensional space. We allow the nature of these interactions to change over time by using a discrete set of dynamical states. Additionally, we parameterize these discrete state transition rules to capture which neural populations are responsible for switching between interaction states. To fit the model, we use variational expectation-maximization with a structured mean-field approximation. After validating the model on simulations, we apply it to two different neural datasets: spiking activity from motor areas in a non-human primate, and calcium imaging from neurons in the nematode C. elegans. In both datasets, the model reveals behaviorally-relevant discrete states with unique inter-population interactions and different populations that predict transitioning between these states.

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 Kindsversuscontinua: a review of psychometric approaches to uncover the structure of psychiatric constructs

2016 ◽  
Vol 46 (8) ◽  
pp. 1567-1579 ◽  
Author(s):  
D. Borsboom ◽  
M. Rhemtulla ◽  
A. O. J. Cramer ◽  
H. L. J. van der Maas ◽  
M. Scheffer ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Latent Variables ◽  
Latent Variable ◽  
Indicator Variables ◽  
Individual Time Series ◽  
Alternative Approaches ◽  
Systems Models ◽  
Grade Of Membership ◽  
Latent Structures ◽  
Exclusive Or

The question of whether psychopathology constructs are discrete kinds or continuous dimensions represents an important issue in clinical psychology and psychiatry. The present paper reviews psychometric modelling approaches that can be used to investigate this question through the application of statistical models. The relation between constructs and indicator variables in models with categorical and continuous latent variables is discussed, as are techniques specifically designed to address the distinction between latent categories as opposed to continua (taxometrics). In addition, we examine latent variable models that allow latent structures to have both continuous and categorical characteristics, such as factor mixture models and grade-of-membership models. Finally, we discuss recent alternative approaches based on network analysis and dynamical systems theory, which entail that the structure of constructs may be continuous for some individuals but categorical for others. Our evaluation of the psychometric literature shows that the kinds–continua distinction is considerably more subtle than is often presupposed in research; in particular, the hypotheses of kinds and continua are not mutually exclusive or exhaustive. We discuss opportunities to go beyond current research on the issue by using dynamical systems models, intra-individual time series and experimental manipulations.

scholarly journals A latent variable approach to decoding neural population activity

2020 ◽  
Author(s):  
Matthew R Whiteway ◽  
Bruno Averbeck ◽  
Daniel A Butts
Keyword(s):  
Latent Variables ◽  
Population Variability ◽  
Model Organisms ◽  
Neural Population ◽  
Simple Extension ◽  
Linear Discriminant ◽  
Variable Approach ◽  
Wide Range ◽  
Neural Populations ◽  
Low Dimensional

AbstractDecoding is a powerful approach for measuring the information contained in the activity of neural populations. As a result, decoding analyses are now used across a wide range of model organisms and experimental paradigms. However, typical analyses employ general purpose decoding algorithms that do not explicitly take advantage of the structure of neural variability, which is often low-dimensional and can thus be effectively characterized using latent variables. Here we propose a new decoding framework that exploits the low-dimensional structure of neural population variability by removing correlated variability that is unrelated to the decoded variable, then decoding the resulting denoised activity. We demonstrate the efficacy of this framework using simulated data, where the true upper bounds for decoding performance are known. A linear version of our decoder provides an estimator for the decoded variable that can be more efficient than other commonly used linear estimators such as linear discriminant analysis. In addition, our proposed decoding framework admits a simple extension to nonlinear decoding that compares favorably to standard feed-forward neural networks. By explicitly modeling shared population variability, the success of the resulting linear and nonlinear decoders also offers a new perspective on the relationship between shared variability and information contained in large neural populations.

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.

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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