scholarly journals Inferring single-trial neural population dynamics using sequential auto-encoders

2017 ◽  
Author(s):  
Chethan Pandarinath ◽  
Daniel J. O’Shea ◽  
Jasmine Collins ◽  
Rafal Jozefowicz ◽  
Sergey D. Stavisky ◽  
...  
Keyword(s):  
Nonlinear Dynamical System ◽  
Simultaneous Recording ◽  
Neural Population ◽  
Single Trial ◽  
Population Activity ◽  
Nonlinear Dynamical ◽  
System A ◽  
Behavioral Choices ◽  
Neural Spiking ◽  
Human Motor

Neuroscience is experiencing a data revolution in which simultaneous recording of many hundreds or thousands of neurons is revealing structure in population activity that is not apparent from single-neuron responses. This structure is typically extracted from trial-averaged data. Single-trial analyses are challenging due to incomplete sampling of the neural population, trial-to-trial variability, and fluctuations in action potential timing. Here we introduce Latent Factor Analysis via Dynamical Systems (LFADS), a deep learning method to infer latent dynamics from single-trial neural spiking data. LFADS uses a nonlinear dynamical system (a recurrent neural network) to infer the dynamics underlying observed population activity and to extract ‘de-noised’ single-trial firing rates from neural spiking data. We apply LFADS to a variety of monkey and human motor cortical datasets, demonstrating its ability to predict observed behavioral variables with unprecedented accuracy, extract precise estimates of neural dynamics on single trials, infer perturbations to those dynamics that correlate with behavioral choices, and combine data from non-overlapping recording sessions (spanning months) to improve inference of underlying dynamics. In summary, LFADS leverages all observations of a neural population’s activity to accurately model its dynamics on single trials, opening the door to a detailed understanding of the role of dynamics in performing computation and ultimately driving behavior.

scholarly journals Multivaluedness in Networks: Exemplars

2020 ◽  
Author(s):  
Anton van Wyk ◽  
Guanrong Chen ◽  
Eric W. M. Wong
Keyword(s):  
Dynamical System ◽  
Random Process ◽  
Nonlinear Dynamical System ◽  
Linear Estimator ◽  
Nonlinear Dynamical ◽  
System A ◽  
Input And Output ◽  
Different Types ◽  
The Impact

This brief presents the first observations of multivaluedness in four systems: a random process, a nonlinear nondynamical system, a nonlinear dynamical system with nonlinearly sensed input and output and an adaptive linear estimator. The preliminary findings reported here, suggest the impact of multivaluedness in different types of networks to range from adverse to benign or even essential.

scholarly journals Gaussian-Process Factor Analysis for Low-Dimensional Single-Trial Analysis of Neural Population Activity

2009 ◽  
Vol 102 (1) ◽  
pp. 614-635 ◽  
Author(s):  
Byron M. Yu ◽  
John P. Cunningham ◽  
Gopal Santhanam ◽  
Stephen I. Ryu ◽  
Krishna V. Shenoy ◽  
...  
Keyword(s):  
Factor Analysis ◽  
Gaussian Process ◽  
Predictive Ability ◽  
Neural Population ◽  
Single Trial ◽  
Two Stage ◽  
Population Activity ◽  
Process Factor ◽  
Low Dimensional ◽  
Neural Population Activity

We consider the problem of extracting smooth, low-dimensional neural trajectories that summarize the activity recorded simultaneously from many neurons on individual experimental trials. Beyond the benefit of visualizing the high-dimensional, noisy spiking activity in a compact form, such trajectories can offer insight into the dynamics of the neural circuitry underlying the recorded activity. Current methods for extracting neural trajectories involve a two-stage process: the spike trains are first smoothed over time, then a static dimensionality-reduction technique is applied. We first describe extensions of the two-stage methods that allow the degree of smoothing to be chosen in a principled way and that account for spiking variability, which may vary both across neurons and across time. We then present a novel method for extracting neural trajectories—Gaussian-process factor analysis (GPFA)—which unifies the smoothing and dimensionality-reduction operations in a common probabilistic framework. We applied these methods to the activity of 61 neurons recorded simultaneously in macaque premotor and motor cortices during reach planning and execution. By adopting a goodness-of-fit metric that measures how well the activity of each neuron can be predicted by all other recorded neurons, we found that the proposed extensions improved the predictive ability of the two-stage methods. The predictive ability was further improved by going to GPFA. From the extracted trajectories, we directly observed a convergence in neural state during motor planning, an effect that was shown indirectly by previous studies. We then show how such methods can be a powerful tool for relating the spiking activity across a neural population to the subject's behavior on a single-trial basis. Finally, to assess how well the proposed methods characterize neural population activity when the underlying time course is known, we performed simulations that revealed that GPFA performed tens of percent better than the best two-stage method.

scholarly journals STABILITY AND STABILIZATION OF NONLINEAR DYNAMICAL SYSTEMS

2017 ◽  
Vol 20 (1) ◽  
pp. 61-70
Author(s):  
P. Sattayatham ◽  
R. Saelim ◽  
S. Sujitjorn
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Stability ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical System ◽  
Feedback Controllers ◽  
Nonlinear Dynamical ◽  
System A ◽  
Continuous Feedback ◽  
Stability And Stabilization ◽  
The Stability

Exponential and asymptotic stability for a class of nonlinear dynamical systems with uncertainties is investigated.  Based on the stability of the nominal system, a class of bounded continuous feedback controllers is constructed.  By such a class of controllers, the results guarantee exponential and asymptotic stability of uncertain nonlinear dynamical system.  A numerical example is also given to demonstrate the use of the main result.

scholarly journals A deep learning framework for inference of single-trial neural population activity from calcium imaging with sub-frame temporal resolution

2021 ◽  
Author(s):  
Feng Zhu ◽  
Harrison A Grier ◽  
Raghav Tandon ◽  
Changjia Cai ◽  
Andrea Giovannucci ◽  
...  
Keyword(s):  
Deep Learning ◽  
Temporal Resolution ◽  
Calcium Imaging ◽  
Temporal Dynamics ◽  
Population Level ◽  
Neural Population ◽  
Single Trial ◽  
Population Activity ◽  
Temporal Precision ◽  
Network States

In many brain areas, neural populations act as a coordinated network whose state is tied to behavior on a moment-by-moment basis and millisecond timescale. Two-photon (2p) calcium imaging is a powerful tool to probe network-scale computation, as it can measure the activity of many individual neurons, monitor multiple layers simultaneously, and sample from identified cell types. However, estimating network states and dynamics from 2p measurements has proven challenging because of noise, inherent nonlinearities, and limitations on temporal resolution. Here we describe RADICaL, a deep learning method to overcome these limitations at the population level. RADICaL extends methods that exploit dynamics in spiking activity for application to deconvolved calcium signals, whose statistics and temporal dynamics are quite distinct from electrophysiologically-recorded spikes. It incorporates a novel network training strategy that exploits the timing of 2p sampling to recover network dynamics with high temporal precision. In synthetic tests, RADICaL infers network states more accurately than previous methods, particularly for high-frequency components. In real 2p recordings from sensorimotor areas in mice performing a "water grab" task, RADICaL infers network states with close correspondence to single-trial variations in behavior, and maintains high-quality inference even when neuronal populations are substantially reduced.

Multivaluedness in Networks: Exemplars

2020 ◽  
Author(s):  
Anton van Wyk ◽  
Guanrong Chen ◽  
Eric W. M. Wong
Keyword(s):  
Dynamical System ◽  
Random Process ◽  
Nonlinear Dynamical System ◽  
Linear Estimator ◽  
Nonlinear Dynamical ◽  
System A ◽  
Input And Output ◽  
Different Types ◽  
The Impact

This brief presents the first observations of multivaluedness in four systems: a random process, a nonlinear nondynamical system, a nonlinear dynamical system with nonlinearly sensed input and output and an adaptive linear estimator. The preliminary findings reported here suggest the impact of multivaluedness in different types of networks to range from adverse to benign or even essential.

Stochastic transition in a classical nonlinear dynamical system: A Lennard-Jones chain

1976 ◽  
Vol 29 (2) ◽  
pp. 1022-1027 ◽  
Author(s):  
E. Diana ◽  
L. Galgani ◽  
G. Casartelli ◽  
G. Casati ◽  
A. Scotti
Keyword(s):  
Dynamical System ◽  
Nonlinear Dynamical System ◽  
Nonlinear Dynamical ◽  
Lennard Jones ◽  
System A ◽  
Stochastic Transition

scholarly journals Multivaluedness in Networks: Exemplars

2020 ◽  
Author(s):  
Anton van Wyk ◽  
Guanrong Chen ◽  
Eric W. M. Wong
Keyword(s):  
Dynamical System ◽  
Random Process ◽  
Nonlinear Dynamical System ◽  
Linear Estimator ◽  
Nonlinear Dynamical ◽  
System A ◽  
Input And Output ◽  
Different Types ◽  
The Impact

This brief presents the first observations of multivaluedness in four systems: a random process, a nonlinear nondynamical system, a nonlinear dynamical system with nonlinearly sensed input and output and an adaptive linear estimator. The preliminary findings reported here suggest the impact of multivaluedness in different types of networks to range from adverse to benign or even essential.

scholarly journals Population dynamics of choice representation in dorsal premotor and primary motor cortex

2018 ◽  
Author(s):  
Diogo Peixoto ◽  
Roozbeh Kiani ◽  
Chandramouli Chandrasekaran ◽  
Stephen I. Ryu ◽  
Krishna V. Shenoy ◽  
...  
Keyword(s):  
Decision Making ◽  
Stimulus Duration ◽  
Primary Motor Cortex ◽  
Population Level ◽  
Motor Preparation ◽  
Neural Population ◽  
Decision Making Process ◽  
Decision Variable ◽  
Single Trial ◽  
Population Activity

SummaryStudies in multiple species have revealed the existence of neural signals that lawfully co-vary with different aspects of the decision-making process, including choice, sensory evidence that supports the choice, and reaction time. These signals, often interpreted as the representation of a decision variable (DV), have been identified in several motor preparation circuits and provide insight about mechanisms underlying the decision-making process. However, single-trial dynamics of this process or its representation at the neural population level remain poorly understood. Here, we examine the representation of the DV in simultaneously recorded neural populations of dorsal premotor (PMd) and primary motor (M1) cortices of monkeys performing a random dots direction discrimination task with arm movements as the behavioral report. We show that single-trial DVs covary with stimulus difficulty in both areas but are stronger and appear earlier in PMd compared to M1 when the stimulus duration is fixed and predictable. When temporal uncertainty is introduced by making the stimulus duration variable, single-trial DV dynamics are accelerated across the board and the two areas become largely indistinguishable throughout the entire trial. These effects are not trivially explained by the faster emergence of motor kinematic signals in PMd and M1. All key aspects of the data were replicated by a computational model that relies on progressive recruitment of units with stable choice-related modulation of neural population activity. In contrast with several recent results in rodents, decision signals in PMd and M1 are not carried by short sequences of activity in non-overlapping groups of neurons but are instead distributed across many neurons, which once recruited, represent the decision stably during individual behavioral epochs of the trial.

scholarly journals Identification of Stochastic Loads Applied to a Nonlinear Dynamical System Using an Uncertain Computational Model

2008 ◽  
Vol 2008 ◽  
pp. 1-16 ◽  
Author(s):  
C. Soize ◽  
A. Batou
Keyword(s):  
Dynamical System ◽  
Computational Model ◽  
Nonlinear Dynamical System ◽  
Likelihood Method ◽  
Parameter Uncertainties ◽  
Model Uncertainties ◽  
Nonlinear Dynamical ◽  
The Real ◽  
System A ◽  
Stochastic Loads

This paper deals with the identification of stochastic loads applied to a nonlinear dynamical system for which a few experimental responses are available using an uncertain computational model. Uncertainties are induced by the use of a simplified computational model to predict the responses of the real system. A nonparametric probabilistic approach of both parameter uncertainties and model uncertainties is implemented in the simplified computational model in order to take into account uncertainties. The level of uncertainties is identified using the maximum likelihood method. The identified stochastic simplified computational model which is obtained is then used to perform the identification of the stochastic loads applied to the real nonlinear dynamical system. A numerical validation of the complete methodology is presented.

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