Synchronization for Nonlinear Complex Spatio-Temporal Networks with Multiple Time-Invariant Delays and Multiple Time-Varying Delays

2018 ◽  
Vol 50 (2) ◽  
pp. 1051-1064 ◽  
Author(s):  
Chengdong Yang ◽  
Tingwen Huang ◽  
Kejia Yi ◽  
Ancai Zhang ◽  
Xiangyong Chen ◽  
...  
Keyword(s):  
Multiple Time ◽  
Time Varying ◽  
Temporal Networks ◽  
Spatio Temporal ◽  
Time Invariant

scholarly journals Encoding sensory and motor patterns as time-invariant trajectories in recurrent neural networks

eLife ◽  
2018 ◽  
Vol 7 ◽  
Author(s):  
Vishwa Goudar ◽  
Dean V Buonomano
Keyword(s):  
Spoken Word ◽  
Multiple Time ◽  
Time Varying ◽  
Motor Patterns ◽  
Complex Time ◽  
Spatial Features ◽  
Temporal Features ◽  
Angular Velocities ◽  
Handwritten Signature ◽  
Time Invariant

Much of the information the brain processes and stores is temporal in nature—a spoken word or a handwritten signature, for example, is defined by how it unfolds in time. However, it remains unclear how neural circuits encode complex time-varying patterns. We show that by tuning the weights of a recurrent neural network (RNN), it can recognize and then transcribe spoken digits. The model elucidates how neural dynamics in cortical networks may resolve three fundamental challenges: first, encode multiple time-varying sensory and motor patterns as stable neural trajectories; second, generalize across relevant spatial features; third, identify the same stimuli played at different speeds—we show that this temporal invariance emerges because the recurrent dynamics generate neural trajectories with appropriately modulated angular velocities. Together our results generate testable predictions as to how recurrent networks may use different mechanisms to generalize across the relevant spatial and temporal features of complex time-varying stimuli.

scholarly journals Encoding Sensory and Motor Patterns as Time-Invariant Trajectories in Recurrent Neural Networks

2017 ◽  
Author(s):  
Vishwa Goudar ◽  
Dean V. Buonomano
Keyword(s):  
Spoken Word ◽  
Multiple Time ◽  
Time Varying ◽  
Motor Patterns ◽  
Complex Time ◽  
Spatial Features ◽  
Temporal Features ◽  
Angular Velocities ◽  
Handwritten Signature ◽  
Time Invariant

AbstractMuch of the information the brain processes and stores is temporal in nature—a spoken word or a handwritten signature, for example, is defined by how it unfolds in time. However, it remains unclear how neural circuits encode complex time-varying patterns. We show that by tuning the weights of a recurrent neural network (RNN), it can recognize and then transcribe spoken digits. The model elucidates how neural dynamics in cortical networks may resolve three fundamental challenges: first, encode multiple time-varying sensory and motor patterns as stable neural trajectories; second, generalize across relevant spatial features; third, identify the same stimuli played at different speeds—we show that this temporal invariance emerges because the recurrent dynamics generate neural trajectories with appropriately modulated angular velocities. Together our results generate testable predictions as to how recurrent networks may use different mechanisms to generalize across the relevant spatial and temporal features of complex time-varying stimuli.

scholarly journals Time Varying Grouping Variables in Markov Latent Class Analysis: Some Problems and Solutions

2018 ◽  
Vol 7 (5) ◽  
pp. 28
Author(s):  
Marcus E. Berzofsky ◽  
Paul P. Biemer
Keyword(s):  
Latent Class Analysis ◽  
Latent Class ◽  
Classification Error ◽  
Model Parameters ◽  
Multiple Time ◽  
Time Varying ◽  
Class Analysis ◽  
Data Sparseness ◽  
Advantages And Disadvantages ◽  
Time Invariant

Markov latent class analysis (MLCA) is a modeling technique for panel or longitudinal data that can be used to estimate the classification error rates (e.g., false positive and false negative rates for dichotomous items) for discrete outcomes with categorical predictors when gold-standard measurements are not available. Because panel surveys collect data at multiple time points, the grouping variables in the model may either be time varying or time invariant (static). Time varying grouping variables may be more correlated with either the latent construct or the measurement errors because they are measured simultaneously with the construct during the measurement process. However, they generate a large number of model parameters that can cause problems with data sparseness, model diagnostic validity, and model convergence. In this paper we investigate whether more parsimonious grouping variables that either summarize the variation of the time varying grouping variable or assume a structure that lacks memory of previous values of the grouping variables can be used instead, without sacrificing model fit or validity. We propose a simple diagnostic approach for comparing the validity of models that use time-invariant summary variables with their time-varying counterparts. To illustrate the methodology, this approach is applied to data from the National Crime Victimization Survey (NCVS) where greater parsimony and a reduction in data sparseness were achieved with no appreciable loss in model validity for the outcome variables considered. The approach is generalized for application to essentially any MLCA using time varying group variables and its advantages and disadvantages are discussed.

scholarly journals Extended dissipativity and non-fragile synchronization for Recurrent neural networks with multiple time-varying delays via sampled-data control

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
R. Anbuvithya ◽  
S. Dheepika Sri ◽  
R. Vadivel ◽  
Nallappan Gunasekaran ◽  
P. Hammachukiattikul
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Multiple Time ◽  
Time Varying ◽  
Sampled Data ◽  
Data Control ◽  
Sampled Data Control

scholarly journals Spatio-temporal integration in plant tropisms

2019 ◽  
Vol 16 (154) ◽  
pp. 20190038 ◽  
Author(s):  
Yasmine Meroz ◽  
Renaud Bastien ◽  
L. Mahadevan
Keyword(s):  
Response Function ◽  
Shoot Growth ◽  
Analytic Solution ◽  
Temporal Integration ◽  
Time Varying ◽  
Local Response ◽  
History Of ◽  
Non Local ◽  
Spatio Temporal ◽  
Plant Shoots

Tropisms, growth-driven responses to environmental stimuli, cause plant organs to respond in space and time and reorient themselves. Classical experiments from nearly a century ago reveal that plant shoots respond to the integrated history of light and gravity stimuli rather than just responding instantaneously. We introduce a temporally non-local response function for the dynamics of shoot growth formulated as an integro-differential equation whose solution allows us to qualitatively reproduce experimental observations associated with intermittent and unsteady stimuli. Furthermore, an analytic solution for the case of a pulse stimulus expresses the response function as a function of experimentally tractable variables, which we calculate for the case of the phototropic response of Arabidopsis hypocotyls. All together, our model enables us to predict tropic responses to time-varying stimuli, manifested in temporal integration phenomena, and sets the stage for the incorporation of additional effects such as multiple stimuli, gravitational sagging, etc.

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