Recognition of temporal patterns using state transitions of neural networks (auditory application)

Author(s):  
R. Futami ◽  
N. Hoshimiya
2020 ◽  
Vol 4 (2) ◽  
pp. 448-466
Author(s):  
Amrit Kashyap ◽  
Shella Keilholz

Large-scale patterns of spontaneous whole-brain activity seen in resting-state functional magnetic resonance imaging (rs-fMRI) are in part believed to arise from neural populations interacting through the structural network (Honey, Kötter, Breakspear, & Sporns, 2007 ). Generative models that simulate this network activity, called brain network models (BNM), are able to reproduce global averaged properties of empirical rs-fMRI activity such as functional connectivity (FC) but perform poorly in reproducing unique trajectories and state transitions that are observed over the span of minutes in whole-brain data (Cabral, Kringelbach, & Deco, 2017 ; Kashyap & Keilholz, 2019 ). The manuscript demonstrates that by using recurrent neural networks, it can fit the BNM in a novel way to the rs-fMRI data and predict large amounts of variance between subsequent measures of rs-fMRI data. Simulated data also contain unique repeating trajectories observed in rs-fMRI, called quasiperiodic patterns (QPP), that span 20 s and complex state transitions observed using k-means analysis on windowed FC matrices (Allen et al., 2012 ; Majeed et al., 2011 ). Our approach is able to estimate the manifold of rs-fMRI dynamics by training on generating subsequent time points, and it can simulate complex resting-state trajectories better than the traditional generative approaches.


Author(s):  
Hongjun Cao ◽  
Borja Ibarz

Hybrid dynamical systems combine evolution equations with state transitions. When the evolution equations are discrete-time (also called map-based), the result is a hybrid discrete-time system. A class of biological neural network models that has recently received some attention falls within this category: map-based neuron models connected by means of fast threshold modulation (FTM). FTM is a connection scheme that aims to mimic the switching dynamics of a neuron subject to synaptic inputs. The dynamic equations of the neuron adopt different forms according to the state (either firing or not firing) and type (excitatory or inhibitory) of their presynaptic neighbours. Therefore, the mathematical model of one such network is a combination of discrete-time evolution equations with transitions between states, constituting a hybrid discrete-time (map-based) neural network. In this paper, we review previous work within the context of these models, exemplifying useful techniques to analyse them. Typical map-based neuron models are low-dimensional and amenable to phase-plane analysis. In bursting models, fast–slow decomposition can be used to reduce dimensionality further, so that the dynamics of a pair of connected neurons can be easily understood. We also discuss a model that includes electrical synapses in addition to chemical synapses with FTM. Furthermore, we describe how master stability functions can predict the stability of synchronized states in these networks. The main results are extended to larger map-based neural networks.


1998 ◽  
Vol 10 (7) ◽  
pp. 1831-1846 ◽  
Author(s):  
Patrick D. Roberts

A general method is presented to classify temporal patterns generated by rhythmic biological networks when synaptic connections and cellular properties are known. The method is discrete in nature and relies on algebraic properties of state transitions and graph theory. Elements of the set of rhythms generated by a network are compared using a metric that quantifies the functional differences among them. The rhythms are then classified according to their location in a metric space. Examples are given, and biological implications are discussed.


Sign in / Sign up

Export Citation Format

Share Document