Neural Rhythms

Oscillators, synchronization, and signal processing


Background:

Inference (prediction) is believed to be a fundamentally important computational function for biological sensory systems. For example, the Bayesian model of sensory (e.g., visual) signal processing postulates that the cortical networks in the brain encode a probabilistic belief about reality. The belief state (modeled as a posterior distribution in the Bayes; formalism) is updated based on a comparison between the novel stimuli (from senses) and the internal prediction.

Objective:

A natural question to ask then is whether there is a rigorous methodology (and algorithms) to implement complex forms of prediction (via Bayes theorem) at the level of neurons - the computing elements of the brain. The goal of our research is to develop neuro-morphic architectures for implementing Bayes rule. One such architecture is the coupled oscillator feedback particle filter model. A single oscillator is a simplified model of a single spiking neuron, and the coupled oscillator model represents a neuronal network.

Presentations:

2013 American Controls Conference Presentation

The mathematics of the coupled oscillator feedback particle filter model is described.

2012 American Controls Conference Simulation

The methodology is described with the aid of a model problem involving estimation of a ''walking gait cycle.''

Animations

2013 American Controls Conference Simulation

The mathematics of the coupled oscillator feedback particle filter model is described.

2012 American Controls Conference Simulation

The methodology is described with the aid of a model problem involving estimation of a ''walking gait cycle.''

Papers:

Tilton, A., P. G. Mehta and S. P. Meyn, ''Multi-dimensional Feedback Particle Filter for Coupled Oscillators,'' In the Proceedings of the American Control Conference, Washington DC, 2421-2427, June 2013.

Abstract and Downloads

This paper presents a methodology for state estimation of coupled oscillators from noisy observations. The methodology is comprised of two parts: modeling and estimation. The objective of the modeling is to express dynamics in terms of the so-called phase variables. For nonlinear estimation, a coupled-oscillator feedback particle filter is introduced.

The filter is based on the construction of a large population of oscillators with mean-field coupling. The empirical distribution of the population encodes the posterior distribution of the phase variables. The methodology is illustrated with two numerical examples.

Tilton, A., E. Hsiao-Wecksler and P. G. Mehta, ''Filtering with Rhythms: Application to Estimation of Gait Cycle,'' In the Proceedings of the American Control Conference, Montreal, 3433-3438, June 2012.

Abstract and Downloads

The aim of this paper is to describe a coupled oscillator model for Bayesian inference. The coupled oscillator model comprises of a large number of oscillators with mean- field coupling. The collective dynamics of the oscillators are used to solve an inference problem: the empirical distribution of the population encodes a ‘belief state’ (posterior distribution) that is continuously updated based on noisy measurements. In effect, the coupled oscillator model works as a particle filter.

The framework is described here with the aid of a model problem involving estimation of a walking gait cycle. For this problem, the coupled oscillator particle filter is developed, and demonstrated on experimental data taken from an Ankle-foot Orthosis (AFO) device.

Acknowledgements:

Financial support from the Air Force Office of Scientific Research (AFOSR) grant FA9550-09-1-0190 and the National Science Foundation (NSF) grant 0931416 is gratefully acknowledged.