We study image segmentation on the basis of locally excitatory globally inhibitory oscillator networks (LEGION), whereby the phases of oscillators encode the binding of pixels. We introduce a potential for each oscillator so that only those oscillators with strong connections from their neighborhood can develop high potentials. Based on the concept of potential, a solution to remove noisy regions in an image is proposed for LEGION, so that it suppresses the oscillators corresponding to noisy regions, without affecting those corresponding to major regions. We show analytically that the resulting oscillator network separates an image into several major regions, plus a background consisting of all noisy regions, and illustrate network properties by computer simulation. The network exhibits a natural capacity in segmenting images. The oscillatory dynamics leads to a computer algorithm, which is applied successfully to segmenting real graylevel images. A number of issues regarding biological plausibility and perceptual organization are discussed. We argue that LEGION provides a novel and effective framework for image segmentation and figure-ground segregation. DeLiang Wang and David Terman Image Segmentation 1.

It is generally believed that a neuron is a threshold element which fires when some variable u reaches a threshold. Here we pursue the question of whether this picture can be justified and study the four-dimensional neuron model of Hodgkin and Huxley as a concrete example. The model is approximated by a response kernel expansion in terms of a single variable, the membrane voltage. The first-order term is linear in the input and has the typical form of an elementary postsynaptic potential. Higher-order kernels take care of nonlinear interactions between input spikes. In contrast to the standard Volterra expansion the kernels depend on the firing time of the most recent output spike. In particular, a zero-order kernel which describes the shape of the spike and the typical afterpotential is included. Our model neuron fires, if the membrane voltage, given by the truncated response kernel expansion crosses a threshold. The threshold model is tested on a spike train generated by t...

We demonstrate that single-variable integrate-and-fire models can quantitatively capture the dynamics of a physiologically-detailed model for fast-spiking cortical neurons. Through a systematic set of approximations, we reduce the conductance based model to two variants of integrate-and-fire models. In the first variant (non-linear integrate-and-fire model), parameters depend on the instantaneous membrane potential whereas in the second variant, they depend on the time elapsed since the last spike (Spike Response Model). The direct reduction links features of the simple models to biophysical features of the full conductance based model. To quantitatively

We propose a biophysical mechanism for the high interspike interval variability observed in cortical spike trains. The key lies in the nonlinear dynamics of cortical spike generation, which are consistent with type I membranes where saddle-node dynamics underlie excitability (Rinzel & Ermentrout, 1989). We present a canonical model for type I membranes, the θ-neuron. The θ-neuron is a phase model whose dynamics reflect salient features of type I membranes. This model generates spike trains with coefficient of variation (CV) above 0.6 when brought to firing by noisy inputs. This happens because the timing of spikes for a type I excitable cell is exquisitely sensitive to the amplitude of the suprathreshold stimulus pulses. A noisy input current, giving random amplitude “kicks” to the cell, evokes highly irregular firing across a wide range of firing rates; an intrinsically oscillating cell gives regular spike trains. We corroborate the results with simulations of the Morris-Lecar (M-L) neural model with random synaptic inputs: type I M-L yields high CVs. When this model is modified to have type II dynamics (periodicity arises via a Hopf bifurcation), however, it gives regular spike trains (CV below 0.3). Our results suggest that the high CV values such as those observed in cortical spike trains are an intrinsic characteristic of type I membranes driven to firing by “random” inputs. In contrast, neural oscillators or neurons exhibiting type II excitability should produce regular spike trains.

Auditory scene analysis is critical for complex auditory processing. We study auditory segregation from the neural network perspective, and develop a framework for primitive auditory scene analysis. The architecture is a laterally coupled two-dimensional network of relaxation oscillators with a global inhibitor. One dimension represents time and another one represents frequency. We show that this architecture, plus systematic delay lines, can in real time group auditory features into a stream by phase synchrony and segregate different streams by desynchronization. The network demonstrates a set of psychological phenomena regarding primitive auditory scene analysis, including dependency on frequency proximity and the rate of presentation, sequential capturing, and competition among different perceptual organizations. We offer a neurocomputational theory - shifting synchronization theory - for explaining how auditory segregation might be achieved in the brain, and the psychological pheno...

University for instruction in the language and principles of chemical engineering, many consultations and much useful advice. Appreciation is also due to the referees, whose comments on an earlier version of the paper have been invaluable. Summary. We propose a new method for estimating parameters in non-linear differential equations. These models represent change in a system by linking the behavior of a derivative of a process to the behavior of the process itself. Current methods for estimating parameters in differential equations from noisy data are computationally intensive and often poorly suited to statistical techniques such as inference and interval estimation. This paper describes a new method that uses noisy data to estimate the parameters defining a system of nonlinear differential equations. The approach is based on a modification of data smoothing methods along with a generalization of profiled estimation. We derive interval estimates and show that these have good coverage properties on data simulated from chemical engineering and neurobiology. The method is demonstrated using real-world data from chemistry and from the progress of the auto-immune disease lupus. Keywords: Differential equations, profiled estimation, estimating equations, Gauss-Newton

Relaxation oscillations exhibiting more than one time scale arise naturally from many physical systems. This paper proposes a method to numerically integrate large systems of relaxation oscillators. The numerical technique, called the singular limit method, is derived from analysis of relaxation oscillations in the singular limit. In such limit, system evolution gives rise to time instants at which fast dynamics takes place and intervals between them during which slow dynamics takes place. A full description of the method is given for LEGION (locally excitatory globally inhibitory oscillator networks), where fast dynamics, characterized by jumping which leads to dramatic phase shifts, is captured in this method by iterative operation and slow dynamics is entirely solved. The singular limit method is evaluated by computer experiments, and it produces remarkable speedup compared to other methods of integrating these systems. The speedup makes it possible to simulate large-scale oscillato...

Abstract not found

A class of cellular automata for reaction-diffusion systems is presented. It is based on a local average for the diffusive dynamics, and closely related to finite difference schemes. The reactive dynamics is implemented as a lookup-table with probabilistic rules. The rules are derived directly and systematically from the given differential equations, using probabilistic rounding to enforce the discretization of the concentration variables. For quantitatively correct modeling, such probabilistic rules are usually necessary, but in some cases a deterministic version proves sufficient. Keywords: Cellular automata, reaction-diffusion systems, probabilistic rounding, simulation, modeling. Introduction Reaction-diffusion systems are an important class of systems to investigate nonlinear behavior. They also represent many problems arising in chemistry, biology, and other disciplines. Nonlinear reaction-diffusion systems can be simulated by standard numerical techniques, such as finite diffe...

The ability of listeners to identify two simultaneously presented vowels can be improved by introducing a difference in fundamental frequency (F0) between the vowels. We propose an explanation for this phenomenon in the form of a computational model of concurrent sound segregation, which is motivated by neurophysiological evidence of oscillatory firing activity in the auditory cortex and thalamus. More specifically, the model represents the perceptual grouping of auditory frequency channels as synchronised (phase-locked with zero phase lag) oscillations in a neural network. Computer simulations on a vowel set used in psychophysical studies confirm that the model qualitatively matches the performance of human listeners; vowel identification performance increases with increasing difference in F0. Additionally, the model is able to replicate other findings relating to the perception of harmonic complexes in which one component is mistuned.