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93
Image segmentation based on oscillatory correlation
 Neural Computation
, 1997
"... 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 ..."
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Cited by 84 (23 self)
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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 figureground segregation. DeLiang Wang and David Terman Image Segmentation 1.
Reduction of the HodgkinHuxley Equations to a SingleVariable Threshold Model
 NEURAL COMPUTATION
, 1997
"... 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 fourdimensional neuron model of Hodgkin and Huxley as a concrete example. The model is approximat ..."
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Cited by 71 (23 self)
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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 fourdimensional 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 firstorder term is linear in the input and has the typical form of an elementary postsynaptic potential. Higherorder 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 zeroorder 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...
Generalized IntegrateandFire Models of Neuronal Activity Approximate Spike Trains of a . . .
"... We demonstrate that singlevariable integrateandfire models can quantitatively capture the dynamics of a physiologicallydetailed model for fastspiking cortical neurons. Through a systematic set of approximations, we reduce the conductance based model to two variants of integrateandfire mode ..."
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Cited by 59 (15 self)
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We demonstrate that singlevariable integrateandfire models can quantitatively capture the dynamics of a physiologicallydetailed model for fastspiking cortical neurons. Through a systematic set of approximations, we reduce the conductance based model to two variants of integrateandfire models. In the first variant (nonlinear integrateandfire 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
Parameter estimation for differential equations: A generalized smoothing approach
 JOURNAL OF THE ROYAL STATISTICAL SOCIETY, SERIES B
, 2007
"... We propose a new method for estimating parameters in nonlinear 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 noi ..."
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Cited by 41 (8 self)
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We propose a new method for estimating parameters in nonlinear 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 realworld data from chemistry and from the progress of the autoimmune disease lupus.
Dynamics of Membrane Excitability Determine Interspike Interval Variability: A Link Between Spike Generation Mechanisms and Cortical Spike Train Statistics
, 1998
"... 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 saddlenode dynamics underlie excitability (Rinzel & Ermentrout ..."
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Cited by 41 (5 self)
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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 saddlenode dynamics underlie excitability (Rinzel & Ermentrout, 1989). We present a canonical model for type I membranes, the θneuron. The θneuron 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 MorrisLecar (ML) neural model with random synaptic inputs: type I ML 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.
Primitive Auditory Segregation Based On Oscillatory Correlation
 Cognitive Science
, 1996
"... 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 twodimensional network of relaxation oscillators with a glob ..."
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Cited by 27 (7 self)
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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 twodimensional 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...
A twocurrent model for the dynamics of cardiac membrane
 Bulletin of Mathematical Biology
"... In this paper we introduce and study a model for electrical activity of cardiac membrane which incorporates only an inward and an outward current. This model is useful for three reasons: (1) Its simplicity, comparable to the FitzHugh–Nagumo model, makes it useful in numerical simulations, especially ..."
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Cited by 25 (3 self)
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In this paper we introduce and study a model for electrical activity of cardiac membrane which incorporates only an inward and an outward current. This model is useful for three reasons: (1) Its simplicity, comparable to the FitzHugh–Nagumo model, makes it useful in numerical simulations, especially in two or three spatial dimensions where numerical efficiency is so important. (2) It can be understood analytically without recourse to numerical simulations. This allows us to determine rather completely how the parameters in the model affect its behavior which in turn provides insight into the effects of the many parameters in more realistic models. (3) It naturally gives rise to a onedimensional map which specifies the action potential duration as a function of the previous diastolic interval. For certain parameter values, this map exhibits a new phenomenon—subcritical alternans— that does not occur for the commonly used exponential map.
On dynamics of integrateandfire neural networks with adaptive conductances
 Frontiers in Neuroscience
, 2008
"... We present a mathematical analysis of a networks with IntegrateandFire neurons with conductance based synapses. Taking into account the realistic fact that the spike time is only known within some finite precision, we propose a model where spikes are effective at times multiple of a characteristic ..."
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Cited by 23 (11 self)
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We present a mathematical analysis of a networks with IntegrateandFire neurons with conductance based synapses. Taking into account the realistic fact that the spike time is only known within some finite precision, we propose a model where spikes are effective at times multiple of a characteristic time scale δ, where δ can be arbitrary small (in particular, well beyond the numerical precision). We make a complete mathematical characterization of the modeldynamics and obtain the following results. The asymptotic dynamics is composed by finitely many stable periodic orbits, whose number and period can be arbitrary large and can diverge in a region of the synaptic weights space, traditionally called the “edge of chaos”, a notion mathematically well defined in the present paper. Furthermore, except at the edge of chaos, there is a onetoone correspondence between the membrane potential trajectories and the raster plot. This shows that the neural code is entirely “in the spikes ” in this case. As a key tool, we introduce an order parameter, easy to compute numerically, and closely related to a natural notion of entropy, providing a relevant characterization of the computational capabilities of the network. This allows us to compare the computational capabilities of leaky and IntegrateandFire models and conductance based models. The present study considers networks with constant input, and without timedependent plasticity, but the framework has been designed for both extensions.
Modelling the Perceptual Segregation of Double Vowels With a Network of Neural Oscillators
, 1996
"... 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 motivate ..."
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Cited by 19 (4 self)
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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 (phaselocked 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.
Cellular Automata for ReactionDiffusion Systems
 Physical Review E
, 1997
"... A class of cellular automata for reactiondiffusion 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 lookuptable with probabilistic rules. The rules are derived directly and s ..."
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Cited by 19 (3 self)
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A class of cellular automata for reactiondiffusion 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 lookuptable 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, reactiondiffusion systems, probabilistic rounding, simulation, modeling. Introduction Reactiondiffusion systems are an important class of systems to investigate nonlinear behavior. They also represent many problems arising in chemistry, biology, and other disciplines. Nonlinear reactiondiffusion systems can be simulated by standard numerical techniques, such as finite diffe...