Wenxue Wang

Bio-Inspired Sensor Design with an Array of Coupled Lasers

The basic idea of the paper is to use neurocomputational features of weakly connected neural networks of oscillators in pattern recognition. Stable synchronized states of the neural networks where artificial neurons are lasers with equal natural frequencies are prespecified with connection matrices. A set of memorized patterns are associated with the prescribed equilibria in phase relations with which neurons oscillate. Any pattern to be recognized in the neighborhood of the memorized patterns will reach the corresponding stable synchronized state. Phase locking takes part in the recognition mechanism. Kuramotos model is used in designing equilibria of laser networks.

Kuramoto Models, Coupled Oscillations and laser networks

In this paper we study the problem of stability for one of the most popular models of coupled phase oscillators, the Kuramoto model. The Kuramoto model is used to describe the phenomenon of collective synchronization, in which an enormous system of oscillators spontaneously locks to a common frequency although the oscillators have distinct natural frequencies. In the paper we consider the stability of the Kuramoto model of coupled oscillators with identical natural frequency and provide a stability analysis of phase difference equilibrium. The stability of the phase difference equilibrium make it possible to apply the Kuramoto model in pattern recognition.

Stability Analysis on Kuramoto Model of Coupled Oscillators

Abstract In this paper we study the problem of stability for one of the most popular models of coupled phase oscillators, the Kuramoto model. The Kuramoto model is used to describe the phenomenon of collective synchronization, in which an enormous system of oscillators spontaneously locks to a common frequency although the oscillators have distinct natural frequencies. In the paper we consider the stability of the Kuramoto model of coupled oscillators with identical natural frequency and provide a stability analysis of phase difference equilibrium. The stability of the phase difference equilibrium make it possible to apply the Kuramoto model in pattern recognition.

Modeling diurnal rhythms with an array of phase dynamic oscillators

Behavior of living organisms is strongly modulated by light especially by the day and night cycle giving rise to a cyclic pattern of activities. Such a pattern helps the organism to coordinate their activities and maintain a balance between what could be performed during the dasiadaypsila and what could be relegated to dasianightpsila. This cyclic pattern, called the dasiacircadian rhythmpsila, is a biological phenomenon observed in a large number of organisms ranging from unicellular bacteria to human beings and is present in data collected at various levels viz. transcriptome, proteome etc. In this paper, our goal is to analyze transcriptome data from cyanothece, a photosynthetic cyanobacteria, for the purpose of discovering genes whose expressions are rhythmic, especially those for which these rhythms have a 24 hours cycle. Subsequently we propose a model with a network of three phase oscillators for each one of the twenty four hours cycle. Each of the three phase oscillators is chosen to maintain a phase difference of 120 degrees between each other. All the oscillators are connected to an internal clock that is designed to maintain a phase activity close to a master clock derived using KaiC proteins. In cyanobacteria it is believed that the KaiC proteins provide the internal rhythm. The model parameters, viz. connection strengths between the master clock and peripheral oscillators and the parameters computing the linear combinations of the oscillator phase variables, are optimized to provide a close match to the observed gene expressions even when the frequency of the internal clock and the natural frequencies of the oscillators vary within a certain range. As a final step, the oscillator network model has been used to isolate genes, and hence the associated subprocesses, whose expression cycles are robust with respect to variations in the oscillator frequencies.

Identification and Modeling of Co-Rhythmic Genes from Micro-array Time Series Data ⋆

Abstract ‘Circadian Rhythm’ is a biological phenomenon observed in a large number of organisms ranging from unicellular bacteria to human beings. In this paper, transcriptome data from Cyanothece, a photosynthetic cyanobacteria, has been analyzed for the purpose of discovering genes whose expressions are rhythmically close (co-rhythmic). Subsequently we study if these rhythms can be modeled, up to phase, using a cascade of three phase oscillators. One of the phase oscillator in the network is derived from the model of a ‘limit cycle oscillator’ using KaiC protein (the master clock). We conclude that ‘Circadian Rhythms in Cyanothece transcriptome data can be dynamically modeled up to phase using a single master clock derived from limit cycle oscillator using KaiC protein cascaded with a pair of interconnected phase oscillators. Biologically substrates of the phase oscillators are presently unknown.

Detection in Bio-inspired Visual Systems using Networks of Oscillators

Animals routinely rely on their eyes to localize fixed and moving targets especially with the goal of either avoiding or capturing them. Detection of position of targets in space is an important problem in such a localization process for the motor control circuit to actuate a successful movement. The purpose of this paper is to sketch a binocular visual system that includes image capturing, retinal projection, sparse representation and data fusion, multi-neural encoding in the cortex down to detection of depth of objects from activity waves using nonlinear dynamics of an oscillatory network. The general strategies from visual circuitry, some of which may not be employed by the animal, could perhaps be employed in building machines with multiple sensors

Detection of depth in binocular visual systems using Kuramoto models

Animals routinely rely on their eyes to localize fixed and moving targets especially with the goal of either avoiding or capturing them. Detection of position of targets in space is an important problem in such a localization process for the motor control circuit to actuate a successful movement. The purpose of this paper is to sketch a binocular visual system that includes image capturing, retinal projection, sparse representation and data fusion, multi-neural encoding in the cortex down to detection of depth of objects from activity waves using nonlinear dynamics of an oscillatory network. The general strategies from visual circuitry, some of which may not be employed by the animal, could perhaps be employed in building machines with multiple sensors

Localization of point targets from cortical waves using ARMA models

Visual stimuli elicit waves of activity that propagate across the visual cortex of turtles. It is believed that these activity waves encode features of the visual stimuli, viz. position and velocity of targets. An important problem is to estimate the target location from the activity waves of the visual cortex. In this paper, we have used a large scale model of the turtle visual cortex to simulate the response of the cortex to stationary and moving visual stimuli. Subsequently, we have estimated the position and velocity of the target from the neural activities of the cortex by constructing an autoregressive and moving average (ARMA) Model. The input to the model is the neuronal response suitably smoothed by a low pass filter. The output of the ARMA model is precisely the prediction of the cortical inputs. This paper illustrates the role of ARMA models in deciphering the location and velocity of visual targets from the associated cortical waves.

Natural target localization from activity waves in the turtle visual cortex

Estimating natural targets in the visual space is an important problem in neuroscience primarily because animals have to negotiate targets in order to accomplish a task. In freshwater turtles, it is believed that the visual cortex plays a role in accomplishing the task of predicting target location. In this paper, we consider a set of fish-images and represent these images with a sparse and an over-complete set of spatial basis functions. The associated coefficient signals are further compressed, along every column, using principal components. This provides an appropriate input to the model of the visual cortex, and the associated cortical response of a large number of pyramidal cells is generated. We estimate the cortical input from the associated neural response by constructing an autoregressive and moving average (ARMA) model. The input to the model is the neuronal response suitably smoothed by a low pass filter. The output of the ARMA model is precisely the prediction of the cortical inputs. This paper illustrates the role of natural scene reconstruction from the activity waves of a set of pyramidal neurons.