A strong winner-take-all model based on integration of potential differences

A dynamic, strong winner-take-all model is presented. It is based on a limited integrator that is fed by potential differences between feedback from a single interneuron and the input value. The model does not require a special nonlinear function in the forward path. In equilibrium state, a single winner neuron transmits its input value to the output without change. For a two-neuron system the behaviour is shown graphically. Equilibrium states are determined for different types of input vectors.     

一种改进的winner-take-all模型及在图像中的应用

作为一种广泛存在于各个领域的竞争现象,关于赢者通吃(winner-take-all)的大部分研究太复杂以至于难以很好地理解该现象。为了用简单的方式解释winner-take-all现象,提出了一个改进的winner-take-all模型,由离散时间差分方程表示,该模型的状态空间是一个矩阵并且模型具有多范数可选性,对应的初始输入矩阵中具有最大输入值的元素最终获胜。对提出模型的收敛性和稳定性进行了严格的理论分析,并将该赢者通吃模型应用于图像处理的实验中,分别比较了单层和多层赢家通吃模型的效率。实验正确地生成了winner-take-all现象,表现了多层winner-take-all图像处理的高性能,理论和实验都验证了所提出模型的正确性和有效性。     

Analysis of oscillations in a reciprocally inhibitory network with synaptic depression

We present and analyze a model of a two-cell reciprocally inhibitory network that oscillates. The principal mechanism of oscillation is short-term synaptic depression. Using a simple model of depression and analyzing the system in certain limits, we can derive analytical expressions for various features of the oscillation, including the parameter regime in which stable oscillations occur, as well as the period and amplitude of these oscillations. These expressions are functions of three parameters: the time constant of depression, the synaptic strengths, and the amount of tonic excitation the cells receive. We compare our analytical results with the output of numerical simulations and obtain good agreement between the two. Based on our analysis, we conclude that the oscillations in our network are qualitatively different from those in networks that oscillate due to postinhibitory rebound, spike-frequency adaptation, or other intrinsic (rather than synaptic) adaptational mechanisms. In particular, our network can oscillate only via the synaptic escape mode of Skinner, Kopell, and Marder (1994).     

Simulating Ramsey-Type Fringes in a Pulsed Microwave-Driven Classical Josephson Junction

We present evidence for a close analogy between the nonlinear behaviour of a pulsed microwave-driven Josephson junction at low temperature and the experimentally observed behaviour of Josephson systems operated below the quantum transition temperature under similar conditions. We specifically address observations of Ramsey-type fringe oscillations, which can be understood in classical nonlinear dynamics as results of slow transient oscillations in a pulsed microwave environment. Simulations are conducted to mimic experimental measurements by recording the statistics of microwave-induced escape events from the anharmonic potential well of a zero-voltage state. Observations consistent with experimentally obtained Ramsey-type oscillations are found in the classical model. An erratum to this article can be found at     

Extracting number-selective responses from coherent oscillations in a computer model

Cortical neurons selective for numerosity may underlie an innate number sense in both animals and humans. We hypothesize that the number- selective responses of cortical neurons may in part be extracted from coherent, object-specific oscillations . Here, indirect evidence for this hypothesis is obtained by analyzing the numerosity information encoded by coherent oscillations in artificially generated spikes trains. Several experiments report that gamma-band oscillations evoked by the same object remain coherent, whereas oscillations evoked by separate objects are uncorrelated. Because the oscillations arising from separate objects would add in random phase to the total power summed across all stimulated neurons, we postulated that the total gamma activity, normalized by the number of spikes, should fall roughly as the square root of the number of objects in the scene, thereby implicitly encoding numerosity. To test the hypothesis, we examined the normalized gamma activity in multiunit spike trains, 50 to 1000 msec in duration, produced by a model feedback circuit previously shown to generate realistic coherent oscillations. In response to images containing different numbers of objects, regardless of their shape, size, or shading, the normalized gamma activity followed a square-root-of-n rule as long as the separation between objects was sufficiently large and their relative size and contrast differences were not too great. Arrays of winner-take-all numerosity detectors, each responding to normalized gamma activity within a particular band, exhibited tuning curves consistent with behavioral data. We conclude that coherent oscillations in principle could contribute to the number-selective responses of cortical neurons, although many critical issues await experimental resolution.     

Orientation tuning properties of simple cells in area V1 derived from an approximate analysis of nonlinear neural field models

We present a general approximation method for the mathematical analysis of spatially localized steady-state solutions in nonlinear neural field models. These models comprise several layers of excitatory and inhibitory cells. Coupling kernels between and inside layers are assumed to be gaussian shaped. In response to spatially localized (i.e., tuned) inputs, such networks typically reveal stationary localized activity profiles in the different layers. Qualitative properties of these solutions, like response amplitudes and tuning widths, are approximated for a whole class of nonlinear rate functions that obey a power law above some threshold and that are zero below. A special case of these functions is the semilinear function, which is commonly used in neural field models. The method is then applied to models for orientation tuning in cortical simple cells: first, to the one-layer model with "difference of gaussians" connectivity kernel developed by Carandini and Ringach (1997) as an abstraction of the biologically detailed simulations of Somers, Nelson, and Sur (1995); second, to a two-field model comprising excitatory and inhibitory cells in two separate layers. Under certain conditions, both models have the same steady states. Comparing simulations of the field models and results derived from the approximation method, we find that the approximation well predicts the tuning behavior of the full model. Moreover, explicit formulas for approximate amplitudes and tuning widths in response to changing input strength are given and checked numerically. Comparing the network behavior for different nonlinearities, we find that the only rate function (from the class of functions under study) that leads to constant tuning widths and a linear increase of firing rates in response to increasing input is the semilinear function. For other nonlinearities, the qualitative network response depends on whether the model neurons operate in a convex (e.g., x(2)) or concave (e.g., sqrt(x)) regime of their rate function. In the first case, tuning gradually changes from input driven at low input strength (broad tuning strongly depending on the input and roughly linear amplitudes in response to input strength) to recurrently driven at moderate input strength (sharp tuning, supralinear increase of amplitudes in response to input strength). For concave rate functions, the network reveals stable hysteresis between a state at low firing rates and a tuned state at high rates. This means that the network can "memorize" tuning properties of a previously shown stimulus. Sigmoid rate functions can combine both effects. In contrast to the Carandini-Ringach model, the two-field model further reveals oscillations with typical frequencies in the beta and gamma range, when the excitatory and inhibitory connections are relatively strong. This suggests a rhythmic modulation of tuning properties during cortical oscillations.     

Optoelectronic winner-take-all VLSI shunting neural network

In this paper we present an analog winner-take-all MOS VLSI (metal-oxide semiconductor/very large scale integration) optoelectronic network. By varying either the input current or circuit parameters, the circuit can evidence several different behaviors such as contrast enhancement, strict winner-take-all, or winner-take-all with hysteresis. Simulation and experimental results from the prototype circuit are also discussed.     

Limit cycle analysis of the verge and foliot clock escapement using impulsive differential equations and Poincaré maps

The verge and foliot escapement mechanism of a mechanical clock is a classical example of a feedback regulator. In this paper we analyse the dynamics of this mechanism to understand its operation from a feedback perspective. Using impulsive differential equations and Poincaré maps to model the dynamics of this closed-loop system, we determine conditions under which the system possesses a limit cycle, and we analyse the period and amplitude of the oscillations in terms of the inertias of the colliding masses and their coefficient of restitution.     

On robust state derivative feedback control for uncertain polytopic systems with uncertain sampling period and network-induced delay

This paper addresses the state derivative feedback control problem for uncertain polytopic systems subject to an uncertain sampling period and network-induced delay. The distinctive contribution relies on the direct design of a robust state derivative feedback controller employing an augmented discretized model derived in terms of the state derivative feedback such that network-induced delay and uncertain sampling periods can be incorporated from the original continuous-time state-space representation into the discretized model. Two augmented models are provided to handle longer input time delays, as well as delays less or equal to the sampling period. In this work, all the uncertain parameters are modeled as a polytopic form whose resulting discrete-time model has matrices with polynomial dependence on the uncertain parameters and an additive norm-bounded term featuring the discretization residual error. Moreover, synthesis conditions are derived using a set of linear matrix inequalities (LMI) to solve the stabilization problem for this class of systems under different input time delays. Finally, numerical simulations are carried out to evaluate the effectiveness of the proposed method.     

Analysis for a class of winner-take-all model

Tam et al. (1996) proposed a simple circuit of winner-take-all (WTA) neural network. Assuming no external input, they derived an analytic equation for its network response time. In this paper, we further analyze the network response time for a class of winner-take-all circuits involving self-decay and show that the network response time of such a class of WTA is the same as that of the simple WTA model.     

Tracking and robustness analysis for controlled microelectromechanical relays

The feedback control problem for microelectromechanical (MEM) relays is complicated by a quadratic nonlinearity in the dynamic model. We show that this nonlinearity imposes constraints on the reference trajectories that can be tracked and on the global convergence rate of the tracking error. Using a dynamic model that is applicable to both electrostatic and electromagnetic MEM relays, we introduce a new class of nonlinear tracking controls. In particular, we use Lyapunov theory to construct a state feedback that yields uniform global asymptotic stability and arbitrarily fast local exponential convergence of the tracking error. We then show how our control can be redesigned with partial‐state feedback under the assumption that only the movable electrode position and the electrical state (i.e. charge or flux) are fed back. Finally, we utilize input‐to‐state stability theory to quantify the robustness of our state feedback controller to parametric uncertainties. Our simulation results illustrate the good stability and tracking performance of the proposed control. They also illustrate how to craft a reference trajectory that satisfies the aforementioned constraints while being compatible with a typical relay operation. Copyright © 2007 John Wiley & Sons, Ltd.     

A competitive-layer model for feature binding and sensory segmentation

We present a recurrent neural network for feature binding and sensory segmentation: the competitive-layer model (CLM). The CLM uses topographically structured competitive and cooperative interactions in a layered network to partition a set of input features into salient groups. The dynamics is formulated within a standard additive recurrent network with linear threshold neurons. Contextual relations among features are coded by pairwise compatibilities, which define an energy function to be minimized by the neural dynamics. Due to the usage of dynamical winner-take-all circuits, the model gains more flexible response properties than spin models of segmentation by exploiting amplitude information in the grouping process. We prove analytic results on the convergence and stable attractors of the CLM, which generalize earlier results on winner-take-all networks, and incorporate deterministic annealing for robustness against local minima. The piecewise linear dynamics of the CLM allows a linear eigensubspace analysis, which we use to analyze the dynamics of binding in conjunction with annealing. For the example of contour detection, we show how the CLM can integrate figure-ground segmentation and grouping into a unified model.     

Anticipation-Based Temporal Sequences Learning in Hierarchical Structure

Temporal sequence learning is one of the most critical components for human intelligence. In this paper, a novel hierarchical structure for complex temporal sequence learning is proposed. Hierarchical organization, a prediction mechanism, and one-shot learning characterize the model. In the lowest level of the hierarchy, we use a modified Hebbian learning mechanism for pattern recognition. Our model employs both active 0 and active 1 sensory inputs. A winner-take-all (WTA) mechanism is used to select active neurons that become the input for sequence learning at higher hierarchical levels. Prediction is an essential element of our temporal sequence learning model. By correct prediction, the machine indicates it knows the current sequence and does not require additional learning. When the prediction is incorrect, one-shot learning is executed and the machine learns the new input sequence as soon as the sequence is completed. A four-level hierarchical structure that isolates letters, words, sentences, and strophes is used in this paper to illustrate the model     

Roles of coherent ongoing oscillations among dynamic cell assemblies in object perception

I constructed a cortical neural network model and investigated possible roles of coherent ongoing oscillations in membrane potentials of neurons in object perception. The model has a hierarchical structure consisting of two lower networks and one higher network that are reciprocally connected via divergent/convergent projections. Information about features and their relationships (or objects) is encoded by the population activities of neurons (or dynamic cell assemblies) of the lower networks and the higher network, respectively. The ongoing state of the network is expressed by 'random itinerancy' among these dynamic cell assemblies. Under the ongoing state, the dynamic cell assemblies belonging to the same object are transiently linked across the networks and coherently oscillate at lower frequencies (approximately 15 Hz). When the model perceives a presented object, the dynamic cell assemblies corresponding to the object are persistently linked together across the networks and coherently oscillate at higher frequencies (approximately 40 Hz). When the feedback pathways are impaired, the dynamic phase transition from the slow- to fast-oscillations is not induced by the object presentation, keeping the lower frequency oscillations (approximately 15 Hz) where the activated dynamic cell assemblies oscillate incoherently. Reaction times to the object presentation are greatly reduced if the ongoing oscillation frequencies fall within a specific range (approximately 20-30 Hz). I suggest that coherent ongoing slow-oscillations in cortical activity may serve as a ready state for sensory input, whereby the brain can respond effectively to sensory stimulation. Top-down processing via feedback pathways may give an essential contribution to the induction of coherent fast-oscillations across multiple cortical areas, by which relevant features are effectively integrated into a unified percept when stimulated with a sensory object.     

Nonrobustness of closed-loop stability for infinite-dimensional systems under sample and hold

It is a well-known principle, for finite-dimensional systems, that applying sampled-and-hold in the feedback loop around a stabilizing state feedback (or dynamic) controller results in a stable sampled-data feedback control system if the sampling period is small enough. The principle extends to infinite-dimensional systems with compact state feedback if either the input operator is bounded or the given state-space system is analytic. In this paper, we give an example for which this principle fails but which nevertheless satisfies certain necessary conditions arising in sampled-data control of infinite-dimensional systems.     

Parameter convergence in adaptive feedback linearizing control of limit cycling systems with input saturation

Adaptive feedback linearizing control schemes are used to suppress limit cycle oscillations in nonlinear systems where the system parameters are either unknown or uncertain. Parameter convergence is desirable in these schemes as it provides a measure of robustness of the scheme and also permits the unknown/uncertain system parameters to be estimated. In recent work, we have shown how using a persistently exciting forcing it is possible to achieve parameter convergence in nonlinear limit cycling systems. In practice, however, limits on the control input to the plant due to saturation must be considered, and the main goal of this work is to analyze the effect of input saturation on parameter convergence in an adaptive feedback linearization framework. In particular, a technique known as control hedging is incorporated and the effectiveness of this method for very severe saturation constraints has been evaluated. Results are presented for a single degree-of-freedom wing rock dynamics model and a multi degree-of-freedom combustion acoustics model showing successful parameter convergence even in the presence of input saturation.     

Simultaneous compensation of input and state delays for nonlinear systems

The problem of compensation of arbitrary large input delay for nonlinear systems was solved recently with the introduction of the nonlinear predictor feedback. In this paper we solve the problem of compensation of input delay for nonlinear systems with simultaneous input and state delays of arbitrary length. The key challenge, in contrast to the case of only input delay, is that the input delay-free system (on which the design and stability proof of the closed-loop system under predictor feedback are based) is infinite-dimensional. We resolve this challenge and we design the predictor feedback law that compensates the input delay. We prove global asymptotic stability of the closed-loop system using two different techniques—one based on the construction of a Lyapunov functional, and one using estimates on solutions. We present two examples, one of a nonlinear delay system in the feedforward form with input delay, and one of a scalar, linear system with simultaneous input and state delays.     

Cooperative robust output regulation problem for discrete‐time linear time‐delay multi‐agent systems

In this paper, we study the cooperative robust output regulation problem for discrete‐time linear multi‐agent systems with both communication and input delays by a distributed internal model approach. We first introduce the distributed internal model for discrete‐time multi‐agent systems with both communication and input delays. Then, we define the so‐called auxiliary system and auxiliary augmented system. Finally, we solve our problem by showing, under some standard assumptions, that if a distributed state feedback control or a distributed output feedback control solves the robust output regulation problem of the auxiliary system, then the same control law solves the cooperative robust output regulation problem of the original multi‐agent systems.     

Method of stochastic sensitivity synthesis in a stabilisation problem for nonlinear discrete systems with incomplete information

A problem of the synthesis of the assigned probabilistic distribution near the equilibrium of stochastic nonlinear discrete-time system with incomplete state information is considered. We construct a static feedback regulator which provides a required stochastic sensitivity of this equilibrium. It is shown that this problem is reduced to the solution of some quadratic matrix equations. The solvability of these quadratic equations is analysed, and attainability sets are described. In the two-dimensional case, two variants of the control input are discussed and compared. These general results are applied to the suppression of large-amplitude oscillations around the equilibria of the stochastically forced Henon model with noisy observations. We show how suggested control technique, by minimising the stochastic sensitivity, allows us to suppress chaos and provide a structural stabilisation.     

Robust control for a nonlinear servomechanism problem

This paper deals with the design of output feedback control to achieve asymptotic tracking and disturbance rejection for a class of nonlinear systems when the exogenous signals are generated by a known linear exosystem. The system under consideration is single-input single-output, input-output linearizable, minimum phase, and modelled by an input-output model of the form of an nth-order differential equation. We assume that, at steady state, the nonlinearities of the system can only introduce a finite number of harmonics of the original exosystem modes. This assumption enables us to identify a linear servo-compensator which is augmented with the original system. Moreover, we augment a series of m integrators at the input side, where m is the highest derivative of the input, and then represent the augmented system by a state model. The augmented system is stabilized via a separation approach in which a robust state feedback controller is designed first to ensure boundedness of all state variables and tracking error convergence; then, a high gain observer and control saturation are used to recover the asymptotic properties achieved under state feedback.