scholarly journals Collective Stability of Networks of Winner-Take-All Circuits

2011 ◽  
Vol 23 (3) ◽  
pp. 735-773 ◽  
Author(s):  
Ueli Rutishauser ◽  
Rodney J. Douglas ◽  
Jean-Jacques Slotine
Keyword(s):  
High Gain ◽  
Stability And Convergence ◽  
Signal Restoration ◽  
State Dependent ◽  
Inhibitory Feedback ◽  
The Stability ◽  
Parameter Ranges ◽  
Winner Take All ◽  
Contraction Theory ◽  
Take All

The neocortex has a remarkably uniform neuronal organization, suggesting that common principles of processing are employed throughout its extent. In particular, the patterns of connectivity observed in the superficial layers of the visual cortex are consistent with the recurrent excitation and inhibitory feedback required for cooperative-competitive circuits such as the soft winner-take-all (WTA). WTA circuits offer interesting computational properties such as selective amplification, signal restoration, and decision making. But these properties depend on the signal gain derived from positive feedback, and so there is a critical trade-off between providing feedback strong enough to support the sophisticated computations while maintaining overall circuit stability. The issue of stability is all the more intriguing when one considers that the WTAs are expected to be densely distributed through the superficial layers and that they are at least partially interconnected. We consider how to reason about stability in very large distributed networks of such circuits. We approach this problem by approximating the regular cortical architecture as many interconnected cooperative-competitive modules. We demonstrate that by properly understanding the behavior of this small computational module, one can reason over the stability and convergence of very large networks composed of these modules. We obtain parameter ranges in which the WTA circuit operates in a high-gain regime, is stable, and can be aggregated arbitrarily to form large, stable networks. We use nonlinear contraction theory to establish conditions for stability in the fully nonlinear case and verify these solutions using numerical simulations. The derived bounds allow modes of operation in which the WTA network is multistable and exhibits state-dependent persistent activities. Our approach is sufficiently general to reason systematically about the stability of any network, biological or technological, composed of networks of small modules that express competition through shared inhibition.

scholarly journals Sequential Activity in Asymmetrically Coupled Winner-Take-All Circuits

2014 ◽  
Vol 26 (9) ◽  
pp. 1973-2004 ◽  
Author(s):  
Hesham Mostafa ◽  
Giacomo Indiveri
Keyword(s):  
Network Architecture ◽  
External Input ◽  
Spike Timing ◽  
Fine Tuning ◽  
Learning Mechanisms ◽  
State Dependent ◽  
Synaptic Dynamics ◽  
Experimental Findings ◽  
Winner Take All ◽  
Take All

Understanding the sequence generation and learning mechanisms used by recurrent neural networks in the nervous system is an important problem that has been studied extensively. However, most of the models proposed in the literature are either not compatible with neuroanatomy and neurophysiology experimental findings, or are not robust to noise and rely on fine tuning of the parameters. In this work, we propose a novel model of sequence learning and generation that is based on the interactions among multiple asymmetrically coupled winner-take-all (WTA) circuits. The network architecture is consistent with mammalian cortical connectivity data and uses realistic neuronal and synaptic dynamics that give rise to noise-robust patterns of sequential activity. The novel aspect of the network we propose lies in its ability to produce robust patterns of sequential activity that can be halted, resumed, and readily modulated by external input, and in its ability to make use of realistic plastic synapses to learn and reproduce the arbitrary input-imposed sequential patterns. Sequential activity takes the form of a single activity bump that stably propagates through multiple WTA circuits along one of a number of possible paths. Because the network can be configured to either generate spontaneous sequences or wait for external inputs to trigger a transition in the sequence, it provides the basis for creating state-dependent perception-action loops. We first analyze a rate-based approximation of the proposed spiking network to highlight the relevant features of the network dynamics and then show numerical simulation results with spiking neurons, realistic conductance-based synapses, and spike-timing dependent plasticity (STDP) rules to validate the rate-based model.

scholarly journals A Nonlinear State Feedback for DC/DC Boost Converters

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
O. Gehan ◽  
E. Pigeon ◽  
T. Menard ◽  
M. Pouliquen ◽  
H. Gualous ◽  
...  
Keyword(s):  
State Feedback ◽  
High Gain ◽  
Stability And Convergence ◽  
Design Parameters ◽  
Robust Controller ◽  
Boost Converters ◽  
Control Approach ◽  
Integral Action ◽  
The Stability ◽  
Nonlinear State

This paper investigates the control problem for static boost type converters using a high gain state feedback robust controller incorporating an integral action. The robust feature allows to achieve the required performance in the presence of parametric uncertainties, while the integral action provides an offset free performance with respect to the desired levels of voltage. The adopted high gain approach is motivated by both fundamental as well as practical considerations, namely the underlying fundamental potential and the design parameter specification simplicity. The stability and convergence analysis has been carried out using an adequate Lyapunov approach, and the control system calibration is achieved throughout a few design parameters which are closely related to the desired dynamical performances. The effectiveness of the proposed control approach has been corroborated by numerical simulations and probing experimental results.

Dynamic analysis of winner-take-all neural networks with global inhibitory feedback

2015 ◽  
Author(s):  
Yongbin Yu ◽  
Ju Jin ◽  
Rongquan Zhang ◽  
Idongesit E. Ebong ◽  
Pinaki Mazumder
Keyword(s):  
Neural Networks ◽  
Dynamic Analysis ◽  
Inhibitory Feedback ◽  
Winner Take All ◽  
Take All

scholarly journals Mechanisms for Stable Bump Activity, Winner-Take-All and Group Selection in Neuronal Spiking Networks

2016 ◽  
Author(s):  
Yanqing Chen
Keyword(s):  
Group Selection ◽  
Major Function ◽  
Recurrent Excitation ◽  
Spiking Network ◽  
Sensory Maps ◽  
Central Nervous Systems ◽  
Spiking Networks ◽  
The Stability ◽  
Winner Take All ◽  
Take All

AbstractA major function of central nervous systems is to discriminate different categories or types of sensory input. Neuronal networks accomplish such tasks by learning different sensory maps at several stages of neural hierarchy, such that different neurons fire selectively to reflect different internal or external patterns and states. The exact mechanisms of such map formation processes in the brain are not totally understood. Here we study the mechanism by which a simple recurrent/reentrant neuronal network accomplish group selection and discrimination to different inputs in order to generate sensory maps. We describe the conditions and mechanism of transition from a rhythmic epileptic state (in which all neurons fire synchronized and indiscriminately to any input) to a winner-take-all state in which only a subset of neurons fire for a specific input. We prove an analytic condition under which a stable bump solution and a soft winner-take-all state can emerge from the local recurrent excitation-inhibition interactions in a three-layer spiking network with distinct excitatory and inhibitory populations, and demonstrate the importance of surround inhibitory connection topology on the stability of dynamic patterns in spiking neural network.

Interest Groups and Elections

2019 ◽  
pp. 339-357
Author(s):  
Jeffrey M. Berry
Keyword(s):  
Political Parties ◽  
Interest Groups ◽  
Campaign Finance ◽  
Organizational Forms ◽  
Super Pacs ◽  
New Organizational Forms ◽  
Winner Take All ◽  
The Impact ◽  
Take All

The relationships between interest groups, political parties, and elections have always been dynamic, but in recent years change has accelerated in ways that have favored some interests over others. This chapter considers these developments as the result of a variety of factors, the most critical of which are the growth of polarization, a new legal landscape for campaign finance, and new organizational forms. The chapter goes on to suggest, that as bipartisanship has ebbed, elections have become winner-take-all affairs and interest groups are pushed to choose sides. The chapter further suggests that the rise of super PACs is especially notable as wealthy individuals have become increasingly important, single sources of campaign money, supplanting in part traditional interest groups, especially conventional PACs. It concludes that even as sums spent by super PACs and other interest groups have skyrocketed, the impact of their direct spending on persuading voters remains uncertain.

Stabilization of networked switched affine systems with event-triggered strategy

2021 ◽  
pp. 014233122110213
Author(s):  
Dandan Li ◽  
Zhiqiang Zuo ◽  
Yijing Wang
Keyword(s):  
Affine Systems ◽  
Switching Law ◽  
Event Time ◽  
Sliding Motion ◽  
State Dependent ◽  
Event Triggering ◽  
Stability Issue ◽  
The Stability ◽  
Event Based ◽  
Selection Of

Using an event-based switching law, we address the stability issue for continuous-time switched affine systems in the network environment. The state-dependent switching law in terms of the region function is firstly developed. We combine the region function with the event-triggering mechanism to construct the switching law. This can provide more candidates for the selection of the next activated subsystem at each switching instant. As a result, it is possible for us to activate the appropriate subsystem to avoid the sliding motion. The Zeno behavior for the switched affine system can be naturally ruled out by guaranteeing a positive minimum inter-event time between two consecutive executions of the event-triggering threshold. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method.

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