1,844 research outputs found

    Robustness analysis of Cohen-Grossberg neural network with piecewise constant argument and stochastic disturbances

    Get PDF
    Robustness of neural networks has been a hot topic in recent years. This paper mainly studies the robustness of the global exponential stability of Cohen-Grossberg neural networks with a piecewise constant argument and stochastic disturbances, and discusses the problem of whether the Cohen-Grossberg neural networks can still maintain global exponential stability under the perturbation of the piecewise constant argument and stochastic disturbances. By using stochastic analysis theory and inequality techniques, the interval length of the piecewise constant argument and the upper bound of the noise intensity are derived by solving transcendental equations. In the end, we offer several examples to illustrate the efficacy of the findings

    Non-perturbative renormalization group analysis of nonlinear spiking networks

    Full text link
    The critical brain hypothesis posits that neural circuits may operate close to critical points of a phase transition, which has been argued to have functional benefits for neural computation. Theoretical and computational studies arguing for or against criticality in neural dynamics largely rely on establishing power laws or scaling functions of statistical quantities, while a proper understanding of critical phenomena requires a renormalization group (RG) analysis. However, neural activity is typically non-Gaussian, nonlinear, and non-local, rendering models that capture all of these features difficult to study using standard statistical physics techniques. Here, we overcome these issues by adapting the non-perturbative renormalization group (NPRG) to work on (symmetric) network models of stochastic spiking neurons. By deriving a pair of Ward-Takahashi identities and making a ``local potential approximation,'' we are able to calculate non-universal quantities such as the effective firing rate nonlinearity of the network, allowing improved quantitative estimates of network statistics. We also derive the dimensionless flow equation that admits universal critical points in the renormalization group flow of the model, and identify two important types of critical points: in networks with an absorbing state there is Directed Percolation (DP) fixed point corresponding to a non-equilibrium phase transition between sustained activity and extinction of activity, and in spontaneously active networks there is a \emph{complex valued} critical point, corresponding to a spinodal transition observed, e.g., in the Lee-Yang ϕ3\phi^3 model of Ising magnets with explicitly broken symmetry. Our Ward-Takahashi identities imply trivial dynamical exponents z∗=2z_\ast = 2 in both cases, rendering it unclear whether these critical points fall into the known DP or Ising universality classes

    An investigation of entorhinal spatial representations in self-localisation behaviours

    Get PDF
    Spatial-modulated cells of the medial entorhinal cortex (MEC) and neighbouring cortices are thought to provide the neural substrate for self-localisation behaviours. These cells include grid cells of the MEC which are thought to compute path integration operations to update self-location estimates. In order to read this grid code, downstream cells are thought to reconstruct a positional estimate as a simple rate-coded representation of space. Here, I show the coding scheme of grid cell and putative readout cells recorded from mice performing a virtual reality (VR) linear location task which engaged mice in both beaconing and path integration behaviours. I found grid cells can encode two unique coding schemes on the linear track, namely a position code which reflects periodic grid fields anchored to salient features of the track and a distance code which reflects periodic grid fields without this anchoring. Grid cells were found to switch between these coding schemes within sessions. When grid cells were encoding position, mice performed better at trials that required path integration but not on trials that required beaconing. This result provides the first mechanistic evidence linking grid cell activity to path integration-dependent behaviour. Putative readout cells were found in the form of ramp cells which fire proportionally as a function of location in defined regions of the linear track. This ramping activity was found to be primarily explained by track position rather than other kinematic variables like speed and acceleration. These representations were found to be maintained across both trial types and outcomes indicating they likely result from recall of the track structure. Together, these results support the functional importance of grid and ramp cells for self-localisation behaviours. Future investigations will look into the coherence between these two neural populations, which may together form a complete neural system for coding and decoding self-location in the brain

    Beam scanning by liquid-crystal biasing in a modified SIW structure

    Get PDF
    A fixed-frequency beam-scanning 1D antenna based on Liquid Crystals (LCs) is designed for application in 2D scanning with lateral alignment. The 2D array environment imposes full decoupling of adjacent 1D antennas, which often conflicts with the LC requirement of DC biasing: the proposed design accommodates both. The LC medium is placed inside a Substrate Integrated Waveguide (SIW) modified to work as a Groove Gap Waveguide, with radiating slots etched on the upper broad wall, that radiates as a Leaky-Wave Antenna (LWA). This allows effective application of the DC bias voltage needed for tuning the LCs. At the same time, the RF field remains laterally confined, enabling the possibility to lay several antennas in parallel and achieve 2D beam scanning. The design is validated by simulation employing the actual properties of a commercial LC medium

    Analog Photonics Computing for Information Processing, Inference and Optimisation

    Full text link
    This review presents an overview of the current state-of-the-art in photonics computing, which leverages photons, photons coupled with matter, and optics-related technologies for effective and efficient computational purposes. It covers the history and development of photonics computing and modern analogue computing platforms and architectures, focusing on optimization tasks and neural network implementations. The authors examine special-purpose optimizers, mathematical descriptions of photonics optimizers, and their various interconnections. Disparate applications are discussed, including direct encoding, logistics, finance, phase retrieval, machine learning, neural networks, probabilistic graphical models, and image processing, among many others. The main directions of technological advancement and associated challenges in photonics computing are explored, along with an assessment of its efficiency. Finally, the paper discusses prospects and the field of optical quantum computing, providing insights into the potential applications of this technology.Comment: Invited submission by Journal of Advanced Quantum Technologies; accepted version 5/06/202

    Global exponential periodicity of nonlinear neural networks with multiple time-varying delays

    Get PDF
    Global exponential periodicity of nonlinear neural networks with multiple time-varying delays is investigated. Such neural networks cannot be written in the vector-matrix form because of the existence of the multiple delays. It is noted that although the neural network with multiple time-varying delays has been investigated by Lyapunov-Krasovskii functional method in the literature, the sufficient conditions in the linear matrix inequality form have not been obtained. Two sets of sufficient conditions in the linear matrix inequality form are established by Lyapunov-Krasovskii functional and linear matrix inequality to ensure that two arbitrary solutions of the neural network with multiple delays attract each other exponentially. This is a key prerequisite to prove the existence, uniqueness, and global exponential stability of periodic solutions. Some examples are provided to demonstrate the effectiveness of the established results. We compare the established theoretical results with the previous results and show that the previous results are not applicable to the systems in these examples

    Breaking Implicit Assumptions of Physical Delay-Feedback Reservoir Computing

    Get PDF
    The Reservoir Computing (RC) paradigm is a supervised machine learning scheme using the natural computational ability of dynamical systems. Such dynamical systems incorporate time delays showcasing intricate dynamics. This richness in dynamics, particularly the system's transient response to external stimuli makes them suitable for RC. A subset of RCs, Delay-Feedback Reservoir Computing (DFRC), is distinguished by its unique features: a system that consists of a single nonlinear node and a delay-line, with `virtual' nodes defined along the delay-line by time-multiplexing procedure of the input. These characteristics render DFRC particularly useful for hardware integration. In this thesis, the aim is to break the implicit assumptions made in the design of physical DFRC based on Mackey-Glass dynamical system. The first assumption we address is the performance of DFRC is not affected by the attenuation in physcial delay-line as the nodes defined along it are 'virtual'. However, our experimental results contradict this. To mitigate the impact of losses along the delay line, we propose a methodology `Devirtualisation', which describes the procedure of directly tapping into the delay lines at the position of a `virtual' node, rather than at the delay line's end. It trade-offs the DFRC system's read-out frequency and the quantity of output lines. Masking plays a crucial role in DFRC, as it defines `virtual' nodes along the delay-line. The second assumption is that the mask used should randomly generated numbers uniformly distributed between [-u,u]. We experimentally compare Binary Weight Mask (BWM) vs. Random Weight Mask (RWM) under different scenarios; and investigate the randomness of BWM signal distribution's impact. The third implicit assumption is that, DFRC is designed to solve time series prediction tasks involving a single input and output with no external feedback. To break this assumption, we propose two approaches to mix multi-input signals into DFRC; to validate these approaches, a novel task for DFRC that inherently necessitates multiple inputs: the control of a forced Van der Pol oscillator system, is proposed
    • …
    corecore