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We present a mathematical analysis of a networks with Integrate-and-Fire neurons and adaptive conductances. Taking into account the realistic fact that the spike time is only known within some \textit{finite} precision, we propose a model…

Biological Physics · Physics 2010-11-09 B. Cessac , T. Vieville

The success of deep learning in the past decade is partially shrouded in the shadow of adversarial attacks. In contrast, the brain is far more robust at complex cognitive tasks. Utilizing the advantage that neurons in the brain communicate…

Neurons and Cognition · Quantitative Biology 2023-06-12 Jianhao Ding , Zhaofei Yu , Tiejun Huang , Jian K. Liu

In this paper a model of neural circuit in the brain has been proposed which is composed of cyclic sub-circuits. A big loop has been defined to be consisting of a feed forward path from the sensory neurons to the highest processing area of…

Neurons and Cognition · Quantitative Biology 2007-06-16 Kaushik Majumdar

Graphical chip-firing is a discrete dynamical system where chips are placed on the vertices of a graph and exchanged via simple firing moves. Recent work has sought to generalize chip-firing on graphs to higher dimensions, wherein graphs…

Combinatorics · Mathematics 2025-03-07 Sarah Brauner , Galen Dorpalen-Barry , Selvi Kara , Caroline Klivans , Lisa Schneider

Encoding static images into spike trains is a fundamental step for enabling Spiking Neural Networks (SNNs) to process visual information. However, widely used methods such as rate coding, Poisson encoding, and time-to-first-spike (TTFS)…

Neural and Evolutionary Computing · Computer Science 2026-04-23 Minchi Hu

Recurrently coupled networks of inhibitory neurons robustly generate oscillations in the gamma band. Nonetheless, the corresponding Wilson-Cowan type firing rate equation for such an inhibitory population does not generate such oscillations…

Neurons and Cognition · Quantitative Biology 2018-01-08 Federico Devalle , Alex Roxin , Ernest Montbrió

Network coding is a highly efficient data dissemination mechanism for wireless networks. Since network coded information can only be recovered after delivering a sufficient number of coded packets, the resulting decoding delay can become…

Information Theory · Computer Science 2016-11-17 Rui A. Costa , Daniele Munaretto , Joerg Widmer , Joao Barros

An unconventional encoding scheme called concurrent coding, has recently been demonstrated and shown to offer interesting features and benefits in comparison to conventional techniques, e.g. robustness against burst errors and improved…

Information Theory · Computer Science 2020-06-29 David M Benton

In computer simulations of spiking neural networks, often it is assumed that every two neurons of the network are connected by a probability of 2\%, 20\% of neurons are inhibitory and 80\% are excitatory. These common values are based on…

Neurons and Cognition · Quantitative Biology 2015-03-06 Hamed Seyed-allaei

In network coding, a flag code is a collection of flags, that is, sequences of nested subspaces of a vector space over a finite field. Due to its definition as the sum of the corresponding subspace distances, the flag distance parameter…

Information Theory · Computer Science 2021-12-01 Clementa Alonso-González , Miguel Ángel Navarro-Pérez

Integrate-and-Fire (IF) is an idealized model of the spike-triggering mechanism of a biological neuron. It is used to realize the bio-inspired event-based principle of information processing in neuromorphic computing. We show that IF is…

Signal Processing · Electrical Eng. & Systems 2025-01-22 Bernhard A. Moser , Anna Werzi , Michael Lunglmayr

Spiking Neural P systems, SNP systems for short, are biologically inspired computing devices based on how neurons perform computations. SNP systems use only one type of symbol, the spike, in the computations. Information is encoded in the…

Neural and Evolutionary Computing · Computer Science 2012-10-24 Francis George C. Cabarle , Kelvin C. Buño , Henry N. Adorna

We study analytically the dynamics of a network of sparsely connected inhibitory integrate-and-fire neurons in a regime where individual neurons emit spikes irregularly and at a low rate. In the limit when the number of neurons N tends to…

Disordered Systems and Neural Networks · Physics 2007-05-23 N. Brunel , V. Hakim

Third-generation neural networks, or Spiking Neural Networks (SNNs), aim at harnessing the energy efficiency of spike-domain processing by building on computing elements that operate on, and exchange, spikes. In this paper, the problem of…

Machine Learning · Statistics 2018-02-23 Alireza Bagheri , Osvaldo Simeone , Bipin Rajendran

The efficient coding theory postulates that single cells in a neuronal population should be optimally configured to efficiently encode information about a stimulus subject to biophysical constraints. This poses the question of how multiple…

Neurons and Cognition · Quantitative Biology 2023-08-11 Shuai Shao , Markus Meister , Julijana Gjorgjieva

Spiking Neural Networks (SNNs) draw inspiration from biological neurons to enable brain-like computation, demonstrating effectiveness in processing temporal information with energy efficiency and biological realism. Most existing SNNs are…

Neural and Evolutionary Computing · Computer Science 2026-03-03 Chengjie Ge , Yufeng Peng , Zihao Li , Qiyu Kang , Xueyang Fu , Xuhao Li , Qixin Zhang , Junhao Ren , Zheng-Jun Zha

In the last century, most sensorimotor studies of cortical neurons relied on average firing rates. Rate coding is efficient for fast sensorimotor processing that occurs within a few seconds. Much less is known about the neural mechanisms…

Neurons and Cognition · Quantitative Biology 2026-05-01 Terrence J. Sejnowski

Does synchronization between action potentials from different neurons in the visual system play a substantial role in solving the binding problem? The binding problem can be studied quantitatively in the broader framework of the information…

Biological Physics · Physics 2007-05-23 Simon R. Schultz , Huw D. R. Golledge , Stefano Panzeri

A Spiking Neural Network (SNN) can be trained indirectly by first training an Artificial Neural Network (ANN) with the conventional backpropagation algorithm, then converting it into an SNN. The conventional rate-coding method for SNNs uses…

Neural and Evolutionary Computing · Computer Science 2021-06-15 Ming Zhang , Nenggan Zheng , De Ma , Gang Pan , Zonghua Gu

Network coding is a technique to maximize communication rates within a network, in communication protocols for simultaneous multi-party transmission of information. Linear network codes are examples of such protocols in which the local…

Quantum Physics · Physics 2015-09-28 Niel de Beaudrap , Martin Roetteler