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A fundamental problem in neuroscience is understanding how working memory -- the ability to store information at intermediate timescales, like 10s of seconds -- is implemented in realistic neuronal networks. The most likely candidate…

Sequences of neural activity arise in many brain areas, including cortex, hippocampus, and central pattern generator circuits that underlie rhythmic behaviors like locomotion. While network architectures supporting sequence generation vary…

Large language models have been successful at tasks involving basic forms of in-context reasoning, such as generating coherent language, as well as storing vast amounts of knowledge. At the core of the Transformer architecture behind such…

The brain can be considered as a system that dynamically optimizes the structure of anatomical connections based on the efficiency requirements of functional connectivity. To illustrate the power of this principle in organizing the…

Neuroscientific evidence shows that for most brain networks all pathways between cortical regions either pass through the thalamus or a transthalamic parallel route exists for any direct corticocortical connection. This paper seeks to…

Many patterning events in multi-cellular organisms rely on cell-to-cell contact signaling, such as the Notch pathway in metazoans. A particularly interesting phenomenon in this form of communication is lateral inhibition where a cell that…

Many research works deal with chaotic neural networks for various fields of application. Unfortunately, up to now these networks are usually claimed to be chaotic without any mathematical proof. The purpose of this paper is to establish,…

Spike-timing dependent plasticity (STDP) is an organizing principle of biological neural networks. While synchronous firing of neurons is considered to be an important functional block in the brain, how STDP shapes neural networks possibly…

Basic binary relations such as equality and inequality are fundamental to relational data structures. Neural networks should learn such relations and generalise to new unseen data. We show in this study, however, that this generalisation…

All higher order central nervous systems exhibit spontaneous neural activity, though the purpose and mechanistic origin of such activity remains poorly understood. We explore the ignition and spread of collective spontaneous…

Building on the first part of this paper, we develop the theory of functional asynchronous networks. We show that a large class of functional asynchronous networks can be (uniquely) represented as feedforward networks connecting events or…

Biological neural networks operate in the presence of task disruptions as they guide organisms toward goals. A familiar stream of stimulus-response causations can be disrupted by subtask streams imposed by the environment. For example,…

The activity of neurons is correlated, and this correlation affects how the brain processes information. We study the neural circuit mechanisms of correlations by analyzing a network model characterized by strong and heterogeneous…

Cognitive control is a suite of processes that helps individuals pursue goals despite resistance or uncertainty about what to do. Although cognitive control has been extensively studied as a dynamic feedback loop of perception, valuation,…

The global dynamics of gene regulatory networks are known to show robustness to perturbations in the form of intrinsic and extrinsic noise, as well as mutations of individual genes. One molecular mechanism underlying this robustness has…

There have been several attempts to mathematically understand neural networks and many more from biological and computational perspectives. The field has exploded in the last decade, yet neural networks are still treated much like a black…

The lack of studying the complex organization of directed network usually limits to the understanding of underlying relationship between network structures and functions. Structural controllability and structural predictability, two…

The structure of the axon-dendrite connections of neurons of the brain creates a rich spatial structure in which provided various combinations of signals surrounding neurons. Structure of dendritic trees and shape of dendritic spines allow…

Advanced feedforward control methods enable mechatronic systems to perform varying motion tasks with extreme accuracy and throughput. The aim of this paper is to develop a data-driven feedforward controller that addresses input…

The task of the brain is to look for structure in the external input. We study a network of integrate-and-fire neurons with several types of recurrent connections that learns the structure of its time-varying feedforward input by attempting…