相关论文: Functional methods for disordered neural networks

These notes attempt a self-contained introduction into statistical field theory applied to neural networks of rate units and binary spins. The presentation consists of three parts: First, the introduction of fundamental notions of…

Understanding of short-term synaptic depression (STSD) and other forms of synaptic plasticity is a topical problem in neuroscience. Here we study the role of STSD in the formation of complex patterns of brain rhythms. We use a cortical…

The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain's network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain…

Random neural networks are dynamical descriptions of randomly interconnected neural units. These show a phase transition to chaos as a disorder parameter is increased. The microscopic mechanisms underlying this phase transition are unknown,…

Neural-network models of high-level brain functions such as memory recall and reasoning often rely on the presence of stochasticity. The majority of these models assumes that each neuron in the functional network is equipped with its own…

Characterizing the in uence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences. In this article we study a primary model of disordered…

This article studies the dynamics of the mean-field approximation of continuous random networks. These networks are stochastic integrodifferential equations driven by Gaussian noise. The kernels in the integral operators are realizations of…

The brain is a highly complex system. Most of such complexity stems from the intermingled connections between its parts, which give rise to rich dynamics and to the emergence of high-level cognitive functions. Disentangling the underlying…

Recent experimental advances in neuroscience have opened new vistas into the immense complexity of neuronal networks. This proliferation of data challenges us on two parallel fronts. First, how can we form adequate theoretical frameworks…

Elucidating the neurophysiological mechanisms underlying neural pattern formation remains an outstanding challenge in Computational Neuroscience. In this paper, we address the issue of understanding the emergence of neural patterns by…

While most models of randomly connected networks assume nodes with simple dynamics, nodes in realistic highly connected networks, such as neurons in the brain, exhibit intrinsic dynamics over multiple timescales. We analyze how the…

Deep neural networks is a branch in machine learning that has seen a meteoric rise in popularity due to its powerful abilities to represent and model high-level abstractions in highly complex data. One area in deep neural networks that is…

Neurons in the brain communicate with spikes, which are discrete events in time and value. Functional network models often employ rate units that are continuously coupled by analog signals. Is there a qualitative difference implied by these…

This essay, derived from a lecture at "The Physics Modeling of Thought" workshop in Berlin in winter 2023, explores the mutually beneficial relationship between theoretical neuroscience and statistical physics through the lens of efficient…

Parkinson's disease (PD) belongs to the class of neurodegenerative disorders that affect the central nervous system. It is usually defined as the gradual loss of dopaminergic neurons in the substantia nigra pars compacta, which causes both…

Machine learning, and in particular neural network models, have revolutionized fields such as image, text, and speech recognition. Today, many important real-world applications in these areas are driven by neural networks. There are also…

Brain rhythms contribute to every aspect of brain function. Here, we study critical and resonance phenomena that precede the emergence of brain rhythms. Using an analytical approach and simulations of a cortical circuit model of neural…

We study pattern formation in class of a large-dimensional neural networks posed on random graphs and subject to spatio-temporal stochastic forcing. Under generic conditions on coupling and nodal dynamics, we prove that the network admits a…

Network analyses in nervous system disorders involves constructing and analyzing anatomical and functional brain networks from neuroimaging data to describe and predict the clinical syndromes that result from neuropathology. A network view…

This review provides a dynamical systems perspective on psychiatric symptoms and disease, and discusses its potential implications for diagnosis, prognosis, and treatment. After a brief introduction into the theory of dynamical systems, we…