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The dynamics of local cortical networks are irregular, but correlated. Dynamic excitatory--inhibitory balance is a plausible mechanism that generates such irregular activity, but it remains unclear how balance is achieved and maintained in…
Neural connectivity at the cellular and mesoscopic level appears very specific and is presumed to arise from highly specific developmental mechanisms. However, there are general shared features of connectivity in systems as different as the…
Self-organization of neural circuitry is an appealing framework for understanding cortical development, yet its applicability remains unconfirmed. Models for the self-organization of neural circuits have been proposed, but experimentally…
Mathematical modeling has broad applications in neuroscience whether modeling the dynamics of a single synapse or an entire network of neurons. In Part I, we model vesicle replenishment and release at the photoreceptor synapse to better…
The dynamics of spatially-structured networks of $N$ interacting stochastic neurons can be described by deterministic population equations in the mean-field limit. While this is known, a general question has remained unanswered: does…
The brain is an assembly of neuronal populations interconnected by structural pathways. Brain activity is expressed on and constrained by this substrate. Therefore, statistical dependencies between functional signals in directly connected…
Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…
Our understanding of neural computation is founded on the assumption that neurons fire in response to a linear summation of inputs. Yet experiments demonstrate that some neurons are capable of complex functions that require interactions…
Partially inspired by features of computation in visual cortex, deep neural networks compute hierarchical representations of their inputs. While these networks have been highly successful in machine learning, it remains unclear to what…
The brain may be thought of as a many-body architecture with a spatio-temporal dynamics described by neuronal structures. The oscillatory nature of brain activity allows these structures (nodes) to be described as a set of coupled…
This paper presents a comprehensive analysis of neural activation patterns across six distinct large language model (LLM) architectures, examining their performance on twelve cognitive task categories. Through systematic measurement of…
Deep neural networks (DNNs) trained on visual tasks develop feature representations that resemble those in the human visual system. Although DNN-based encoding models can accurately predict brain responses to visual stimuli, they offer…
We develop a formalism to describe the equilibrium distributions for segments of confined branched networks consisting of stiff filaments. This is applicable to certain situations of cytoskeleton in cells, such as for example actin…
A core component present in many successful neural network architectures, is an MLP block of two fully connected layers with a non-linear activation in between. An intriguing phenomenon observed empirically, including in transformer…
Networks of the brain are composed of a very large number of neurons connected through a random graph and interacting after random delays that both depend on the anatomical distance between cells. In order to comprehend the role of these…
Despite rapid adoption and deployment of large language models (LLMs), the internal computations of these models remain opaque and poorly understood. In this work, we seek to understand how high-level human-interpretable features are…
The dynamical properties of a diluted fully-inhibitory network of pulse-coupled neurons are investigated. Depending on the coupling strength, two different phases can be observed. At low coupling the evolution rapidly converges towards…
We study the dynamics of excitable integrate-and-fire neurons in a small-world network. At low densities $p$ of directed random connections, a localized transient stimulus results in either self-sustained persistent activity or in a brief…
Spike timing dependent plasticity (STDP) is believed to play an important role in shaping the structure of neural circuits. Here we show that STDP generates effective interactions between synapses of different neurons, which were neglected…
The population activity of random networks of excitatory and inhibitory leaky integrate-and-fire (LIF) neurons has been studied extensively. In particular, a state of asynchronous activity with low firing rates and low pairwise correlations…