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We discuss the effects of common synaptic inputs in a recurrent neural network. Because of the effects of these common synaptic inputs, the correlation between neural inputs cannot be ignored, and thus the network exhibits sample…
Understanding neural networks is challenging due to their high-dimensional, interacting components. Inspired by human cognition, which processes complex sensory data by chunking it into recurring entities, we propose leveraging this…
We consider an excitatory random network of leaky integrate-and-fire pulse coupled neurons. The neurons are connected as in a directed Erd\"os-Renyi graph with average connectivity $<k>$ scaling as a power law with the number of neurons in…
We study the collective dynamics of strongly diffusively coupled excitable elements on small random tree networks. Stochastic external inputs are applied to the leaves causing large spiking events. Those events propagate along the tree…
We designed a model-based analysis to predict the occurrence of population patterns in distributed spiking activity. Using a maximum entropy principle with a Markovian assumption, we obtain a model that accounts for both spatial and…
The proliferation of multi-unit cortical recordings over the last two decades, especially in macaques and during motor-control tasks, has generated interest in neural "population dynamics": the time evolution of neural activity across a…
We consider a fitness-structured population model with competition and migration between nearest neighbors. Under a combination of large population and rare migration limits we are particularly interested in the asymptotic behavior of the…
Dynamic community detection provides a coherent description of network clusters over time, allowing one to track the growth and death of communities as the network evolves. However, modularity maximization, a popular method for performing…
Cooperative effects in neural networks appear because a neuron fires only if a minimal number $m$ of its inputs are excited. The multiple inputs requirement leads to a percolation model termed {\it quorum percolation}. The connectivity…
We investigate the emergence and persistence of communities through a recently proposed mechanism of adaptive rewiring in coevolutionary networks. We characterize the topological structures arising in a coevolutionary network subject to an…
We revisit the dynamics of a prototypical model of balanced activity in networks of spiking neutrons. A detailed investigation of the thermodynamic limit for fixed density of connections (massive coupling) shows that, when inhibition…
The critical brain hypothesis posits that neural circuitry operates near criticality to reap the computational benefits of accessing a wide range of timescales. The theory of critical phenomena generally predicts heavy-tailed (power-law)…
We study molecular dynamics within populations of diffusively coupled cells under the assumption of fast diffusive exchange. As a technical tool, we propose conditions on boundedness and ultimate boundedness for systems with a singular…
Sensory processing is often characterized as implementing probabilistic inference: networks of neurons compute posterior beliefs over unobserved causes given the sensory inputs. How these beliefs are computed and represented by neural…
Neurons can display highly variable dynamics. While such variability presumably supports the wide range of behaviors generated by the organism, their gene expressions are relatively stable in the adult brain. This suggests that neuronal…
Understanding how network function constrains neural connectivity is a central challenge in neuroscience. An influential approach is to train neural networks with gradient descent on cognitive tasks and characterize the resulting…
The recent proliferation of research into transformer based natural language processing has led to a number of studies which attempt to detect the presence of human-like cognitive behavior in the models. We contend that, as is true of human…
This study aims to review recent research on the collective behaviour of excitatory and inhibitory (E-I) spiking neural networks. The research methodology used is Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA)…
Most nervous systems encode information about stimuli in the responding activity of large neuronal networks. This activity often manifests itself as dynamically coordinated sequences of action potentials. Since multiple electrode recordings…
Neural Processes (NPs) are appealing due to their ability to perform fast adaptation based on a context set. This set is encoded by a latent variable, which is often assumed to follow a simple distribution. However, in real-word settings,…