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We consider a free boundary model of epithelial cell migration with logistic growth and nonlinear diffusion induced by mechanical interactions. Using numerical simulations, phase plane and perturbation analysis, we find and analyse…
We propose a framework for jointly modeling the geometry and functionality in high dimensional functional surfaces. The proposed mixed effects model characterizes effects of subject-specific covariates and exogenous stimuli on functional…
Recent evidence in rodent cerebral cortex and olfactory bulb suggests that short-term dynamics of excitatory synaptic transmission is correlated to stereotypical connectivity motifs. It was observed that neurons with short-term facilitating…
The central nervous system is composed of many individual units -- from cells to areas -- that are connected with one another in a complex pattern of functional interactions that supports perception, action, and cognition. One natural and…
To thrive in dynamic environments, animals must be capable of rapidly and flexibly adapting behavioral responses to a changing context and internal state. Examples of behavioral flexibility include faster stimulus responses when attentive…
This paper describes how realistic neuromorphic networks can have their connectivity fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the two-dimensional…
This paper models the dynamics of a large set of interacting neurons within the framework of statistical field theory. We use a method initially developed in the context of statistical field theory [44] and later adapted to complex systems…
We report on both analytical and numerical results concerning stochastic Hopfield--like neural automata exhibiting the following (biologically inspired) features: (1) Neurons and synapses evolve in time as in contact with respective baths…
Understanding the nature of the changes exhibited by evolving neuronal dynamics from high-dimensional activity data is essential for advancing neuroscience, particularly in the study of neuronal network development and the pathophysiology…
Spiking neural network models characterize the emergent collective dynamics of circuits of biological neurons and help engineer neuro-inspired solutions across fields. Most dynamical systems' models of spiking neural networks typically…
Cortical neurons are subject to sustained and irregular synaptic activity which causes important fluctuations of the membrane potential (Vm). We review here different methods to characterize this activity and its impact on spike generation.…
We demonstrate that waves in distinct layers of a neuronal network can become phase-locked by common spatiotemporal noise. This phenomenon is studied for stationary bumps, traveling waves, and breathers. A weak noise expansion is used to…
We propose a hierarchically modular, dynamical neural network model whose architecture minimizes a specifically designed energy function and defines its temporal characteristics. The model has an internal and an external space that are…
We propose a dynamical neural network model with a hierarchical and modular structure. The network architecture can be derived by minimizing an energy function that is originally designed based on two kinds of neurons with quite different…
Biological systems represent time from microseconds to years. An important gap in our knowledge concerns the mechanisms for encoding time intervals of hundreds of milliseconds to minutes that matter for tasks like navigation, communication,…
In recent years, there has been increasing interest in developing models and tools to address the complex patterns of connectivity found in brain tissue. Specifically, this is due to a need to understand how emergent properties emerge from…
Perceptual similarity is a cognitive judgment that represents the end-stage of a complex cascade of hierarchical processing throughout visual cortex. Previous studies have shown a correspondence between the similarity of coarse-scale fMRI…
In this paper, we report on the generation and propagation of traveling pulses in a homogeneous network of diffusively coupled, excitable, slow-fast dynamical neurons. The spatially extended system is modelled using the nearest neighbor…
Complex coherent dynamics is present in a wide variety of neural systems. A typical example is the voltage transitions between up and down states observed in cortical areas in the brain. In this work, we study this phenomenon via a…
Synaptic plasticity dynamically shapes the connectivity of neural systems and is key to learning processes in the brain. To what extent the mechanisms of plasticity can be exploited to drive a neural network and make it perform some kind of…