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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…
Time series analysis has proven to be a powerful method to characterize several phenomena in biology, neuroscience and economics, and to understand some of their underlying dynamical features. Despite a plethora of methods have been…
Designing network parameters that can effectively represent complex networks is of significant importance for the analysis of time-varying complex networks. This paper introduces a novel thermodynamic framework for analyzing complex…
A complete understanding of the brain requires an integrated description of the numerous scales of neural organization. It means studying the interplay of genes, synapses, and even whole brain regions which ultimately leads to different…
The functioning of an organ such as the brain emerges from interactions between its constituent parts. Further, this interaction is not immutable in time but rather unfolds in a succession of patterns, thereby allowing the brain to adapt to…
The possibility that evolutionary forces -- together with a few fundamental factors such as thermodynamic constraints, specific computational features enabling information processing, and ecological processes -- might constrain the logic of…
When brain signals are recorded in an electroencephalogram or some similar large-scale record of brain activity, oscillatory patterns are typically observed that are thought to reflect the aggregate electrical activity of the underlying…
In the human brain, internal states are often correlated over time (due to local recurrence and other intrinsic circuit properties), punctuated by abrupt transitions. At first glance, temporal smoothness of internal states presents a…
We introduce and study a new model of interacting neural networks, incorporating the spatial dimension (e.g. position of neurons across the cortex) and some learning processes. The dynamic of each neural network is described via the elapsed…
In this work, we present a mathematical model for cyclic and sequential patterns of brain activity, combining heteroclinic dynamics with discrete neural-field models. We first show that spatial-discrete neural-field equations with…
The generation of spikes by neurons is energetically a costly process and the evaluation of the metabolic energy required to maintain the signalling activity of neurons a challenge of practical interest. Neuron models are frequently used to…
Structure entails function and thus a structural description of the brain will help to understand its function and may provide insights into many properties of brain systems, from their robustness and recovery from damage, to their dynamics…
A neural correlate of parametric working memory is a stimulus specific rise in neuron firing rate that persists long after the stimulus is removed. Network models with local excitation and broad inhibition support persistent neural…
Cortical networks, in-vitro as well as in-vivo, can spontaneously generate a variety of collective dynamical events such as network spikes, UP and DOWN states, global oscillations, and avalanches. Though each of them have been variously…
Brain-computer interfaces surged extraordinary developments in recent years, and a significant discrepancy now exists between the abundance of available data and the limited headway made in achieving a unified theoretical framework. This…
Understanding the evolution of brain functional networks over time is of great significance for the analysis of cognitive mechanisms and the diagnosis of neurological diseases. Existing methods often have difficulty in capturing the…
Cortical activity recorded through EEG and MEG reflects complex dynamics that span multiple temporal and spatial scales. Spectral analyses of these signals consistently reveal power-law behaviour, a hallmark of turbulent systems. In this…
While ubiquitous, energy redistribution remains a poorly understood facet of the nonequilibrium thermodynamics of biomolecules. At the molecular level, finite-size effects, pronounced nonlinearities, and ballistic processes produce behavior…
Educational multimedia has become increasingly important in modern learning environments because of its cost-effectiveness and ability to overcome the temporal and spatial limitations of traditional methods. However, the complex cognitive…
Energy landscapes are a useful aid for the understanding of dynamical systems, and a valuable tool for their analysis. For a broad class of rate models of neural networks, we derive a global Lyapunov function which provides an energy…