Related papers: Statistical Field Theory and Neural Structures Dyn…
A general expansion scheme based on the concept of linked cluster expansion from the theory of classical spin systems is constructed for models of interacting electrons. It is shown that with a suitable variational formulation of mean-field…
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…
Most complex systems are nonlinear, relying on emergent behavior from interacting subsystems, often characterized by oscillatory dynamics. Collective oscillatory behavior is essential for the proper functioning of many real world systems.…
Mean field theory is a device to analyze the collective behavior of a dynamical system comprising many interacting particles. The theory allows to reduce the behavior of the system to the properties of a handful of parameters. In neural…
Recurrent neural networks (RNNs) are widely used throughout neuroscience as models of local neural activity. Many properties of single RNNs are well characterized theoretically, but experimental neuroscience has moved in the direction of…
Systems of interacting objects often evolve under the influence of field effects that govern their dynamics, yet previous works have abstracted away from such effects, and assume that systems evolve in a vacuum. In this work, we focus on…
In this work we study the dynamics of systems composed of numerous interacting elements interconnected through a random weighted directed graph, such as models of random neural networks. We develop an original theoretical approach based on…
The current understanding of deep neural networks can only partially explain how input structure, network parameters and optimization algorithms jointly contribute to achieve the strong generalization power that is typically observed in…
Macroscopic studies of cortical tissue reveal a prevalence of oscillatory activity, that reflect a fine tuning of neural interactions. This research extends neural field theories by incorporating generalized oscillatory dynamics into…
The cerebral cortex spontaneously displays different patterns of activity that evolve over time according to the brain state. Sleep, wakefulness, resting states, and attention are examples of a wide spectrum of physiological states that can…
We analyze the emergent regimes and the stimulus-response relationship of a population of noisy map neurons by means of a mean-field model, derived within the framework of cumulant approach complemented by the Gaussian closure hypothesis.…
Complementarity is one of the main features underlying the interactions in biological and biochemical systems. Inspired by those systems we propose a model for the dynamical evolution of a system composed by agents that interact due to…
As people coordinate in daily interactions, they engage in different patterns of behavior to achieve successful outcomes. This includes both synchrony - the temporal coordination of the same behaviors at the same time - and complementarity…
Revealing physical interactions in complex systems from observed collective dynamics constitutes a fundamental inverse problem in science. Current reconstruction methods require access to a system's model or dynamical data at a level of…
Many neural systems display cascading behavior characterized by uninterrupted sequences of neuronal firing. This gap precludes an understanding of how variations in network structure manifest in neural dynamics and either support or impinge…
The current social reality is characterized by all-encompassing change, which disrupts existing social structures at all levels. Yet the prevailing view of society is based on the ontological primacy of stable hierarchical structures, which…
Active inference is a normative principle underwriting perception, action, planning, decision-making and learning in biological or artificial agents. From its inception, its associated process theory has grown to incorporate complex…
We propose a statistical mechanics approach to a coevolving spin system with an adaptive network of interactions. The dynamics of node states and network connections is driven by both spin configuration and network topology. We consider a…
The static synaptic connectivity of neuronal circuits stands in direct contrast to the dynamics of their function. As in changing community interactions, different neurons can participate actively in various combinations to effect behaviors…
Understanding the basic operational logics of the nervous system is essential to advancing neuroscientific research. However, theoretical efforts to tackle this fundamental problem are lacking, despite the abundant empirical data about the…