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Non-reciprocal couplings are frequently found in systems out-of-equilibrium such as neuronal networks. We consider generalized Kuramoto models with non-reciprocal adaptive couplings. The non-reciprocity refers to the type of couplings…
Recent physiological measurements have provided clear evidence about scale-free avalanche brain activity and EEG spectra, feeding the classical enigma of how such a chaotic system can ever learn or respond in a controlled and reproducible…
The unique dynamical features of the critical state endow the brain with properties which are fundamental for adaptive behavior. This proposal, put forward with Per Bak several years ago, is now supported by a wide body of empirical…
Adaptive quantum circuits-where a quantum many-body state is controlled using measurements and conditional unitary operations-are a powerful paradigm for state preparation and quantum error correction tasks. They can support two types of…
Living systems operate in a critical dynamical regime -- between order and chaos -- where they are both resilient to perturbation, and flexible enough to evolve. To characterize such critical dynamics, the established 'structural theory' of…
Habituation - a phenomenon in which a dynamical system exhibits a diminishing response to repeated stimulations that eventually recovers when the stimulus is withheld - is universally observed in living systems from animals to unicellular…
This paper introduces a framework for quantitative characterization of the controllability of time-varying linear systems (or networks) in terms of input novelty. The motivation for such an approach comes from the study of biophysical…
In the mammalian nervous system, various synaptic plasticity rules act, either individually or synergistically, and over wide-ranging timescales to dictate the processes that enable learning and memory formation. To mimic biological…
Stochastic resonance is a phenomenon in which noise enhances the response of a system to an input signal. The brain is an example of a system that has to detect and transmit signals in a noisy environment, suggesting that it is a good…
We introduce a two-parameter ensemble of random discrete-time Markov models that simultaneously captures critical slowing down and broken detailed balance. Extending a previously studied heterogeneous Markov ensemble, we incorporate…
The neural activity of the human brain is dominated by self-sustained activities. External sensory stimuli influence this autonomous activity but they do not drive the brain directly. Most standard artificial neural network models are…
Chaotic synchronization is generally extremely sensitive to the presence of noise and other inference in the channel. Is this sensitivity a fundamental property of chaotic synchronization or is it related to the choice of synchronization…
The neural networks of the human brain act as very efficient parallel processing computers co-ordinating memory related responses to a multitude of input signals from sensory organs. Information storage, update and appropriate retrieval are…
We study the critical behavior of the dissipative abelian sandpile model on Z with dissipative sites at arbitrary positions (x_k). This is equivalent to studying whether the expected stopping time of a trapped random walk on Z is finite.…
In this paper, we study properties of sensitivity, transitivity and chaos for non-autonomous discrete systems(NDS). Firstly, we present some different sufficient conditions for NDS to be chaotic. Then, we relate the transitivity with the…
The behavior of the network and its stability are governed by both dynamics of individual nodes as well as their topological interconnections. Attention mechanism as an integral part of neural network models was initially designed for…
In order to remain adaptable to a dynamic environment, neural activity must be simultaneously both sensitive and stable. To solve this problem, the brain has been hypothesised to sit near a critical boundary. Yet, precisely how criticality…
Functional connectivity is a fundamental property of neural networks that quantifies the segregation and integration of information between cortical areas. Due to mathematical complexity, a theory that could explain how the parameters of…
The cortex exhibits self-sustained highly-irregular activity even under resting conditions, whose origin and function need to be fully understood. It is believed that this can be described as an "asynchronous state" stemming from the…
The dynamic core hypothesis posits that consciousness is correlated with simultaneously integrated and differentiated assemblies of transiently synchronized brain regions. We represented time-dependent functional interactions using dynamic…