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This paper concerns the long-term behaviour of a system of interacting random walks labeled by vertices of a finite graph. The model is reversible which allows to use the method of electric networks in the study. In addition, examples of…
Biological nervous systems typically perform the control of numerous degrees of freedom for example in animal limbs. Neuromorphic engineers study these systems by emulating them in hardware for a deeper understanding and its possible…
The millimeter-long soil-dwelling nematode {\it C. elegans} propels itself by producing undulations that propagate along its body and turns by assuming highly curved shapes. According to our recent study [PLoS ONE \textbf{7}, e40121 (2012)]…
We propose a new partial-observability model for online learning problems where the learner, besides its own loss, also observes some noisy feedback about the other actions, depending on the underlying structure of the problem. We represent…
Recordings of whole brain activity with single neuron resolution are now feasible in simple organisms. Yet, it is still challenging to appropriately simplify such complex, noisy, and multivariate data in order to reveal general principles…
Complex networks can often be decomposed into less complex sub-networks whose structures can give hints about the functional organization of the network as a whole. However, these structural motifs can only tell one part of the functional…
We review recent advances in the theory of trapped fermions using techniques borrowed from random matrix theory (RMT) and, more generally, from the theory of determinantal point processes. In the presence of a trap, and in the limit of a…
Maxmin-$\omega$ is a new threshold model, where each node in a network waits for the arrival of states from a fraction $\omega$ of neighborhood nodes before processing its own state, and subsequently transmitting it to downstream nodes.…
We investigate topological properties of a chiral honeycomb lattice model with next-nearest-neighbor hoppings characterized by the reflection symmetry breaking. Topological nontriviality is detected by analyzing effective Dirac Hamiltonian,…
Recurrence is a fundamental characteristic of dynamical systems with complicated behavior. Understanding the inner structure of recurrence is challenging, especially if the system has many degrees of freedom and is subject to noise. We…
A simple discrete planar dynamical model for the ideal (logical) R-S flip-flop circuit is developed with an eye toward mimicking the dynamical behavior observed for actual physical realizations of this circuit. It is shown that the model…
T-wave alternans (TWA) is a potential marker for sudden cardiac death, but its reliable analysis is often constrained to noise-free environments, limiting its utility in real-world settings. We explore model-based T-wave estimation to…
To understand the sophisticated control mechanisms of the human's endocrine system is a challenging task that is a crucial step towards precise medical treatment of many disfunctions and diseases. Although mathematical models describing the…
When two periodic potentials compete in materials, one may adopt the other, which straightforwardly generates topological defects. Of particular interest are domain walls in charge-, dipole-, and spin-ordered systems, which govern…
It is quite possible that the Technicolor problems are related to the poorly known self-energy expression, or the way chiral symmetry breaking (CSB) is realized in non-abelian gauge theories. Actually, the only known laboratory to test the…
Flow networks are essential for both living organisms and enginneered systems. These networks often present complex dynamics controlled, at least in part, by their topology. Previous works have shown that topologically complex networks…
Organisms are equipped with regulatory systems that display a variety of dynamical behaviours ranging from simple stable steady states, to switching and multistability, to oscillations. Earlier work has shown that oscillations in protein…
Electrical circuits offer a unique platform to explore physical phenomena, from topology to non-Hermitian effects. Investigations of the fundamental properties of this metamaterial platform are crucial to distinguish observed/measured…
Many natural processes occur over characteristic spatial and temporal scales. This paper presents tools for (i) flexibly and scalably coarse-graining cellular automata and (ii) identifying which coarse-grainings express an automaton's…
The interplay between non-trivial band topology and strong electronic correlations is a central challenge in modern condensed matter physics. We investigate this competition on a two-leg ladder model with a p-wave-like hybridisation between…