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In the present paper, we introduce and analyze elephant random walks (ERWs) on bipartite periodic lattices arising as coverings of dipole graphs. We focus on lattices whose admissible step directions in the two parts of the bipartition are…
Many patterning events in multi-cellular organisms rely on cell-to-cell contact signaling, such as the Notch pathway in metazoans. A particularly interesting phenomenon in this form of communication is lateral inhibition where a cell that…
Combining strong electron correlations [1-4] and nontrivial electronic topology [5] holds great promise for discovery. So far, this regime has been rarely accessed and systematic studies are much needed to advance the field. Here we…
This work introduces a new theoretical model for active matter ("complementary-spins" or c-spins), exploring the interplay of positional and orientational order in mobile agents with rotational freedom, divided into two populations with…
In this work we study biological neural networks from an algorithmic perspective, focusing on understanding tradeoffs between computation time and network complexity. Our goal is to abstract real neural networks in a way that, while not…
The effect of undesirable high-frequency free-layer switching in magnetic multilayer systems, referred to as back hopping, is investigated by means of the spin-diffusion model. A possible origin of the back-hopping effect is found to be the…
Motility is a fundamental feature of living matter, encompassing single cells and collective behavior. Such living systems are characterized by non-conservativity of energy and a large diversity of spatio-temporal patterns. Thus,…
Walking animals, like stick insects, cockroaches or ants, demonstrate a fascinating range of locomotive abilities and complex behaviors. The locomotive behaviors can consist of a variety of walking patterns along with adaptation that allow…
Motivated by recent experiments reporting unconventional collective modes in the charge density-wave (CDW) state of rare-earth tritellurides $R$Te$_3$, we derive from a multi-orbital microscopic model on the square net a CDW Ginzburg-Landau…
We study the exponential relaxation of observables, propagated with a non-Hermitian transfer matrix, an example being out-of-time-ordered correlations (OTOC) in brickwall (BW) random quantum circuits. Until a time that scales as the system…
In this paper we introduce the notion of Random Walk in Changing Environment - a random walk in which each step is performed in a different graph on the same set of vertices, or more generally, a weighted random walk on the same vertex and…
The structure and design of optimal supply networks is an important topic in complex networks research. A fundamental trait of natural and man-made networks is the emergence of loops and the trade-off governing their formation: adding…
Incommensurate charge density waves (CDW) have the extraordinary ability to display non-Ohmic behavior when submitted to an external field. The mechanism leading to this non trivial dynamics is still not well understood, although recent…
We study mechanisms for wavenumber selection in a minimal model for run-and-tumble dynamics. We show that nonlinearity in tumbling rates induces the existence of a plethora of traveling- and standing-wave patterns, as well as a subtle…
The Random Walk Pinning Model (RWPM) is a statistical mechanics model in which the trajectory of a continuous time random walk $X=(X_t)_{t\geq 0}$ is rewarded according to the time it spends together with a moving catalyst. More…
We study transient behaviour in the dynamics of complex systems described by a set of non-linear ODE's. Destabilizing nature of transient trajectories is discussed and its connection with the eigenvalue-based linearization procedure. The…
Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the…
This thesis examines edge-reinforced random walks with some modifications to the standard definition. An overview of known results relating to the standard model is given and the proof of recurrence for the standard linearly edge-reinforced…
We focus on the dynamical feature for a $p$-wave superconductor model in different parameter regions in terms of the appearance of gapless edge modes in reel geometry. Firstly, we show the parameter region with gapless edge modes versus a…
In this paper, we propose a kernel method for exact tail asymptotics of a random walk to neighborhoods in the quarter plane. This is a two-dimensional method, which does not require a determination of the unknown generating function(s).…