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We analyze the static and dynamical properties of a one-dimensional topological lattice, the fermionic Su-Schrieffer-Heeger model, in the presence of on-site interactions. Based on a study of charge and spin correlation functions, we…
The correlation function of a one-dimensional interface over a random substrate, bound to the substrate by a pressure term, is studied by Monte-Carlo simulation. It is found that the height correlation < h_i ; h_{i+j} >, averaged over the…
Recently, Chatterjee has introduced a new coefficient of correlation which has several natural properties. In particular, the coefficient attains its maximal value if and only if one variable is a measurable function of the other variable.…
We propose a mechanism enabling the appearance of border cells -- neurons firing at the boundaries of the navigated enclosures. The approach is based on the recent discovery of discrete complex analysis on a triangular lattice, which allows…
We consider two-dimensional Coulomb systems for which the coincidence set contains an outpost in the form of a suitable Jordan curve. We study asymptotics for correlations along the union of the outpost and the outer boundary of the…
We characterize some asymptotic properties of edge exchangeable random graphs in terms of the measure used to generate them. In particular, we give a necessary and sufficient condition for eventual forever connectedness, a sufficient…
The correlation functions are calculated for the two dimensional Ising model with free boundary conditions and the two dimensional Ising model with periodic boundary conditions.
The framework of geometric extremes is based on the convergence of scaled sample clouds onto a limit set, characterized by a gauge function, with the shape of the limit set determining extremal dependence structures. While it is known that…
We study an extension of the classical graph cut problem, wherein we replace the modular (sum of edge weights) cost function by a submodular set function defined over graph edges. Special cases of this problem have appeared in different…
Ordered polarity alignment of a cell population plays a vital role in biology, such as in hair follicle alignment and asymmetric cell division. Here, we propose a theoretical framework for the understanding of generic dynamical properties…
Multi-particle dynamics in one-dimensional asymmetric exclusion processes with disorder is investigated theoretically by computational and analytical methods. It is argued that the general phase diagram consists of three non-equilibrium…
We study the correspondence between boundary spectrum of non-chiral topological orders on an open manifold $\mathcal{M}$ with gapped boundaries and the entanglement spectrum in the bulk of gapped topological orders on a closed manifold. The…
We construct unitary, stable, and interacting conformal boundary conditions for a free massless scalar in four dimensions by coupling it to edge modes living on a boundary. The boundary theories we consider are bosonic and fermionic QED$_3$…
We give an account of the Axelrod-Bennet model that describes formation of a bimodal coalition. We present its initial formalism and applications and reformulate the problem in terms of the Hopfield model. This allowed us to analyze a…
By taking the interacting spinor-scalar theory on the $AdS_{d+1}$ space we calculate the boundary CFT correlation functions using AdS/CFT correspondence.
We derive the statistical limit of the spectral autocorrelation function and of the survival probability for the indirect photodissociation of molecules in the regime of non-overlapping resonances. The results are derived in the framework…
The interaction of a nonrelativistic charged particle beam, travelling parallel to the surface of a sharp-edged dielectric wedge is analyzed. The general expressions for excitation probability are obtained for a beam moving along the…
We study the autocorrelation function of different types of eigenfunctions in quantum mechanical systems with either chaotic or mixed classical limits. We obtain an expansion of the autocorrelation function in terms of the correlation…
In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent…
This paper considers the edge-connectivity and restricted edge-connectivity of replacement product graphs, gives some bounds on edge-connectivity and restricted edge-connectivity of replacement product graphs and determines the exact values…