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We consider a dipolar Bose-Einstein condensate trapped in an array of two-well systems with an arbitrary orientations of the dipoles relative to the system's axis. The system can be built as a chain of local traps sliced into two parallel…
In this work, we consider a binary classification problem and cast it into a binary hypothesis testing framework, where the observations can be perturbed by an adversary. To improve the adversarial robustness of a classifier, we include an…
We present a comparative investigation of two-dimensional tractor magnet configurations, analyzing both theoretical predictions and experimental results with a focus on the minimal tractor magnet. The minimal tractor magnet consists of a…
This paper studies the Laplacian spectrum and the average effective resistance of (large) graphs that are sampled from graphons. Broadly speaking, our main finding is that the Laplacian eigenvalues of a large dense graph can be effectively…
It is well known that in many real networks, such as brain networks and scientific collaboration networks, there exist higher-order nonpairwise relations among nodes, i.e., interactions between among than two nodes at a time. This…
In complex networked systems theory, an important question is how to evaluate the system robustness to external perturbations. With this task in mind, I investigate the propagation of noise in multi-layer networked systems. I find that, for…
A two-dimensional bistable lattice is a periodic triangular network of non-linear bi-stable rods. The energy of each rod is piecewise quadratic and has two minima. Consequently, a rod undergoes a reversible phase transition when its…
Networks are useful descriptions of the structure of many complex systems. Unsurprisingly, it is thus important to analyze the robustness of networks in many scientific disciplines. In applications in communication, logistics, finance,…
We classify connected 2-node excitatory-inhibitory networks under various conditions. We assume that, as well as for connections, there are two distinct node-types, excitatory and inhibitory. In our classification we consider four different…
Resonances in an electric circuit occur when capacitive and inductive components are present together. Such resonances appear in admittance measurements depending on the circuit's parameters and the driving AC frequency. In this study, we…
The macroscopic surface electric susceptibility determines the linear optical properties of an insulating single-layer two-dimensional atomic crystal, and can be expressed in terms of the microscopic polarizability of the atoms. We compute…
We investigate the laminar flow of two-fluid mixtures inside a simple network of inter-connected tubes. The fluid system is comprised of two miscible Newtonian fluids of different viscosity which do not mix and remain as nearly distinct…
The transmittance of intersection between narrow quantum strips is studied. It is assumed that strip widths are less than the electron wavelength, so that they are tunnel conductors. In this assumption the Schr\"odinger equation is reduced…
Recent work in theoretical computer science and scientific computing has focused on nearly-linear-time algorithms for solving systems of linear equations. While introducing several novel theoretical perspectives, this work has yet to lead…
Formal Laplace operators are analyzed for a large class of resistance networks with vertex weights. The graphs are completed with respect to the minimal resistance path metric. Compactness and a novel connectivity hypothesis for the…
We consider a Hubbard-like model of strongly-interacting spinless fermions and hardcore bosons on a square lattice, such that nearest neighbor occupation is forbidden. Stripes (lines of holes across the lattice forming antiphase walls…
Common models describing magnetotransport properties of periodically modulated two--dimensional systems often either directly start from a semiclassical approach or give results well conceivable within the semiclassical framework. Recently,…
A $2$-uniform tolerance on a lattice is a compatible tolerance relation such that all of its blocks are 2-element. We characterize permuting pairs of 2-uniform tolerances on lattices of finite length. In particular, any two 2-uniform…
We discuss two possible ways of representing tolerances: first, as a homomorphic image of some congruence; second, as the relational composition of some compatible relation with its converse. The second way is independent from the variety…
We consider a general class of two-dimensional spin systems, with continuous but not necessarily smooth, possibly long-range, $O(N)$-symmetric interactions, for which we establish algebraically decaying upper bounds on spin-spin…