相关论文: Periodic boundary conditions on staggered grids: U…

In computational models of particle packings with periodic boundary conditions, it is assumed that the packing is attached to exact copies of itself in all possible directions. The periodicity of the boundary then requires that all of the…

Consider a collection of points in the plane and the sets of slopes or directions of the lines between pairs of points. It is known that the algebraic matroid on the set of direction constraints between the points is equivalent to the…

We study a ferromagnetic Ising model with a staggered cell-board magnetic field previously proposed for image processing [Maruani et al., Markov Processes Relat. Fields 1 (1995) \cite{MPS}]. We complement previous results on the existence…

We say a closed point $x$ on a curve $C$ is sporadic if $C$ has only finitely many closed points of degree at most $\operatorname{deg}(x)$ and that $x$ is isolated if it is not in a family of effective degree $d$ divisors parametrized by…

We examine the conditions under which a signed graph contains an edge or a vertex that is contained in a unique negative circle or a unique positive circle. For an edge in a unique signed circle, the positive and negative case require the…

Stacked area charts are a widely used visualization technique for numerical time series. The x-axis represents time, and the time series are displayed as horizontal, variable-height layers stacked on top of each other. The height of each…

We study uniqueness of solutions to degenerate parabolic problems, posed in bounded domains, where no boundary conditions are imposed. Under suitable assumptions on the operator, uniqueness is obtained for solutions that satisfy an…

We prove the possibility of achieving unidirectional edge modes in time-modulated supercell structures. Such finite structures consist of two trimers repeated periodically. Because of their symmetry, they admit degenerate edge eigenspaces.…

Periodic $2$nd order ordinary differential operators on $\R$ are known to have the edges of their spectra to occur only at the spectra of periodic and antiperiodic boundary value problems. The multi-dimensional analog of this property is…

This paper investigates structural changes in the parameters of first-order autoregressive models by analyzing the edge eigenvalues of the precision matrices. Specifically, edge eigenvalues in the precision matrix are observed if and only…

Plane wave density functional theory codes generally assume periodicity in all three dimensions. This causes difficulties when studying charged systems, for instance energies per unit cell become infinite, and, even after being renormalised…

Graph coloring is one of the most famous computational problems with applications in a wide range of areas such as planning and scheduling, resource allocation, and pattern matching. So far coloring problems are mostly studied on static…

We study the interplay between disorder and topology for the localized edge states of light in topological zigzag arrays of resonant dielectric nanoparticles. We characterize topological properties by the winding number that depends on both…

This article is concerned with the existence and uniqueness of solutions to some fractional order boundary value problems. Our results are based on some fixed point theorems. For the applicability of our results, we provide an example.

We investigate edge-intersection graphs of paths in the plane grid, regarding a parameter called the bend-number. I.e., every vertex is represented by a grid path and two vertices are adjacent if and only if the two grid paths share at…

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…

In this paper, we introduce a new identifiability criteria for linear structural equation models, which we call regression identifiability. We provide necessary and sufficient graphical conditions for a directed edge to be regression…

Temporal graphs provide a useful model for many real-world networks. Unfortunately the majority of algorithmic problems we might consider on such graphs are intractable. There has been recent progress in defining structural parameters which…

We prove existence and uniqueness of solutions, continuous dependence from the initial datum and stability with respect to the boundary condition in a class of initial--boundary value problems for systems of balance laws. The particular…

Tight-binding model on a finite chain is studied with four-fold alternated hopping parameters $t_{1,2,3,4}$. Imposing the open boundary conditions, the corresponding recursion is solved analytically with special attention paid to the…