Related papers: Tiling with Boundaries: Dense digital images have …
Profiling core-periphery structures in networks has attracted significant attention, leading to the development of various methods. Among these, the rich-core method is distinguished for being entirely parameter-free and scalable to large…
A tiling is a decomposition of a polygon into finitely many non-overlapping triangles. We prove that if a regular n-gon, $n \geq 5$, $n \neq 28$, can be tiled with similar right triangles, then one of the angles of these triangles is in…
Semantic segmentation and hyperspectral unmixing are two central problems in spectral image analysis. The former assigns each pixel a discrete label corresponding to its material class, whereas the latter estimates pure material spectra,…
Here we prove that a graph without some three induced subgraphs has chromatic number at the most equal to its maximum clique size plus one. Further we show that the bounds are tight and give examples to show that each of the three forbidden…
Delamination is a critical mode of failure that occurs between plies in a composite laminate. The cohesive element, developed based on the cohesive zone model, is widely used for modeling delamination. However, standard cohesive elements…
A digraph is connected-homogeneous if any isomorphism between finite connected induced subdigraphs extends to an automorphism of the digraph. We consider locally-finite connected-homogeneous digraphs with more than one end. In the case that…
As connected devices continue to decrease in size, we explore the idea of leveraging everyday surfaces such as tabletops and walls to augment the wireless capabilities of devices. Specifically, we introduce Surface MIMO, a technique that…
Existing image complexity metrics cannot distinguish meaningful content from noise. This means that white noise images, which contain no meaningful information, are judged as highly complex. We present a new image complexity metric through…
The miniaturization of electronic devices has led to the prominence, in technological applications, of ultra-thin films with a thickness ranging from a few tens of nanometers to just about 1-2 nanometers. While these materials are still…
For planar graphs, it is well known that high connectivity implies a Hamiltonian cycle and hence any 4-connected planar graph has a near-perfect matching. Nevertheless, whether 6-connected 1-planar graphs admit near-perfect matchings…
This paper develops a symplectic bifurcation theory for integrable systems in dimension four. We prove that if an integrable system has no hyperbolic singularities and its bifurcation diagram has no vertical tangencies, then the fibers of…
We revisit the minimum-link path problem: Given a polyhedral domain and two points in it, connect the points by a polygonal path with minimum number of edges. We consider settings where the vertices and/or the edges of the path are…
We consider the range of random analytic functions with finite radius of convergence. We show that any unbounded random Taylor series with rotationally invariant coefficients has dense image in the plane. We moreover show that if in…
A lower bound on the amount of noise that must be added to a GHZ-like entangled state to make it separable (also called the random robustness) is found using the transposition condition. The bound is applicable to arbitrary numbers of…
We discuss a scheme for a full superdense coding of entangled photon states employing only linear-optics elements. By using the mixed basis consisting of four states that are unambiguously distinguishable by a standard and polarizing beam…
An equilateral triangle cannot be dissected into finitely many mutually incongruent equilateral triangles [Tutte 1948]. Therefore Tuza [Tuza 1991] asked for the largest number $s=s(n)$ such that there is a tiling of an equilateral triangle…
A major research area in discrete geometry is to consider the best way to partition the $d$-dimensional Euclidean space $\mathbb{R}^d$ under various quality criteria. In this paper we introduce a new type of space partitioning that is…
We propose a mid-level image segmentation framework that combines multiple figure-ground hypothesis (FG) constrained at different locations and scales, into interpretations that tile the entire image. The problem is cast as optimization…
The screening of an individual low-dimensional object can be strongly influenced by the objects nearby. We propose that such environment's influence can be absorbed into an effective polarizability, instead of its intrinsic polarizability.…
Simple intersections between one-dimensional channels can act as coherent beam splitters for non-interacting electrons. Here we examine how coherent splitting at such intersections is affected by inter-particle interactions, in the special…