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Let F be a family of n pairwise intersecting circles in the plane. We show that the number of lenses, that is convex digons, in the arrangement induced by F is at most 2n - 2. This bound is tight. Furthermore, if no two circles in F touch, then the geometr ...
We examine the connection of two graph parameters, the size of a minimum feedback arcs set and the acyclic disconnection. A feedback arc set of a directed graph is a subset of arcs such that after deletion the graph becomes acyclic. The acyclic disconnecti ...
Spectral algorithms are some of the main tools in optimization and inference problems on graphs. Typically, the graph is encoded as a matrix and eigenvectors and eigenvalues of the matrix are then used to solve the given graph problem. Spectral algorithms ...
Modern integrated circuits are tiny yet incredibly complex technological artifacts, composed of millions and billions of individual structures working in unison.Managing their complexity and facilitating their design drove part of the co-evolution of moder ...
Orthogonal group synchronization is the problem of estimating n elements Z(1),& mldr;,Z(n) from the rxr orthogonal group given some relative measurements R-ij approximate to Z(i)Z(j)(-1). The least-squares formulation is nonconvex. To avoid its local minim ...
Sometimes treatment effects are absent in a subgroup of the population. For example, penicillin has no effect on severe symptoms in individuals infected by resistant Staphylococcus aureus, and codeine has no effect on pain in individuals with certain polym ...
There is a bias in the inference pipeline of most diffusion models. This bias arises from a signal leak whose distribution deviates from the noise distribution, creating a discrepancy between training and inference processes. We demonstrate that this signa ...
The growing popularity of virtual reality systems has led to a renewed interest in understanding the neurophysiological correlates of the illusion of self-motion (vection), a phenomenon that can be both intentionally induced or avoided in such systems, dep ...
In this paper, we propose a novel approach that employs kinetic equations to describe the collective dynamics emerging from graph-mediated pairwise interactions in multi-agent systems. We formally show that for large graphs and specific classes of interact ...
An efficient characterization of scientifically significant locations is essential prior to the return of humans to the Moon. The highest resolution imagery acquired from orbit of south-polar shadowed regions and other relevant locations remains, at best, ...
