相关论文: A Bramble like Witness for Large Branch-Width
Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have…
We use a tensor unfolding technique to prove a new identifiability result for discrete bipartite graphical models, which have a bipartite graph between an observed and a latent layer. This model family includes popular models such as…
A graph class $\mathcal{C}$ has polynomial expansion if there is a polynomial function $f$ such that for every graph $G\in \mathcal{C}$, each of the depth-$r$ minors of $G$ has average degree at most $f(r)$. In this note, we study…
We apply a framework for the description of random tilings without height representation, which was proposed recently, to the special case of quasicrystalline random tilings. Several important examples are discussed, thereby demonstrating…
A new approach is suggested to quantum differential calculus on certain quantum varieties. It consists in replacing quantum de Rham complexes with differentials satisfying Leibniz rule by those which are in a sense close to Koszul complexes…
X-ray tomography is performed to acquire 3D images of crumpled aluminum foils. We develop an algorithm to trace out the labyrinthian paths in the three perpendicular cross sections of the data matrices. The tangent-tangent correlation…
In this paper we introduce and study a new family of combinatorial simplicial complexes, which we call immediate snapshot complexes. Our construction and terminology is strongly motivated by theoretical distributed computing, as these…
We introduce a technique called graph fission which takes in a graph which potentially contains only one observation per node (whose distribution lies in a known class) and produces two (or more) independent graphs with the same node/edge…
Characterizing entanglement is central for quantum information science. Special observables which indicate entanglement, so-called entanglement witnesses, are a widely used tool for this task. The construction of these witnesses typically…
In 2003, van Dam and Haemers posed a fundamental question in spectral graph theory: does there exist a ``sensible'' matrix whose spectrum determines a random graph up to isomorphism? This paper introduces the class of {\em natural graph…
Branching-stable processes have recently appeared as counterparts of stable subordinators, when addition of real variables is replaced by branching mechanism for point processes. Here, we are interested in their domains of attraction and…
Recent progress in theories of quantum information has determined nonclassical correlation defined differently from widely-used entanglement as an important property to evaluate computation and communication with mixed quantum states. We…
A differential version of the classical Weil descent is established in all characteristics. It yields a theory of differential restriction of scalars for differential varieties over finite differential field extensions. This theory is then…
For $d\ge 2$ and an odd prime power $q$, consider the vector space $\mathbb{F}_q^d$ over the finite field $\mathbb{F}_q$, where the distance between two points $(x_1,\ldots,x_d)$ and $(y_1,\ldots,y_d)$ is defined as $\sum_{i=1}^d…
We prove that the Kauffman bracket skein algebra of a cylinder over a surface with boundary, defined over complex numbers, is isomorphic to the observables of an appropriate lattice gauge field theory.
While branching network structures abound in nature, their objective analysis is more difficult than expected because existing quantitative methods often rely on the subjective judgment of branch structures. This problem is particularly…
Camouflaged objects attempt to conceal their texture into the background and discriminating them from the background is hard even for human beings. The main objective of this paper is to explore the camouflaged object segmentation problem,…
Building on earlier work, we construct linear sigma models for strings on curved spaces in the presence of branes. Our models include an extremely general class of brane-worldvolume gauge field configurations. We explain in an accessible…
The Weibull function is widely used to describe skew distributions observed in nature. However, the origin of this ubiquity is not always obvious to explain. In the present paper, we consider the well-known Galton-Watson branching process…
Phylogenetic networks are an important way to represent evolutionary histories that involve reticulations such as hybridization or horizontal gene transfer, yet fundamental questions such as how many networks there are that satisfy certain…