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We investigate the asymptotic number of induced subgraphs in power-law uniform random graphs. We show that these induced subgraphs appear typically on vertices with specific degrees, which are found by solving an optimization problem.…
This is the third in a series of papers which outlines an approach to the classification of $\mathcal{N}{=}2$ superconformal field theories at rank 2 via the study of their Coulomb branch geometries. Here we use the fact that the encoding…
Let H be a graph, and let C_H(G) be the number of (subgraph isomorphic) copies of H contained in a graph G. We investigate the fundamental problem of estimating C_H(G). Previous results cover only a few specific instances of this general…
In many scenarios, especially biomedical applications, the correct delineation of complex fine-scaled structures such as neurons, tissues, and vessels is critical for downstream analysis. Despite the strong predictive power of deep learning…
Understanding the structure of a graph along with the structure of its subgraphs is important for several problems in graph theory. Two examples are the Reconstruction Conjecture and isomorph-free generation. This paper raises the question…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
We define the class of high dimensional graph manifolds. These are compact smooth manifolds supporting a decomposition into finitely many pieces, each of which is diffeomorphic to the product of a torus with a finite volume hyperbolic…
In this paper, we introduce the concept of self-amplifying structures for hypergraphs, positioning it as a key element for understanding propagation and internal reinforcement in complex systems. To quantify this phenomenon, we define the…
This paper aims at constructing a good graph for discovering intrinsic data structures in a semi-supervised learning setting. Firstly, we propose to build a non-negative low-rank and sparse (referred to as NNLRS) graph for the given data…
The guessing number of a directed graph (digraph), equivalent to the entropy of that digraph, was introduced as a direct criterion on the solvability of a network coding instance. This paper makes two contributions on the guessing number.…
We study vertex-ordering problems in loop-free digraphs subject to constraints on the left-going arcs, focusing on existence conditions and computational complexity. As an intriguing special case, we explore vertex-specific lower and upper…
For random combinatorial optimization problems, there has been much progress in establishing laws of large numbers and computing limiting constants for the optimal value of various problems. However, there has not been as much success in…
The graph reconstruction conjecture states that all graphs on at least three vertices are determined up to isomorphism by their deck. In this paper, a general framework for this problem is proposed to simply explain the reconstruction of…
We study noncrossing geometric graphs and their disjoint compatible geometric matchings. Given a cycle (a polygon) P we want to draw a set of pairwise disjoint straight-line edges with endpoints on the vertices of P such that these new…
Performing inference in graphs is a common task within several machine learning problems, e.g., image segmentation, community detection, among others. For a given undirected connected graph, we tackle the statistical problem of exactly…
Optimization problems consist of either maximizing or minimizing an objective function. Instead of looking for a maximum solution (resp. minimum solution), one can find a minimum maximal solution (resp. maximum minimal solution). Such…
The problem of construction of irreducible representations of quantum $A^q_n$ algebras is solved at the level of explicit integration of the linear (inhomogeneous) system in finite differences in the n-dimensional space. The general…
We consider linear codes over a finite field of odd characteristic, derived from determinantal varieties, obtained from symmetric matrices of bounded ranks. A formula for the weight of a code word is derived. Using this formula, we have…
The inverse problem of diffraction theory in essence amounts to the reconstruction of the atomic positions of a solid from its diffraction image. From a mathematical perspective, this is a notoriously difficult problem, even in the…
Given a graph $G$, the maximal induced subgraphs problem asks to enumerate all maximal induced subgraphs of $G$ that belong to a certain hereditary graph class. While its optimization version, known as the minimum vertex deletion problem in…