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We investigate the universality of microscopic eigenvalue correlations for Random Matrix Theories with the global symmetries of the QCD partition function. In this article we analyze the case of real valued chiral Random Matrix Theories…
This paper is devoted to the analysis of charged superselection sectors in the framework of the locally covariant quantum field theories. We shall analize sharply localizable charges, and use net-cohomology of J.E. Roberts as a main tool.…
Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques…
This work provides the first unifying theoretical framework for node (positional) embeddings and structural graph representations, bridging methods like matrix factorization and graph neural networks. Using invariant theory, we show that…
A Robinson similarity matrix is a symmetric matrix where the entry values on all rows and columns increase toward the diagonal. Decompose the Robinson matrix into the sum of k {0, 1}-matrices, then these k {0, 1}-matrices are the adjacency…
Symmetries in a network connectivity regulate how the graph's functioning organizes into clustered states. Classical methods for tracing the symmetry group of a network require very high computational costs, and therefore they are of hard,…
We investigate $(0,1)$-matrices that are {\em convex}, which means that the ones are consecutive in every row and column. These matrices occur in discrete tomography. The notion of ranked essential sets, known for permutation matrices, is…
The success of graph embeddings or node representation learning in a variety of downstream tasks, such as node classification, link prediction, and recommendation systems, has led to their popularity in recent years. Representation learning…
In this paper, we derive nearly tight probabilistic norm bounds for a class of random matrices we call graph matrices. While the classical case of symmetric matrices with independent random entries (Wigner's matrices) is a special case, in…
The phenomenon of spontaneous synchronization is universal and only recently advances have been made in the quantum domain. Being synchronization a kind of temporal correlation among systems, it is interesting to understand its connection…
Suppose we are given a system of coupled oscillators on an unknown graph along with the trajectory of the system during some period. Can we predict whether the system will eventually synchronize? Even with a known underlying graph…
Connectedness and bipartiteness are basic properties of classical graphs, and the purpose of this paper is to investigate the case of quantum graphs. We introduce the notion of connectedness and bipartiteness of quantum graphs in terms of…
The congruence orbit of a matrix has a natural connection with the linear complementarity problem on simplicial cones formulated for the matrix. In terms of the two approaches -- the congruence orbit and the family of all simplicial cones…
Conformal nets are a classical topic in quantum field theory: they assign operator algebras to one-dimensional manifolds, and have close connections with one-dimensional topological field theories. It seems to be well-known that the usual…
We study a class of parametrizations of convex cones of positive semidefinite matrices with prescribed zeros. Each such cone corresponds to a graph whose non-edges determine the prescribed zeros. Each parametrization in this class is a…
The paper studies sequential reasoning over graph-structured data, which stands as a fundamental task in various trending fields like automated math problem solving and neural graph algorithm learning, attracting a lot of research interest.…
In this paper, we present two main results. First, by only one conjecture (Conjecture 2.9) for recognizing a vertex symmetric graph, which is the hardest task for our problem, we construct an algorithm for finding an isomorphism between two…
Here, the structural symmetries of a hypergraph are represented through equivalence relations on the vertex set of the hypergraph. A matrix associated with the hypergraph may not reflect a specific structural symmetry. In the context of a…
We define notions of local topological convergence and local geometric convergence for embedded graphs in $\mathbb{R}^n,$ and study their properties. The former is related to Benjamini-Schramm convergence, and the latter to weak convergence…
Representation learning for graphs enables the application of standard machine learning algorithms and data analysis tools to graph data. Replacing discrete unordered objects such as graph nodes by real-valued vectors is at the heart of…