相关论文: Graph Reconstruction and Quantum Statistical Mecha…
The $k$-deck of a graph is the multiset of its subgraphs induced by $k$ vertices. A graph or graph property is $l$-reconstructible if it is determined by the deck of subgraphs obtained by deleting $l$ vertices. We show that the degree list…
Reconstructing a signal on a graph from observations on a subset of the vertices is a fundamental problem in the field of graph signal processing. It is often assumed that adding additional observations to an observation set will reduce the…
The question whether there exists a hypergraph whose degrees are equal to a given sequence of integers is a well-known reconstruction problem in graph theory, which is motivated by discrete tomography. In this paper we approach the problem…
This paper addresses the problem of sparse recovery with graph constraints in the sense that we can take additive measurements over nodes only if they induce a connected subgraph. We provide explicit measurement constructions for several…
Using von Neumann algebras, we extend the theory of quantum computation on a graph to a theory of computation on an arbitrary topological space.
Finding coarse representations of large graphs is an important computational problem in the fields of scientific computing, large scale graph partitioning, and the reduction of geometric meshes. Of particular interest in all of these fields…
After a brief review of spin networks and their interpretation as wave functions for the (space) geometry, we discuss the renormalisation of the area operator in loop quantum gravity. In such a background independent framework, we propose…
Given a unitary operator in a finite dimensional complex Hilbert space, its unitary reduction to a subspace is defined. The application to quantum graphs is discussed. It is shown how the reduction allows to generate the scattering matrices…
This note aims to highlight the link between representable functionals and derivations on a Banach quasi *-algebra, i.e. a mathematical structure that can be seen as the completion of a normed *-algebra in the case the multiplication is…
A graph is $\ell$-reconstructible if it is determined by its multiset of induced subgraphs obtained by deleting $\ell$ vertices. We prove that strongly regular graphs with at least six vertices are $2$-reconstructible.
A number of applications in engineering, social sciences, physics, and biology involve inference over networks. In this context, graph signals are widely encountered as descriptors of vertex attributes or features in graph-structured data.…
We obtain a condensed reconstruction of algebraic quantum theory, emphasizing its foundational aspects and algebraic structure. We obtain the $W^*$-algebra structure from elementary assumptions about observers and how they can observe…
L. A. Bunimovich and B. Z. Webb developed a theory for transforming a finite weighted graph while preserving its spectrum, referred as isospectral reduction theory. In this work we extend this theory to a class of operators on Banach spaces…
We initiate the study of approximate quantum fractional revival in graphs, a generalization of pretty good quantum state transfer in graphs. We give a complete characterization of approximate fractional revival in a graph in terms of the…
Unprecedented increase of complexity and scale of data is expected in computation necessary for the tracking detectors of the High Luminosity Large Hadron Collider (HL-LHC) experiments. While currently used Kalman filter based algorithms…
We develop a general spectral framework to analyze quantum fractional revival in quantum spin networks. In particular, we introduce generalizations of the notions of cospectral and strongly cospectral vertices to arbitrary subsets of…
Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance,…
When working with quantum states, analysis of the final quantum state generated through probabilistic measurements is essential. This analysis is typically conducted by constructing the density matrix from either partial or full tomography…
In this job, we will present a theory called Quantum Tomography that is the natural extension of the theory of detection of signals in classical telecommunications to Quantum Mechanics. This theory mainly consists in the reconstruction of a…
This paper is first-line research expanding GANs into graph topology analysis. By leveraging the hierarchical connectivity structure of a graph, we have demonstrated that generative adversarial networks (GANs) can successfully capture…