Related papers: Gauge-invariant uniqueness theorems for $P$-graphs
An invariant for cospectral graphs is a property shared by all cospectral graphs. In this paper, we establish three novel arithmetic invariants for cospectral graphs, revealing deep connections between spectral properties and combinatorial…
This article proposes a graphical model that handles mixed-type, multi-group data. The motivation for such a model originates from real-world observational data, which often contain groups of samples obtained under heterogeneous conditions…
For a set-endofunctor $F$, we extend the notion of universal $F$-coalgebras to $F$-graphs. These generalized coalgebras are models for various types of graphs, such as (un)directed (hyper)graphs, relational structures or fuzzy graphs. The…
The following two loosely connected sets of topics are reviewed in these lecture notes: 1) Gauge invariance, its treatment in field theories and its implications for internal symmetries and edge states such as those in the quantum Hall…
We provide inverse semigroup and groupoid models for the Toeplitz and Cuntz-Krieger algebras of finitely aligned higher-rank graphs. Using these models, we prove a uniqueness theorem for the Cuntz-Krieger algebra.
Let $\Gamma$ be a simple undirected graph on a finite vertex set and let $A$ be its adjacency matrix. Then $\Gamma$ is {\it singular} if $A$ is singular. The problem of characterising singular graphs is easy to state but very difficult to…
A classification of the possible symmetric principal bundles with a compact gauge group, a compact symmetry group and a base manifold which is regularly foliated by the orbits of the symmetry group is derived. A generalization of Wang's…
Let $C^*(E)$ be the graph C$^*$-algebra of a row-finite graph $E$. We give a complete description of the vertex sets of the gauge-invariant regular ideals of $C^*(E)$. It is shown that when $E$ satisfies Condition (L) the regular ideals…
There is arbitrariness in optimum solutions of graph-theoretic problems that can give rise to unfairness. Incorporating fairness in such problems, however, can be done in multiple ways. For instance, fairness can be defined on an individual…
We present a general diagrammatic theory for determining consistent electromagnetic response functions in strongly correlated fermionic superfluids. The general treatment of correlations beyond BCS theory requires a new theoretical…
We study an algebraic analog of a C*-algebra associated to a generalized Boolean dynamical system which parallels the relation between graph C*-algebras and Leavitt path algebras. We prove that such algebras are Cuntz-Pimsner algebras and…
The binding number $b(G)$ of a graph, introduced by Woodall [J. Combin. Theory, Ser. B, 1973], is a central topic of both structural and extremal graph theory. It is closely related to fundamental combinatorial and structural properties of…
We study the analytic and topological invariants associated with complex normal surface singularities. Our goal is to provide topological formulae for several discrete analytic invariants whenever the analytic structure is generic (with…
We construct new examples of ergodic coactions of compact quantum groups, in which the multiplicity of an irreducible corepresentation can be strictly larger than the dimension of the latter. These examples are obtained using a bijective…
We define $G$-cospectrality of two $G$-gain graphs $(\Gamma,\psi)$ and $(\Gamma',\psi')$, proving that it is a switching isomorphism invariant. When $G$ is a finite group, we prove that $G$-cospectrality is equivalent to cospectrality with…
Applications to quantum gravity of some results in C*-algebras are developed. We open by describing why algebra may be an integral aspect of quantum gravity. By interpreting the inner automorphisms of a C*-algebra as families of parallel…
We study the existence and regularity of invariant graphs for bundle maps (or bundle correspondences with generating bundle maps motivated by ill-posed differential equations) having some relative partial hyperbolicity on non-trivial and…
Gaussian graphical models have become a well-recognized tool for the analysis of conditional independencies within a set of continuous random variables. From an inferential point of view, it is important to realize that they are composite…
A dominating set in a graph $G$ is a set $S$ of vertices such that every vertex of $G$ is either in $S$ or is adjacent to a vertex in $S$. Nordhaus-Gaddum inequailties relate a graph $G$ to its complement $\bar{G}$. In this spirit Wagner…
We propose a conceptually economical and computationally tractable completion of the foundations of gauge theory on quantum principal bundles \`{a} la Brzezi\'{n}ski--Majid to the case of general differential calculi and strong bimodule…