Related papers: Computational Holonomy Decomposition of Transforma…
In recent papers, Margolis, Rhodes and Schilling proved that the complexity of a finite semigroup is computable. This solved a problem that had been open for more than 50 years. The purpose of this paper is to survey the basic results of…
Motivated by the wide-ranging applications of Hamiltonian decompositions in distributed computing, coded caching, routing, resource allocation, load balancing, and fault tolerance, our work presents a comprehensive design for Hamiltonian…
This paper introduces new structural decompositions for almost symmetric numerical semigroups through the combinatorial lens of Young diagrams. To do that, we use the foundational correspondence between numerical sets and Young diagrams,…
Developing robust representations of chemical structures that enable models to learn topological inductive biases is challenging. In this manuscript, we present a representation of atomistic systems. We begin by proving that our…
We explain a correct proof of the decomposition theorem for direct images of constant Hodge modules by proper K\"ahler morphisms of complex manifolds. We also give some examples showing certain difficulty in the non-constant Hodge module…
We study the satisfiability problem of symbolic finite automata and decompose it into the satisfiability problem of the theory of the input characters and the monadic second-order theory of the indices of accepted words. We use our…
The modular decomposition is a technique that applies but is not restricted to graphs. The notion of module naturally appears in the proofs of many graph theoretical theorems. Computing the modular decomposition tree is an important…
The aim of this paper is to explain how, through the work of a number of people, some algebraic structures related to groupoids have yielded algebraic descriptions of homotopy n-types. Further, these descriptions are explicit, and in some…
We present a general, systematic, and efficient method for decomposing any given exponential operator of bosonic mode operators, describing an arbitrary multi-mode Hamiltonian evolution, into a set of universal unitary gates. Although our…
We develop a holonomy reduction procedure for general Cartan geometries. We show that, given a reduction of holonomy, the underlying manifold naturally decomposes into a disjoint union of initial submanifolds. Each such submanifold…
We show here that the Hamiltonian for an electronic system may be written exactly in terms of fluctuation operators that transition constituent fragments between internally correlated states, accounting rigorously for inter-fragment…
Consider a finite-dimensional algebra $A$ and any of its moduli spaces $\mathcal{M}(A,\mathbf{d})^{ss}_{\theta}$ of representations. We prove a decomposition theorem which relates any irreducible component of…
Computational indistinguishability is a key property in cryptography and verification of security protocols. Current tools for proving it rely on cryptographic game transformations. We follow Bana and Comon's approach, axiomatizing what an…
In this note we formulate and prove a version of Cartan decomposition for holomorphic loop groups, similar to Cartan decomposition for $p$-adic loop groups, discussed proved by Garland (and later by the authors by geometric mathods). The…
In this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field, generalizing results of Rhodes for the field of complex numbers. Applications are…
We introduce a formal definition of Wolfram's notion of computational process based on cellular automata, a physics-like model of computation. There is a natural classification of these processes into decidable, intermediate and complete.…
We describe a new approach towards the systematic construction of finite groups up to isomorphism. This approach yields a practical algorithm for the construction of finite solvable groups up to isomorphism. We report on a GAP…
Widely used complex code refactoring tools lack a solid reasoning about the correctness of the transformations they implement, whilst interest in proven correct refactoring is ever increasing as only formal verification can provide true…
In this article we survey recent progress in the algorithmic theory of matrix semigroups. The main objective in this area of study is to construct algorithms that decide various properties of finitely generated subsemigroups of an infinite…
In this chapter we provide an overview of computational modeling for semantic change using large and semi-large textual corpora. We aim to provide a key for the interpretation of relevant methods and evaluation techniques, and also provide…