相关论文: Exploring Steinitz-Rademacher polyhedra: A challen…

We develop new perturbative tools to accurately study radiatively-induced first-order phase transitions. Previous perturbative methods have suffered internal inconsistencies and been unsuccessful in reproducing lattice data, which is often…

The existing algorithm to compute and verify the automata associated with an automatic group deals only with the subclass of shortlex automatic groups. This paper describes the extension of the algorithm to deal with automatic groups…

Since the 1970s with the work of McNaughton, Papert and Sch\"utzenberger, a regular language is known to be definable in the first-order logic if and only if its syntactic monoid is aperiodic. This algebraic characterisation of a…

We study the head-on collision of two equal-mass momentarily stationary black holes, using black hole perturbation theory up to second order. Compared to first-order results, this significantly improves agreement with numerically computed…

The computational complexity of reasoning within the Dempster-Shafer theory of evidence is one of the main points of criticism this formalism has to face. To overcome this difficulty various approximation algorithms have been suggested that…

We present the problem stated in intuitive language as problem 2 at the 52nd International Mathematical Olympiad as a formal statement, and prove that it is valid in ordered regular incidence planes, the weakest ordered geometry whose…

A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…

Cycle polytopes of matroids have been introduced in combinatorial optimization as a generalization of important classes of polyhedral objects like cut polytopes and Eulerian subgraph polytopes associated to graphs. Here we start an…

The unification of statistical (data-driven) and symbolic (knowledge-driven) methods is widely recognised as one of the key challenges of modern AI. Recent years have seen large number of publications on such hybrid neuro-symbolic AI…

Rough set theory is a useful tool to deal with uncertain, granular and incomplete knowledge in information systems. And it is based on equivalence relations or partitions. Matroid theory is a structure that generalizes linear independence…

Rademacher complexity is often used to characterize the learnability of a hypothesis class and is known to be related to the class size. We leverage this observation and introduce a new technique for estimating the size of an arbitrary…

This article aims to explain the Nested Benders algorithm for the solution of large-scale stochastic programming problems in a way that is intelligible to someone coming to it for the first time. In doing so it gives an explanation of…

Polytopes are one of the most primitive concepts underlying geometry. Discovery and study of polytopes with complex structures provides a means of advancing scientific knowledge. Construction of polytopes with specific extremal structure is…

In this paper, we study the Hochschild cohomology of diagrams of algebras introduced by Gerstenhaber and Schack and provide computations for filtrations of incidence algebras. Our aims are threefold: firstly, we revisit and explore the…

In this article we review some problems in physics, chemistry and mathematics that lead naturally to a class of polyhedra which include the Platonic solids. Examples include the study of electrons on a sphere, cages of carbon atoms, central…

First-order logic is a natural way of expressing properties of computation. It is traditionally used in various program logics for expressing the correctness properties and certificates. Although such representations are expressive for some…

We give a new proof of Steinitz's classical theorem in the case of plane triangulations, which allows us to obtain a new general bound on the grid size of the simplicial polytope realizing a given triangulation, subexponential in a number…

A proof for a conjecture by Shadrin and Zvonkine, relating the entries of a matrix arising in the study of Hurwitz numbers to a certain sequence of rational numbers, is given. The main tools used are iteration matrices of formal power…

We explore the idea of using automatic and similar kind of presentations of structures to deal with the conceptual problem of natural proof-theoretic ordinal notations. We conclude that this approach still does not meet the goals.

We introduce a new notion of "regularity structure" that provides an algebraic framework allowing to describe functions and / or distributions via a kind of "jet" or local Taylor expansion around each point. The main novel idea is to…