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The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
We introduce a functorial construction which, from a monoid, produces a set-operad. We obtain new (symmetric or not) operads as suboperads or quotients of the operad obtained from the additive monoid. These involve various familiar…
We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar…
In the field of complex networks and graph theory, new results are typically tested on graphs generated by a variety of algorithms such as the Erd\H{o}s-R\'{e}nyi model or the Barab\'{a}si-Albert model. Unfortunately, most graph generating…
We consider, and make precise, a certain extension of the Radon-Nikodym derivative operator, to functions which are additive, but not necessarily sigma-additive, on a subset of a given sigma-algebra. We give applications to probability…
Set functions are a feature of functional logic programming to encapsulate all results of a non-deterministic computation in a single data structure. Given a function $f$ of a functional logic program written in Curry, we describe a…
Regular colored graphs are dual representations of pure colored D-dimensional complexes. These graphs can be classified with respect to an integer, their degree, much like maps are characterized by the genus. We analyse the structure of…
Deep generative models have achieved remarkable success in various data domains, including images, time series, and natural languages. There remain, however, substantial challenges for combinatorial structures, including graphs. One of the…
A subclass of nondeterministic Finite Automata generated by means of regular Grammars (GFAs, for short) is introduced. A process algebra is proposed, whose semantics maps a term to a GFA. We prove a representability theorem: for each GFA…
This is an investigation of the role of shuffling and concatenating in the theory of graph drawing. A simple syntactic description of these and related operations is proved complete in the context of finite partial orders, as general as…
In the context of interactive theorem provers based on a dependent type theory, automation tactics (dedicated decision procedures, call of automated solvers, ...) are often limited to goals which are exactly in some expected logical…
We give a simpler proof using automata theory of a recent result of Kapovich, Weidmann and Myasnikov according to which so-called benign graphs of groups preserve decidability of the generalized word problem. These include graphs of groups…
Compositionality is thought to be a key component of language, and various compositional benchmarks have been developed to empirically probe the compositional generalization of existing sequence processing models. These benchmarks often…
In this note we consider $k$-regular multigraphs, where the possible edge multiplicities are controlled. These structures are considered in a question recently posed by Brendan McKay. We express the generating functions using the scalar…
The paper studies complementary choice functions, i.e. monotonic and consistent choice functions. Such choice functions were introduced and used in the work \cite{RY} for investigation of matchings with complementary contracts. Three…
This paper studies which functions computed by $\mathbb{Z}$-weighted automata can be realized by $\mathbb{N}$-weighted automata, under two extra assumptions: commutativity (the order of letters in the input does not matter) and polynomial…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
Several methods are discussed that construct a finite automaton given a context-free grammar, including both methods that lead to subsets and those that lead to supersets of the original context-free language. Some of these methods of…
Traditional treatments of formal logic provide: 1. A syntax for formulas. 2. An inference relation between sets of formulas. 3. A rule for assigning meaning to formulas (semantics) that is sound with respect to the inference relation. First…
We study functional graphs generated by quadratic polynomials over prime fields. We introduce efficient algorithms for methodical computations and provide the values of various direct and cumulative statistical parameters of interest. These…