Related papers: Analysis of Boolean Equation Systems through Struc…
The problem of finding the connected components of a graph is considered. The algorithms addressed to solve the problem are used to solve such problems on graphs as problems of finding points of articulation, bridges, maximin bridge, etc. A…
Recent advances in the integration of deep learning with automated theorem proving have centered around the representation of logical formulae as inputs to deep learning systems. In particular, there has been a growing interest in adapting…
Monotone Boolean functions, and the monotone Boolean circuits that compute them, have been intensively studied in complexity theory. In this paper we study the structure of Boolean functions in terms of the minimum number of negations in…
Number types for exact computation are usually based on directed acyclic graphs. A poor graph structure can impair the efficency of their evaluation. In such cases the performance of a number type can be drastically improved by…
Boolean networks have been widely used in many areas of science and engineering to represent various dynamical behaviour. In systems biology, they became useful tools to study the dynamical characteristics of large-scale biomolecular…
Real-world data is often times associated with irregular structures that can analytically be represented as graphs. Having access to this graph, which is sometimes trivially evident from domain knowledge, provides a better representation of…
We study multivariate polynomials over `structured' grids. We begin by proposing an interpretation as to what it means for a finite subset of a field to be structured; we do so by means of a numerical parameter, the nullity. We then extend…
Graphs are ubiquitous data structures for representing interactions between entities. With an emphasis on the use of graphs to represent chemical molecules, we explore the task of learning to generate graphs that conform to a distribution…
Network structure optimization is a fundamental task in complex network analysis. However, almost all the research on Bayesian optimization is aimed at optimizing the objective functions with vectorial inputs. In this work, we first present…
Recurrence plots exhibit line structures which represent typical behaviour of the investigated system. The local slope of these line structures is connected with a specific transformation of the time scales of different segments of the…
In this paper, we show that the solution to a large class of "tiling" problems is given by a polynomial sequence of binomial type. More specifically, we show that the number of ways to place a fixed set of polyominos on an $n\times n$…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
We present a structural clustering algorithm for large-scale datasets of small labeled graphs, utilizing a frequent subgraph sampling strategy. A set of representatives provides an intuitive description of each cluster, supports the…
We consider the problem of learning the structure of a pairwise graphical model over continuous and discrete variables. We present a new pairwise model for graphical models with both continuous and discrete variables that is amenable to…
As a common generalization of previously solved optimization problems concerning bipartite stable matchings, we describe a strongly polynomial network flow based algorithm for computing $\ell$ disjoint stable matchings with minimum total…
Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…
We investigate the power of graph isomorphism algorithms based on algebraic reasoning techniques like Gr\"obner basis computation. The idea of these algorithms is to encode two graphs into a system of equations that are satisfiable if and…
We refine the complexity landscape for enumeration problems by introducing very low classes defined by using Boolean circuits as enumerators. We locate well-known enumeration problems, e.g., from graph theory, Gray code enumeration, and…
This paper presents a novel method for structural data recognition using a large number of graph models. In general, prevalent methods for structural data recognition have two shortcomings: 1) Only a single model is used to capture…
We describe recent achievements in the theory of weight systems, which are functions on chord diagrams satisfying so-called $4$-term relations. Our main attention is devoted to constructions of weight systems. The two main sources of these…