Related papers: Structural Analysis of Boolean Equation Systems
Iterative solvers are widely used to accurately simulate physical systems. These solvers require initial guesses to generate a sequence of improving approximate solutions. In this contribution, we introduce a novel method to accelerate…
In this work, we introduce Regularity Structures B-series which are used for describing solutions of singular stochastic partial differential equations (SPDEs). We define composition and substitutions of these B-series and as in the context…
Understanding which system structure can sustain stable dynamics is a fundamental step in the design and analysis of large scale dynamical systems. Towards this goal, we investigate here the structural stability of systems with a random…
Probabilistic graphical models (PGMs) provide a compact and flexible framework to model very complex real-life phenomena. They combine the probability theory which deals with uncertainty and logical structure represented by a graph which…
We investigate the presence of localized solutions in models described by a single real scalar field with generalized dynamics. The study offers a method to solve very intricate nonlinear ordinary differential equations, and we illustrate…
We present a novel approach for graph classification based on tabularizing graph data via new variants of the Weisfeiler-Leman algorithm and then applying methods for tabular data. The variants are obtained by modifying the underlying…
We refine and advance the study of the local structure of idempotent finite algebras started in [A.Bulatov, The Graph of a Relational Structure and Constraint Satisfaction Problems, LICS, 2004]. We introduce a graph-like structure on an…
We study algorithmic learning of algebraic structures. In our framework, a learner receives larger and larger pieces of an arbitrary copy of a computable structure and, at each stage, is required to output a conjecture about the isomorphism…
We design and analyse a new numerical method to solve ODE system based on the structural method. We compute approximations of solutions together with its derivatives up to order $K$ by solving an entire block corresponding to $R$ time…
Linear structural equation models, which relate random variables via linear interdependencies and Gaussian noise, are a popular tool for modeling multivariate joint distributions. These models correspond to mixed graphs that include both…
In this paper, we investigate space-time tradeoffs for answering Boolean conjunctive queries. The goal is to create a data structure in an initial preprocessing phase and use it for answering (multiple) queries. Previous work has developed…
We generalise the concept of duality to systems of ordinary difference equations (or maps). We propose a procedure to construct a chain of systems of equations which are dual, with respect to an integral $H$, to the given system, by…
We investigate Feynman graphs and their Feynman rules from the viewpoint of graph complexes. We focus on graph homology and on the appearance of cubical complexes when either reducing internal edges or when removing them by putting them on…
In this paper, we consider to what degree the structure of a linear system is determined by the system's input/output behavior. The structure of a linear system is a directed graph where the vertices represent the variables in the system…
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…
We consider a graphical model where a multivariate normal vector is associated with each node of the underlying graph and estimate the graphical structure. We minimize a loss function obtained by regressing the vector at each node on those…
In this paper we introduce a general framework for the study of limits of relational structures in general and graphs in particular, which is based on a combination of model theory and (functional) analysis. We show how the various…
Existing structural analysis methods may fail to find all hidden constraints for a system of differential-algebraic equations with parameters if the system is structurally unamenable for certain values of the parameters. In this paper, for…
A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…
We propose an alternative proof concerning necessary and sufficient conditions to split the problem of searching for d-separators and building the skeleton of a DAG into small problems for every node of a separation tree T. The proof is…