相关论文: A new way to evaluate MOY graphs
A theory graph is a network of axiomatic theories connected with meaning-preserving mappings called theory morphisms. Theory graphs are well suited for organizing large bodies of mathematical knowledge. Traditional and formal proofs do not…
Real data collected from different applications that have additional topological structures and connection information are amenable to be represented as a weighted graph. Considering the node labeling problem, Graph Neural Networks (GNNs)…
We considers how a particular kind of graph corresponds to multiplicative intuitionistic linear logic formula. The main feature of the graphical notation is that it absorbs certain symmetries between conjunction and implication. We look at…
New theoretical approaches about forecasting stock markets are proposed. A mathematization of the stock market in terms of arithmetical relations is given, where some simple (non-differential, non-fractal) expressions are also suggested as…
The notion of a $k$-11-representable graph was introduced by Jeff Remmel in 2017 and studied by Cheon et al.\ in 2019 as a natural extension of the extensively studied notion of word-representable graphs, which are precisely…
A new class of rational parametrization has been developed and it was used to generate a new family of rational functions B-splines $\displaystyle{{\left({}^{\alpha}{\mathbf B}_{i}^{k} \right)}_{i=0}^{k}}$ which depends on an index $\alpha…
In this note we classify when a skew Schur function is a positive linear combination of power sum symmetric functions. We then use this to determine precisely when any scalar multiple of a skew Schur function is the chromatic symmetric…
The purpose of this paper is to develop a "calculus" on graphs that allows graph theory to have new connections to analysis. For example, our framework gives rise to many new partial differential equations on graphs, most notably a new…
Matrix Graph Grammars (MGG) is a novel approach to the study of graph dynamics ([15]). In the present contribution we look at MGG as a formal grammar and as a model of computation, which is a necessary step in the more ambitious program of…
Ancestral graphs are a class of graphs that encode conditional independence relations arising in DAG models with latent and selection variables, corresponding to marginalization and conditioning. However, for any ancestral graph, there may…
We introduce a symbolic method for the evaluation of definite integrals containing combinations of various functions, including exponentials, logarithm and products of Bessel functions of different types. The method we develop is naturally…
In this paper, we give a new class of reconstructible graphs, which is an extension of my paper `A class of reconstructible graphs'.
The syntax of modal graphs is defined in terms of the continuous cut and broken cut following Charles Peirce's notation in the gamma part of his graphical logic of existential graphs. Graphical calculi for normal modal logics are developed…
We study the relation between algebraic structures and Graph Theory. We have defined five different weighted digraphs associated to a finite dimensional algebra over a field in order to tackle important properties of the associated…
Many existing approaches for estimating feature importance are problematic because they ignore or hide dependencies among features. A causal graph, which encodes the relationships among input variables, can aid in assigning feature…
Recent developments in Machine Learning approaches for modelling physical systems have begun to mirror the past development of numerical methods in the computational sciences. In this survey, we begin by providing an example of this with…
We propose a novel score-based approach to learning a directed acyclic graph (DAG) from observational data. We adapt a recently proposed continuous constrained optimization formulation to allow for nonlinear relationships between variables…
Variety of machine learning problems can be formulated as an optimization task for some (surrogate) loss function. Calculation of loss function can be viewed in terms of stochastic computation graphs (SCG). We use this formalism to analyze…
In this paper we present a proof system that operates on graphs instead of formulas. Starting from the well-known relationship between formulas and cographs, we drop the cograph-conditions and look at arbitrary undirected) graphs. This…
A new class of isospectral graphs is presented. These graphs are isospectral with respect to both the normalised Laplacian on the discrete graph and the standard differential Laplacian on the corresponding metric graph. The new class of…