Related papers: Hypergraph Horn functions
We review remarkable results in several mathematical scenarios, including graph theory, division algebras, cross product formalism and matroid theory. Specifically, we mention the following subjects: (1) the Euler relation in graph theory,…
The Sine Gordon theory is generalized to include several cosine terms. This is similar to the world sheet description of a string propagating in a tachyon background. This model is studied as a (boundary) 2d euclidean field theory and also…
It is known that the entropy function over a set of jointly distributed random variables is a submodular set function. However, not any submodular function is of this form. In this paper, we consider a family of submodular set functions,…
Deep Neural Networks (DNN) applications are increasingly becoming a part of our everyday life, from medical applications to autonomous cars. Traditional validation of DNN relies on accuracy measures, however, the existence of adversarial…
At present, practical application and theoretical discussion of rough sets are two hot problems in computer science. The core concepts of rough set theory are upper and lower approximation operators based on equivalence relations. Matroid,…
We suggest to associate with each knot the set of coefficients of its HOMFLY polynomial expansion into the Schur functions. For each braid representation of the knot these coefficients are defined unambiguously as certain combinations of…
Learning from structured data is a core machine learning task. Commonly, such data is represented as graphs, which normally only consider (typed) binary relationships between pairs of nodes. This is a substantial limitation for many domains…
The present article reveals important properties of the confluent Heun's functions. We derive a set of novel relations for confluent Heun's functions and their derivatives of arbitrary order. Specific new subclasses of confluent Heun's…
A {\em connectivity function on} a set $E$ is a function $\lambda:2^E\rightarrow \mathbb R$ such that $\lambda(\emptyset)=0$, that $\lambda(X)=\lambda(E-X)$ for all $X\subseteq E$ and that $\lambda(X\cap Y)+\lambda(X\cup Y)\leq…
Verification problems of programs written in various paradigms (such as imperative, logic, concurrent, functional, and object-oriented ones) can be reduced to problems of solving Horn clause constraints on predicate variables that represent…
Robustness in complex systems is of significant engineering and economic importance. However, conventional attack-based a posteriori robustness assessments incur prohibitive computational overhead. Recently, deep learning methods, such as…
Many complex networks exhibit hierarchical, tree-like structures, making hyperbolic space a natural candidate wherein to learn representations of them. Based on this observation, Hyperbolic Graph Neural Networks (HGNNs) have been widely…
We compare two classes of functions arising from genus-one superstring amplitudes: modular and holomorphic graph functions. We focus on their analytic properties, we recall the known asymptotic behaviour of modular graph functions and we…
Motivated by applications in automated verification of higher-order functional programs, we develop a notion of constrained Horn clauses in higher-order logic and a decision problem concerning their satisfiability. We show that, although…
Persistent homology (PH) encodes global information, such as cycles, and is thus increasingly integrated into graph neural networks (GNNs). PH methods in GNNs typically traverse an increasing sequence of subgraphs. In this work, we first…
Despite there being significant work on developing spectral, and metric embedding based approximation algorithms for hypergraph generalizations of conductance, little is known regarding the approximability of hypergraph partitioning…
A very popular model in machine learning is the feedforward neural network (FFN). The FFN can approximate general functions and mitigate the curse of dimensionality. Here we introduce FFNs which represent sections of holomorphic line…
In this paper, we introduce new classes of functions that extend the known classes of functions of complex variable, such as entire functions, meromorphic functions, rational functions and polynomial functions and take values in the set of…
Let k be a field of characteristic zero. We consider graded subalgebras A of k[x_1,...,x_m]/(x_1^2,...,x_m^2) generated by d linearly independant linear forms. Representations of matroids over k provide a natural description of the…
The lifted horn map of a holomorphic function with a simple parabolic point is well known to be a complete local conjugacy invariant; this is a classical result proved independently by \'Ecalle, Voronin, Martinet and Ramis. Lanford and…