Related papers: Kernels, Truth and Satisfaction
Family members' satisfaction with one another is central to creating healthy and supportive family environments. In this work, we propose and implement a novel computational technique aimed at exploring the possible relationship between the…
In this thesis, we analyze the stochastic completeness of a heat kernel on graphs which is a function of three variables: a pair of vertices and a continuous time, for infinite, locally finite, connected graphs. For general graphs, a…
Given a graph and two integers $k$ and $\ell$, Partial Vertex Cover asks for a set of at most $k$ vertices whose deletion results in a graph with at most $\ell$ edges. Based on the expansion lemma, we provide a problem kernel with $(\ell +…
Given only information in the form of similarity triplets "Object A is more similar to object B than to object C" about a data set, we propose two ways of defining a kernel function on the data set. While previous approaches construct a…
We present a polyhedral description of kernels in orientations of line multigraphs. Given a digraph $D$, let $FK(D)$ denote the fractional kernel polytope defined on $D$, and let ${\sigma}(D)$ denote the linear system defining $FK(D)$. A…
We define a family of kernels for mixed continuous/discrete hierarchical parameter spaces and show that they are positive definite.
Graph kernels are often used in bioinformatics and network applications to measure the similarity between graphs; therefore, they may be used to construct efficient graph classifiers. Many graph kernels have been developed thus far, but to…
For a digraph $D$ of order $n$ and an integer $1 \leq k \leq n-1$, the $k$-token digraph of $D$ is the graph whose vertices are all $k$-subsets of vertices of $D$ and, given two such $k$-subsets $A$ and $B$, $(A,B)$ is an arc in the…
In a digraph, a kernel is a subset of vertices that is both independent and absorbing. Kernels have important applications in combinatorics and outside. Kernels do not always exist and finding sufficient conditions ensuring their existence…
An independent vertex subset $S$ of the directed graph $G$ is a kernel if the set of out-neighbors of $S$ is $V(G)\setminus S$. An independent vertex subset $Q$ of $G$ is a quasi-kernel if the union of the first and second out-neighbors…
The problem of graph learning concerns the construction of an explicit topological structure revealing the relationship between nodes representing data entities, which plays an increasingly important role in the success of many graph-based…
We consider the Trivially Perfect Editing problem, where one is given an undirected graph $G = (V,E)$ and a parameter $k \in \mathbb{N}$ and seeks to edit (add or delete) at most $k$ edges from $G$ to obtain a trivially perfect graph. The…
Necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a k-connected simple graph are detailed. Conditions are also given under which such a sequence is necessarily k-connected.
The power graph of a group is the graph whose vertex set is the set of non-trivial elements of group, two elements being adjacent if one is a power of the other. We define a new power graph and study on connectivity, diameter and clique…
We begin the study of completeness of affine connections, especially those on statistical manifolds as well as on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.
Graph-structured data arise ubiquitously in many application domains. A fundamental problem is to quantify their similarities. Graph kernels are often used for this purpose, which decompose graphs into substructures and compare these…
Neural networks are often represented as graphs of connections between neurons. However, despite their wide use, there is currently little understanding of the relationship between the graph structure of the neural network and its…
We prove that the satisfaction relation $\mathcal{N}\models\varphi[\vec a]$ of first-order logic is not absolute between models of set theory having the structure $\mathcal{N}$ and the formulas $\varphi$ all in common. Two models of set…
Graph kernel is a powerful tool measuring the similarity between graphs. Most of the existing graph kernels focused on node labels or attributes and ignored graph hierarchical structure information. In order to effectively utilize graph…
A graph is called matching covered if for its every edge there is a maximum matching containing it. It is shown that minimal matching covered graphs contain a perfect matching.