Related papers: Inductive construction of path homology chains

In recent years, there has been significant interest in characterizing the induced subgraph obstructions to bounded treewidth and pathwidth. While this has recently been resolved for pathwidth, the case of treewidth remains open, and prior…

The simple graphs $G=(V,E)$ that satisfy $|E'|\leq 2|V'|-l$ for any subgraph (and for $l=1,2,3$) are the $(2,l)$-sparse graphs. Those that also satisfy $|E|=2|V|-l$ are the $(2,l)$-tight graphs. These can be characterised by their…

Let $P$ be a set of $n \geq 5$ points in convex position in the plane. The path graph $G(P)$ of $P$ is an abstract graph whose vertices are non-crossing spanning paths of $P$, such that two paths are adjacent if one can be obtained from the…

Given the set of paths through a digraph, the result of uniformly deleting some vertices and identifying others along each path is coherent in such a way as to yield the set of paths through another digraph, called a \emph{path abstraction}…

Pathway enrichment analysis has become a key tool for biomedical researchers to gain insight into the underlying biology of differentially expressed genes, proteins and metabolites. It reduces complexity and provides a system-level view of…

We say a graph $G$ has a Hamiltonian path if it has a path containing all vertices of $G$. For a graph $G$, let $\sigma_2(G)$ denote the minimum degree sum of two nonadjacent vertices of $G$; restrictions on $\sigma_2(G)$ are known as…

A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…

Path integrals represent a powerful route to quantization: they calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration.…

We introduce a new topological invariant of complex line arrangements in the complex projective plane, derived from the interaction between their complement and the boundary of a regular neighbourhood. The motivation is to identify Zariski…

Bandelt and Mulder's structural characterization of Bipartite Distance Hereditary graphs asserts that such graphs can be built inductively starting from a single vertex and by repeatedly adding either pending vertices or twins (i.e.,…

Integrated Gradients (IG), a widely used axiomatic path-based attribution method, assigns importance scores to input features by integrating model gradients along a straight path from a baseline to the input. While effective in some cases,…

Half-Heusler compounds are known for their various compositions and multifunctional properties including topological phases. In this study, we investigate the topological classification of this class of materials based on the ordering of…

Robust heteroclinic networks are invariant sets that can appear as attractors in symmetrically coupled or otherwise constrained dynamical systems. These networks may have a very complicated structure that is poorly understood and determined…

Graph Convolutional Networks (GCNs) are predominantly tailored for graphs displaying homophily, where similar nodes connect, but often fail on heterophilic graphs. The strategy of adopting distinct approaches to learn from homophilic and…

In this paper we introduce a primitive path homology theory on the category of simple digraphs. On the subcategory of asymmetric digraphs, this theory coincides with the path homology theory which was introduced by Grigor'yan, Lin, Muranov,…

Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a…

In recommender systems, user-item interactions can be modeled as a bipartite graph, where user and item nodes are connected by undirected edges. This graph-based view has motivated the rapid adoption of graph neural networks (GNNs), which…

Using the theory of distributive series of monads, we construct an $(\infty,0)$-coherator called the \emph{inductive coherator}. The category of models out of the inductive coherator serve as a model for $\infty$-groupoids that possess an…

The increasing prevalence of graph-structured data across various domains has intensified greater interest in graph classification tasks. While numerous sophisticated graph learning methods have emerged, their complexity often hinders…

We study the Induced $H$ Partition problem from the parameterized complexity point of view. In the Induced $H$ Partition problem the task is to partition vertices of a graph $G$ into sets $V_1,V_2,\dots,V_n$ such that the graph $H$ is…