Related papers: Reinforcement Learning the Chromatic Symmetric Fun…

We present a use of modern data-based machine learning approaches to suppress self-sustained collective oscillations typically signaled by ensembles of degenerative neurons in the brain. The proposed hybrid model relies on two major…

As the popularity of graph data increases, there is a growing need to count the occurrences of subgraph patterns of interest, for a variety of applications. Many graphs are massive in scale and also fully dynamic (with insertions and…

Deep graph clustering, which aims to group nodes into disjoint clusters by neural networks in an unsupervised manner, has attracted great attention in recent years. Although the performance has been largely improved, the excellent…

We consider the problem of distributed lossless computation of a function of two sources by one common user. To do so, we first build a bipartite graph, where two disjoint parts denote the individual source outcomes. We then project the…

The chromatic polynomial and its generalization, the chromatic symmetric function, are two important graph invariants. Celebrated theorems of Birkhoff, Whitney, and Stanley show how both objects can be expressed in three different ways: as…

We present a multiple colour generalisation of the model of graph interacting urns studied by Benaim et. al., Random Struct. Alg., 46: 614-634, 2015. We show that for complete graphs and for a broad class of reinforcement functions…

We present the Chromatic Persistence Algorithm (CPA), an event-driven method for computing persistent cohomological features of weighted graphs via graphic arrangements, a classical object in computational geometry. We establish rigorous…

The dichromatic number of a digraph $D$ is the minimum number of colors needed to color its vertices in such a way that each color class induces an acyclic digraph. As it generalizes the notion of the chromatic number of graphs, it has been…

We introduce a randomized topological augmentor based on Schur complements for Graph Contrastive Learning (GCL). Given a graph laplacian matrix, the technique generates unbiased approximations of its Schur complements and treats the…

Let $\mathcal{C} = \{c_1,c_2, c_3, \ldots,c_k\}$ be a certain type of proper $k$-colouring of a given graph $G$ and $\theta(c_i)$ denote the number of times a particular colour $c_i$ is assigned to the vertices of $G$. Then, the colouring…

A common theme of enumerative combinatorics is formed by counting functions that are polynomials evaluated at positive integers. In this expository paper, we focus on four families of such counting functions connected to hyperplane…

Combinatorial optimization is frequently used in computer vision. For instance, in applications like semantic segmentation, human pose estimation and action recognition, programs are formulated for solving inference in Conditional Random…

A new algorithm to obtain the chromatic number of a finite, connected graph is proposed in this paper. The algorithm is based on contraction of non adjacent vertices.

We review the combinatorial, topological, algebraic and metric properties supported by $(D+1)$-colored graphs, with a focus on those that are pertinent to the study of tensor model theories. We show how to extract a limiting continuum…

Reinforcement learning algorithms are typically designed for discrete-time dynamics, even though the underlying real-world control systems are often continuous in time. In this paper, we study the problem of continuous-time reinforcement…

It is known that the set of all solutions of a commutant lifting and other interpolation problems admits a Redheffer linear-fractional parametrization. The method of unitary coupling identifies solutions of the lifting problem with minimal…

Cumulative prospect theory (CPT) is known to model human decisions well, with substantial empirical evidence supporting this claim. CPT works by distorting probabilities and is more general than the classic expected utility and coherent…

In this paper we develop a functional calculus for a countable system of generators of contraction strongly continuous semigroups. As a symbol class of such calculus we use the algebra of polynomial tempered distributions. We prove a…

For each indifference graph, there is an associated regular semisimple Hessenberg variety, whose cohomology recovers the chromatic symmetric function of the graph. The decomposition theorem applied to the forgetful map from the regular…

Classification and regression in which the inputs are graphs of arbitrary size and shape have been paid attention in various fields such as computational chemistry and bioinformatics. Subgraph indicators are often used as the most…