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Most of todays work on knowledge graph completion is concerned with sub-symbolic approaches that focus on the concept of embedding a given graph in a low dimensional vector space. Against this trend, we propose an approach called AnyBURL…
The chromatic symmetric $X_G$ function is a symmetric function generalization of the chromatic polynomial of a graph, introduced by Stanley (1995). Stanley gave an expansion formula for $X_G$ in terms of the power sum symmetric functions…
Stanley associated with a graph G a symmetric function X_G which reduces to G's chromatic polynomial under a certain specialization of variables. He then proved various theorems generalizing results about the chromatic polynomial, as well…
Motivated by the question of which structural properties of a graph can be recovered from the chromatic symmetric function (CSF), we study the CSF of connected unicyclic graphs. While it is known that there can be non-isomorphic unicyclic…
Despite significant advances, continual learning models still suffer from catastrophic forgetting when exposed to incrementally available data from non-stationary distributions. Rehearsal approaches alleviate the problem by maintaining and…
The vertex coloring problem to find chromatic numbers is known to be unsolvable in polynomial time. Although various algorithms have been proposed to efficiently compute chromatic numbers, they tend to take an enormous amount of time for…
Recent advances in one-shot learning have produced models that can learn from a handful of labeled examples, for passive classification and regression tasks. This paper combines reinforcement learning with one-shot learning, allowing the…
We prove that the number of Hamiltonian paths on the complement of an acyclic digraph is equal to the number of cycle covers. As an application, we obtain a new expansion of the chromatic symmetric function of incomparability graphs in…
The $e$-positivity conjecture and the $e$-unimodality conjecture of chromatic quasisymmetric functions are proved for some classes of natural unit interval orders. Recently, J. Shareshian and M. Wachs introduced chromatic quasisymmetric…
We introduce a generalization of the well known graph (vertex) coloring problem, which we call the problem of \emph{component coloring of graphs}. Given a graph, the problem is to color the vertices using minimum number of colors so that…
Quantification learning is the task of predicting the label distribution of a set of instances. We study this problem in the context of graph-structured data, where the instances are vertices. Previously, this problem has only been…
Summation formulas, such as the Euler-Maclaurin expansion or Gregory's quadrature, have found many applications in mathematics, ranging from accelerating series, to evaluating fractional sums and analyzing asymptotics, among others. We show…
In this paper we derive an efficient algorithm to learn the parameters of structured predictors in general graphical models. This algorithm blends the learning and inference tasks, which results in a significant speedup over traditional…
Skewing operators play a central role in the symmetric function theory because of the importance of the product structure of the symmetric function space. The theory of noncommutative symmetric functions is a useful tool for studying…
Graphs can be used to represent and reason about systems and a variety of metrics have been devised to quantify their global characteristics. However, little is currently known about how to construct a graph or improve an existing one given…
Many real-world problems can be reduced to combinatorial optimization on a graph, where the subset or ordering of vertices that maximize some objective function must be found. With such tasks often NP-hard and analytically intractable,…
A method for correcting for detector smearing effects using machine learning techniques is presented. Compared to the standard approaches the method can use more than one reconstructed variable to infere the value of the unsmeared quantity…
We prove a functional central limit theorem for subgraph counts in a dynamic version of the random connection model. To establish tightness, we develop a dynamic extension of the cumulant method.
Continuous-time reinforcement learning (CTRL) provides a principled framework for sequential decision-making in environments where interactions evolve continuously over time. Despite its empirical success, the theoretical understanding of…
We study the distributional behavior of additive arithmetic functions evaluated at integers drawn from the harmonic distribution. Our main result shows that a broad family of such functions converges in law to conditioned Dickman-type…