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In many applications signals reside on the vertices of weighted graphs. Thus, there is the need to learn low dimensional representations for graph signals that will allow for data analysis and interpretation. Existing unsupervised…
Perhaps the most important problem in representation theory in the 1970s and early 1980s was the determination of the multiplicity of composition factors in a Verma module. This problem was settled by the proof of the Kazhdan-Lusztig…
General factors are a generalization of matchings. Given a graph $G$ with a set $\pi(v)$ of feasible degrees, called a degree constraint, for each vertex $v$ of $G$, the general factor problem is to find a (spanning) subgraph $F$ of $G$…
We propose the method for obtaining invariants of arbitrary representations of Lie groups that reduces this problem to known problems of linear algebra. The basis of this method is the idea of a special extension of the representation…
Given a planar graph $G$ and an integer $b$, OrthogonalPlanarity is the problem of deciding whether $G$ admits an orthogonal drawing with at most $b$ bends in total. We show that OrthogonalPlanarity can be solved in polynomial time if $G$…
Multidimensional contractions of irreducible representations of the Cayley-Klein unitary algebras in the Gel'fand-Zetlin basis are considered. Contracted over different parameters, algebras can turn out to be isomorphic. In this case method…
We provide a necessary and sufficient condition for the representability of a function as the classical multidimensional Laplace transform, when the support of the representing measure is contained in some generalized semi-algebraic set.…
According to our microscopic cosmological model, masses of charged leptons can be calculated by curvatures of hyper-spherical surfaces embedded in a 3D time-like subspace. In this study, a higher-dimensional Lagrangian representation is…
The multiplicity of a weight in a finite-dimensional irreducible representation of a simple Lie algebra g can be computed via Kostant's weight multiplicity formula. This formula consists of an alternating sum over the Weyl group (a finite…
This paper discusses the mathematical framework for designing methods of large deformation matching (LDM) for image registration in computational anatomy. After reviewing the geometrical framework of LDM image registration methods, a…
We review the higher gauge symmetries in double and exceptional field theory from the viewpoint of an embedding tensor construction. This is based on a (typically infinite-dimensional) Lie algebra $\frak{g}$ and a choice of representation…
We discuss two possible ways of representing tolerances: first, as a homomorphic image of some congruence; second, as the relational composition of some compatible relation with its converse. The second way is independent from the variety…
Representation learning models for graphs are a successful family of techniques that project nodes into feature spaces that can be exploited by other machine learning algorithms. Since many real-world networks are inherently dynamic, with…
Mining graph data has become a popular research topic in computer science and has been widely studied in both academia and industry given the increasing amount of network data in the recent years. However, the huge amount of network data…
Braid groups are an important and flexible tool used in several areas of science, such as Knot Theory (Alexander's theorem), Mathematical Physics (Yang-Baxter's equation) and Algebraic Geometry (monodromy invariants). In this note we will…
The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…
In this article, we analyze the Pontryagin model adopting different geometric-covariant approaches. In particular, we focus on the manner in which boundary conditions must be imposed on the background manifold in order to reproduce an…
We define Leavitt path algebras of hypergraphs generalizing simultaneously Leavitt path algebras of finitely separated graphs and Leavitt path algebras of row-finite vertex-weighted graphs. We find linear bases for those algebras, compute…
This work formalizes the associational task of predicting node attribute evolution in temporal graphs from the perspective of learning equivariant representations. We show that node representations in temporal graphs can be cast into two…
An \emph{obstacle representation} of a graph consists of a set of polygonal obstacles and a distinct point for each vertex such that two points see each other if and only if the corresponding vertices are adjacent. Obstacle representations…