Related papers: Moment graphs in representation theory and geometr…
In this paper we introduce the theory of derivatives of moments and (moment) functionals to represent moment functionals by Gaussian mixtures, characteristic functions of polytopes, and simple functions of polytopes. We study, among other…
We describe several general methods for calculating weights of mixed tilting sheaves. We introduce a notion called "non-cancellation property" which implies a strong uniqueness of mixed tilting sheaves and enables one to calculate their…
Different graph generalizations have been recently used in an ad-hoc manner to represent multilayer networks, i.e. systems formed by distinct layers where each layer can be seen as a network. Similar constructions have also been used to…
Let V be the vector space of all skew-symmetric (non-associative) complex algebras of dimension n and L the algebraic subset of V of all Lie algebras. We consider the moment map for the action of GL(n) on the projective space P(V) and study…
We present the algebraic representation and basic algorithms for MultiAspect Graphs (MAGs). A MAG is a structure capable of representing multilayer and time-varying networks, as well as higher-order networks, while also having the property…
Molecular graphs generally contain subgraphs (known as groups) that are identifiable and significant in composition, functionality, geometry, etc. Flat latent representations (node embeddings or graph embeddings) fail to represent, and…
Inspired by the notion of action convergence in graph limit theory, we introduce a measure-theoretic representation of matrices, and we use it to define a new notion of pseudo-metric on the space of matrices. Moreover, we show that such…
The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
Grassmann and flag varieties lead many lives in pure and applied mathematics. Here we focus on the algebraic complexity of solving various problems in linear algebra and statistics as optimization problems over these varieties. The measure…
Representation learning on text-attributed graphs (TAGs) integrates structural connectivity with rich textual semantics, enabling applications in diverse domains. Current methods largely rely on contrastive learning to maximize cross-modal…
We introduce moment maps for continuous unitary representations of general topological groups. For solvable separable locally compact groups, we prove that the closure of the image of the moment map of any representation is convex.
We initiate the study of a new parameterization of graph problems. In a multiple interval representation of a graph, each vertex is associated to at least one interval of the real line, with an edge between two vertices if and only if an…
In a confluence of combinatorics and geometry, simultaneous representations provide a way to realize combinatorial objects that share common structure. A standard case in the study of simultaneous representations is the sunflower case where…
Lattice current algebras were introduced as a regularization of the left- and right moving degrees of freedom in the WZNW model. They provide examples of lattice theories with a local quantum symmetry $U_q(\sg)$. Their representation theory…
The complexity class NP of decision problems that can be solved nondeterministically in polynomial time is of great theoretical and practical importance where the notion of polynomial-time reductions between NP-problems is a key concept for…
In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…
We give a general description of the moment cone associated with an arbitrary finite-dimensional unitary representation of a compact, connected Lie group in terms of finitely many linear inequalities. Our method is based on combining…
We study an analogue of the Achar-Riche "mixed modular derived category" for moment graphs. In particular, given a Coxeter group $W$ and a reflection faithful representation $\mathfrak{h}$, we introduce a category that plays the role of…
High-dimensional multiplex graphs are characterized by their high number of complementary and divergent dimensions. The existence of multiple hierarchical latent relations between the graph dimensions poses significant challenges to…
We explain the construction of minimal tilting complexes for objects of highest weight categories and we study in detail the minimal tilting complexes for standard objects and simple objects. For certain categories of representations of…