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We study generalized complex cohomologies of generalized complex structures constructed from certain symplectic fibre bundles over complex manifolds. We apply our results in the case of left-invariant generalized complex structures on…

This paper explores the properties of directed graphs, termed generalized action graphs, which exhibit a strong connection to certain number sequences. Focusing on the structural and combinatorial aspects, we investigate the conditions…

We prove that there are at most two possibilities for the base of a Lagrangian fibration from a complex projective irreducible symplectic fourfold.

In this paper, we introduce two local graph features for missing link prediction tasks on ogbl-citation2. We define the features as Circle Features, which are borrowed from the concept of circle of friends. We propose the detailed computing…

For a split reductive group defined over a number field, we first introduce the notations of arithmetic torsors and arithmetic Higgs torsors. Then we construct arithmetic characteristic curves associated to arithmetic Higgs torsors, based…

We describe structural properties of strongly connected finite directed graphs, that are invariants of the topological conjugacy of their Markov-Dyck shifts. For strongly connected finite directed graphs with these properties topological…

The geometric dual of a cellularly embedded graph is a fundamental concept in graph theory and also appears in many other branches of mathematics. The partial dual is an essential generalization which can be obtained by forming the…

We give a constructive method for realizing an arbitrary directed graph (with no one-cycles) as a heteroclinic or an excitable dynamic network in the phase space of a system of coupled cells of two types. In each case, the system is…

We generalize the class of split graphs to the directed case and show that these split digraphs can be identified from their degree sequences. The first degree sequence characterization is an extension of the concept of splittance to…

Combinatorial and topological structures, such as graphs, simplicial complexes, and cell complexes, form the foundation of geometric and topological deep learning (GDL and TDL) architectures. These models aggregate signals over such…

We develop a real-analytic framework, called perplex analysis, in which the complex, split-complex, and dual numbers arise as members of a single four-parameter family of two-dimensional commutative real algebras. Within this unified…

Great part of the interest in complex networks has been motivated by the presence of structured, frequently non-uniform, connectivity. Because diverse connectivity patterns tend to result in distinct network dynamics, and also because they…

We study directed random graphs (random graphs whose edges are directed) as they evolve in discrete time by the addition of nodes and edges. For two distinct evolution strategies, one that forces the graph to a condition of near acyclicity…

Bidirected graphs generalize directed and undirected graphs in that edges are oriented locally at every node. The natural notion of the degree of a node that takes into account (local) orientations is that of net-degree. In this paper, we…

Strongly chordal graphs are a subclass of chordal graphs. Farber also established a number of different characterisations for this class of graphs. These include an intersection graph characterisation that is analogous to a similar…

It is known that the canonical double cover of any connected nonbipartite graph have an automorphism group of the form $H \rtimes \mathbb{Z}_2$, where $H$ is the set of automorphism which preserve bipartite parts. We construct connected…

Graph neural networks (GNNs) have emerged as powerful tools for learning protein structures by capturing spatial relationships at the residue level. However, existing GNN-based methods often face challenges in learning multiscale…

We exhibit a characteristic structure of the class of all regular graphs of degree d that stems from the spectra of their adjacency matrices. The structure has a fractal threadlike appearance. Points with coordinates given by the mean and…

In the present paper, we construct the generalized Kuperberg bracket for two-component links with one component fibred. We consider a new geometrical complexity for such links and establish minimality of diagrams in a strong sense.

This paper undertakes a study of the structure of the fibers of the Chevalley exponentiation maps $f_{(i_1,\dots ,i_d)}$. The fibers of these maps $f_{(i_1,\dots ,i_d)}$ encode the nonnegative real relations amongst exponentiated Chevalley…