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The transmission of a vertex in a connected graph is the sum of distances from that vertex to all the other vertices. A connected graph is transmission irregular if any two distinct vertices have different transmissions. We present an…
We give an algorithm to calculate the minimal and maximal genus of the orientable closed surface where a graph $G$ can be embedded. For this, we construct some special branched coverings of the 2-sphere. We apply this algorithm to calculate…
A revised formula for the inclusive cross section for double parton scattering in terms of the modified collinear two-parton distributions extracted from deep inelastic scattering is suggested. The possible phenomenological issues are…
Recently, one has seen a surge of interest in developing such methods including ones for learning such representations for (undirected) graphs (while preserving important properties). However, most of the work to date on embedding graphs…
A closed expression is derived for the probability distribution of the transfer matrix of a particle moving in a one-dimensional system with delta-correlated, weak disorder. The change in the distribution as a function of wire length is…
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…
Review of a matrix method used in optics of thin films for the calculation of reflectance, transmittance, absorptance, the electric field distribution inside the stack and the photonic dispersion considering the stack as perfect…
We found the eigenvalues of the transfer matrix for the 2-D inhomogeneous statistical model with twisted boundary condition by using the analytic Bethe Ansatz method. In the uniform case, the derived hamiltonian generalizes the 1-D Hubbard…
A real quadratic matrix is generalized doubly stochastic (g.d.s.) if all of its row sums and column sums equal one. We propose numerically stable methods for generating such matrices having possibly orthogonality property or/and satisfying…
Networks of genetic expression can be modelled by hypergraphs with the additional structure that real coefficients are given to each vertex-edge incidence. The spectra, i.e. the multiset of the eigenvalues, of such hypergraphs, are known to…
Bidirected graphs are a common generalisation of directed graphs where arcs can also be incoming to both their incident nodes, or outgoing from both their incident nodes. Such arcs allow a walk to change direction. Some algorithms can…
Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks…
The light propagation through a stack of two media with different refractive indices, which are aligned according to different quasiperiodic sequences determined by metallic means, is studied using the transfer matrix method. The focus lies…
We investigate the problem of multiplex graph embedding, that is, graphs in which nodes interact through multiple types of relations (dimensions). In recent years, several methods have been developed to address this problem. However, the…
We evaluate several classes of high weight hypergeometric series via Gamma, polylogarithm and elliptic integrals, mainly through distribution relations.
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…
Network embedding is an important step in many different computations based on graph data. However, existing approaches are limited to small or middle size graphs with fewer than a million edges. In practice, web or social network graphs…
For a given hypergraph, an orientation can be assigned to the vertex-edge incidences. This orientation is used to define the adjacency and Laplacian matrices. In addition to studying these matrices, several related structures are…
An arithmetical structure on a graph is given by a labeling of the vertices which satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical…
Three-way data can be conveniently modelled by using matrix variate distributions. Although there has been a lot of work for the matrix variate normal distribution, there is little work in the area of matrix skew distributions. Three matrix…