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To every tree we associate a filtered cochain complex. Its cohomology and the corresponding spectral sequence have clear combinatorial description. If a tree is the Dynkin diagram of a simple plane curve singularity, the graded Euler…
A set of independence statements may define the independence structure of interest in a family of joint probability distributions. This structure is often captured by a graph that consists of nodes representing the random variables and of…
Generalized matrix Lotka-Volterra lattice equations are obtained in a systematic way from a "master equation" possessing a bicomplex formulation.
The Kronecker product is an invaluable tool for data-sparse representations of large networks and matrices with countless applications in machine learning, graph theory and numerical linear algebra. In some instances, the sparsity pattern…
Given an admissible map F for a homogeneous network N, it is known that the Jacobian DF(x) around a fully synchronous point x = (x0, ..., x0) is again an admissible map for N. Motivated by this, we study the spectra of linear admissible…
A vertex $v$ of a connected graph $G$ is said to be a boundary vertex of $G$ if for some other vertex $u$ of $G$, no neighbor of $v$ is further away from $u$ than $v$. The boundary $\partial(G)$ of $G$ is the set of all of its boundary…
We compute the Groebner basis of a system of polynomial equations related to the Jacobian conjecture using a recursive formula for the Catalan numbers.
In the present paper, we are concerned with the study of the spectral distribution of matrix-sequences showing a non-Hermitian block structure with Toeplitz blocks. We use the notion of geometric mean of matrices and the theory of…
A linkage diagram is obtained from the Carter diagram $\Gamma$ by adding an extra root $\gamma$, so that the resulting subset of roots is linearly independent. With every linkage diagram we associate the linkage label vector…
In this work, for the given adjacency matrix of a graph, we present an algorithm which checks the connectivity of a graph and computes all of its connected components. Also, it is mathematically proved that the algorithm presents all the…
A recursive algebraic method which allows to obtain the Feynman or Schwinger parametric representation of a generic L-loops and (E+1) external lines diagram, in a scalar $\phi ^{3}\oplus \phi ^{4}$ theory, is presented. The representation…
In this paper, we consider the problem of deriving new eigenvalue distributions of real-valued Wishart matrices that arises in many scientific and engineering applications. The distributions are derived using the tools from the theory of…
The derivation of the phase transition in the model of Ga\'zdzicki and Gorenstein is generalized and simplified by using a geometrical construction.
We deduce decompositions of natural representations of general linear groups and symmetric groups from combinatorial bijections involving tableaux. These include some of Howe's dualities, Gelfand models, the Schur-Weyl decomposition of…
We consider problems of estimation of structured covariance matrices, and in particular of matrices with a Toeplitz structure. We follow a geometric viewpoint that is based on some suitable notion of distance. To this end, we overview and…
Simple algebraic rules can produce complex networks with rich structures. These graphs are obtained when looking at a monoid operating on a ring. There are relations to dynamical systems theory and number theory. This document illustrates…
Let the join of two graphs be the union of two disjoint graphs connected by $j$ edges in a one-to-one manner. In previous work by Gyurov and Pinzon, which generalized the results of Badura and Rara, the determinant of the adjacency matrix…
We show how to represent a class of expressions involving discrete sums over partitions as matrix models. We apply this technique to the partition functions of 2* theories, i.e. Seiberg-Witten theories with the massive hypermultiplet in the…
Supposing Kotz-Riesz type I and II distributions and their corresponding independent univariate Riesz distributions the associated generalised matrix multivariate T distributions, termed matrix multivariate T-Riesz distributions are…
The Gauss-Manin connection of a family of hypersurfaces governs the change of the period matrix along the family. This connection can be complicated even when the equations defining the family look simple. When this is the case, it is…