Related papers: Stochastic matrices and majorization in max algebr…

In this paper, we consider the nonstationary matrix-valued time series with common stochastic trends. Unlike the traditional factor analysis which flattens matrix observations into vectors, we adopt a matrix factor model in order to fully…

This paper proposes the density and characteristic functions of a general matrix quadratic form $\mathbf{X}^{*}\mathbf{AX}$, when $\mathbf{A} = \mathbf{A}^{*}$, $\mathbf{X}$ has a matrix multivariate elliptical distribution and…

Let X_N= (X_1^(N), ..., X_p^(N)) be a family of N-by-N independent, normalized random matrices from the Gaussian Unitary Ensemble. We state sufficient conditions on matrices Y_N =(Y_1^(N), ..., Y_q^(N)), possibly random but independent of…

Recently, the authors studied the connection between each maximal monotone operator T and a family H(T) of convex functions. Each member of this family characterizes the operator and satisfies two particular inequalities. The aim of this…

Determinant maximization provides an elegant generalization of problems in many areas, including convex geometry, statistics, machine learning, fair allocation of goods, and network design. In an instance of the determinant maximization…

We present a new construction of crossed-product duality for maximal coactions that uses Fischer's work on maximalizations. Given a group $G$ and a coaction $(A,\delta)$ we define a generalized fixed-point algebra as a certain subalgebra of…

For a primal-dual pair of conic linear problems that are described by convex cones $S\subset X$, $T\subset Y$, bilinear symmetric objective functions $\langle\cdot,\cdot\rangle_X$, $\langle\cdot,\cdot\rangle_Y$ and a linear operator…

This manuscript investigates the stochastic comparisons of the second-order statistics from dependent and heterogeneous general semi-parametric family of distributions observations. Some sufficient conditions on the usual stochastic order…

Let $n$ and $s$ be fixed integers such that $n\geq 2$ and $1\leq s\leq \frac{n}{2}$. Let $M_n(\mathbb{K})$ be the ring of all $n\times n$ matrices over a field $\mathbb{K}$. If a map $\delta:M_n(\mathbb{K})\rightarrow M_n(\mathbb{K})$…

Representations of quantum superalgebras provide a natural framework in which to model supersymmetric quantum systems. Each quantum superalgebra, belonging to the class of quasi-triangular Hopf superalgebras, contains a universal R-matrix…

We follow a stream of the history of positive matrices and positive functionals, as applied to algebraic sums of squares decompositions, with emphasis on the interaction between classical moment problems, function theory of one or several…

The present paper provides a study of high-dimensional statistical arbitrage that combines factor models with the tools from stochastic control, obtaining closed-form optimal strategies which are both interpretable and computationally…

We derive exact matrix integral representations for different sums over partitions. The characteristic feature of all obtained matrix models is the presence of logarithmic (or, vice versa, exponential) terms in the potential. Our derivation…

The paper investigates the properties of a class of resource allocation algorithms for communication networks: if a node of this network has $x$ requests to transmit, then it receives a fraction of the capacity proportional to $\log(1+x)$,…

We show that the large-charge formalism can be successfully applied to models that go beyond the vector models discussed so far in the literature. We study the explicit example of a conformal $SU(3)$ matrix model in 2+1 space-time…

We apply tropical geometry to study matrix algebras over a field with valuation. Using the shapes of min-max convexity, known as polytropes, we revisit the graduated orders introduced by Plesken and Zassenhaus. These are classified by the…

The aim of this paper is to study the dominant dimension of two important classes of finite dimensional algebras, namely, hereditary algebras and tree algebras. We derive an explicit formula for the dominant dimension of each class.

We formulate and propose an algorithm (MultiRank) for the ranking of nodes and layers in large multiplex networks. MultiRank takes into account the full multiplex network structure of the data and exploits the dual nature of the network in…

The object of the present paper is to study certain properties and characteristics of the operator $Q_{p,\beta}^{\alpha}$defined on p-valent analytic function by using technique of differential subordination.We also obtained result…

We study solutions of the Yang-Baxter equation on a tensor product of an arbitrary finite-dimensional and an arbitrary infinite-dimensional representations of the rank one symmetry algebra. We consider the cases of the Lie algebra sl_2, the…