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As well known, permanent of a square (0,1)-matrix $A$ of order $n$ enumerates the permutations $\beta$ of $1,2,...,n$ with the incidence matrices $B\leq A.$ To obtain enumerative information on even and odd permutations with condition…
Recursive blocked algorithms have proven to be highly efficient at the numerical solution of the Sylvester matrix equation and its generalizations. In this work, we show that these algorithms extend in a seamless fashion to…
Colloidal systems observed in video microscopy are often analysed using the displacements correlation matrix of particle positions. In non-thermal systems, the inverse of this matrix can be interpreted as a pair-interaction potential…
We study hypercyclicity, Devaney chaos, topological mixing properties and strong mixing in the measure-theoretic sense for operators on topological vector spaces with invariant sets. More precisely, our purpose is to establish links between…
Let $C_n$ denote a cyclic group of order $n$. In this paper we investigate modules and chain complexes over the constant integral Mackey functor $\underline{\mathbb{Z}}$ and perform some related homological calculations. Along the way we…
We present general links between statistics of non-Hermitian random matrices and the distribution of the number of cycles of some specific random permutations. In particular, we derive explicit formulas for the generating functions of the…
Transfer matrices and matrix product operators play an ubiquitous role in the field of many body physics. This paper gives an ideosyncratic overview of applications, exact results and computational aspects of diagonalizing transfer matrices…
The relationships between port-Hamiltonian systems modeling and the notion of monotonicity are explored. The earlier introduced notion of incrementally port-Hamiltonian systems is extended to maximal cyclically monotone relations, together…
In this article we answer a question raised by N. Feldman in \cite{Feldman} concerning the dynamics of tuples of operators on $\mathbb{R}^n$. In particular, we prove that for every positive integer $n\geq 2$ there exist $n$ tuples $(A_1,…
For a fixed positive integer $k$, any element $g$ of the permutation group $S_{k}$ acts on the tensor product vertex operator algebra $V^{\otimes k}$ in the obvious way. In this paper, we determine the $S$-matrix of $\left(V^{\otimes…
Equiangular Algorithm generates a set of equiangular normalized vectors with given angle {\theta} using a set of linearly independence vectors in a real inner product space, which span the same subspaces. The outcome of EA on column vectors…
This paper continues the application of circuit theory to experimental design started by the first two authors. The theory gives a very special and detailed representation of the kernel of the design model matrix. This representation turns…
Tensor decompositions have become essential tools for feature extraction and compression of multiway data. Recent advances in tensor operators have enabled desirable properties of standard matrix algebra to be retained for multilinear…
A complete classification of continuous, dually epi-translation invariant, and rotation equivariant valuations on convex functions is established. This characterizes the recently introduced functional Minkowski vectors, which naturally…
We use finite connectivity equilibrium replica theory to solve models of finitely connected unit-length vectorial spins, with random pair-interactions which are of the orthogonal matrix type. Since the spins are continuous and the…
This paper generalizes the results obtained in an earlier paper (math.OA/0003087) for finite factors to infinite but still semifinite factors. First we give a characterization of cyclic and separating vectors for infinite semifinite factors…
Many complex engineering systems consist of multiple subsystems that are developed by different teams of engineers. To analyse, simulate and control such complex systems, accurate yet computationally efficient models are required. Modular…
Factor models are a very efficient way to describe high dimensional vectors of data in terms of a small number of common relevant factors. This problem, which is of fundamental importance in many disciplines, is usually reformulated in…
A powerful time series analysis modeling technique is presented to describe cycle-to-cycle variability in memristors. These devices show variability linked to the inherent stochasticity of device operation and it needs to be accurately…
We generalize entanglement detection with covariance matrices for an arbitrary set of observables. A generalized uncertainty relation is constructed using the covariance and commutation matrices, then a criterion is established by…