Related papers: Stochastic matrices and majorization in max algebr…
We investigate convex polytopes of doubly stochastic matrices having special structures: symmetric, Hankel symmetric, centrosymmetric, and both symmetric and Hankel symmetric. We determine dimensions of these polytopes and classify their…
Majorisation, also called rearrangement inequalities, yields a type of stochastic ordering in which two or more distributions can be compared. In this paper we argue that majorisation is a good candidate as a theory for uncertainty. We…
In this article, we introduce finite mixture models (FMMs) renowned for capturing population heterogeneity. Our focus lies in establishing stochastic comparisons between two arithmetic (finite) mixture models, employing the vector…
This paper summarizes results on some topics in the max-plus convex geometry, mainly concerning the role of multiorder, Kleene stars and cyclic projectors, and relates them to some topics in max algebra. The multiorder principle leads to…
In the present paper we introduce a concept of doubly stochastic quadratic operator. We prove necessary and sufficient conditions for doubly stochasticity of operator. Besides, we prove that the set of all doubly stochastic operators forms…
A generalization of recent group-theoretic matrix multiplication algorithms to an analogue of the theory of partial matrix multiplication is presented. We demonstrate that the added flexibility of this approach can in some cases improve…
We consider multi-task learning, which simultaneously learns related prediction tasks, to improve generalization performance. We factorize a coefficient matrix as the product of two matrices based on a low-rank assumption. These matrices…
Design matrices are sparse matrices in which the supports of different columns intersect in a few positions. Such matrices come up naturally when studying problems involving point sets with many collinear triples. In this work we consider…
This work focuses on modeling of time-varying covariance matrices using the state covariance of linear stochastic systems. Following concepts from optimal mass transport and the Schr\"odinger bridge problem (SBP), we investigate several…
We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice binary operations are each presented as a pair of partial…
A transversal matroid $M$ of rank $r$ on $[n]$ can be associated to a family of binary matrices corresponding to different presentations of $M$. We describe those matrices which arise from unique maximal presentations of size $r$- giving a…
We recall the concept of Baxterisation of an R-matrix, or of a monodromy matrix, which corresponds to build, from one point in the $ R$-matrix parameter space, the algebraic variety where the spectral parameter(s) live. We show that the…
Random matrices tend to be well conditioned, and we employ this well known property to advance matrix computations. We prove that our algorithms employing Gaussian random matrices are efficient, but in our tests the algorithms have…
We consider the general problem of learning about a matrix through vector-matrix-vector queries. These queries provide the value of $\boldsymbol{u}^{\mathrm{T}}\boldsymbol{M}\boldsymbol{v}$ over a fixed field $\mathbb{F}$ for a specified…
We investigate different notions of linear independence and of matrix rank that are relevant for max-plus or tropical semirings. The factor rank and tropical rank have already received attention, we compare them with the ranks defined in…
A systematic scheme is developed for solving conformal algebra of the massive vertex operators in the old covariant first quantized string theory. Using the first massive level in the covariant spectrum of bosonic open string theory in flat…
We consider a class of sparsity-inducing optimization problems whose constraint set is regularizer-compatible, in the sense that, the constraint set becomes easy-to-project-onto after a coordinate transformation induced by the…
This is the part II of a two-part work started in arXiv:0807.3356 [math.QA]. In part I, Cardy algebras were studied, a notion which arises from the classification of genus-0,1 open-closed rational conformal field theories. In this part, we…
Majorization is a basic concept in matrix theory that has found applications in numerous settings over the past century. Power majorization is a more specialized notion that has been studied in the theory of inequalities. On the other hand,…
Matrices are the most common representations of graphs. They are also used for the representation of algebras and cluster algebras. This paper shows some properties of matrices in order to facilitate the understanding and locating…