Related papers: Q-system Cluster Algebras, Paths and Total Positiv…
The solution of potential-driven steady-state flow in large networks is required in various engineering applications, such as transport of natural gas or water through pipeline networks. The resultant system of nonlinear equations depends…
A positive definite completion problem pertains to determining whether the unspecified positions of a partial (or incomplete) matrix can be completed in a desired subclass of positive definite matrices. In this paper we study an important…
The notion of completely positive invariant conjugate-bilinear map in a partial *-algebra is introduced and a generalized Stinespring theorem is proven. Applications to the existence of integrable extensions of *-representations of…
This is a survey article for "Handbook of Linear Algebra", 2nd ed., Chapman & Hall/CRC, 2014. An informal introduction to representations of quivers and finite dimensional algebras from a linear algebraist's point of view is given. The…
This article proves the existence of completely positive quasimultiplicative maps from the group algebra of imprimitive reflection groups to the set of bounded operators, and uses those linear maps to define creation and annihilation…
We show that an operator valued $\alpha$-completely positive map on a group G is given by a unitary representation of G on a Krein space which satisfies some condition. Moreover, two unitary equivalent such unitary representations define…
We present a brief review on integrability of multispecies zero range process in one dimension introduced recently. The topics range over stochastic $R$ matrices of quantum affine algebra $U_q (A^{(1)}_n)$, matrix product construction of…
We introduce the method of path-sums which is a tool for exactly evaluating a function of a discrete matrix with possibly non-commuting entries, based on the closed-form resummation of infinite families of terms in the corresponding Taylor…
For quantum systems described by finite matrices, linear and affine maps of matrices are shown to provide equivalent descriptions of evolution of density matrices for a subsystem caused by unitary Hamiltonian evolution in a larger system;…
Fomin-Zelevinsky conjectured that in any cluster algebra, the cluster monomials are linearly independent and that the exchange graph and cluster complex are independent of the choice of coefficients. We confirm these conjectures for all…
A quiver is an oriented graph. Quiver mutation is an elementary operation on quivers. It appeared in physics in Seiberg duality in the nineties and in mathematics in the definition of cluster algebras by Fomin-Zelevinsky in 2002. We show,…
We consider the clustering problem of attributed graphs. Our challenge is how we can design an effective and efficient clustering method that precisely captures the hidden relationship between the topology and the attributes in real-world…
The Feynman Path Integral is extended in order to capture all solutions of a quantum field theory. This is done via a choice of appropriate integration cycles, parametrized by M in SL(2,C), i.e., the space of allowed integration cycles is…
We consider matrices with entries that are polynomials in $q$ arising from natural $q$-generalisations of two well-known formulas that count: forests on $n$ vertices with $k$ components; and trees on $n+1$ vertices where $k$ children of the…
Let $A$ be the path algebra of a finite acyclic quiver $Q$ over a finite field. We realize the quantum cluster algebra with principal coefficients associated to $Q$ as a sub-quotient of a certain Hall algebra involving the category of…
We define a functorial "Artin map" attached to any small $\bf{Z}$-linear stable $\infty$-category, which in the case of perfect complexes over a global field recovers the usual Artin map from the idele class group to the abelianized…
We present a natural multiplicative theory of integer partitions (which are usually considered in terms of addition), and find many theorems of classical number theory arise as particular cases of extremely general combinatorial structure…
We discuss selected topics on the topology of moduli spaces of curves and maps, emphasizing their relation with Gromov--Witten theory and integrable systems.
This paper is an introduction to diagrammatic methods for representing quantum processes and quantum computing. We review basic notions for quantum information and quantum computing. We discuss topological diagrams and some issues about…
A number of models of linear logic are based on or closely related to linear algebra, in the sense that morphisms are "matrices" over appropriate coefficient sets. Examples include models based on coherence spaces, finiteness spaces and…