In this paper we present an efficient approach for comparing protein structures based on distance matrices. In the first step, the distance matrices are calculated and normalized in order to avoid the scaling distortion. Further, versions from these matrices are saved on different scales and for each two protein structures we compare their respective equal-scaled matrices. Thus, we avoid the pr...

We study a natural random walk over the upper triangular matrices, with entries in the field Z2, generated by steps which add row i + 1 to row i. We show that the mixing time of the lazy random walk is O(n) which is optimal up to constants. Our proof makes key use of the linear structure of the group and extends to walks on the upper triangular matrices over the fields Zq for q prime.

(1) 2) vertex models and analytic Bethe ansätze We introduce fusion U q (G (1) 2) vertex models related to fundamental representations. The eigenvalues of their row to row transfer matrices are derived through analytic Bethe ansätze. By combining these results with our previous studies on functional relations among transfer matrices(the T-system), we conjecture explicit eigenvalues for a wide c...

The paper presents a subspace type of identification method for multivariable linear parameter-varying systems in state space representation with affine parameter dependence. It is shown that a major problem with subspace methods for this kind of systems is the enormous dimensions of the data matrices involved. To overcome the curse of dimensionality, we suggest to use only the most dominant ro...

$R_+^{n\times n}$ denotes the set of $n\times n$ non-negative matrices. For $A\in R_+^{n\times let $\Omega(A)$ be all matrices that can formed by permuting elements within each row $A$. Formally: $$\Omega(A)=\{B\in n}: \forall i\;\exists\text{ a permutation }\phi_i\; \text{s.t.}\ b_{i,j}=a_{i,\phi_i(j)}\;\forall j\}.$$ $B\in\Omega(A)$ $\rho(B)$ denote spectral radius or largest non negative eig...

A permuted graph matrix is a matrix V ∈ C(m+n)×m such that every row of the m×m identity matrix Im appears at least once as a row of V . Permuted graph matrices can be used in some contexts in place of orthogonal matrices, for instance when giving a basis for a subspace U ⊆ Cm+n, or to normalize matrix pencils in a suitable sense. In these applications the permuted graph matrix can be chosen wi...

Abstract. Monotone triangles are certain triangular arrays of integers, which correspond to n × n alternating sign matrices when prescribing (1, 2, . . . , n) as bottom row of the monotone triangle. In this article we define halved monotone triangles, a specialization of which correspond to vertically symmetric alternating sign matrices. We derive an operator formula for the number of halved mo...

An Alternating sign matrix is a square matrix of 0’s, 1’s, and −1’s in which the sum of the entries in each row or column is 1 and the signs of the nonzero entries in each row or column alternate. This paper attempts to define an analogue to alternating sign matrices which is infinite and periodic. After showing the analogue we define shares desirable cahracteristics with alternating sign matri...

We consider the set Σ(R, C) of all m×n matrices having 0-1 entries and prescribed row sums R = (r1, . . . , rm) and column sums C = (c1, . . . , cn). We prove an asymptotic estimate for the cardinality |Σ(R, C)| via the solution to a convex optimization problem. We show that if Σ(R, C) is sufficiently large, then a random matrix D ∈ Σ(R, C) sampled from the uniform probability measure in Σ(R, C...

In a typical MapReduce job, each map task processing one piece of the input file. If two input matrices are stored in separate HDFS files, one map task would not be able to access the two input matrices at the same time. To deal with this problem, we propose a efficient matrix multiplication in Hadoop. For dense matrices, we use plain row major order to store the matrices on HDFS; For sparse ma...