Recently, Jeĺınek derived that the number of self-dual interval orders of reduced size n is twice the number of row-Fishburn matrices of size n by using generating functions. In this paper, we present a bijective proof of this relation by establishing a bijection between two variations of upper-triangular matrices of nonnegative integers. Using the bijection, we provide a combinatorial proof of...

Let d = (d1, d2, . . . , dn) be a vector of nonnegative integers. We study the number of symmetric 0-1 matrices whose row sum vector equals d. While previous work has focussed on the case of zero diagonal, we allow diagonal entries to equal 1. Specifically, for D ∈ {1, 2} we define the set GD(d) of all n × n symmetric 0-1 matrices with row sums given by d, where each diagonal entry is multiplie...

Many patch-based image denoising algorithms can be formulated as applying a smoothing filter to the noisy image. Expressed as matrices, the smoothing filters must be row normalized so that each row sums to unity. Surprisingly, if we apply a column normalization before the row normalization, the performance of the smoothing filter can often be significantly improved. Prior works showed that such...

In this paper we consider the problem of estimating simultaneously low-rank and row-wise sparse matrices from nested linear measurements where the linear operator consists of the product of a linear operatorW and a matrix Ψ . Leveraging the nested structure of the measurement operator, we propose a computationally efficient two-stage algorithm for estimating the simultaneously structured target...

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...