The minimum backward Fréchet distance (MBFD) problem is a natural optimization problem for the weak Fréchet distance, a variant of the well-known Fréchet distance. In this problem, a threshold ε and two polygonal curves, T1 and T2, are given. The objective is to find a pair of walks on T1 and T2, which minimizes the union of the portions of backward movements while the distance between the movi...

Protein structure alignment is a fundamental problem in computational and structural biology. While there has been lots of experimental/heuristic methods and empirical results, very few results are known regarding the algorithmic/complexity aspects of the problem, especially on protein local structure alignment. A well-known measure to characterize the similarity of two polygonal chains is the ...

A new bound for the condition number of the matrix exponential is presented. Using the bound, we propose an efficient approximation to the condition number, denoted by κg(s,X), that avoids the computation of the Fréchet derivative of the matrix exponential that underlies condition number estimation in the existing algorithms. We exploit the identity eX = (eX/2 s )2 s for a nonnegative integer s...

Given two polygonal curves in the plane, there are many ways to define a notion of similarity between them. One measure that is extremely popular is the Fréchet distance. Since it has been proposed by Alt and Godau in 1992, many variants and extensions have been studied. Nonetheless, even more than 20 years later, the original O(n log n) algorithm by Alt and Godau for computing the Fréchet dist...

Let $R$ be a commutative ring with identity and $M$ be an unitary $R$-module. The intersection graph of an $R$-module $M$, denoted by $Gamma(M)$, is a simple graph whose vertices are all non-trivial submodules of $M$ and two distinct vertices $N_1$ and $N_2$ are adjacent if and only if $N_1cap N_2neq 0$. In this article, we investigate the concept of a planar intersection graph and maximal subm...

In frequency-domain optical diffusion imaging, the magnitude and the phase of modulated light propagated through a highly scattering medium are used to reconstruct an image of the scattering and absorption coefficients in the medium. Although current reconstruction algorithms have been applied with some success, there are opportunities for improving both the accuracy of the reconstructions and ...

This is the first time we had an opportunity to read this paper by M. Fréchet and we enjoyed doing that very much. In brief, M. Fréchet demonstrates that measured with the classical sample variance estimator, the variability of the sample mean is smaller than the variability of the sample median in fairly general classes of distributions for the sample. However, he points out the fact that meas...

In this article, we study the consistency of the template estimation with the Fréchet mean in quotient spaces. The Fréchet mean in quotient spaces is often used when the observations are deformed or transformed by a group action. We show that in most cases this estimator is actually inconsistent. We exhibit a sufficient condition for this inconsistency, which amounts to the folding of the distr...

In this work, we introduce $H^*$-condition on the set of submodules of a module. Let $M$ be a module. We say $M$ satisfies $H^*$ provided that for every submodule $N$ of $M$, there is a direct summand$D$ of $M$ such that $(N+D)/N$ and $(N+D)/D$ are cosingular. We show that over a right perfect right $GV$-ring,a homomorphic image of a $H^*$ duo module satisfies $H^*$.