Search results for "Distance matrix"

CRiSPy-CUDA: Computing Species Richness in 16S rRNA Pyrosequencing Datasets with CUDA

2011

Pyrosequencing technologies are frequently used for sequencing the 16S rRNA marker gene for metagenomic studies of microbial communities. Computing a pairwise genetic distance matrix from the produced reads is an important but highly time consuming task. In this paper, we present a parallelized tool (called CRiSPy) for scalable pairwise genetic distance matrix computation and clustering that is based on the processing pipeline of the popular ESPRIT software package. To achieve high computational efficiency, we have designed massively parallel CUDA algorithms for pairwise k-mer distance and pairwise genetic distance computation. We have also implemented a memory-efficient sparse matrix clust…

Covering and differentiation

1995

Information and hierarchical structure in financial markets

1999

I investigate the information content present in the time series of stock prices of a portfolio of stocks traded in a financial market. By investigating the correlation coefficient between pairs of stocks I provide a working definition of a generalized distance between the stocks of the portfolio. This generalized distance is used to obtain an ultrametric distance matrix between the stocks. The ultrametric structure of the portfolio investigated has associated a taxonomy which is meaningful from an economic point of view.

Finite linear spaces in which any n-gon is euclidean

1986

Abstract An n-gon of a linear space is a set S of n points no three of which are collinear. By a diagonal point of S we mean a point p off S with the property that at least two lines through p intersect S in two points. The number of diagonal points is called the type of S. For example, a 4-gon has at most three diagonal points. We call an n-gon euclidean if (roughly speaking) it contains the maximal possible number of 4-gons of type 3. In this paper, we characterize all finite linear spaces in which, for a fixed number n ⩾ 5, any n-gon is euclidean. It turns out that these structures are essentially projective spaces or punctured projective spaces.

Some inequalities involving the euclidean condition of a matrix

1960

Reducing the bandwidth of a sparse matrix with tabu search

2001

The bandwidth of a matrix { } ij a A = is defined as the maximum absolute difference between i and j for which 0 ≠ ij a . The problem of reducing the bandwidth of a matrix consists of finding a permutation of the rows and columns that keeps the nonzero elements in a band that is as close as possible to the main diagonal of the matrix. This NP-complete problem can also be formulated as a labeling of vertices on a graph, where edges are the nonzero elements of the corresponding symmetrical matrix. Many bandwidth reduction algorithms have been developed since the 1960s and applied to structural engineering, fluid dynamics and network analysis. For the most part, these procedures do not incorpo…

Newton Method for Minimal Learning Machine

2021

Minimal Learning Machine (MLM) is a distance-based supervised machine learning method for classification and regression problems. Its main advances are simple formulation and fast learning. Computing the MLM prediction in regression requires a solution to the optimization problem, which is determined by the input and output distance matrix mappings. In this paper, we propose to use the Newton method for solving this optimization problem in multi-output regression and compare the performance of this algorithm with the most popular Levenberg–Marquardt method. According to our knowledge, MLM has not been previously studied in the context of multi-output regression in the literature. In additio…

Cotas inferiores para el QAP-Arbol

1985

The Tree-QAP is a special case of the Quadratic Assignment Problem where the flows not equal zero form a tree. No condition is required for the distance matrix. In this paper we present an integer programming formulation for the Tree-QAP. We use this formulation to construct four Lagrangean relaxations that produce several lower bounds for this problem. To solve one of the relaxed problems we present a Dynamic Programming algorithm which is a generalization of the algorithm of this type that gives a lower bound for the Travelling Salesman Problem. A comparison is given between the lower bounds obtained by each ralaxation for examples with size from 12 to 25.

A Concept for Quantitative Comparison of Mathematical and Natural Language and its possible Effect on Learning

2017

Starting with the question whether there is a connection between the mathematical capabilities of a person and his or her mother tongue, we introduce a new modeling approach to quantitatively compare natural languages with mathematical language. The question arises from educational assessment studies that indicate such a relation. Texts written in natural languages can be deconstructed into a dependence graph, in simple cases a dependence tree. The same kind of deconstruction is also possible for mathematical texts. This gives an idea of how to quantitatively compare mathematical and natural language. To that end, we develop algorithms to define the distance between graphs. In this paper, w…

Isolated roundings and flattenings of submanifolds in Euclidean spaces

2005

We introduce the concepts of rounding and flattening of a smooth map $g$ of an $m$-dimensional manifold $M$ to the euclidean space $\R^n$ with $m<n$, as those points in $M$ such that the image $g(M)$ has contact of type $\Sigma^{m,\dots,m}$ with a hypersphere or a hyperplane of $\R^n$, respectively. This includes several known special points such as vertices or flattenings of a curve in $\R^n$, umbilics of a surface in $\R^3$, or inflections of a surface in $\R^4$.