Search

Topology was introduced in the visualization literature some 15 years ago as a mathematical language to describe and capture the salient structures of symmetric second-order tensor fields. Yet, despite significant theoretical and algorithmic advances, this approach has failed to gain wide acceptance in visualization practice over the last decade. In fact, the very idea of a versatile visualization methodology for tensor fields that could transcend application domains has been virtually abandoned in favor of problem-specific feature definitions and visual representations. We propose to revisit the basic idea underlying topology from a different perspective. To do so, we introduce a Lagrangian metaphor that transposes to the structural analysis of eigenvector fields a perspective that is commonly used in the study of fluid flows. Indeed, one can view eigenvector fields as the local superimposition of two vector fields, from which a bidirectional flow field can be defined. This allows us to analyze the structure of a tensor field through the behavior of fictitious particles advected by this flow. Specifically, we show that the separatrices of 3D tensor field topology can in fact be captured in a fuzzy and numerically more robust setting as ridges of a trajectory coherence measure. As a result, we propose an alternative structure characterization strategy for the visual analysis of practical 3D tensor fields, which we demonstrate on several synthetic and computational datasets.

Discovering aliases in Thai sports news is a challenging task. This paper presents an approach to identifying aliases by analyzing cooccurrence relationships between named entities. Semantically similar names are computed using two vector methods - Latent Semantic Analysis (LSA) and correlation matrix (COM). The LSA method decomposes a name-by-document matrix (NDM) into singular-value and singular-vector matrices. The truncated left singular vector matrix is used for identifying name similarity. The COM method constructs a name-byname matrix (NNM) from the NDM and then directly measures similarity among name vectors using simple calculations. Both methods are weighted by the same weighting schemes. Obtained similarity relations among names are filtered out based on name types. Our preliminary experimental results show that the COM method performs better than the LSA method.

While usually SVM training tries to solve the dual of the standard SVM minimization problem, alternative algorithms that solve the Nearest Point Problem (NPP) for the convex hulls of the positive and negative samples have been shown to also provide effective SVM training. They are variants of the Mitchell---Demyanov---Malozemov (MDM) algorithm and although they perform a two vector weight update, they must compute 4 possible updating vectors before deciding which ones to use. In this work we shall propose a 4---vector version of the MDM algorithm that requires substantially less iterations than the previous 2---vector MDM algorithms and leads to faster training if kernel operations are cached.

The theorem presented in this paper is a general solution for the optimal superimposition between two protein structures, which is actually the problem of the weighted optimal rigid superimposition between two vector sets with the same size. The theorem gives not only the rotational and translational parameters, but also the minimal value of the mean squared deviation of the optimal superimposition.

In this paper we introduce a vector ISA extension to facilitate sparse matrix manipulation on vector processors (VPs). First we introduce a new Block Based Compressed Storage (BBCS) format for sparse matrix representation and a Block-wise Sparse Matrix-Vector Multiplication approach. Additionally, we propose two vector instructions, Multiple Inner Product and Accumulate (MIPA) and LoaD Section (LDS), specially tuned to increase the VP performance when executing sparse matrix-vector multiplications.

This paper is concerned with the analysis and implementation on a computer consisting of two vector processors of the Preconditioned Simultaneous Displacements method with an additive preconditioner for solving large sparse systems of linear equations. This method converges for systems with coefficient matrices that are symmetric positive definite or irreducible L-matrices with a strong diagonal dominance.

We try to explain the succession of periodic and chaotic behaviours observed in B.Z.Z. reaction (See many contributions in this volume). We define an abstract mathematical object: “Mixed vector fields”which is very similar to ROSSLER models with, however, some new features inspired by the above mentioned experiments. Our model is not purely speculative and is closely related to a modified version of the Oregonator taken from TYSON.