In this paper, we study how to present gene expression data to display similarities by trying to find a linear ordering of genes such that genes with similar expression profiles will be close in this ordering. In general, finding the best possible order is intractable, and furthermore an unrestricted ordering may not be desired. Therefore we concentrate on the case in which hierarchical cluster...

We obtain improved bounds on the complexity of m distinct faces in an arrangement of n pseudo-segments, n circles, or n unit circles. The bounds are worst-case optimal for unit circles; they are also worst-case optimal for the case of pseudo-segments, except when the number of faces is very small, in which case our upper bound is a polylogarithmic factor from the best-known lower bound. For gen...

A mathematical formulation for the simultaneous design and layout of batch process facilities is proposed. The model determines simultaneously the optimal plant topology (i.e. the choice of the plant equipment and the associated connections), the layout (i.e. the arrangement of processing equipment storage vessels and their interconnecting pipe-work over a two-dimensional space) and the optimal...

We study the set of all pseudoline arrangements with contact points which cover a given support. We define a natural notion of flip between these arrangements and study the graph of these flips. In particular, we provide an enumeration algorithm for arrangements with a given support, based on the properties of certain greedy pseudoline arrangements and on their connection with sorting networks....

We introduce the notions of order type (or: dual arrangement) and visibility type (or: tangent visibility graph) for conngurations of disjoint convex sets in the plane. We develop optimal algorithms for computing and sweeping the order type, and also give a worst case optimal algorithm for computing the tangent visibility graph. The methods are based on a relation, introduced in this paper, bet...

Given n points in the plane and an integer k, the slope selection problem is to nd the pair of points whose connecting line has the k-th smallest slope. (In dual setting, given n lines in the plane, we want to nd the vertex of their arrangement with the k-th smallest x-coordinate.) Cole et al. 6] have given an O(n log n) solution (which is optimal), using the parametric searching technique of M...

A circular consecutive-k-out-of-n: F system consists of n components arranged along a circular path. This system fails if and only if k or more consecutive components fail. As the number of components n increases, the amount of calculation to solve optimal component arrangement problems in this kind of system exactly would be too much. In this paper, we propose two types of simulated annealing ...

The pairwise dissimilarities of a set of items can be intuitively visualized by a 2D arrangement of the items, in which the distances reflect the dissimilarities. Such an arrangement can be obtained by multidimensional scaling (MDS). We propose a method for the inverse process: inferring the pairwise dissimilarities from multiple 2D arrangements of items. Perceptual dissimilarities are classica...

This paper presents a 0.25 scale quasi-three-dimensional hydraulic model experiment of transient fluid flow phenomena during continuous casting steel. The relationship between the process and jump phenomenon is established. in mold divided into four stages (I–IV) from beginning to end casting. filling involves I–II investigated by high-speed camera. part cast start. In this paper, behavior vari...