The presence of clusters in a data set is sometimes due to the existence of certain relations among the measured variables which vary depending on some hidden factors. In these cases, observations could be grouped in a natural way around linear and nonlinear structures and, thus, the problem of doing robust clustering around linear affine subspaces has recently been tackled through the minimiza...

Universal descriptions are appealing because they simplify the description of different (but similar) physical systems, allow the determination of general properties, and have practical applications. Recently, the concept of universality has been applied to the dependence of the sputtering (ejection) yield due to energetic cluster bombardment versus the energy of the incident cluster. It was ob...

let $e$ be an elliptic curve over $bbb{q}$ with the given weierstrass equation $ y^2=x^3+ax+b$. if $d$ is a squarefree integer, then let $e^{(d)}$ denote the $d$-quadratic twist of $e$ that is given by $e^{(d)}: y^2=x^3+ad^2x+bd^3$. let $e^{(d)}(bbb{q})$ be the group of $bbb{q}$-rational points of $e^{(d)}$. it is conjectured by j. silverman that there are infinitely many primes $p$ for which $...

s e l e c t i o n o f a p p r o p r i a t e g r o u n d m o t i o n i s a k e y e l e m e n t w i t h i n a n y s e i s m i c a s s e s s m e n t o f s t r u c t u r e s. m a n y m e t h o d o l o g i e s h a v e b e e n d e v e l o p e d i n o r d e r t o s e l e c t a n d s c a l e g r o u n d m o t i o n r e c o r d s f o r t h e p u r p o s e o f r e s p o n s e h i s t o r y a n a l y s i ...

we are concerned with perturbations of the Hamiltonian system of the type c L(t)q + W&, q) = 0, t E R, WI where q = (ql, , qN) E WN, W E C1(W x WN,R), and L(t) E C(W,WN2) is a positive definite symmetric matrix. Variational arguments are used to prove the existence of homoclinic solutions for system (HS). @ 2003 Elsevier Science Ltd. All rights reserved. KeywordsHomoclinic orbits, Duffing equat...

Given a set S of n points in the plane, we deene a Manhattan Network on S as a rectilinear network G with the property that for every pair of points in S, the network G contains the shortest rectilinear path between them. A Minimum Manhattan Network on S is a Manhattan network of minimum possible length. A Manhattan network can be thought of as a graph G = (V; E), where the vertex set V corresp...

Proposition 1. Suppose the disjoint compacta E1' £2 are regular and), = p/q is rational. Set -r = )./(). + 1) and construct the Leja-Bagby points for the condenser (£1, E~) and corresponding rationals rn(Z) E Rnp,nq as in [1, p. 259], /fthe associated sequence {O"n}~l of signed measures defined in (7.9) of [1] coffi'erges in the weakstar sense to the signed measure jL, then jL = J1,*(-r), ~\!he...

The segmentation of urban scene mobile laser scanning (MLS) data into meaningful street objects is a great challenge due to the scene complexity of street environments, especially in the vicinity of street objects such as poles and trees. This paper proposes a three-stage method for the segmentation of urban MLS data at the object level. The original unorganized point cloud is first voxelized, ...

Denote points in Euclidean n-space, Rn, by x = (x1, . . . ,xn) and let E and ∂E denote the closure and boundary of E ⊆Rn, respectively. Let 〈x, y〉 denote the standard inner product in Rn, |x| = 〈x,x〉1/2, and set B(x,r)= {y ∈Rn : |y− x| < r} whenever x ∈Rn, r > 0. Define k-dimensional Hausdorffmeasure, 1≤ k ≤ n, in Rn as follows: for fixed δ > 0 and E ⊆Rn, let L(δ)= {B(xi,ri)} be such that E ⊆ ⋃...

We prove that for q ≥ 1, there exists r(q) < 1 such that for p > r(q), the number of points in large boxes which belongs to the infinite cluster has a normal central limit behaviour under the random cluster measure φp,q on Z, d ≥ 2. Particularly, we can take r(q) = p∗g for d = 2, which is commonly conjectured to be equal to pc. These results are used to prove a qdimensional central limit theore...