An Intuitive Approach to Geometric Continuity for Parametric Curves and Surfaces (Extended Abstract)

The notion of geometric continuity is extended to an arbitrary order for curves and surfaces, and an intuitive development of constraints equations is presented that are necessary for it. The constraints result from a direct application of the univariate chain rule for curves, and the bivariate chain rule for surfaces. The constraints provide for the introduction of quantities known as shape parameters. The approach taken is important for several reasons: First, it generalizes geometric continuity to arbitrary order for both curves and surfaces. Second, it shows the fundamental connection between geometric continuity of curves and geometric continuity of surfaces. Third, due to the chain rule derivation, constraints of any order can be determined more easily than derivations based exclusively on geometric measures

The scaling limit of the incipient infinite cluster in high-dimensional percolation. II. Integrated super-Brownian excursion

For independent nearest-neighbour bond percolation on Z^d with d >> 6, we prove that the incipient infinite cluster's two-point function and three-point function converge to those of integrated super-Brownian excursion (ISE) in the scaling limit. The proof is based on an extension of the new expansion for percolation derived in a previous paper, and involves treating the magnetic field as a complex variable. A special case of our result for the two-point function implies that the probability that the cluster of the origin consists of n sites, at the critical point, is given by a multiple of n^{-3/2}, plus an error term of order n^{-3/2-\epsilon} with \epsilon >0. This is a strong statement that the critical exponent delta is given by delta =2.Comment: 56 pages, 3 Postscript figures, in AMS-LaTeX, with graphicx, epic, and xr package

Random solids and random solidification: What can be learned by exploring systems obeying permanent random constraints?

In many interesting physical settings, such as the vulcanization of rubber, the introduction of permanent random constraints between the constituents of a homogeneous fluid can cause a phase transition to a random solid state. In this random solid state, particles are permanently but randomly localized in space, and a rigidity to shear deformations emerges. Owing to the permanence of the random constraints, this phase transition is an equilibrium transition, which confers on it a simplicity (at least relative to the conventional glass transition) in the sense that it is amenable to established techniques of equilibrium statistical mechanics. In this Paper I shall review recent developments in the theory of random solidification for systems obeying permanent random constraints, with the aim of bringing to the fore the similarities and differences between such systems and those exhibiting the conventional glass transition. I shall also report new results, obtained in collaboration with Weiqun Peng, on equilibrium correlations and susceptibilities that signal the approach of the random solidification transition, discussing the physical interpretation and values of these quantities both at the Gaussian level of approximation and, via a renormalization-group approach, beyond.Comment: Paper presented at the "Unifying Concepts in Glass Physics" workshop, International Centre for Theoretical Physics, Trieste, Italy (September 15-18, 1999

Staphylococcus aureus nasal colonization in HIV-seropositive and HIV-seronegative drug users

Nasal colonization plays an important role in the pathogenesis of Staphylococcus aureus infections. To identify characteristics associated with colonization, we studied a cross-section of a well-described cohort of HIV-seropositive and -seronegative active and former drug users considered at risk for staphylococcal infections. Sixty percent of the 217 subjects were Hispanic, 36% were women, 25% actively used injection drugs, 23% actively used inhalational drugs, 23% received antibiotics, and 35% were HIV-seropositive. Forty-one percent of subjects had positive nasal cultures for S. aureus. The antibiotic susceptibility patterns were similar to the local hospital's outpatient isolates and no dominant strain was identified by arbitrarily primed polymerase chain reaction (AB-PCR). Variables significantly and independently associated with colonization included antibiotic use (odds ratio [OR] = 0.37; confidence interval [CI] = 0.18-0.77), active inhalational drug use within the HIV-seropositive population (OR = 2.36; CI = 1.10-5.10) and female gender (OR = 1.97; CI = 1.09-3.57). Characteristics not independently associated included injection drug use, HIV status, and CD4 count. The association with active inhalational drug use, a novel finding, may reflect alterations in the integrity of the nasal mucosa. The lack of association between HIV infection and S. aureus colonization, which is contrary to most previous studies, could be explained by our rigorous control for confounding variables or by a limited statistical power due to the sample sizes

Bulk and Interfacial Shear Thinning of Immiscible Polymers

Nonequilibrium molecular dynamics simulations are used to study the shear thinning behavior of immiscible symmetric polymer blends. The phase separated polymers are subjected to a simple shear flow imposed by moving a wall parallel to the fluid-fluid interface. The viscosity begins to shear thin at much lower rates in the bulk than at the interface. The entire shear rate dependence of the interfacial viscosity is consistent with a shorter effective chain length $s^*$ that also describes the width of the interface. This $s^*$ is independent of chain length $N$ and is a function only of the degree of immiscibility of the two polymers. Changes in polymer conformation are studied as a function of position and shear rate.Shear thinning correlates more closely with a decrease in the component of the radius of gyration along the velocity gradient than with elongation along the flow. At the interface, this contraction of chains is independent of $N$ and consistent with the bulk behavior for chains of length $s^*$. The distribution of conformational changes along chains is also studied. Central regions begin to stretch at a shear rate that decreases with increasing $N$, while shear induced changes at the ends of chains are independent of $N$.Comment: 8 pages, 8 figure

Bootstrapping Smooth Functions of Slope Parameters and Innovation Variances in VAR(∞) Models *

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/101814/1/1468-2354.t01-1-00016.pd

Media Reporting and Business Cycles: Empirical Evidence based on News Data

Recent literature suggests that news shocks could be an important driver of economic cycles. In this article, we use a direct measure of news sentiment derived from media reports. This allows us to examine whether innovations in the reporting tone correlate with changes in the assessment and expectations of the business situation as reported by firms in the German manufacturing sector. We fi nd that innovations in news reporting affect business expectations, even when conditioning on the current business situation and industrial production. The dynamics of the empirical model con rm theoretical predictions that news innovations affect real variables such as production via changes in expectations. Looking at individual sectors within manufacturing, we fi nd that macroeconomic news is at least as important for business expectations as sector-spefici c news. This is consistent with the existence of information complementarities across sectors

Application of Approximate Pattern Matching in Two Dimensional Spaces to Grid Layout for Biochemical Network Maps

Background For visualizing large-scale biochemical network maps, it is important to calculate the coordinates of molecular nodes quickly and to enhance the understanding or traceability of them. The grid layout is effective in drawing compact, orderly, balanced network maps with node label spaces, but existing grid layout algorithms often require a high computational cost because they have to consider complicated positional constraints through the entire optimization process. Results We propose a hybrid grid layout algorithm that consists of a non-grid, fast layout (preprocessor) algorithm and an approximate pattern matching algorithm that distributes the resultant preprocessed nodes on square grid points. To demonstrate the feasibility of the hybrid layout algorithm, it is characterized in terms of the calculation time, numbers of edge-edge and node-edge crossings, relative edge lengths, and F-measures. The proposed algorithm achieves outstanding performances compared with other existing grid layouts. Conclusions Use of an approximate pattern matching algorithm quickly redistributes the laid-out nodes by fast, non-grid algorithms on the square grid points, while preserving the topological relationships among the nodes. The proposed algorithm is a novel use of the pattern matching, thereby providing a breakthrough for grid layout. This application program can be freely downloaded from http://www.cadlive.jp/hybridlayout/hybridlayout.html