Numerical-asymptotic boundary integral methods in high-frequency acoustic scattering

In this article we describe recent progress on the design, analysis and implementation of hybrid numerical-asymptotic boundary integral methods for boundary value problems for the Helmholtz equation that model time harmonic acoustic wave scattering in domains exterior to impenetrable obstacles. These hybrid methods combine conventional piecewise polynomial approximations with high-frequency asymptotics to build basis functions suitable for representing the oscillatory solutions. They have the potential to solve scattering problems accurately in a computation time that is (almost) independent of frequency and this has been realized for many model problems. The design and analysis of this class of methods requires new results on the analysis and numerical analysis of highly oscillatory boundary integral operators and on the high-frequency asymptotics of scattering problems. The implementation requires the development of appropriate quadrature rules for highly oscillatory integrals. This article contains a historical account of the development of this currently very active field, a detailed account of recent progress and, in addition, a number of original research results on the design, analysis and implementation of these methods.

Existence and asymptotic behaviour for the parabolic-parabolic Keller-Segel system with singular data

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Lipopolysaccharide-Induced Sickness Behaviour Evaluated in Different Models of Anxiety and Innate Fear in Rats

The fact that there is a complex and bidirectional communication between the immune and nervous systems has been well demonstrated. Lipopolysaccharide (LPS), a component of gram-negative bacteria, is widely used to systematically stimulate the immune system and generate profound physiological and behavioural changes, also known as sickness behaviour (e.g. anhedonia, lethargy, loss of appetite, anxiety, sleepiness). Different ethological tools have been used to analyse the behavioural modifications induced by LPS; however, many researchers analysed only individual tests, a single LPS dose or a unique ethological parameter, thus leading to disagreements regarding the data. In the present study, we investigated the effects of different doses of LPS (10, 50, 200 and 500 mu g/kg, i.p.) in young male Wistar rats (weighing 180200 g; 89 weeks old) on the ethological and spatiotemporal parameters of the elevated plus maze, light-dark box, elevated T maze, open-field tests and emission of ultrasound vocalizations. There was a dose-dependent increase in anxiety-like behaviours caused by LPS, forming an inverted U curve peaked at LPS 200 mu g/kg dose. However, these anxiety-like behaviours were detected only by complementary ethological analysis (stretching, grooming, immobility responses and alarm calls), and these reactions seem to be a very sensitive tool in assessing the first signs of sickness behaviour. In summary, the present work clearly showed that there are resting and alertness reactions induced by opposite neuroimmune mechanisms (neuroimmune bias) that could lead to anxiety behaviours, suggesting that misunderstanding data could occur when only few ethological variables or single doses of LPS are analysed. Finally, it is hypothesized that this bias is an evolutionary tool that increases animals security while the body recovers from a systemic infection.

Simultaneous 3D object tracking and camera parameter estimation by Bayesian methods and transdimensional MCMC sampling

Multi-camera 3D tracking systems with overlapping cameras represent a powerful mean for scene analysis, as they potentially allow greater robustness than monocular systems and provide useful 3D information about object location and movement. However, their performance relies on accurately calibrated camera networks, which is not a realistic assumption in real surveillance environments. Here, we introduce a multi-camera system for tracking the 3D position of a varying number of objects and simultaneously refin-ing the calibration of the network of overlapping cameras. Therefore, we introduce a Bayesian framework that combines Particle Filtering for tracking with recursive Bayesian estimation methods by means of adapted transdimensional MCMC sampling. Addi-tionally, the system has been designed to work on simple motion detection masks, making it suitable for camera networks with low transmission capabilities. Tests show that our approach allows a successful performance even when starting from clearly inaccurate camera calibrations, which would ruin conventional approaches.

Modern mathematical methods and models; a book of experimental text materials.

v. 1. Multicomponent methods.--v. 2. Mathematical models.

Analysis of Melanoma Onset: Assessing Familial Aggregation by Using Estimating Equations and Fitting Variance Components via Bayesian Random Effects Models

We investigate whether relative contributions of genetic and shared environmental factors are associated with an increased risk in melanoma. Data from the Queensland Familial Melanoma Project comprising 15,907 subjects arising from 1912 families were analyzed to estimate the additive genetic, common and unique environmental contributions to variation in the age at onset of melanoma. Two complementary approaches for analyzing correlated time-to-onset family data were considered: the generalized estimating equations (GEE) method in which one can estimate relationship-specific dependence simultaneously with regression coefficients that describe the average population response to changing covariates; and a subject-specific Bayesian mixed model in which heterogeneity in regression parameters is explicitly modeled and the different components of variation may be estimated directly. The proportional hazards and Weibull models were utilized, as both produce natural frameworks for estimating relative risks while adjusting for simultaneous effects of other covariates. A simple Markov Chain Monte Carlo method for covariate imputation of missing data was used and the actual implementation of the Bayesian model was based on Gibbs sampling using the free ware package BUGS. In addition, we also used a Bayesian model to investigate the relative contribution of genetic and environmental effects on the expression of naevi and freckles, which are known risk factors for melanoma.

Asymptotic Behaviour of Colength of Varieties of Lie Algebras

This project was partially supported by RFBR, grants 99-01-00233, 98-01-01020 and 00-15-96128.

A Note on the Asymptotic Behaviour of a Periodic Multitype Galton-Watson Branching Process

2000 Mathematics Subject Classification: 60J80.

Asymptotic Behaviour of a Supercritical Galton-Watson Process with Controlled Binomial Migration

AMS subject classification: 60J80, 62F12, 62P10.

The Asymptotic Behaviour of the First Eigenvalue of Linear Second-Order Elliptic Equations in Divergente Form

2000 Mathematics Subject Classification: 35J70, 35P15.