Program
26.10.2012 A.J. Maciejewski (UZ), "N-body Problem in Mathematics and Astronomy: Dynamics of Old and Newly Discovered Planetary/Multiple Star Systems."
Abstract: This lecture is dedicated to discussing the fundamental properties of the N-body problem and the related mathematical challenges. We will consider the classical gravitational N-body problem involving material points and its various variants (restricted problems and Hill's problem). I will present the problem of central configurations and the issue of non-collision singularities. One of the significant applications of the N-body problem is the study of dynamics and determination of parameters of planets and their orbits in extrasolar planetary systems. I will discuss the challenges associated with such applications. Variants of the N-body problem where one or more bodies are extended objects (e.g., rigid bodies) also play an important role in applications. The problem of two rigid bodies, for example, is used to study the dynamics of binary asteroids. I will demonstrate how the complexity of the problem qualitatively changes when transitioning from point N-body problems to extended N-body problems.
11.12.2009 Piotr Wojdyllo (IMPAN), "Acoustic Simulation of Interiors and Its Applications."
Abstract: Motivated by the applications for compression and the study of subjective sound quality, we investigate diffusion models of sound propagation in enclosures composed of different materials. The diffusion model accounts for the sound delay when propagating through materials and performs well in cases where reverberation times, which are critical properties of the enclosure, are important. The computational complexity of the method is reasonable compared to the state-of-the-art.
20.11.2009 Prof. Andrzej Królak (IMPAN), "Searching for Gravitational Waves."
Abstract: I will present one of the phenomena predicted by general relativity, namely gravitational waves, and the methods for detecting these waves. Since the amplitudes of gravitational waves are extremely small, their detection is a significant challenge for statistical signal detection methods. I will present a range of mathematical tools and numerical algorithms that optimize the problem of detecting gravitational wave signals and estimating their parameters. I will also demonstrate the application of these methods to the analysis of real data from currently operating gravitational wave detectors.
29.05.2009 Stefano Olla (CEREMADE, France), "Macroscopic Non-Equilibrium Evolution of a System of Anharmonic Oscillators."
20.05.2016, 15:00, Prof. Piotr Gwiazda (UW and IMPAN), "Age-Structured Population Model of Infectious Disease Spread Applied to Data on Varicella Prevalence in Poland"
Abstract:
The dynamics of infectious disease transmission is often best understood by considering the population's structure concerning specific features, such as age or immunity level. The practical utility of such models depends on appropriate calibration with observed data. Here, we discuss the Bayesian approach to data assimilation in the case of a two-state age-structured model. These types of models are frequently used to describe disease dynamics (e.g., force of infection) based on prevalence data collected at several time points. We demonstrate that when the explicit solution to the model equation is known, accounting for the data collection process within the Bayesian framework allows for obtaining an unbiased posterior distribution for the parameters determining the force of infection. Furthermore, we show analytically and through numerical tests that the posterior distribution of these parameters is stable concerning cohort approximation (Escalator Boxcar Train) to the solution. Finally, we apply the technique to calibrate the model based on observed sero-prevalence of varicella in Poland.