Alternatives to the EM algorithm for ML estimation of location,scatter matrix,and degree of freedom of the Student t distribution

Numerical Algorithms - In this paper, we consider maximum likelihood estimations of the degree of freedom parameter ν, the location parameter μ and the scatter matrix Σ of the...     

Generalized multiresolution analysis on unstructured grids

Summary. Efficiency of high-order essentially non-oscillatory (ENO) approximations of conservation laws can be drastically improved if ideas of multiresolution analysis are taken into account. These methods of data compression not only reduce the necessary amount of discrete data but can also serve as tools in detecting local low-dimensional features in the numerical solution. We describe the mathematical background of the generalized multiresolution analysis as developed by Abgrall and Harten in [14], [15] and [3]. We were able to ultimately reduce the functional analytic background to matrix-vector operations of linear algebra. We consider the example of interpolation on the line as well as the important case of multiresolution analysis of cell average data which is used in finite volume approximations. In contrast to Abgrall and Harten, we develop a robust agglomeration procedure and recovery algorithms based on least-squeare polynomials. The efficiency of our algorithms is documented by means of several examples. Received April 4, 1998 / Revised version August 2, 1999 / Published online June 8, 2000     

Interfaces between coexisting phases in polymer mixtures: What can we learn from Monte Carlo simulations?

Symmetric binary polymer mixtures are studied by Monte Carlo simulation of the bond fluctuation model, considering both interfaces between coexisting bulk phases and interfaces confined in thin films. It is found that the critical behavior of interfacial tension and width is compatible with that of the Ising model, as expected from the universality principle. In the strong segregation limit, only qualitative but not quantitative agreement with the self-consistent field (SCF) theory is found. It is argued that the SCF theory requires but for the short chains studied (N = 32 effective monomer units per chain), the limit is only reached for close to unity. Also, the effective χ-parameter decreases in the interface. It is shown that the interfacial width w does not increase by the adsorption of block copolymers as long as their areal density is still dilute (“mushroom” regime). But a broadening of interfaces does occur for thin films confined between walls at distance D, due to fluctuations that lead to for short-range forces, in agreement with experiment.