An iterative contractive framework for probe methods: LASSO

We present a new iterative approach called Line Adaptation for the Singular Sources Objective (LASSO) to object or shape reconstruction based on the singular sources method (or probe method) for the reconstruction of scatterers from the far-field pattern of scattered acoustic or electromagnetic waves. The scheme is based on the construction of an indicator function given by the scattered field for incident point sources in its source point from the given far-field patterns for plane waves. The indicator function is then used to drive the contraction of a surface which surrounds the unknown scatterers. A stopping criterion for those parts of the surfaces that touch the unknown scatterers is formulated. A splitting approach for the contracting surfaces is formulated, such that scatterers consisting of several separate components can be reconstructed. Convergence of the scheme is shown, and its feasibility is demonstrated using a numerical study with several examples

Binary Assignments of Amino Acids from Pattern Conservation

We develop a simple optimization procedure for assigning binary values to the amino acids. The binary values are determined by a maximization of the degree of pattern conservation in groups of closely related protein sequences. The maximization is carried out at fixed composition. For compositions approximately corresponding to an equipartition of the residues, the optimal encoding is found to be strongly correlated with hydrophobicity. The stability of the procedure is demonstrated. Our calculations are based upon sequences in the SWISS-PROT database.Comment: 9 pages, 4 Postscript figures. References and figure adde

Studies of an Off-Lattice Model for Protein Folding: Sequence Dependence and Improved Sampling at Finite Temperature

We study the thermodynamic behavior of a simple off-lattice model for protein folding. The model is two-dimensional and has two different ``amino acids''. Using numerical simulations of all chains containing eight or ten monomers, we examine the sequence dependence at a fixed temperature. It is shown that only a few of the chains exist in unique folded state at this temperature, and the energy level spectra of chains with different types of behavior are compared. Furthermore, we use this model as a testbed for two improved Monte Carlo algorithms. Both algorithms are based on letting some parameter of the model become a dynamical variable; one of the algorithms uses a fluctuating temperature and the other a fluctuating monomer sequence. We find that by these algorithms one gains large factors in efficiency in comparison with conventional methods.Comment: 17 pages, 9 Postscript figures. Combined with chem-ph/950500

Evidence for Non-Random Hydrophobicity Structures in Protein Chains

The question of whether proteins originate from random sequences of amino acids is addressed. A statistical analysis is performed in terms of blocked and random walk values formed by binary hydrophobic assignments of the amino acids along the protein chains. Theoretical expectations of these variables from random distributions of hydrophobicities are compared with those obtained from functional proteins. The results, which are based upon proteins in the SWISS-PROT data base, convincingly show that the amino acid sequences in proteins differ from what is expected from random sequences in a statistical significant way. By performing Fourier transforms on the random walks one obtains additional evidence for non-randomness of the distributions. We have also analyzed results from a synthetic model containing only two amino-acid types, hydrophobic and hydrophilic. With reasonable criteria on good folding properties in terms of thermodynamical and kinetic behavior, sequences that fold well are isolated. Performing the same statistical analysis on the sequences that fold well indicates similar deviations from randomness as for the functional proteins. The deviations from randomness can be interpreted as originating from anticorrelations in terms of an Ising spin model for the hydrophobicities. Our results, which differ from previous investigations using other methods, might have impact on how permissive with respect to sequence specificity the protein folding process is -- only sequences with non-random hydrophobicity distributions fold well. Other distributions give rise to energy landscapes with poor folding properties and hence did not survive the evolution.Comment: 16 pages, 8 Postscript figures. Minor changes, references adde

On sequential multiscale inversion and data assimilation

Multiscale approaches are very popular for example for solving partial differential equations and in many applied fields dealing with phenomena which take place on different levels of detail. The broad idea of a multiscale approach is to decompose your problem into different scales or levels and to use these decompositions either for constructing appropriate approximations or to solve smaller problems on each of these levels, leading to increased stability or increased efficiency. The idea of sequential multiscale is to first solve the problem in a large-scale subspace and then successively move to finer scale spaces. Our goal is to analyse the sequential multiscale approach applied to an inversion or state estimation problem. We work in a generic setup given by a Hilbert space environment. We work out the analysis both for an unregularized and a regularized sequential multiscale inversion. In general the sequential multiscale approach is not equivalent to a full solution, but we show that under appropriate assumptions we obtain convergence of an iterative sequential multiscale version of the method. For the regularized case we develop a strategy to appropriately adapt the regularization when an iterative approach is taken. We demonstrate the validity of the iterative sequential multiscale approach by testing the method on an integral equation as it appears for atmospheric temperature retrieval from infrared satellite radiances

Source Retrieval for Plagiarism Detection

Plagiarism has become a serious problem mainly because of the electronically available documents. An online document retrieval is a weighty part of a modern anti-plagiarism tool. This paper describes an architecture and concepts of a real-world document retrieval system, which is a part of a general anti-plagiarism software. Up to date systems for plagiarism detection are discussed from the source retrieval perspective. The key approaches of source retrieval are compared. The system recommendations stem from design, implementation, and several years of operation experience of a nationwide plagiarism solution at Masaryk University in the Czech Republic. The design can be adapted to many situations. Proper usage of such systems contributes to the gradual improvement of the quality of student theses.Plagiarism has become a serious problem mainly because of the electronically available documents. An online document retrieval is a weighty part of a modern anti-plagiarism tool. This paper describes an architecture and concepts of a real-world document retrieval system, which is a part of a general anti-plagiarism software. Up to date systems for plagiarism detection are discussed from the source retrieval perspective. The key approaches of source retrieval are compared. The system recommendations stem from design, implementation, and several years of operation experience of a nationwide plagiarism solution at Masaryk University in the Czech Republic. The design can be adapted to many situations. Proper usage of such systems contributes to the gradual improvement of the quality of student theses

Local Interactions and Protein Folding: A 3D Off-Lattice Approach

The thermodynamic behavior of a three-dimensional off-lattice model for protein folding is probed. The model has only two types of residues, hydrophobic and hydrophilic. In absence of local interactions, native structure formation does not occur for the temperatures considered. By including sequence independent local interactions, which qualitatively reproduce local properties of functional proteins, the dominance of a native state for many sequences is observed. As in lattice model approaches, folding takes place by gradual compactification, followed by a sequence dependent folding transition. Our results differ from lattice approaches in that bimodal energy distributions are not observed and that high folding temperatures are accompanied by relatively low temperatures for the peak of the specific heat. Also, in contrast to earlier studies using lattice models, our results convincingly demonstrate that one does not need more than two types of residues to generate sequences with good thermodynamic folding properties in three dimensions.Comment: 18 pages, 11 Postscript figure

In situ growth regime characterization of cubic GaN using reflection high energy electron diffraction

Cubic GaN layers were grown by plasma-assisted molecular beam epitaxy on 3C-SiC (001)substrates. In situ reflection high energy electron diffraction was used to quantitatively determine the Ga coverage of the GaN surface during growth. Using the intensity of the electron beam as a probe,optimum growth conditions of c-GaN were found when a 1 ML Ga coverage is formed at the surface. 1 micrometer thick c-GaN layers had a minimum surface roughness of 2.5 nm when a Ga coverage of 1 ML was established during growth. These samples revealed also a minimum full width at half maximum of the (002)rocking curve.Comment: 3pages with 4 figure