Vitaly L. Galinsky

Automatic registration of microarray images. II. Hexagonal grid

MOTIVATION In the first part of this paper the author presented an efficient, robust and completely automated algorithm for spot and block indexing in microarray images with rectangular grids. Although the rectangular grid is currently the most common type of grouping the probes on microarray slides, there is another microarray technology based on bundles of optical fibers where the probes are packed in hexagonal grids. The hexagonal grid provides both advantages and drawbacks over the standard rectangular packing and of course requires adaptation and/or modification of the algorithm of spot indexing presented in the first part of the paper. RESULTS In the second part of the paper the author presents a version of the spot indexing algorithm adapted for microarray images with spots packed in hexagonal structures. The algorithm is completely automated, works with hexagonal grids of different types and with different parameters of grid spacing and rotation as well as spot sizes. It can successfully trace the local and global distortions of the grid, including non-orthogonal transformations. Similar to the algorithm from part I, it scales linearly with the grid size, the time complexity is O(M), where M is total number of grid points in hexagonal grid. The algorithm has been tested both on CCD and scanned images with spot expression rates as low as 2%. The processing time of an image with about 50 000 hex grid points was less than a second. For images with high expression rates ( approximately 90%) the registration time is even smaller, around a quarter of a second. SUPPLEMENTARY INFORMATION http://fleece.ucsd.edu/~vit/Registration_Supplement.pdf

Fluid models for kinetic effects on coherent nonlinear Alfvén waves. II. Numerical solutions

The influence of various kinetic effects (e.g., Landau damping, diffusive and collisional dissipation, and finite Larmor radius terms) on the nonlinear evolution of finite amplitude Alfvenic wave trains in a finite-β environment is systematically investigated using a novel, kinetic nonlinear Schrodinger (KNLS) equation. The dynamics of Alfven waves is sensitive to the sense of polarization as well as the angle of propagation with respect to the ambient magnetic field. Numerical solution for the case with Landau damping reveals the formation of dissipative structures, which are quasi-stationary, S-polarized directional (and rotational) discontinuities which self-organize from parallel propagating, linearly polarized waves. Parallel propagating circularly polarized packets evolve to a few circularly polarized Alfven harmonics on large scales. Stationary arc-polarized rotational discontinuities form from obliquely propagating waves. Collisional dissipation, even if weak, introduces enhanced wave damping when...

DISSIPATIVE DYNAMICS OF COLLISIONLESS NONLINEAR ALFVEN WAVE TRAINS

The nonlinear dynamics of collisionless Alfv{grave e}n trains, including resonant particle effects, is studied using the kinetic nonlinear Schr{umlt o}dinger (KNLS) equation model. Numerical solutions of the KNLS reveal the dynamics of Alfv{acute e}n waves to be sensitive to the sense of polarization as well as the angle of propagation with respect to the ambient magnetic field. The combined effects of both wave nonlinearity and Landau damping result in the evolutionary formation of {ital stationary} S - and arc-polarized directional and rotational discontinuities. These wave forms are frequently observed in the interplanetary plasma. {copyright} {ital 1997 } {ital The American Physical Society}

Automatic registration of microarray images. I. Rectangular grid

MOTIVATION The analysis of high-throughput experiment data provided by microarrays becomes increasingly more and more important part of modern biological science. Microarrays allow to conduct genotyping or gene expression experiments on hundreds of thousands of test genes in parallel. Because of the large and constantly growing amount of experimental data the necessity of efficiency, robustness and complete automation of microarray image analysis algorithms is gaining significant attention in the field of microarray processing. RESULTS The author presents here an efficient and completely automatic image registration algorithm (that is an algorithm for spots and blocks indexing) that allows to process a wide variety of microarray slides with different parameters of grid and block spacing as well as spot sizes. The algorithm scales linearly with the grid size, the time complexity is O(M), where M is number of rows x number of columns. It can successfully cope with local and global distortions of the grid, such as focal distortions and non-orthogonal transformations. The algorithm has been tested both on CCD and scanned images and showed very good performance-the processing time of a single slide with 44 blocks of 200 x 200 grid points (or 1 760 000 grid points total) was about 10 s. AVAILABILITY The test implementation of the algorithm will be available upon request for academics. SUPPLEMENTARY INFORMATION http://fleece.ucsd.edu/~vit/Registration_Supplement.pdf

Macro-scale instability of the ion shell distribution function in the divergent solar wind

As a result of cyclotron interaction with Alfven waves propagating from the sun, pitch angle diffusion of resonant particles takes place and a shell-like distribution function of resonant ions is formed at each distance from the sun. Stability of the solar wind ion shell-like distribution function with respect to excitation of waves at larger distances is addressed. It is shown in linear approximation, that in the case when the phase velocity of Alfven waves decreases with distance, ions with shell distribution excite outward propagating Alfven waves with smaller phase velocities when they advance to larger distances. The nonlinear dynamics of the wave spectrum as well as the evolution of the ion distribution function are studied. The characteristic spectrum at the high-frequency edge of the magnetohydrodynamic fluctuations is explained.

Automated segmentation and shape characterization of volumetric data

Characterization of complex shapes embedded within volumetric data is an important step in a wide range of applications. Standard approaches to this problem employ surface-based methods that require inefficient, time consuming, and error prone steps of surface segmentation and inflation to satisfy the uniqueness or stability of subsequent surface fitting algorithms. Here we present a novel method based on a spherical wave decomposition (SWD) of the data that overcomes several of these limitations by directly analyzing the entire data volume, obviating the segmentation, inflation, and surface fitting steps, significantly reducing the computational time and eliminating topological errors while providing a more detailed quantitative description based upon a more complete theoretical framework of volumetric data. The method is demonstrated and compared to the current state-of-the-art neuroimaging methods for segmentation and characterization of volumetric magnetic resonance imaging data of the human brain.

Simultaneous Multi-Scale Diffusion Estimation and Tractography Guided by Entropy Spectrum Pathways

We have developed a method for the simultaneous estimation of local diffusion and the global fiber tracts based upon the information entropy flow that computes the maximum entropy trajectories between locations and depends upon the global structure of the multi-dimensional and multi-modal diffusion field. Computation of the entropy spectrum pathways requires only solving a simple eigenvector problem for the probability distribution for which efficient numerical routines exist, and a straight forward integration of the probability conservation through ray tracing of the convective modes guided by a global structure of the entropy spectrum coupled with a small scale local diffusion. The intervoxel diffusion is sampled by multi b-shell multi q-angle diffusion weighted imaging data expanded in spherical waves. This novel approach to fiber tracking incorporates global information about multiple fiber crossings in every individual voxel and ranks it in the most scientifically rigorous way. This method has potential significance for a wide range of applications, including studies of brain connectivity.

YOABS: yet other aligner of biological sequences—an efficient linearly scaling nucleotide aligner

MOTIVATION Explosive growth of short-read sequencing technologies in the recent years resulted in rapid development of many new alignment algorithms and programs. But most of them are not efficient or not applicable for reads > or approximately equal to 200 bp because these algorithms specifically designed to process short queries with relatively low sequencing error rates. However, the current trend to increase reliability of detection of structural variations in assembled genomes as well as to facilitate de novo sequencing demand complimenting high-throughput short-read platforms with long-read mapping. Thus, algorithms and programs for efficient mapping of longer reads are becoming crucial. However, the choice of long-read aligners effective in terms of both performance and memory are limited and includes only handful of hash table (BLAT, SSAHA2) or trie (Burrows-Wheeler Transform - Smith-Waterman (BWT-SW), Burrows-Wheeler Alignerr - Smith-Waterman (BWA-SW)) based algorithms. RESULTS New O(n) algorithm that combines the advantages of both hash and trie-based methods has been designed to effectively align long biological sequences (> or approximately equal to 200 bp) against a large sequence database with small memory footprint (e.g. ~2 GB for the human genome). The algorithm is accurate and significantly more fast than BLAT or BWT-SW, but similar to BWT-SW it can find all local alignments. It is as accurate as SSAHA2 or BWA-SW, but uses 3+ times less memory and 10+ times faster than SSAHA2, several times faster than BWA-SW with low error rates and almost two times less memory. AVAILABILITY AND IMPLEMENTATION The prototype implementation of the algorithm will be available upon request for non-commercial use in academia (local hit table binary and indices are at ftp://styx.ucsd.edu).

Excitation of nonlinear Alfvén waves by an ion beam in a plasma: 1. Right‐hand polarized waves

A self-consistent theory of MHD wave excitation in the solar wind plasma by a cold ion beam moving along the ambient magnetic field is developed. Using analytical and numerical technics, we investigate the linear stage of the exponential growth of wave amplitudes, their saturation due to trapping or pitch angle diffusion of resonant ions and the steepening of the wave profile due to plasma nonlinearity. The derivative nonlinear Schrodinger equation was used to describe the nonlinear input of plasma particles, and a hybrid method of incomplete numerical simulation was used to investigate strongly nonlinear motion of resonant particles. We have studied the temporal behavior of wave energy for waves propagating in both positive and negative directions in relation to the magnetic field, directions and we have found that in cases under consideration the steepening profile developed only for right-hand polarized waves. The physical mechanism for wave steepening is higher harmonic generation due to plasma nonlinearity.

The DNLS equation and parametric decay instability

A model that describes the interaction of nonlinear Alfvén packets propagating in opposite directions parallel to the ambient magnetic field is constructed. This model incorporates both (i) the parametric interaction of harmonics propagating in the same direction, which can be responsible for the transportation of the wave energy to the short-wavelength region of the spectrum, and (ii) the parametric interaction of Alfvén waves propagating in opposite directions, which can be responsible for the excitation of backward-propagating waves by the parametric decaylike instability of the forward-propagating fluctuations.