Statistical comparison of clouds and star clusters

The extent to which the projected distribution of stars in a cluster is due to a large-scale radial gradient, and the extent to which it is due to fractal sub-structure, can be quantified -- statistically -- using the measure ${\cal Q} = \bar{m}/\bar{s}$. Here $\bar{m}$ is the normalized mean edge length of its minimum spanning tree (i.e. the shortest network of edges connecting all stars in the cluster) and $\bar{s}$ is the correlation length (i.e. the normalized mean separation between all pairs of stars). We show how ${\cal Q}$ can be indirectly applied to grey-scale images by decomposing the image into a distribution of points from which $\bar{m}$ and $\bar{s}$ can be calculated. This provides a powerful technique for comparing the distribution of dense gas in a molecular cloud with the distribution of the stars that condense out of it. We illustrate the application of this technique by comparing ${\cal Q}$ values from simulated clouds and star clusters.Comment: Accepted 2010 October 27. Received 2010 October 25; in original form 2010 September 13 The paper contains 7 figures and 2 table

Use of light scattering in characterizing reactively ion etched profiles

Currently, profile control in plasma etching of submicron structures requires inspection of cleaved samples by scanning electron microscopy. This is time consuming, destructive, and limited to a small subset of processed wafers. We show that light scattering can be used to rapidly characterize submicron differences in reactively ion etched, periodic Si structures. A similar approach has been used previously to monitor etching rates and undercutting using specular and first order diffraction peaks. Here, we measure all orders scattered over 180° as a function of incident angle and polarization and focus on the use of this technique coupled with statistical methodology to distinguish subtle changes in line profile. Although scatter from grating test patterns is examined here, this method should also be applicable to complex, submicron device structures

Geometry of jet spaces and integrable systems

An overview of some recent results on the geometry of partial differential equations in application to integrable systems is given. Lagrangian and Hamiltonian formalism both in the free case (on the space of infinite jets) and with constraints (on a PDE) are discussed. Analogs of tangent and cotangent bundles to a differential equation are introduced and the variational Schouten bracket is defined. General theoretical constructions are illustrated by a series of examples.Comment: 54 pages; v2-v6 : minor correction

Time warping of evolutionary distant temporal gene expression data based on noise suppression

<p>Abstract</p> <p>Background</p> <p>Comparative analysis of genome wide temporal gene expression data has a broad potential area of application, including evolutionary biology, developmental biology, and medicine. However, at large evolutionary distances, the construction of global alignments and the consequent comparison of the time-series data are difficult. The main reason is the accumulation of variability in expression profiles of orthologous genes, in the course of evolution.</p> <p>Results</p> <p>We applied Pearson distance matrices, in combination with other noise-suppression techniques and data filtering to improve alignments. This novel framework enhanced the capacity to capture the similarities between the temporal gene expression datasets separated by large evolutionary distances. We aligned and compared the temporal gene expression data in budding (<it>Saccharomyces cerevisiae</it>) and fission (<it>Schizosaccharomyces pombe</it>) yeast, which are separated by more then ~400 myr of evolution. We found that the global alignment (time warping) properly matched the duration of cell cycle phases in these distant organisms, which was measured in prior studies. At the same time, when applied to individual ortholog pairs, this alignment procedure revealed groups of genes with distinct alignments, different from the global alignment.</p> <p>Conclusion</p> <p>Our alignment-based predictions of differences in the cell cycle phases between the two yeast species were in a good agreement with the existing data, thus supporting the computational strategy adopted in this study. We propose that the existence of the alternative alignments, specific to distinct groups of genes, suggests presence of different synchronization modes between the two organisms and possible functional decoupling of particular physiological gene networks in the course of evolution.</p

Network Theory Analysis of Antibody-Antigen Reactivity Data: The Immune Trees at Birth and Adulthood

Motivation: New antigen microarray technology enables parallel recording of antibody reactivities with hundreds of antigens. Such data affords system level analysis of the immune system’s organization using methods and approaches from network theory. Here we measured the reactivity of 290 antigens (for both the IgG and IgM isotypes) of 10 healthy mothers and their term newborns. We constructed antigen correlation networks (or immune networks) whose nodes are the antigens and the edges are the antigen-antigen reactivity correlations, and we also computed their corresponding minimum spanning trees (MST) – maximal information reduced sub-graphs. We quantify the network organization (topology) in terms of the network theory divergence rate measure and rank the antigen importance in the full antigen correlation networks by the eigen-value centrality measure. This analysis makes possible the characterization and comparison of the IgG and IgM immune networks at birth (newborns) and adulthood (mothers) in terms of topology and node importance. Results: Comparison of the immune network topology at birth and adulthood revealed partial conservation of the IgG immune network topology, and significant reorganization of the IgM immune networks. Inspection of the antigen importance revealed some dominant (in terms of high centrality) antigens in the IgG and IgM networks at birth, which retain their importance at adulthood