Steiner’s formula in the Heisenberg group

Steiner’s tube formula states that the volume of an ϵ-neighborhood of a smooth regular domain in Rn is a polynomial of degree n in the variable ϵ whose coefficients are curvature integrals (also called quermassintegrals). We prove a similar result in the sub-Riemannian setting of the first Heisenberg group. In contrast to the Euclidean setting, we find that the volume of an ϵ-neighborhood with respect to the Heisenberg metric is an analytic function of ϵ that is generally not a polynomial. The coefficients of the series expansion can be explicitly written in terms of integrals of iteratively defined canonical polynomials of just five curvature terms.

SrGAP2-Dependent Integration of Membrane Geometry and Slit-Robo-Repulsive Cues Regulates Fibroblast Contact Inhibition of Locomotion

Migrating fibroblasts undergo contact inhibition of locomotion (CIL), a process that was discovered five decades ago and still is not fully understood at the molecular level. We identify the Slit2-Robo4-srGAP2 signaling network as a key regulator of CIL in fibroblasts. CIL involves highly dynamic contact protrusions with a specialized actin cytoskeleton that stochastically explore cell-cell overlaps between colliding fibroblasts. A membrane curvature-sensing F-BAR domain pre-localizes srGAP2 to protruding edges and terminates their extension phase in response to cell collision. A FRET-based biosensor reveals that Rac1 activity is focused in a band at the tip of contact protrusions, in contrast to the broad activation gradient in contact-free protrusions. SrGAP2 specifically controls the duration of Rac1 activity in contact protrusions, but not in contact-free protrusions. We propose that srGAP2 integrates cell edge curvature and Slit-Robo-mediated repulsive cues to fine-tune Rac1 activation dynamics in contact protrusions to spatiotemporally coordinate CIL.

Characterization of OSIRIS NAC filters for the interpretation of multispectral data of comet 67P/Churyumov-Gerasimenko

Context. We interpret multicolor data from OSIRIS NAC for the remote-sensing exploration of comet 67P/Churyumov-Gerasimenko. Aims. We determine the most meaningful definition of color maps for the characterization of surface variegation with filters available on OSIRIS NAC. Methods. We analyzed laboratory spectra of selected minerals and olivine-pyroxene mixtures seen through OSIRIS NAC filters, with spectral methods existing in the literature: reflectance ratios, minimum band wavelength, spectral slopes, band tilt, band curvature, and visible tilt. Results. We emphasize the importance of reflectance ratios and particularly the relation of visible tilt vs. band tilt. This technique provides a reliable diagnostic of the presence of silicates. Color maps constructed by red-green-blue colors defined with the green, orange, red, IR, and Fe2O3 filters let us define regions that may significantly differ in composition.

Creating Useful Products From Connecticut's 2000 LIDAR Data Set JHR 08-314 Project 07-2

The State of Connecticut owns a LIght Detection and Ranging (LIDAR) data set that was collected in 2000 as part of the State’s periodic aerial reconnaissance missions. Although collected eight years ago, these data are just now becoming ready to be made available to the public. These data constitute a massive “point cloud”, being a long list of east-north-up triplets in the State Plane Coordinate System Zone 0600 (SPCS83 0600), orthometric heights (NAVD 88) in US Survey feet. Unfortunately, point clouds have no structure or organization, and consequently they are not as useful as Triangulated Irregular Networks (TINs), digital elevation models (DEMs), contour maps, slope and aspect layers, curvature layers, among others. The goal of this project was to provide the computational infrastructure to create a first cut of these products and to serve them to the public via the World Wide Web. The products are available at http://clear.uconn.edu/data/ct_lidar/index.htm.

Cis-acting elements and developmental regulators govern toxin gene expression in Bacillus anthracis

Expression of the structural genes for the anthrax toxin proteins is coordinately controlled by host-related signals such as elevated CO2 , and the trans-acting positive regulator, AtxA. No specific binding of AtxA to the toxin gene promoters has been demonstrated and no sequence-based similarities are apparent in the promoter regions of toxin genes. We hypothesized that the toxin genes possess common structural features that are required for positive regulation. To test this hypothesis, I performed an extensive characterization of the toxin gene promoters. I determined the minimal sequences required for atxA-mediated toxin gene expression and compared these sequences for structural similarities. In silico modeling and in vitro experiments indicated significant curvature within these regions. Random mutagenesis revealed that point mutations associated with reduced transcriptional activity, mostly mapped to areas of high curvature. This work enabled the identification of two potential cis-acting elements implicated in AtxA-mediated regulation of the toxin genes. In addition to the growth condition requirements and AtxA, toxin gene expression is under growth phase regulation. The transition state regulator AbrB represses atxA expression to influence toxin synthesis. Here I report that toxin gene expression also requires sigH, a gene encoding the RNA polymerase sigma factor associated with development in B. subtilis. In the well-studied B. subtilis system, σH is part of a feedback control pathway that involves AbrB and the major response regulator of sporulation initiation, Spo0A. My data indicate that in B. anthracis, regulatory relationships exist between these developmental regulators and atxA . Interestingly, during growth in toxin-inducing conditions, sigH and abrB expression deviates from that described for B. subtilis, affecting expression of the atxA gene. These findings, combined with previous observations, suggest that the steady state level of atxA expression is critical for optimal toxin gene transcription. I propose a model whereby, under toxin-inducing conditions, control of toxin gene expression is fine-tuned by the independent effects of the developmental regulators on the expression of atxA . The growth condition-dependent changes in expression of these regulators may be crucial for the correct timing and uninterrupted expression of the toxin genes during infection. ^

Modeling Techniques for the High-Resolution Interpretation of Cryo-Electron Microscopy Reconstructions

Essential biological processes are governed by organized, dynamic interactions between multiple biomolecular systems. Complexes are thus formed to enable the biological function and get dissembled as the process is completed. Examples of such processes include the translation of the messenger RNA into protein by the ribosome, the folding of proteins by chaperonins or the entry of viruses in host cells. Understanding these fundamental processes by characterizing the molecular mechanisms that enable then, would allow the (better) design of therapies and drugs. Such molecular mechanisms may be revealed trough the structural elucidation of the biomolecular assemblies at the core of these processes. Various experimental techniques may be applied to investigate the molecular architecture of biomolecular assemblies. High-resolution techniques, such as X-ray crystallography, may solve the atomic structure of the system, but are typically constrained to biomolecules of reduced flexibility and dimensions. In particular, X-ray crystallography requires the sample to form a three dimensional (3D) crystal lattice which is technically di‑cult, if not impossible, to obtain, especially for large, dynamic systems. Often these techniques solve the structure of the different constituent components within the assembly, but encounter difficulties when investigating the entire system. On the other hand, imaging techniques, such as cryo-electron microscopy (cryo-EM), are able to depict large systems in near-native environment, without requiring the formation of crystals. The structures solved by cryo-EM cover a wide range of resolutions, from very low level of detail where only the overall shape of the system is visible, to high-resolution that approach, but not yet reach, atomic level of detail. In this dissertation, several modeling methods are introduced to either integrate cryo-EM datasets with structural data from X-ray crystallography, or to directly interpret the cryo-EM reconstruction. Such computational techniques were developed with the goal of creating an atomic model for the cryo-EM data. The low-resolution reconstructions lack the level of detail to permit a direct atomic interpretation, i.e. one cannot reliably locate the atoms or amino-acid residues within the structure obtained by cryo-EM. Thereby one needs to consider additional information, for example, structural data from other sources such as X-ray crystallography, in order to enable such a high-resolution interpretation. Modeling techniques are thus developed to integrate the structural data from the different biophysical sources, examples including the work described in the manuscript I and II of this dissertation. At intermediate and high-resolution, cryo-EM reconstructions depict consistent 3D folds such as tubular features which in general correspond to alpha-helices. Such features can be annotated and later on used to build the atomic model of the system, see manuscript III as alternative. Three manuscripts are presented as part of the PhD dissertation, each introducing a computational technique that facilitates the interpretation of cryo-EM reconstructions. The first manuscript is an application paper that describes a heuristics to generate the atomic model for the protein envelope of the Rift Valley fever virus. The second manuscript introduces the evolutionary tabu search strategies to enable the integration of multiple component atomic structures with the cryo-EM map of their assembly. Finally, the third manuscript develops further the latter technique and apply it to annotate consistent 3D patterns in intermediate-resolution cryo-EM reconstructions. The first manuscript, titled An assembly model for Rift Valley fever virus, was submitted for publication in the Journal of Molecular Biology. The cryo-EM structure of the Rift Valley fever virus was previously solved at 27Å-resolution by Dr. Freiberg and collaborators. Such reconstruction shows the overall shape of the virus envelope, yet the reduced level of detail prevents the direct atomic interpretation. High-resolution structures are not yet available for the entire virus nor for the two different component glycoproteins that form its envelope. However, homology models may be generated for these glycoproteins based on similar structures that are available at atomic resolutions. The manuscript presents the steps required to identify an atomic model of the entire virus envelope, based on the low-resolution cryo-EM map of the envelope and the homology models of the two glycoproteins. Starting with the results of the exhaustive search to place the two glycoproteins, the model is built iterative by running multiple multi-body refinements to hierarchically generate models for the different regions of the envelope. The generated atomic model is supported by prior knowledge regarding virus biology and contains valuable information about the molecular architecture of the system. It provides the basis for further investigations seeking to reveal different processes in which the virus is involved such as assembly or fusion. The second manuscript was recently published in the of Journal of Structural Biology (doi:10.1016/j.jsb.2009.12.028) under the title Evolutionary tabu search strategies for the simultaneous registration of multiple atomic structures in cryo-EM reconstructions. This manuscript introduces the evolutionary tabu search strategies applied to enable a multi-body registration. This technique is a hybrid approach that combines a genetic algorithm with a tabu search strategy to promote the proper exploration of the high-dimensional search space. Similar to the Rift Valley fever virus, it is common that the structure of a large multi-component assembly is available at low-resolution from cryo-EM, while high-resolution structures are solved for the different components but lack for the entire system. Evolutionary tabu search strategies enable the building of an atomic model for the entire system by considering simultaneously the different components. Such registration indirectly introduces spatial constrains as all components need to be placed within the assembly, enabling the proper docked in the low-resolution map of the entire assembly. Along with the method description, the manuscript covers the validation, presenting the benefit of the technique in both synthetic and experimental test cases. Such approach successfully docked multiple components up to resolutions of 40Å. The third manuscript is entitled Evolutionary Bidirectional Expansion for the Annotation of Alpha Helices in Electron Cryo-Microscopy Reconstructions and was submitted for publication in the Journal of Structural Biology. The modeling approach described in this manuscript applies the evolutionary tabu search strategies in combination with the bidirectional expansion to annotate secondary structure elements in intermediate resolution cryo-EM reconstructions. In particular, secondary structure elements such as alpha helices show consistent patterns in cryo-EM data, and are visible as rod-like patterns of high density. The evolutionary tabu search strategy is applied to identify the placement of the different alpha helices, while the bidirectional expansion characterizes their length and curvature. The manuscript presents the validation of the approach at resolutions ranging between 6 and 14Å, a level of detail where alpha helices are visible. Up to resolution of 12 Å, the method measures sensitivities between 70-100% as estimated in experimental test cases, i.e. 70-100% of the alpha-helices were correctly predicted in an automatic manner in the experimental data. The three manuscripts presented in this PhD dissertation cover different computation methods for the integration and interpretation of cryo-EM reconstructions. The methods were developed in the molecular modeling software Sculptor (http://sculptor.biomachina.org) and are available for the scientific community interested in the multi-resolution modeling of cryo-EM data. The work spans a wide range of resolution covering multi-body refinement and registration at low-resolution along with annotation of consistent patterns at high-resolution. Such methods are essential for the modeling of cryo-EM data, and may be applied in other fields where similar spatial problems are encountered, such as medical imaging.

Modelos digitales de elevación generados por captura directa e indirecta de datos fuente : evaluación de su calidad

La información básica sobre el relieve de una cuenca hidrográfica, mediante metodologías analítico-descriptivas, permite a quienes evalúan proyectos relacionados con el uso de los recursos naturales, tales como el manejo integrado de cuencas, estudios sobre impacto ambiental, degradación de suelos, deforestación, conservación de los recursos hídricos, entre otros, contar para su análisis con los parámetros físicos necesarios. Estos procesos mencionados tienen un fuerte componente espacial y el empleo de Sistemas de Información Geográfica (SIG) son de suma utilidad, siendo los Modelos Digitales de Elevación (DEM) y sus derivados un componente relevante de esta base de datos. Los productos derivados de estos modelos, como pendiente, orientación o curvatura, resultarán tan precisos como el DEM usado para derivarlos. Por otra parte, es fundamental maximizar la habilidad del modelo para representar las variaciones del terreno; para ello se debe seleccionar una adecuada resolución (grilla) de acuerdo con los datos disponibles para su generación. En este trabajo se evalúa la calidad altimétrica de seis DEMs generados a partir de dos sistemas diferentes de captura de datos fuente y de distintas resoluciones de grilla. Para determinar la exactitud de los DEMs habitualmente se utiliza un grupo de puntos de control considerados como "verdad de campo" que se comparan con los generados por el modelo en la misma posición geográfica. El área seleccionada para realizar el estudio está ubicada en la localidad de Arrecifes, provincia de Buenos Aires (Argentina) y tiene una superficie de aproximadamente 120 ha. Los resultados obtenidos para los dos algoritmos y para los tres tamaños de grilla analizados presentaron los siguientes resultados: el algoritmo DEM from contourn, un RMSE (Root Mean Squared Error) de ± 0,11 m (para grilla de 1 m), ± 0,11 m (para grilla de 5 m) y de ± 0,15 m (para grilla de 10 m). Para el algoritmo DEM from vector/points, un RMSE de ± 0,09 m (para grilla de 1 m), ± 0,11 m (para grilla de 5 m) y de ± 0,11 m (para grilla de 10 m). Los resultados permiten concluir que el DEM generado a partir de puntos acotados del terreno como datos fuente y con el menor tamaño de grilla es el único que satisface los valores enumerados en la bibliografía, tanto nacional como internacional, lo que lo hace apto para proyectos relacionados con recursos naturales a nivel de ecotopo (predial). El resto de los DEMs generados presentan un RMSE que permite asegurar su aptitud para la evaluación de proyectos relacionados con el uso de los recursos naturales a nivel de unidad de paisaje (conjunto de ecotopos).

Population structure, growth and production of the surf clam Donax hanleyanus (Bivalvia: Donacidae) from northern Argentinean beaches

The surf clams Mesodesma mactroides Reeve, 1854 and Donax hanleyanus Philippi, 1847 are the two dominating species in macrobenthic communities of sandy beaches off northern Argentina, with the latter now surpassing M. mactroides populations in abundance and biomass. Before stock decimation caused by exploitation (during the 1940s and 1950s) and mass mortality events (1995, 1999 and 2007) M. mactroides was the prominent primary consumer in the intertidal ecosystem and an important economic resource in Argentina. Since D. hanleyanus was not commercially fished and not affected by mass mortality events, it took over as the dominant species, but did never reach the former abundance of M. mactroides. Currently abundance and biomass of both surf clams are a multiple smaller than those of forty years ago, indicating the conservation status of D. hanleyanus and M. mactroides as endangered. Therefore the aim of this study is to analyse the population dynamics (population structure, growth and reproductive biology) of D. hanleyanus and M. mactroides, and to compare the results with historical data in order to detect possible differences within surf clam populations forty years ago and at present.

Spicule dimensions of Siphonodictyon spp., raw data, biometry and frequency distributions

Early descriptions for species of Aka were poor in detail, and the only spicule type that occurs in this genus does not vary much between species, which led to taxonomic confusion. Moreover, the type specimens of 5 species of Aka are lost, causing considerable problems. Mediterranean specimens of Aka were identified as Aka labyrinthica (Hancock, 1849) by Topsent (1900), even though this species was originally described from the Indo-Pacific. All following publications on Mediterranean Aka accepted Topsent's decision. We assessed this problem with new samples from the Ionian Sea. Our material consisted of only one specimen of Aka, and we had to rely mainly on spicule characters for comparison to other species. We developed a system for species recognition solely based on spicular characters and biometry, involving a combination of the parameters oxea length, width, tip form and angle of curvature. This approach was surprisingly accurate. Forming ratios of the above parameters was less helpful, but can sometimes provide additional information. We identified our sample as Aka infesta (Johnson, 1899), and describe it as a minute-fistulate species with large, multicamerate erosion traces and stout, smooth oxeas. Our data further imply that A. labyrinthica sensu Hancock has not yet been found in the Mediterranean. A. labyrinthica sensu Topsent is a collection of different species not including A. labyrinthica sensu Hancock.

(Table 3) Leaf area and leaf nitrogen for deciduous, evergreen, forb and graminoid species at Barrow, Svalbard and Zackenberg

Arctic vegetation is characterized by high spatial variability in plant functional type (PFT) composition and gross primary productivity (P). Despite this variability, the two main drivers of P in sub-Arctic tundra are leaf area index (LT) and total foliar nitrogen (NT). LT and NT have been shown to be tightly coupled across PFTs in sub-Arctic tundra vegetation, which simplifies up-scaling by allowing quantification of the main drivers of P from remotely sensed LT. Our objective was to test the LT-NT relationship across multiple Arctic latitudes and to assess LT as a predictor of P for the pan-Arctic. Including PFT-specific parameters in models of LT-NT coupling provided only incremental improvements in model fit, but significant improvements were gained from including site-specific parameters. The degree of curvature in the LT-NT relationship, controlled by a fitted canopy nitrogen extinction co-efficient, was negatively related to average levels of diffuse radiation at a site. This is consistent with theoretical predictions of more uniform vertical canopy N distributions under diffuse light conditions. Higher latitude sites had higher average leaf N content by mass (NM), and we show for the first time that LT-NT coupling is achieved across latitudes via canopy-scale trade-offs between NM and leaf mass per unit leaf area (LM). Site-specific parameters provided small but significant improvements in models of P based on LT and moss cover. Our results suggest that differences in LT-NT coupling between sites could be used to improve pan-Arctic models of P and we provide unique evidence that prevailing radiation conditions can significantly affect N allocation over regional scales.

Set of Matlab function to study geometrical parameters or channels

This set of functions allows one to compute the radius of curvature of a river in planform for the purpose of making correlations with other geometric parameters of a channel. The code may also be used to compute the width of a channel.

Numerical simulation of the upward propagation of a flame in a vertical tube filled with a very lean mixture.

Upwardpropagation of a premixed flame in averticaltubefilled with a very leanmixture is simulated numerically using a single irreversible Arrhenius reaction model with infinitely high activation energy. In the absence of heat losses and preferential diffusion effects, a curved flame with stationary shape and velocity close to those of an open bubble ascending in the same tube is found for values of the fuel mass fraction above a certain minimum that increases with the radius of the tube, while the numerical computations cease to converge to a stationary solution below this minimum mass fraction. The vortical flow of the gas behind the flame and in its transport region is described for tubes of different radii. It is argued that this flow may become unstable when the fuel mass fraction is decreased, and that this instability, together with the flame stretch due to the strong curvature of the flame tip in narrow tubes, may be responsible for the minimum fuel mass fraction. Radiation losses and a Lewis number of the fuel slightly above unity decrease the final combustion temperature at the flame tip and increase the minimum fuel mass fraction, while a Lewis number slightly below unity has the opposite effect.