Some Results On Convex Greedy Embedding Conjecture for 3-Connected Planar Graphs

A greedy embedding of a graph $G = (V,E)$ into a metric space $(X,d)$ is a function $x : V(G) \to X$ such that in the embedding for every pair of non-adjacent vertices $x(s), x(t)$ there exists another vertex $x(u)$ adjacent to $x(s)$ which is closer to $x(t)$ than $x(s)$. This notion of greedy embedding was defined by Papadimitriou and Ratajczak (Theor. Comput. Sci. 2005), where authors conjectured that every 3-connected planar graph has a greedy embedding (possibly planar and convex) in the Euclidean plane. Recently, greedy embedding conjecture has been proved by Leighton and Moitra (FOCS 2008). However, their algorithm do not result in a drawing that is planar and convex for all 3-connected planar graph in the Euclidean plane. In this work we consider the planar convex greedy embedding conjecture and make some progress. We derive a new characterization of planar convex greedy embedding that given a 3-connected planar graph $G = (V,E)$, an embedding x: V \to \bbbr^2 of $G$ is a planar convex greedy embedding if and only if, in the embedding $x$, weight of the maximum weight spanning tree ($T$) and weight of the minimum weight spanning tree (\func{MST}) satisfies \WT(T)/\WT(\func{MST}) \leq (\card{V}-1)^{1 - \delta}, for some $0 < \delta \leq 1$.Comment: 19 pages, A short version of this paper has been accepted for presentation in FCT 2009 - 17th International Symposium on Fundamentals of Computation Theor

Galaxy tools and workflows for sequence analysis with applications in molecular plant pathology

The Galaxy Project offers the popular web browser-based platform Galaxy for running bioinformatics tools and constructing simple workflows. Here, we present a broad collection of additional Galaxy tools for large scale analysis of gene and protein sequences. The motivating research theme is the identification of specific genes of interest in a range of non-model organisms, and our central example is the identification and prediction of "effector" proteins produced by plant pathogens in order to manipulate their host plant. This functional annotation of a pathogen's predicted capacity for virulence is a key step in translating sequence data into potential applications in plant pathology. This collection includes novel tools, and widely-used third-party tools such as NCBI BLASTC wrapped for use within Galaxy. Individual bioinformatics software tools are typically available separately as standalone packages, or in online browserbased form. The Galaxy framework enables the user to combine these and other tools to automate organism scale analyses as workflows, without demanding familiarity with command line tools and scripting.Workflows created using Galaxy can be saved and are reusable, so may be distributed within and between research groups, facilitating the construction of a set of standardised, reusable bioinformatic protocols. The Galaxy tools and workflows described in this manuscript are open source and freely available from the Galaxy Tool Shed (http://usegalaxy.org/toolshed or http://toolshed.g2.bx.psu.edu)

Multi-timescale Solar Cycles and the Possible Implications

Based on analysis of the annual averaged relative sunspot number (ASN) during 1700 -- 2009, 3 kinds of solar cycles are confirmed: the well-known 11-yr cycle (Schwabe cycle), 103-yr secular cycle (numbered as G1, G2, G3, and G4, respectively since 1700); and 51.5-yr Cycle. From similarities, an extrapolation of forthcoming solar cycles is made, and found that the solar cycle 24 will be a relative long and weak Schwabe cycle, which may reach to its apex around 2012-2014 in the vale between G3 and G4. Additionally, most Schwabe cycles are asymmetric with rapidly rising-phases and slowly decay-phases. The comparisons between ASN and the annual flare numbers with different GOES classes (C-class, M-class, X-class, and super-flare, here super-flare is defined as $\geq$ X10.0) and the annal averaged radio flux at frequency of 2.84 GHz indicate that solar flares have a tendency: the more powerful of the flare, the later it takes place after the onset of the Schwabe cycle, and most powerful flares take place in the decay phase of Schwabe cycle. Some discussions on the origin of solar cycles are presented.Comment: 8 pages, 4 figure

Behavioral characterization of a model of differential susceptibility to obesity induced by standard and personalized cafeteria diet feeding

Indexación: Scopus.Despite the increase in obesity prevalence over the last decades, humans show large inter-individual variability for susceptibility to diet-induced obesity. Understanding the biological basis of this susceptibility could identify new therapeutic alternatives against obesity. We characterized behavioral changes associated with propensity to obesity induced by cafeteria (CAF) diet consumption in mice. We show that Balb/c mice fed a CAF diet display a large inter-individual variability in susceptibility to diet-induced obesity, such that based on changes in adiposity we can classify mice as obesity prone (OP) or obesity resistant (OR). Both OP and OR were hyperphagic relative to control-fed mice but caloric intake was similar between OP and OR mice. In contrast, OR had a larger increase in locomotor activity following CAF diet compared to OP mice. Obesity resistant and prone mice showed similar intake of sweet snacks, but OR ate more savory snacks than OP mice. Two bottle sucrose preference tests showed that OP decreased their sucrose preference compared to OR mice after CAF diet feeding. Finally, to test the robustness of the OR phenotype in response to further increases in caloric intake, we fed OR mice with a personalized CAF (CAF-P) diet based on individual snack preferences. When fed a CAF-P diet, OR increased their calorie intake compared to OP mice fed the standard CAF diet, but did not reach adiposity levels observed in OP mice. Together, our data show the contribution of hedonic intake, individual snack preference and physical activity to individual susceptibility to obesity in Balb/c mice fed a standard and personalized cafeteria-style diet. © 2015.https://www.sciencedirect.com/science/article/pii/S0031938415301311?via%3Dihu

Fast Evaluation of Interlace Polynomials on Graphs of Bounded Treewidth

We consider the multivariate interlace polynomial introduced by Courcelle (2008), which generalizes several interlace polynomials defined by Arratia, Bollobas, and Sorkin (2004) and by Aigner and van der Holst (2004). We present an algorithm to evaluate the multivariate interlace polynomial of a graph with n vertices given a tree decomposition of the graph of width k. The best previously known result (Courcelle 2008) employs a general logical framework and leads to an algorithm with running time f(k)*n, where f(k) is doubly exponential in k. Analyzing the GF(2)-rank of adjacency matrices in the context of tree decompositions, we give a faster and more direct algorithm. Our algorithm uses 2^{3k^2+O(k)}*n arithmetic operations and can be efficiently implemented in parallel.Comment: v4: Minor error in Lemma 5.5 fixed, Section 6.6 added, minor improvements. 44 pages, 14 figure

Acoustic Power Absorption and its Relation with Vector Magnetic Field of a Sunspot

The distribution of acoustic power over sunspots shows an enhanced absorption near the umbra--penumbra boundary. Earlier studies revealed that the region of enhanced absorption coincides with the region of strongest transverse potential field. The aim of this paper is to (i) utilize the high-resolution vector magnetograms derived using Hinode SOT/SP observations and study the relationship between the vector magnetic field and power absorption and (ii) study the variation of power absorption in sunspot penumbrae due to the presence of spine-like radial structures. It is found that (i) both potential and observed transverse fields peak at a similar radial distance from the center of the sunspot, and (ii) the magnitude of the transverse field, derived from Hinode observations, is much larger than the potential transverse field derived from SOHO/MDI longitudinal field observations. In the penumbra, the radial structures called spines (intra-spines) have stronger (weaker) field strength and are more vertical (horizontal). The absorption of acoustic power in the spine and intra-spine shows different behaviour with the absorption being larger in the spine as compared to the intra-spine.Comment: 18 pages, 7 figures, In Press Solar Physics, Topical Issue on Helio-and-Astroseismolog

The Magnetic Sun: Reversals and Long-Term Variations

A didactic introduction to current thinking on some aspects of the solar dynamo is given for geophysicists and planetary scientists.Comment: 17 pages, 9 figures; Space Science Rev., in pres

Seismology of the Sun : Inference of Thermal, Dynamic and Magnetic Field Structures of the Interior

Recent overwhelming evidences show that the sun strongly influences the Earth's climate and environment. Moreover existence of life on this Earth mainly depends upon the sun's energy. Hence, understanding of physics of the sun, especially the thermal, dynamic and magnetic field structures of its interior, is very important. Recently, from the ground and space based observations, it is discovered that sun oscillates near 5 min periodicity in millions of modes. This discovery heralded a new era in solar physics and a separate branch called helioseismology or seismology of the sun has started. Before the advent of helioseismology, sun's thermal structure of the interior was understood from the evolutionary solution of stellar structure equations that mimicked the present age, mass and radius of the sun. Whereas solution of MHD equations yielded internal dynamics and magnetic field structure of the sun's interior. In this presentation, I review the thermal, dynamic and magnetic field structures of the sun's interior as inferred by the helioseismology.Comment: To be published in the proceedings of the meeting "3rd International Conference on Current Developments in Atomic, Molecular, Optical and Nano Physics with Applications", December 14-16, 2011, New Delhi, Indi

Regularity issues in the problem of fluid structure interaction

We investigate the evolution of rigid bodies in a viscous incompressible fluid. The flow is governed by the 2D Navier-Stokes equations, set in a bounded domain with Dirichlet boundary conditions. The boundaries of the solids and the domain have H\"older regularity $C^{1, \alpha}$, $0 < \alpha \le 1$. First, we show the existence and uniqueness of strong solutions up to collision. A key ingredient is a BMO bound on the velocity gradient, which substitutes to the standard $H^2$ estimate for smoother domains. Then, we study the asymptotic behaviour of one $C^{1, \alpha}$ body falling over a flat surface. We show that collision is possible in finite time if and only if $\alpha < 1/2$

Multiwavelength studies of MHD waves in the solar chromosphere: An overview of recent results

The chromosphere is a thin layer of the solar atmosphere that bridges the relatively cool photosphere and the intensely heated transition region and corona. Compressible and incompressible waves propagating through the chromosphere can supply significant amounts of energy to the interface region and corona. In recent years an abundance of high-resolution observations from state-of-the-art facilities have provided new and exciting ways of disentangling the characteristics of oscillatory phenomena propagating through the dynamic chromosphere. Coupled with rapid advancements in magnetohydrodynamic wave theory, we are now in an ideal position to thoroughly investigate the role waves play in supplying energy to sustain chromospheric and coronal heating. Here, we review the recent progress made in characterising, categorising and interpreting oscillations manifesting in the solar chromosphere, with an impetus placed on their intrinsic energetics.Comment: 48 pages, 25 figures, accepted into Space Science Review