Pixel and Voxel Representations of Graphs

We study contact representations for graphs, which we call pixel representations in 2D and voxel representations in 3D. Our representations are based on the unit square grid whose cells we call pixels in 2D and voxels in 3D. Two pixels are adjacent if they share an edge, two voxels if they share a face. We call a connected set of pixels or voxels a blob. Given a graph, we represent its vertices by disjoint blobs such that two blobs contain adjacent pixels or voxels if and only if the corresponding vertices are adjacent. We are interested in the size of a representation, which is the number of pixels or voxels it consists of. We first show that finding minimum-size representations is NP-complete. Then, we bound representation sizes needed for certain graph classes. In 2D, we show that, for $k$-outerplanar graphs with $n$ vertices, $\Theta(kn)$ pixels are always sufficient and sometimes necessary. In particular, outerplanar graphs can be represented with a linear number of pixels, whereas general planar graphs sometimes need a quadratic number. In 3D, $\Theta(n^2)$ voxels are always sufficient and sometimes necessary for any $n$-vertex graph. We improve this bound to $\Theta(n\cdot \tau)$ for graphs of treewidth $\tau$ and to $O((g+1)^2n\log^2n)$ for graphs of genus $g$. In particular, planar graphs admit representations with $O(n\log^2n)$ voxels

Universal Geometric Graphs

We introduce and study the problem of constructing geometric graphs that have few vertices and edges and that are universal for planar graphs or for some sub-class of planar graphs; a geometric graph is \emph{universal} for a class $\mathcal H$ of planar graphs if it contains an embedding, i.e., a crossing-free drawing, of every graph in $\mathcal H$. Our main result is that there exists a geometric graph with $n$ vertices and $O(n \log n)$ edges that is universal for $n$-vertex forests; this extends to the geometric setting a well-known graph-theoretic result by Chung and Graham, which states that there exists an $n$-vertex graph with $O(n \log n)$ edges that contains every $n$-vertex forest as a subgraph. Our $O(n \log n)$ bound on the number of edges cannot be improved, even if more than $n$ vertices are allowed. We also prove that, for every positive integer $h$, every $n$-vertex convex geometric graph that is universal for $n$-vertex outerplanar graphs has a near-quadratic number of edges, namely $\Omega_h(n^{2-1/h})$; this almost matches the trivial $O(n^2)$ upper bound given by the $n$-vertex complete convex geometric graph. Finally, we prove that there exists an $n$-vertex convex geometric graph with $n$ vertices and $O(n \log n)$ edges that is universal for $n$-vertex caterpillars.Comment: 20 pages, 8 figures; a 12-page extended abstracts of this paper will appear in the Proceedings of the 46th Workshop on Graph-Theoretic Concepts in Computer Science (WG 2020

Modeling and Performance Analysis of Priority Queuing Systems

The paper presents the results of modeling and analysis of data performance on systems that support QoS (Quality of Service). In order to evaluate the performance of the modeled systems used were TPN (Timed Petri Nets). Studied were mechanisms of traffic shaping systems based on PQS (Priority Queuing System). Tested was the impact of the mechanism of generating traffic using TPN. Moreover, discussed were the basic mechanisms and queuing systems occurring in QoS structures. It is shown that models can be effectively used in the modeling and analysis of the performance of computer systems

Ratio of the Isolated Photon Cross Sections at \sqrt{s} = 630 and 1800 GeV

The inclusive cross section for production of isolated photons has been measured in \pbarp collisions at $\sqrt{s} = 630$ GeV with the \D0 detector at the Fermilab Tevatron Collider. The photons span a transverse energy ($E_T$) range from 7-49 GeV and have pseudorapidity $|\eta| < 2.5$. This measurement is combined with to previous \D0 result at $\sqrt{s} = 1800$ GeV to form a ratio of the cross sections. Comparison of next-to-leading order QCD with the measured cross section at 630 GeV and ratio of cross sections show satisfactory agreement in most of the $E_T$ range.Comment: 7 pages. Published in Phys. Rev. Lett. 87, 251805, (2001

Tight Regulation of the intS Gene of the KplE1 Prophage: A New Paradigm for Integrase Gene Regulation

Temperate phages have the ability to maintain their genome in their host, a process called lysogeny. For most, passive replication of the phage genome relies on integration into the host's chromosome and becoming a prophage. Prophages remain silent in the absence of stress and replicate passively within their host genome. However, when stressful conditions occur, a prophage excises itself and resumes the viral cycle. Integration and excision of phage genomes are mediated by regulated site-specific recombination catalyzed by tyrosine and serine recombinases. In the KplE1 prophage, site-specific recombination is mediated by the IntS integrase and the TorI recombination directionality factor (RDF). We previously described a sub-family of temperate phages that is characterized by an unusual organization of the recombination module. Consequently, the attL recombination region overlaps with the integrase promoter, and the integrase and RDF genes do not share a common activated promoter upon lytic induction as in the lambda prophage. In this study, we show that the intS gene is tightly regulated by its own product as well as by the TorI RDF protein. In silico analysis revealed that overlap of the attL region with the integrase promoter is widely encountered in prophages present in prokaryotic genomes, suggesting a general occurrence of negatively autoregulated integrase genes. The prediction that these integrase genes are negatively autoregulated was biologically assessed by studying the regulation of several integrase genes from two different Escherichia coli strains. Our results suggest that the majority of tRNA-associated integrase genes in prokaryotic genomes could be autoregulated and that this might be correlated with the recombination efficiency as in KplE1. The consequences of this unprecedented regulation for excisive recombination are discussed

Bose-Einstein Condensation in Magnetic Insulators

The elementary excitations in antiferromagnets are magnons, quasiparticles with integer spin and Bose statistics. In an experiment their density is controlled efficiently by an applied magnetic field and can be made finite to cause the formation of a Bose-Einstein condensate (BEC). Studies of magnon condensation in a growing number of magnetic materials provide a unique window into an exciting world of quantum phase transitions (QPT) and exotic quantum states.Comment: 17 pages, 3 figure

The global distribution of fatal pesticide self-poisoning: Systematic review

<p>Abstract</p> <p>Background</p> <p>Evidence is accumulating that pesticide self-poisoning is one of the most commonly used methods of suicide worldwide, but the magnitude of the problem and the global distribution of these deaths is unknown.</p> <p>Methods</p> <p>We have systematically reviewed the worldwide literature to estimate the number of pesticide suicides in each of the World Health Organisation's six regions and the global burden of fatal self-poisoning with pesticides. We used the following data sources: Medline, EMBASE and psycINFO (1990–2007), papers cited in publications retrieved, the worldwide web (using Google) and our personal collections of papers and books. Our aim was to identify papers enabling us to estimate the proportion of a country's suicides due to pesticide self-poisoning.</p> <p>Results</p> <p>We conservatively estimate that there are 258,234 (plausible range 233,997 to 325,907) deaths from pesticide self-poisoning worldwide each year, accounting for 30% (range 27% to 37%) of suicides globally. Official data from India probably underestimate the incidence of suicides; applying evidence-based corrections to India's official data, our estimate for world suicides using pesticides increases to 371,594 (range 347,357 to 439,267). The proportion of all suicides using pesticides varies from 4% in the European Region to over 50% in the Western Pacific Region but this proportion is not concordant with the volume of pesticides sold in each region; it is the pattern of pesticide use and the toxicity of the products, not the quantity used, that influences the likelihood they will be used in acts of fatal self-harm.</p> <p>Conclusion</p> <p>Pesticide self-poisoning accounts for about one-third of the world's suicides. Epidemiological and toxicological data suggest that many of these deaths might be prevented if (a) the use of pesticides most toxic to humans was restricted, (b) pesticides could be safely stored in rural communities, and (c) the accessibility and quality of care for poisoning could be improved.</p