Data Structures for Halfplane Proximity Queries and Incremental Voronoi Diagrams

We consider preprocessing a set $S$ of $n$ points in convex position in the plane into a data structure supporting queries of the following form: given a point $q$ and a directed line $\ell$ in the plane, report the point of $S$ that is farthest from (or, alternatively, nearest to) the point $q$ among all points to the left of line $\ell$. We present two data structures for this problem. The first data structure uses $O(n^{1+\varepsilon})$ space and preprocessing time, and answers queries in $O(2^{1/\varepsilon} \log n)$ time, for any $0 < \varepsilon < 1$. The second data structure uses $O(n \log^3 n)$ space and polynomial preprocessing time, and answers queries in $O(\log n)$ time. These are the first solutions to the problem with $O(\log n)$ query time and $o(n^2)$ space. The second data structure uses a new representation of nearest- and farthest-point Voronoi diagrams of points in convex position. This representation supports the insertion of new points in clockwise order using only $O(\log n)$ amortized pointer changes, in addition to $O(\log n)$-time point-location queries, even though every such update may make $\Theta(n)$ combinatorial changes to the Voronoi diagram. This data structure is the first demonstration that deterministically and incrementally constructed Voronoi diagrams can be maintained in $o(n)$ amortized pointer changes per operation while keeping $O(\log n)$-time point-location queries.Comment: 17 pages, 6 figures. Various small improvements. To appear in Algorithmic

Stresses in isostatic granular systems and emergence of force chains

Progress is reported on several questions that bedevil understanding of granular systems: (i) are the stress equations elliptic, parabolic or hyperbolic? (ii) how can the often-observed force chains be predicted from a first-principles continuous theory? (iii) How to relate insight from isostatic systems to general packings? Explicit equations are derived for the stress components in two dimensions including the dependence on the local structure. The equations are shown to be hyperbolic and their general solutions, as well as the Green function, are found. It is shown that the solutions give rise to force chains and the explicit dependence of the force chains trajectories and magnitudes on the local geometry is predicted. Direct experimental tests of the predictions are proposed. Finally, a framework is proposed to relate the analysis to non-isostatic and more realistic granular assemblies.Comment: 4 pages, 2 figures, Corrected typos and clkearer text, submitted to Phys. Rev. Let

Stress in frictionless granular material: Adaptive Network Simulations

We present a minimalistic approach to simulations of force transmission through granular systems. We start from a configuration containing cohesive (tensile) contact forces and use an adaptive procedure to find the stable configuration with no tensile contact forces. The procedure works by sequentially removing and adding individual contacts between adjacent beads, while the bead positions are not modified. In a series of two-dimensional realizations, the resulting force networks are shown to satisfy a linear constraint among the three components of average stress, as anticipated by recent theories. The coefficients in the linear constraint remain nearly constant for a range of shear loadings up to about .6 of the normal loading. The spatial distribution of contact forces shows strong concentration along ``force chains". The probability of contact forces of magnitude f shows an exponential falloff with f. The response to a local perturbing force is concentrated along two characteristic rays directed downward and laterally.Comment: 8 pages, 8 figure

Development of Stresses in Cohesionless Poured Sand

The pressure distribution beneath a conical sandpile, created by pouring sand from a point source onto a rough rigid support, shows a pronounced minimum below the apex (`the dip'). Recent work of the authors has attempted to explain this phenomenon by invoking local rules for stress propagation that depend on the local geometry, and hence on the construction history, of the medium. We discuss the fundamental difference between such approaches, which lead to hyperbolic differential equations, and elastoplastic models, for which the equations are elliptic within any elastic zones present .... This displacement field appears to be either ill-defined, or defined relative to a reference state whose physical existence is in doubt. Insofar as their predictions depend on physical factors unknown and outside experimental control, such elastoplastic models predict that the observations should be intrinsically irreproducible .... Our hyperbolic models are based instead on a physical picture of the material, in which (a) the load is supported by a skeletal network of force chains ("stress paths") whose geometry depends on construction history; (b) this network is `fragile' or marginally stable, in a sense that we define. .... We point out that our hyperbolic models can nonetheless be reconciled with elastoplastic ideas by taking the limit of an extremely anisotropic yield condition.Comment: 25 pages, latex RS.tex with rspublic.sty, 7 figures in Rsfig.ps. Philosophical Transactions A, Royal Society, submitted 02/9

A kilobit hidden SNFS discrete logarithm computation

We perform a special number field sieve discrete logarithm computation in a 1024-bit prime field. To our knowledge, this is the first kilobit-sized discrete logarithm computation ever reported for prime fields. This computation took a little over two months of calendar time on an academic cluster using the open-source CADO-NFS software. Our chosen prime $p$ looks random, and $p--1$ has a 160-bit prime factor, in line with recommended parameters for the Digital Signature Algorithm. However, our p has been trapdoored in such a way that the special number field sieve can be used to compute discrete logarithms in $\mathbb{F}\_p^*$ , yet detecting that p has this trapdoor seems out of reach. Twenty-five years ago, there was considerable controversy around the possibility of back-doored parameters for DSA. Our computations show that trapdoored primes are entirely feasible with current computing technology. We also describe special number field sieve discrete log computations carried out for multiple weak primes found in use in the wild. As can be expected from a trapdoor mechanism which we say is hard to detect, our research did not reveal any trapdoored prime in wide use. The only way for a user to defend against a hypothetical trapdoor of this kind is to require verifiably random primes

Role of prostaglandins and specific place in therapy of bimatoprost in the treatment of elevated intraocular pressure and ocular hypertension: A closer look at the agonist properties of bimatoprost and the prostamides

Bimatoprost is the only representative of a novel class of prostaglandin ethanolamide (prostamide) compounds used therapeutically as an efficacious treatment for glaucoma. The pathways through which bimatoprost works to improve uveoscleral outflow to relieve elevated intraocular pressure are similar to those of the conventional prostaglandins used in glaucoma therapy, with some evidence of a preferential action at the trabecular meshwork. The pharmacology of bimatoprost is however, unclear. Pharmacological evidence supports a specific and distinct receptor-mediated agonist activity of bimatoprost at ‘prostamide’ receptors, which is selective to the prostamides as a class. However, other studies have reported either activity of bimatoprost at additional prostanoid and nonprostanoid receptors, or a conversion of bimatoprost to metabolites with agonist activity at prostaglandin FP receptors in the human eye. The formation of endogenous prostamides has been demonstrated in vivo, by a novel pathway involving the cyclooxygenase-2-mediated conversion of endogenous cannabinoid (endocannabinoid) substrates. Irrespective of the pharmacology of bimatoprost and the prostamides in general, further studies are needed to determine the biological role and biochemical pathology of prostamides in the human eye, particularly in glaucoma. Such studies may improve our understanding of uveoscleral flow and may offer new treatments for controlling intraocular pressure

Physiological responses to folate overproduction in lactobacillys plantarum WCFS1.

<p>Abstract</p> <p>Background</p> <p>Using a functional genomics approach we addressed the impact of folate overproduction on metabolite formation and gene expression in <it>Lactobacillus plantarum </it>WCFS1. We focused specifically on the mechanism that reduces growth rates in folate-overproducing cells.</p> <p>Results</p> <p>Metabolite formation and gene expression were determined in a folate-overproducing- and wild-type strain. Differential metabolomics analysis of intracellular metabolite pools indicated that the pool sizes of 18 metabolites differed significantly between these strains. The gene expression profile was determined for both strains in pH-regulated chemostat culture and batch culture. Apart from the expected overexpression of the 6 genes of the folate gene cluster, no other genes were found to be differentially expressed both in continuous and batch cultures. The discrepancy between the low transcriptome and metabolome response and the 25% growth rate reduction of the folate overproducing strain was further investigated. Folate production per se could be ruled out as a contributing factor, since in the absence of folate production the growth rate of the overproducer was also reduced by 25%. The higher metabolic costs for DNA and RNA biosynthesis in the folate overproducing strain were also ruled out. However, it was demonstrated that folate-specific mRNAs and proteins constitute 8% and 4% of the total mRNA and protein pool, respectively.</p> <p>Conclusion</p> <p>Folate overproduction leads to very little change in metabolite levels or overall transcript profile, while at the same time the growth rate is reduced drastically. This shows that <it>Lactobacillus plantarum </it>WCFS1 is unable to respond to this growth rate reduction, most likely because the growth-related transcripts and proteins are diluted by the enormous amount of gratuitous folate-related transcripts and proteins.</p

Study of shock waves generation, hot electron production and role of parametric instabilities in an intensity regime relevant for the shock ignition

We present experimental results at intensities relevant to Shock Ignition obtained at the sub-ns Prague Asterix Laser System in 2012 . We studied shock waves produced by laser-matter interaction in presence of a pre-plasma. We used a first beam at 1ω (1315 nm) at 7 × 10 13 W/cm 2 to create a pre-plasma on the front side of the target and a second at 3ω (438 nm) at ∼ 10 16 W/cm 2 to create the shock wave. Multilayer targets composed of 25 (or 40 μm) of plastic (doped with Cl), 5 μm of Cu (for Kα diagnostics) and 20 μm of Al for shock measurement were used. We used X-ray spectroscopy of Cl to evaluate the plasma temperature, Kα imaging and spectroscopy to evaluate spatial and spectral properties of the fast electrons and a streak camera for shock breakout measurements. Parametric instabilities (Stimulated Raman Scattering, Stimulated Brillouin Scattering and Two Plasmon Decay) were studied by collecting the back scattered light and analysing its spectrum. Back scattered energy was measured with calorimeters. To evaluate the maximum pressure reached in our experiment we performed hydro simulations with CHIC and DUED codes. The maximum shock pressure generated in our experiment at the front side of the target during laser-interaction is 90 Mbar. The conversion efficiency into hot electrons was estimated to be of the order of ∼ 0.1% and their mean energy in the order ∼50 keV. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distributio

Static avalanches and Giant stress fluctuations in Silos

We propose a simple model for arch formation in silos. We show that small pertubations (such as the thermal expansion of the beads) may lead to giant stress fluctuations on the bottom plate of the silo. The relative amplitude $\Delta$ of these fluctuations are found to be power-law distributed, as $\Delta^{-\tau}$, $\tau \simeq 1.0$. These fluctuations are related to large scale `static avalanches', which correspond to long-range redistributions of stress paths within the silo.Comment: 10 pages, 4 figures.p

Stress Propagation through Frictionless Granular Material

We examine the network of forces to be expected in a static assembly of hard, frictionless spherical beads of random sizes, such as a colloidal glass. Such an assembly is minimally connected: the ratio of constraint equations to contact forces approaches unity for a large assembly. However, the bead positions in a finite subregion of the assembly are underdetermined. Thus to maintain equilibrium, half of the exterior contact forces are determined by the other half. We argue that the transmission of force may be regarded as unidirectional, in contrast to the transmission of force in an elastic material. Specializing to sequentially deposited beads, we show that forces on a given buried bead can be uniquely specified in terms of forces involving more recently added beads. We derive equations for the transmission of stress averaged over scales much larger than a single bead. This derivation requires the Ansatz that statistical fluctuations of the forces are independent of fluctuations of the contact geometry. Under this Ansatz, the $d(d+1)/2$-component stress field can be expressed in terms of a d-component vector field. The procedure may be generalized to non-sequential packings. In two dimensions, the stress propagates according to a wave equation, as postulated in recent work elsewhere. We demonstrate similar wave-like propagation in higher dimensions, assuming that the packing geometry has uniaxial symmetry. In macroscopic granular materials we argue that our approach may be useful even though grains have friction and are not packed sequentially.=17Comment: 15 pages, 4 figures, revised vertion for Phys. Rev.