Violator Spaces: Structure and Algorithms

Sharir and Welzl introduced an abstract framework for optimization problems, called LP-type problems or also generalized linear programming problems, which proved useful in algorithm design. We define a new, and as we believe, simpler and more natural framework: violator spaces, which constitute a proper generalization of LP-type problems. We show that Clarkson's randomized algorithms for low-dimensional linear programming work in the context of violator spaces. For example, in this way we obtain the fastest known algorithm for the P-matrix generalized linear complementarity problem with a constant number of blocks. We also give two new characterizations of LP-type problems: they are equivalent to acyclic violator spaces, as well as to concrete LP-type problems (informally, the constraints in a concrete LP-type problem are subsets of a linearly ordered ground set, and the value of a set of constraints is the minimum of its intersection).Comment: 28 pages, 5 figures, extended abstract was presented at ESA 2006; author spelling fixe

A Measurement of Newton's Gravitational Constant

A precision measurement of the gravitational constant $G$ has been made using a beam balance. Special attention has been given to determining the calibration, the effect of a possible nonlinearity of the balance and the zero-point variation of the balance. The equipment, the measurements and the analysis are described in detail. The value obtained for G is 6.674252(109)(54) 10^{-11} m3 kg-1 s-2. The relative statistical and systematic uncertainties of this result are 16.3 10^{-6} and 8.1 10^{-6}, respectively.Comment: 26 pages, 20 figures, Accepted for publication by Phys. Rev.

Twist and writhe dynamics of stiff filaments

This letter considers the dynamics of a stiff filament, in particular the coupling of twist and bend via writhe. The time dependence of the writhe of a filament is $W_r^2\sim L t^{1/4}$ for a linear filament and $W_r^2\sim t^{1/2} / L$ for a curved filament. Simulations are used to study the relative importance of crankshaft motion and tube like motion in twist dynamics. Fuller's theorem, and its relation with the Berry phase, is reconsidered for open filamentsComment: 7 Pages with 2 figure

The Viscous Nonlinear Dynamics of Twist and Writhe

Exploiting the "natural" frame of space curves, we formulate an intrinsic dynamics of twisted elastic filaments in viscous fluids. A pair of coupled nonlinear equations describing the temporal evolution of the filament's complex curvature and twist density embodies the dynamic interplay of twist and writhe. These are used to illustrate a novel nonlinear phenomenon: ``geometric untwisting" of open filaments, whereby twisting strains relax through a transient writhing instability without performing axial rotation. This may explain certain experimentally observed motions of fibers of the bacterium B. subtilis [N.H. Mendelson, et al., J. Bacteriol. 177, 7060 (1995)].Comment: 9 pages, 4 figure

Volume 17. Article 1. Oceanography of Long Island Sound.

https://elischolar.library.yale.edu/bulletin_yale_bingham_oceanographic_collection/1157/thumbnail.jp

Ringer's lactate improves liver recovery in a murine model of acetaminophen toxicity

<p>Abstract</p> <p>Background</p> <p>Acetaminophen (APAP) overdose induces massive hepatocyte necrosis. Liver regeneration is a vital process for survival after a toxic insult. Since hepatocytes are mostly in a quiescent state (G₀), the regeneration process requires the priming of hepatocytes by cytokines such as TNF-α and IL-6. Ringer's lactate solution (RLS) has been shown to increase serum TNF-α and IL-6 in patients and experimental animals; in addition, RLS also provides lactate, which can be used as an alternative metabolic fuel to meet the higher energy demand by liver regeneration. Therefore, we tested whether RLS therapy improves liver recovery after APAP overdose.</p> <p>Methods</p> <p>C57BL/6 male mice were intraperitoneally injected with a single dose of APAP (300 mg/kg dissolved in 1 mL sterile saline). Following 2 hrs of APAP challenge, the mice were given 1 mL RLS or Saline treatment every 12 hours for a total of 72 hours.</p> <p>Results</p> <p>72 hrs after APAP challenge, compared to saline-treated group, RLS treatment significantly lowered serum transaminases (ALT/AST) and improved liver recovery seen in histopathology. This beneficial effect was associated with increased hepatic tissue TNF-α concentration, enhanced hepatic NF-κB DNA binding and increased expression of cell cycle protein cyclin D1, three important factors in liver regeneration.</p> <p>Conclusion</p> <p>RLS improves liver recovery from APAP hepatotoxicity.</p

Realization of the farad from the dc quantum Hall effect with digitally-assisted impedance bridges

A new traceability chain for the derivation of the farad from dc quantum Hall effect has been implemented at INRIM. Main components of the chain are two new coaxial transformer bridges: a resistance ratio bridge, and a quadrature bridge, both operating at 1541 Hz. The bridges are energized and controlled with a polyphase direct-digital-synthesizer, which permits to achieve both main and auxiliary equilibria in an automated way; the bridges and do not include any variable inductive divider or variable impedance box. The relative uncertainty in the realization of the farad, at the level of 1000 pF, is estimated to be 64E-9. A first verification of the realization is given by a comparison with the maintained national capacitance standard, where an agreement between measurements within their relative combined uncertainty of 420E-9 is obtained.Comment: 15 pages, 11 figures, 3 table

Electron Counting Capacitance Standard with an improved five-junction R-pump

The Electron Counting Capacitance Standard currently pursued at PTB aims to close the Quantum Metrological Triangle with a final precision of a few parts in 10^7. This paper reports the considerable progress recently achieved with a new generation of single-electron tunnelling devices. A five-junction R-pump was operated with a relative charge transfer error of five electrons in 10^7, and was used to successfully perform single-electron charging of a cryogenic capacitor. The preliminary result for the single-electron charge quantum has an uncertainty of less than two parts in 10^6 and is consistent with the value of the elementary charge.Comment: 16 pages, 9 figures, 1 tabl

Influence of solvent granularity on the effective interaction between charged colloidal suspensions

We study the effect of solvent granularity on the effective force between two charged colloidal particles by computer simulations of the primitive model of strongly asymmetric electrolytes with an explicitly added hard sphere solvent. Apart from molecular oscillating forces for nearly touching colloids which arise from solvent and counterion layering, the counterions are attracted towards the colloidal surfaces by solvent depletion providing a simple statistical description of hydration. This, in turn, has an important influence on the effective forces for larger distances which are considerably reduced as compared to the prediction based on the primitive model. When these forces are repulsive, the long-distance behaviour can be described by an effective Yukawa pair potential with a solvent-renormalized charge. As a function of colloidal volume fraction and added salt concentration, this solvent-renormalized charge behaves qualitatively similar to that obtained via the Poisson-Boltzmann cell model but there are quantitative differences. For divalent counterions and nano-sized colloids, on the other hand, the hydration may lead to overscreened colloids with mutual attraction while the primitive model yields repulsive forces. All these new effects can be accounted for through a solvent-averaged primitive model (SPM) which is obtained from the full model by integrating out the solvent degrees of freedom. The SPM was used to access larger colloidal particles without simulating the solvent explicitly.Comment: 14 pages, 16 craphic

The Phylogeny of the Four Pan-American MtDNA Haplogroups: Implications for Evolutionary and Disease Studies

Only a limited number of complete mitochondrial genome sequences belonging to Native American haplogroups were available until recently, which left America as the continent with the least amount of information about sequence variation of entire mitochondrial DNAs. In this study, a comprehensive overview of all available complete mitochondrial DNA (mtDNA) genomes of the four pan-American haplogroups A2, B2, C1, and D1 is provided by revising the information scattered throughout GenBank and the literature, and adding 14 novel mtDNA sequences. The phylogenies of haplogroups A2, B2, C1, and D1 reveal a large number of sub-haplogroups but suggest that the ancestral Beringian population(s) contributed only six (successful) founder haplotypes to these haplogroups. The derived clades are overall starlike with coalescence times ranging from 18,000 to 21,000 years (with one exception) using the conventional calibration. The average of about 19,000 years somewhat contrasts with the corresponding lower age of about 13,500 years that was recently proposed by employing a different calibration and estimation approach. Our estimate indicates a human entry and spread of the pan-American haplogroups into the Americas right after the peak of the Last Glacial Maximum and comfortably agrees with the undisputed ages of the earliest Paleoindians in South America. In addition, the phylogenetic approach also indicates that the pathogenic status proposed for various mtDNA mutations, which actually define branches of Native American haplogroups, was based on insufficient grounds