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

Compendium for precise ac measurements of the quantum Hall resistance

In view of the progress achieved in the field of the ac quantum Hall effect, the Working Group of the Comite Consultatif d'Electricite et Magnetisme (CCEM) on the AC Quantum Hall Effect asked the authors of this paper to write a compendium which integrates their experiences with ac measurements of the quantum Hall resistance. In addition to the important early work performed at the Bureau International des Poids et Mesures and the National Physical Laboratory, UK, further experience has been gained during a collaboration of the authors' institutes NRC, METAS, and PTB, and excellent agreement between the results of different national metrology institutes has been achieved. This compendium summarizes the present state of the authors' knowledge and reviews the experiences, tests and precautions that the authors have employed to achieve accurate measurements of the ac quantum Hall effect. This work shows how the ac quantum Hall effect can be reliably used as a quantum standard of ac resistance having a relative uncertainty of a few parts in 10^8.Comment: 26 pages, 8 figure

Seismotectonics of the Pamir

Based on a 2 year seismic record from a local network, we characterize the deformation of the seismogenic crust of the Pamir in the northwestern part of the India-Asia collision zone. We located more than 6000 upper crustal earthquakes in a regional 3-D velocity model. For 132 of these events, we determined source mechanisms, mostly through full waveform moment tensor inversion of locally and regionally recorded seismograms. We also produced a new and comprehensive neotectonic map of the Pamir, which we relate to the seismic deformation. Along Pamir's northern margin, where GPS measurements show significant shortening, we find thrust and dextral strike-slip faulting along west to northwest trending planes, indicating slip partitioning between northward thrusting and westward extrusion. An active, north-northeast trending, sinistral transtensional fault system dissects the Pamir's interior, connecting the lakes Karakul and Sarez, and extends by distributed faulting into the Hindu Kush of Afghanistan. East of this lineament, the Pamir moves northward en bloc, showing little seismicity and internal deformation. The western Pamir exhibits a higher amount of seismic deformation; sinistral strike-slip faulting on northeast trending or conjugate planes and normal faulting indicate east-west extension and north-south shortening. We explain this deformation pattern by the gravitational collapse of the western Pamir Plateau margin and the lateral extrusion of Pamir rocks into the Tajik-Afghan depression, where it causes thin-skinned shortening of basin sediments above an evaporitic décollement. Superposition of Pamir's bulk northward movement and collapse and westward extrusion of its western flank causes the gradual change of surface velocity orientations from north-northwest to due west observed by GPS geodesy. The distributed shear deformation of the western Pamir and the activation of the Sarez-Karakul fault system may ultimately be caused by the northeastward propagation of India's western transform margin into Asia, thereby linking deformation in the Pamir all the way to the Chaman fault in the south in Afghanistan

The 2008 Nura earthquake sequence at the Pamir-Tian Shan collision zone, southern Kyrgyzstan

We analyzed the 5 October 2008, Mw 6.6 Nura earthquake, which occurred in the border triangle between Kyrgyzstan, Tajikistan, and China, and its aftershock series based on locally recorded seismic data. More than 3000 aftershocks were detected and located, using a double-difference technique and a regional 3-D velocity model. Moment tensors for the main event and the 42 largest aftershocks were determined by full-waveform inversion of long-period displacement seismograms. The Nura main shock was a shallow (∼3.4 km deep) reverse faulting event and occurred on an approximately east striking rupture plane situated east of the Alai Valley, along the Pamir Frontal Thrust of the Trans Alai Range, the leading edge of the Pamir Thrust System. Its presumed rupture plane dips steeply (∼59°) southward. The aftershocks constitute several distinct clusters that can be attributed to the activation of an array of individual faults including the one that was presumably broken by the main shock. Background seismicity occurred mainly further south, behind the crest of the Trans Alai Range, in an approximately east trending zone of dextral transpressional motion in the interior of the Pamir Thrust System. We show that nearly all reactivated structures lie in regions that experienced an increase in Coulomb stress due to the main shock rupture. The Nura earthquake sequence indicates slip partitioning between north-south shortening that creates large earthquakes along the Pamir Frontal Thrust, and lateral movement in the interior of the Pamir Thrust System.This research was funded by DFG bundle TIPAGE (PAK 443), the CAME project bundle TIPTIMON funded by the German Federal Ministry of Education and Research (support code 03G0809), and GFZ. We acknowledge funding for the Earthquake Task Force deployment by GFZ and the Hannover Rück reinsurance company

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.

Forming a Mogi Doughnut in the Years Prior to and Immediately Before the 2014 M8.1 Iquique, Northern Chile, Earthquake

Asperities are patches where the fault surfaces stick until they break in earthquakes. Locating asperities and understanding their causes in subduction zones is challenging because they are generally located offshore. We use seismicity, interseismic and coseismic slip, and the residual gravity field to map the asperity responsible for the 2014M8.1 Iquique, Chile, earthquake. For several years prior to the mainshock, seismicity occurred exclusively downdip of the asperity. Two weeks before the mainshock, a series of foreshocks first broke the upper plate then the updip rim of the asperity. This seismicity formed a ring around the slip patch (asperity) that later ruptured in the mainshock. The asperity correlated both with high interseismic locking and a circular gravity low, suggesting that it is controlled by geologic structure. Most features of the spatiotemporal seismicity pattern can be explained by a mechanical model in which a single asperity is stressed by relative plate motion

The Anti-Sigma Factor MucA of Pseudomonas aeruginosa: Dramatic Differences of a mucA22 vs. a ΔmucA Mutant in Anaerobic Acidified Nitrite Sensitivity of Planktonic and Biofilm Bacteria in vitro and During Chronic Murine Lung Infection

Mucoid mucA22 Pseudomonas aeruginosa (PA) is an opportunistic lung pathogen of cystic fibrosis (CF) and chronic obstructive pulmonary disease (COPD) patients that is highly sensitive to acidified nitrite (A-NO2-). In this study, we first screened PA mutant strains for sensitivity or resistance to 20 mM A-NO2- under anaerobic conditions that represent the chronic stages of the aforementioned diseases. Mutants found to be sensitive to A-NO2- included PA0964 (pmpR, PQS biosynthesis), PA4455 (probable ABC transporter permease), katA (major catalase, KatA) and rhlR (quorum sensing regulator). In contrast, mutants lacking PA0450 (a putative phosphate transporter) and PA1505 (moaA2) were A-NO2- resistant. However, we were puzzled when we discovered that mucA22 mutant bacteria, a frequently isolated mucA allele in CF and to a lesser extent COPD, were more sensitive to A-NO2- than a truncated ΔmucA deletion (Δ157–194) mutant in planktonic and biofilm culture, as well as during a chronic murine lung infection. Subsequent transcriptional profiling of anaerobic, A-NO2--treated bacteria revealed restoration of near wild-type transcript levels of protective NO2- and nitric oxide (NO) reductase (nirS and norCB, respectively) in the ΔmucA mutant in contrast to extremely low levels in the A-NO2--sensitive mucA22 mutant. Proteins that were S-nitrosylated by NO derived from A-NO2- reduction in the sensitive mucA22 strain were those involved in anaerobic respiration (NirQ, NirS), pyruvate fermentation (UspK), global gene regulation (Vfr), the TCA cycle (succinate dehydrogenase, SdhB) and several double mutants were even more sensitive to A-NO2-. Bioinformatic-based data point to future studies designed to elucidate potential cellular binding partners for MucA and MucA22. Given that A-NO2- is a potentially viable treatment strategy to combat PA and other infections, this study offers novel developments as to how clinicians might better treat problematic PA infections in COPD and CF airway diseases

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

Strong duality in conic linear programming: facial reduction and extended duals

The facial reduction algorithm of Borwein and Wolkowicz and the extended dual of Ramana provide a strong dual for the conic linear program $$(P) \sup {<c, x> | Ax \leq_K b}$$ in the absence of any constraint qualification. The facial reduction algorithm solves a sequence of auxiliary optimization problems to obtain such a dual. Ramana's dual is applicable when (P) is a semidefinite program (SDP) and is an explicit SDP itself. Ramana, Tuncel, and Wolkowicz showed that these approaches are closely related; in particular, they proved the correctness of Ramana's dual using certificates from a facial reduction algorithm. Here we give a clear and self-contained exposition of facial reduction, of extended duals, and generalize Ramana's dual: -- we state a simple facial reduction algorithm and prove its correctness; and -- building on this algorithm we construct a family of extended duals when $K$ is a {\em nice} cone. This class of cones includes the semidefinite cone and other important cones.Comment: A previous version of this paper appeared as "A simple derivation of a facial reduction algorithm and extended dual systems", technical report, Columbia University, 2000, available from http://www.unc.edu/~pataki/papers/fr.pdf Jonfest, a conference in honor of Jonathan Borwein's 60th birthday, 201

The crust in the pamir: Insights from receiver functions

The Cenozoic convergence between India and Asia has created Earth's thickest crust in the Pamir‐Tibet Plateau by extreme crustal shortening. Here we study the crustal structure of the Pamir and western Tian Shan, the adjacent margins of the Tajik, Tarim, and Ferghana Basins, and the Hindu Kush, using data collected by temporary seismic experiments. We derive, compare, and combine independent observations from P and S receiver functions. The obtained Moho depth varies from ~40 km below the basins to a double‐normal thickness of 65–75 km underneath the Pamir and Hindu Kush. A Moho doublet—with the deeper interface down to a depth of ~90 km—coincides with the arc of intermediate‐depth seismicity underneath the Pamir, where Asian continental lower crust delaminates and rolls back. The crust beneath most of the Central and South Pamir has a low Vp/Vs ratio (<1.70), suggesting a dominantly felsic composition, probably a result of delamination/foundering of the mafic rocks of the lower crust. Beneath the Cenozoic gneiss domes of the Central and South Pamir, which represent extensional core complexes, the Vp/Vs ratios are moderate to high (~1.75), consistent with the previously observed, midcrustal low‐velocity zones, implying the presence of crustal partial melts. Even higher crustal average Vp/Vs ratios up to 1.90 are found in the sedimentary basins and along the Main Pamir Thrust. The ratios along the latter—the active thrust front of the Pamir—may reflect fluid accumulations within a strongly fractured fault system