Low Space External Memory Construction of the Succinct Permuted Longest Common Prefix Array

The longest common prefix (LCP) array is a versatile auxiliary data structure in indexed string matching. It can be used to speed up searching using the suffix array (SA) and provides an implicit representation of the topology of an underlying suffix tree. The LCP array of a string of length $n$ can be represented as an array of length $n$ words, or, in the presence of the SA, as a bit vector of $2n$ bits plus asymptotically negligible support data structures. External memory construction algorithms for the LCP array have been proposed, but those proposed so far have a space requirement of $O(n)$ words (i.e. $O(n \log n)$ bits) in external memory. This space requirement is in some practical cases prohibitively expensive. We present an external memory algorithm for constructing the $2n$ bit version of the LCP array which uses $O(n \log \sigma)$ bits of additional space in external memory when given a (compressed) BWT with alphabet size $\sigma$ and a sampled inverse suffix array at sampling rate $O(\log n)$. This is often a significant space gain in practice where $\sigma$ is usually much smaller than $n$ or even constant. We also consider the case of computing succinct LCP arrays for circular strings

Evaluation of the London Measure of Unplanned Pregnancy in a United States population of women

Copyright @ 2012 Morof et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Objective: To evaluate the reliability and validity of the London Measure of Unplanned Pregnancy (a U.K.-developed measure of pregnancy intention), in English and Spanish translation, in a U.S. population of women. Methods: A psychometric evaluation study of the London Measure of Unplanned Pregnancy (LMUP), a six-item, self-completion paper measure was conducted with 346 women aged 15–45 who presented to San Francisco General Hospital for termination of pregnancy or antenatal care. Analyses of the two language versions were carried out separately. Reliability (internal consistency) was assessed using Cronbach’s alpha and item-total correlations. Test-retest reliability (stability) was assessed using weighted Kappa. Construct validity was assessed using principal components analysis and hypothesis testing. Results: Psychometric testing demonstrated that the LMUP was reliable and valid in both U.S. English (alpha = 0.78, all item-total correlations .0.20, weighted Kappa = 0.72, unidimensionality confirmed, hypotheses met) and Spanish translation (alpha = 0.84, all item-total correlations .0.20, weighted Kappa = 0.77, unidimensionality confirmed, hypotheses met). Conclusion: The LMUP was reliable and valid in U.S. English and Spanish translation and therefore may now be used with U.S. women.The study was funded by an anonymous donation

Airborne observations of methane emissions from rice cultivation in the Sacramento Valley of California

Airborne measurements of methane (CH4) and carbon dioxide (CO2) were taken over the rice growing region of California's Sacramento Valley in the late spring of 2010 and 2011. From these and ancillary measurements, we show that CH4 mixing ratios were higher in the planetary boundary layer above the Sacramento Valley during the rice growing season than they were before it, which we attribute to emissions from rice paddies. We derive daytime emission fluxes of CH4 between 0.6 and 2.0% of the CO2 taken up by photosynthesis on a per carbon, or mole to mole, basis. We also use a mixing model to determine an average CH 4/CO2 flux ratio of -0.6% for one day early in the growing season of 2010. We conclude the CH4/CO2 flux ratio estimates from a single rice field in a previous study are representative of rice fields in the Sacramento Valley. If generally true, the California Air Resources Board (CARB) greenhouse gas inventory emission rate of 2.7×1010g CH4/yr is approximately three times lower than the range of probable CH4 emissions (7.8-9.3×10 10g CH4/yr) from rice cultivation derived in this study. We attribute this difference to decreased burning of the residual rice crop since 1991, which leads to an increase in CH4 emissions from rice paddies in succeeding years, but which is not accounted for in the CARB inventory. © 2012. American Geophysical Union. All Rights Reserved

Recognizing Members of the Tournament Equilibrium Set is NP-hard

A recurring theme in the mathematical social sciences is how to select the "most desirable" elements given a binary dominance relation on a set of alternatives. Schwartz's tournament equilibrium set (TEQ) ranks among the most intriguing, but also among the most enigmatic, tournament solutions that have been proposed so far in this context. Due to its unwieldy recursive definition, little is known about TEQ. In particular, its monotonicity remains an open problem up to date. Yet, if TEQ were to satisfy monotonicity, it would be a very attractive tournament solution concept refining both the Banks set and Dutta's minimal covering set. We show that the problem of deciding whether a given alternative is contained in TEQ is NP-hard.Comment: 9 pages, 3 figure

Global organization of metabolic fluxes in the bacterium, Escherichia coli

Cellular metabolism, the integrated interconversion of thousands of metabolic substrates through enzyme-catalyzed biochemical reactions, is the most investigated complex intercellular web of molecular interactions. While the topological organization of individual reactions into metabolic networks is increasingly well understood, the principles governing their global functional utilization under different growth conditions pose many open questions. We implement a flux balance analysis of the E. coli MG1655 metabolism, finding that the network utilization is highly uneven: while most metabolic reactions have small fluxes, the metabolism's activity is dominated by several reactions with very high fluxes. E. coli responds to changes in growth conditions by reorganizing the rates of selected fluxes predominantly within this high flux backbone. The identified behavior likely represents a universal feature of metabolic activity in all cells, with potential implications to metabolic engineering.Comment: 15 pages 4 figure

Dynamic walking features and improved walking performance in multiple sclerosis patients treated with fampridine (4-aminopyridine)

Background: Impaired walking capacity is a frequent confinement in Multiple Sclerosis (MS). Patients are affected by limitations in coordination, walking speed and the distance they may cover. Also abnormal dynamic walking patterns have been reported, involving continuous deceleration over time. Fampridine (4-aminopyridine), a potassium channel blocker, may improve walking in MS. The objective of the current study was to comprehensively examine dynamic walking characteristics and improved walking capacity in MS patients treated with fampridine. Methods: A sample of N = 35 MS patients (EDSS median: 4) underwent an electronic walking examination prior to (Time 1), and during treatment with fampridine (Time 2). Patients walked back and forth a distance of 25 ft for a maximum period of 6 min (6-minute 25-foot-walk). Besides the total distance covered, average speed on the 25-foot distance and on turns was determined separately for each test minute, at Time 1 and Time 2. Results: Prior to fampridine administration, 27/35 patients (77 %) were able to complete the entire 6 min of walking, while following the administration, 34/35 patients (97 %) managed to walk for 6 min. In this context, walking distance considerably increased and treatment was associated with faster walking and turning across all six test minutes (range of effect sizes: partial eta squared = .34-.72). Importantly, previously reported deceleration across test minutes was consistently observable at Time 1 and Time 2. Discussion: Fampridine administration is associated with improved walking speed and endurance. Regardless of a treatment effect of fampridine, the previously identified, abnormal dynamic walking feature, i.e. the linear decline in walking speed, may represent a robust feature. Conclusions: The dynamic walking feature might hence be considered as a candidate for a new outcome measure in clinical studies involving interventions other than symptomatic treatment, such as immune-modulating medication. Trial registration: DRKS00009228 (German Clinical Trials Register). Date obtained: 25.08.2015

Euler-Heisenberg lagrangians and asymptotic analysis in 1+1 QED, part 1: Two-loop

We continue an effort to obtain information on the QED perturbation series at high loop orders, and particularly on the issue of large cancellations inside gauge invariant classes of graphs, using the example of the l - loop N - photon amplitudes in the limit of large photons numbers and low photon energies. As was previously shown, high-order information on these amplitudes can be obtained from a nonperturbative formula, due to Affleck et al., for the imaginary part of the QED effective lagrangian in a constant field. The procedure uses Borel analysis and leads, under some plausible assumptions, to a number of nontrivial predictions already at the three-loop level. Their direct verification would require a calculation of this `Euler-Heisenberg lagrangian' at three-loops, which seems presently out of reach. Motivated by previous work by Dunne and Krasnansky on Euler-Heisenberg lagrangians in various dimensions, in the present work we initiate a new line of attack on this problem by deriving and proving the analogous predictions in the simpler setting of 1+1 dimensional QED. In the first part of this series, we obtain a generalization of the formula of Affleck et al. to this case, and show that, for both Scalar and Spinor QED, it correctly predicts the leading asymptotic behaviour of the weak field expansion coefficients of the two loop Euler-Heisenberg lagrangians.Comment: 28 pages, 1 figures, final published version (minor modifications, refs. added

On the gauge boson's properties in a candidate technicolor theory

The technicolor scenario replaces the Higgs sector of the standard model with a strongly interacting sector. One candidate for a realization of such a sector is two-technicolor Yang-Mills theory coupled to two degenerate flavors of adjoint, massless techniquarks. Using lattice gauge theory the properties of the technigluons in this scenario are investigated as a function of the techniquark mass towards the massless limit. For that purpose the minimal Landau gauge two-point and three-point correlation functions are determined, including a detailed systematic error analysis. The results are, within the relatively large systematic uncertainties, compatible with a behavior very similar to QCD at finite techniquark mass. However, the limit of massless techniquarks exhibits features which could be compatible with a (quasi-)conformal behavior.Comment: 27 pages, 17 figures, 1 table; v2: persistent notational error corrected, some minor modification

Braided racks, Hurwitz actions and Nichols algebras with many cubic relations

We classify Nichols algebras of irreducible Yetter-Drinfeld modules over groups such that the underlying rack is braided and the homogeneous component of degree three of the Nichols algebra satisfies a given inequality. This assumption turns out to be equivalent to a factorization assumption on the Hilbert series. Besides the known Nichols algebras we obtain a new example. Our method is based on a combinatorial invariant of the Hurwitz orbits with respect to the action of the braid group on three strands.Comment: v2: 35 pages, 6 tables, 14 figure

Truncated Schwinger-Dyson Equations and Gauge Covariance in QED3

We study the Landau-Khalatnikov-Fradkin transformations (LKFT) in momentum space for the dynamically generated mass function in QED3. Starting from the Landau gauge results in the rainbow approximation, we construct solutions in other covariant gauges. We confirm that the chiral condensate is gauge invariant as the structure of the LKFT predicts. We also check that the gauge dependence of the constituent fermion mass is considerably reduced as compared to the one obtained directly by solving SDE.Comment: 17 pages, 11 figures. v3. Improved and Expanded. To appear in Few Body System