Fast Witness Extraction Using a Decision Oracle

The gist of many (NP-)hard combinatorial problems is to decide whether a universe of $n$ elements contains a witness consisting of $k$ elements that match some prescribed pattern. For some of these problems there are known advanced algebra-based FPT algorithms which solve the decision problem but do not return the witness. We investigate techniques for turning such a YES/NO-decision oracle into an algorithm for extracting a single witness, with an objective to obtain practical scalability for large values of $n$. By relying on techniques from combinatorial group testing, we demonstrate that a witness may be extracted with $O(k\log n)$ queries to either a deterministic or a randomized set inclusion oracle with one-sided probability of error. Furthermore, we demonstrate through implementation and experiments that the algebra-based FPT algorithms are practical, in particular in the setting of the $k$-path problem. Also discussed are engineering issues such as optimizing finite field arithmetic.Comment: Journal version, 16 pages. Extended abstract presented at ESA'1

Bleeding changes after levonorgestrel 52-mg intrauterine system insertion for contraception in women with self-reported heavy menstrual bleeding.

BackgroundThe levonorgestrel 52-mg intrauterine system has proven efficacy for heavy menstrual bleeding treatment in clinical trials, but few data exist to demonstrate how rapidly the effects occur and the effects in women with self-reported heavy bleeding, as seen commonly in clinical practice.ObjectiveEvaluate changes in bleeding patterns in women with self-reported heavy menstrual bleeding before levonorgestrel 52-mg intrauterine system insertion.Study designA total of 1714 women aged 16-45 years old received a levonorgestrel 52-mg intrauterine system in a multicenter trial evaluating contraceptive efficacy and safety for up to 10 years. At screening, participants described their baseline menstrual bleeding patterns for the previous 3 months. Participants completed daily diaries with subjective evaluation of bleeding information for the first 2 years. For this analysis, we included women with at least 1 complete 28-day cycle of intrauterine system use and excluded women using a hormonal or copper intrauterine contraception in the month prior to study enrollment. We evaluated changes in menstrual bleeding and discontinuation for bleeding complaints per 28-day cycle over 26 cycles (2 years) in women who self-reported their baseline pattern as heavy. We also compared rates of amenorrhea, defined as no bleeding or spotting, within the entire study population in women with subjective heavy menstrual bleeding at baseline compared with those who did not complain of heavy menstrual bleeding.ResultsOf the 1513 women in this analysis, 150 (9.9%) reported baseline heavy menstrual bleeding. The majority of women reported no longer experiencing heavy menstrual bleeding by the end of cycle 1 (112/150, 74.7%) with even greater rates by cycle 2 (124/148, 83.8%). At the end of cycles 6, 13, and 26, 129 of 140 (92.1%; 95% confidence interval, 87.7%-96.6%), 114 of 123 (92.7%; 95% confidence interval, 88.1%-97.3%), and 100 of 103 (97.1%; 95% confidence interval, 93.8%-100%) women reported no heavy menstrual bleeding, respectively. After cycles 13 and 26, 63 of 123 (51.2%; 95% confidence interval, 42.4%-60.1%) and 66 of 103 (64.1%; 95% confidence interval, 54.8%-73.3%), respectively, reported their bleeding as amenorrhea or spotting only. A lower proportion of women with baseline self-reported heavy menstrual bleeding reported amenorrhea as compared with women in the overall study cohort without heavy menstrual bleeding at the end of 6 cycles (319 [25.5%] vs 21 [15.0%], P=.005) and 13 cycles (382 [34.4%] vs 26 [21.1%], P=.003); differences were not significant after 19 cycles (367 [37.2%] vs 36 [31.0%], P=.022) and 26 cycles (383 [43.5%] vs 38 [36.9%], P=.21). Only 4 (2.7%) women with baseline heavy menstrual bleeding discontinued for bleeding complaints (2 for heavy menstrual bleeding and 2 for irregular bleeding), all within the first year.ConclusionMost women who self-report heavy menstrual bleeding experience significant improvement quickly after levonorgestrel 52-mg intrauterine system insertion. Discontinuation for bleeding complaints among women with baseline heavy menstrual bleeding is very low

Stochastic dynamics of remote knock-on permeation in biological ion channels

Brownian dynamics simulations provide evidence for a remote knock-on mechanism facilitating the permeation of a biological ion channel by an ion that is initially trapped at the selectivity filter (SF). Unlike the case of conventional direct knock-on, the second ion that instigates permeation does not need to enter the channel. Nor does it necessarily take the place of the permeating ion at the SF, and it can even be of a different ionic species. The study is based on the simultaneous, self-consistent, solution of the coupled Poisson and Langevin equations for a simple generic model, taking account of all the charges present. The new permeation mechanism involves electrostatic amplification attributable to the permittivity mismatch between water and protein: the arrival of the instigating ion at the channel entrance reduces the exit barrier for the ion trapped at the SF, facilitating escape

Self-organized enhancement of conductivity in biological ion channels

We discuss an example of self-organization in a biological system. It arises from long-range ion–ion interactions, and it leads us to propose a new kind of enhanced conduction in ion channels. The underlying mechanism involves charge fluctuations near the channel mouth, amplified by the mismatch between the relative permittivities of water and the protein of the channel walls. We use Brownian dynamics simulations to show that, as in conventional 'knock on' permeation, these interactions can strongly enhance the channel current; but unlike the conventional mechanism, the enhancement occurs without the instigating bath ion entering the channel. The transition between these two mechanisms is clearly demonstrated, emphasizing their distinction. A simple model accurately reproduces the observed phenomena. We point out that electrolyte plus protein of low relative permittivity are universal in living systems, so that long-range ion–ion correlations of the kind considered must be common

Isoscalar short-range current in the deuteron induced by an intermediate dibaryon

A new model for short-range isoscalar currents in the deuteron and in the NN system is developed; it is based on the generation of an intermediate dibaryon which is the basic ingredient for the medium- and short-range NN interaction which was proposed recently by the present authors.This new current model can very well describe the experimental data for the three basic deuteron observables of isoscalar magnetic type, viz. the magnetic moment, the circular polarization of the photon in the $np\to d\gamma$ process at thermal neutron energies and the structure function B up to Q$^2$=60 fm$^{-2}$.Comment: LaTex, 22 pages with 8 figure

A Conserved Vector Current test using low energy beta-beams

We discuss the possibility of testing the weak currents and, in particular, the weak magnetism term through the measurement of the electron anti-neutrinos capture by protons at a low energy beta-beam facility. We analyze the sensitivity using both the total number of events and the angular distribution of the positrons emitted in a water Cerenkov detector. We show that the weak magnetism form factor might be determined with better than several percent accuracy using the angular distribution. This offers a new way of testing the Conserved Vector Current hypothesis.Comment: 8 pages, 5 figure

Glassy states in lattice models with many coexisting crystalline phases

We study the emergence of glassy states after a sudden cooling in lattice models with short range interactions and without any a priori quenched disorder. The glassy state emerges whenever the equilibrium model possesses a sufficient number of coexisting crystalline phases at low temperatures, provided the thermodynamic limit be taken before the infinite time limit. This result is obtained through simulations of the time relaxation of the standard Potts model and some exclusion models equipped with a local stochastic dynamics on a square lattice.Comment: 12 pages, 4 figure

Can HERA See an eu−−>ece u --> e c Signal of a Virtual Leptoquark?

Virtual leptoquarks could be detected at HERA through some nonstandard effects. Here we explore the possibility that virtual leptoquarks could be discovered via $e u --> e c$ scattering, assuming integrated luminosity of 200 pb$^{-1}$ and charm identification efficiency of 1%. We study the implications of low energy data for the leptoquarks couplings and find that the most relevant bound for the HERA cross sections comes from inclusive $c --> e^+e^-~+~any$. This bound implies that the $e u --> e c$ cross sections for virtual leptoquarks are just too small for observation of the signal. With an improvement by a factor of ~2 on the luminosity or on charm identification it could be possible to see virtual leptoquarks with {\it maximum couplings} up to ~1.5 - 2 TeV. However, the prospects for discovering the virtual particles if their couplings are somewhat below present bounds are very dim. We point out that this cross section could be very large for leptoquarks lighter than HERA's kinematical limit, and if such a leptoquark is discovered we recommend searching for a possible $e u --> e c$ signal. Our results may also serve as an update on the maximum cross sections for leptoquark mediated $e u --> \mu c$ scattering.Comment: 15 Pages (LaTeX), including 4 postscript figures at the end of the file. Feynman diagrams available by reques

Controlled switching of discrete solitons in waveguide arrays

We suggest an effective method for controlling nonlinear switching in arrays of weakly coupled optical waveguides. We demonstrate the digitized switching of a narrow input beam for up to eleven waveguides in the engineered waveguide arrays.Comment: 15 pages, four figures. Accepted in Optics Letter

Covariant Quantization of d=4 Brink-Schwarz Superparticle with Lorentz Harmonics

Covariant first and second quantization of the free d=4 massless superparticle are implemented with the introduction of purely gauge auxiliary spinor Lorentz harmonics. It is shown that the general solution of the condition of maslessness is a sum of two independent chiral superfields with each of them corresponding to finite superspin. A translationally covariant, in general bijective correspondence between harmonic and massless superfields is constructed. By calculation of the commutation function it is shown that in the considered approach only harmonic fields with correct connection between spin and statistics and with integer negative homogeneity index satisfy the microcausality condition. It is emphasized that harmonic fields that arise are reducible at integer points. The index spinor technique is used to describe infinite-component fields of finite spin; the equations of motion of such fields are obtained, and for them Weinberg's theorem on the connection between massless helicity particles and the type of nongauge field that describes them is generalized.Comment: V2: 1 + 26 pages, published versio