The complexity of weighted boolean #CSP*

This paper gives a dichotomy theorem for the complexity of computing the partition function of an instance of a weighted Boolean constraint satisfaction problem. The problem is parameterized by a finite set F of nonnegative functions that may be used to assign weights to the configurations (feasible solutions) of a problem instance. Classical constraint satisfaction problems correspond to the special case of 0,1-valued functions. We show that computing the partition function, i.e., the sum of the weights of all configurations, is FP#P-complete unless either (1) every function in F is of “product type,” or (2) every function in F is “pure affine.” In the remaining cases, computing the partition function is in P

What is the excess risk of infertility in women after genital chlamydia infection? A systematic review of the evidence

Methods: Twelve databases were searched, limited to peer-reviewed literature published from January 1970 to September 2007. Conference abstracts and reference lists from reviews published since 2000 and from key articles were hand-searched. Studies were selected for review if they met the following criteria: (1) the study population comprised women of child-bearing age (defined as 15–45 years) and incorporated a comparison group of women documented as "chlamydia negative"; (2) the study outcomes included either infertility or successful pregnancy; and (3) the study design was one of the following: cohort, randomised controlled trial, "before and after" study, screening trial and systematic review. Studies were excluded if they described genital infections that either did not include Chlamydia trachomatis or described genital chlamydial co-infection, in which no data were available for C trachomatis infection alone. Results: 3349 studies were identified by the search. One study satisfied the inclusion criteria, a longitudinal investigation measuring pregnancy rates in adolescent women with and without current chlamydial infection at baseline. That study reported no significant difference in subsequent pregnancy rates; however, it had serious methodological limitations, which restricted its conclusions. Conclusions: This systematic review demonstrates the absence of valid evidence on the attributable risk of post-infective tubal factor infertility after genital chlamydial infection. The findings contribute empirical data to the growing debate surrounding previous assumptions about the natural history of chlamydial infection in women

Automating Pólya Theory: The Computational Complexity of the Cycle Index Polynomial

AbstractIn this paper we investigate the computational difficulty of evaluating and approximately evaluating Pólya′s cycle index polynomial. We start by investigating the difficulty of determining a particular coefficient of the cycle index polynomial. In particular, we consider the following problem, in which i is taken to be a fixed positive integer: Given a set of generators for a permutation group G whose degree, n, is a multiple of i, determine the coefficient of xn/ii in the cycle index polynomial of G. We show that this problem is #P-hard for every fixed i >1. Next, we consider the evaluation problem. Let y1, y2, ... stand for an arbitrary fixed sequence of non-negative real numbers. The cycle index evaluation problem that is associated with this sequence is the following: Given a set of generators for a degree n permutation group G, evaluate the cycle index polynomial of G at the point (y1, ..., yn). We show that if there exists an i such that yi ≠ yi1 and yi ≠ 0 then the evaluation problem associated with y1, y2, ..., is #P-hard. We observe that the evaluation problem is solvable in polynomial time if yj = yj1 for every positive integer j and that it is solvable in polynomial time if yj = 0 for every integer j >1. Finally, we consider the approximate evaluation problem. We show that it is NP-hard to approximately solve the evaluation problem if there exists an i such that yi > yi1. Furthermore, we show that it is NP-hard to approximately solve the evaluation problem if y1 = y2 = ··· = y for some positive non-integer y. We derive some corollaries of our results which deal with the computational difficulty of counting equivalence classes of combinatorial structures

Contention Resolution with Heterogeneous Job Sizes

Abstract. We study the problem of contention resolution for differentsized jobs on a simple channel. When a job makes a run attempt, it learns only whether the attempt succeeded or failed. We first analyze binary exponential backoff, and show that it achieves a makespan of V2 Θ( logn) with high probability, where V is the total work of all n contending jobs. This bound is significantly larger than when jobs are constant sized. A variant of exponential backoff, however, achieves makespan O(V logV) with high probability. Finally, we introduce a new protocol, size-hashed backoff, specifically designed for jobs of multiple sizes that achieves makespan O(V log 3 logV). The error probability of the first two bounds is polynomially small in n and the latter is polynomially small in logV.

Anisotropy at the end of the cosmic ray spectrum?

The starburst galaxies M82 and NGC253 have been proposed as the primary sources of cosmic rays with energies above $10^{18.7}$ eV. For energies \agt 10^{20.3} eV the model predicts strong anisotropies. We calculate the probabilities that the latter can be due to chance occurrence. For the highest energy cosmic ray events in this energy region, we find that the observed directionality has less than 1% probability of occurring due to random fluctuations. Moreover, during the first 5 years of operation at Auger, the observation of even half the predicted anisotropy has a probability of less than $10^{-5}$ to occur by chance fluctuation. Thus, this model can be subject to test at very small cost to the Auger priors budget and, whatever the outcome of that test, valuable information on the Galactic magnetic field will be obtained.Comment: Final version to be published in Physical Review

Approximating Fixation Probabilities in the Generalized Moran Process

We consider the Moran process, as generalized by Lieberman et al. (Nature 433:312–316, 2005). A population resides on the vertices of a finite, connected, undirected graph and, at each time step, an individual is chosen at random with probability proportional to its assigned “fitness” value. It reproduces, placing a copy of itself on a neighbouring vertex chosen uniformly at random, replacing the individual that was there. The initial population consists of a single mutant of fitness r>0 placed uniformly at random, with every other vertex occupied by an individual of fitness 1. The main quantities of interest are the probabilities that the descendants of the initial mutant come to occupy the whole graph (fixation) and that they die out (extinction); almost surely, these are the only possibilities. In general, exact computation of these quantities by standard Markov chain techniques requires solving a system of linear equations of size exponential in the order of the graph so is not feasible. We show that, with high probability, the number of steps needed to reach fixation or extinction is bounded by a polynomial in the number of vertices in the graph. This bound allows us to construct fully polynomial randomized approximation schemes (FPRAS) for the probability of fixation (when r≥1) and of extinction (for all r>0)

Extragalactic Sources for Ultra High Energy Cosmic Ray Nuclei

In this article we examine the hypothesis that the highest energy cosmic rays are complex nuclei from extragalactic sources. Under reasonable physical assumptions, we show that the nearby metally rich starburst galaxies (M82 and NGC 253) can produce all the events observed above the ankle. This requires diffusion of particles below $10^{20}$ eV in extragalactic magnetic fields $B \approx 15$ nG. Above $10^{19}$ eV, the model predicts the presence of significant fluxes of medium mass and heavy nuclei with small rate of change of composition. Notwithstanding, the most salient feature of the starburst-hypothesis is a slight anisotropy induced by iron debris just before the spectrum-cutoff.Comment: To appear in Phys. Rev. D, reference adde

Black Hole Chromosphere at the LHC

If the scale of quantum gravity is near a TeV, black holes will be copiously produced at the LHC. In this work we study the main properties of the light descendants of these black holes. We show that the emitted partons are closely spaced outside the horizon, and hence they do not fragment into hadrons in vacuum but more likely into a kind of quark-gluon plasma. Consequently, the thermal emission occurs far from the horizon, at a temperature characteristic of the QCD scale. We analyze the energy spectrum of the particles emerging from the "chromosphere", and find that the hard hadronic jets are almost entirely suppressed. They are replaced by an isotropic distribution of soft photons and hadrons, with hundreds of particles in the GeV range. This provides a new distinctive signature for black hole events at LHC.Comment: Incorporates changes made for the version to be published in Phys. Rev. D. Additional details provided on the effect of the chromosphere in cosmic ray shower

Expansions for the Bollobas-Riordan polynomial of separable ribbon graphs

We define 2-decompositions of ribbon graphs, which generalise 2-sums and tensor products of graphs. We give formulae for the Bollobas-Riordan polynomial of such a 2-decomposition, and derive the classical Brylawski formula for the Tutte polynomial of a tensor product as a (very) special case. This study was initially motivated from knot theory, and we include an application of our formulae to mutation in knot diagrams.Comment: Version 2 has minor changes. To appear in Annals of Combinatoric