The decimation process in random k-SAT

Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. Non-rigorous statistical mechanics ideas have inspired a message passing algorithm called Belief Propagation Guided Decimation for finding satisfying assignments of F. This algorithm can be viewed as an attempt at implementing a certain thought experiment that we call the Decimation Process. In this paper we identify a variety of phase transitions in the decimation process and link these phase transitions to the performance of the algorithm

Biometry of late Quaternary coccoliths from the Southern Cadiz region

The Cadiz region lies between the Iberian borderland and Morocco, west of the Strait of Gibraltar and the Western Mediterranean. Core GeoB9064-1 (35°24,91’N 6°50,72’W) is located in the southwest at a depth of 702 m, close to the Al Arraich mud volcano field 30 km off the Moroccan margin„ and has a length of 544 cm. Like most coastal regions, the southern Cadiz region is characterised by a coccolith assemblage dominated by the placoliths Emiliania huxleyi and Gephyrocapsa muellerae.Late Quaternary fluctuations are pronounced in this core, as shown by geochemical (TOC and CaC03) and XRF analysis (K, Mg, Fe, etc.), but also in abundances of coccoliths and more particularly Emiliania huxleyi. These can be related to upwelling and/or bottom currents.Colmenero-Hidalgo (2002) has split up Emiliania huxleyi in a larger coldwater and smaller warmwater variety based on a 4 µm cut-off value. Colmenero-Hid algo (2004) identified a deglacial decrease in the larger coldwater variety.In this study, 100 Emiliania huxleyi and 100 Gephyrocapsa muellerae lengths were measured in 30 samples. Comparison of the biometry of Emiliania huxleyi and Gephyrocapsa muellerae shows that these both species have similar fluctuations and both become smaller during the Holocene, revealing the splitting of Emiliania huxleyi in two morphotypes, to be more complex. A new method to tackle this problem is proposed

On the combination of omics data for prediction of binary outcomes

Enrichment of predictive models with new biomolecular markers is an important task in high-dimensional omic applications. Increasingly, clinical studies include several sets of such omics markers available for each patient, measuring different levels of biological variation. As a result, one of the main challenges in predictive research is the integration of different sources of omic biomarkers for the prediction of health traits. We review several approaches for the combination of omic markers in the context of binary outcome prediction, all based on double cross-validation and regularized regression models. We evaluate their performance in terms of calibration and discrimination and we compare their performance with respect to single-omic source predictions. We illustrate the methods through the analysis of two real datasets. On the one hand, we consider the combination of two fractions of proteomic mass spectrometry for the calibration of a diagnostic rule for the detection of early-stage breast cancer. On the other hand, we consider transcriptomics and metabolomics as predictors of obesity using data from the Dietary, Lifestyle, and Genetic determinants of Obesity and Metabolic syndrome (DILGOM) study, a population-based cohort, from Finland

Fine and ultrafine particle number and size measurements from industrial combustion processes : primary emissions field data

This study is to our knowledge the first to present the results of on-line measurements of residual nanoparticle numbers downstream of the flue gas treatment systems of a wide variety of medium- and large-scale industrial installations. Where available, a semi-quantitative elemental composition of the sampled particles is carried out using a Scanning Electron Microscope coupled with an Energy Dispersive Spectrometer (SEM-EDS). The semi-quantitative elemental composition as a function of the particle size is presented. EU's Best Available Technology documents (BAT) show removal efficiencies of Electrostatic Precipitator (ESP) and bag filter dedusting systems exceeding 99% when expressed in terms of weight. Their efficiency decreases slightly for particles smaller than 1 mu m but when expressed in terms of weight, still exceeds 99% for bag filters and 96% for ESP. This study reveals that in terms of particle numbers, residual nanoparticles (NP) leaving the dedusting systems dominate by several orders of magnitude. In terms of weight, all installations respect their emission limit values and the contribution of NP to weight concentrations is negligible, despite their dominance in terms of numbers. Current World Health Organisation regulations are expressed in terms of PM2.5 wt concentrations and therefore do not reflect the presence or absence of a high number of NP. This study suggests that research is needed on possible additional guidelines related to NP given their possible toxicity and high potential to easily enter the blood stream when inhaled by humans

Random Costs in Combinatorial Optimization

The random cost problem is the problem of finding the minimum in an exponentially long list of random numbers. By definition, this problem cannot be solved faster than by exhaustive search. It is shown that a classical NP-hard optimization problem, number partitioning, is essentially equivalent to the random cost problem. This explains the bad performance of heuristic approaches to the number partitioning problem and allows us to calculate the probability distributions of the optimum and sub-optimum costs.Comment: 4 pages, Revtex, 2 figures (eps), submitted to PR

Counting Lattice Animals in High Dimensions

We present an implementation of Redelemeier's algorithm for the enumeration of lattice animals in high dimensional lattices. The implementation is lean and fast enough to allow us to extend the existing tables of animal counts, perimeter polynomials and series expansion coefficients in $d$-dimensional hypercubic lattices for $3 \leq d\leq 10$. From the data we compute formulas for perimeter polynomials for lattice animals of size $n\leq 11$ in arbitrary dimension $d$. When amended by combinatorial arguments, the new data suffices to yield explicit formulas for the number of lattice animals of size $n\leq 14$ and arbitrary $d$. We also use the enumeration data to compute numerical estimates for growth rates and exponents in high dimensions that agree very well with Monte Carlo simulations and recent predictions from field theory.Comment: 18 pages, 7 figures, 6 tables; journal versio

Vortices in the presence of a nonmagnetic atom impurity in 2D XY ferromagnets

Using a model of nonmagnetic impurity potential, we have examined the behavior of planar vortex solutions in the classical two-dimensional XY ferromagnets in the presence of a spin vacancy localized out of the vortex core. Our results show that a spinless atom impurity gives rise to an effective potential that repels the vortex structure.Comment: 6 pages, 2 figures, RevTex

Number partitioning as random energy model

Number partitioning is a classical problem from combinatorial optimisation. In physical terms it corresponds to a long range anti-ferromagnetic Ising spin glass. It has been rigorously proven that the low lying energies of number partitioning behave like uncorrelated random variables. We claim that neighbouring energy levels are uncorrelated almost everywhere on the energy axis, and that energetically adjacent configurations are uncorrelated, too. Apparently there is no relation between geometry (configuration) and energy that could be exploited by an optimization algorithm. This ``local random energy'' picture of number partitioning is corroborated by numerical simulations and heuristic arguments.Comment: 8+2 pages, 9 figures, PDF onl

Switching between different vortex states in 2-dimensional easy-plane magnets due to an ac magnetic field

Using a discrete model of 2-dimensional easy-plane classical ferromagnets, we propose that a rotating magnetic field in the easy plane can switch a vortex from one polarization to the opposite one if the amplitude exceeds a threshold value, but the backward process does not occur. Such switches are indeed observed in computer simulations.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let