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

Should liver enzymes be checked in a patient taking niacin?

No randomized trials directly address the question of frequency of liver enzyme monitoring with niacin use. Niacin use is associated with early and late hepatotoxicity (strength of recommendation [SOR]: B, based on incidence data from randomized controlled trials and systematic reviews of cohort studies). Long-acting forms of niacin (Slo-Niacin) are more frequently associated with hepatotoxicity than the immediate-release (Niacor, Nicolar) or extended-release (Niaspan) forms (SOR: B, based on 1 randomized controlled trial and systematic reviews of cohort studies)

Noise-induced switching between vortex states with different polarization in classical two-dimensional easy-plane magnets

In the 2-dimensional anisotropic Heisenberg model with XY-symmetry there are non-planar vortices which exhibit a localized structure of the z-components of the spins around the vortex center. We study how thermal noise induces a transition of this structure from one polarization to the opposite one. We describe the vortex core by a discrete Hamiltonian and consider a stationary solution of the Fokker-Planck equation. We find a bimodal distribution function and calculate the transition rate using Langer's instanton theory (1969). The result is compared with Langevin dynamics simulations for the full many-spin model.Comment: 15 pages, 4 figures, Phys. Rev. B., in pres

Statistics of lattice animals (polyominoes) and polygons

We have developed an improved algorithm that allows us to enumerate the number of site animals (polyominoes) on the square lattice up to size 46. Analysis of the resulting series yields an improved estimate, $\tau = 4.062570(8)$, for the growth constant of lattice animals and confirms to a very high degree of certainty that the generating function has a logarithmic divergence. We prove the bound $\tau > 3.90318.$ We also calculate the radius of gyration of both lattice animals and polygons enumerated by area. The analysis of the radius of gyration series yields the estimate $\nu = 0.64115(5)$, for both animals and polygons enumerated by area. The mean perimeter of polygons of area $n$ is also calculated. A number of new amplitude estimates are given.Comment: 10 pages, 2 eps figure

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

Monte Carlo study of the critical temperature for the planar rotator model with nonmagnetic impurities

We performed Monte Carlo simulations to calculate the Berezinskii-Kosterlitz-Thouless (BKT) temperature $T_{BKT}$ for the two-dimensional planar rotator model in the presence of nonmagnetic impurity concentration $(\rho)$. As expected, our calculation shows that the BKT temperature decreases as the spin vacancies increase. There is a critical dilution $\rho_c \approx 0.3$ at which $T_{BKT} =0$. The effective interaction between a vortex-antivortex pair and a static nonmagnetic impurity is studied analytically. A simple phenomenological argument based on the pair-impurity interaction is proposed to justify the simulations.Comment: 5 pages, 5 figures, Revetex fil

Criticality of natural absorbing states

We study a recently introduced ladder model which undergoes a transition between an active and an infinitely degenerate absorbing phase. In some cases the critical behaviour of the model is the same as that of the branching annihilating random walk with $N\geq 2$ species both with and without hard-core interaction. We show that certain static characteristics of the so-called natural absorbing states develop power law singularities which signal the approach of the critical point. These results are also explained using random walk arguments. In addition to that we show that when dynamics of our model is considered as a minimum finding procedure, it has the best efficiency very close to the critical point.Comment: 6 page

The Perturbative Pole Mass in QCD

It is widely believed that the pole mass of a quark is infrared-finite and gauge-independent to all orders in perturbation theory. This seems not to have been proved in the literature. A proof is provided here.Comment: 12 pages REVTeX with 2 figures; archiving published version with note and references added. If you thought this was proven long ago see http://www-theory.fnal.gov/people/ask/TeX/mPole

Spin-dynamics simulations of the triangular antiferromagnetic XY model

Using Monte Carlo and spin-dynamics methods, we have investigated the dynamic behavior of the classical, antiferromagnetic XY model on a triangular lattice with linear sizes $L \leq 300$. The temporal evolutions of spin configurations were obtained by solving numerically the coupled equations of motion for each spin using fourth-order Suzuki-Trotter decompositions of exponential operators. From space- and time-displaced spin-spin correlation functions and their space-time Fourier transforms we obtained the dynamic structure factor $S({\bf q},w)$ for momentum ${\bf q}$ and frequency $\omega$. Below $T_{KT}$(Kosterlitz-Thouless transition), both the in-plane ($S^{xx}$) and the out-of-plane ($S^{zz}$) components of $S({\bf q},\omega)$ exhibit very strong and sharp spin-wave peaks. Well above $T_{KT}$, $S^{xx}$ and $S^{zz}$ apparently display a central peak, and spin-wave signatures are still seen in $S^{zz}$. In addition, we also observed an almost dispersionless domain-wall peak at high $\omega$ below $T_{c}$(Ising transition), where long-range order appears in the staggered chirality. Above $T_{c}$, the domain-wall peak disappears for all $q$. The lineshape of these peaks is captured reasonably well by a Lorentzian form. Using a dynamic finite-size scaling theory, we determined the dynamic critical exponent $z$ = 1.002(3). We found that our results demonstrate the consistency of the dynamic finite-size scaling theory for the characteristic frequeny $\omega_{m}$ and the dynamic structure factor $S({\bf q},\omega)$ itself.Comment: 8 pages, RevTex, 10 figures, submitted to PR

On the ground states of the Bernasconi model

The ground states of the Bernasconi model are binary +1/-1 sequences of length N with low autocorrelations. We introduce the notion of perfect sequences, binary sequences with one-valued off-peak correlations of minimum amount. If they exist, they are ground states. Using results from the mathematical theory of cyclic difference sets, we specify all values of N for which perfect sequences do exist and how to construct them. For other values of N, we investigate almost perfect sequences, i.e. sequences with two-valued off-peak correlations of minimum amount. Numerical and analytical results support the conjecture that almost perfect sequences do exist for all values of N, but that they are not always ground states. We present a construction for low-energy configurations that works if N is the product of two odd primes.Comment: 12 pages, LaTeX2e; extended content, added references; submitted to J.Phys.