Layering in the Ising model

We consider the three-dimensional Ising model in a half-space with a boundary field (no bulk field). We compute the low-temperature expansion of layering transition lines

Anomalous synchronization threshold in coupled logistic maps

We consider regular lattices of coupled chaotic maps. Depending on lattice size, there may exist a window in parameter space where complete synchronization is eventually attained after a transient regime. Close outside this window, an intermittent transition to synchronization occurs. While asymptotic transversal Lyapunov exponents allow to determine the synchronization threshold, the distribution of finite-time Lyapunov exponents, in the vicinity of the critical frontier, is expected to provide relevant information on phenomena such as intermittency. In this work we scrutinize the distribution of finite-time exponents when the local dynamics is ruled by the logistic map $x \mapsto 4x(1-x)$. We obtain a theoretical estimate for the distribution of finite-time exponents, that is markedly non-Gaussian. The existence of correlations, that spoil the central limit approximation, is shown to modify the typical intermittent bursting behavior. The present scenario could apply to a wider class of systems with different local dynamics and coupling schemes.Comment: 6 pages, 6 figure

On scattering of solitons for the Klein-Gordon equation coupled to a particle

We establish the long time soliton asymptotics for the translation invariant nonlinear system consisting of the Klein-Gordon equation coupled to a charged relativistic particle. The coupled system has a six dimensional invariant manifold of the soliton solutions. We show that in the large time approximation any finite energy solution, with the initial state close to the solitary manifold, is a sum of a soliton and a dispersive wave which is a solution of the free Klein-Gordon equation. It is assumed that the charge density satisfies the Wiener condition which is a version of the ``Fermi Golden Rule''. The proof is based on an extension of the general strategy introduced by Soffer and Weinstein, Buslaev and Perelman, and others: symplectic projection in Hilbert space onto the solitary manifold, modulation equations for the parameters of the projection, and decay of the transversal component.Comment: 47 pages, 2 figure

Enhanced drug delivery capabilities from stents coated with absorbable polymer and crystalline drug

Current drug eluting stent (DES) technology is not optimized with regard to the pharmacokinetics of drug delivery. A novel, absorbable-coating sirolimus-eluting stent (AC-SES) was evaluated for its capacity to deliver drug more evenly within the intimal area rather than concentrating drug around the stent struts and for its ability to match coating erosion with drug release. The coating consisted of absorbable poly-lactide-co-glycolic acid (PLGA) and crystalline sirolimus deposited by a dry-powder electrostatic process. The AC-SES demonstrated enhanced drug stability under simulated use conditions and consistent drug delivery balanced with coating erosion in a porcine coronary implant model. The initial drug burst was eliminated and drug release was sustained after implantation. The coating was absorbed within 90 days. Following implantation into porcine coronary arteries the AC-SES coating is distributed in the surrounding intimal tissue over the course of several weeks. Computational modeling of drug delivery characteristics demonstrates how distributed coating optimizes the load of drug immediately around each stent strut and extends drug delivery between stent struts. The result was a highly efficient arterial uptake of drug with superior performance to a clinical bare metal stent (BMS). Neointimal thickness (0.17 ± 0.07 mm vs. 0.28 ± 0.11 mm) and area percent stenosis (22 ± 9% vs. 35 ± 12%) were significantly reduced (p < 0.05) by the AC-SES compared to the BMS 30 days after stent implantation in an overlap configuration in porcine coronary arteries. Inflammation was significantly reduced in the AC-SES compared to the BMS at both 30 and 90 days after implantation. Biocompatible, rapidly absorbable stent coatings enable the matching of drug release with coating erosion and provide for the controlled migration of coating material into tissue to reduce vicissitudes in drug tissue levels, optimizing efficacy and reducing potential toxicity.Micell Technologies, Inc.National Institutes of Health (U.S.) (R01 GM49039

Validity of numerical trajectories in the synchronization transition of complex systems

We investigate the relationship between the loss of synchronization and the onset of shadowing breakdown {\it via} unstable dimension variability in complex systems. In the neighborhood of the critical transition to strongly non-hyperbolic behavior, the system undergoes on-off intermittency with respect to the synchronization state. There are potentially severe consequences of these facts on the validity of the computer-generated trajectories obtained from dynamical systems whose synchronization manifolds share the same non-hyperbolic properties.Comment: 4 pages, 4 figure

The Race Between Stars and Quasars in Reionizing Cosmic Hydrogen

The cosmological background of ionizing radiation has been dominated by quasars once the Universe aged by ~2 billion years. At earlier times (redshifts z>3), the observed abundance of bright quasars declined sharply, implying that cosmic hydrogen was reionized by stars instead. Here, we explain the physical origin of the transition between the dominance of stars and quasars as a generic feature of structure formation in the concordance LCDM cosmology. At early times, the fraction of baryons in galaxies grows faster than the maximum (Eddington-limited) growth rate possible for quasars. As a result, quasars were not able to catch up with the rapid early growth of stellar mass in their host galaxies.Comment: 5 pages, 1 figure, Accepted for publication in JCA

Professionalism, Golf Coaching and a Master of Science Degree: A commentary

As a point of reference I congratulate Simon Jenkins on tackling the issue of professionalism in coaching. As he points out coaching is not a profession, but this does not mean that coaching would not benefit from going through a professionalization process. As things stand I find that the stimulus article unpacks some critically important issues of professionalism, broadly within the context of golf coaching. However, I am not sure enough is made of understanding what professional (golf) coaching actually is nor how the development of a professional golf coach can be facilitated by a Master of Science Degree (M.Sc.). I will focus my commentary on these two issues

Optimal designs for rational function regression

We consider optimal non-sequential designs for a large class of (linear and nonlinear) regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. The proposed method treats D-, E-, A-, and $\Phi_p$-optimal designs in a unified manner, and generates a polynomial whose zeros are the support points of the optimal approximate design, generalizing a number of previously known results of the same flavor. The method is based on a mathematical optimization model that can incorporate various criteria of optimality and can be solved efficiently by well established numerical optimization methods. In contrast to previous optimization-based methods proposed for similar design problems, it also has theoretical guarantee of its algorithmic efficiency; in fact, the running times of all numerical examples considered in the paper are negligible. The stability of the method is demonstrated in an example involving high degree polynomials. After discussing linear models, applications for finding locally optimal designs for nonlinear regression models involving rational functions are presented, then extensions to robust regression designs, and trigonometric regression are shown. As a corollary, an upper bound on the size of the support set of the minimally-supported optimal designs is also found. The method is of considerable practical importance, with the potential for instance to impact design software development. Further study of the optimality conditions of the main optimization model might also yield new theoretical insights.Comment: 25 pages. Previous version updated with more details in the theory and additional example

Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions

Excess contributions to the free energy due to interfaces occur for many problems encountered in the statistical physics of condensed matter when coexistence between different phases is possible (e.g. wetting phenomena, nucleation, crystal growth, etc.). This article reviews two methods to estimate both interfacial free energies and line tensions by Monte Carlo simulations of simple models, (e.g. the Ising model, a symmetrical binary Lennard-Jones fluid exhibiting a miscibility gap, and a simple Lennard-Jones fluid). One method is based on thermodynamic integration. This method is useful to study flat and inclined interfaces for Ising lattices, allowing also the estimation of line tensions of three-phase contact lines, when the interfaces meet walls (where "surface fields" may act). A generalization to off-lattice systems is described as well. The second method is based on the sampling of the order parameter distribution of the system throughout the two-phase coexistence region of the model. Both the interface free energies of flat interfaces and of (spherical or cylindrical) droplets (or bubbles) can be estimated, including also systems with walls, where sphere-cap shaped wall-attached droplets occur. The curvature-dependence of the interfacial free energy is discussed, and estimates for the line tensions are compared to results from the thermodynamic integration method. Basic limitations of all these methods are critically discussed, and an outlook on other approaches is given

Prognostic Value of a Polygenic Risk Score for Coronary Heart Disease in Individuals Aged 70 Years and Older

Background: The use of a polygenic risk score (PRS) to improve risk prediction of coronary heart disease (CHD) events has been demonstrated to have clinical utility in the general adult population. However, the prognostic value of a PRS for CHD has not been examined specifically in older populations of individuals aged ≥70 years, who comprise a distinct high-risk subgroup. The objective of this study was to evaluate the predictive value of a PRS for incident CHD events in a prospective cohort of older individuals without a history of cardiovascular events. Methods: We used data from 12 792 genotyped, healthy older individuals enrolled into the ASPREE trial (Aspirin in Reducing Events in the Elderly), a randomized double-blind placebo-controlled clinical trial investigating the effect of daily 100 mg aspirin on disability-free survival. Participants had no previous history of diagnosed atherothrombotic cardiovascular events, dementia, or persistent physical disability at enrollment. We calculated a PRS (meta-genomic risk score) consisting of 1.7 million genetic variants. The primary outcome was a composite of incident myocardial infarction or CHD death over 5 years. Results: At baseline, the median population age was 73.9 years, and 54.9% were female. In total, 254 incident CHD events occurred. When the PRS was added to conventional risk factors, it was independently associated with CHD (hazard ratio, 1.24 [95% CI, 1.08-1.42], P=0.002). The area under the curve of the conventional model was 70.53 (95% CI, 67.00-74.06), and after inclusion of the PRS increased to 71.78 (95% CI, 68.32-75.24, P=0.019), demonstrating improved prediction. Reclassification was also improved, as the continuous net reclassification index after adding PRS to the conventional model was 0.25 (95% CI, 0.15-0.28). Conclusion: A PRS for CHD performs well in older people and improves prediction over conventional cardiovascular risk factors. Our study provides evidence that genomic risk prediction for CHD has clinical utility in individuals aged 70 years and older. Registration: URL: https://www.clinicaltrials.gov; Unique identifier: NCT01038583