The fast sampling algorithm for Lie-Trotter products

A fast algorithm for path sampling in path integral Monte Carlo simulations is proposed. The algorithm utilizes the Levy-Ciesielski implementation of Lie-Trotter products to achieve a mathematically proven computational cost of n*log_2(n) with the number of time slices n, despite the fact that each path variable is updated separately, for reasons of optimality. In this respect, we demonstrate that updating a group of random variables simultaneously results in loss of efficiency.Comment: 4 pages, 1 figure; fast rejection from Phys. Rev. Letts; transfered to PRE as a Rapid Communication. Eq. 6 to 10 contained some inconsistencies that have been repaired in the present version; A sample code implementing the algorithm for LJ clusters is available from the author upon reques

On the efficient Monte Carlo implementation of path integrals

We demonstrate that the Levy-Ciesielski implementation of Lie-Trotter products enjoys several properties that make it extremely suitable for path-integral Monte Carlo simulations: fast computation of paths, fast Monte Carlo sampling, and the ability to use different numbers of time slices for the different degrees of freedom, commensurate with the quantum effects. It is demonstrated that a Monte Carlo simulation for which particles or small groups of variables are updated in a sequential fashion has a statistical efficiency that is always comparable to or better than that of an all-particle or all-variable update sampler. The sequential sampler results in significant computational savings if updating a variable costs only a fraction of the cost for updating all variables simultaneously or if the variables are independent. In the Levy-Ciesielski representation, the path variables are grouped in a small number of layers, with the variables from the same layer being statistically independent. The superior performance of the fast sampling algorithm is shown to be a consequence of these observations. Both mathematical arguments and numerical simulations are employed in order to quantify the computational advantages of the sequential sampler, the Levy-Ciesielski implementation of path integrals, and the fast sampling algorithm.Comment: 14 pages, 3 figures; submitted to Phys. Rev.

Upon the existence of short-time approximations of any polynomial order for the computation of density matrices by path integral methods

In this article, I provide significant mathematical evidence in support of the existence of short-time approximations of any polynomial order for the computation of density matrices of physical systems described by arbitrarily smooth and bounded from below potentials. While for Theorem 2, which is ``experimental'', I only provide a ``physicist's'' proof, I believe the present development is mathematically sound. As a verification, I explicitly construct two short-time approximations to the density matrix having convergence orders 3 and 4, respectively. Furthermore, in the Appendix, I derive the convergence constant for the trapezoidal Trotter path integral technique. The convergence orders and constants are then verified by numerical simulations. While the two short-time approximations constructed are of sure interest to physicists and chemists involved in Monte Carlo path integral simulations, the present article is also aimed at the mathematical community, who might find the results interesting and worth exploring. I conclude the paper by discussing the implications of the present findings with respect to the solvability of the dynamical sign problem appearing in real-time Feynman path integral simulations.Comment: 19 pages, 4 figures; the discrete short-time approximations are now treated as independent from their continuous version; new examples of discrete short-time approximations of order three and four are given; a new appendix containing a short review on Brownian motion has been added; also, some additional explanations are provided here and there; this is the last version; to appear in Phys. Rev.

Probabilistic study of the speed of approach to equilibrium for an inelastic Kac model

This paper deals with a one--dimensional model for granular materials, which boils down to an inelastic version of the Kac kinetic equation, with inelasticity parameter $p>0$. In particular, the paper provides bounds for certain distances -- such as specific weighted $\chi$--distances and the Kolmogorov distance -- between the solution of that equation and the limit. It is assumed that the even part of the initial datum (which determines the asymptotic properties of the solution) belongs to the domain of normal attraction of a symmetric stable distribution with characteristic exponent \a=2/(1+p). With such initial data, it turns out that the limit exists and is just the aforementioned stable distribution. A necessary condition for the relaxation to equilibrium is also proved. Some bounds are obtained without introducing any extra--condition. Sharper bounds, of an exponential type, are exhibited in the presence of additional assumptions concerning either the behaviour, near to the origin, of the initial characteristic function, or the behaviour, at infinity, of the initial probability distribution function

Self-similarity and power-like tails in nonconservative kinetic models

In this paper, we discuss the large--time behavior of solution of a simple kinetic model of Boltzmann--Maxwell type, such that the temperature is time decreasing and/or time increasing. We show that, under the combined effects of the nonlinearity and of the time--monotonicity of the temperature, the kinetic model has non trivial quasi-stationary states with power law tails. In order to do this we consider a suitable asymptotic limit of the model yielding a Fokker-Planck equation for the distribution. The same idea is applied to investigate the large-time behavior of an elementary kinetic model of economy involving both exchanges between agents and increasing and/or decreasing of the mean wealth. In this last case, the large-time behavior of the solution shows a Pareto power law tail. Numerical results confirm the previous analysis

The direction of research into visual disability and quality of life in glaucoma

<p>Abstract</p> <p>Background</p> <p>Glaucoma will undoubtedly impact on a person's ability to function as they go about their day-to-day life. The purpose of this study is to investigate the amount of published knowledge in quality of life (QoL) and visual disability studies for glaucoma, and make comparisons with similar research in other chronic conditions.</p> <p>Methods</p> <p>A systematic literature search of the Global Health, EMBASE Psychiatry and MEDLINE databases. Title searches for glaucoma and six other example chronic diseases were entered alongside a selection of keywords chosen to capture studies focusing on QoL and everyday task ability. These results were further filtered during a manual search of resulting abstracts. Outcomes were the number of publications per year for each disease, number relating to QoL and type of glaucoma QoL research.</p> <p>Results</p> <p>Fifteen years ago there were no published studies relating to the impact of glaucoma on QoL but by 2009 this had risen to 1.2% of all glaucoma articles. The number of papers relating to QoL as a proportion of all papers in glaucoma in the past 10 years (0.6%) is smaller than for AMD and some other disabling chronic diseases. Most QoL studies in glaucoma (82%) involve questionnaires.</p> <p>Conclusion</p> <p>QoL studies in glaucoma are increasing in number but represent a tiny minority of the total publications in glaucoma research. There are fewer QoL articles in glaucoma compared to some other disabling chronic conditions. The majority of QoL articles in glaucoma research use questionnaires; performance-based measures of visual disability may offer an additional method of determining how the disease impacts on QoL.</p

Functional tissue engineering of ligament healing

Ligaments and tendons are dense connective tissues that are important in transmitting forces and facilitate joint articulation in the musculoskeletal system. Their injury frequency is high especially for those that are functional important, like the anterior cruciate ligament (ACL) and medial collateral ligament (MCL) of the knee as well as the glenohumeral ligaments and the rotator cuff tendons of the shoulder. Because the healing responses are different in these ligaments and tendons after injury, the consequences and treatments are tissue- and site-specific. In this review, we will elaborate on the injuries of the knee ligaments as well as using functional tissue engineering (FTE) approaches to improve their healing. Specifically, the ACL of knee has limited capability to heal, and results of non-surgical management of its midsubstance rupture have been poor. Consequently, surgical reconstruction of the ACL is regularly performed to gain knee stability. However, the long-term results are not satisfactory besides the numerous complications accompanied with the surgeries. With the rapid development of FTE, there is a renewed interest in revisiting ACL healing. Approaches such as using growth factors, stem cells and scaffolds have been widely investigated. In this article, the biology of normal and healing ligaments is first reviewed, followed by a discussion on the issues related to the treatment of ACL injuries. Afterwards, current promising FTE methods are presented for the treatment of ligament injuries, including the use of growth factors, gene delivery, and cell therapy with a particular emphasis on the use of ECM bioscaffolds. The challenging areas are listed in the future direction that suggests where collection of energy could be placed in order to restore the injured ligaments and tendons structurally and functionally

Mycolactone Gene Expression Is Controlled by Strong SigA-Like Promoters with Utility in Studies of Mycobacterium ulcerans and Buruli Ulcer

Mycolactone A/B is a lipophilic macrocyclic polyketide that is the primary virulence factor produced by Mycobacterium ulcerans, a human pathogen and the causative agent of Buruli ulcer. In M. ulcerans strain Agy99 the mycolactone polyketide synthase (PKS) locus spans a 120 kb region of a 174 kb megaplasmid. Here we have identified promoter regions of this PKS locus using GFP reporter assays, in silico analysis, primer extension, and site-directed mutagenesis. Transcription of the large PKS genes mlsA1 (51 kb), mlsA2 (7 kb) and mlsB (42 kb) is driven by a novel and powerful SigA-like promoter sequence situated 533 bp upstream of both the mlsA1 and mlsB initiation codons, which is also functional in Escherichia coli, Mycobacterium smegmatis and Mycobacterium marinum. Promoter regions were also identified upstream of the putative mycolactone accessory genes mup045 and mup053. We transformed M. ulcerans with a GFP-reporter plasmid under the control of the mls promoter to produce a highly green-fluorescent bacterium. The strain remained virulent, producing both GFP and mycolactone and causing ulcerative disease in mice. Mosquitoes have been proposed as a potential vector of M. ulcerans so we utilized M. ulcerans-GFP in microcosm feeding experiments with captured mosquito larvae. M. ulcerans-GFP accumulated within the mouth and midgut of the insect over four instars, whereas the closely related, non-mycolactone-producing species M. marinum harbouring the same GFP reporter system did not. This is the first report to identify M. ulcerans toxin gene promoters, and we have used our findings to develop M. ulcerans-GFP, a strain in which fluorescence and toxin gene expression are linked, thus providing a tool for studying Buruli ulcer pathogenesis and potential transmission to humans

Estrogenic botanical supplements, health-related quality of life, fatigue, and hormone-related symptoms in breast cancer survivors: a HEAL study report

<p>Abstract</p> <p>Background</p> <p>It remains unclear whether estrogenic botanical supplement (EBS) use influences breast cancer survivors' health-related outcomes.</p> <p>Methods</p> <p>We examined the associations of EBS use with health-related quality of life (HRQOL), with fatigue, and with 15 hormone-related symptoms such as hot flashes and night sweats among 767 breast cancer survivors participating in the Health, Eating, Activity, and Lifestyle (HEAL) Study. HRQOL was measured by the Medical Outcomes Study short form-36 physical and mental component scale summary score. Fatigue was measured by the Revised-Piper Fatigue Scale score.</p> <p>Results</p> <p>Neither overall EBS use nor the number of EBS types used was associated with HRQOL, fatigue, or hormone-related symptoms. However, comparisons of those using each specific type of EBS with non-EBS users revealed the following associations. Soy supplements users were more likely to have a better physical health summary score (odds ratio [OR] = 1.66, 95% confidence interval [CI] = 1.02-2.70). Flaxseed oil users were more likely to have a better mental health summary score (OR = 1.76, 95% CI = 1.05-2.94). Ginseng users were more likely to report severe fatigue and several hormone-related symptoms (all ORs ≥ 1.7 and all 95% CIs exclude 1). Red clover users were less likely to report weight gain, night sweats, and difficulty concentrating (all OR approximately 0.4 and all 95% CIs exclude 1). Alfalfa users were less likely to experience sleep interruption (OR = 0.28, 95% CI = 0.12-0.68). Dehydroepiandrosterone users were less likely to have hot flashes (OR = 0.33, 95% CI = 0.14-0.82).</p> <p>Conclusions</p> <p>Our findings indicate that several specific types of EBS might have important influences on a woman's various aspects of quality of life, but further verification is necessary.</p