The Vlasov limit and its fluctuations for a system of particles which interact by means of a wave field

In two recent publications [Commun. PDE, vol.22, p.307--335 (1997), Commun. Math. Phys., vol.203, p.1--19 (1999)], A. Komech, M. Kunze and H. Spohn studied the joint dynamics of a classical point particle and a wave type generalization of the Newtonian gravity potential, coupled in a regularized way. In the present paper the many-body dynamics of this model is studied. The Vlasov continuum limit is obtained in form equivalent to a weak law of large numbers. We also establish a central limit theorem for the fluctuations around this limit.Comment: 68 pages. Smaller corrections: two inequalities in sections 3 and two inequalities in section 4, and definition of a Banach space in appendix A1. Presentation of LLN and CLT in section 4.3 improved. Notation improve

Regulatory control and the costs and benefits of biochemical noise

Experiments in recent years have vividly demonstrated that gene expression can be highly stochastic. How protein concentration fluctuations affect the growth rate of a population of cells, is, however, a wide open question. We present a mathematical model that makes it possible to quantify the effect of protein concentration fluctuations on the growth rate of a population of genetically identical cells. The model predicts that the population's growth rate depends on how the growth rate of a single cell varies with protein concentration, the variance of the protein concentration fluctuations, and the correlation time of these fluctuations. The model also predicts that when the average concentration of a protein is close to the value that maximizes the growth rate, fluctuations in its concentration always reduce the growth rate. However, when the average protein concentration deviates sufficiently from the optimal level, fluctuations can enhance the growth rate of the population, even when the growth rate of a cell depends linearly on the protein concentration. The model also shows that the ensemble or population average of a quantity, such as the average protein expression level or its variance, is in general not equal to its time average as obtained from tracing a single cell and its descendants. We apply our model to perform a cost-benefit analysis of gene regulatory control. Our analysis predicts that the optimal expression level of a gene regulatory protein is determined by the trade-off between the cost of synthesizing the regulatory protein and the benefit of minimizing the fluctuations in the expression of its target gene. We discuss possible experiments that could test our predictions.Comment: Revised manuscript;35 pages, 4 figures, REVTeX4; to appear in PLoS Computational Biolog

Theorems on existence and global dynamics for the Einstein equations

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living Rev. Rel. 5 (2002)

Numerical Approaches to Spacetime Singularities

This Living Review updates a previous version which its itself an update of a review article. Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic cases. Examples of numerical investigations into the formation of naked singularities, critical behavior in collapse, passage through the Cauchy horizon, chaos of the Mixmaster singularity, and singularities in spatially inhomogeneous cosmologies are discussed.Comment: 51 pages, 6 figures may be found in online version: Living Rev. Relativity 2002-1 at www.livingreviews.or

The Global Burden of Latent Tuberculosis Infection: A Re-estimation Using Mathematical Modelling.

BACKGROUND: The existing estimate of the global burden of latent TB infection (LTBI) as "one-third" of the world population is nearly 20 y old. Given the importance of controlling LTBI as part of the End TB Strategy for eliminating TB by 2050, changes in demography and scientific understanding, and progress in TB control, it is important to re-assess the global burden of LTBI. METHODS AND FINDINGS: We constructed trends in annual risk in infection (ARI) for countries between 1934 and 2014 using a combination of direct estimates of ARI from LTBI surveys (131 surveys from 1950 to 2011) and indirect estimates of ARI calculated from World Health Organisation (WHO) estimates of smear positive TB prevalence from 1990 to 2014. Gaussian process regression was used to generate ARIs for country-years without data and to represent uncertainty. Estimated ARI time-series were applied to the demography in each country to calculate the number and proportions of individuals infected, recently infected (infected within 2 y), and recently infected with isoniazid (INH)-resistant strains. Resulting estimates were aggregated by WHO region. We estimated the contribution of existing infections to TB incidence in 2035 and 2050. In 2014, the global burden of LTBI was 23.0% (95% uncertainty interval [UI]: 20.4%-26.4%), amounting to approximately 1.7 billion people. WHO South-East Asia, Western-Pacific, and Africa regions had the highest prevalence and accounted for around 80% of those with LTBI. Prevalence of recent infection was 0.8% (95% UI: 0.7%-0.9%) of the global population, amounting to 55.5 (95% UI: 48.2-63.8) million individuals currently at high risk of TB disease, of which 10.9% (95% UI:10.2%-11.8%) was isoniazid-resistant. Current LTBI alone, assuming no additional infections from 2015 onwards, would be expected to generate TB incidences in the region of 16.5 per 100,000 per year in 2035 and 8.3 per 100,000 per year in 2050. Limitations included the quantity and methodological heterogeneity of direct ARI data, and limited evidence to inform on potential clearance of LTBI. CONCLUSIONS: We estimate that approximately 1.7 billion individuals were latently infected with Mycobacterium tuberculosis (M.tb) globally in 2014, just under a quarter of the global population. Investment in new tools to improve diagnosis and treatment of those with LTBI at risk of progressing to disease is urgently needed to address this latent reservoir if the 2050 target of eliminating TB is to be reached

Weak Decays Beyond Leading Logarithms

We review the present status of QCD corrections to weak decays beyond the leading logarithmic approximation including particle-antiparticle mixing and rare and CP violating decays. After presenting the basic formalism for these calculations we discuss in detail the effective hamiltonians for all decays for which the next-to-leading corrections are known. Subsequently, we present the phenomenological implications of these calculations. In particular we update the values of various parameters and we incorporate new information on m_t in view of the recent top quark discovery. One of the central issues in our review are the theoretical uncertainties related to renormalization scale ambiguities which are substantially reduced by including next-to-leading order corrections. The impact of this theoretical improvement on the determination of the Cabibbo-Kobayashi-Maskawa matrix is then illustrated in various cases.Comment: 229 pages, 32 PostScript figures (included); uses RevTeX, epsf.sty, rotate.sty, rmpbib.sty (included), times.sty (included; requires LaTeX 2e); complete PostScript version available at ftp://feynman.t30.physik.tu-muenchen.de/pub/preprints/tum-100-95.ps.gz or ftp://feynman.t30.physik.tu-muenchen.de/pub/preprints/tum-100-95.ps2.gz (scaled down and rotated version to print two pages on one sheet of paper

Combining macula clinical signs and patient characteristics for age-related macular degeneration diagnosis: a machine learning approach

Background: To investigate machine learning methods, ranging from simpler interpretable techniques to complex (non-linear) “black-box” approaches, for automated diagnosis of Age-related Macular Degeneration (AMD). Methods: Data from healthy subjects and patients diagnosed with AMD or other retinal diseases were collected during routine visits via an Electronic Health Record (EHR) system. Patients’ attributes included demographics and, for each eye, presence/absence of major AMD-related clinical signs (soft drusen, retinal pigment epitelium, defects/ pigment mottling, depigmentation area, subretinal haemorrhage, subretinal fluid, macula thickness, macular scar, subretinal fibrosis). Interpretable techniques known as white box methods including logistic regression and decision trees as well as less interpreitable techniques known as black box methods, such as support vector machines (SVM), random forests and AdaBoost, were used to develop models (trained and validated on unseen data) to diagnose AMD. The gold standard was confirmed diagnosis of AMD by physicians. Sensitivity, specificity and area under the receiver operating characteristic (AUC) were used to assess performance. Results: Study population included 487 patients (912 eyes). In terms of AUC, random forests, logistic regression and adaboost showed a mean performance of (0.92), followed by SVM and decision trees (0.90). All machine learning models identified soft drusen and age as the most discriminating variables in clinicians’ decision pathways to diagnose AMD. C Conclusions: Both black-box and white box methods performed well in identifying diagnoses of AMD and their decision pathways. Machine learning models developed through the proposed approach, relying on clinical signs identified by retinal specialists, could be embedded into EHR to provide physicians with real time (interpretable) support

Synthesis and propagation of complement C3 by microglia/monocytes in the aging retina

INTRODUCTION Complement activation is thought to contribute to the pathogenesis of age-related macular degeneration (AMD), which may be mediated in part by para-inflammatory processes. We aimed to investigate the expression and localization of C3, a crucial component of the complement system, in the retina during the course of aging. METHODS SD rats were born and reared in low-light conditions, and euthanized at post-natal (P) days 100, 450, or 750. Expression of C3, IBA1, and Ccl- and Cxcl- chemokines was assessed by qPCR, and in situ hybridization. Thickness of the ONL was assessed in retinal sections as a measure of photoreceptor loss, and counts were made of C3-expressing monocytes. RESULTS C3 expression increased significantly at P750, and correlated with thinning of the ONL, at P750, and up-regulation of GFAP. In situ hybridization showed that C3 was expressed by microglia/monocytes, mainly from within the retinal vasculature, and occasionally the ONL. The number of C3-expressing microglia increased significantly by P750, and coincided spatiotemporally with thinning of the ONL, and up-regulation of Ccl- and Cxcl- chemokines. CONCLUSIONS Our data suggest that recruited microglia/monocytes contribute to activation of complement in the aging retina, through local expression of C3 mRNA. C3 expression coincides with age-related thinning of the ONL at P750, although it is unclear whether the C3-expressing monocytes are a cause or consequence. These findings provide evidence of activation of complement during natural aging, and may have relevance to cellular events underling the pathogenesis of age-related retinal diseases.Funding provided by Australian Research Council Centres of Excellence Program Grant (CE0561903)

Trichomonas vaginalis: Clinical relevance, pathogenicity and diagnosis

Trichomonas vaginalis is the etiological agent of trichomoniasis, the most prevalent non-viral sexually transmitted disease worldwide. Trichomoniasis is a widespread, global health concern and occurring at an increasing rate. Infections of the female genital tract can cause a range of symptoms, including vaginitis and cervicitis, while infections in males are generally asymptomatic. The relatively mild symptoms, and lack of evidence for any serious sequelae, have historically led to this disease being under diagnosed, and under researched. However, growing evidence that T. vaginalis infection is associated with other disease states with high morbidity in both men and women has increased the efforts to diagnose and treat patients harboring this parasite. The pathology of trichomoniasis results from damage to the host epithelia, caused by a variety of processes during infection and recent work has highlighted the complex interactions between the parasite and host, commensal microbiome and accompanying symbionts. The commercial release of a number of nucleic acid amplification tests (NAATs) has added to the available diagnostic options. Immunoassay based Point of Care testing is currently available, and a recent initial evaluation of a NAAT Point of Care system has given promising results, which would enable testing and treatment in a single visit

Genetic variation and exercise-induced muscle damage: implications for athletic performance, injury and ageing.

Prolonged unaccustomed exercise involving muscle lengthening (eccentric) actions can result in ultrastructural muscle disruption, impaired excitation-contraction coupling, inflammation and muscle protein degradation. This process is associated with delayed onset muscle soreness and is referred to as exercise-induced muscle damage. Although a certain amount of muscle damage may be necessary for adaptation to occur, excessive damage or inadequate recovery from exercise-induced muscle damage can increase injury risk, particularly in older individuals, who experience more damage and require longer to recover from muscle damaging exercise than younger adults. Furthermore, it is apparent that inter-individual variation exists in the response to exercise-induced muscle damage, and there is evidence that genetic variability may play a key role. Although this area of research is in its infancy, certain gene variations, or polymorphisms have been associated with exercise-induced muscle damage (i.e. individuals with certain genotypes experience greater muscle damage, and require longer recovery, following strenuous exercise). These polymorphisms include ACTN3 (R577X, rs1815739), TNF (-308 G>A, rs1800629), IL6 (-174 G>C, rs1800795), and IGF2 (ApaI, 17200 G>A, rs680). Knowing how someone is likely to respond to a particular type of exercise could help coaches/practitioners individualise the exercise training of their athletes/patients, thus maximising recovery and adaptation, while reducing overload-associated injury risk. The purpose of this review is to provide a critical analysis of the literature concerning gene polymorphisms associated with exercise-induced muscle damage, both in young and older individuals, and to highlight the potential mechanisms underpinning these associations, thus providing a better understanding of exercise-induced muscle damage