Perturbed and non-perturbed brownian taboo processes

ABSTRACT. – In this paper we study the Brownian taboo process, which is a version of Brownian motion conditioned to stay within a finite interval, and the α-perturbed Brownian taboo process, which is an analogous version of an α-perturbed Brownian motion.We are particularly interested in the asymptotic behaviour of the supremum of the taboo process, and our main results give integral tests for upper and lower functions of the supremum as t →∞. In the Brownian case these include extensions of recent results in Lambert [4], but are proved in a quite different way. 2001 Éditions scientifiques et médicales Elsevier SAS AMS classification: 60K05; 60J15 RÉSUMÉ. – Dans cet article, nous étudions le processus Brownien tabou qui est une version du mouvement Brownien, conditionné à rester dans un intervalle fini, et le processus Brownien tabou α-perturbé qui est une version semblable du mouvement Brownien α-perturbé. Nous sommes particulièrement intéressés par le comportement asymptotique du supremum du processus tabou et nos principaux résultats fournissent des intégrales tests pour des fonctions majorantes et minorantes du supremum lorsque t → ∞. Dans le cas Brownien, ces résultats incluent des extensions de résultats récents de Lambert [4], mais ceux-ci sont prouvés de maníère différente. 2001 Éditions scientifiques et médicales Elsevier SAS 1

Oceanography : oxygen and climate dynamics

Author Posting. © The Author(s), 2014. This is the author's version of the work. It is posted here by permission of Nature Publishing Group for personal use, not for redistribution. The definitive version was published in Nature Climate Change 4 (2014): 862-863, doi:10.1038/nclimate2386.Low oxygen levels in tropical oceans shape marine ecosystems and biogeochemistry with climate change expected to expand these regions. Now, a study indicates that regional dynamics control tropical oxygen trends, bucking projected global reductions in ocean oxygen.2015-03-2

Haplotype analysis of the PPARgamma Pro12Ala and C1431T variants reveals opposing associations with body weight.

BACKGROUND: Variation at the PPARG locus may influence susceptibility to type 2 diabetes and related traits. The Pro12Ala polymorphism may modulate receptor activity and is associated with protection from type 2 diabetes. However, there have been inconsistent reports of its association with obesity. The silent C1431T polymorphism has not been as extensively studied, but the rare T allele has also been inconsistently linked to increases in weight. Both rare alleles are in linkage disequilibrium and the independent associations of these two polymorphisms have not been addressed. RESULTS: We have genotyped a large population with type 2 diabetes (n = 1107), two populations of non-diabetics from Glasgow (n = 186) and Dundee (n = 254) and also a healthy group undergoing physical training (n = 148) and investigated the association of genotype with body mass index. This analysis has demonstrated that the Ala12 and T1431 alleles are present together in approximately 70% of the carriers. By considering the other 30% of individuals with haplotypes that only carry one of these polymorphisms, we have demonstrated that the Ala12 allele is consistently associated with a lower BMI, whilst the T1431 allele is consistently associated with higher BMI. CONCLUSION: This study has therefore revealed an opposing interaction of these polymorphisms, which may help to explain previous inconsistencies in the association of PPARG polymorphisms and body weight

Fine Motor Skills in Children With Prenatal Alcohol Exposure or Fetal Alcohol Spectrum Disorder

Objective: Prenatal alcohol exposure (PAE) can cause fetal alcohol spectrum disorders (FASD)and associated neurodevelopmental impairments. It is uncertain which types of fine motor skills are most likely to be affected after PAE or which assessment tools are most appropriate to use in FASD diagnostic assessments. This systematic review examined which types of fine motor skills are impaired in children with PAE or FASD; which fine motor assessments are appropriate for FASD diagnosis; and whether fine motor impairments are evident at both “low” and “high” PAE levels. Methods: A systematic review of relevant databases was undertaken using key terms. Relevant studies were extracted using a standardized form, and methodological quality was rated using a critical appraisal tool. Results: Twenty-four studies met inclusion criteria. Complex fine motor skills, such as visual-motor integration, were more frequently impaired than basic fine motor skills, such as grip strength. Assessment tools that specifically assessed fine motor skills more consistently identified impairments than those which assessed fine motor skills as part of a generalized neurodevelopmental assessment. Fine motor impairments were associated with “moderate” to “high” PAE levels. Few studies reported fine motor skills of children with “low” PAE levels, so the effect of lower PAE levels on fine motor skills remains uncertain. Conclusions: Comprehensive assessment of a range of fine motor skills in children with PAE is important to ensure an accurate FASD diagnosis and develop appropriate therapeutic interventions for children with PAE-related fine motor impairments

Rates of glycaemic deterioration in a real-world population with type 2 diabetes

Aims/hypothesis: There is considerable variability in how diabetes progresses after diagnosis. Progression modelling has largely focused on 'time to failure' methods, yet determining a 'coefficient of failure' has many advantages. We derived a rate of glycaemic deterioration in type 2 diabetes, using a large real-world cohort, and aimed to investigate the clinical, biochemical, pharmacological and immunological variables associated with fast and slow rates of glycaemic deterioration. Methods: An observational cohort study was performed using the electronic medical records from participants in the Genetics of Diabetes Audit and Research in Tayside Study (GoDARTS). A model was derived based on an individual's observed HbA(1c) measures from the first eligible HbA(1c) after the diagnosis of diabetes through to the study end (defined as insulin initiation, death, leaving the area or end of follow-up). Each HbA(1c) measure was time-dependently adjusted for the effects of non-insulin glucose-lowering drugs, changes in BMI and corticosteroid use. GAD antibody (GADA) positivity was defined as GAD titres above the 97.5th centile of the population distribution. Results: The mean (95% CI) glycaemic deterioration for type 2 diabetes and GADA-positive individuals was 1.4 (1.3, 1.4) and 2.8 (2.4, 3.3) mmol/mol HbA(1c) per year, respectively. A younger age of diagnosis, lower HDL-cholesterol concentration, higher BMI and earlier calendar year of diabetes diagnosis were independently associated with higher rates of glycaemic deterioration in individuals with type 2 diabetes. The rate of deterioration in those diagnosed at over 70 years of age was very low, with 66% having a rate of deterioration of less than 1.1 mmol/mol HbA(1c) per year, and only 1.5% progressing more rapidly than 4.4 mmol/mol HbA(1c) per year. Conclusions/interpretation: We have developed a novel approach for modelling the progression of diabetes in observational data across multiple drug combinations. This approach highlights how glycaemic deterioration in those diagnosed at over 70 years of age is minimal, supporting a stratified approach to diabetes management

Research frontiers in the analysis of coupled biogeochemical cycles

Author Posting. © Ecological Society of America, 2011. This article is posted here by permission of Ecological Society of America for personal use, not for redistribution. The definitive version was published in Frontiers in Ecology and the Environment 9 (2011): 74–80, doi:10.1890/100137.The analysis of coupled biogeochemical cycles (CBCs) addresses the scientific basis for some of today's major environmental problems. Drawing from information presented at a series of sessions on CBCs held at the 2009 Annual Meeting of the Ecological Society of America and from the research community's expertise, we identify several principal research themes that justify action and investment. Critical areas for research include: coupling of major element cycles to less studied yet equally important trace element cycles; analyzing CBCs across ecosystem boundaries; integrating experimental results into regional- and global-scale models; and expanding the analysis of human interactions with CBCs arising from human population growth, urbanization, and geoengineering. To advance the current understanding of CBCs and to address the environmental challenges of the 21st century, scientists must maintain and synthesize data from existing observational and experimental networks, develop new instrumentation networks, and adopt emerging technologies.We thank the National Science Foundation (NSF) and the Ecological Society of America (ESA) for their financial and logistical support of the Coupled Biogeochemical Cycles sessions held at the 2009 ESA Annual Meeting, and the publication of this special feature issue of Frontiers. ACF was supported by the NSF (DEB- 0743564) and the US Department of Energy’s (DOE’s) Office of Biological and Environmental Research (10- DOE-1053). SCD was supported by the Center for Microbial Oceanography, Research and Education (NSF EF-0424599). RBJ was supported by the NSF (DEB #0717191) and by the DOE’s National Institute for Climate Change Research

Feller Processes: The Next Generation in Modeling. Brownian Motion, L\'evy Processes and Beyond

We present a simple construction method for Feller processes and a framework for the generation of sample paths of Feller processes. The construction is based on state space dependent mixing of L\'evy processes. Brownian Motion is one of the most frequently used continuous time Markov processes in applications. In recent years also L\'evy processes, of which Brownian Motion is a special case, have become increasingly popular. L\'evy processes are spatially homogeneous, but empirical data often suggest the use of spatially inhomogeneous processes. Thus it seems necessary to go to the next level of generalization: Feller processes. These include L\'evy processes and in particular Brownian motion as special cases but allow spatial inhomogeneities. Many properties of Feller processes are known, but proving the very existence is, in general, very technical. Moreover, an applicable framework for the generation of sample paths of a Feller process was missing. We explain, with practitioners in mind, how to overcome both of these obstacles. In particular our simulation technique allows to apply Monte Carlo methods to Feller processes.Comment: 22 pages, including 4 figures and 8 pages of source code for the generation of sample paths of Feller processe

Randomly Charged Polymers, Random Walks, and Their Extremal Properties

Motivated by an investigation of ground state properties of randomly charged polymers, we discuss the size distribution of the largest Q-segments (segments with total charge Q) in such N-mers. Upon mapping the charge sequence to one--dimensional random walks (RWs), this corresponds to finding the probability for the largest segment with total displacement Q in an N-step RW to have length L. Using analytical, exact enumeration, and Monte Carlo methods, we reveal the complex structure of the probability distribution in the large N limit. In particular, the size of the longest neutral segment has a distribution with a square-root singularity at l=L/N=1, an essential singularity at l=0, and a discontinuous derivative at l=1/2. The behavior near l=1 is related to a another interesting RW problem which we call the "staircase problem". We also discuss the generalized problem for d-dimensional RWs.Comment: 33 pages, 19 Postscript figures, RevTe

Impact of phytoplankton community size on a linked global ocean optical and ecosystem model

Author Posting. © The Author(s), 2011. This is the author's version of the work. It is posted here by permission of Elsevier for personal use, not for redistribution. The definitive version was published in Journal of Marine Systems 89 (2012): 61-75, doi:10.1016/j.jmarsys.2011.08.002.We isolated the effect phytoplankton cell size has on varying remote sensing reflectance spectra (Rrs(λ)) in the presence of optically active constituents by using optical and radiative transfer models linked in an offline diagnostic calculation to a global biogeochemical/ecosystem/circulation model with explicit phytoplankton size classes. Two case studies were carried out, each with several scenarios to isolate the effects of chlorophyll concentration, phytoplankton cell size, and size-varying phytoplankton absorption on Rrs(λ). The goal of the study was to determine the relative contribution of phytoplankton cell size and chlorophyll to overall Rrs(λ) and to understand where a standard band ratio algorithm (OC4) may under/overestimate chlorophyll due to Rrs(λ) being significantly affected by phytoplankton size. Phytoplankton cell size was found to contribute secondarily to Rrs(λ) variability and to amplify or dampen the seasonal cycle in Rrs(λ), driven by chlorophyll. Size and chlorophyll were found to change in phase at low to mid-latitudes, but were anti-correlated or poorly correlated at high latitudes. Phytoplankton size effects increased model calculated Rrs(443) in the subtropical ocean during local spring through early fall months in both hemispheres and decreased Rrs(443) in the Northern Hemisphere high latitude regions during local summer to fall months. This study attempts to tease apart when/where variability about the OC4 relationship may be associated with cell size variability. The OC4 algorithm may underestimate [Chl] when the fraction of microplankton is elevated, which occurs in the model simulations during local spring/summer months at high latitudes in both hemispheres.Funding for this study came from a NASA Earth and Space Science Fellowship and University of Rhode Island Graduate School Oceanography Alumni Fellowship, both awarded to C. Mouw. The CCSM-3 BEC simulations were generated with support from NASA Ocean Biology and Biogeochemistry Program (NNX07AL80G) and the NSF Center for Microbial Oceanography Research and Education (C-MORE, EF-0424599)

Fractional moment bounds and disorder relevance for pinning models

We study the critical point of directed pinning/wetting models with quenched disorder. The distribution K(.) of the location of the first contact of the (free) polymer with the defect line is assumed to be of the form K(n)=n^{-\alpha-1}L(n), with L(.) slowly varying. The model undergoes a (de)-localization phase transition: the free energy (per unit length) is zero in the delocalized phase and positive in the localized phase. For \alpha<1/2 it is known that disorder is irrelevant: quenched and annealed critical points coincide for small disorder, as well as quenched and annealed critical exponents. The same has been proven also for \alpha=1/2, but under the assumption that L(.) diverges sufficiently fast at infinity, an hypothesis that is not satisfied in the (1+1)-dimensional wetting model considered by Forgacs et al. (1986) and Derrida et al. (1992), where L(.) is asymptotically constant. Here we prove that, if 1/21, then quenched and annealed critical points differ whenever disorder is present, and we give the scaling form of their difference for small disorder. In agreement with the so-called Harris criterion, disorder is therefore relevant in this case. In the marginal case \alpha=1/2, under the assumption that L(.) vanishes sufficiently fast at infinity, we prove that the difference between quenched and annealed critical points, which is known to be smaller than any power of the disorder strength, is positive: disorder is marginally relevant. Again, the case considered by Forgacs et al. (1986) and Derrida et al. (1992) is out of our analysis and remains open.Comment: 20 pages, 1 figure; v2: few typos corrected, references revised. To appear on Commun. Math. Phy