Random walks and Lévy processes as rough paths

We consider random walks and L\'evy processes in a homogeneous group $G$. For all $p > 0$, we completely characterise (almost) all $G$-valued L\'evy processes whose sample paths have finite $p$-variation, and give sufficient conditions under which a sequence of $G$-valued random walks converges in law to a L\'evy process in $p$-variation topology. In the case that $G$ is the free nilpotent Lie group over $\mathbb{R}^d$, so that processes of finite $p$-variation are identified with rough paths, we demonstrate applications of our results to weak convergence of stochastic flows and provide a L\'evy-Khintchine formula for the characteristic function of the signature of a L\'evy process. At the heart of our analysis is a criterion for tightness of $p$-variation for a collection of c\`adl\`ag strong Markov processes.Comment: 36 pages. Revised from previous version. To appear in Probability Theory and Related Field

Realizability of the Lorentzian (n,1)-Simplex

In a previous article [JHEP 1111 (2011) 072; arXiv:1108.4965] we have developed a Lorentzian version of the Quantum Regge Calculus in which the significant differences between simplices in Lorentzian signature and Euclidean signature are crucial. In this article we extend a central result used in the previous article, regarding the realizability of Lorentzian triangles, to arbitrary dimension. This technical step will be crucial for developing the Lorentzian model in the case of most physical interest: 3+1 dimensions. We first state (and derive in an appendix) the realizability conditions on the edge-lengths of a Lorentzian n-simplex in total dimension n=d+1, where d is the number of space-like dimensions. We then show that in any dimension there is a certain type of simplex which has all of its time-like edge lengths completely unconstrained by any sort of triangle inequality. This result is the d+1 dimensional analogue of the 1+1 dimensional case of the Lorentzian triangle.Comment: V1: 15 pages, 2 figures. V2: Minor clarifications added to Introduction and Discussion sections. 1 reference updated. This version accepted for publication in JHEP. V3: minor updates and clarifications, this version closely corresponds to the version published in JHE

Construction of Lp\mathcal L^p-strong Feller Processes via Dirichlet Forms and Applications to Elliptic Diffusions

We provide a general construction scheme for $\mathcal L^p$-strong Feller processes on locally compact separable metric spaces. Starting from a regular Dirichlet form and specified regularity assumptions, we construct an associated semigroup and resolvents of kernels having the $\mathcal L^p$-strong Feller property. They allow us to construct a process which solves the corresponding martingale problem for all starting points from a known set, namely the set where the regularity assumptions hold. We apply this result to construct elliptic diffusions having locally Lipschitz matrix coefficients and singular drifts on general open sets with absorption at the boundary. In this application elliptic regularity results imply the desired regularity assumptions

Representation of Markov chains by random maps: existence and regularity conditions

We systematically investigate the problem of representing Markov chains by families of random maps, and which regularity of these maps can be achieved depending on the properties of the probability measures. Our key idea is to use techniques from optimal transport to select optimal such maps. Optimal transport theory also tells us how convexity properties of the supports of the measures translate into regularity properties of the maps via Legendre transforms. Thus, from this scheme, we cannot only deduce the representation by measurable random maps, but we can also obtain conditions for the representation by continuous random maps. Finally, we present conditions for the representation of Markov chain by random diffeomorphisms.Comment: 22 pages, several changes from the previous version including extended discussion of many detail

Interventions to Promote Cancer Awareness and Early Presentation: Systematic Review

Low cancer awareness contributes to delay in presentation for cancer symptoms and may lead to delay in cancer diagnosis. The aim of this study was to review the evidence for the effectiveness of interventions to raise cancer awareness and promote early presentation in cancer to inform policy and future research. We searched bibliographic databases and reference lists for randomised controlled trials of interventions delivered to individuals, and controlled or uncontrolled studies of interventions delivered to communities. We found some evidence that interventions delivered to individuals modestly increase cancer awareness in the short term and insufficient evidence that they promote early presentation. We found limited evidence that public education campaigns reduce stage at presentation of breast cancer, malignant melanoma and retinoblastoma

Partitioning of on-demand electron pairs

We demonstrate the high fidelity splitting of electron pairs emitted on demand from a dynamic quantum dot by an electronic beam splitter. The fidelity of pair splitting is inferred from the coincidence of arrival in two detector paths probed by a measurement of the partitioning noise. The emission characteristic of the on-demand electron source is tunable from electrons being partitioned equally and independently to electron pairs being split with a fidelity of 90%. For low beam splitter transmittance we further find evidence of pair bunching violating statistical expectations for independent fermions

Temporal and Spatial Patterns of Ambient Endotoxin Concentrations in Fresno, California

BackgroundEndotoxins are found in indoor dust generated by human activity and pets, in soil, and adsorbed onto the surfaces of ambient combustion particles. Endotoxin concentrations have been associated with respiratory symptoms and the risk of atopy and asthma in children.ObjectiveWe characterized the temporal and spatial variability of ambient endotoxin in Fresno/Clovis, California, located in California's Central Valley, to identify correlates and potential predictors of ambient endotoxin concentrations in a cohort of children with asthma [Fresno Asthmatic Children's Environment Study (FACES)].MethodsBetween May 2001 and October 2004, daily ambient endotoxin and air pollutants were collected at the central ambient monitoring site of the California Air Resources Board in Fresno and, for shorter time periods, at 10 schools and indoors and outdoors at 84 residences in the community. Analyses were restricted to May-October, the dry months during which endotoxin concentrations are highest.ResultsDaily endotoxin concentration patterns were determined mainly by meteorologic factors, particularly the degree of air stagnation. Overall concentrations were lowest in areas distant from agricultural activities. Highest concentrations were found in areas immediately downwind from agricultural/pasture land. Among three other measured air pollutants [fine particulate matter, elemental carbon (a marker of traffic in Fresno), and coarse particulate matter (PMc)], PMc was the only pollutant correlated with endotoxin. Endotoxin, however, was the most spatially variable.ConclusionsOur data support the need to evaluate the spatial/temporal variability of endotoxin concentrations, rather than relying on a few measurements made at one location, in studies of exposure and and respiratory health effects, particularly in children with asthma and other chronic respiratory diseases

Dermatological remedies in the traditional pharmacopoeia of Vulture-Alto Bradano, inland southern Italy

Dermatological remedies make up at least one-third of the traditional pharmacopoeia in southern Italy. The identification of folk remedies for the skin is important both for the preservation of traditional medical knowledge and in the search for novel antimicrobial agents in the treatment of skin and soft tissue infection (SSTI). Our goal is to document traditional remedies from botanical, animal, mineral and industrial sources for the topical treatment of skin ailments. In addition to SSTI remedies for humans, we also discuss certain ethnoveterinary applications. Field research was conducted in ten communities in the Vulture-Alto Bradano area of the Basilicata province, southern Italy. We randomly sampled 112 interviewees, stratified by age and gender. After obtaining prior informed consent, we collected data through semi-structured interviews, participant-observation, and small focus groups techniques. Voucher specimens of all cited botanic species were deposited at FTG and HLUC herbaria located in the US and Italy. We report the preparation and topical application of 116 remedies derived from 38 plant species. Remedies are used to treat laceration, burn wound, wart, inflammation, rash, dental abscess, furuncle, dermatitis, and other conditions. The pharmacopoeia also includes 49 animal remedies derived from sources such as pigs, slugs, and humans. Ethnoveterinary medicine, which incorporates both animal and plant derived remedies, is addressed. We also examine the recent decline in knowledge regarding the dermatological pharmacopoeia. The traditional dermatological pharmacopoeia of Vulture-Alto Bradano is based on a dynamic folk medical construct of natural and spiritual illness and healing. Remedies are used to treat more than 45 skin and soft tissue conditions of both humans and animals. Of the total 165 remedies reported, 110 have never before been published in the mainland southern Italian ethnomedical literature