Explicit formulae in probability and in statistical physics

We consider two aspects of Marc Yor's work that have had an impact in statistical physics: firstly, his results on the windings of planar Brownian motion and their implications for the study of polymers; secondly, his theory of exponential functionals of Levy processes and its connections with disordered systems. Particular emphasis is placed on techniques leading to explicit calculations.Comment: 14 pages, 2 figures. To appear in Seminaire de Probabilites, Special Issue Marc Yo

Mixed-Meal Tolerance Test Versus Glucagon Stimulation Test for the Assessment of β-Cell Function in Therapeutic Trials in Type 1 Diabetes

OBJECTIVE—β-Cell function in type 1 diabetes clinical trials is commonly measured by C-peptide response to a secretagogue in either a mixed-meal tolerance test (MMTT) or a glucagon stimulation test (GST). The Type 1 Diabetes TrialNet Research Group and the European C-peptide Trial (ECPT) Study Group conducted parallel randomized studies to compare the sensitivity, reproducibility, and tolerability of these procedures

Exponential martingales and changes of measure for counting processes

We give sufficient criteria for the Dol\'eans-Dade exponential of a stochastic integral with respect to a counting process local martingale to be a true martingale. The criteria are adapted particularly to the case of counting processes and are sufficiently weak to be useful and verifiable, as we illustrate by several examples. In particular, the criteria allow for the construction of for example nonexplosive Hawkes processes as well as counting processes with stochastic intensities depending on diffusion processes

Reexamining the effects of gestational age, fetal growth, and maternal smoking on neonatal mortality

BACKGROUND: Low birth weight (<2,500 g) is a strong predictor of infant mortality. Yet low birth weight, in isolation, is uninformative since it is comprised of two intertwined components: preterm delivery and reduced fetal growth. Through nonparametric logistic regression models, we examine the effects of gestational age, fetal growth, and maternal smoking on neonatal mortality. METHODS: We derived data on over 10 million singleton live births delivered at ≥ 24 weeks from the 1998–2000 U.S. natality data files. Nonparametric multivariable logistic regression based on generalized additive models was used to examine neonatal mortality (deaths within the first 28 days) in relation to fetal growth (gestational age-specific standardized birth weight), gestational age, and number of cigarettes smoked per day. All analyses were further adjusted for the confounding effects due to maternal age and gravidity. RESULTS: The relationship between standardized birth weight and neonatal mortality is nonlinear; mortality is high at low z-score birth weights, drops precipitously with increasing z-score birth weight, and begins to flatten for heavier infants. Gestational age is also strongly associated with mortality, with patterns similar to those of z-score birth weight. Although the direct effect of smoking on neonatal mortality is weak, its effects (on mortality) appear to be largely mediated through reduced fetal growth and, to a lesser extent, through shortened gestation. In fact, the association between smoking and reduced fetal growth gets stronger as pregnancies approach term. CONCLUSIONS: Our study provides important insights regarding the combined effects of fetal growth, gestational age, and smoking on neonatal mortality. The findings suggest that the effect of maternal smoking on neonatal mortality is largely mediated through reduced fetal growth

Relationships between riverine and terrestrial dissolved organic carbon: Concentration, radiocarbon signature, specific UV absorbance

The transfer of dissolved organic carbon (DOC) from land to watercourses plays a major role in the carbon cycle, and in the transport and fate of associated organic and inorganic contaminants. We investigated, at global scale, how the concentrations and properties of riverine DOC depend upon combinations of terrestrial source solutions. For topsoil, subsoil, groundwater and river solutions in different Köppen-Geiger climatic zones, we compiled published and new values of DOC concentration ([DOC]), radiocarbon signature (DO14C), and specific UV absorbance (SUVA). The average value of each DOC variable decreased significantly in magnitude from topsoil to subsoil to groundwater, permitting the terrestrial sources to be distinguished. We used the terrestrial data to simulate the riverine distributions of each variable, and also relationships between pairs of variables. To achieve good matches between observed and simulated data, it was necessary to optimise the distributions of water fractions contributed by each of the three terrestrial sources, and also to reduce the mean input terrestrial [DOC] values, to about 60% of the measured ones. One possible explanation for the required lowering of the modelled terrestrial [DOC] values might be unrepresentative sampling of terrestrial DOC, including dilution effects; another is the loss of DOC during riverine transport. High variations in simulated riverine DOC variables, which match observed data, are due predominantly to variations in source solution values, with a lesser contribution from the different combinations of source waters. On average, most DOC in rivers draining catchments with forest and/or grass-shrub land cover comes in similar amounts from topsoil and subsoil, with about 10% from groundwater. In rivers draining croplands, subsoil and groundwater solutions are the likely dominant DOC sources, while in wetland rivers most DOC is from topsoil

Schmidt-hammer exposure ages from periglacial patterned ground (sorted circles) in Jotunheimen, Norway, and their interpretative problems

© 2016 Swedish Society for Anthropology and Geography Periglacial patterned ground (sorted circles and polygons) along an altitudinal profile at Juvflya in central Jotunheimen, southern Norway, is investigated using Schmidt-hammer exposure-age dating (SHD). The patterned ground surfaces exhibit R-value distributions with platycurtic modes, broad plateaus, narrow tails, and a negative skew. Sample sites located between 1500 and 1925 m a.s.l. indicate a distinct altitudinal gradient of increasing mean R-values towards higher altitudes interpreted as a chronological function. An established regional SHD calibration curve for Jotunheimen yielded mean boulder exposure ages in the range 6910 ± 510 to 8240 ± 495 years ago. These SHD ages are indicative of the timing of patterned ground formation, representing minimum ages for active boulder upfreezing and maximum ages for the stabilization of boulders in the encircling gutters. Despite uncertainties associated with the calibration curve and the age distribution of the boulders, the early-Holocene age of the patterned ground surfaces, the apparent cessation of major activity during the Holocene Thermal Maximum (HTM) and continuing lack of late-Holocene activity clarify existing understanding of the process dynamics and palaeoclimatic significance of large-scale sorted patterned ground as an indicator of a permafrost environment. The interpretation of SHD ages from patterned ground surfaces remains challenging, however, owing to their diachronous nature, the potential for a complex history of formation, and the influence of local, non-climatic factors