Asymptotics for the Wiener sausage among Poissonian obstacles

We consider the Wiener sausage among Poissonian obstacles. The obstacle is called hard if Brownian motion entering the obstacle is immediately killed, and is called soft if it is killed at certain rate. It is known that Brownian motion conditioned to survive among obstacles is confined in a ball near its starting point. We show the weak law of large numbers, large deviation principle in special cases and the moment asymptotics for the volume of the corresponding Wiener sausage. One of the consequence of our results is that the trajectory of Brownian motion almost fills the confinement ball.Comment: 19 pages, Major revision made for publication in J. Stat. Phy

Detecting Extrasolar Planets with Integral Field Spectroscopy

Observations of extrasolar planets using Integral Field Spectroscopy (IFS), if coupled with an extreme Adaptive Optics system and analyzed with a Simultaneous Differential Imaging technique (SDI), are a powerful tool to detect and characterize extrasolar planets directly; they enhance the signal of the planet and, at the same time, reduces the impact of stellar light and consequently important noise sources like speckles. In order to verify the efficiency of such a technique, we developed a simulation code able to test the capabilities of this IFS-SDI technique for different kinds of planets and telescopes, modelling the atmospheric and instrumental noise sources. The first results obtained by the simulations show that many significant extrasolar planet detections are indeed possible using the present 8m-class telescopes within a few hours of exposure time. The procedure adopted to simulate IFS observations is presented here in detail, explaining in particular how we obtain estimates of the speckle noise, Adaptive Optics corrections, specific instrumental features, and how we test the efficiency of the SDI technique to increase the signal-to-noise ratio of the planet detection. The most important results achieved by simulations of various objects, from 1 M_J to brown dwarfs of 30 M_J, for observations with an 8 meter telescope, are then presented and discussed.Comment: 60 pages, 37 figures, accepted in PASP, 4 Tables adde

Scaled penalization of Brownian motion with drift and the Brownian ascent

We study a scaled version of a two-parameter Brownian penalization model introduced by Roynette-Vallois-Yor in arXiv:math/0511102. The original model penalizes Brownian motion with drift $h\in\mathbb{R}$ by the weight process ${\big(\exp(\nu S_t):t\geq 0\big)}$ where $\nu\in\mathbb{R}$ and $\big(S_t:t\geq 0\big)$ is the running maximum of the Brownian motion. It was shown there that the resulting penalized process exhibits three distinct phases corresponding to different regions of the $(\nu,h)$-plane. In this paper, we investigate the effect of penalizing the Brownian motion concurrently with scaling and identify the limit process. This extends a result of Roynette-Yor for the ${\nu<0,~h=0}$ case to the whole parameter plane and reveals two additional "critical" phases occurring at the boundaries between the parameter regions. One of these novel phases is Brownian motion conditioned to end at its maximum, a process we call the Brownian ascent. We then relate the Brownian ascent to some well-known Brownian path fragments and to a random scaling transformation of Brownian motion recently studied by Rosenbaum-Yor.Comment: 32 pages; made additions to Section

Small-scale solar magnetic fields

As we resolve ever smaller structures in the solar atmosphere, it has become clear that magnetism is an important component of those small structures. Small-scale magnetism holds the key to many poorly understood facets of solar magnetism on all scales, such as the existence of a local dynamo, chromospheric heating, and flux emergence, to name a few. Here, we review our knowledge of small-scale photospheric fields, with particular emphasis on quiet-sun field, and discuss the implications of several results obtained recently using new instruments, as well as future prospects in this field of research.Comment: 43 pages, 18 figure

Syncopation and the Score

The first and second authors were supported by an EPSRC DTA (www.epsrc.ac.uk) studentship

APOE genotype influences insulin resistance, apolipoprotein CII and CIII according to plasma fatty acid profile in the Metabolic Syndrome

Metabolic markers associated with the Metabolic Syndrome (MetS) may be affected by interactions between the APOE genotype and plasma fatty acids (FA). In this study, we explored FA-gene interactions between the missense APOE polymorphisms and FA status on metabolic markers in MetS. Plasma FA, blood pressure, insulin sensitivity and lipid concentrations were determined at baseline and following a 12-week randomized, controlled, parallel, dietary FA intervention in 442 adults with MetS (LIPGENE study). FA-APOE gene interactions at baseline and following change in plasma FA were assessed using adjusted general linear models. At baseline E4 carriers had higher plasma concentrations of total cholesterol (TC), low-density lipoprotein cholesterol (LDL-C) and apolipoprotein B (apo B) compared with E2 carriers; and higher TC, LDL-C and apo B compared with E3/E3. Whilst elevated plasma n-3 polyunsaturated FA (PUFA) was associated with a beneficially lower concentration of apo CIII in E2 carriers, a high proportion of plasma C16:0 was associated with insulin resistance in E4 carriers. Following FA intervention, a reduction in plasma long-chain n-3 PUFA was associated with a reduction in apo CII concentration in E2 carriers. Our novel data suggest that individuals with MetS may benefit from personalized dietary interventions based on APOE genotype

Evidence for multiple rhythmic skills

Rhythms, or patterns in time, play a vital role in both speech and music. Proficiency in a number of rhythm skills has been linked to language ability, suggesting that certain rhythmic processes in music and language rely on overlapping resources. However, a lack of understanding about how rhythm skills relate to each other has impeded progress in understanding how language relies on rhythm processing. In particular, it is unknown whether all rhythm skills are linked together, forming a single broad rhythmic competence, or whether there are multiple dissociable rhythm skills. We hypothesized that beat tapping and rhythm memory/sequencing form two separate clusters of rhythm skills. This hypothesis was tested with a battery of two beat tapping and two rhythm memory tests. Here we show that tapping to a metronome and the ability to adjust to a changing tempo while tapping to a metronome are related skills. The ability to remember rhythms and to drum along to repeating rhythmic sequences are also related. However, we found no relationship between beat tapping skills and rhythm memory skills. Thus, beat tapping and rhythm memory are dissociable rhythmic aptitudes. This discovery may inform future research disambiguating how distinct rhythm competencies track with specific language functions