184 research outputs found
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 by the weight process
where and
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 -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 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
Recommended from our members
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
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