22,940 research outputs found
Analysis of the 3DVAR Filter for the Partially Observed Lorenz '63 Model
The problem of effectively combining data with a mathematical model
constitutes a major challenge in applied mathematics. It is particular
challenging for high-dimensional dynamical systems where data is received
sequentially in time and the objective is to estimate the system state in an
on-line fashion; this situation arises, for example, in weather forecasting.
The sequential particle filter is then impractical and ad hoc filters, which
employ some form of Gaussian approximation, are widely used. Prototypical of
these ad hoc filters is the 3DVAR method. The goal of this paper is to analyze
the 3DVAR method, using the Lorenz '63 model to exemplify the key ideas. The
situation where the data is partial and noisy is studied, and both discrete
time and continuous time data streams are considered. The theory demonstrates
how the widely used technique of variance inflation acts to stabilize the
filter, and hence leads to asymptotic accuracy
Relative abundance and size composition of subtidal abalone, Haliotis spp., sea urchin, Strongylocentrotus spp., and abundance of sea stars off Fitzgerald marine reserve, September 1993
Data were collected at twenty-six dive stations at seven discrete latitudes along Fitzgerald Marine Reserve (FMR). Dive stations were targeted at three stratified depth zones: shallow (6.1 m), medium (10.7 m), and deep (16.8 m) in six of the seven locations. Two types of line
transects, emergent and invasive, were completed by separate dive teams at each dive station. The area surveyed totalled 1,510 m2 for emergent and 560 m2 for invasive transects.
Reef habitat dominated all depth zones, with moveable boulder and cobble increasing at medium and shallow depths. Encrusting coraline and surface algae dominated (49%), followed by turf (37%), sub-canopy (11.2%), and rare canopy (0.2%). Canopy was found only at shallow depths. Turf and sub-canopy decreased with depth.
Only two species of abalone, red, Haliotis rufescens, and flat, H. walallensis, were found. Flat abalone were extremely rare with only two found on invasive transects (0.004 abalone m-2). Red abalone densities were low at both emergent (0.02 abalone m-2, s.e.=O.Ol) and
invasive (0.07 abalone m-2, s.e.=0.03 ) transects. Red abalone concentrations differed significantly by depth and location. No abalone were found at deep depths and only one
sport-legal (178 mm shell length) abalone was found at medium depth. One commercial legal (198 mm shell length) abalone was found on the entire survey. Most sport-legal abalone were located in cryptic habitat in shallow invasive transects (38%), compared to 7% on emergent transects. The only evidence of recruitment was found on invasive transects where three young-of-the-year (<=31 mm shell length) red abalone were found. Evidence from our survey and other sources suggests that sport and commercial fisheries are not sustainable off the San Mateo coast.
Red urchin, Stongylocentrotus franciscanus, were more abundant than purple urchin, S. purpuratus, or red abalone. Red urchin densities were lower in emergent (1.08 urchin m-2,s.e.=0.04) than invasive (1.52, s.e.=0.06 m-2) transects. Densities of red urchin at deep stations in areas of lower algal abundance and potentially greater commercial fishing pressure were about one-half the densities at medium and shallow depths. ANOVA showed significant differences by depth and location. Mean Test Diameter (MTD) increased from deep to medium to shallow depths, while juvenile (<=50 mm) MTD showed an inverse
relationship with depth. Shallow-depth invasive transects revealed a missing mode of 83 mm red urchin. This size mode was not found in emergent transects, probably due to cryptic habitat.
Purple urchin were found at low densities at all three depth strata. Purple urchin densities were comparable in emergent (0.11 urchin m-2, s.e.=0.02 ) and invasive (0.09 urchin m-2,s.e.=0.03) transects. ANOVA showed densities varied significantly by location but not depth. 'Juvenile' purple urchin abundance showed an inverse relation to juvenile red urchin, increasing from deep to shallow depths. Purple urchin MTD of 84 mm (s.d.=23) was larger
than reported for intertidal areas off FMR.
Sea stars were found in high abundance off FMR. Bat stars, Asterina minata, had the highest densities (0.79 sea stars m-2, s.e.=0.03) followed by Pisaster sp. (0.47 sea stars m-2,s.e.=0.03 ), and sunflower stars, Pycnopodia helianthoides, (0.11 sea stars m-2, s.e.=0.04).
Pisaster sp. was the only group of sea stars where differences in density were significant by depth or location. (30pp.
Data Assimilation: A Mathematical Introduction
These notes provide a systematic mathematical treatment of the subject of
data assimilation
Two Wide Planetary-mass Companions to Solar-type Stars in Upper Scorpius
At wide separations, planetary-mass and brown dwarf companions to solar-type stars occupy a curious region of
parameter space not obviously linked to binary star formation or solar system scale planet formation. These
companions provide insight into the extreme case of companion formation (either binary or planetary), and
due to their relative ease of observation when compared to close companions, they offer a useful template
for our expectations of more typical planets. We present the results from an adaptive optics imaging survey
for wide (~50–500 AU) companions to solar-type stars in Upper Scorpius. We report one new discovery of a
~14 M_J companion around GSC 06214−00210and confirm that the candidate planetary-mass companion 1RXS
J160929.1−210524 detected by Lafrenière et al. is in fact comoving with its primary star. In our survey, these
two detections correspond to ~4% of solar-type stars having companions in the 6–20 M_J mass and ~200–500 AU
separation range. This figure is higher than would be expected if brown dwarfs and planetary-mass companions
were drawn from an extrapolation of the binary mass function. Finally, we discuss implications for the formation
of these objects
Robustness of Majorana Fermion induced Fractional Josephson Effect
It is shown in previous works that the coupling between two Majorana end
states in superconducting quantum wires leads to fractional Josephson effect.
However, in realistic experimental conditions, multiple bands of the wires are
occupied and the Majorana end states are accompanied by other fermionic end
states. This raises the question concerning the robustness of fractional
Josephson effect in these situations. In this work, we show that the absence of
the avoided energy crossing which gives rise to the fractional Josephson effect
is robust, even when the Majorana fermions are coupled with arbitrary strengths
to other fermions. Moreover, we calculate the temperature dependence of the
fractional Josephson current and show that it is suppressed by thermal
excitations to the other fermion bound states.Comment: 4+ pages, 3 figure
Probing Non-Abelian Statistics in nu=12/5 Quantum Hall State
The tunneling current and shot noise of the current between two Fractional
Quantum Hall (FQH) edges in the FQH state in electronic
Mach-Zehnder interferometer are studied. It is shown that the tunneling current
and shot noise can be used to probe the existence of parafermion
statistics in the FQH state. More specifically, the dependence of
the current on the Aharonov-Bohm flux in the Read-Rezayi state is asymmetric
under the change of the sign of the applied voltage. This property is absent in
the Abelian Laughlin states. Moreover the Fano factor can exceed 12.7 electron
charges in the FQH state . This number well exceeds the maximum
possible Fano factor in all Laughlin states and the Moore-Read
state which was shown previously to be and respectively.Comment: 10 pages, 6 figure
Well-Posedness And Accuracy Of The Ensemble Kalman Filter In Discrete And Continuous Time
The ensemble Kalman filter (EnKF) is a method for combining a dynamical model
with data in a sequential fashion. Despite its widespread use, there has been
little analysis of its theoretical properties. Many of the algorithmic
innovations associated with the filter, which are required to make a useable
algorithm in practice, are derived in an ad hoc fashion. The aim of this paper
is to initiate the development of a systematic analysis of the EnKF, in
particular to do so in the small ensemble size limit. The perspective is to
view the method as a state estimator, and not as an algorithm which
approximates the true filtering distribution. The perturbed observation version
of the algorithm is studied, without and with variance inflation. Without
variance inflation well-posedness of the filter is established; with variance
inflation accuracy of the filter, with resepct to the true signal underlying
the data, is established. The algorithm is considered in discrete time, and
also for a continuous time limit arising when observations are frequent and
subject to large noise. The underlying dynamical model, and assumptions about
it, is sufficiently general to include the Lorenz '63 and '96 models, together
with the incompressible Navier-Stokes equation on a two-dimensional torus. The
analysis is limited to the case of complete observation of the signal with
additive white noise. Numerical results are presented for the Navier-Stokes
equation on a two-dimensional torus for both complete and partial observations
of the signal with additive white noise
Metabolic perturbations associated with the consumption of a ketogenic medium-chain TAG diet in dogs with idiopathic epilepsy
Consumption of diets containing medium-chain TAG (MCT) has been shown to confer neuroprotective effects. We aim to identify the global metabolic perturbations associated with consumption of a ketogenic diet (medium-chain TAG diet (MCTD)) in dogs with idiopathic epilepsy. We used ultra-performance liquid chromatography-MS (UPLC-MS) to generate metabolic and lipidomic profiles of fasted canine serum and made comparisons between the MCTD and standardised placebo diet phases. We identified metabolites that differed significantly between diet phases using metabolite fragmentation profiles generated by tandem MS (UPLC–MS/MS). Consumption of the MCTD resulted in significant differences in serum metabolic profiles when compared with the placebo diet, where sixteen altered lipid metabolites were identified. Consumption of the MCTD resulted in reduced abundances of palmitoylcarnitine, octadecenoylcarnitine, stearoylcarnitine and significant changes, both reduced and increased abundances, of phosphatidylcholine (PC) metabolites. There was a significant increase in abundance of the saturated C17 : 0 fatty acyl moieties during the MCTD phase. Lysophosphatidylcholine (17 : 0) (P=0·01) and PC (17:0/20:4) (P=0·03) were both significantly higher in abundance during the MCTD. The data presented in this study highlight global changes in lipid metabolism, and, of particular interest, in the C17 : 0 moieties, as a result of MCT consumption. Elucidating the global metabolic response of MCT consumption will not only improve the administration of current ketogenic diets for neurological disease models but also provides new avenues for research to develop better diet therapies with improved neuroprotective efficacies. Future studies should clarify the involvement and importance of C17 : 0 moieties in endogenous MCT metabolic pathways
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