The Kalman-Levy filter

The Kalman filter combines forecasts and new observations to obtain an estimation which is optimal in the sense of a minimum average quadratic error. The Kalman filter has two main restrictions: (i) the dynamical system is assumed linear and (ii) forecasting errors and observational noises are taken Gaussian. Here, we offer an important generalization to the case where errors and noises have heavy tail distributions such as power laws and L\'evy laws. The main tool needed to solve this ``Kalman-L\'evy'' filter is the ``tail-covariance'' matrix which generalizes the covariance matrix in the case where it is mathematically ill-defined (i.e. for power law tail exponents $\mu \leq 2$). We present the general solution and discuss its properties on pedagogical examples. The standard Kalman-Gaussian filter is recovered for the case $\mu = 2$. The optimal Kalman-L\'evy filter is found to deviate substantially fro the standard Kalman-Gaussian filter as $\mu$ deviates from 2. As $\mu$ decreases, novel observations are assimilated with less and less weight as a small exponent $\mu$ implies large errors with significant probabilities. In terms of implementation, the price-to-pay associated with the presence of heavy tail noise distributions is that the standard linear formalism valid for the Gaussian case is transformed into a nonlinear matrice equation for the Kalman-L\'evy filter. Direct numerical experiments in the univariate case confirms our theoretical predictions.Comment: 41 pages, 9 figures, correction of errors in the general multivariate cas

Cardiac Device‐Related Endocarditis Complicated by Spinal Abscess

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90084/1/j.1540-8159.2011.03288.x.pd

Radiogalaxies in the Sloan Digital Sky Survey: spectral index-environment correlations

We analyze optical and radio properties of radiogalaxies detected in the Sloan Digital Sky Survey (SDSS). The sample of radio sources are selected from the catalogue of Kimball & Ivezi\'c (2008) with flux densities at 325, 1400 and 4850 MHz, using WENSS, NVSS and GB6 radio surveys and from flux measurements at 74 MHz taken from VLA Low-frequency Sky Survey \citep{cohen}. We study radiogalaxy spectral properties using radio colour-colour diagrams and find that our sample follows a single power law from 74 to 4850 MHz. The spectral index vs. spectroscopic redshift relation ($\alpha-z$) is not significant for our sample of radio sources. We analyze a subsample of radio sources associated with clusters of galaxies identified from the maxBCG catalogue and find that about 40% of radio sources with ultra steep spectra (USS, $\alpha<-1$, where $S_\nu \propto \nu^{\alpha}$) are associated with galaxy clusters or groups of galaxies. We construct a Hubble diagram of USS radio sources in the optical $r$ band up to $z\sim0$.8 and compare our results with those for normal galaxies selected from different optical surveys and find that USS radio sources are around as luminous as the central galaxies in the maxBCG cluster sample and typically more than 4 magnitudes brighter than normal galaxies at $z\sim0$.3. We study correlations between spectral index, richness and luminosity of clusters associated with radio sources. We find that USS at low redshift are rare, most of them reside in regions of unusually high ambient density, such of those found in rich cluster of galaxies. Our results also suggest that clusters of galaxies associated with steeper than the average spectra have higher richness counts and are populated by luminous galaxies in comparison with those environments associated to radio sources with flatter than the average spectra. A plausible explanation for our results is that radio emission is more pressure confined in higher gas density environments such as those found in rich clusters of galaxies and as a consequence radio lobes in rich galaxy clusters will expand adiabatically and lose energy via synchrotron and inverse Compton losses, resulting in a steeper radio spectra.Comment: 13 pages, 14 figures; accepted for publication in Monthly Notices of the Royal Astronomical Society Main Journal

A statistical gap-filling method to interpolate global monthly surface ocean carbon dioxide data

We have developed a statistical gap-filling method adapted to the specific coverage and prop-erties of observed fugacity of surface ocean CO2(fCO2). We have used this method to interpolate the Sur-face Ocean CO2Atlas (SOCAT) v2 database on a 2.5832.58 global grid (south of 708N) for 1985–2011 atmonthly resolution. The method combines a spatial interpolation based on a ‘‘radius of influence’’ to deter-mine nearby similar fCO2values with temporal harmonic and cubic spline curve-fitting, and also fits long-term trends and seasonal cycles. Interannual variability is established using deviations of observations fromthe fitted trends and seasonal cycles. An uncertainty is computed for all interpolated values based on thespatial and temporal range of the interpolation. Tests of the method using model data show that it performsas well as or better than previous regional interpolation methods, but in addition it provides a near-globaland interannual coverage

Contact, the feature pool and the speech community : The emergence of Multicultural London English.

In Northern Europe’s major cities, new varieties of the host languages are emerging in the multilingual inner cities. While some analyse these ‘multiethnolects’ as youth styles, we take a variationist approach to an emerging ‘Multicultural London English’ (MLE), asking: (1) what features characterise MLE? (2) at what age(s) are they acquired? (3) is MLE vernacularised? (4) when did MLE emerge, and what factors enabled its emergence? We argue that innovations in the diphthongs and the quotative system are generated from the specific sociolinguistics of inner-city London, where at least half the population is undergoing group second-language acquisition and where high linguistic diversity leads to a feature pool to select from. We look for incrementation (Labov) in the acquisition of the features, but find this only for two ‘global’ changes, BE LIKE and GOOSE-fronting, for which adolescents show the highest usage. Community-internal factors explain the age-related variation in the remaining features

A possible architecture of the planetary system HR 8799

HR8799 is a nearby A-type star with a debris disk and three planetary candidates recently imaged directly. We undertake a coherent analysis of various portions of observational data on all known components of the system. The goal is to elucidate the architecture and evolutionary status of the system. We try to further constrain the age and orientation of the system, orbits and masses of the companions, as well as the location of dust. From the high luminosity of debris dust and dynamical constraints, we argue for a rather young system's age of <50Myr. The system must be seen nearly, but not exactly, pole-on. Our analysis of the stellar rotational velocity yields an inclination of 13-30deg, whereas i>20deg is needed for the system to be dynamically stable, which suggests a probable inclination range of 20-30deg. The spectral energy distribution is naturally reproduced with two dust rings associated with two planetesimal belts. The inner "asteroid belt" is located at ~10AU inside the orbit of the innermost companion and a "Kuiper belt" at >100AU is just exterior to the orbit of the outermost companion. The dust masses in the inner and outer ring are estimated to be ~1E-05 and 4E-02 M_earth, respectively. We show that all three planetary candidates may be stable in the mass range suggested in the discovery paper by Marois et al. 2008 (between 5 and 13 Jupiter masses), but only for some of all possible orientations. Stable orbits imply a double (4:2:1) mean-motion resonance between all three companions. We finally show that in the cases where the companions themselves are orbitally stable, the dust-producing planetesimal belts are also stable against planetary perturbations.Comment: 12 pages, 14 figures, 4 tables, accepted to be published in Astronomy & Astrophysics (May 20, 2009

Multiwavelength characterization of faint ultra steep spectrum radio sources: a search for high-redshift radio galaxies

Context. Ultra steep spectrum (USS) radio sources are one of the efficient tracers of powerful high-z radio galaxies (HzRGs). In contrast to searches for powerful HzRGs from radio surveys of moderate depths, fainter USS samples derived from deeper radio surveys can be useful in finding HzRGs at even higher redshifts and in unveiling a population of obscured weaker radio-loud AGN at moderate redshifts. Aims. Using our 325 MHz GMRT observations (5σ ∼ 800 μJy) and 1.4 GHz VLA observations (5σ ∼ 80−100 μJy) available in two subfields (VLA-VIMOS VLT Deep Survey (VLA-VVDS) and Subaru X-ray Deep Field (SXDF)) of the XMM-LSS field, we derive a large sample of 160 faint USS radio sources and characterize their nature. Methods. The optical and IR counterparts of our USS sample sources are searched using existing deep surveys, at respective wavelengths. We attempt to unveil the nature of our faint USS sources using diagnostic techniques based on mid-IR colors, flux ratios of radio to mid-IR, and radio luminosities. Results. Redshift estimates are available for 86/116 (∼74%) USS sources in the VLA-VVDS field and for 39/44 (∼87%) USS sources in the SXDF fields with median values (zmedian) ∼1.18 and ∼1.57, respectively, which are higher than estimates for non-USS radio sources (zmedian non−USS ∼ 0.99 and ∼0.96), in the two subfields. The MIR color–color diagnostic and radio luminosities are consistent with most of our USS sample sources at higher redshifts (z > 0.5) being AGN. The flux ratio of radio to mid-IR (S 1.4 GHz/S 3.6 μm) versus redshift diagnostic plot suggests that more than half of our USS sample sources distributed over z ∼ 0.5 to 3.8 are likely to be hosted in obscured environments. A significant fraction (∼26% in the VLA-VVDS and ∼13% in the SXDF) of our USS sources without redshift estimates mostly remain unidentified in the existing optical, IR surveys, and exhibit high radio to mid-IR flux ratio limits similar to HzRGs, and so, can be considered as potential HzRG candidates. Conclusions. Our study shows that the criterion of ultra steep spectral index remains a reasonably efficient method to select high-z sources even at sub-mJy flux densities. In addition to powerful HzRG candidates, our faint USS sample also contains populations of weaker radio-loud AGNs potentially hosted in obscured environments

Sprouty2 mediated tuning of signalling is essential for somite myogenesis

Background: Negative regulators of signal transduction cascades play critical roles in controlling different aspects of normal embryonic development. Sprouty2 (Spry2) negatively regulates receptor tyrosine kinases (RTK) and FGF signalling and is important in differentiation, cell migration and proliferation. In vertebrate embryos, Spry2 is expressed in paraxial mesoderm and in forming somites. Expression is maintained in the myotome until late stages of somite differentiation. However, its role and mode of action during somite myogenesis is still unclear. Results: Here, we analysed chick Spry2 expression and showed that it overlaps with that of myogenic regulatory factors MyoD and Mgn. Targeted mis-expression of Spry2 led to inhibition of myogenesis, whilst its C-terminal domain led to an increased number of myogenic cells by stimulating cell proliferation. Conclusions: Spry2 is expressed in somite myotomes and its expression overlaps with myogenic regulatory factors. Overexpression and dominant-negative interference showed that Spry2 plays a crucial role in regulating chick myogenesis by fine tuning of FGF signaling through a negative feedback loop. We also propose that mir-23, mir-27 and mir-128 could be part of the negative feedback loop mechanism. Our analysis is the first to shed some light on in vivo Spry2 function during chick somite myogenesis

Stress corrosion cracking in Al-Zn-Mg-Cu aluminum alloys in saline environments

Copyright 2013 ASM International. This paper was published in Metallurgical and Materials Transactions A, 44A(3), 1230 - 1253, and is made available as an electronic reprint with the permission of ASM International. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplications of any material in this paper for a fee or for commercial purposes, or modification of the content of this paper are prohibited.Stress corrosion cracking of Al-Zn-Mg-Cu (AA7xxx) aluminum alloys exposed to saline environments at temperatures ranging from 293 K to 353 K (20 °C to 80 °C) has been reviewed with particular attention to the influences of alloy composition and temper, and bulk and local environmental conditions. Stress corrosion crack (SCC) growth rates at room temperature for peak- and over-aged tempers in saline environments are minimized for Al-Zn-Mg-Cu alloys containing less than ~8 wt pct Zn when Zn/Mg ratios are ranging from 2 to 3, excess magnesium levels are less than 1 wt pct, and copper content is either less than ~0.2 wt pct or ranging from 1.3 to 2 wt pct. A minimum chloride ion concentration of ~0.01 M is required for crack growth rates to exceed those in distilled water, which insures that the local solution pH in crack-tip regions can be maintained at less than 4. Crack growth rates in saline solution without other additions gradually increase with bulk chloride ion concentrations up to around 0.6 M NaCl, whereas in solutions with sufficiently low dichromate (or chromate), inhibitor additions are insensitive to the bulk chloride concentration and are typically at least double those observed without the additions. DCB specimens, fatigue pre-cracked in air before immersion in a saline environment, show an initial period with no detectible crack growth, followed by crack growth at the distilled water rate, and then transition to a higher crack growth rate typical of region 2 crack growth in the saline environment. Time spent in each stage depends on the type of pre-crack (“pop-in” vs fatigue), applied stress intensity factor, alloy chemistry, bulk environment, and, if applied, the external polarization. Apparent activation energies (E a) for SCC growth in Al-Zn-Mg-Cu alloys exposed to 0.6 M NaCl over the temperatures ranging from 293 K to 353 K (20 °C to 80 °C) for under-, peak-, and over-aged low-copper-containing alloys (~0.8 wt pct), they are typically ranging from 20 to 40 kJ/mol for under- and peak-aged alloys, and based on limited data, around 85 kJ/mol for over-aged tempers. This means that crack propagation in saline environments is most likely to occur by a hydrogen-related process for low-copper-containing Al-Zn-Mg-Cu alloys in under-, peak- and over-aged tempers, and for high-copper alloys in under- and peak-aged tempers. For over-aged high-copper-containing alloys, cracking is most probably under anodic dissolution control. Future stress corrosion studies should focus on understanding the factors that control crack initiation, and insuring that the next generation of higher performance Al-Zn-Mg-Cu alloys has similar longer crack initiation times and crack propagation rates to those of the incumbent alloys in an over-aged condition where crack rates are less than 1 mm/month at a high stress intensity factor