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

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 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

Modeling spatial innovation diffusion from radiocarbon dates and regression residuals: The case of early old world pottery

This article introduces a method of exploratory analysis of the geographical factors influencing large-scale innovation diffusion, and illustrates its application to the case of early pottery dispersal in the Old World. Regression techniques are used to identify broad-scale spatiotemporal trends in the innovation's first occurrence, and regression residuals are then analyzed to identify geographical variation (climate, biomes) that may have influenced local rates of diffusion. The boundaries between the modeled diffusion zones segregate the western half of the map into a Eurasian hunter-gatherer pottery-using zone affiliated by cultural descent to the Siberian center of innovation, and a lower-latitude farming and pastoralist zone affiliated by cultural descent to the north African center of innovation. However, the correlation coefficients suggest that this baseline model has limited explanatory power, with geographical patterning in the residuals indicating that habitat also greatly affected rates of spread of the new technology. Earlier-than-predicted ages for early pottery tend to occur in locations with mean annual temperature in the range approximately 0-15°C. This favorable temperature range typically includes Mediterranean, grassland, and temperate forest biome types, but of these, the Mediterranean and the temperate deciduous forest biomes are the only ones on which regression residuals indicate earlier-than-predicted first observed pottery dates. © 2014 by the Arizona Board of Regents on behalf of the University of Arizona

Measuring the Density of States of the Inner and Outer Wall of Double-Walled Carbon Nanotubes

This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).The combination of ultraviolet photoelectron spectroscopy and metastable helium induced electron spectroscopy is used to determine the density of states of the inner and outer coaxial carbon nanotubes. Ultraviolet photoelectron spectroscopy typically measures the density of states across the entire carbon nanotube, while metastable helium induced electron spectroscopy measures the density of states of the outermost layer alone. The use of double-walled carbon nanotubes in electronic devices allows for the outer wall to be functionalised whilst the inner wall remains defect free and the density of states is kept intact for electron transport. Separating the information of the inner and outer walls enables development of double-walled carbon nanotubes to be independent, such that the charge transport of the inner wall is maintained and confirmed whilst the outer wall is modified for functional purposes.This research received no external funding

B2 0902+34: A Collapsing Protogiant Elliptical Galaxy at z=3.4

We have used the visible integral-field replicable unit spectrograph prototype (VIRUS-P), a new integral field spectrograph, to study the spatially and spectrally resolved Lyman-alpha emission line structure in the radio galaxy B2 0902+34 at z=3.4. We observe a halo of Lyman-alpha emission with a velocity dispersion of 250 km/s extending to a radius of 50 kpc. A second feature is revealed in a spatially resolved region where the line profile shows blueshifted structure. This may be viewed as either HI absorption at -450 km/s or secondary emission at -900 km/s from the primary peak. Our new data, in combination with the 21 cm absorption, suggest two important and unexplained discrepancies. First, nowhere in the line profiles of the Lyman-alpha halo is the 21 cm absorber population evident. Second, the 21 cm absorption redshift is higher than the Lyman-alpha emission redshift. In an effort to explain these two traits, we have undertaken the first three dimensional Monte Carlo simulations of resonant scattering in radio galaxies. Though simple, the model produces the features in the Lyman-alpha data and predicts the 21 cm properties. To reach agreement between this model and the data, global infall of the HI is strictly necessary. The amount of gas necessary to match the model and data is surprisingly high, >= 10E12 solar masses, an order of magnitude larger than the stellar mass. The collapsing structure and large gas mass lead us to interpret B2 0902+34 as a protogiant elliptical galaxy.Comment: 30 pages, 8 figures, 4 tables, accepted in Ap