A Statistical Framework and Analysis for Perfect Radar Pulse Compression

Perfect radar pulse compression coding is a potential emerging field which aims at providing rigorous analysis and fundamental limit radar experiments. It is based on finding non-trivial pulse codes, which we can make statistically equivalent, to the radar experiments carried out with elementary pulses of some shape. A common engineering-based radar experiment design, regarding pulse-compression, often omits the rigorous theory and mathematical limitations. In this work our aim is to develop a mathematical theory which coincides with understanding the radar experiment in terms of the theory of comparison of statistical experiments. We review and generalize some properties of the It\^{o} measure. We estimate the unknown i.e. the structure function in the context of Bayesian statistical inverse problems. We study the posterior for generalized $d$-dimensional inverse problems, where we consider both real-valued and complex-valued inputs for posteriori analysis. Finally this is then extended to the infinite dimensional setting, where our analysis suggests the underlying posterior is non-Gaussian

Bayesian inversion with {\alpha}-stable priors

We propose to use L\'evy {\alpha}-stable distributions for constructing priors for Bayesian inverse problems. The construction is based on Markov fields with stable-distributed increments. Special cases include the Cauchy and Gaussian distributions, with stability indices {\alpha} = 1, and {\alpha} = 2, respectively. Our target is to show that these priors provide a rich class of priors for modelling rough features. The main technical issue is that the {\alpha}-stable probability density functions do not have closed-form expressions in general, and this limits their applicability. For practical purposes, we need to approximate probability density functions through numerical integration or series expansions. Current available approximation methods are either too time-consuming or do not function within the range of stability and radius arguments needed in Bayesian inversion. To address the issue, we propose a new hybrid approximation method for symmetric univariate and bivariate {\alpha}-stable distributions, which is both fast to evaluate, and accurate enough from a practical viewpoint. Then we use approximation method in the numerical implementation of {\alpha}-stable random field priors. We demonstrate the applicability of the constructed priors on selected Bayesian inverse problems which include the deconvolution problem, and the inversion of a function governed by an elliptic partial differential equation. We also demonstrate hierarchical {\alpha}-stable priors in the one-dimensional deconvolution problem. We employ maximum-a-posterior-based estimation at all the numerical examples. To that end, we exploit the limited-memory BFGS and its bounded variant for the estimator

Broadband Meter-Wavelength Observations of Ionospheric Scintillation

Intensity scintillations of cosmic radio sources are used to study astrophysical plasmas like the ionosphere, the solar wind, and the interstellar medium. Normally these observations are relatively narrow band. With Low Frequency Array (LOFAR) technology at the Kilpisj\"arvi Atmospheric Imaging Receiver Array (KAIRA) station in northern Finland we have observed scintillations over a 3 octave bandwidth. ``Parabolic arcs'', which were discovered in interstellar scintillations of pulsars, can provide precise estimates of the distance and velocity of the scattering plasma. Here we report the first observations of such arcs in the ionosphere and the first broad-band observations of arcs anywhere, raising hopes that study of the phenomenon may similarly improve the analysis of ionospheric scintillations. These observations were made of the strong natural radio source Cygnus-A and covered the entire 30-250\,MHz band of KAIRA. Well-defined parabolic arcs were seen early in the observations, before transit, and disappeared after transit although scintillations continued to be obvious during the entire observation. We show that this can be attributed to the structure of Cygnus-A. Initial results from modeling these scintillation arcs are consistent with simultaneous ionospheric soundings taken with other instruments, and indicate that scattering is most likely to be associated more with the topside ionosphere than the F-region peak altitude. Further modeling and possible extension to interferometric observations, using international LOFAR stations, are discussed.Comment: 11 pages, 17 figure

Establishment success of sooty beech scale insects, Ultracoelostoma sp., on different host tree species in New Zealand

The sooty beech scale insect (Ultracoelostoma sp.) (Hemiptera: Margarodidae) exhibits a highly patchy distribution at local and regional scales. A major factor driving this common distributional phenomenon in other phloem-feeding insects is aggregation and local adaptation. The aim of this study was to determine if Ultracoelostoma was locally adapted to its natal host trees, by contrasting the establishment rates of first instar “crawlers” in reciprocal transfers to natal versus novel hosts. Although there are two closely-related species of sooty beech scale insect, the morphological characters of crawlers in this study were intermediate between those of U. assimile and U. brittini. However, all of the voucher specimens examined had consistent morphology, indicating that they belong to one species which we refer to as Ultracoelostoma sp. Reciprocal transfers of crawlers were carried out between individual red beech (Nothofagus fusca), as well as between mountain beech (N. solandri) and red beech trees, to ascertain if insects had become locally adapted to their individual host tree or to host species. In total, 480 crawlers were placed in enclosures on their natal and novel host trees, of which only 32 (6.7 %) became established. No evidence for local adaptation, either to individual host trees or to host tree species, was found. There was also no difference in crawler establishment between natal and novel hosts. However, crawlers originating from mountain beech trees had significantly higher establishment rates on both natal mountain beech and novel red beech hosts, than did crawlers originating from red beech trees. The superior ability of mountain beech crawlers to become established, even on novel red beech trees, suggests that scale insects on mountain beech trees have higher individual fitness (possibly due to maternal effects mediated by differences in host nutritional quality, defensive compounds or growth rate). This increased fitness may result in crawlers being better provisioned to search for appropriate establishment sites. The results of this study indicate that beech scale insects perform better on mountain beech at this site, although crawlers did not preferentially establish on mountain beech

European Red List of Habitats Part 1. Marine habitats

The European Red List of Habitats provides an overview of the risk of collapse (degree of endangerment) of marine, terrestrial and freshwater habitats in the European Union (EU28) and adjacent regions (EU28+), based on a consistent set of categories and criteria, and detailed data and expert knowledge from involved countries1. A total of 257 benthic marine habitat types were assessed. In total, 19% (EU28) and 18% (EU28+) of the evaluated habitats were assessed as threatened in categories Critically Endangered, Endangered and Vulnerable. An additional 12% were Near Threatened in the EU28 and 11% in the EU28+. These figures are approximately doubled if Data Deficient habitats are excluded. The percentage of threatened habitat types differs across the regional seas. The highest proportion of threatened habitats in the EU28 was found in the Mediterranean Sea (32%), followed by the North-East Atlantic (23%), the Black Sea (13%) and then the Baltic Sea (8%). There was a similar pattern in the EU28+. The most frequently cited pressures and threats were similar across the four regional seas: pollution (eutrophication), biological resource use other than agriculture or forestry (mainly fishing but also aquaculture), natural system modifications (e.g. dredging and sea defence works), urbanisation and climate change. Even for habitats where the assessment outcome was Data Deficient, the Red List assessment process has resulted in the compilation of a substantial body of useful information to support the conservation of marine habitats