Scalar and vector Slepian functions, spherical signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and, particularly for applications in the geosciences, for scalar and vectorial signals defined on the surface of a unit sphere.Comment: Submitted to the 2nd Edition of the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verlag. This is a slightly modified but expanded version of the paper arxiv:0909.5368 that appeared in the 1st Edition of the Handbook, when it was called: Slepian functions and their use in signal estimation and spectral analysi

Comparison of outcomes following a cytological or histological diagnosis of malignant mesothelioma

Background: Survival with the epithelioid subtype of malignant mesothelioma (MM) is longer than the biphasic or sarcomatoid subtypes. There is concern that cytology-diagnosed epithelioid MM may underdiagnose the biphasic subtype. This study examines survival differences between patients with epithelioid MM diagnosed by cytology only and other subtypes diagnosed by histology. Methods: Demographics, diagnosis method, MM subtype and survival were extracted from the Western Australia (WA) Mesothelioma Registry, which records details of all MM cases occurring in WA. Results: A total of 2024 MM cases were identified over 42 years. One thousand seven hundred forty-four (86.2%) were male, median (IQR) age was 68.6 (60.4–77.0) years. A total of 1212 (59.9%) cases were identified as epithelioid subtype of which 499 (41.2%) were diagnosed using fluid cytology only. Those with a cytology-only diagnosis were older than the histology group (median 70.2 vs 67.6 years, P<0.001), but median survival was similar (cytology 10.6 (5.5–19.2) vs histology 11.1 (4.8–19.8) months, P=0.727) and Cox regression modelling adjusting for age, sex, site and time since first exposure showed no difference in survival between the different diagnostic approaches. Conclusions: Survival of cytologically and histologically diagnosed epithelioid MM cases does not differ. A diagnostic tap should be considered adequate to diagnose epithelioid MM without need for further invasive testing

The effects of weather and climate change on dengue

There is much uncertainty about the future impact of climate change on vector-borne diseases. Such uncertainty reflects the difficulties in modelling the complex interactions between disease, climatic and socioeconomic determinants. We used a comprehensive panel dataset from Mexico covering 23 years of province-specific dengue reports across nine climatic regions to estimate the impact of weather on dengue, accounting for the effects of non-climatic factors

Germ Line Origin and Somatic Mutations Determine the Target Tissues in Systemic AL-Amyloidosis

BACKGROUND: Amyloid is insoluble aggregated proteins deposited in the extra cellular space. About 25 different proteins are known to form amyloid in vivo and are associated with severe diseases such as Alzheimer's disease, prion diseases and type-2 diabetes. Light chain (AL) -amyloidosis is unique among amyloid diseases in that the fibril protein, a monoclonal immunoglobulin light chain, varies between individuals and that no two AL-proteins with identical primary structures have been described to date. The variability in tissue distribution of amyloid deposits is considerably larger in systemic AL-amyloidosis than in any other form of amyloidosis. The reason for this variation is believed to be based on the differences in properties of the amyloidogenic immunoglobulin light chain. However, there is presently no known relationship between the structure of an AL-protein and tissue distribution. METHODOLOGY/PRINCIPAL FINDINGS: We compared the pattern of amyloid deposition in four individuals with amyloid protein derived from variable light chain gene O18-O8, the source of a high proportion of amyloidogenic light chains, and in whom all or most of the fibril protein had been determined by amino acid sequencing. In spite of great similarities between the structures of the proteins, there was a pronounced variability in deposition pattern. We also compared the tissue distribution in these four individuals with that of four other patients with AL-amyloid derived from the L2-L16 gene. Although the interindividual variations were pronounced, liver and kidney involvement was much more evident in the latter four. CONCLUSIONS/SIGNIFICANCE: We conclude that although the use of a specific gene influences the tissue distribution of amyloid, each light chain exhibits one or more determinants of organ-specificity, which originate from somatic mutations and post-translational modifications. Eventual identification of such determinants could lead to improved treatment of patients with AL amyloidosis

Computational modelling of wound healing insights to develop new treatments

About 1% of the population will suffer a severe wound during their life. Thus, it is really important to develop new techniques in order to properly treat these injuries due to the high socioeconomically impact they suppose. Skin substitutes and pressure based therapies are currently the most promising techniques to heal these injuries. Nevertheless, we are still far from finding a definitive skin substitute for the treatment of all chronic wounds. As a first step in developing new tissue engineering tools and treatment techniques for wound healing, in silico models could help in understanding the mechanisms and factors implicated in wound healing. Here, we review mathematical models of wound healing. These models include different tissue and cell types involved in healing, as well as biochemical and mechanical factors which determine this process. Special attention is paid to the contraction mechanism of cells as an answer to the tissue mechanical state. Other cell processes such as differentiation and proliferation are also included in the models together with extracellular matrix production. The results obtained show the dependency of the success of wound healing on tissue composition and the importance of the different biomechanical and biochemical factors. This could help to individuate the adequate concentration of growth factors to accelerate healing and also the best mechanical properties of the new skin substitute depending on the wound location in the body and its size and shape. Thus, the feedback loop of computational models, experimental works and tissue engineering could help to identify the key features in the design of new treatments to heal severe wounds

Studies of the Decay B+- -> D_CP K+-

We report studies of the decay B+- -> D_CP K+-, where D_CP denotes neutral D mesons that decay to CP eigenstates. The analysis is based on a 29.1/fb data sample of collected at the \Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric e+ e- storage ring. Ratios of branching fractions of Cabibbo-suppressed to Cabibbo-favored processes involving D_CP are determined to be B(B- -> D_1 K-)/B(B- -> D_1 pi-)=0.125 +- 0.036 +- 0.010 and B(B- -> D_2 K-)/B(B- -> D_2 pi-)=0.119 +- 0.028 +- 0.006, where indices 1 and 2 represent the CP=+1 and CP=-1 eigenstates of the D0 - anti D0 system, respectively. We also extract the partial rate asymmetries for B+- -> D_CP K+-, finding A_1 = 0.29 +- 0.26 +- 0.05 and A_2 = -0.22 +- 0.24 +- 0.04.Comment: 10 pages, 2 figures, submitted to Physical Review Letter

The Pioneer Anomaly

Radio-metric Doppler tracking data received from the Pioneer 10 and 11 spacecraft from heliocentric distances of 20-70 AU has consistently indicated the presence of a small, anomalous, blue-shifted frequency drift uniformly changing with a rate of ~6 x 10^{-9} Hz/s. Ultimately, the drift was interpreted as a constant sunward deceleration of each particular spacecraft at the level of a_P = (8.74 +/- 1.33) x 10^{-10} m/s^2. This apparent violation of the Newton's gravitational inverse-square law has become known as the Pioneer anomaly; the nature of this anomaly remains unexplained. In this review, we summarize the current knowledge of the physical properties of the anomaly and the conditions that led to its detection and characterization. We review various mechanisms proposed to explain the anomaly and discuss the current state of efforts to determine its nature. A comprehensive new investigation of the anomalous behavior of the two Pioneers has begun recently. The new efforts rely on the much-extended set of radio-metric Doppler data for both spacecraft in conjunction with the newly available complete record of their telemetry files and a large archive of original project documentation. As the new study is yet to report its findings, this review provides the necessary background for the new results to appear in the near future. In particular, we provide a significant amount of information on the design, operations and behavior of the two Pioneers during their entire missions, including descriptions of various data formats and techniques used for their navigation and radio-science data analysis. As most of this information was recovered relatively recently, it was not used in the previous studies of the Pioneer anomaly, but it is critical for the new investigation.Comment: 165 pages, 40 figures, 16 tables; accepted for publication in Living Reviews in Relativit