Slepian functions and their use in 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 on the surface of a sphere.Comment: Submitted to the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verla

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

f(R) theories

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.Comment: 156 pages, 14 figures, Invited review article in Living Reviews in Relativity, Published version, Comments are welcom

Acute wound management: revisiting the approach to assessment, irrigation, and closure considerations

Abstract Background As millions of emergency department (ED) visits each year include wound care, emergency care providers must remain experts in acute wound management. The variety of acute wounds presenting to the ED challenge the physician to select the most appropriate management to facilitate healing. A complete wound history along with anatomic and specific medical considerations for each patient provides the basis of decision making for wound management. It is essential to apply an evidence‐based approach and consider each wound individually in order to create the optimal conditions for wound healing. Aims A comprehensive evidence‐based approach to acute wound management is an essential skill set for any emergency physician or acute care practitioner. This review provides an overview of current evidence and addresses frequent pitfalls. Methods A systematic review of the literature for acute wound management was performed. Results A structured MEDLINE search was performed regarding acute wound management including established wound care guidelines. The data obtained provided the framework for evidence‐based recommendations and current best practices for wound care. Conclusion Acute wound management varies based on the wound location and characteristics. No single approach can be applied to all wounds; however, a systematic approach to acute wound care integrated with current best practices provides the framework for exceptional wound management

One step closer to understanding the role of bacteria in diabetic foot ulcers: characterising the microbiome of ulcers

Background: The aim of this study was to characterise the microbiome of new and recurrent diabetic foot ulcers using 16S amplicon sequencing (16S AS), allowing the identification of a wider range of bacterial species that may be important in the development of chronicity in these debilitating wounds. Twenty patients not receiving antibiotics for the past three months were selected, with swabs taken from each individual for culture and 16S AS. DNA was isolated using a combination of bead beating and kit extraction. Samples were sequenced on the Illumina Hiseq 2500 platform. Results: Conventional laboratory culture showed positive growth from only 55 % of the patients, whereas 16S AS was positive for 75 % of the patients (41 unique genera, representing 82 different operational taxonomic units (OTU’s). S. aureus was isolated in 72 % of culture-positive samples, whereas the most commonly detected bacteria in all ulcers were Peptoniphilusspp., Anaerococcus spp. and Corynebacterium spp., with the addition of Staphylococcus spp. in new ulcers. The majority of OTU’s residing in both new and recurrent ulcers (over 67 %) were identified as facultative or strict anaerobic Gram-positive organisms. Principal component analysis (PCA) showed no difference in clustering between the two groups (new and recurrent ulcers). Conclusions: The abundance of anaerobic bacteria has important implications for treatment as it suggests that the microbiome of each ulcer “starts afresh” and that, although diverse, are not distinctly different from one another with respect to new or recurrent ulcers. Therefore, when considering antibiotic therapy the duration of current ulceration may be a more important consideration than a history of healed ulcer

Mapping and simulating systematics due to spatially-varying observing conditions in DES Science Verification data

Spatially-varying depth and characteristics of observing conditions, such as seeing, airmass, or sky background, are major sources of systematic uncertainties in modern galaxy survey analyses, in particular in deep multi-epoch surveys. We present a framework to extract and project these sources of systematics onto the sky, and apply it to the Dark Energy Survey (DES) to map the observing conditions of the Science Verification (SV) data. The resulting distributions and maps of sources of systematics are used in several analyses of DES SV to perform detailed null tests with the data, and also to incorporate systematics in survey simulations. We illustrate the complementarity of these two approaches by comparing the SV data with the BCC-UFig, a synthetic sky catalogue generated by forward-modelling of the DES SV images. We analyse the BCC-UFig simulation to construct galaxy samples mimicking those used in SV galaxy clustering studies. We show that the spatially-varying survey depth imprinted in the observed galaxy densities and the redshift distributions of the SV data are successfully reproduced by the simulation and well-captured by the maps of observing conditions. The combined use of the maps, the SV data and the BCC-UFig simulation allows us to quantify the impact of spatial systematics on $N(z)$, the redshift distributions inferred using photometric redshifts. We conclude that spatial systematics in the SV data are mainly due to seeing fluctuations and are under control in current clustering and weak lensing analyses. The framework presented here is relevant to all multi-epoch surveys, and will be essential for exploiting future surveys such as the Large Synoptic Survey Telescope (LSST), which will require detailed null-tests and realistic end-to-end image simulations to correctly interpret the deep, high-cadence observations of the sky

Pre-Stimulus Activity Predicts the Winner of Top-Down vs. Bottom-Up Attentional Selection

Our ability to process visual information is fundamentally limited. This leads to competition between sensory information that is relevant for top-down goals and sensory information that is perceptually salient, but task-irrelevant. The aim of the present study was to identify, from EEG recordings, pre-stimulus and pre-saccadic neural activity that could predict whether top-down or bottom-up processes would win the competition for attention on a trial-by-trial basis. We employed a visual search paradigm in which a lateralized low contrast target appeared alone, or with a low (i.e., non-salient) or high contrast (i.e., salient) distractor. Trials with a salient distractor were of primary interest due to the strong competition between top-down knowledge and bottom-up attentional capture. Our results demonstrated that 1) in the 1-sec pre-stimulus interval, frontal alpha (8–12 Hz) activity was higher on trials where the salient distractor captured attention and the first saccade (bottom-up win); and 2) there was a transient pre-saccadic increase in posterior-parietal alpha (7–8 Hz) activity on trials where the first saccade went to the target (top-down win). We propose that the high frontal alpha reflects a disengagement of attentional control whereas the transient posterior alpha time-locked to the saccade indicates sensory inhibition of the salient distractor and suppression of bottom-up oculomotor capture