On the (parameterized) complexity of recognizing well-covered (r,l)-graphs.

An (r,ℓ)(r,ℓ)-partition of a graph G is a partition of its vertex set into r independent sets and ℓℓ cliques. A graph is (r,ℓ)(r,ℓ) if it admits an (r,ℓ)(r,ℓ)-partition. A graph is well-covered if every maximal independent set is also maximum. A graph is (r,ℓ)(r,ℓ)-well-covered if it is both (r,ℓ)(r,ℓ) and well-covered. In this paper we consider two different decision problems. In the (r,ℓ)(r,ℓ)-Well-Covered Graph problem ((r,ℓ)(r,ℓ) wcg for short), we are given a graph G, and the question is whether G is an (r,ℓ)(r,ℓ)-well-covered graph. In the Well-Covered (r,ℓ)(r,ℓ)-Graph problem (wc (r,ℓ)(r,ℓ) g for short), we are given an (r,ℓ)(r,ℓ)-graph G together with an (r,ℓ)(r,ℓ)-partition of V(G) into r independent sets and ℓℓ cliques, and the question is whether G is well-covered. We classify most of these problems into P, coNP-complete, NP-complete, NP-hard, or coNP-hard. Only the cases wc(r, 0)g for r≥3r≥3 remain open. In addition, we consider the parameterized complexity of these problems for several choices of parameters, such as the size αα of a maximum independent set of the input graph, its neighborhood diversity, or the number ℓℓ of cliques in an (r,ℓ)(r,ℓ)-partition. In particular, we show that the parameterized problem of deciding whether a general graph is well-covered parameterized by αα can be reduced to the wc (0,ℓ)(0,ℓ) g problem parameterized by ℓℓ, and we prove that this latter problem is in XP but does not admit polynomial kernels unless coNP⊆NP/polycoNP⊆NP/poly

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

Interaction Between Convection and Pulsation

This article reviews our current understanding of modelling convection dynamics in stars. Several semi-analytical time-dependent convection models have been proposed for pulsating one-dimensional stellar structures with different formulations for how the convective turbulent velocity field couples with the global stellar oscillations. In this review we put emphasis on two, widely used, time-dependent convection formulations for estimating pulsation properties in one-dimensional stellar models. Applications to pulsating stars are presented with results for oscillation properties, such as the effects of convection dynamics on the oscillation frequencies, or the stability of pulsation modes, in classical pulsators and in stars supporting solar-type oscillations.Comment: Invited review article for Living Reviews in Solar Physics. 88 pages, 14 figure

Evaluation of the Widal tube agglutination test for the diagnosis of typhoid fever among children admitted to a rural hdospital in Tanzania and a comparison with previous studies

BACKGROUND: The diagnosis of typhoid fever is confirmed by culture of Salmonella enterica serotype Typhi (S. typhi). However, a more rapid, simpler, and cheaper diagnostic method would be very useful especially in developing countries. The Widal test is widely used in Africa but little information exists about its reliability. METHODS: We assessed the performance of the Widal tube agglutination test among febrile hospitalized Tanzanian children. We calculated the sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV) of various anti-TH and -TO titers using culture-confirmed typhoid fever cases as the "true positives" and all other febrile children with blood culture negative for S. typhi as the "true negatives." RESULTS: We found that 16 (1%) of 1,680 children had culture-proven typhoid fever. A single anti-TH titer of 1:80 and higher was the optimal indicator of typhoid fever. This had a sensitivity of 75%, specificity of 98%, NPV of 100%, but PPV was only 26%. We compared our main findings with those from previous studies. CONCLUSION: Among febrile hospitalized Tanzanian children with a low prevalence of typhoid fever, a Widal titer of > or = 1:80 performed well in terms of sensitivity, specificity, and NPV. However a test with improved PPV that is similarly easy to apply and cost-efficient is desirable

Role of carbon cycle observations and knowledge in carbon management

Author Posting. © Annual Reviews, 2003. This article is posted here by permission of Annual Reviews for personal use, not for redistribution. The definitive version was published in Annual Review of Environment and Resources 28 (2003): 521-558, doi:10.1146/annurev.energy.28.011503.163443.Agriculture and industrial development have led to inadvertent changes in the natural carbon cycle. As a consequence, concentrations of carbon dioxide and other greenhouse gases have increased in the atmosphere and may lead to changes in climate. The current challenge facing society is to develop options for future management of the carbon cycle. A variety of approaches has been suggested: direct reduction of emissions, deliberate manipulation of the natural carbon cycle to enhance sequestration, and capture and isolation of carbon from fossil fuel use. Policy development to date has laid out some of the general principles to which carbon management should adhere. These are summarized as: how much carbon is stored, by what means, and for how long. To successfully manage carbon for climate purposes requires increased understanding of carbon cycle dynamics and improvement in the scientific capabilities available for measurement as well as for policy needs. The specific needs for scientific information to underpin carbon cycle management decisions are not yet broadly known. A stronger dialogue between decision makers and scientists must be developed to foster improved application of scientific knowledge to decisions. This review focuses on the current knowledge of the carbon cycle, carbon measurement capabilities (with an emphasis on the continental scale) and the relevance of carbon cycle science to carbon sequestration goals.The National Center for Atmospheric Research is supported by the National Science Foundation

Measurement of proton, deuteron, triton, and alpha particle emission after nuclear muon capture on Al, Si, and Ti with the AlCap experiment

Background: Heavy charged particles after nuclear muon capture are an important nuclear physics background to the muon-to-electron conversion experiments Mu2e and COMET, which will search for charged lepton flavor violation at an unprecedented level of sensitivity. Purpose: The AlCap experiment aimed to measure the yield and energy spectra of protons, deuterons, tritons, and α particles emitted after the nuclear capture of muons stopped in Al, Si, and Ti in the low-energy range relevant for the muon-to-electron conversion experiments. Methods: Individual charged particle types were identified in layered silicon detector packages and their initial energy distributions were unfolded from the observed energy spectra. Results: The proton yields per muon capture were determined as Y p ( Al ) = 26.64 ( 28 stat. ) ( 77 syst. ) × 10 − 3 and Y p ( Ti ) = 26.48 ( 35 ) ( 80 ) × 10 − 3 in the energy range 3.5–20.0 MeV, and as Y p ( Si ) = 52.5 ( 6 ) ( 18 ) × 10 − 3 in the energy range 4.0–20.0 MeV. Detailed information on yields and energy spectra for all observed nuclei are presented in the paper. Conclusions: The yields in the candidate muon stopping targets, Al and Ti, are approximately half of that in Si, which was used in the past to estimate this background. The reduced background allows for less shielding and a better energy resolution in these experiments. It is anticipated that the comprehensive information presented in this paper will stimulate modern theoretical calculations of the rare process of muon capture with charged particle emission and inform the design of future muon-to-electron conversion experiments

Mitochondrial Disease in Autism Spectrum Disorder Patients: A Cohort Analysis

Previous reports indicate an association between autism spectrum disorders (ASD) and disorders of mitochondrial oxidative phosphorylation. One study suggested that children with both diagnoses are clinically indistinguishable from children with idiopathic autism. There are, however, no detailed analyses of the clinical and laboratory findings in a large cohort of these children. Therefore, we undertook a comprehensive review of patients with ASD and a mitochondrial disorder.We reviewed medical records of 25 patients with a primary diagnosis of ASD by DSM-IV-TR criteria, later determined to have enzyme- or mutation-defined mitochondrial electron transport chain (ETC) dysfunction. Twenty-four of 25 patients had one or more major clinical abnormalities uncommon in idiopathic autism. Twenty-one patients had histories of significant non-neurological medical problems. Nineteen patients exhibited constitutional symptoms, especially excessive fatigability. Fifteen patients had abnormal neurological findings. Unusual developmental phenotypes included marked delay in early gross motor milestones (32%) and unusual patterns of regression (40%). Levels of blood lactate, plasma alanine, and serum ALT and/or AST were increased at least once in 76%, 36%, and 52% of patients, respectively. The most common ETC disorders were deficiencies of complex I (64%) and complex III (20%). Two patients had rare mtDNA mutations of likely pathogenicity.Although all patients' initial diagnosis was idiopathic autism, careful clinical and biochemical assessment identified clinical findings that differentiated them from children with idiopathic autism. These and prior data suggest a disturbance of mitochondrial energy production as an underlying pathophysiological mechanism in a subset of individuals with autism