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

Use of Antihypertensives, Blood Pressure, and Estimated Risk of Dementia in Late Life: An Individual Participant Data Meta-Analysis

Importance: The utility of antihypertensives and ideal blood pressure (BP) for dementia prevention in late life remains unclear and highly contested. Objectives: To assess the associations of hypertension history, antihypertensive use, and baseline measured BP in late life (age >60 years) with dementia and the moderating factors of age, sex, and racial group. Data Source and Study Selection: Longitudinal, population-based studies of aging participating in the Cohort Studies of Memory in an International Consortium (COSMIC) group were included. Participants were individuals without dementia at baseline aged 60 to 110 years and were based in 15 different countries (US, Brazil, Australia, China, Korea, Singapore, Central African Republic, Republic of Congo, Nigeria, Germany, Spain, Italy, France, Sweden, and Greece). Data Extraction and Synthesis: Participants were grouped in 3 categories based on previous diagnosis of hypertension and baseline antihypertensive use: healthy controls, treated hypertension, and untreated hypertension. Baseline systolic BP (SBP) and diastolic BP (DBP) were treated as continuous variables. Reporting followed the Preferred Reporting Items for Systematic Review and Meta-Analyses of Individual Participant Data reporting guidelines. Main Outcomes and Measures: The key outcome was all-cause dementia. Mixed-effects Cox proportional hazards models were used to assess the associations between the exposures and the key outcome variable. The association between dementia and baseline BP was modeled using nonlinear natural splines. The main analysis was a partially adjusted Cox proportional hazards model controlling for age, age squared, sex, education, racial group, and a random effect for study. Sensitivity analyses included a fully adjusted analysis, a restricted analysis of those individuals with more than 5 years of follow-up data, and models examining the moderating factors of age, sex, and racial group. Results: The analysis included 17 studies with 34 519 community dwelling older adults (20 160 [58.4%] female) with a mean (SD) age of 72.5 (7.5) years and a mean (SD) follow-up of 4.3 (4.3) years. In the main, partially adjusted analysis including 14 studies, individuals with untreated hypertension had a 42% increased risk of dementia compared with healthy controls (hazard ratio [HR], 1.42; 95% CI 1.15-1.76; P = .001) and 26% increased risk compared with individuals with treated hypertension (HR, 1.26; 95% CI, 1.03-1.53; P = .02). Individuals with treated hypertension had no significant increased dementia risk compared with healthy controls (HR, 1.13; 95% CI, 0.99-1.28; P = .07). The association of antihypertensive use or hypertension status with dementia did not vary with baseline BP. There was no significant association of baseline SBP or DBP with dementia risk in any of the analyses. There were no significant interactions with age, sex, or racial group for any of the analyses. Conclusions and Relevance: This individual patient data meta-analysis of longitudinal cohort studies found that antihypertensive use was associated with decreased dementia risk compared with individuals with untreated hypertension through all ages in late life. Individuals with treated hypertension had no increased risk of dementia compared with healthy controls

Olfactory discrimination predicts cognitive decline among community-dwelling older adults

The presence of olfactory dysfunction in individuals at higher risk of Alzheimer's disease has significant diagnostic and screening implications for preventive and ameliorative drug trials. Olfactory threshold, discrimination and identification can be reliably recorded in the early stages of neurodegenerative diseases. The current study has examined the ability of various olfactory functions in predicting cognitive decline in a community-dwelling sample. A group of 308 participants, aged 46–86 years old, were recruited for this study. After 3 years of follow-up, participants were divided into cognitively declined and non-declined groups based on their performance on a neuropsychological battery. Assessment of olfactory functions using the Sniffin' Sticks battery indicated that, contrary to previous findings, olfactory discrimination, but not olfactory identification, significantly predicted subsequent cognitive decline (odds ratio=0.869; P<0.05; 95% confidence interval=0.764−0.988). The current study findings confirm previously reported associations between olfactory and cognitive functions, and indicate that impairment in olfactory discrimination can predict future cognitive decline. These findings further our current understanding of the association between cognition and olfaction, and support olfactory assessment in screening those at higher risk of dementia

Heterologous Expression of Membrane Proteins: Choosing the Appropriate Host

International audienceBACKGROUND: Membrane proteins are the targets of 50% of drugs, although they only represent 1% of total cellular proteins. The first major bottleneck on the route to their functional and structural characterisation is their overexpression; and simply choosing the right system can involve many months of trial and error. This work is intended as a guide to where to start when faced with heterologous expression of a membrane protein. METHODOLOGY/PRINCIPAL FINDINGS: The expression of 20 membrane proteins, both peripheral and integral, in three prokaryotic (E. coli, L. lactis, R. sphaeroides) and three eukaryotic (A. thaliana, N. benthamiana, Sf9 insect cells) hosts was tested. The proteins tested were of various origins (bacteria, plants and mammals), functions (transporters, receptors, enzymes) and topologies (between 0 and 13 transmembrane segments). The Gateway system was used to clone all 20 genes into appropriate vectors for the hosts to be tested. Culture conditions were optimised for each host, and specific strategies were tested, such as the use of Mistic fusions in E. coli. 17 of the 20 proteins were produced at adequate yields for functional and, in some cases, structural studies. We have formulated general recommendations to assist with choosing an appropriate system based on our observations of protein behaviour in the different hosts. CONCLUSIONS/SIGNIFICANCE: Most of the methods presented here can be quite easily implemented in other laboratories. The results highlight certain factors that should be considered when selecting an expression host. The decision aide provided should help both newcomers and old-hands to select the best system for their favourite membrane protein

The primary and recycling sources of OH during the NACHTT-2011 campaign: HONO as an important OH primary source in the wintertime

We present OH observations from Nitrogen, Aerosol Composition, and Halogens on a Tall Tower 2011 (NACHTT-11) held at the Boulder Atmospheric Observatory in Weld County, Colorado. Average OH levels at noon were ~ 2.7 × 106 molecules cm-3 at 2 m above ground level. Nitrous acid (HONO) photolysis was the dominant OH source (80.4%) during this campaign, while alkene ozonolysis (4.9%) and ozone photolysis (14.7%) were smaller contributions to OH production. To evaluate recycling sources of OH from HO2 and RO2, an observationally constrained University of Washington Chemical Mechanism (UWCM) box model (version 2.1) was employed to simulate ambient OH levels over several scenarios. For the base run, not constrained by observed HONO, the model significantly underestimated OH by a factor of 5.3 in the morning (9:00–11:00) and by a factor of 3.2 in the afternoon (13:00–15:00). The results suggest that known chemistry cannot constrain HONO and, subsequently, OH during the observational period. When HONO is constrained in the model by observations (&lt; 50 m), the discrepancy between observation and model simulation improves to a factor of 1.3 in the morning and a factor 1.1 in the afternoon, within the 35% estimated instrumental uncertainty. However, the model produces both a morning and afternoon maximum in OH, in contrast to the observations, which show strong evidence for morning OH production but no distinct morning maximum. Two additional OH sources were also considered, although they do not improve the differences in modeled and measured temporal OH profiles. First, the impact of daytime HONO gradients near the ground surface (&lt; 20 m) was evaluated. Strong HONO gradients were observed between 06:00 and 09:00 MST (mountain standard time), especially within 20 m of the surface. When constrained to HONO observed below 20 m (rather than 50 m), the model produced an even larger morning OH maximum, in contrast to the observations. Second, Cl atoms from ClNO2 photolysis producing RO2 from reaction with alkanes, while significant, produced steady state Cl atom levels (~ 103 atoms cm3) that were too low to significantly perturb measured OH through reactions of organic peroxy radicals produced from Cl reactions with volatile organic compounds