Operator theory and function theory in Drury-Arveson space and its quotients

The Drury-Arveson space $H^2_d$, also known as symmetric Fock space or the $d$-shift space, is a Hilbert function space that has a natural $d$-tuple of operators acting on it, which gives it the structure of a Hilbert module. This survey aims to introduce the Drury-Arveson space, to give a panoramic view of the main operator theoretic and function theoretic aspects of this space, and to describe the universal role that it plays in multivariable operator theory and in Pick interpolation theory.Comment: Final version (to appear in Handbook of Operator Theory); 42 page

Exoplanet Atmosphere Measurements from Transmission Spectroscopy and other Planet-Star Combined Light Observations

It is possible to learn a great deal about exoplanet atmospheres even when we cannot spatially resolve the planets from their host stars. In this chapter, we overview the basic techniques used to characterize transiting exoplanets - transmission spectroscopy, emission and reflection spectroscopy, and full-orbit phase curve observations. We discuss practical considerations, including current and future observing facilities and best practices for measuring precise spectra. We also highlight major observational results on the chemistry, climate, and cloud properties of exoplanets.Comment: Accepted review chapter; Handbook of Exoplanets, eds. Hans J. Deeg and Juan Antonio Belmonte (Springer-Verlag). 22 pages, 6 figure

Vitamin D Receptor Gene Polymorphisms Modify Cardiometabolic Response to Vitamin D Supplementation in T2DM Patients

There is conflicting evidence on the favorable effects of vitamin D supplementation on metabolic profile in Type 2 diabetes mellitus (T2DM) patients and this might be due to genetic variations in vitamin D receptors (VDRs). Thus, we studied the metabolic effects of a 12-month vitamin D supplementation in T2DM patients according to VDR polymorphisms. A total of 204 T2DM subjects received 2000 IU vitamin D3 daily for 12 months. Serum 25(OH)D and metabolic profiles were measured at baseline and after 12 months. VDR polymorphisms (Taq-I, Bsm-I, Apa-I and Fok-I) were identified using TaqMan genotyping assays. Vitamin D supplementation significantly increased HOMA β-cell function (p = 0.003) as well as significantly decreased triglycerides, total and LDL-cholesterol (p < 0.001). The lowest increment in 25(OH)D levels was detected in patients with Fok-I CC genotypes (p < 0.0001). With vitamin D supplementation, Taq-I GG genotype carriers showed significant improvements in triglycerides, LDL- and total cholesterol, insulin, HbA1c and HOMA-IR (p < 0.005, 0.01, < 0.001, < 0.005, 0.03 and 0.01, respectively). Similarly, Bsm-I TT genotype carriers showed significant improvements in triglycerides (p = 0.01), insulin and HOMA-IR (p-values < 0.05). In conclusion, improvements in metabolic profile due to vitamin D supplementation is influenced by VDR polymorphisms, specifically for carriers of Taq-I GG and Bsm-I TT genotypes

The Cosmological Baryon Density from the Deuterium Abundance at a redshift z = 3.57

We present a measurement of the deuterium to hydrogen ratio in a quasar absorption system at redshift z = 3.57 towards QSO 1937-1009. We use a two component fit, with redshifts determined from unsaturated metal lines, to fit the hydrogen and deuterium features simultaneously. We find a low value of D/H = 2.3 \pm 0.6 \times 10^{-5}, which does not agree with other measurements of high D/H (Songaila et al. 1994, Carswell et al. 1994). The absorption system is very metal poor, with metallicities less than 1/100 solar. Standard models of chemical evolution show the astration of deuterium is limited to a few percent from primordial for systems this metal-poor, so we believe our value represents the primordial one. Using predictions of standard big-bang nucleosynthesis and measurements of the cosmic microwave background, our measurement gives the density of baryons in units of the critical density, $\Omega_b h^2 = 0.024 \pm 0.006$, where H_0 = 100 h km s^{-1] Mpc^{-1}.Comment: 10 pages, 2 Figures, also available at http://nately.ucsd.edu/ ; submitted to Natur

Anthropometric measures in relation to Basal Cell Carcinoma: a longitudinal study

BACKGROUND: The relationship between anthropometric indices and risk of basal cell carcinoma (BCC) is largely unknown. We aimed to examine the association between anthropometric measures and development of BCC and to demonstrate whether adherence to World Health Organisation guidelines for body mass index, waist circumference, and waist/hip ratio was associated with risk of BCC, independent of sun exposure. METHODS: Study participants were participants in a community-based skin cancer prevention trial in Nambour, a town in southeast Queensland (latitude 26°S). In 1992, height, weight, and waist and hip circumferences were measured for all 1621 participants and weight was remeasured at the end of the trial in 1996. Prevalence proportion ratios were calculated using a log-binomial model to estimate the risk of BCC prior to or prevalent in 1992, while Poisson regression with robust error variances was used to estimate the relative risk of BCC during the follow-up period. RESULTS: At baseline, 94 participants had a current BCC, and 202 had a history of BCC. During the 5-year follow-up period, 179 participants developed one or more new BCCs. We found no significant association between any of the anthropometric measures or indices and risk of BCC after controlling for potential confounding factors including sun exposure. There was a suggestion that short-term weight gain may increase the risk of developing BCC for women only. CONCLUSION: Adherence to World Health Organisation guidelines for body mass index, waist circumference and waist/hip ratio is not significantly associated with occurrence of basal cell carcinomas of the skin

A chemical survey of exoplanets with ARIEL

Thousands of exoplanets have now been discovered with a huge range of masses, sizes and orbits: from rocky Earth-like planets to large gas giants grazing the surface of their host star. However, the essential nature of these exoplanets remains largely mysterious: there is no known, discernible pattern linking the presence, size, or orbital parameters of a planet to the nature of its parent star. We have little idea whether the chemistry of a planet is linked to its formation environment, or whether the type of host star drives the physics and chemistry of the planet’s birth, and evolution. ARIEL was conceived to observe a large number (~1000) of transiting planets for statistical understanding, including gas giants, Neptunes, super-Earths and Earth-size planets around a range of host star types using transit spectroscopy in the 1.25–7.8 μm spectral range and multiple narrow-band photometry in the optical. ARIEL will focus on warm and hot planets to take advantage of their well-mixed atmospheres which should show minimal condensation and sequestration of high-Z materials compared to their colder Solar System siblings. Said warm and hot atmospheres are expected to be more representative of the planetary bulk composition. Observations of these warm/hot exoplanets, and in particular of their elemental composition (especially C, O, N, S, Si), will allow the understanding of the early stages of planetary and atmospheric formation during the nebular phase and the following few million years. ARIEL will thus provide a representative picture of the chemical nature of the exoplanets and relate this directly to the type and chemical environment of the host star. ARIEL is designed as a dedicated survey mission for combined-light spectroscopy, capable of observing a large and well-defined planet sample within its 4-year mission lifetime. Transit, eclipse and phase-curve spectroscopy methods, whereby the signal from the star and planet are differentiated using knowledge of the planetary ephemerides, allow us to measure atmospheric signals from the planet at levels of 10–100 part per million (ppm) relative to the star and, given the bright nature of targets, also allows more sophisticated techniques, such as eclipse mapping, to give a deeper insight into the nature of the atmosphere. These types of observations require a stable payload and satellite platform with broad, instantaneous wavelength coverage to detect many molecular species, probe the thermal structure, identify clouds and monitor the stellar activity. The wavelength range proposed covers all the expected major atmospheric gases from e.g. H2O, CO2, CH4 NH3, HCN, H2S through to the more exotic metallic compounds, such as TiO, VO, and condensed species. Simulations of ARIEL performance in conducting exoplanet surveys have been performed – using conservative estimates of mission performance and a full model of all significant noise sources in the measurement – using a list of potential ARIEL targets that incorporates the latest available exoplanet statistics. The conclusion at the end of the Phase A study, is that ARIEL – in line with the stated mission objectives – will be able to observe about 1000 exoplanets depending on the details of the adopted survey strategy, thus confirming the feasibility of the main science objectives.Peer reviewedFinal Published versio

Modeling autosomal dominant Alzheimer's disease with machine learning

INTRODUCTION: Machine learning models were used to discover novel disease trajectories for autosomal dominant Alzheimer's disease. METHODS: Longitudinal structural magnetic resonance imaging, amyloid positron emission tomography (PET), and fluorodeoxyglucose PET were acquired in 131 mutation carriers and 74 non-carriers from the Dominantly Inherited Alzheimer Network; the groups were matched for age, education, sex, and apolipoprotein ε4 (APOE ε4). A deep neural network was trained to predict disease progression for each modality. Relief algorithms identified the strongest predictors of mutation status. RESULTS: The Relief algorithm identified the caudate, cingulate, and precuneus as the strongest predictors among all modalities. The model yielded accurate results for predicting future Pittsburgh compound B (R2  = 0.95), fluorodeoxyglucose (R2  = 0.93), and atrophy (R2  = 0.95) in mutation carriers compared to non-carriers. DISCUSSION: Results suggest a sigmoidal trajectory for amyloid, a biphasic response for metabolism, and a gradual decrease in volume, with disease progression primarily in subcortical, middle frontal, and posterior parietal regions

Neural networks for genetic epidemiology: past, present, and future

During the past two decades, the field of human genetics has experienced an information explosion. The completion of the human genome project and the development of high throughput SNP technologies have created a wealth of data; however, the analysis and interpretation of these data have created a research bottleneck. While technology facilitates the measurement of hundreds or thousands of genes, statistical and computational methodologies are lacking for the analysis of these data. New statistical methods and variable selection strategies must be explored for identifying disease susceptibility genes for common, complex diseases. Neural networks (NN) are a class of pattern recognition methods that have been successfully implemented for data mining and prediction in a variety of fields. The application of NN for statistical genetics studies is an active area of research. Neural networks have been applied in both linkage and association analysis for the identification of disease susceptibility genes

A continuum from clear to cloudy hot-Jupiter exoplanets without primordial water depletion

Thousands of transiting exoplanets have been discovered, but spectral analysis of their atmospheres has so far been dominated by a small number of exoplanets and data spanning relatively narrow wavelength ranges (such as 1.1–1.7 micrometres). Recent studies show that some hot-Jupiter exoplanets have much weaker water absorption features in their near-infrared spectra than predicted. The low amplitude of water signatures could be explained by very low water abundances, which may be a sign that water was depleted in the protoplanetary disk at the planet’s formation location, but it is unclear whether this level of depletion can actually occur. Alternatively, these weak signals could be the result of obscuration by clouds or hazes, as found in some optical spectra. Here we report results from a comparative study of ten hot Jupiters covering the wavelength range 0.3–5 micrometres, which allows us to resolve both the optical scattering and infrared molecular absorption spectroscopically. Our results reveal a diverse group of hot Jupiters that exhibit a continuum from clear to cloudy atmospheres. We find that the difference between the planetary radius measured at optical and infrared wavelengths is an effective metric for distinguishing different atmosphere types. The difference correlates with the spectral strength of water, so that strong water absorption lines are seen in clear-atmosphere planets and the weakest features are associated with clouds and hazes. This result strongly suggests that primordial water depletion during formation is unlikely and that clouds and hazes are the cause of weaker spectral signatures

Atmospheric retrieval of exoplanets

Exoplanetary atmospheric retrieval refers to the inference of atmospheric properties of an exoplanet given an observed spectrum. The atmospheric properties include the chemical compositions, temperature profiles, clouds/hazes, and energy circulation. These properties, in turn, can provide key insights into the atmospheric physicochemical processes of exoplanets as well as their formation mechanisms. Major advancements in atmospheric retrieval have been made in the last decade, thanks to a combination of state-of-the-art spectroscopic observations and advanced atmospheric modeling and statistical inference methods. These developments have already resulted in key constraints on the atmospheric H2O abundances, temperature profiles, and other properties for several exoplanets. Upcoming facilities such as the JWST will further advance this area. The present chapter is a pedagogical review of this exciting frontier of exoplanetary science. The principles of atmospheric retrievals of exoplanets are discussed in detail, including parametric models and statistical inference methods, along with a review of key results in the field. Some of the main challenges in retrievals with current observations are discussed along with new directions and the future landscape