Eisenstein series and automorphic representations

We provide an introduction to the theory of Eisenstein series and automorphic forms on real simple Lie groups G, emphasising the role of representation theory. It is useful to take a slightly wider view and define all objects over the (rational) adeles A, thereby also paving the way for connections to number theory, representation theory and the Langlands program. Most of the results we present are already scattered throughout the mathematics literature but our exposition collects them together and is driven by examples. Many interesting aspects of these functions are hidden in their Fourier coefficients with respect to unipotent subgroups and a large part of our focus is to explain and derive general theorems on these Fourier expansions. Specifically, we give complete proofs of the Langlands constant term formula for Eisenstein series on adelic groups G(A) as well as the Casselman--Shalika formula for the p-adic spherical Whittaker function associated to unramified automorphic representations of G(Q_p). In addition, we explain how the classical theory of Hecke operators fits into the modern theory of automorphic representations of adelic groups, thereby providing a connection with some key elements in the Langlands program, such as the Langlands dual group LG and automorphic L-functions. Somewhat surprisingly, all these results have natural interpretations as encoding physical effects in string theory. We therefore also introduce some basic concepts of string theory, aimed toward mathematicians, emphasising the role of automorphic forms. In particular, we provide a detailed treatment of supersymmetry constraints on string amplitudes which enforce differential equations of the same type that are satisfied by automorphic forms. Our treatise concludes with a detailed list of interesting open questions and pointers to additional topics which go beyond the scope of this book.Comment: 326 pages. Detailed and example-driven exposition of the subject with highlighted applications to string theory. v2: 375 pages. Substantially extended and small correction

User's guide for the Total-Ozone Mapping Spectrometer (TOMS) instrument first year ozone T data set

The TOMS experiment and algorithms are described. Detailed information on the data available on computer tape is provided

User's guide for SBUV/TOMS ozone derivative products

A series of products are available derived from the total-ozone and ozone vertical profile results for the Solar Backscattered Ultraviolet/Total-Ozone Mapping Spectrometer (SBUV/TOMS) Nimbus-7 operation. Products available are (1) orbital height-latitude cross sections of the SBUV profile data, (2) daily global total ozone contours in polar coordinates, (3) daily averages of total ozone in global 5x5 degree latitude-longitude grid, (4) daily, monthly and quarterly averages of total ozone and profile data in 10 degree latitude zones, (5) tabular presentation of zonal means, (6) daily global total ozone and profile contours in polar coordinates. The ""Derivative Products User's Guide'' describes each of these products in detail, including their derivation and presentation format. Information is provided on how to order the tapes and microfilm from the National Space Science Data Center

User's guide for the Solar Backscattered Ultraviolet (SBUV) instrument first year ozone-S data set

Total-ozone and ozone vertical profile results for Solar Backscattered Ultraviolet/Total Ozone Mapping Spectrometer (SBUV/TOMS) Nimbus 7 operation from November 1978 to November 1979 are available. The algorithm used have been thoroughly tested, the instrument performance has been examined in details, and the ozone results have been compared with Dobson, Umkehr, balloon, and rocket observations. The accuracy and precision of the satellite ozone data are good to at least within the ability of the ground truth to check and are self-consistent to within the specifications of the instrument. The 'SBUV User's Guide' describes the SBUV experiment and algorithms used. Detailed information on the data available on computer tape is provided including how to order tapes from the National Space Science Data Center

Stochastic semi-continuous simulation for extreme flood estimation in catchments with combined rainfall–snowmelt flood regimes

Simulation methods for extreme flood estimation represent an important complement to statistical flood frequency analysis because a spectrum of catchment conditions potentially leading to extreme flows can be assessed. In this paper, stochastic, semi-continuous simulation is used to estimate extreme floods in three catchments located in Norway, all of which are characterised by flood regimes in which snowmelt often has a significant role. The simulations are based on SCHADEX, which couples a precipitation probabilistic model with a hydrological simulation such that an exhaustive set of catchment conditions and responses is simulated. The precipitation probabilistic model is conditioned by regional weather patterns, and a bottom–up classification procedure was used to define a set of weather patterns producing extreme precipitation in Norway. SCHADEX estimates for the 1000-year (Q1000) discharge are compared with those of several standard methods, including event-based and long-term simulations which use a single extreme precipitation sequence as input to a hydrological model, statistical flood frequency analysis based on the annual maximum series, and the GRADEX method. The comparison suggests that the combination of a precipitation probabilistic model with a long-term simulation of catchment conditions, including snowmelt, produces estimates for given return periods which are more in line with those based on statistical flood frequency analysis, as compared with the standard simulation methods, in two of the catchments. In the third case, the SCHADEX method gives higher estimates than statistical flood frequency analysis and further suggests that the seasonality of the most likely Q1000 events differs from that of the annual maximum flows. The semi-continuous stochastic simulation method highlights the importance of considering the joint probability of extreme precipitation, snowmelt rates and catchment saturation states when assigning return periods to floods estimated by precipitation-runoff methods. The SCHADEX methodology, as applied here, is dependent on observed discharge data for calibration of a hydrological model, and further study to extend its application to ungauged catchments would significantly enhance its versatility

The PPIP5K Family Member Asp1 Controls Inorganic Polyphosphate Metabolism in S. pombe

Inorganic polyphosphate (polyP) which is ubiquitously present in both prokaryotic and eukaryotic cells, consists of up to hundreds of orthophosphate residues linked by phosphoanhydride bonds. The biological role of this polymer is manifold and diverse and in fungi ranges from cell cycle control, phosphate homeostasis and virulence to post-translational protein modification. Control of polyP metabolism has been studied extensively in the budding yeast Saccharomyces cerevisiae. In this yeast, a specific class of inositol pyrophosphates (IPPs), named IP7, made by the IP6K family member Kcs1 regulate polyP synthesis by associating with the SPX domains of the vacuolar transporter chaperone (VTC) complex. To assess if this type of regulation was evolutionarily conserved, we determined the elements regulating polyP generation in the distantly related fission yeast Schizosaccharomyces pombe. Here, the VTC machinery is also essential for polyP generation. However, and in contrast to S. cerevisiae, a different IPP class generated by the bifunctional PPIP5K family member Asp1 control polyP metabolism. The analysis of Asp1 variant S. pombe strains revealed that cellular polyP levels directly correlate with Asp1-made IP8 levels, demonstrating a dose-dependent regulation. Thus, while the mechanism of polyP synthesis in yeasts is conserved, the IPP player regulating polyP metabolism is diverse

Eisenstein series and automorphic representations

We provide an introduction to the theory of Eisenstein series and automorphic forms on real simple Lie groups G, emphasising the role of representation theory. It is useful to take a slightly wider view and define all objects over the (rational) adeles A, thereby also paving the way for connections to number theory, representation theory and the Langlands program. Most of the results we present are already scattered throughout the mathematics literature but our exposition collects them together and is driven by examples. Many interesting aspects of these functions are hidden in their Fourier coefficients with respect to unipotent subgroups and a large part of our focus is to explain and derive general theorems on these Fourier expansions. Specifically, we give complete proofs of Langlands' constant term formula for Eisenstein series on adelic groups G(A) as well as the Casselman--Shalika formula for the p-adic spherical Whittaker vector associated to unramified automorphic representations of G(Q_p). Somewhat surprisingly, all these results have natural interpretations as encoding physical effects in string theory. We therefore introduce also some basic concepts of string theory, aimed toward mathematicians, emphasising the role of automorphic forms. In addition, we explain how the classical theory of Hecke operators fits into the modern theory of automorphic representations of adelic groups, thereby providing a connection with some key elements in the Langlands program, such as the Langlands dual group LG and automorphic L-functions. Our treatise concludes with a detailed list of interesting open questions and pointers to additional topics where automorphic forms occur in string theory

Translation, cross-cultural adaptation, and reliability of the Understanding COPD questionnaire for use in Brazil

ABSTRACT Objective: To translate the Understanding COPD (UCOPD) questionnaire into Portuguese, adapt it for use in Brazil, and assess its reliability. Methods: The UCOPD questionnaire consists of two sections, designated section A and section B. Section A comprises 18 items divided into three domains: “About COPD”, “Managing Symptoms of COPD”, and “Accessing Help and Support”. Section B includes five questions regarding patient satisfaction with the educational component of pulmonary rehabilitation programs. The UCOPD questionnaire was applied twice on the same day by two different raters (with a 10-min interval between applications) and once again 15-20 days later. The Wilcoxon test was used in order to compare the scores among applications. Reliability was assessed by the intraclass correlation coefficient and Bland-Altman plots. Results: The study sample consisted of 50 COPD patients (35 men; mean age, 65.3 ± 7.91 years; mean FEV1, 36.4 ± 16.2% of the predicted value). Inter-rater intraclass correlation coefficients for section A total scores and domain scores ranged from moderate to high. Section A scores and domain scores had no significant differences regarding test-retest reliability (p < 0.05). The test-retest and inter-rater Cronbach’s alpha coefficients for section A total scores were 0.93 and 0.86, respectively (p < 0.001). There were no floor or ceiling effects. Conclusions: The Brazilian Portuguese version of the UCOPD questionnaire is reliable

User's guide for the Solar Backscattered Ultraviolet (SBUV) and the Total Ozone Mapping Spectrometer (TOMS) RUT-S and RUT-T data sets: October 31, 1978 to November 1, 1980

Raw data from the Solar Backscattered Ultrviolet/Total Ozone Mapping Spectrometer (SBUV/TOMS) Nimbus 7 operation are available on computer tape. These data are contained on two separate sets of RUTs (Raw Units Tapes) for SBUV and TOMS, labelled RUT-S and RUT-T respectively. The RUT-S and RUT-T tapes contain uncalibrated radiance and irradiance data, housekeeping data, wavelength and electronic calibration data, instrument field-of-view location and solar ephemeris information. These tapes also contain colocated cloud, terrain pressure and snow/ice thickness data, each derived from an independent source. The "RUT User's Guide" describes the SBUV and TOMS experiments, the instrument calibration and performance, operating schedules, and data coverage, and provides an assessment of RUT-S and -T data quality. It also provides detailed information on the data available on the computer tapes