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

Nimbus 7 Solar Backscatter Ultraviolet (SBUV) spectral scan solar irradiance and Earth radiance product user's guide

The archived tape products from the spectral scan mode measurements of solar irradiance (SUNC tapes) and Earth radiance (EARTH tapes) by the Solar Backscatter UV (SBUV) instrument aboard Nimbus 7 are described. Incoming radiation from 160 to 400 nm is measured at intervals of 0.2 nm. The scan-to-scan repeatability of the solar irradiance measurements ranges from approximately 0.5 to 1 percent longward of 280 nm, to 2 percent around 210 nm and 4 percent near 175 nm. The repeatability of the Earth radiance values ranges from 2 to 3 percent at longer wavelengths and low zenith angles to 10 percent at shorter wavelengths and high zenith angles. The tape formats are described in detail, including file structure and contents of each type of record. Catalogs of the tapes and the time period covered are provided, along with lists of the days lacking solar irradiance measurements and the days dedicated to Earth radiance measurements. The method for production of the tapes is outlined and quality control measures are described. How radiances and irradiances are derived from the raw counts, the corrections for changes in instrument sensitivity, and related uncertainties are discussed

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

Emergence of behavior in a self-organized living matter network

What is the origin of behavior? Although typically associated with a nervous system, simple life forms also show complex behavior – thus serving as a model to study how behaviors emerge. Among them, the slime mold Physarum polycephalum, growing as a single giant cell, is renowned for its sophisticated behavior. Here, we show how locomotion and morphological adaptation behavior emerge from self-organized patterns of rhythmic contractions of the actomyosin lining of the tubes making up the network-shaped organism. We quantify the spatio-temporal contraction dynamics by decomposing experimentally recorded contraction patterns into spatial contraction modes. Surprisingly, we find a continuous spectrum of modes, as opposed to few dominant modes. Over time, activation of modes along this continuous spectrum is highly dynamic, resulting in contraction patterns of varying regularity. We show that regular patterns are associated with stereotyped behavior by triggering a behavioral response with a food stimulus. Furthermore, we demonstrate that the continuous spectrum of modes and the existence of irregular contraction patterns persist in specimens with a morphology as simple as a single tube. Our data suggests that the continuous spectrum of modes allows for dynamic transitions between a plethora of specific behaviors with transitions marked by highly irregular contraction states. By mapping specific behaviors to states of active contractions, we provide the basis to understand behavior’s complexity as a function of biomechanical dynamics. This perspective will likely stimulate bio-inspired design of soft robots with a similarly rich behavioral repertoire as P. polycephalum

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

Nimbus 7 solar backscatter ultraviolet (SBUV) ozone products user's guide

Three ozone tape products from the Solar Backscatter Ultraviolet (SBUV) experiment aboard Nimbus 7 were archived at the National Space Science Data Center. The experiment measures the fraction of incoming radiation backscattered by the Earth's atmosphere at 12 wavelengths. In-flight measurements were used to monitor changes in the instrument sensitivity. Total column ozone is derived by comparing the measurements with calculations of what would be measured for different total ozone amounts. The altitude distribution is retrieved using an optimum statistical technique for the inversion. The estimated initial error in the absolute scale for total ozone is 2 percent, with a 3 percent drift over 8 years. The profile error depends on latitude and height, smallest at 3 to 10 mbar; the drift increases with increasing altitude. Three tape products are described. The High Density SBUV (HDSBUV) tape contains the final derived products - the total ozone and the vertical ozone profile - as well as much detailed diagnostic information generated during the retrieval process. The Compressed Ozone (CPOZ) tape contains only that subset of HDSBUV information, including total ozone and ozone profiles, considered most useful for scientific studies. The Zonal Means Tape (ZMT) contains daily, weekly, monthly and quarterly averages of the derived quantities over 10 deg latitude zones

“everything in one place”

Purpose: To describe older adults’ perspectives on a new patient education manual for the recovery process after hip fracture. Materials and methods: The Fracture Recovery for Seniors at Home (FReSH) Start manual is an evidence- based manual for older adults with fall-related hip fracture. The manual aims to support the transition from hospital to home by facilitating self- management of the recovery process. We enrolled 31 community-dwelling older adults with previous fall-related hip fracture and one family member. We collected data using a telephone-based questionnaire with eight five-point Likert items and four semi-structured open-ended questions to explore participants’ perceptions on the structure, content, and illustration of the manual. The questionnaire also asked participants to rate the overall utility (out of 10 points) and length of the manual. We used content analysis to describe main themes from responses to the open-ended interview questions. Results: Participants’ ratings for structure, content, and illustrations ranged from 4 to 5 (agree to highly agree), and the median usefulness rating was 9 (10th percentile: 7, 90th percentile: 10). Main themes from the content analysis included: ease of use and presentation; health literacy; illustration utility; health care team delivery; general impression, information support from hospital to home; emotional and decision-making support; and the novelty of the manual. Conclusion: The FReSH Start manual was perceived as comprehensive in content and acceptable for use with older adults post-fall- related hip fracture. Participants expressed a need for delivery and explanation of the manual by a health care team member

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

Relações morfométricas para árvores dominantes de Pinus taeda no Estado do Paraná.

Este trabalho objetivou estudar as relações morfométricas de árvores dominantes de Pinus taeda no município de Ponta Grossa, Paraná. Em cada amostra a árvore de maior diâmetro a altura do peito (DAP) foi considerada dominante em relação às suas vizinhas. Destas foram mensuradas dap, altura total, altura da copa e oito raios de copa. As variáveis morfométricas analisadas foram: diâmetro de copa, altura da copa, proporção de copa, grau de esbeltez, índice de saliência, índice de abrangência e formal de copa. Estas foram correlacionadas com o dap e altura através de correlação de Pearson. De acordo com os índices, as árvores analisadas possuem média instabilidade, copas arredondadas e não há necessidade de desbaste na área. O diâmetro a altura do peito se correlacionou melhor com as variáveis morfométricas estudadas, indicando que estas sofrem alterações conforme as árvores incrementam em diâmetro