Elliptic curves, modular forms, and sums of Hurwitz class numbers

Let H(N) denote the Hurwitz class number. It is known that if $p$ is a prime, then {equation*} \sum_{|r|<2\sqrt p}H(4p-r^2) = 2p. {equation*} In this paper, we investigate the behavior of this sum with the additional condition $r\equiv c\pmod m$. Three different methods will be explored for determining the values of such sums. First, we will count isomorphism classes of elliptic curves over finite fields. Second, we will express the sums as coefficients of modular forms. Third, we will manipulate the Eichler-Selberg trace for ula for Hecke operators to obtain Hurwitz class number relations. The cases $m=2,3$ and 4 are treated in full. Partial results, as well as several conjectures, are given for $m=5$ and 7.Comment: Preprint of an old pape

A New Algorithm for Supernova Neutrino Transport and Some Applications

We have developed an implicit, multi-group, time-dependent, spherical neutrino transport code based on the Feautrier variables, the tangent-ray method, and accelerated ${\bf \Lambda}$ iteration. The code achieves high angular resolution, is good to O($v/c$), is equivalent to a Boltzmann solver (without gravitational redshifts), and solves the transport equation at all optical depths with precision. In this paper, we present our formulation of the relevant numerics and microphysics and explore protoneutron star atmospheres for snapshot post-bounce models. Our major focus is on spectra, neutrino-matter heating rates, Eddington factors, angular distributions, and phase-space occupancies. In addition, we investigate the influence on neutrino spectra and heating of final-state electron blocking, stimulated absorption, velocity terms in the transport equation, neutrino-nucleon scattering asymmetry, and weak magnetism and recoil effects. Furthermore, we compare the emergent spectra and heating rates obtained using full transport with those obtained using representative flux-limited transport formulations to gauge their accuracy and viability. Finally, we derive useful formulae for the neutrino source strength due to nucleon-nucleon bremsstrahlung and determine bremsstrahlung's influence on the emergent $\nu_{\mu}$ and $\nu_{\tau}$ neutrino spectra.Comment: 58 pages, single-spaced LaTeX, 23 figures, revised title, also available at http://jupiter.as.arizona.edu/~burrows/papers, accepted for publication in the Ap.

Multiple and Multidimensional life transitions in the context of life-limiting health conditions:Longitudinal study focussing on perspectives of Young Adults, Families and Professionals

Background: There is a dearth of literature that investigates life transitions of young adults (YAs) with life-limiting conditions, families and professionals. The scant literature that is available has methodological limitations, including not listening to the voice of YAs, collecting data retrospectively, at one time point, from one group’s perspective and single case studies. The aim of this study was to address the gaps found in our literature review and provide a clearer understanding of the multiple and multi-dimensional life transitions experienced by YAs and significant others, over a period of time. Methods: This qualitative study used a longitudinal design and data were collected using semi-structured interviews over a 6-month period at 3 time points. Participants included 12 YAs with life-limiting conditions and their nominated significant others (10 family members and 11 professionals). Data were analysed using a thematic analysis approach. Results: Life transitions of YA and significant others are complex; they experience multiple and multi-dimensional transitions across several domains. The findings challenge the notion that all life transitions are triggered by health transitions of YAs, and has highlighted environmental factors (attitudinal and systemic) that can be changed to facilitate smoother transitions in various aspects of their lives. Conclusions: This study makes a unique and significant contribution to literature. It provides evidence and rich narratives for policy makers and service providers to change policies and practices that are in line with the needs of YAs with life-limiting conditions as they transition to adulthood. Families and professionals have specific training needs that have not yet been met fully

Secretory structures in plants: lessons from the Plumbaginaceae on their origin, evolution and roles in stress tolerance

Special IssueThe Plumbaginaceae (non-core Caryophyllales) is a family well known for species adapted to a wide range of arid and saline habitats. Of its salt-tolerant species, at least 45 are in the genus Limonium; two in each of Aegialitis, Limoniastrum and Myriolimon, and one each in Psylliostachys, Armeria, Ceratostigma, Goniolimon and Plumbago. All the halophytic members of the family have salt glands, which are also common in the closely related Tamaricaceae and Frankeniaceae. The halophytic species of the three families can secrete a range of ions (Na+, K+, Ca2+, Mg2+, Cl−, HCO3 −, SO4 2-) and other elements (As, Cd, Cr, Cu, Fe, Mn, Ni, Pb and Zn). Salt glands are, however, absent in salt-tolerant members of the sister family Polygonaceae. We describe the structure of the salt glands in the three families and consider whether glands might have arisen as a means to avoid the toxicity of Na+ and/or Cl− or to regulate Ca2+ concentrations within the leaves. We conclude that the establishment of lineages with salt glands took place after the split between the Polygonaceae and its sister group the Plumbaginaceaeinfo:eu-repo/semantics/publishedVersio

Adiposity, hormone replacement therapy use and breast cancer risk by age and hormone receptor status: a large prospective cohort study

INTRODUCTION: Associations of hormone-receptor positive breast cancer with excess adiposity are reasonably well characterized; however, uncertainty remains regarding the association of body mass index (BMI) with hormone-receptor negative malignancies, and possible interactions by hormone replacement therapy (HRT) use. METHODS: Within the European EPIC cohort, Cox proportional hazards models were used to describe the relationship of BMI, waist and hip circumferences with risk of estrogen-receptor (ER) negative and progesterone-receptor (PR) negative (n = 1,021) and ER+PR+ (n = 3,586) breast tumors within five-year age bands. Among postmenopausal women, the joint effects of BMI and HRT use were analyzed. RESULTS: For risk of ER-PR- tumors, there was no association of BMI across the age bands. However, when analyses were restricted to postmenopausal HRT never users, a positive risk association with BMI (third versus first tertile HR = 1.47 (1.01 to 2.15)) was observed. BMI was inversely associated with ER+PR+ tumors among women aged ≤49 years (per 5 kg/m2 increase, HR = 0.79 (95%CI 0.68 to 0.91)), and positively associated with risk among women ≥65 years (HR = 1.25 (1.16 to 1.34)). Adjusting for BMI, waist and hip circumferences showed no further associations with risks of breast cancer subtypes. Current use of HRT was significantly associated with an increased risk of receptor-negative (HRT current use compared to HRT never use HR: 1.30 (1.05 to 1.62)) and positive tumors (HR: 1.74 (1.56 to 1.95)), although this risk increase was weaker for ER-PR- disease (Phet = 0.035). The association of HRT was significantly stronger in the leaner women (BMI ≤22.5 kg/m2) than for more overweight women (BMI ≥25.9 kg/m2) for, both, ER-PR- (HR: 1.74 (1.15 to 2.63)) and ER+PR+ (HR: 2.33 (1.84 to 2.92)) breast cancer and was not restricted to any particular HRT regime. CONCLUSIONS: An elevated BMI may be positively associated with risk of ER-PR- tumors among postmenopausal women who never used HRT. Furthermore, postmenopausal HRT users were at an increased risk of ER-PR- as well as ER+PR+ tumors, especially among leaner women. For hormone-receptor positive tumors, but not for hormone-receptor negative tumors, our study confirms an inverse association of risk with BMI among young women of premenopausal age. Our data provide evidence for a possible role of sex hormones in the etiology of hormone-receptor negative tumors

TRY plant trait database – enhanced coverage and open access

Plant traits - the morphological, anatomical, physiological, biochemical and phenological characteristics of plants - determine how plants respond to environmental factors, affect other trophic levels, and influence ecosystem properties and their benefits and detriments to people. Plant trait data thus represent the basis for a vast area of research spanning from evolutionary biology, community and functional ecology, to biodiversity conservation, ecosystem and landscape management, restoration, biogeography and earth system modelling. Since its foundation in 2007, the TRY database of plant traits has grown continuously. It now provides unprecedented data coverage under an open access data policy and is the main plant trait database used by the research community worldwide. Increasingly, the TRY database also supports new frontiers of trait‐based plant research, including the identification of data gaps and the subsequent mobilization or measurement of new data. To support this development, in this article we evaluate the extent of the trait data compiled in TRY and analyse emerging patterns of data coverage and representativeness. Best species coverage is achieved for categorical traits - almost complete coverage for ‘plant growth form’. However, most traits relevant for ecology and vegetation modelling are characterized by continuous intraspecific variation and trait–environmental relationships. These traits have to be measured on individual plants in their respective environment. Despite unprecedented data coverage, we observe a humbling lack of completeness and representativeness of these continuous traits in many aspects. We, therefore, conclude that reducing data gaps and biases in the TRY database remains a key challenge and requires a coordinated approach to data mobilization and trait measurements. This can only be achieved in collaboration with other initiatives

Differential cross section measurements for the production of a W boson in association with jets in proton–proton collisions at √s = 7 TeV

Measurements are reported of differential cross sections for the production of a W boson, which decays into a muon and a neutrino, in association with jets, as a function of several variables, including the transverse momenta (pT) and pseudorapidities of the four leading jets, the scalar sum of jet transverse momenta (HT), and the difference in azimuthal angle between the directions of each jet and the muon. The data sample of pp collisions at a centre-of-mass energy of 7 TeV was collected with the CMS detector at the LHC and corresponds to an integrated luminosity of 5.0 fb[superscript −1]. The measured cross sections are compared to predictions from Monte Carlo generators, MadGraph + pythia and sherpa, and to next-to-leading-order calculations from BlackHat + sherpa. The differential cross sections are found to be in agreement with the predictions, apart from the pT distributions of the leading jets at high pT values, the distributions of the HT at high-HT and low jet multiplicity, and the distribution of the difference in azimuthal angle between the leading jet and the muon at low values.United States. Dept. of EnergyNational Science Foundation (U.S.)Alfred P. Sloan Foundatio

Optimasi Portofolio Resiko Menggunakan Model Markowitz MVO Dikaitkan dengan Keterbatasan Manusia dalam Memprediksi Masa Depan dalam Perspektif Al-Qur`an

Risk portfolio on modern finance has become increasingly technical, requiring the use of sophisticated mathematical tools in both research and practice. Since companies cannot insure themselves completely against risk, as human incompetence in predicting the future precisely that written in Al-Quran surah Luqman verse 34, they have to manage it to yield an optimal portfolio. The objective here is to minimize the variance among all portfolios, or alternatively, to maximize expected return among all portfolios that has at least a certain expected return. Furthermore, this study focuses on optimizing risk portfolio so called Markowitz MVO (Mean-Variance Optimization). Some theoretical frameworks for analysis are arithmetic mean, geometric mean, variance, covariance, linear programming, and quadratic programming. Moreover, finding a minimum variance portfolio produces a convex quadratic programming, that is minimizing the objective function ðð¥with constraintsð ð 𥠥 ðandð´ð¥ = ð. The outcome of this research is the solution of optimal risk portofolio in some investments that could be finished smoothly using MATLAB R2007b software together with its graphic analysis

Juxtaposing BTE and ATE – on the role of the European insurance industry in funding civil litigation

One of the ways in which legal services are financed, and indeed shaped, is through private insurance arrangement. Two contrasting types of legal expenses insurance contracts (LEI) seem to dominate in Europe: before the event (BTE) and after the event (ATE) legal expenses insurance. Notwithstanding institutional differences between different legal systems, BTE and ATE insurance arrangements may be instrumental if government policy is geared towards strengthening a market-oriented system of financing access to justice for individuals and business. At the same time, emphasizing the role of a private industry as a keeper of the gates to justice raises issues of accountability and transparency, not readily reconcilable with demands of competition. Moreover, multiple actors (clients, lawyers, courts, insurers) are involved, causing behavioural dynamics which are not easily predicted or influenced. Against this background, this paper looks into BTE and ATE arrangements by analysing the particularities of BTE and ATE arrangements currently available in some European jurisdictions and by painting a picture of their respective markets and legal contexts. This allows for some reflection on the performance of BTE and ATE providers as both financiers and keepers. Two issues emerge from the analysis that are worthy of some further reflection. Firstly, there is the problematic long-term sustainability of some ATE products. Secondly, the challenges faced by policymakers that would like to nudge consumers into voluntarily taking out BTE LEI

Search for stop and higgsino production using diphoton Higgs boson decays

Results are presented of a search for a "natural" supersymmetry scenario with gauge mediated symmetry breaking. It is assumed that only the supersymmetric partners of the top-quark (stop) and the Higgs boson (higgsino) are accessible. Events are examined in which there are two photons forming a Higgs boson candidate, and at least two b-quark jets. In 19.7 inverse femtobarns of proton-proton collision data at sqrt(s) = 8 TeV, recorded in the CMS experiment, no evidence of a signal is found and lower limits at the 95% confidence level are set, excluding the stop mass below 360 to 410 GeV, depending on the higgsino mass