The Seven-sphere and its Kac-Moody Algebra

We investigate the seven-sphere as a group-like manifold and its extension to a Kac-Moody-like algebra. Covariance properties and tensorial composition of spinors under $S^7$ are defined. The relation to Malcev algebras is established. The consequences for octonionic projective spaces are examined. Current algebras are formulated and their anomalies are derived, and shown to be unique (even regarding numerical coefficients) up to redefinitions of the currents. Nilpotency of the BRST operator is consistent with one particular expression in the class of (field-dependent) anomalies. A Sugawara construction is given.Comment: 22 pages. Macropackages used: phyzzx, epsf. Three epsf figure files appende

Duality between a deterministic cellular automaton and a bosonic quantum field theory in 1+1 dimensions

Methods developed in a previous paper are employed to define an exact correspondence between the states of a deterministic cellular automaton in 1+1 dimensions and those of a bosonic quantum field theory. The result may be used to argue that quantum field theories may be much closer related to deterministic automata than what is usually thought possible. Version 2 had a minor typo corrected and notation was made more consistent.Comment: 18 pages (incl. Title page). No figure

Derivations and automorphisms of free nilpotent Lie algebras and their quotiens

Let \n_{d,t} be the free nilpotent Lie algebra of type $d$ and nilindex $t$. Starting out with the derivation algebra and the automorphism group of \n_{d,t}, we get a natural description of derivations and automorphisms of any generic nilpotent Lie algebra of the same type and nilindex. Moreover, along the paper we discuss several examples to illustrate the obtained results.Comment: 13 page

Developing a core outcome set for future infertility research : An international consensus development study

STUDY QUESTION: Can a core outcome set to standardize outcome selection, collection and reporting across future infertility research be developed? SUMMARY ANSWER: A minimum data set, known as a core outcome set, has been developed for randomized controlled trials (RCTs) and systematic reviews evaluating potential treatments for infertility. WHAT IS KNOWN ALREADY: Complex issues, including a failure to consider the perspectives of people with fertility problems when selecting outcomes, variations in outcome definitions and the selective reporting of outcomes on the basis of statistical analysis, make the results of infertility research difficult to interpret. STUDY DESIGN, SIZE, DURATION: A three-round Delphi survey (372 participants from 41 countries) and consensus development workshop (30 participants from 27 countries). PARTICIPANTS/MATERIALS, SETTING, METHODS: Healthcare professionals, researchers and people with fertility problems were brought together in an open and transparent process using formal consensus science methods. MAIN RESULTS AND THE ROLE OF CHANCE: The core outcome set consists of: viable intrauterine pregnancy confirmed by ultrasound (accounting for singleton, twin and higher multiple pregnancy); pregnancy loss (accounting for ectopic pregnancy, miscarriage, stillbirth and termination of pregnancy); live birth; gestational age at delivery; birthweight; neonatal mortality; and major congenital anomaly. Time to pregnancy leading to live birth should be reported when applicable. LIMITATIONS, REASONS FOR CAUTION: We used consensus development methods which have inherent limitations, including the representativeness of the participant sample, Delphi survey attrition and an arbitrary consensus threshold. WIDER IMPLICATIONS OF THE FINDINGS: Embedding the core outcome set within RCTs and systematic reviews should ensure the comprehensive selection, collection and reporting of core outcomes. Research funding bodies, the Standard Protocol Items: Recommendations for Interventional Trials (SPIRIT) statement, and over 80 specialty journals, including the Cochrane Gynaecology and Fertility Group, Fertility and Sterility and Human Reproduction, have committed to implementing this core outcome set. STUDY FUNDING/COMPETING INTEREST(S): This research was funded by the Catalyst Fund, Royal Society of New Zealand, Auckland Medical Research Fund and Maurice and Phyllis Paykel Trust. The funder had no role in the design and conduct of the study, the collection, management, analysis or interpretation of data, or manuscript preparation. B.W.J.M. is supported by a National Health and Medical Research Council Practitioner Fellowship (GNT1082548). S.B. was supported by University of Auckland Foundation Seelye Travelling Fellowship. S.B. reports being the Editor-in-Chief of Human Reproduction Open and an editor of the Cochrane Gynaecology and Fertility group. J.L.H.E. reports being the Editor Emeritus of Human Reproduction. J.M.L.K. reports research sponsorship from Ferring and Theramex. R.S.L. reports consultancy fees from Abbvie, Bayer, Ferring, Fractyl, Insud Pharma and Kindex and research sponsorship from Guerbet and Hass Avocado Board. B.W.J.M. reports consultancy fees from Guerbet, iGenomix, Merck, Merck KGaA and ObsEva. C.N. reports being the Co Editor-in-Chief of Fertility and Sterility and Section Editor of the Journal of Urology, research sponsorship from Ferring, and retains a financial interest in NexHand. A.S. reports consultancy fees from Guerbet. E.H.Y.N. reports research sponsorship from Merck. N.L.V. reports consultancy and conference fees from Ferring, Merck and Merck Sharp and Dohme. The remaining authors declare no competing interests in relation to the work presented. All authors have completed the disclosure form

Polycystic ovary syndrome

The document attached has been archived with permission from the editor of the Medical Journal of Australia. An external link to the publisher’s copy is included.Polycystic ovary syndrome (PCOS) affects 5-20% of women of reproductive age worldwide. The condition is characterized by hyperandrogenism, ovulatory dysfunction and polycystic ovarian morphology (PCOM) - with excessive androgen production by the ovaries being a key feature of PCOS. Metabolic dysfunction characterized by insulin resistance and compensatory hyperinsulinaemia is evident in the vast majority of affected individuals. PCOS increases the risk for type 2 diabetes mellitus, gestational diabetes and other pregnancy-related complications, venous thromboembolism, cerebrovascular and cardiovascular events and endometrial cancer. PCOS is a diagnosis of exclusion, based primarily on the presence of hyperandrogenism, ovulatory dysfunction and PCOM. Treatment should be tailored to the complaints and needs of the patient and involves targeting metabolic abnormalities through lifestyle changes, medication and potentially surgery for the prevention and management of excess weight, androgen suppression and/or blockade, endometrial protection, reproductive therapy and the detection and treatment of psychological features. This Primer summarizes the current state of knowledge regarding the epidemiology, mechanisms and pathophysiology, diagnosis, screening and prevention, management and future investigational directions of the disorder.Robert J Norman, Ruijin Wu and Marcin T Stankiewic

Obesity at age 20 and the risk of miscarriages, irregular periods and reported problems of becoming pregnant: the Adventist Health Study-2

In a group of 46,000 North-American Adventist women aged 40 and above, we investigated the relationships between body mass index (BMI, kg/m(2)) at age 20 and the proportion of women who reported at least one miscarriage, periods with irregular menstruation or failing to become pregnant even if trying for more than one straight year. Approximately 31, 14 and 17 %, respectively, reported the three different problems related to reproduction. Positive age- and marital status adjusted relationships were found between BMI at age 20 and periods with irregular menstruation or failing to become pregnant even if trying for more than 1 year, but not with the risk of miscarriages. Women with BMI ≥ 32.5 kg/m(2) when aged 20 had approximately 2.0 (95 % CI: 1.6, 2.4) and 1.5 (95 % CI: 1.3, 1.9) higher odds for irregular periods or failing to get pregnant, respectively, than women with BMI in the 20–24.9 kg/m(2) bracket. These relationships were consistently found in a number of strata of the population, including the large proportion of the women who never had smoked or never used alcohol. Underweight (BMI < 18.5 kg/m(2)) when aged 20 marginally (approximately 15 %) increased the risk of failing to get pregnant within a year. Thus, obesity at age 20 increases the risk of reporting some specific reproductive problems, but not the risk of miscarriages. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s10654-012-9749-8) contains supplementary material, which is available to authorized users

Direct Measurements of Colloidal Solvophoresis under Imposed Solvent and Solute Gradients

We describe a microfluidic system that enables direct visualization and measurement of diffusiophoretic migration of colloids in response to imposed solution gradients. Such measurements have proven difficult or impossible in macroscopic systems due to difficulties in establishing solution gradients that are sufficiently strong yet hydrodynamically stable. We validate the system with measurements of the concentration-dependent diffusiophoretic mobility of polystyrene colloids in NaCl gradients, confirming that diffusiophoretic migration velocities are proportional to gradients in the logarithm of electrolyte concentration. We then perform the first direct measurement of the concentration-dependent "solvophoretic" mobility of colloids in ethanol-water gradients, whose dependence on concentration and gradient strength was not known either theoretically or experimentally, but which our measurements reveal to be proportional to the gradient in the logarithm of ethanol mole fraction. Finally, we examine solvophoretic migration under a variety of qualitatively distinct chemical gradients, including solvents that are miscible or have finite solubility with water, an electrolyte for which diffusiophoresis proceeds down concentration gradients (unlike for most electrolytes), and a nonelectrolyte (sugar). Our technique enables the direct characterization of diffusiophoretic mobilities of various colloids under various solvent and solute gradients, analogous to the electrophoretic ζ-potential measurements that are routinely used to characterize suspensions. We anticipate that such measurements will provide the feedback required to test and develop theories for solvophoretic and diffusiophoretic migration and ultimately to the conceptual design and engineering of particles that respond in a desired way to their chemical environments