Elliptic logarithms, diophantine approximation and the Birch and Swinnerton-Dyer conjecture

Most, if not all, unconditional results towards the abc-conjecture rely ultimately on classical Baker's method. In this article, we turn our attention to its elliptic analogue. Using the elliptic Baker's method, we have recently obtained a new upper bound for the height of the S-integral points on an elliptic curve. This bound depends on some parameters related to the Mordell-Weil group of the curve. We deduce here a bound relying on the conjecture of Birch and Swinnerton-Dyer, involving classical, more manageable quantities. We then study which abc-type inequality over number fields could be derived from this elliptic approach.Comment: 20 pages. Some changes, the most important being on Conjecture 3.2, three references added ([Mas75], [MB90] and [Yu94]) and one reference updated [BS12]. Accepted in Bull. Brazil. Mat. So

Non-equilibrium Dynamics of O(N) Nonlinear Sigma models: a Large-N approach

We study the time evolution of the mass gap of the O(N) non-linear sigma model in 2+1 dimensions due to a time-dependent coupling in the large-$N$ limit. Using the Schwinger-Keldysh approach, we derive a set of equations at large $N$ which determine the time dependent gap in terms of the coupling. These equations lead to a criterion for the breakdown of adiabaticity for slow variation of the coupling leading to a Kibble-Zurek scaling law. We describe a self-consistent numerical procedure to solve these large-$N$ equations and provide explicit numerical solutions for a coupling which starts deep in the gapped phase at early times and approaches the zero temperature equilibrium critical point $g_c$ in a linear fashion. We demonstrate that for such a protocol there is a value of the coupling $g= g_c^{\rm dyn}> g_c$ where the gap function vanishes, possibly indicating a dynamical instability. We study the dependence of $g_c^{\rm dyn}$ on both the rate of change of the coupling and the initial temperature. We also verify, by studying the evolution of the mass gap subsequent to a sudden change in $g$, that the model does not display thermalization within a finite time interval $t_0$ and discuss the implications of this observation for its conjectured gravitational dual as a higher spin theory in $AdS_4$.Comment: 22 pages, 9 figures. Typos corrected, references rearranged and added.v3 : sections rearranged, abstract modified, comment about Kibble-Zurek scaling correcte

Suicide Seasonality: Complex Demodulation as a Novel Approach in Epidemiologic Analysis

Seasonality of suicides is well-known and nearly ubiquitous, but recent evidence showed inconsistent patterns of decreasing or increasing seasonality in different countries. Furthermore, strength of seasonality was hypothesized to be associated with suicide prevalence. This study aimed at pointing out methodological difficulties in examining changes in suicide seasonality. METHODODOLOGY/PRINCIPAL FINDINGS: The present study examines the hypothesis of decreasing seasonality with a superior method that allows continuous modeling of seasonality. Suicides in Austria (1970-2008, N = 67,741) were analyzed with complex demodulation, a local (point-in-time specific) version of harmonic analysis. This avoids the need to arbitrarily split the time series, as is common practice in the field of suicide seasonality research, and facilitates incorporating the association with suicide prevalence. Regression models were used to assess time trends and association of amplitude and absolute suicide numbers. Results showed that strength of seasonality was associated with absolute suicide numbers, and that strength of seasonality was stable during the study period when this association was taken into account.Continuous modeling of suicide seasonality with complex demodulation avoids spurious findings that can result when time series are segmented and analyzed piecewise or when the association with suicide prevalence is disregarded

Effective action in a higher-spin background

We consider a free massless scalar field coupled to an infinite tower of background higher-spin gauge fields via minimal coupling to the traceless conserved currents. The set of Abelian gauge transformations is deformed to the non-Abelian group of unitary operators acting on the scalar field. The gauge invariant effective action is computed perturbatively in the external fields. The structure of the various (divergent or finite) terms is determined. In particular, the quadratic part of the logarithmically divergent (or of the finite) term is expressed in terms of curvatures and related to conformal higher-spin gravity. The generalized higher-spin Weyl anomalies are also determined. The relation with the theory of interacting higher-spin gauge fields on anti de Sitter spacetime via the holographic correspondence is discussed.Comment: 40 pages, Some errors and typos corrected, Version published in JHE

Holographic Brownian Motion in Magnetic Environments

Using the gauge/gravity correspondence, we study the dynamics of a heavy quark in two strongly-coupled systems at finite temperature: Super-Yang-Mills in the presence of a magnetic field and non-commutative Super-Yang-Mills. In the former, our results agree qualitatively with the expected behavior from weakly-coupled theories. In the latter, we propose a Langevin equation that accounts for the effects of non-commutativity and we find new interesting features. The equation resembles the structure of Brownian motion in the presence of a magnetic field and implies that the fluctuations along non-commutative directions are correlated. Moreover, our results show that the viscosity is smaller than the commutative case and that the diffusion properties of the quark are unaffected by non-commutativity. Finally, we compute the random force autocorrelator and verify that the fluctuation-dissipation theorem holds in the presence of non-commutativity.Comment: 34 pages. v2: typos corrected. v3: title and abstract slightly modified in order to better reflect the contents of the paper; footnote 3 and one reference were also added; version accepted for publication in JHE

Thermodynamic analysis of the Quantum Critical behavior of Ce-lattice compounds

A systematic analysis of low temperature magnetic phase diagrams of Ce compounds is performed in order to recognize the thermodynamic conditions to be fulfilled by those systems to reach a quantum critical regime and, alternatively, to identify other kinds of low temperature behaviors. Based on specific heat ($C_m$) and entropy ($S_m$) results, three different types of phase diagrams are recognized: i) with the entropy involved into the ordered phase ($S_{MO}$) decreasing proportionally to the ordering temperature ($T_{MO}$), ii) those showing a transference of degrees of freedom from the ordered phase to a non-magnetic component, with their $C_m(T_{MO})$ jump ($\Delta C_m$) vanishing at finite temperature, and iii) those ending in a critical point at finite temperature because their $\Delta C_m$ do not decrease with $T_{MO}$ producing an entropy accumulation at low temperature. Only those systems belonging to the first case, i.e. with $S_{MO}\to 0$ as $T_{MO}\to 0$, can be regarded as candidates for quantum critical behavior. Their magnetic phase boundaries deviate from the classical negative curvature below $T\approx 2.5$\,K, denouncing frequent misleading extrapolations down to T=0. Different characteristic concentrations are recognized and analyzed for Ce-ligand alloyed systems. Particularly, a pre-critical region is identified, where the nature of the magnetic transition undergoes significant modifications, with its $\partial C_m/\partial T$ discontinuity strongly affected by magnetic field and showing an increasing remnant entropy at $T\to 0$. Physical constraints arising from the third law at $T\to 0$ are discussed and recognized from experimental results

Assessing the suitability of copper thiocyanate as a hole-transport layer in inverted CsSnI3 perovskite photovoltaics

We report the fndings of a study into the suitability of copper (I) thiocyanate (CuSCN) as a hole-transport layer in inverted photovoltaic (PV) devices based on the black gamma phase (B-γ) of CsSnl3 perovskite. Remarkably, when B-γ-CsSnI3 perovskite is deposited from a dimethylformamide solution onto a 180–190nm thick CuSCN flm supported on an indium-tin oxide (ITO) electrode, the CuSCN layer is completely displaced leaving a perovskite layer with high uniformity and coverage of the underlying ITO electrode. This fnding is confrmed by detailed analysis of the thickness and composition of the film that remains after perovskite deposition, together with photovoltaic device studies. The results of this study show that, whilst CuSCN has proved to be an excellent hole-extraction layer for high performance lead-perovskite and organic photovoltaics, it is unsuitable as a hole-transport layer in inverted B-γCsSnI3 perovskite photovoltaics processed from solution

Getting the right balance: insole design alters the static balance of people with diabetes and neuropathy

BACKGROUND: Over 1 in 3 older people with diabetes sustain a fall each year. Postural instability has been identified as independent risk factor for falls within people with Diabetic Peripheral Neuropathy (DPN). People with DPN, at increased risk of falls, are routinely required to wear offloading insoles, yet the impact of these insoles on postural stability and postural control is unknown. The aim of this study was to evaluate the effect of a standard offloading insole and its constituent parts on the balance in people with DPN. METHODS: A random sample of 50 patients with DPN were observed standing for 3 × 30 s, and stepping in response to a light, under five conditions presented in a random order; as defined by a computer program; 1) no insole, 2) standard diabetic: a standard offloading insole made from EVA/poron®, and three other insoles with one design component systematically altered 3) flat: diabetic offloading insole with arch fill removed, 4) low resilient memory: diabetic offloading insole with the cover substituted with low resilience memory V9, 5) textured: diabetic offloading insole with a textured PVC surface added (Algeos Ltd). After each condition participants self-rated perceived steadiness. RESULTS: Insole design effected static balance and balance perception, but not stepping reaction time in people with DPN. The diabetic and memory shaped insoles (with arch fill) significantly increased centre of pressure velocity (14 %, P = 0.006), (13 %, P = 0.001), and path length (14 %, P = 0.006), (13 %, P = 001), when compared to the no insole condition. The textured shaped and flat soft insole had no effect on static balance when compared to the no insole condition (P > 0.05). CONCLUSION: Insoles have an effect on static balance but not stepping reaction time. This effect is independent of neuropathy severity. The addition of a textured cover seems to counter the negative effect of an arch fill, even in participants with severe sensation loss. Static balance is unaffected by material softness or resilience. Current best practice of providing offloading insoles, with arch fill, to increase contact area and reduce peak pressure could be making people more unstable. Whilst flat, soft insoles maybe the preferable design option for those with poor balance. There is a need to develop an offloading insole that can reduce diabetic foot ulcer risk, without compromising balance

Use of selected complementary and alternative medicine (CAM) treatments in veterans with cancer or chronic pain: a cross-sectional survey

BACKGROUND: Complementary and alternative medicine (CAM) is emerging as an important form of care in the United States. We sought to measure the prevalence of selected CAM use among veterans attending oncology and chronic pain clinics and to describe the characteristics of CAM use in this population. METHODS: The self-administered, mail-in survey included questions on demographics, health beliefs, medical problems and 6 common CAM treatments (herbs, dietary supplements, chiropractic care, massage therapy, acupuncture and homeopathy) use. We used the chi-square test to examine bivariate associations between our predictor variables and CAM use. RESULTS: Seventy-two patients (27.3%) reported CAM use within the past 12 months. CAM use was associated with more education (p = 0.02), higher income (p = 0.006), non-VA insurance (p = 0.003), additional care outside the VA (p = 0.01) and the belief that lifestyle contributes to illness (p = 0.015). The diagnosis of chronic pain versus cancer was not associated with differential CAM use (p = 0.15). Seventy-six percent of CAM non-users reported that they would use it if offered at the VA. CONCLUSION: Use of 6 common CAM treatments among these veterans is lower than among the general population, but still substantial. A large majority of veterans reported interest in using CAM modalities if they were offered at the VA. A national assessment of veteran interest in CAM may assist VA leaders to respond to patients' needs