Lower Bounds for Heights in Relative Galois Extensions

The goal of this paper is to obtain lower bounds on the height of an algebraic number in a relative setting, extending previous work of Amoroso and Masser. Specifically, in our first theorem we obtain an effective bound for the height of an algebraic number $\alpha$ when the base field $\mathbb{K}$ is a number field and $\mathbb{K}(\alpha)/\mathbb{K}$ is Galois. Our second result establishes an explicit height bound for any non-zero element $\alpha$ which is not a root of unity in a Galois extension $\mathbb{F}/\mathbb{K}$, depending on the degree of $\mathbb{K}/\mathbb{Q}$ and the number of conjugates of $\alpha$ which are multiplicatively independent over $\mathbb{K}$. As a consequence, we obtain a height bound for such $\alpha$ that is independent of the multiplicative independence condition

Ray and wave chaos in asymmetric resonant optical cavities

Optical resonators are essential components of lasers and other wavelength-sensitive optical devices. A resonator is characterized by a set of modes, each with a resonant frequency omega and resonance width Delta omega=1/tau, where tau is the lifetime of a photon in the mode. In a cylindrical or spherical dielectric resonator, extremely long-lived resonances are due to `whispering gallery' modes in which light circulates around the perimeter trapped by total internal reflection. These resonators emit light isotropically. Recently, a new category of asymmetric resonant cavities (ARCs) has been proposed in which substantial shape deformation leads to partially chaotic ray dynamics. This has been predicted to give rise to a universal, frequency-independent broadening of the whispering-gallery resonances, and highly anisotropic emission. Here we present solutions of the wave equation for ARCs which confirm many aspects of the earlier ray-optics model, but also reveal interesting frequency-dependent effects characteristic of quantum chaos. For small deformations the lifetime is controlled by evanescent leakage, the optical analogue of quantum tunneling. We find that the lifetime is much shortened by a process known as `chaos-assisted tunneling'. In contrast, for large deformations (~10%) some resonances are found to have longer lifetimes than predicted by the ray chaos model due to `dynamical localization'.Comment: 4 pages RevTeX with 7 Postscript figure

No imminent quantum supremacy by boson sampling

It is predicted that quantum computers will dramatically outperform their conventional counterparts. However, large-scale universal quantum computers are yet to be built. Boson sampling is a rudimentary quantum algorithm tailored to the platform of photons in linear optics, which has sparked interest as a rapid way to demonstrate this quantum supremacy. Photon statistics are governed by intractable matrix functions known as permanents, which suggests that sampling from the distribution obtained by injecting photons into a linear-optical network could be solved more quickly by a photonic experiment than by a classical computer. The contrast between the apparently awesome challenge faced by any classical sampling algorithm and the apparently near-term experimental resources required for a large boson sampling experiment has raised expectations that quantum supremacy by boson sampling is on the horizon. Here we present classical boson sampling algorithms and theoretical analyses of prospects for scaling boson sampling experiments, showing that near-term quantum supremacy via boson sampling is unlikely. While the largest boson sampling experiments reported so far are with 5 photons, our classical algorithm, based on Metropolised independence sampling (MIS), allowed the boson sampling problem to be solved for 30 photons with standard computing hardware. We argue that the impact of experimental photon losses means that demonstrating quantum supremacy by boson sampling would require a step change in technology.Comment: 25 pages, 9 figures. Comments welcom

Bridge-specific fragility analysis: when is it really necessary?

In seismic assessment of bridges the research focus has recently shifted on the derivation of bridge-specific fragility curves that account for the effect of different geometry, structural system, component and soil properties, on the seismic behaviour. In this context, a new, component-based methodology for the derivation of bridge-specific fragility curves has been recently proposed by the authors, with a view to overcoming the inherent difficulties in assessing all bridges of a road network and the drawbacks of existing methodologies, which use the same group of fragility curves for bridges within the same typological class. The main objective of this paper is to critically assess the necessity of bridge-specific fragility analysis, starting from the effect of structure-specific parameters on component capacity (limit state thresholds), seismic demand, and fragility curves. The aforementioned methodology is used to derive fragility curves for all bridges within an actual road network, with a view to investigating the consistency of adopting generic fragility curves for bridges that fall within the same class and quantifying the degree of over- or under-estimation of the probability of damage when generic bridge classes are considered. Moreover, fragility curves for all representative bridges of the analysed concrete bridge classes are presented to illustrate the differentiation in bridge fragility for varying structural systems, bridge geometry, total bridge length and maximum pier height. Based on the above, the relevance of bridge-specific fragility analysis is assessed, and pertinent conclusions are drawn

Classification of patients with knee osteoarthritis in clinical phenotypes: data from the osteoarthritis initiative

<div><p>Objectives</p><p>The existence of phenotypes has been hypothesized to explain the large heterogeneity characterizing the knee osteoarthritis. In a previous systematic review of the literature, six main phenotypes were identified: Minimal Joint Disease (MJD), Malaligned Biomechanical (MB), Chronic Pain (CP), Inflammatory (I), Metabolic Syndrome (MS) and Bone and Cartilage Metabolism (BCM). The purpose of this study was to classify a sample of individuals with knee osteoarthritis (KOA) into pre-defined groups characterized by specific variables that can be linked to different disease mechanisms, and compare these phenotypes for demographic and health outcomes.</p><p>Methods</p><p>599 patients were selected from the OAI database FNIH at 24 months’ time to conduct the study. For each phenotype, cut offs of key variables were identified matching the results from previous studies in the field and the data available for the sample. The selection process consisted of 3 steps. At the end of each step, the subjects classified were excluded from the further classification stages. Patients meeting the criteria for more than one phenotype were classified separately into a ‘complex KOA’ group.</p><p>Results</p><p>Phenotype allocation (including complex KOA) was successful for 84% of cases with an overlap of 20%. Disease duration was shorter in the MJD while the CP phenotype included a larger number of Women (81%). A significant effect of phenotypes on WOMAC pain (F = 16.736 p <0.001) and WOMAC physical function (F = 14.676, p < 0.001) was identified after controlling for disease duration.</p><p>Conclusion</p><p>This study signifies the feasibility of a classification of KOA subjects in distinct phenotypes based on subgroup-specific characteristics.</p></div

Transport through a strongly coupled graphene quantum dot in perpendicular magnetic field

We present transport measurements on a strongly coupled graphene quantum dot in a perpendicular magnetic field. The device consists of an etched single-layer graphene flake with two narrow constrictions separating a 140 nm diameter island from source and drain graphene contacts. Lateral graphene gates are used to electrostatically tune the device. Measurements of Coulomb resonances, including constriction resonances and Coulomb diamonds prove the functionality of the graphene quantum dot with a charging energy of around 4.5 meV. We show the evolution of Coulomb resonances as a function of perpendicular magnetic field, which provides indications of the formation of the graphene specific 0th Landau level. Finally, we demonstrate that the complex pattern superimposing the quantum dot energy spectra is due to the formation of additional localized states with increasing magnetic field.Comment: 6 pages, 4 figure

Examining the Moderating Role of Rational-Versus Emotional-Focused Websites: The Case of Boutique Hotels

This article examines whether emotional or rational advertising appeals are more effective for website hospitality services. Specifically, it considers how attitudes towards websites, service expectations and attitudes towards boutique hotels may influence the two different types of advertising appeals and purchase intention. Results show that websites using emotional appeals tend to show a positive relationship between attitude towards hotels and attitude towards websites and purchase intention. It also indicates that emotional advertisements are better at gaining and retaining interest and attention, and as such can be highly beneficial for small boutique hotels. This article provides several marketing and business policy implications to aid practitioners and strategists in making better decisions

Abnormalities in autonomic function in obese boys at-risk for insulin resistance and obstructive sleep apnea.

Study objectivesCurrent evidence in adults suggests that, independent of obesity, obstructive sleep apnea (OSA) can lead to autonomic dysfunction and impaired glucose metabolism, but these relationships are less clear in children. The purpose of this study was to investigate the associations among OSA, glucose metabolism, and daytime autonomic function in obese pediatric subjects.MethodsTwenty-three obese boys participated in: overnight polysomnography; a frequently sampled intravenous glucose tolerance test; and recordings of spontaneous cardiorespiratory data in both the supine (baseline) and standing (sympathetic stimulus) postures.ResultsBaseline systolic blood pressure and reactivity of low-frequency heart rate variability to postural stress correlated with insulin resistance, increased fasting glucose, and reduced beta-cell function, but not OSA severity. Baroreflex sensitivity reactivity was reduced with sleep fragmentation, but only for subjects with low insulin sensitivity and/or low first-phase insulin response to glucose.ConclusionsThese findings suggest that vascular sympathetic activity impairment is more strongly affected by metabolic dysfunction than by OSA severity, while blunted vagal autonomic function associated with sleep fragmentation in OSA is enhanced when metabolic dysfunction is also present

Psychosocial developmental milestones in men with classic galactosemia

Patients with classic galactosemia suffer from several long term effects of their disease. Research in a group of mainly female patients has shown that these patients may also have a developmental delay with regard to their social aptitude. To study if male galactosemia patients achieve psychosocial developmental milestones more slowly than male peers from the general Dutch population, we assessed their development with the Course of Life Questionnaire (CoLQ). A total of 18 male galactosemia patients participated in this study (response rate 69%): 11 Dutch patients and seven American patients. We found severe delays in the social and psychosexual scales of this questionnaire, but not on the autonomy axis. These results are comparable to an earlier study with a limited number of male patients. The observed delays could be secondary to less developed social skills, cognitive dysfunction, or disrupted language development. We strongly recommend screening of galactosemia patients for developmental delays, to ensure early intervention through social skills training