A caricature of a singular curvature flow in the plane

We study a singular parabolic equation of the total variation type in one dimension. The problem is a simplification of the singular curvature flow. We show existence and uniqueness of weak solutions. We also prove existence of weak solutions to the semi-discretization of the problem as well as convergence of the approximating sequences. The semi-discretization shows that facets must form. For a class of initial data we are able to study in details the facet formation and interactions and their asymptotic behavior. We notice that our qualitative results may be interpreted with the help of a special composition of multivalued operators

Coexistence of opposite opinions in a network with communities

The Majority Rule is applied to a topology that consists of two coupled random networks, thereby mimicking the modular structure observed in social networks. We calculate analytically the asymptotic behaviour of the model and derive a phase diagram that depends on the frequency of random opinion flips and on the inter-connectivity between the two communities. It is shown that three regimes may take place: a disordered regime, where no collective phenomena takes place; a symmetric regime, where the nodes in both communities reach the same average opinion; an asymmetric regime, where the nodes in each community reach an opposite average opinion. The transition from the asymmetric regime to the symmetric regime is shown to be discontinuous.Comment: 14 pages, 4 figure

Magneto-optical Selection Rules in Bilayer Bernal Graphene

The low-frequency magneto-optical properties of bilayer Bernal graphene are studied by the tight-binding model with four most important interlayer interactions taken into account. Since the main features of the wave functions are well depicted, the Landau levels can be divided into two groups based on the characteristics of the wave functions. These Landau levels lead to four categories of absorption peaks in the optical absorption spectra. Such absorption peaks own complex optical selection rules and these rules can be reasonably explained by the characteristics of the wave functions. In addition, twin-peak structures, regular frequency-dependent absorption rates and complex field-dependent frequencies are also obtained in this work. The main features of the absorption peaks are very different from those in monolayer graphene and have their origin in the interlayer interactions

MYOD1 involvement in myopathy

[Excerpt] Introduction Myogenic Differentiation 1 (MYOD1) encodes a transcription factor that plays an important role in myogenic determination into mature skeletal muscle [1]. The first loss-of-function mutation of MYOD1 in humans was described in three siblings with perinatal lethal fetal akinesia [2].[...]We thank the individual and family. Funding was provided by The Fonds de recherche du Québec - Santé (FRQS) and Canadian Institutes of Health Research (CIHR) to P.M.C., Fundação para a Ciência e Tecnologia (FCT) with the fellowship SFRH/BD/84650/2010 to F.L. and Groupe Pasteur Mutualité Foundation (GPM Foundation) to M.M.info:eu-repo/semantics/publishedVersio

Strain-induced Evolution of Electronic Band Structures in a Twisted Graphene Bilayer

Here we study the evolution of local electronic properties of a twisted graphene bilayer induced by a strain and a high curvature. The strain and curvature strongly affect the local band structures of the twisted graphene bilayer; the energy difference of the two low-energy van Hove singularities decreases with increasing the lattice deformations and the states condensed into well-defined pseudo-Landau levels, which mimic the quantization of massive Dirac fermions in a magnetic field of about 100 T, along a graphene wrinkle. The joint effect of strain and out-of-plane distortion in the graphene wrinkle also results in a valley polarization with a significant gap, i.e., the eight-fold degenerate Landau level at the charge neutrality point is splitted into two four-fold degenerate quartets polarized on each layer. These results suggest that strained graphene bilayer could be an ideal platform to realize the high-temperature zero-field quantum valley Hall effect.Comment: 4 figure

Statistical Inference for Valued-Edge Networks: Generalized Exponential Random Graph Models

Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks, exponential random graph models are a ubiquitous means of analysis. However, they are limited by an inability to model networks with valued edges. We solve this problem by introducing a class of generalized exponential random graph models capable of modeling networks whose edges are valued, thus greatly expanding the scope of networks applied researchers can subject to statistical analysis

Two band gap field-dependent thermal conductivity of MgB2MgB_2

The thermal conductivity $\kappa (H,T)$ of the new superconductor $MgB_2$ was studied as a function of the temperature and a magnetic field. No anomaly in the thermal conductivity $\kappa (H,T)$ is observed around the superconducting transition in absence or presence of magnetic fields up to 14 Tesla; upon that field the superconductivity of $MgB_2$ persisted. The thermal conductivity in zero-field shows a $T$-linear increase up to 50K. The thermal conductivity is found to increase with increasing field at high fields. We interpret the findings as if there are two subsystems of quasiparticles with different field-dependent characters in a two ($L$ and $S$)-band superconductor reacting differently with the vortex structure. The unusual enhancement of $\kappa (H ,T)$ at low temperature but higher than a ($H_{c2S}\simeq 3T$) critical field is interpreted as a result of the overlap of the low energy states outside the vortex cores in the $S$-band.Comment: 6 pages,3 figure

Graphene-based modulation-doped superlattice structures

The electronic transport properties of graphene-based superlattice structures are investigated. A graphene-based modulation-doped superlattice structure geometry is proposed and consist of periodically arranged alternate layers: InAs/graphene/GaAs/graphene/GaSb. Undoped graphene/GaAs/graphene structure displays relatively high conductance and enhanced mobilities at elevated temperatures unlike modulation-doped superlattice structure more steady and less sensitive to temperature and robust electrical tunable control on the screening length scale. Thermionic current density exhibits enhanced behaviour due to presence of metallic (graphene) mono-layers in superlattice structure. The proposed superlattice structure might become of great use for new types of wide-band energy gap quantum devices.Comment: 5 figure

Light smoking at base-line predicts a higher mortality risk to women than to men; evidence from a cohort with long follow-up

BACKGROUND: There is conflicting evidence as to whether smoking is more harmful to women than to men. The UK Cotton Workers’ Cohort was recruited in the 1960s and contained a high proportion of men and women smokers who were well matched in terms of age, job and length of time in job. The cohort has been followed up for 42 years. METHODS: Mortality in the cohort was analysed using an individual relative survival method and Cox regression. Whether smoking, ascertained at baseline in the 1960s, was more hazardous to women than to men was examined by estimating the relative risk ratio women to men, smokers to never smoked, for light (1–14), medium (15–24), heavy (25+ cigarettes per day) and former smoking. RESULTS: For all-cause mortality relative risk ratios were 1.35 for light smoking at baseline (95% CI 1.07-1.70), 1.15 for medium smoking (95% CI 0.89-1.49) and 1.00 for heavy smoking (95% CI 0.63-1.61). Relative risk ratios for light smoking at baseline for circulatory system disease was 1.42 (95% CI 1.01 to 1.98) and for respiratory disease was 1.89 (95% CI 0.99 to 3.63). Heights of participants provided no explanation for the gender difference. CONCLUSIONS: Light smoking at baseline was shown to be significantly more hazardous to women than to men but the effect decreased as consumption increased indicating a dose response relationship. Heavy smoking was equally hazardous to both genders. This result may help explain the conflicting evidence seen elsewhere. However gender differences in smoking cessation may provide an alternative explanation