On the Hilbert eigenvariety at exotic and CM classical weight 1 points

Let $F$ be a totally real number field and let $f$ be a classical cuspidal $p$-regular Hilbert modular eigenform over $F$ of parallel weight $1$. Let $x$ be the point on the $p$-adic Hilbert eigenvariety $\mathcal E$ corresponding to an ordinary $p$-stabilization of $f$. We show that if the $p$-adic Schanuel Conjecture is true, then $\mathcal E$ is smooth at $x$ if $f$ has CM. If we additionally assume that $F/\mathbb Q$ is Galois, we show that the weight map is \'etale at $x$ if $f$ has either CM or exotic projective image (which is the case for almost all cuspidal Hilbert modular eigenforms of parallel weight $1$). We prove these results by showing that the completed local ring of the eigenvariety at $x$ is isomorphic to a universal nearly ordinary Galois deformation ring.Comment: The material in the introduction and the final sections was reorganized. The sections on background material were substantially shortene

The Eisenstein ideal of weight kk and ranks of Hecke algebras

Let $p$ and $\ell$ be primes such that $p > 3$ and $p \mid \ell-1$ and $k$ be an even integer. We use deformation theory of pseudo-representations to study the completion of the Hecke algebra acting on the space of cuspidal modular forms of weight $k$ and level $\Gamma_0(\ell)$ at the maximal Eisenstein ideal containing $p$. We give a necessary and sufficient condition for the $\mathbb{Z}_p$-rank of this Hecke algebra to be greater than $1$ in terms of vanishing of the cup products of certain global Galois cohomology classes. We also recover some of the results proven by Wake and Wang-Erickson for $k=2$ using our methods. In addition, we prove some $R=\mathbb{T}$ theorems under certain hypothesis.Comment: 33 pages, Comments are welcom

Temperature enhanced persistent currents and "ϕ0/2\phi_0/2 periodicity"

We predict a non-monotonous temperature dependence of the persistent currents in a ballistic ring coupled strongly to a stub in the grand canonical as well as in the canonical case. We also show that such a non-monotonous temperature dependence can naturally lead to a $\phi_0/2$ periodicity of the persistent currents, where $\phi_0$=h/e. There is a crossover temperature $T^*$, below which persistent currents increase in amplitude with temperature while they decrease above this temperature. This is in contrast to persistent currents in rings being monotonously affected by temperature. $T^*$ is parameter-dependent but of the order of $\Delta_u/\pi^2k_B$, where $\Delta_u$ is the level spacing of the isolated ring. For the grand-canonical case $T^*$ is half of that for the canonical case.Comment: some typos correcte

The Time-Varying Cardiovascular Benefits of Glucagon-Like Peptide-1 Receptor Agonist Therapy in Patients with Type 2 Diabetes Mellitus: Evidence from Large Multinational Trials

Aims: To evaluate the time-varying cardio-protective effect of glucagon-like peptide-1 receptor agonists (GLP-1RAs) using pooled data from eight contemporary cardiovascular outcome trials using the difference in the restricted mean survival time (ΔRMST) as the effect estimate. Material and Methods: Data from eight multinational cardiovascular outcome randomized controlled trials of GLP-1RAs for type 2 diabetes mellitus were pooled. Flexible parametric survival models were fit from published Kaplan-Meier plots. The differences between arms in RMST (ΔRMST) were calculated at 12, 24, 36 and 48 months. ΔRMST values were pooled using an inverse variance-weighted random-effects model; heterogeneity was tested with Cochran\u27s Q statistic. The endpoints studied were: three-point major adverse cardiovascular events (MACE), all-cause mortality, stroke, cardiovascular mortality and myocardial infarction. Results: We included eight large (3183-14 752 participants, total = 60 080; median follow-up range: 1.5 to 5.4 years) GLP-1RA trials. Among GLP-1RA recipients, we observed an average delay in three-point MACE of 0.03, 0.15, 0.37 and 0.63 months at 12, 24, 36 and 48 months, respectively. At 48 months, while cardiovascular mortality was comparable in both arms (pooled ΔRMST 0.163 [−0.112, 0.437]; P = 0.24), overall survival was higher (ΔRMST = 0.261 [0.08-0.43] months) and stroke was delayed (ΔRMST 0.22 [0.15-0.33]) in patients receiving GLP-1RAs. Conclusions: Glucagon-like peptide-1 receptor agonists may delay the occurrence of MACE by an average of 0.6 months at 48 months, with meaningfully larger gains in patients with cardiovascular disease. This metric may be easier for clinicians and patients to interpret than hazard ratios, which assume a knowledge of absolute risk in the absence of treatment

Dihedral Universal Deformations

This article deals with universal deformations of dihedral representations with a particular focus on the question when the universal deformation is dihedral. Results are obtained in three settings: (1) representation theory, (2) algebraic number theory, (3) modularity. As to (1), we prove that the universal deformation is dihedral if all infinitesimal deformations are dihedral. Concerning (2) in the setting of Galois representations of number fields, we give sufficient conditions to ensure that the universal deformation relatively unramified outside a finite set of primes is dihedral, and discuss in how far these conditions are necessary. As side-results, we obtain cases of the unramified Fontaine-Mazur conjecture, and in many cases positively answer a question of Greenberg and Coleman on the splitting behaviour at p of p-adic Galois representations attached to newforms. As to (3), we prove a modularity theorem of the form `R=T' for parallel weight one Hilbert modular forms for cases when the minimal universal deformation is dihedral.Comment: 43 pages; minor corrections and improvements following referee's comment

Metastability and paramagnetism in superconducting mesoscopic disks

A projected order parameter is used to calculate, not only local minima of the Ginzburg-Landau energy functional, but also saddle points or energy barriers responsible for the metastabilities observed in superconducting mesoscopic disks (Geim et al. Nature {\bf 396}, 144 (1998)). We calculate the local minima magnetization and find the energetic instability points between vortex configurations with different vorticity. We also find that, for any vorticity, the supercurrent can reverse its flow direction on decreasing the magnetic field before one vortex can escape.Comment: Modified version as to appear in Phys. Rev. Let

Hysteresis in mesoscopic superconducting disks: the Bean-Livingston barrier

The magnetization behavior of mesoscopic superconducting disks can show hysteretic behavior which we explain by using the Ginzburg-Landau (GL) theory and properly taking into account the de-magnetization effects due to geometrical form factors. In large disks the Bean-Livingston surface barrier is responsible for the hysteresis. While in small disks a volume barrier is responsible for this hysteresis. It is shown that although the sample magnetization is diamagnetic (negative), the measured magnetization can be positive at certain fields as observed experimentally, which is a consequence of the de-magnetization effects and the experimental set up.Comment: Latex file, 4 ps file

Vortex phase diagram for mesoscopic superconducting disks

Solving numerically the 3D non linear Ginzburg-Landau (GL) equations, we study equilibrium and nonequilibrium phase transitions between different superconducting states of mesoscopic disks which are thinner than the coherence length and the penetration depth. We have found a smooth transition from a multi-vortex superconducting state to a giant vortex state with increasing both the disk thickness and the magnetic field. A vortex phase diagram is obtained which shows, as function of the magnetic field, a re-entrant behavior between the multi-vortex and the giant vortex state.Comment: 5 figures (post script files) include