Local models for Galois deformation rings and applications

We construct projective varieties in mixed characteristic whose singularities model, in generic cases, those of tamely potentially crystalline Galois deformation rings for unramified extensions of $\mathbb{Q}_p$ with small regular Hodge-Tate weights. We establish several significant facts about their geometry including a unibranch property at special points and a representation theoretic description of the irreducible components of their special fibers. We derive from these geometric results a number of local and global consequences: the Breuil-M\'ezard conjecture in arbitrary dimension for tamely potentially crystalline deformation rings with small Hodge-Tate weights (with appropriate genericity conditions), the weight part of Serre's conjecture for $U(n)$ as formulated by Herzig (for global Galois representations which satisfy the Taylor-Wiles hypotheses and are sufficiently generic at $p$), and an unconditional formulation of the weight part of Serre's conjecture for wildly ramified representations

Colength one deformation rings

Let $K/\mathbf{Q}_p$ be a finite unramified extension, $\overline{\rho}:\mathrm{Gal}(\overline{\mathbf{Q}}_p/K)\rightarrow\mathrm{GL}_n(\overline{\mathbf{F}}_p)$ a continuous representation, and $\tau$ a tame inertial type of dimension $n$. We explicitly determine, under mild regularity conditions on $\tau$, the potentially crystalline deformation ring $R^{\eta,\tau}_{\overline{\rho}}$ in parallel Hodge--Tate weights $\eta=(n-1,\cdots,1,0)$ and inertial type $\tau$ when the \emph{shape} of $\overline{\rho}$ with respect to $\tau$ has colength at most one. This has application to the modularity of a class of shadow weights in the weight part of Serre's conjecture. Along the way we make unconditional the local-global compatibility results of \cite{PQ} and further study the geometry of moduli spaces of Fontaine--Laffaille representations in terms of colength one weights.Comment: Major revision: shortened some of the arguments, removed the appendix and fixed a number of typos. Comments welcome

Electron transfer and H2 evolution in hybrid systems based on [FeFe]-hydrogenase anchored on modified TiO2

© 2016 Hydrogen Energy Publications LLC The hybrid systems composed by [FeFe]-hydrogenase anchored to the surface of three distinct types of TiO2 (anatase) have been investigated using Electron Paramagnetic Resonance (EPR) spectroscopy in dark and under illumination. The three supports were bare TiO2 nitrogen doped TiO2 (N-TiO2) and a sub-stoichiometric form of the same oxide (TiO2−x) exhibiting blue color. EPR spectroscopy has shown that the electrons photogenerated by irradiation of the supports are stabilised by the solid forming Ti3+ paramagnetic ions while, in the case of the hybrid systems electrons are scavenged by the anchored protein becoming available for H+ reduction. The ability of the three hybrid systems in hydrogen production under solar light illumination has been compared. The formation of H2 is higher for the system containing N-TiO2 (yellow) with respect to that based on the bare oxide (white) indicating that the visible light absorbed, due to the presence of N states, is actually exploited for hydrogen production. The system containing reduced blue TiO2, in spite of its deep coloration, is less active suggesting that a specific type of visible light absorption is needed to produce photoexcited electrons capable to interact with the anchored protein

Rockfall threatening cumae archeological site fruition (Phlegraean fields park—naples)

Natural hazards threaten many archaeological sites in the world; therefore, susceptibility analysis is essential to reduce their impacts and support site fruition by visitors. In this paper, rockfall susceptibility analysis of the western slope of the Cumae Mount in the Cumae Archaeological Site (Phlegraean Fields, Naples), already affected by rockfall events, is described as support to a management plan for fruition and site conservation. Being the first Greek settlement in southern Italy, the site has great historical importance and offers unique historical elements such as the Cumaean Sibyl’s Cave. The analysis began with a 3D modeling of the slope through digital terrestrial photogrammetry, which forms a basis for a geomechanical analysis. Digital discontinuity measurements and cluster analysis provide data for kinematic analysis, which pointed out the planar, wedge and toppling failure potential. Subsequently, a propagation-based susceptibility analysis was completed into a GIS environment: it shows that most of the western sector of the site is susceptible to rockfall, including the access course, a segment of the Cumana Railroad and its local station. The work highlights the need for specific mitigation measures to increase visitor safety and the efficacy of filed-based digital reconstruction to support susceptibility analysis in rockfall prone areas

Total Anatomical Reconstruction during Robot-assisted Radical Prostatectomy: Implications on Early Recovery of Urinary Continence

Background: The introduction of robotics revolutionized prostate cancer surgery because the magnified three-dimensional vision system and wristed instruments allow microsurgery to be performed. The advantages of robotic surgery could lead to improved continence outcomes in terms of early recovery compared with the traditional surgical methods. Objective: To describe the total anatomical reconstruction (TAR) technique during robot-assisted radical prostatectomy (RARP). Primary endpoint: evaluation of the continence rate at different time points. Secondary endpoint: evaluation of urine leakage and anastomosis stenosis rates related to the technique. Design, setting, and participants: June, 2013 to November, 2014; prospective consecutive series of patients with localized prostate cancer (cT1-3, cN0, cM0). Surgical procedure: RARP with TAR was performed in all cases. Lymph node dissection was performed if the risk of lymph nodal metastasis was over 5%, according to the Briganti updated nomogram. Measurements: Preoperative, intraoperative, postoperative, and pathological variables were analyzed. Enrolled patients were arbitrarily divided into three groups according to a time criterion. The relationships between the learning curve and the trend of the above-mentioned variables were analyzed using LOESS analysis. Continence was rigorously analyzed preoperatively and at 24h, 1 wk, 4 wk, 12 wk, and 24 wk after catheter removal. Results and limitations: In total, 252 patients were analyzed. The continence rates immediately after catheter removal and at 1 wk, 4 wk, 12 wk, and 24 wk after RARP were 71.8%, 77.8%, 89.3%, 94.4%, and 98.0%, respectively. Multivariate analysis revealed that the nerve sparing technique, D'Amico risk groups, lymph node dissection, and prostate volume were involved in the early recovery of urinary continence. One ileal perforation requiring reoperation was recorded. The transfusion rate was 0.8%. Thirty-one (12.3%) postoperative complications were recorded up to 6 mo after surgery. Among these, eight acute urinary retentions (3.2%) and three urine leakages (1.2%) were recorded. There was a lack of randomization and comparison with other techniques. Both anatomical dissection of the prostatic apex and TAR were used. The results may not be generalized to low-volume centers. Conclusions: The TAR technique showed promising results in the early recovery of urinary continence, as well as watertight anastomosis and a low rate of urine leakage. The oncologic results were not affected. Comparative studies are needed to support the quality of reported results

Multiple sclerosis patients treated with cladribine tablets: expert opinion on practical management after year 4

Multiple sclerosis (MS) is a chronic, progressive neurological disease involving neuroinflammation, neurodegeneration, and demyelination. Cladribine tablets are approved for immune reconstitution therapy in patients with highly active relapsing–remitting MS based on favorable efficacy and tolerability results from the CLARITY study that have been confirmed in long-term extension studies. The approved 4-year dosing regimen foresees a cumulative dose of 3.5 mg/kg administered in two cycles administered 1 year apart, followed by 2 years of observation. Evidence on managing patients beyond year 4 is scarce; therefore, a group of 10 neurologists has assessed the available evidence and formulated an expert opinion on management of the growing population of patients now completing the approved 4-year regimen. We propose five patient categories based on response to treatment during the first 4-year regimen, and corresponding management pathways that envision close monitoring with clinical visits, magnetic resonance imaging (MRI) and/or biomarkers. At the first sign of clinical or radiological disease activity, patients should receive a highly effective disease-modifying therapy, comprising either a full cladribine regimen as described in regulatory documents (cumulative dose 7.0 mg/kg) or a comparably effective treatment. Re-treatment decisions should be based on the intensity and timing of onset of disease activity, clinical and radiological assessments, as well as patient eligibility for treatment and treatment preference

Scaling up Electronic Spin Qubits into a Three-Dimensional Metal-Organic Framework

Practical implementation of highly coherent molecular spin qubits for challenging technological applications, such as quantum information processing or quantum sensing, requires precise organization of electronic qubit molecular components into extended frameworks. Realization of spatial control over qubit–qubit distances can be achieved by coordination chemistry approaches through an appropriate choice of the molecular building blocks. However, translating single qubit molecular building units into extended arrays does not guarantee a priori retention of long quantum coherence and spin–lattice relaxation times due to the introduced modifications over qubit–qubit reciprocal distances and molecular crystal lattice phonon structure. In this work, we report the preparation of a three-dimensional (3D) metal–organic framework (MOF) based on vanadyl qubits, [VO­(TCPP-Zn2-bpy)] (TCPP = tetracarboxylphenylporphyrinate; bpy = 4,4′-bipyridyl) (1), and the investigation of how such structural modifications influence qubits’ performances. This has been done through a multitechnique approach where the structure and properties of a representative molecular building block of formula [VO­(TPP)] (TPP = tetraphenylporphyrinate) (2) have been compared with those of the 3D MOF 1. Pulsed electron paramagnetic resonance measurements on magnetically diluted samples in titanyl isostructural analogues revealed that coherence times are retained almost unchanged for 1 with respect to 2 up to room temperature, while the temperature dependence of the spin–lattice relaxation time revealed insights into the role of low-energy vibrations, detected through terahertz spectroscopy, on the spin dynamics