On the genus of projective curves not contained in hypersurfaces of given degree

Fix integers r >= 4 and i >= 2 (for r = 4 assume i >= 3). Assume that the rational number s defined by the equation ((i + 1)(2))s + (i + 1) = ((r + i) )(i)is( ) an integer. Fix an integer d >= s. Divide d - 1 = ms + epsilon, 0 <= epsilon <= s - 1, and set G(r;d, i) := ((m)(2))s + m epsilon. As a number, 2 G(r; d, i) is nothing but the Castelnuovo's bound G(s + 1;d) for a curve of degree d in Ps+1. In the present paper we prove that G(r; d, i) is also an upper bound for the genus of a reduced and irreducible complex projective curve in P-r, of degree d >> max{ r,i}, not contained in hypersurfaces of degree <= i. We prove that the bound G(r; d, i) is sharp if and only if there exists an integral surface S subset of P-r of degree s, not contained in hypersurfaces of degree <= i. Such a surface, if existing, is necessarily the isomorphic projection of a rational normal scroll surface of degree s in Ps+1 The existence of such a surface S is known for r >= 5, and 2 <= i <= 3. It follows that, when r >= 5, and i = 2 or i = 3, the bound G(r; d, i) is sharp, and the extremal curves are isomorphic projection in P-r of Castelnuovo's curves of degree d in Ps+1. We do not know whether the bound G(r; d, i) is sharp for i > 3

The genus of curves in P-4 and P-5 not contained in quadrics

A classical problem in the theory of projective curves is the classification of all their possible genera in terms of the degree and the dimension of the space where they are embedded. Fixed integers r, d, s, Castelnuovo-Halphen's theory states a sharp upper bound for the genus of a non-degenerate, reduced and irreducible curve of degree d in P-r, under the condition of being not contained in a surface of degree < s. This theory can be generalized in several ways. For instance, fixed integers r, d, k, one may ask for the maximal genus of a curve of degree d in P-r, not contained in a hypersurface of degree < k. In the present paper we examine the genus of curves C of degree d in p(r) not contained in quadrics (i.e. h(0) (P-r, I-C(2)) = 0). When r = 4 and r = 5, and d >> 0, we exhibit a sharp upper bound for the genus. For certain values of r >= 7, we are able to determine a sharp bound except for a constant term, and the argument applies also to curves not contained in cubics

Mode Confinement in Photonic Quasi-Crystal Point-Defect Cavities for Particle Accelerators

In this Letter, we present a study of the confinement properties of point-defect resonators in finite-size photonic-bandgap structures composed of aperiodic arrangements of dielectric rods, with special emphasis on their use for the design of cavities for particle accelerators. Specifically, for representative geometries, we study the properties of the fundamental mode (as a function of the filling fraction, structure size, and losses) via 2-D and 3-D full-wave numerical simulations, as well as microwave measurements at room temperature. Results indicate that, for reduced-size structures, aperiodic geometries exhibit superior confinement properties by comparison with periodic ones.Comment: 4 pages, 4 figures, accepted for publication in Applied Physics Letter

Transport in strongly-coupled graphene-LaAlO3/SrTiO3 hybrid systems

We report on the transport properties of hybrid devices obtained by depositing graphene on a LaAlO3/SrTiO3 oxide junction hosting a 4 nm-deep two-dimensional electron system. At low graphene-oxide inter-layer bias the two electron systems are electrically isolated, despite their small spatial separation, and very efficient reciprocal gating is shown. A pronounced rectifying behavior is observed for larger bias values and ascribed to the interplay between electrostatic depletion and tunneling across the LaAlO3 barrier. The relevance of these results in the context of strongly-coupled bilayer systems is discussed.Comment: 10 pages, 3 figure

In a large Juvenile Idiopathic Arthritis (JIA) cohort, concomitant celiac disease is associated with family history of autoimmunity and a more severe JIA course: a retrospective study

Background: A higher prevalence of celiac disease (CD) has been reported in patients with juvenile idiopathic arthritis (JIA) compared to the general population. Factors related to the increased risk of co-occurrence and associated disease course have not been fully elucidated. Aims of this study were to determine the prevalence of CD in a large Southern Italian cohort of children with JIA, describe their clinical features and disease course and investigate risk factors associated with their co-occurrence. Findings: Demographic, clinical and laboratory data of all patients with JIA admitted to our Pediatric Rheumatology Unit from January 2001 to June 2019, who underwent CD screening, were retrospectively extracted from clinical charts and analyzed. Eight of 329 JIA patients were diagnosed with CD, resulting in a prevalence higher than the general Italian population (2.4% vs 0.93%, p < 0.05). Familiarity for autoimmunity was reported by 87.5% patients with JIA and CD compared to 45.8% of those without CD (p < 0.05). 87.5% patients with JIA and CD required both a conventional Disease Modifying Anti-Rheumatic Drug (DMARD) and a biological DMARD over time compared to 36.4% of those without CD (p < 0.05). Conclusion: A higher CD prevalence was found in a large JIA cohort, supporting the need for CD screening in all JIA children, especially those with a family history of autoimmunity, found to be associated with the co-occurrence of the two diseases. This is clinically relevant since patients with CD and JIA more often required a step-up therapy, suggesting a more severe JIA clinical course

Hybrid photonic-bandgap accelerating cavities

In a recent investigation, we studied two-dimensional point-defected photonic bandgap cavities composed of dielectric rods arranged according to various representative periodic and aperiodic lattices, with special emphasis on possible applications to particle acceleration (along the longitudinal axis). In this paper, we present a new study aimed at highlighting the possible advantages of using hybrid structures based on the above dielectric configurations, but featuring metallic rods in the outermost regions, for the design of extremely-high quality factor, bandgap-based, accelerating resonators. In this framework, we consider diverse configurations, with different (periodic and aperiodic) lattice geometries, sizes, and dielectric/metal fractions. Moreover, we also explore possible improvements attainable via the use of superconducting plates to confine the electromagnetic field in the longitudinal direction. Results from our comparative studies, based on numerical full-wave simulations backed by experimental validations (at room and cryogenic temperatures) in the microwave region, identify the candidate parametric configurations capable of yielding the highest quality factor.Comment: 13 pages, 5 figures, 3 tables. One figure and one reference added; minor changes in the tex

Brivaracetam use in clinical practice: a Delphi consensus on its role as first add-on therapy in focal epilepsy and beyond

Background Antiseizure medications remain the cornerstone of treatment for epilepsy, although a proportion of individuals with the condition will continue to experience seizures despite appropriate therapy. Treatment choices for epilepsy are based on variables related to both the individual patient and the available medications. Brivaracetam is a third-generation agent antiseizure medication.Methods We carried out a Delphi consensus exercise to define the role of brivaracetam in clinical practice and to provide guidance about its use as first add-on ASM and in selected clinical scenarios. A total of 15 consensus statements were drafted by an expert panel following review of the literature and all were approved in the first round of voting by panelists. The consensus indicated different clinical scenarios for which brivaracetam can be a good candidate for treatment, including first add-on use.Results Overall, brivaracetam was considered to have many advantageous characteristics that render it a suitable option for patients with focal epilepsy, including a fast onset of action, favorable pharmacokinetic profile with few drug-drug interactions, broad-spectrum activity, and being well tolerated across a range of doses. Brivaracetam is also associated with sustained clinical response and good tolerability in the long term.Conclusions These characteristics also make it suitable as an early add-on for the elderly and for patients with post-stroke epilepsy or status epilepticus as highlighted by the present Delphi consensus

Probing charge transfer during metal-insulator transitions in graphene-LaAlO3/SrTiO3 systems

Two-dimensional electron systems (2DESs) at the interface between LaAlO3 (LAO) and SrTiO3 (STO) perovskite oxides display a wide class of tunable phenomena ranging from superconductivity to metal-insulator transitions. Most of these effects are strongly sensitive to surface physics and often involve charge transfer mechanisms, which are, however, hard to detect. In this work, we realize hybrid field-effect devices where graphene is used to modulate the transport properties of the LAO/STO 2DES. Different from a conventional gate, graphene is semimetallic and allows us to probe charge transfer with the oxide structure underneath the field-effect electrode. In LAO/STO samples with a low initial carrier density, graphene-covered regions turn insulating when the temperature is lowered to 3 K, but conduction can be restored in the oxide structure by increasing the temperature or by field effect. The evolution of graphene's electron density is found to be inconsistent with a depletion of LAO/STO, but it rather points to a localization of interfacial carriers in the oxide structure.Two-dimensional electron systems (2DESs) at the interface between LaAlO3 (LAO) and SrTiO3 (STO) perovskite oxides display a wide class of tunable phenomena ranging from superconductivity to metal-insulator transitions. Most of these effects are strongly sensitive to surface physics and often involve charge transfer mechanisms, which are, however, hard to detect. In this work, we realize hybrid field-effect devices where graphene is used to modulate the transport properties of the LAO/STO 2DES. Different from a conventional gate, graphene is semimetallic and allows us to probe charge transfer with the oxide structure underneath the field-effect electrode. In LAO/STO samples with a low initial carrier density, graphene-covered regions turn insulating when the temperature is lowered to 3 K, but conduction can be restored in the oxide structure by increasing the temperature or by field effect. The evolution of graphene's electron density is found to be inconsistent with a depletion of LAO/STO, but it rather p..