Safety and efficacy of calcipotriene plus betamethasone dipropionate topical suspension in the treatment of extensive scalp psoriasis in adolescents ages 12 to 17 years.

The objective of this study was to assess the safety and efficacy of the fixed combination calcipotriene 0.005% plus betamethasone dipropionate 0.064% topical suspension in adolescents with extensive scalp psoriasis. In this phase II, open-label, 8-week study, adolescents with psoriasis (ages 12-17 years) with 20% or more of the scalp area affected (at least moderate severity according to Investigator's Global Assessment [IGA]) were assigned to once-daily treatment with calcipotriene plus betamethasone dipropionate topical suspension. The primary endpoint was safety, focusing on calcium metabolism and hypothalamic-pituitary-adrenal axis function. Secondary efficacy endpoints were the proportion of patient's achieving treatment success (clear or almost clear disease according to the IGA and clear or very mild disease according to the Patient's Global Assessment [PaGA]) and percentage change in investigator-assessed Total Sign Score (TSS). Pruritus was also assessed. Overall, 31 patients received treatment. Sixteen patients (52%) experienced a total of 20 adverse events; 19 were considered unrelated to study treatment, 14 were mild, and none were serious or lesional or perilesional on the scalp. One patient showed signs of mild adrenal suppression at week 4; the patient discontinued treatment and had normal test results at follow-up 4 weeks later. No cases of hypercalcemia were reported. By treatment end, treatment success was reported for 17 patients (55%) according to the IGA and 18 (58%) according to the PGA. Mean TSS improved from 6.9 at baseline to 2.9 at treatment end (59% improvement). By week 8, 28 patients (90%) experienced mild or no itching, versus 20 (65%) at baseline. Once-daily calcipotriene plus betamethasone dipropionate topical suspension was well tolerated and efficacious for the treatment of scalp psoriasis in adolescents

Deformations of modules of maximal grade and the Hilbert scheme at determinantal schemes

Let R be a polynomial ring and M a finitely generated graded R-module of maximal grade (which means that the ideal I_t(\cA) generated by the maximal minors of a homogeneous presentation matrix, \cA, of M has maximal codimension in R). Suppose X:=Proj(R/I_t(\cA)) is smooth in a sufficiently large open subset and dim X > 0. Then we prove that the local graded deformation functor of M is isomorphic to the local Hilbert (scheme) functor at X \subset Proj(R) under a week assumption which holds if dim X > 1. Under this assumptions we get that the Hilbert scheme is smooth at (X), and we give an explicit formula for the dimension of its local ring. As a corollary we prove a conjecture of R. M. Mir\'o-Roig and the author that the closure of the locus of standard determinantal schemes with fixed degrees of the entries in a presentation matrix is a generically smooth component V of the Hilbert scheme. Also their conjecture on the dimension of V is proved for dim X > 0. The cohomology H^i_{*}({\cN}_X) of the normal sheaf of X in Proj(R) is shown to vanish for 0 < i < dim X-1. Finally the mentioned results, slightly adapted, remain true replacing R by any Cohen-Macaulay quotient of a polynomial ring.Comment: 24 page

Computing noncommutative deformations of presheaves and sheaves of modules

We describe a noncommutative deformation theory for presheaves and sheaves of modules that generalizes the commutative deformation theory of these global algebraic structures, and the noncommutative deformation theory of modules over algebras due to Laudal. In the first part of the paper, we describe a noncommutative deformation functor for presheaves of modules on a small category, and an obstruction theory for this functor in terms of global Hochschild cohomology. An important feature of this obstruction theory is that it can be computed in concrete terms in many interesting cases. In the last part of the paper, we describe noncommutative deformation functors for sheaves and quasi-coherent sheaves of modules on a ringed space $(X, \mathcal{A})$. We show that for any good $\mathcal{A}$-affine open cover $\mathsf{U}$ of $X$, the forgetful functor $\mathsf{QCoh}(\mathcal{A}) \to \mathsf{PreSh}(\mathsf{U}, \mathcal{A})$ induces an isomorphism of noncommutative deformation functors. \emph{Applications.} We consider noncommutative deformations of quasi-coherent $\mathcal{A}$-modules on $X$ when $(X, \mathcal{A}) = (X, \mathcal{O}_X)$ is a scheme or $(X, \mathcal{A}) = (X, \mathcal{D})$ is a D-scheme in the sense of Beilinson and Bernstein. In these cases, we may use any open affine cover of $X$ closed under finite intersections to compute noncommutative deformations in concrete terms using presheaf methods. We compute the noncommutative deformations of the left $\mathcal{D}_X$-module $\mathcal{O}_X$ when $X$ is an elliptic curve as an example.Comment: 22 pages, AMS-LaTeX. Some results from earlier versions have been omitted to focus on the main results in the pape

Extremal Transitions and Five-Dimensional Supersymmetric Field Theories

We study five-dimensional supersymmetric field theories with one-dimensional Coulomb branch. We extend a previous analysis which led to non-trivial fixed points with $E_n$ symmetry ($E_8$, $E_7$, $E_6$, $E_5=Spin(10)$, $E_4=SU(5)$, $E_3=SU(3)\times SU(2)$, $E_2=SU(2)\times U(1)$ and $E_1=SU(2)$) by finding two new theories: $\tilde E_1$ with $U(1)$ symmetry and $E_0$ with no symmetry. The latter is a non-trivial theory with no relevant operators preserving the super-Poincar\'e symmetry. In terms of string theory these new field theories enable us to describe compactifications of the type I' theory on $S^1/Z_2$ with 16, 17 or 18 background D8-branes. These theories also play a crucial role in compactifications of M-theory on Calabi--Yau spaces, providing physical models for the contractions of del Pezzo surfaces to points (thereby completing the classification of singularities which can occur at codimension one in K\"ahler moduli). The structure of the Higgs branch yields a prediction which unifies the known mathematical facts about del Pezzo transitions in a quite remarkable way.Comment: 21 pages, 3 figures, minor change to appendi

Chromosomal bar codes produced by multicolor fluorescence in situ hybridization with multiple YAC clones and whole chromosome painting probes

Colored chromosome staining patterns, termed chromosomal ‘bar codes’ (CBCs), were obtained on human chromosomes by fluorescence in situ hybridization (FISH) with pools of Alu-PCR products from YAC dones containing human DNA inserts ranging from 100 kbp to 1 Mbp. In contrast to conventional G- or R-bands, the chromosomal position, extent, Individual color and relative signal intensity of each ‘bar’ could be modified depending on probe selection and labeling procedures. Alu-PCR amplification products were generated from 31 YAC clones which mapped to 37 different chromosome bands. For multiple color FISH, Alu-PCR amplification products from various clones were either biotinylated or labeled with digoxigenin. Probes from up to twenty YAC clones were used simultaneously to produce CBCs on selected human chromosomes. Evaluation using a cooled CCD camera and digital image analysis confirmed the high reproducibility of the bars from one metaphase spread to another. Combinatorial FISH with mixtures of whole chromosome paint probes was applied to paint seven chromosomes simultaneously in different colors along with a set of YAC clones which map to these chromosomes. We discuss the potential to construct analytical chromosomal bar codes adapted to particular needs of cytogenetic investigations and automated image analysis

Homological Type of Geometric Transitions

The present paper gives an account and quantifies the change in topology induced by small and type II geometric transitions, by introducing the notion of the \emph{homological type} of a geometric transition. The obtained results agree with, and go further than, most results and estimates, given to date by several authors, both in mathematical and physical literature.Comment: 36 pages. Minor changes: A reference and a related comment in Remark 3.2 were added. This is the final version accepted for publication in the journal Geometriae Dedicat