A categorification of Morelli's theorem

We prove a theorem relating torus-equivariant coherent sheaves on toric varieties to polyhedrally-constructible sheaves on a vector space. At the level of K-theory, the theorem recovers Morelli's description of the K-theory of a smooth projective toric variety. Specifically, let $X$ be a proper toric variety of dimension $n$ and let M_\bR = \mathrm{Lie}(T_\bR^\vee)\cong \bR^n be the Lie algebra of the compact dual (real) torus T_\bR^\vee\cong U(1)^n. Then there is a corresponding conical Lagrangian \Lambda \subset T^*M_\bR and an equivalence of triangulated dg categories \Perf_T(X) \cong \Sh_{cc}(M_\bR;\Lambda), where \Perf_T(X) is the triangulated dg category of perfect complexes of torus-equivariant coherent sheaves on $X$ and \Sh_{cc}(M_\bR;\Lambda) is the triangulated dg category of complex of sheaves on M_\bR with compactly supported, constructible cohomology whose singular support lies in $\Lambda$. This equivalence is monoidal---it intertwines the tensor product of coherent sheaves on $X$ with the convolution product of constructible sheaves on M_\bR.Comment: 20 pages. This is a strengthened version of the first half of arXiv:0811.1228v3, with new results; the second half becomes arXiv:0811.1228v

Minimal Family Unification

Absract It is proposed that there exist, within a new $SU(2)^{'}$, a gauged discrete group $Q_6$ (the order 12 double dihedral group) acting as a family symmetry. This nonabelian finite group can explain hierarchical features of families, using an assignment for quarks and leptons dictated by the requirements of anomaly cancellation and of no additional quarks.Comment: 10 pages, IFP-701-UNC;VAND-TH-94-

Topological Orbifold Models and Quantum Cohomology Rings

We discuss the toplogical sigma model on an orbifold target space. We describe the moduli space of classical minima for computing correlation functions involving twisted operators, and show, through a detailed computation of an orbifold of ${\bf CP}^1$ by the dihedral group $D_{4},$ how to compute the complete ring of observables. Through this procedure, we compute all the rings from dihedral ${\bf CP}^1$ orbifolds; we note a similarity with rings derived from perturbed $D-$series superpotentials of the $A-D-E$ classification of $N = 2$ minimal models. We then consider ${\bf CP}^2/D_4,$ and show how the techniques of topological-anti-topological fusion might be used to compute twist field correlation functions for nonabelian orbifolds.Comment: 48 pages, harvmac, HUTP-92/A06

NC Calabi-Yau Orbifolds in Toric Varieties with Discrete Torsion

Using the algebraic geometric approach of Berenstein et {\it al} (hep-th/005087 and hep-th/009209) and methods of toric geometry, we study non commutative (NC) orbifolds of Calabi-Yau hypersurfaces in toric varieties with discrete torsion. We first develop a new way of getting complex $d$ mirror Calabi-Yau hypersurfaces $H_{\Delta}^{\ast d}$ in toric manifolds $M_{\Delta }^{\ast (d+1)}$ with a $C^{\ast r}$ action and analyze the general group of the discrete isometries of $H_{\Delta}^{\ast d}$. Then we build a general class of $d$ complex dimension NC mirror Calabi-Yau orbifolds where the non commutativity parameters $\theta_{\mu \nu}$ are solved in terms of discrete torsion and toric geometry data of $M_{\Delta}^{(d+1)}$ in which the original Calabi-Yau hypersurfaces is embedded. Next we work out a generalization of the NC algebra for generic $d$ dimensions NC Calabi-Yau manifolds and give various representations depending on different choices of the Calabi-Yau toric geometry data. We also study fractional D-branes at orbifold points. We refine and extend the result for NC $T^{2})/(\mathbf{{Z_{2}}\times {Z_{2})}}$ to higher dimensional torii orbifolds in terms of Clifford algebra.Comment: 38 pages, Late

An Analytic Study of the Professional Development Research in Early Childhood Education

The goal of this study was to examine empirical research on the design, delivery, and measurement of the effects of professional development (PD) for early childhood educators in order to provide insight into what the field has accomplished as well as suggest directions for future PD programs and research. Through the use of rigorous inclusion criteria outlined by S. M. Wilson, R. E. Floden, and J. Ferrini-Mundy (2001), 73 studies were included and analyzed. On average, 25% (M = 12.68, SD = 9.99) of references in each study were specifically about PD. The majority of studies (n = 39) targeted some form of language and literacy instruction, whereas only 5 studies targeted math and 1 study targeted science. A total of 35 different delivery mechanisms were used to provide PD, with 40 studies including some form of coaching and 45 including training workshops. The studies used a wide range of methods to measure PD-related outcomes: 51% (n = 37) of studies examined changes in teacher practice, 18% (n = 13) measured changes in teachers’ knowledge, 40% (n = 29) measured changes in children’s learning, and 11% (n = 8) measured changes in children’s behavior. Practice or Policy: Based on the results of this study, there are 4 major ways in which PD for early childhood educators can be developed. Researchers and providers of PD should (a) continue to draw from multiple resources to inform PD implementation designs, (b) include more diversity in the content of instruction targeted by PD, (c) experiment with innovative formats for delivering PD, and (d) create better means of evaluating PD

Serotonin transporter gene (SLC6A4) polymorphism and susceptibility to a home-visiting maternal-infant attachment intervention delivered by community health workers in South Africa: reanalysis of a randomized controlled trial

Background Clear recognition of the damaging effects of poverty on early childhood development has fueled an interest in interventions aimed at mitigating these harmful consequences. Psychosocial interventions aimed at alleviating the negative impacts of poverty on children are frequently shown to be of benefit, but effect sizes are typically small to moderate. However, averaging outcomes over an entire sample, as is typically done, could underestimate efficacy because weaker effects on less susceptible individuals would dilute estimation of effects on those more disposed to respond. This study investigates whether a genetic polymorphism of the serotonin transporter gene moderates susceptibility to a psychosocial intervention. Methods and findings We reanalyzed data from a randomized controlled trial of a home-visiting program delivered by community health workers in a black, isiXhosa-speaking population in Khayelitsha, South Africa. The intervention, designed to enhance maternal-infant attachment, began in the third trimester and continued until 6 mo postpartum. Implemented between April 1999 and February 2003, the intervention comprised 16 home visits delivered to 220 mother–infant dyads by specially trained community health workers. A control group of 229 mother–infant dyads did not receive the intervention. Security of maternal-infant attachment was the main outcome measured at infant age 18 mo. Compared to controls, infants in the intervention group were significantly more likely to be securely attached to their primary caregiver (odds ratio [OR] = 1.7, p = 0.029, 95% CI [1.06, 2.76], d = 0.29). After the trial, 162 intervention and 172 control group children were reenrolled in a follow-up study at 13 y of age (December 2012–June 2014). At this time, DNA collected from 279 children (134 intervention and 145 control) was genotyped for a common serotonin transporter polymorphism. There were both genetic data and attachment security data for 220 children (110 intervention and 110 control), of whom 40% (44 intervention and 45 control) carried at least one short allele of the serotonin transporter gene. For these 220 individuals, carrying at least one short allele of the serotonin transporter gene was associated with a 26% higher rate of attachment security relative to controls (OR = 3.86, p = 0.008, 95% CI [1.42, 10.51], d = 0.75), whereas there was a negligible (1%) difference in security between intervention and control group individuals carrying only the long allele (OR = 0.95, p = 0.89, 95% CI [0.45, 2.01], d = 0.03). Expressed in terms of absolute risk, for those with the short allele, the probability of secure attachment being observed in the intervention group was 84% (95% CI [73%, 95%]), compared to 58% (95% CI [43%, 72%]) in the control group. For those with two copies of the long allele, 70% (95% CI [59%, 81%]) were secure in the intervention group, compared to 71% (95% CI [60%, 82%]) of infants in the control group. Controlling for sex, maternal genotype, and indices of socioeconomic adversity (housing, employment, education, electricity, water) did not change these results. A limitation of this study is that we were only able to reenroll 49% of the original sample randomized to the intervention and control conditions. Attribution of the primary outcome to causal effects of intervention in the present subsample should therefore be treated with caution. Conclusions When infant genotype for serotonin transporter polymorphism was taken into account, the effect size of a maternal-infant attachment intervention targeting impoverished pregnant women increased more than 2.5-fold when only short allele carriers were considered (from d = 0.29 for all individuals irrespective of genotype to d = 0.75) and decreased 10-fold when only those carrying two copies of the long allele were considered (from d = 0.29 for all individuals to d = 0.03). Genetic differential susceptibility means that averaging across all participants is a misleading index of efficacy. The study raises questions about how policy-makers deal with the challenge of balancing equity (equal treatment for all) and efficacy (treating only those whose genes render them likely to benefit) when implementing psychosocial interventions

An Alternative Neo-Kohlbergian Approach in Social Pedagogy

In many countries social pedagogues apply ART (Aggression Replacement Training), a multimodal programme designed to help juveniles with severe behaviour problems. In this programme Lawrence Kohlberg’s theory of moral development makes up an important element. The first part of this article offers a presentation of Kohlberg’s theory and some of the critique made of it. The second part describes how the Kohlbergian tradition is implemented in ART. In the final part of the article a problem with the ART programme is pointed out and an alternative neo-Kohlbergian approach is described. This method may prove to be a viable approach in the field of social pedagogy and an adequate supplement to the ART programme