On Duality Walls in String Theory

Following the RG flow of an N=1 quiver gauge theory and applying Seiberg duality whenever necessary defines a duality cascade, that in simple cases has been understood holographically. It has been argued that in certain cases, the dualities will pile up at a certain energy scale called the duality wall, accompanied by a dramatic rise in the number of degrees of freedom. In string theory, this phenomenon is expected to occur for branes at a generic threefold singularity, for which the associated quiver has Lorentzian signature. We here study sequences of Seiberg dualities on branes at the C_3/Z_3 orbifold singularity. We use the naive beta functions to define an (unphysical) scale along the cascade. We determine, as a function of initial conditions, the scale of the wall as well as the critical exponent governing the approach to it. The position of the wall is piecewise linear, while the exponent appears to be constant. We comment on the possible implications of these results for physical walls.Comment: 22 pages, 2 figures. v2: physical interpretation rectified, reference adde

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

Quantum-mechanical model for particles carrying electric charge and magnetic flux in two dimensions

We propose a simple quantum mechanical equation for $n$ particles in two dimensions, each particle carrying electric charge and magnetic flux. Such particles appear in (2+1)-dimensional Chern-Simons field theories as charged vortex soliton solutions, where the ratio of charge to flux is a constant independent of the specific solution. As an approximation, the charge-flux interaction is described here by the Aharonov-Bohm potential, and the charge-charge interaction by the Coulomb one. The equation for two particles, one with charge and flux ($q, \Phi/Z$) and the other with ($-Zq, -\Phi$) where $Z$ is a pure number is studied in detail. The bound state problem is solved exactly for arbitrary $q$ and $\Phi$ when $Z>0$. The scattering problem is exactly solved in parabolic coordinates in special cases when $q\Phi/2\pi\hbar c$ takes integers or half integers. In both cases the cross sections obtained are rather different from that for pure Coulomb scattering.Comment: 12 pages, REVTeX, no figur

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

Parents' assessment of parent-child interaction interventions – a longitudinal study in 101 families

<p>Abstract</p> <p>Background</p> <p>The aim of the study was to describe families with small children who participated in parent-child interaction interventions at four centres in Sweden, and to examine long term and short term changes regarding the parents' experience of parental stress, parental attachment patterns, the parents' mental health and life satisfaction, the parents' social support and the children's problems.</p> <p>Methods</p> <p>In this longitudinal study a consecutive sample of 101 families (94 mothers and 54 fathers) with 118 children (median age 3 years) was assessed, using self-reports, at the outset of the treatment (T1), six months later (T2) and 18 months after the beginning of treatment (T3). Analysis of the observed differences was carried out using Wilcoxon's Signed-Rank test and Cohen's d.</p> <p>Results</p> <p>The results from commencement of treatment showed that the parents had considerable problems in all areas examined. At the outset of treatment (T1) the mothers showed a higher level of problem load than the fathers on almost all scales. In the families where the children's problems have also been measured (children from the age of four) it appeared that they had problems of a nature and degree otherwise found in psychiatric populations. We found a clear general trend towards a positive development from T1 to T2 and this development was also reinforced from T2 to T3. Aggression in the child was one of the most common causes for contact. There were few undesired or unplanned interruptions of the treatment, and the attrition from the study was low.</p> <p>Conclusion</p> <p>This study has shown that it is possible to reach mothers as well as fathers with parenting problems and to create an intervention program with very low dropout levels – which is of special importance for families with small children displaying aggressive behaviour. The parents taking part in this study showed clear improvement trends after six months and this development was reinforced a year later. This study suggests the necessity of clinical development and future research concerning the role of fathers in parent-child interaction interventions.</p

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