Calabi-Yau Orbifolds and Torus Coverings

The theory of coverings of the two-dimensional torus is a standard part of algebraic topology and has applications in several topics in string theory, for example, in topological strings. This paper initiates applications of this theory to the counting of orbifolds of toric Calabi-Yau singularities, with particular attention to Abelian orbifolds of C^D. By doing so, the work introduces a novel analytical method for counting Abelian orbifolds, verifying previous algorithm results. One identifies a p-fold cover of the torus T^{D-1} with an Abelian orbifold of the form C^D/Z_p, for any dimension D and a prime number p. The counting problem leads to polynomial equations modulo p for a given Abelian subgroup of S_D, the group of discrete symmetries of the toric diagram for C^D. The roots of the polynomial equations correspond to orbifolds of the form C^D/Z_p, which are invariant under the corresponding subgroup of S_Ds. In turn, invariance under this subgroup implies a discrete symmetry for the corresponding quiver gauge theory, as is clearly seen by its brane tiling formulation.Comment: 33 pages, 5 figures, 7 tables; version published on JHE

Finite-size scaling considerations on the ground state microcanonical temperature in entropic sampling simulations

In this work we discuss the behavior of the microcanonical temperature $\frac{\partial S(E)}{\partial E}$ obtained by means of numerical entropic sampling studies. It is observed that in almost all cases the slope of the logarithm of the density of states $S(E)$ is not infinite in the ground state, since as expected it should be directly related to the inverse temperature $\frac{1}{T}$. Here we show that these finite slopes are in fact due to finite-size effects and we propose an analytic expression $a\ln(bL)$ for the behavior of $\frac{\varDelta S}{\varDelta E}$ when $L\rightarrow\infty$. To test this idea we use three distinct two-dimensional square lattice models presenting second-order phase transitions. We calculated by exact means the parameters $a$ and $b$ for the two-states Ising model and for the $q=3$ and $4$ states Potts model and compared with the results obtained by entropic sampling simulations. We found an excellent agreement between exact and numerical values. We argue that this new set of parameters $a$ and $b$ represents an interesting novel issue of investigation in entropic sampling studies for different models

An Assessment of the Model of Concentration Addition for Predicting the Estrogenic Activity of Chemical Mixtures in Wastewater Treatment Works Effluents

The effects of simple mixtures of chemicals, with similar mechanisms of action, can be predicted using the concentration addition model (CA). The ability of this model to predict the estrogenic effects of more complex mixtures such as effluent discharges, however, has yet to be established. Effluents from 43 U.K. wastewater treatment works were analyzed for the presence of the principal estrogenic chemical contaminants, estradiol, estrone, ethinylestradiol, and nonylphenol. The measured concentrations were used to predict the estrogenic activity of each effluent, employing the model of CA, based on the relative potencies of the individual chemicals in an in vitro recombinant yeast estrogen screen (rYES) and a short-term (14-day) in vivo rainbow trout vitellogenin induction assay. Based on the measured concentrations of the four chemicals in the effluents and their relative potencies in each assay, the calculated in vitro and in vivo responses compared well and ranged between 3.5 and 87 ng/L of estradiol equivalents (E2 EQ) for the different effluents. In the rYES, however, the measured E2 EQ concentrations in the effluents ranged between 0.65 and 43 ng E2 EQ/L, and they varied against those predicted by the CA model. Deviations in the estimation of the estrogenic potency of the effluents by the CA model, compared with the measured responses in the rYES, are likely to have resulted from inaccuracies associated with the measurement of the chemicals in the extracts derived from the complex effluents. Such deviations could also result as a consequence of interactions between chemicals present in the extracts that disrupted the activation of the estrogen response elements in the rYES. E2 EQ concentrations derived from the vitellogenic response in fathead minnows exposed to a series of effluent dilutions were highly comparable with the E2 EQ concentrations derived from assessments of the estrogenic potency of these dilutions in the rYES. Together these data support the use of bioassays for determining the estrogenic potency of WwTW effluents, and they highlight the associated problems for modeling approaches that are reliant on measured concentrations of estrogenic chemicals

General Form of the Color Potential Produced by Color Charges of the Quark

Constant electric charge $e$ satisfies the continuity equation $\partial_\mu j^{\mu}(x)= 0$ where $j^\mu(x)$ is the current density of the electron. However, the Yang-Mills color current density $j^{\mu a}(x)$ of the quark satisfies the equation $D_\mu[A] j^{\mu a}(x)= 0$ which is not a continuity equation ($\partial_\mu j^{\mu a}(x)\neq 0$) which implies that a color charge $q^a(t)$ of the quark is not constant but it is time dependent where $a=1,2,...8$ are color indices. In this paper we derive general form of color potential produced by color charges of the quark. We find that the general form of the color potential produced by the color charges of the quark at rest is given by \Phi^a(x) =A_0^a(t,{\bf x}) =\frac{q^b(t-\frac{r}{c})}{r}\[\frac{{\rm exp}[g\int dr \frac{Q(t-\frac{r}{c})}{r}] -1}{g \int dr \frac{Q(t-\frac{r}{c})}{r}}\]_{ab} where $dr$ integration is an indefinite integration, ~~ $Q_{ab}(\tau_0)=f^{abd}q^d(\tau_0)$, ~~$r=|{\vec x}-{\vec X}(\tau_0)|$, ~~$\tau_0=t-\frac{r}{c}$ is the retarded time, ~~$c$ is the speed of light, ~~${\vec X}(\tau_0)$ is the position of the quark at the retarded time and the repeated color indices $b,d$(=1,2,...8) are summed. For constant color charge $q^a$ we reproduce the Coulomb-like potential $\Phi^a(x)=\frac{q^a}{r}$ which is consistent with the Maxwell theory where constant electric charge $e$ produces the Coulomb potential $\Phi(x)=\frac{e}{r}$.Comment: Final version, two more sections added, 45 pages latex, accepted for publication in JHE

A Tonnetz Model for pentachords

This article deals with the construction of surfaces that are suitable for representing pentachords or 5-pitch segments that are in the same $T/I$ class. It is a generalization of the well known \"Ottingen-Riemann torus for triads of neo-Riemannian theories. Two pentachords are near if they differ by a particular set of contextual inversions and the whole contextual group of inversions produces a Tiling (Tessellation) by pentagons on the surfaces. A description of the surfaces as coverings of a particular Tiling is given in the twelve-tone enharmonic scale case.Comment: 27 pages, 12 figure

Recognition of Face Identity and Emotion in Expressive Specific Language Impairment

Objective: To study face and emotion recognition in children with mostly expressive specific language impairment (SLI-E). Subjects and Methods: A test movie to study perception and recognition of faces and mimic-gestural expression was applied to 24 children diagnosed as suffering from SLI-E and an age-matched control group of normally developing children. Results: Compared to a normal control group, the SLI-E children scored significantly worse in both the face and expression recognition tasks with a preponderant effect on emotion recognition. The performance of the SLI-E group could not be explained by reduced attention during the test session. Conclusion: We conclude that SLI-E is associated with a deficiency in decoding non-verbal emotional facial and gestural information, which might lead to profound and persistent problems in social interaction and development. Copyright (C) 2012 S. Karger AG, Base

Chiral Modulations in Curved Space I: Formalism

The goal of this paper is to present a formalism that allows to handle four-fermion effective theories at finite temperature and density in curved space. The formalism is based on the use of the effective action and zeta function regularization, supports the inclusion of inhomogeneous and anisotropic phases. One of the key points of the method is the use of a non-perturbative ansatz for the heat-kernel that returns the effective action in partially resummed form, providing a way to go beyond the approximations based on the Ginzburg-Landau expansion for the partition function. The effective action for the case of ultra-static Riemannian spacetimes with compact spatial section is discussed in general and a series representation, valid when the chemical potential satisfies a certain constraint, is derived. To see the formalism at work, we consider the case of static Einstein spaces at zero chemical potential. Although in this case we expect inhomogeneous phases to occur only as meta-stable states, the problem is complex enough and allows to illustrate how to implement numerical studies of inhomogeneous phases in curved space. Finally, we extend the formalism to include arbitrary chemical potentials and obtain the analytical continuation of the effective action in curved space.Comment: 22 pages, 3 figures; version to appear in JHE

Elliptic logarithms, diophantine approximation and the Birch and Swinnerton-Dyer conjecture

Most, if not all, unconditional results towards the abc-conjecture rely ultimately on classical Baker's method. In this article, we turn our attention to its elliptic analogue. Using the elliptic Baker's method, we have recently obtained a new upper bound for the height of the S-integral points on an elliptic curve. This bound depends on some parameters related to the Mordell-Weil group of the curve. We deduce here a bound relying on the conjecture of Birch and Swinnerton-Dyer, involving classical, more manageable quantities. We then study which abc-type inequality over number fields could be derived from this elliptic approach.Comment: 20 pages. Some changes, the most important being on Conjecture 3.2, three references added ([Mas75], [MB90] and [Yu94]) and one reference updated [BS12]. Accepted in Bull. Brazil. Mat. So

How Mistimed and Unwanted Pregnancies Affect Timing of Antenatal Care Initiation in three Districts in Tanzania

Early antenatal care (ANC) initiation is a doorway to early detection and management of potential complications associated with pregnancy. Although the literature reports various factors associated with ANC initiation such as parity and age, pregnancy intentions is yet to be recognized as a possible predictor of timing of ANC initiation. Data originate from a cross-sectional household survey on health behaviour and service utilization patterns. The survey was conducted in 2011 in Rufiji, Kilombero and Ulanga districts in Tanzania on 910 women of reproductive age who had given birth in the past two years. ANC initiation was considered to be early only if it occurred in the first trimester of pregnancy gestation. A recently completed pregnancy was defined as mistimed if a woman wanted it later, and if she did not want it at all the pregnancy was termed as unwanted. Chisquare was used to test for associations and multinomial logistic regression was conducted to examine how mistimed and unwanted pregnancies affect timing of ANC initiation. Although 49.3% of the women intended to become pregnant, 50.7% (34.9% mistimed and 15.8% unwanted) became pregnant unintentionally. While ANC initiation in the 1st trimester was 18.5%, so was 71.7% and 9.9% in the 2nd and 3rd trimesters respectively. Multivariate analysis revealed that ANC initiation in the 2nd trimester was 1.68 (95% CI 1.10‒2.58) and 2.00 (95% CI 1.05‒3.82) times more likely for mistimed and unwanted pregnancies respectively compared to intended pregnancies. These estimates rose to 2.81 (95% CI 1.41‒5.59) and 4.10 (95% CI 1.68‒10.00) respectively in the 3rd trimester. We controlled for gravidity, age, education, household wealth, marital status, religion, district of residence and travel time to a health facility. Late ANC initiation is a significant maternal and child health consequence of mistimed and unwanted pregnancies in Tanzania. Women should be empowered to delay or avoid pregnancies whenever they need to do so. Appropriate counseling to women, especially those who happen to conceive unintentionally is needed to minimize the possibility of delaying ANC initiation.\u