A small transitive family of continuous functions on the Cantor set

In this paper we show that, when we iteratively add Sacks reals to a model of ZFC we have for every two reals in the extension a continuous function defined in the ground model that maps one of the reals onto the other.Comment: 11 page

Resonant Generation of Topological Modes in Trapped Bose Gases

Trapped Bose atoms cooled down to temperatures below the Bose-Einstein condensation temperature are considered. Stationary solutions to the Gross-Pitaevskii equation (GPE) define the topological coherent modes, representing nonground-state Bose-Einstein condensates. These modes can be generated by means of alternating fields whose frequencies are in resonance with the transition frequencies between two collective energy levels corresponding to two different topological modes. The theory of resonant generation of these modes is generalized in several aspects: Multiple-mode formation is described; a shape-conservation criterion is derived, imposing restrictions on the admissible spatial dependence of resonant fields; evolution equations for the case of three coherent modes are investigated; the complete stability analysis is accomplished; the effects of harmonic generation and parametric conversion for the topological coherent modes are predicted. All considerations are realized both by employing approximate analytical methods as well as by numerically solving the GPE. Numerical solutions confirm all conclusions following from analytical methods.Comment: One reference modifie

Metallo-dielectric diamond and zinc-blende photonic crystals

It is shown that small inclusions of a low absorbing metal can have a dramatic effect on the photonic band structure. In the case of diamond and zinc-blende photonic crystals, several complete photonic band gaps (CPBG's) can open in the spectrum, between the 2nd-3rd, 5th-6th, and 8th-9th bands. Unlike in the purely dielectric case, in the presence of small inclusions of a low absorbing metal the largest CPBG for a moderate dielectric constant (epsilon<=10) turns out to be the 2nd-3rd CPBG. The 2nd-3rd CPBG is the most important CPBG, because it is the most stable against disorder. For a diamond and zinc-blende structure of nonoverlapping dielectric and metallo-dielectric spheres, a CPBG begins to decrease with an increasing dielectric contrast roughly at the point where another CPBG starts to open--a kind of gap competition. A CPBG can even shrink to zero when the dielectric contrast increases further. Metal inclusions have the biggest effect for the dielectric constant 2<=epsilon<=12, which is a typical dielectric constant at near infrared and in the visible for many materials, including semiconductors and polymers. It is shown that one can create a sizeable and robust 2nd-3rd CPBG at near infrared and visible wavelengths even for a photonic crystal which is composed of more than 97% low refractive index materials (n<=1.45, i.e., that of silica glass or a polymer). These findings open the door for any semiconductor and polymer material to be used as genuine building blocks for the creation of photonic crystals with a CPBG and significantly increase the possibilities for experimentalists to realize a sizeable and robust CPBG in the near infrared and in the visible. One possibility is a construction method using optical tweezers, which is analyzed here.Comment: 25 pp, 23 figs, RevTex, to appear in Phys Rev B. For more information look at http://www.amolf.nl/research/photonic_materials_theory/moroz/moroz.htm

Grain-Boundary Structural Relaxation in Sb2Se3{\mathrm{Sb}}_{2}{\mathrm{Se}}_{3} Thin-Film Photovoltaics

Grain boundaries play an important role in the efficiency of thin-film photovoltaics, where the absorber layer is invariably polycrystalline. Density-functional-theory simulations have previously identified a “self-healing” mechanism in Sb2Se3 that passivates the grain boundaries. During “self-healing,” extensive structural relaxation at the grain boundary removes the band-gap electronic defect states that give rise to high carrier recombination rates. In this work, lattice imaging in a transmission electron microscope is used to uncover evidence for the theoretically proposed structural relaxation in Sb2Se3. The strain measured along the [010] crystal direction is found to be dependent on the nature of the grain-boundary plane. For a (010) grain boundary, the strain and structural relaxation is minimal, since no covalent bonds are broken by termination of the grain. On the other hand, strains of up to approximately 4% extending approximately 2 nm into the grain interior are observed for a (041) grain boundary, where grain termination results in significant structural relaxation due to the ideal atomic coordination being disrupted. These results are consistent with theory and suggest that Sb2Se3 may have a high level of grain-boundary-defect tolerance

Obesity and Breast Cancer Metastasis across Genomic Subtypes

Background: Obese women have higher risk of aggressive breast tumors and distant metastasis. However, obesity has rarely been assessed in association with metastasis in diverse populations. Methods: In the Carolina Breast Cancer Study Phase 3 (2008–2013), waist-to-hip ratio (WHR), body mass index (BMI), and molecular subtype [PAM50 risk-of-recurrence (ROR) score] were assessed. Obesity measures were evaluated in association with metastasis within five years of diagnosis, overall and stratified by race and ROR score. Absolute risk of metastasis and risk differences between strata were calculated using the Kaplan–Meier estimator, adjusted for age, grade, stage, race, and ER status. Relative frequency of metastatic site and multiplicity were estimated in association with obesity using generalized linear models. Results: High-WHR was associated with higher risk of metastasis (5-year risk difference, RD, 4.3%; 95% confidence interval, 2.2–6.5). It was also associated with multiple metastases and metastases at all sites except brain. The 5-year risk of metastasis differed by race (11.2% and 6.9% in Black and non-Black, respectively) and ROR score (19.5% vs. 6.6% in high vs. low-to-intermediate ROR-PT). Non-Black women and those with low-to-intermediate ROR scores had similar risk in high- and low-WHR strata. However, among Black women and those with high ROR, risk of metastasis was elevated among high-WHR (RDBlack/non-Black = 4.6%, RDHigh/Low-Int = 3.1%). Patterns of metastasis were similar by BMI. Conclusions: WHR is associated with metastatic risk, particularly among Black women and those with high-risk tumors. Impact: Understanding how risk factors for metastasis interact may help in tailoring care plans and surveillance among patients with breast cancer

Homeownership and parenting practices: Evidence from the community advantage panel

This study examines whether there is a significant relationship between homeownership and engaged parenting practices among low- and moderate-income households. Using analytic methods which account for selection effects and clustering, we test whether homeownership can act as a protective factor against parental disengagement from children. Controlling for individual characteristics, analyses demonstrate that homeowners are more likely than renters to demonstrate engaged parenting behaviors such as organizing structured activities for their children. While renters are more likely to read to their children, the children of homeowners spend less time watching television and playing video games. Implications for low-income housing policy are discussed in light of these findings

Substructures in lens galaxies: PG1115+080 and B1555+375, two fold configurations

We study the anomalous flux ratio which is observed in some four-image lens systems, where the source lies close to a fold caustic. In this case two of the images are close to the critical curve and their flux ratio should be equal to unity, instead in several cases the observed value differs significantly. The most plausible solution is to invoke the presence of substructures, as for instance predicted by the Cold Dark Matter scenario, located near the two images. In particular, we analyze the two fold lens systems PG1115+080 and B1555+375, for which there are not yet satisfactory models which explain the observed anomalous flux ratios. We add to a smooth lens model, which reproduces well the positions of the images but not the anomalous fluxes, one or two substructures described as singular isothermal spheres. For PG1115+080 we consider a smooth model with the influence of the group of galaxies described by a SIS and a substructure with mass $\sim 10^{5} M_{\odot}$ as well as a smooth model with an external shear and one substructure with mass $\sim 10^{8} M_{\odot}$ . For B1555+375 either a strong external shear or two substructures with mass $\sim 10^{7} M_{\odot}$ reproduce the data quite well.Comment: 26 pages, updated bibliography, Accepted for publication in Astrophysics & Space Scienc