A Coloring Problem for Infinite Words

In this paper we consider the following question in the spirit of Ramsey theory: Given $x\in A^\omega,$ where $A$ is a finite non-empty set, does there exist a finite coloring of the non-empty factors of $x$ with the property that no factorization of $x$ is monochromatic? We prove that this question has a positive answer using two colors for almost all words relative to the standard Bernoulli measure on $A^\omega.$ We also show that it has a positive answer for various classes of uniformly recurrent words, including all aperiodic balanced words, and all words $x\in A^\omega$ satisfying $\lambda_x(n+1)-\lambda_x(n)=1$ for all $n$ sufficiently large, where $\lambda_x(n)$ denotes the number of distinct factors of $x$ of length $n.$Comment: arXiv admin note: incorporates 1301.526

Testing Primordial Black Holes as Dark Matter through LISA

The idea that primordial black holes (PBHs) can comprise most of the dark matter of the universe has recently reacquired a lot of momentum. Observational constraints, however, rule out this possibility for most of the PBH masses, with a notable exception around $10^{-12} M_\odot$. These light PBHs may be originated when a sizeable comoving curvature perturbation generated during inflation re-enters the horizon during the radiation phase. During such a stage, it is unavoidable that gravitational waves (GWs) are generated. Since their source is quadratic in the curvature perturbations, these GWs are generated fully non-Gaussian. Their frequency today is about the mHz, which is exactly the range where the LISA mission has the maximum of its sensitivity. This is certainly an impressive coincidence. We show that this scenario of PBHs as dark matter can be tested by LISA by measuring the GW two-point correlator. On the other hand, we show that the short observation time (as compared to the age of the universe) and propagation effects of the GWs across the perturbed universe from the production point to the LISA detector suppress the bispectrum to an unobservable level. This suppression is completely general and not specific to our model.Comment: 22 pages, 12 figures. v3: matching published versio

Kerr black hole lensing for generic observers in the strong deflection limit

We generalize our previous work on gravitational lensing by a Kerr black hole in the strong deflection limit, removing the restriction to observers on the equatorial plane. Starting from the Schwarzschild solution and adding corrections up to the second order in the black hole spin, we perform a complete analytical study of the lens equation for relativistic images created by photons passing very close to a Kerr black hole. We find out that, to the lowest order, all observables (including shape and shift of the black hole shadow, caustic drift and size, images position and magnification) depend on the projection of the spin on a plane orthogonal to the line of sight. In order to break the degeneracy between the black hole spin and its inclination relative to the observer, it is necessary to push the expansion to higher orders. In terms of future VLBI observations, this implies that very accurate measures are needed to determine these two parameters separately.Comment: 17 pages, 4 figures, one section added, to appear on Physical Review

Quantum spin Hall effect in bound states in continuum

Moving the polarization of the incident wave along a meridian of the Poincaré sphere, experimentally we show that the coupling with the fundamental Bloch's surface waves of the mode, provide a spatially coherent, macroscopic spinmomentum locked propagation along the symmetry axes of the PhCM. This novel mechanism of light-spin manipulation enables a versatile implementation of spin-optical structures that may pave the way to novel strategies for light spin technology and photonic multiplatform implementations

Analytic Kerr black hole lensing for equatorial observers in the strong deflection limit

In this paper we present an analytical treatment of gravitational lensing by Kerr black holes in the limit of very large deflection angles, restricting to observers in the equatorial plane. We accomplish our objective starting from the Schwarzschild black hole and adding corrections up to second order in the black hole spin. This is sufficient to provide a full description of all caustics and the inversion of lens mapping for sources near them. On the basis of these formulae we argue that relativistic images of Low Mass X-ray Binaries around Sgr A* are very likely to be seen by future X-ray interferometry missions.Comment: 19 pages, 9 figures, published on Phys. Rev.

Functional assessment of cancer therapy questionnaire for breast cancer (FACT-B+4): Italian version validation

BACKGROUND: Improvements in breast cancer diagnosis and treatment led to an increased incidence of survivors' rate. The healthcare system has to face new problems related not only to the treatment of the disease, but also to the management of the quality of life after the diagnosis. The aim of this study was to validate the Italian version of the Functional Assessment of Cancer Therapy - Breast (FACT-B+4) questionnaire and to evaluate its reliability. METHODS: The questionnaire was administered twice, with an interval of three days between each administration, to a cohort of women of the Breast Surgical Unit, PoliclincoUmberto I. Cronbach's alpha was used as a measure of the internal consistency of the Italian version. RESULTS: The Italian version of the tool was administered to 55 subjects. The Cronbach's alpha for most scores registered values >0.7, both at baseline and at the follow-up analysis, therefore the subscale showed good internal consistency. CONCLUSIONS: The Italian version of FACT-B+4 demonstrated acceptable reliability properties in the Breast Unit patients. The use of this questionnaire seemed to be effective and in line with the results derived from the English and Spanishversions. Internal consistency and validity had similar performance results

The Ineludible non-Gaussianity of the Primordial Black Hole Abundance

We study the formation of primordial black holes when they are generated by the collapse of large overdensities in the early universe. Since the density contrast is related to the comoving curvature perturbation by a nonlinear relation, the overdensity statistics is unavoidably non-Gaussian. We show that the abundance of primordial black holes at formation may not be captured by a perturbative approach which retains the first few cumulants of the non-Gaussian probability distribution. We provide two techniques to calculate the non-Gaussian abundance of primordial black holes at formation, one based on peak theory and the other on threshold statistics. Our results show that the unavoidable non-Gaussian nature of the inhomogeneities in the energy density makes it harder to generate PBHs. We provide simple (semi-)analytical expressions to calculate the non-Gaussian abundances of the primordial black holes and show that for both narrow and broad power spectra the gaussian case from threshold statistics is reproduced by increasing the amplitude of the power spectrum by a factor ${\cal O}(2\div 3)$.Comment: 26 pages, 10 figures, matching published versio

Effect of a commercial root growth enhancer on the turfgrass species "Lolium perenne" and the weed "Poa annua"

Se pretende comprobar si la aplicación de un enraizante durante la resiembra otoñal de la cespitosa “Lolium perenne” sobre las calles de los campos de golf conformados por “Cynodon dactylon”, favoreciese la competencia de “L. perenne” frente a Poa annua, mala hierba que germina precisamente en esta época. Se realizaron 2 ensayos iguales en cámara de crecimiento aplicando 10 dosis distintas del enraizante en ambas especies y se determinó al final del ensayo, tanto el crecimiento como el peso seco de la parte aérea y radical de ambas especies. Tan sólo en uno de los 2 ensayos el enraizante parece favorecer a la cespitosa frente a “P. annua” por lo que no puede concluirse categóricamente que el enraizante pueda ser un medio de control efectivo frente a la mala hierba.It is intended to check the performance of a root growth enhancer in order to promote “Lolium perenne” competiveness over “Poa annua”, during the overseeding cultural practice on “Cynodon dactylon” golf course fairway, as “P. annua” naturally germinates at the same time. Two equal laboratory experiments were conducted testing 10 doses of the root enhancer in both species. At the end of the experiments seedling growth and root and leaf dry weight were determined for both species. The tested product only promotes “L. perenne” competiveness in one experiment, therefore it cannot be concluded the root enhancer could be an effective weed control method