Geometric Phase Integrals and Irrationality Tests

Let $F(x)$ be an analytical, real valued function defined on a compact domain $\mathcal {B}\subset\mathbb{R}$. We prove that the problem of establishing the irrationality of $F(x)$ evaluated at $x_0\in \mathcal{B}$ can be stated with respect to the convergence of the phase of a suitable integral $I(h)$, defined on an open, bounded domain, for $h$ that goes to infinity. This is derived as a consequence of a similar equivalence, that establishes the existence of isolated solutions of systems equations of analytical functions on compact real domains in $\mathbb{R}^p$, if and only if the phase of a suitable ``geometric'' complex phase integral $I(h)$ converges for $h\rightarrow \infty$. We finally highlight how the method can be easily adapted to be relevant for the study of the existence of rational or integer points on curves in bounded domains, and we sketch some potential theoretical developments of the method

Stem-Like Adaptive Aneuploidy and Cancer Quasispecies

We analyze and reinterpret experimental evidence from the literature to argue for an ability of tumor cells to self-regulate their aneuploidy rate. We conjecture that this ability is mediated by a diversification factor that exploits molecular mechanisms common to embryo stem cells and, to a lesser extent, adult stem cells, that is eventually reactivated in tumor cells. Moreover, we propose a direct use of the quasispecies model to cancer cells based on their significant genomic instability (i.e. aneuploidy rate), by defining master sequences lengths as the sum of all copy numbers of physically distinct whole and fragmented chromosomes. We compute an approximate error threshold such that any aneuploidy rate larger than the threshold would lead to a loss of fitness of a tumor population, and we confirm that highly aneuploid cancer populations already function with aneuploidy rates close to the estimated threshold

Testing a quintessence model with CMBR peaks location

We show that a model of quintessence with exponential potential, which allows to obtain general exact solutions, can generate locations of CMBR peaks which are fully compatible with present observational dataComment: 7 pages, no figure

A Parametric Framework for the Comparison of Methods of Very Robust Regression

There are several methods for obtaining very robust estimates of regression parameters that asymptotically resist 50% of outliers in the data. Differences in the behaviour of these algorithms depend on the distance between the regression data and the outliers. We introduce a parameter $\lambda$ that defines a parametric path in the space of models and enables us to study, in a systematic way, the properties of estimators as the groups of data move from being far apart to close together. We examine, as a function of $\lambda$, the variance and squared bias of five estimators and we also consider their power when used in the detection of outliers. This systematic approach provides tools for gaining knowledge and better understanding of the properties of robust estimators.Comment: Published in at http://dx.doi.org/10.1214/13-STS437 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Counterterms in type I Supergravities

We compute the one-loop divergences of D=10, N=1 supergravity and of its reduction to D=8. We study the tensor structure of the counterterms appearing in D=8 and D=10 and compare these to expressions previously found in the low energy expansion of string theory. The infinities have the primitive Yang-Mills tree amplitude as a common factor.Comment: 26 pages, Latex, 4 eps figure

Local orientational ordering in fluids of spherical molecules with dipolar-like anisotropic adhesion

We discuss some interesting physical features stemming from our previous analytical study of a simple model of a fluid with dipolar-like interactions of very short range in addition to the usual isotropic Baxter potential for adhesive spheres. While the isotropic part is found to rule the global structural and thermodynamical equilibrium properties of the fluid, the weaker anisotropic part gives rise to an interesting short-range local ordering of nearly spherical condensation clusters, containing short portions of chains having nose-to-tail parallel alignment which runs antiparallel to adjacent similar chains.Comment: 13 pages and 6 figure

Are collapse models testable with quantum oscillating systems? The case of neutrinos, kaons, chiral molecules

Collapse models provide a theoretical framework for understanding how classical world emerges from quantum mechanics. Their dynamics preserves (practically) quantum linearity for microscopic systems, while it becomes strongly nonlinear when moving towards macroscopic scale. The conventional approach to test collapse models is to create spatial superpositions of mesoscopic systems and then examine the loss of interference, while environmental noises are engineered carefully. Here we investigate a different approach: We study systems that naturally oscillate --creating quantum superpositions-- and thus represent a natural case-study for testing quantum linearity: neutrinos, neutral mesons, and chiral molecules. We will show how spontaneous collapses affect their oscillatory behavior, and will compare them with environmental decoherence effects. We will show that, contrary to what previously predicted, collapse models cannot be tested with neutrinos. The effect is stronger for neutral mesons, but still beyond experimental reach. Instead, chiral molecules can offer promising candidates for testing collapse models.Comment: accepted by NATURE Scientific Reports, 12 pages, 1 figures, 2 table

Fingerprinting dark energy

Dark energy perturbations are normally either neglected or else included in a purely numerical way, obscuring their dependence on underlying parameters like the equation of state or the sound speed. However, while many different explanations for the dark energy can have the same equation of state, they usually differ in their perturbations so that these provide a fingerprint for distinguishing between different models with the same equation of state. In this paper we derive simple yet accurate approximations that are able to characterize a specific class of models (encompassing most scalar-field models) which is often generically called "dark energy". We then use the approximate solutions to look at the impact of the dark energy perturbations on the dark matter power spectrum and on the integrated Sachs-Wolfe effect in the cosmic microwave background radiation.Comment: 11 pages, 5 figures, minor changes to match published versio