Partial stratification of secant varieties of Veronese varieties via curvilinear subschemes

We give a partial "quasi-stratification" of the secant varieties of the order $d$ Veronese variety $X_{m,d}$ of $\mathbb {P}^m$. It covers the set $\sigma_t(X_{m,d})^{\dagger}$ of all points lying on the linear span of curvilinear subschemes of $X_{m,d}$, but two "quasi-strata" may overlap. For low border rank two different "quasi-strata" are disjoint and we compute the symmetric rank of their elements. Our tool is the Hilbert schemes of curvilinear subschemes of Veronese varieties. To get a stratification we attach to each $P\in \sigma_t(X_{m,d})^{\dagger}$ the minimal label of a quasi-stratum containing it.Comment: 16 page

Ab Initio Electron-Phonon Interactions Using Atomic Orbital Wavefunctions

The interaction between electrons and lattice vibrations determines key physical properties of materials, including their electrical and heat transport, excited electron dynamics, phase transitions, and superconductivity. We present a new ab initio method that employs atomic orbital (AO) wavefunctions to compute the electron-phonon (e-ph) interactions in materials and interpolate the e-ph coupling matrix elements to fine Brillouin zone grids. We detail the numerical implementation of such AO-based e-ph calculations, and benchmark them against direct density functional theory calculations and Wannier function (WF) interpolation. The key advantages of AOs over WFs for e-ph calculations are outlined. Since AOs are fixed basis functions associated with the atoms, they circumvent the need to generate a material-specific localized basis set with a trial-and-error approach, as is needed in WFs. Therefore, AOs are ideal to compute e-ph interactions in chemically and structurally complex materials for which WFs are challenging to generate, and are also promising for high-throughput materials discovery. While our results focus on AOs, the formalism we present generalizes e-ph calculations to arbitrary localized basis sets, with WFs recovered as a special case

Test of Universality in the Ising Spin Glass Using High Temperature Graph Expansion

We calculate high-temperature graph expansions for the Ising spin glass model with 4 symmetric random distribution functions for its nearest neighbor interaction constants J_{ij}. Series for the Edwards-Anderson susceptibility \chi_EA are obtained to order 13 in the expansion variable (J/(k_B T))^2 for the general d-dimensional hyper-cubic lattice, where the parameter J determines the width of the distributions. We explain in detail how the expansions are calculated. The analysis, using the Dlog-Pad\'e approximation and the techniques known as M1 and M2, leads to estimates for the critical threshold (J/(k_B T_c))^2 and for the critical exponent \gamma in dimensions 4, 5, 7 and 8 for all the distribution functions. In each dimension the values for \gamma agree, within their uncertainty margins, with a common value for the different distributions, thus confirming universality.Comment: 13 figure

Two theoretical interpretations of the dissonance between fertility intentions and behaviour

In the paper we outline two possible theoretical interpretations for the inconsistency often observed between fertility intentions and fertility behaviour. We draw on socio-psychological models of human behaviour which emphasise the role of normative-affective factors on decision-making processes. The first interpretation is based on the observation that family and fertility choices are gradually shifting from a zone where behaviour is normative regulated to a zone of normative indifference, where mere rational decision-making based on cost-benefit considerations is at work. The dissonance between fertility choices and declared intentions depends on the fact that the former are based on rational considerations, while the latter are still constrained by a normative familistic philosophy. The second interpretation assumes the existence of an interposing mechanism in the sequence expectations-behaviour. These mechanisms, as anxiety and avoidance dispositions, filter the passage from individual value orientations in the affective sphere to their actual behaviour. We base our argument on two sets of information. First, we use a survey which allows us to construct empirical indicators of psychological dispositions connected to expectations related to family and fertility behaviours (Abacus 1996, Italy). Second, we analyse 54 non-structured interviews conducted in Northern Italy, which give a detailed picture of the hypothesised mechanisms and suggest new directions for research.

Sum rules of codon usage probabilities

In the crystal basis model of the genetic code, it is deduced that the sum of usage probabilities of the codons with C and A in the third position for the quartets and/or sextets is independent of the biological species for vertebrates. A comparison with experimental data shows that the prediction is satisfied within about 5 %.Comment: 7 page

Selection bias in dynamically-measured super-massive black hole samples: consequences for pulsar timing arrays

Supermassive black hole -- host galaxy relations are key to the computation of the expected gravitational wave background (GWB) in the pulsar timing array (PTA) frequency band. It has been recently pointed out that standard relations adopted in GWB computations are in fact biased-high. We show that when this selection bias is taken into account, the expected GWB in the PTA band is a factor of about three smaller than previously estimated. Compared to other scaling relations recently published in the literature, the median amplitude of the signal at $f=1$yr$^{-1}$ drops from $1.3\times10^{-15}$ to $4\times10^{-16}$. Although this solves any potential tension between theoretical predictions and recent PTA limits without invoking other dynamical effects (such as stalling, eccentricity or strong coupling with the galactic environment), it also makes the GWB detection more challenging.Comment: 6 pages 4 figures, submitted to MNRAS letter

The Spin Glass Transition : Exponents and Dynamics

Numerical simulations on Ising Spin Glasses show that spin glass transitions do not obey the usual universality rules which hold at canonical second order transitions. On the other hand the dynamics at the approach to the transition appear to take up a universal form for all spin glasses. The implications for the fundamental physics of transitions in complex systems are addressed.Comment: 4 pages (Latex) with 3 figures (postscript), accepted for publication in Physica