The Halo Mass Function from Excursion Set Theory with a Non-Gaussian Trispectrum

A sizeable level of non-Gaussianity in the primordial cosmological perturbations may be induced by a large trispectrum, i.e. by a large connected four-point correlation function. We compute the effect of a primordial non-Gaussian trispectrum on the halo mass function, within excursion set theory. We use the formalism that we have developed in a previous series of papers and which allows us to take into account the fact that, in the presence of non-Gaussianity, the stochastic evolution of the smoothed density field, as a function of the smoothing scale, is non-markovian. In the large mass limit, the leading-order term that we find agrees with the leading-order term of the results found in the literature using a more heuristic Press-Schecther (PS)-type approach. Our approach however also allows us to evaluate consistently the subleading terms, which depend not only on the four-point cumulant but also on derivatives of the four-point correlator, and which cannot be obtained within non-Gaussian extensions of PS theory. We perform explicitly the computation up to next-to-leading order.Comment: LaTeX file, 15 page

A hydrodynamical homotopy co-momentum map and a multisymplectic interpretation of higher order linking numbers

In this article a homotopy co-momentum map (\`a la Callies-Fr\'egier-Rogers-Zambon) trangressing to the standard hydrodynamical co-momentum map of Arnol'd, Marsden and Weinstein and others is constructed and then generalized to a special class of Riemannian manifolds. Also, a covariant phase space interpretation of the coadjoint orbits associated to the Euler evolution for perfect fluids and in particular of Brylinski's manifold of smooth oriented knots is discussed. As an application of the above homotopy co-momentum map, a reinterpretation of the (Massey) higher order linking numbers in terms of conserved quantities within the multisymplectic framework is provided and knot theoretic analogues of first integrals in involution are determined.Comment: 21 pages, 3 figures. The present version focuses on the connections between multisymplectic geometry, hydrodynamics and vortices. The derivation of the HOMFLYPT polynomial via geometric quantization has been proposed as a separate preprint, see "Derivation of the HOMFLYPT knot polynomial via helicity and geometric quantization ", arXiv:1910.xxx

Transition to ballistic regime for heat transport in helium II

The size-dependent and flux-dependent effective thermal conductivity of narrow capillaries filled with superfluid helium is analyzed from a thermodynamic continuum perspective. The classical Landau evaluation of the effective thermal conductivity of quiescent superfluid, or the Gorter-Mellinck regime of turbulent superfluids, are extended to describe the transition to ballistic regime in narrow channels wherein the radius $R$ is comparable to (or smaller than) the phonon mean-free path $\ell$ in superfluid helium. To do so we start from an extended equation for the heat flux incorporating non-local terms, and take into consideration a heat slip flow along the walls of the tube. This leads from an effective thermal conductivity proportional to $R^2$ (Landau regime) to another one proportional to $R\ell$ (ballistic regime). We consider two kinds of flows: along cylindrical pipes and along two infinite parallel plates.Comment: 16 page

Scaling in soft spheres: fragility invariance on the repulsive potential softness

We address the question of the dependence of the fragility of glass forming supercooled liquids on the softness of an interacting potential by performing numerical simulation of a binary mixture of soft spheres with different power n of the interparticle repulsive potential. We show that the temperature dependence of the diffusion coefficients for various $n$ collapses onto a universal curve, supporting the unexpected view that fragility is not related to the hard core repulsion. We also find that the configurational entropy correlates with the slowing down of the dynamics for all studied n.Comment: 4 pages, 4 figure

Modelling Italian potential output and the output gap

The aim of the paper is to estimate a reliable quarterly time-series of potential output for the Italian economy, exploiting four alternative approaches: a Bayesian unobserved component method, a univariate time-varying autoregressive model, a production function approach and a structural VAR. Based on a wide range of evaluation criteria, all methods generate output gaps that accurately describe the Italian business cycle over the past three decades. All output gap measures are subject to non-negligible revisions when new data become available. Nonetheless they still prove to be informative about the current cyclical phase and, unlike the evidence reported in most of the literature, helpful at predicting inflation compared with simple benchmarks. We assess also the performance of output gap estimates obtained by combining the four original indicators, using either equal weights or Bayesian averaging, showing that the resulting measures (i) are less sensitive to revisions; (ii) are at least as good as the originals at tracking business cycle fluctuations; (iii) are more accurate as inflation predictors.potential output, business cycle, Phillips curve, output gap

Modelling the evolution of transcription factor binding preferences in complex eukaryotes

Transcription factors (TFs) exert their regulatory action by binding to DNA with specific sequence preferences. However, different TFs can partially share their binding sequences due to their common evolutionary origin. This `redundancy' of binding defines a way of organizing TFs in `motif families' by grouping TFs with similar binding preferences. Since these ultimately define the TF target genes, the motif family organization entails information about the structure of transcriptional regulation as it has been shaped by evolution. Focusing on the human TF repertoire, we show that a one-parameter evolutionary model of the Birth-Death-Innovation type can explain the TF empirical ripartition in motif families, and allows to highlight the relevant evolutionary forces at the origin of this organization. Moreover, the model allows to pinpoint few deviations from the neutral scenario it assumes: three over-expanded families (including HOX and FOX genes), a set of `singleton' TFs for which duplication seems to be selected against, and a higher-than-average rate of diversification of the binding preferences of TFs with a Zinc Finger DNA binding domain. Finally, a comparison of the TF motif family organization in different eukaryotic species suggests an increase of redundancy of binding with organism complexity.Comment: 14 pages, 5 figures. Minor changes. Final version, accepted for publicatio

Random Access in Massive MIMO by Exploiting Timing Offsets and Excess Antennas

Massive MIMO systems, where base stations are equipped with hundreds of antennas, are an attractive way to handle the rapid growth of data traffic. As the number of user equipments (UEs) increases, the initial access and handover in contemporary networks will be flooded by user collisions. In this paper, a random access protocol is proposed that resolves collisions and performs timing estimation by simply utilizing the large number of antennas envisioned in Massive MIMO networks. UEs entering the network perform spreading in both time and frequency domains, and their timing offsets are estimated at the base station in closed-form using a subspace decomposition approach. This information is used to compute channel estimates that are subsequently employed by the base station to communicate with the detected UEs. The favorable propagation conditions of Massive MIMO suppress interference among UEs whereas the inherent timing misalignments improve the detection capabilities of the protocol. Numerical results are used to validate the performance of the proposed procedure in cellular networks under uncorrelated and correlated fading channels. With $2.5\times10^3$ UEs that may simultaneously become active with probability 1\% and a total of $16$ frequency-time codes (in a given random access block), it turns out that, with $100$ antennas, the proposed procedure successfully detects a given UE with probability 75\% while providing reliable timing estimates.Comment: 30 pages, 6 figures, 1 table, submitted to Transactions on Communication