The one-point probability distribution function (pdf) is computed for the $25\hmpc$-smoothed density field of rich clusters of galaxies in the Abell/\aco\ catalogs. The observed pdf is compared to the pdf s drawn similarly from mock catalogs of clusters in cosmological simulations of Gaussian and several non-Gaussian initial conditions. Several statistics allow significant rejection of the non-Gaussian models tested here, and fail to reject the Gaussian model. A comparison with the predictions of second-order perturbation theory and a log-normal model for cdm Gaussian initial conditions yield a linear biasing factor $b_c/b_o \simeq 4$ and $b_c/b_o\simeq 3.7$ for $R\geq 0$ clusters.; Comment: To appear in the proceedings of the XXXth MORIOND meeting: "Clustering in the Universe". 8 pages, compressed uuencoded file

The stochastic $\phi^4$-theory in $d-$dimensions dynamically develops domain wall structures within which the order parameter is not continuous. We develop a statistical theory for the $\phi^4$-theory driven with a random forcing which is white in time and Gaussian-correlated in space. A master equation is derived for the probability density function (PDF) of the order parameter, when the forcing correlation length is much smaller than the system size, but much larger than the typical width of the domain walls. Moreover, exact expressions for the one-point PDF and all the moments $<\phi^n>$ are given. We then investigate the intermittency issue in the strong coupling limit, and derive the tail of the PDF of the increments $\phi(x_2) - \phi(x_1)$. The scaling laws for the structure functions of the increments are obtained through numerical simulations. It is shown that the moments of field increments defined by, $C_b=< |\phi(x_2)-\phi(x_1)|^b>$, behave as $|x_1-x_2|^{\xi_b}$, where $\xi_b=b$ for $b\leq 1$, and $\xi_b=1$ for $b\geq1$; Comment: 22 pages, 6 figures. to appear in Nuclear. Phys. B

For a known weak signal in additive white noise, the asymptotic performance of a locally optimum processor (LOP) is shown to be given by the Fisher information (FI) of a standardized even probability density function (PDF) of noise in three cases: (i) the maximum signal-to-noise ratio (SNR) gain for a periodic signal; (ii) the optimal asymptotic relative efficiency (ARE) for signal detection; (iii) the best cross-correlation gain (CG) for signal transmission. The minimal FI is unity, corresponding to a Gaussian PDF, whereas the FI is certainly larger than unity for any non-Gaussian PDFs. In the sense of a realizable LOP, it is found that the dichotomous noise PDF possesses an infinite FI for known weak signals perfectly processed by the corresponding LOP. The significance of FI lies in that it provides a upper bound for the performance of locally optimum processing.; Comment: 8 pages, 1 figure

The dynamics of pigment-pigment and pigment-protein interactions in light-harvesting complexes is studied with a novel approach which combines molecular dynamics (MD) simulations with quantum chemistry (QC) calculations. The MD simulations of an LH-II complex, solvated and embedded in a lipid bilayer at physiological conditions (with total system size of 87,055 atoms) revealed a pathway of a water molecule into the B800 binding site, as well as increased dimerization within the B850 BChl ring, as compared to the dimerization found for the crystal structure. The fluctuations of pigment (B850 BChl) excitation energies, as a function of time, were determined via ab initio QC calculations based on the geometries that emerged from the MD simulations. From the results of these calculations we constructed a time-dependent Hamiltonian of the B850 exciton system from which we determined the linear absorption spectrum. Finally, a polaron model is introduced to describe quantum mechanically both the excitonic and vibrational (phonon) degrees of freedom. The exciton-phonon coupling that enters into the polaron model, and the corresponding phonon spectral function are derived from the MD/QC simulations. It is demonstrated that, in the framework of the polaron model...

In this paper we focus on a type of inverse problem in which the data is expressed as an unknown function of the sought and unknown model function (or its discretised representation as a model parameter vector). In particular, we deal with situations in which training data is not available. Then we cannot model the unknown functional relationship between data and the unknown model function (or parameter vector) with a Gaussian Process of appropriate dimensionality. A Bayesian method based on state space modelling is advanced instead. Within this framework, the likelihood is expressed in terms of the probability density function ($pdf$) of the state space variable and the sought model parameter vector is embedded within the domain of this $pdf$. As the measurable vector lives only inside an identified sub-volume of the system state space, the $pdf$ of the state space variable is projected onto the space of the measurables, and it is in terms of the projected state space density that the likelihood is written; the final form of the likelihood is achieved after convolution with the distribution of measurement errors. Application motivated vague priors are invoked and the posterior probability density of the model parameter vectors, given the data is computed. Inference is performed by taking posterior samples with adaptive MCMC. The method is illustrated on synthetic as well as real galactic data.

The level of precision achieved by the experimental measurements at the LHC requires the inclusion of higher order electroweak effects to the processes of $ pp $ scattering. In particular the photon-induced process $ \gamma\gamma \to \ell^+\ell^- $ make a significant contribution ($ \sim 10 \%$) to the dilepton invariant mass distribution. To evaluate the cross-section of this process one need to know the parton distribution function (PDF) of the photon in the proton $ \gamma (x,\mu^2) $. The aim of the current study is to investigate the impact of QED corrections on PDFs and describe the implementation of QED-modified evolution equations into beta release of new version of {\tt QCDNUM} program. The {\tt APPLGRID} interface to {\tt SANC} Monte Carlo generator for fast evaluation of photon-induced cross-section is also outlined. The results were cross-checked with {\tt partonevolution} program, {\tt MRST2004QED} PDF set and {\tt APFEL} program. The described developments are planned to include into {\tt HERAFitter} package and can be used to determine the photon PDF using new data from the LHC experiments.

Using a non-perturbative method developed in a previous work (paper II), we derive the probability distribution $P(\delta_R)$ of the density contrast within spherical cells in the quasi-linear regime for some non-Gaussian initial conditions. We describe three such models. The first one is a straightforward generalization of the Gaussian scenario. It can be seen as a phenomenological description of a density field where the tails of the linear density contrast distribution would be of the form $P_L(\delta_L) \sim e^{-|\delta_L|^{-\alpha}}$, where $\alpha$ is no longer restricted to 2 (as in the Gaussian case). We derive exact results for $P(\delta_R)$ in the quasi-linear limit. The second model is a physically motivated isocurvature CDM scenario. Our approach needs to be adapted to this specific case and in order to get convenient analytical results we introduce a simple approximation (which is not related to the gravitational dynamics but to the initial conditions). Then, we find a good agreement with the available results from numerical simulations for the pdf of the linear density contrast for $\delta_{L,R} \ga 0$. We can expect a similar accuracy for the non-linear pdf $P(\delta_R)$. Finally, the third model corresponds to the small deviations from Gaussianity which arise in standard slow-roll inflation. We obtain exact results for the pdf of the density field in the quasi-linear limit...

Using a non-perturbative method developed in a previous article (paper II) we investigate the tails of the probability distribution $P(\rho_R)$ of the overdensity within spherical cells. We show that our results for the low-density tail of the pdf agree with perturbative results when the latter are finite (up to the first subleading term), that is for power-spectra with $-3

Link permanente para citações:

We present a theoretical attack on the classical problem of intermittency and anomalous scaling in turbulence. Our focus is on an ideal situation: high Reynolds number isotropic turbulence driven by steady large scale forcing. Moreover, the fluid is incompressible and no confining boundaries are present. We start from a good set of basis functions for the velocity field. These are real and divergence-free. To each wave-vector k in Fourier space there is one pair of basis functions with respectively left and right-handed polarity. Isotropy makes all k on the shell of constant |k| statistically equivalent. Consequently, the coefficients, X+ and X-, to the basis functions in that shell become two random variables whose joint pdf describes the statistics at scale L =2*pi/|k|. Moreover, (X+)**2+(X-)**2 becomes a random variable for the energy. Switching to polar coordinates, the joint pdf expands in azimuthal modes. We focus on the axisymmetric mode which is itself a pdf and characterized by it radial profile P(r;L). Observations from both shell model and DNS data indicate that (1) the moments of P(r;L) scale as power laws in L, and (2) the profile obeys an affine symmetry P(r;L)=C(L)*f((lnr-mu(L))/sigma(L)). We raise the question: What statistics agree with both observation? The answer is pleasing. We find the functions f...

We report the proof that the extension of Gibrat's law in the middle scale region is unique and the probability distribution function (pdf) is also uniquely derived from the extended Gibrat's law and the law of detailed balance. In the proof, two approximations are employed. The pdf of growth rate is described as tent-shaped exponential functions and the value of the origin of the growth rate distribution is constant. These approximations are confirmed in profits data of Japanese companies 2003 and 2004. The resultant profits pdf fits with the empirical data with high accuracy. This guarantees the validity of the approximations.; Comment: 6 pages, 5 figures

We report the proof that the expression of extended Gibrat's law is unique and the probability distribution function (pdf) is also uniquely derived from the law of detailed balance and the extended Gibrat's law. In the proof, two approximations are employed that the pdf of growth rate is described as tent-shaped exponential functions and that the value of the origin of growth rate is constant. These approximations are confirmed in profits data of Japanese companies 2003 and 2004. The resultant profits pdf fits with the empirical data with high accuracy. This guarantees the validity of the approximations.; Comment: 11 pages, 8 figures

The microscopic dynamics and aging of a soft thermosensitive suspension was investigated by looking at the thermal fluctuations of tracers in the suspension. Below and above the glass transition, the dense microgel particles suspension was found to develop an heterogeneous dynamics, featured by a non Gaussian Probability Distribution Function (PDF) of the probes' displacements, with an exponential tail. We show that non Gaussian shapes are a characteristic of the ensemble-averaged PDF, while local PDF remain Gaussian. This shows that the scenario behind the non Gaussian van Hove functions is a spatially heterogeneous dynamics, characterized by a spatial distribution of locally homogeneous dynamical environments through the sample, on the considered time scales. We characterize these statistical distributions of dynamical environments, in the liquid, supercooled, and glass states, and show that it can explain the observed exponential tail of the van Hove functions observed in the concentrated states. The intensity of spatial heterogeneities was found to amplify with increasing volume fraction. In the aging regime, it tends to increase as the glass gets more arrested.; Comment: 19 pages, 10 figures, Soft Matter accepted

Numerical evidence of non-diffusive transport in three-dimensional, resistive pressure-gradient-driven plasma turbulence is presented. It is shown that the probability density function (pdf) of test particles' radial displacements is strongly non-Gaussian and exhibits algebraic decaying tails. To model these results we propose a macroscopic transport model for the pdf based on the use of fractional derivatives in space and time, that incorporate in a unified way space-time non-locality (non-Fickian transport), non-Gaussianity, and non-diffusive scaling. The fractional diffusion model reproduces the shape, and space-time scaling of the non-Gaussian pdf of turbulent transport calculations. The model also reproduces the observed super-diffusive scaling.

The latest CTEQ6.6 parton distributions, obtained by global analysis of hard scattering data in the framework of general-mass perturbative QCD, are employed to study theoretical predictions and their uncertainties for significant processes at the Fermilab Tevatron and CERN Large Hadron Collider. The previously observed increase in predicted cross sections for the standard-candle W and Z boson production processes in the general-mass scheme (compared to those in the zero-mass scheme) is further investigated and quantified. A novel method to constrain PDF uncertainties in LHC observables, by effectively exploiting PDF-induced correlations with benchmark standard model cross sections, is presented. Using this method, we show that the top-antitop pair cross section can potentially serve as a standard candle observable for the LHC processes dominated by initial-state gluon scattering. Among other benefits, precise measurements of $t\bar{t}$ cross sections would reduce PDF uncertainties in predictions for single-top quark and Higgs boson production in the standard model and minimal supersymmetric standard model.; Comment: 32 pages, 15 figures; figures with embedded fonts available at http://hep.pa.msu.edu/cteq/public/6.6/pdfs/; extended discussion of small-x strangeness...

The structural parameters of a magnitude-limited sample of 148 unbarred S0-Sb galaxies were derived to study the correlations between bulge and disk parameters as well as the probability distribution function (PDF) of the intrinsic equatorial ellipticity of bulges. A new algorithm (GASP2D) was used to perform the bidimensional bulge-disk decomposition of the J-band galaxy images extracted from the archive of the 2MASS survey. The PDF of intrinsic ellipticities was derived from the distribution of the observed ellipticities of the bulges and misalignments between the the bulges and disks. About 80% of the observed bulges are not oblate but triaxial ellipsoids. Their mean axial ratio in the equatorial plane is =0.85. There is not significant dependence of their PDF on morphology, light concentration or luminosity. This has to be explained by the different scenarios of bulge formation.; Comment: 2 pages, 1 figure to appear in the proceedings of "Formation and Evolution of Galaxy Disks", Rome, October 2007, Eds. J. Funes and E. M. Corsini