On page 39, Vol. viii, No. 2, September 18, 1925, multiply the right-hand side of formula (2) by the factor See PDF for Equation. On page 44, immediately after formula (1) the text should be continued as follows: Let us suppose a membrane to be separated by two solutions of KCl of different concentrations K1 and K2 and these concentrations and the corresponding concentrations of K+ within the membrane, which are in equilibrium with the outside solutions, to be so high that the H+ ions may be neglected. When a small electric current flows across the system, practically the K+ ions alone are transferred and that in a reversible manner. Therefore the total P.D. is practically See PDF for Equation This P.D. is composed of two P.D.'s at the boundaries and the diffusion potential within the membrane. Suppose the immobility of the anions is not absolute but only relative as compared with the mobility of the cations, KCl would gradually penetrate into the membrane to equal concentration with the outside solution on either side and no boundary potential would be established. In this case the diffusion P.D. within the membrane is the only P.D., amounting to See PDF for Equation but, V being practically = 0, it would result that See PDF for Equation So the definitive result is the same as in the former case. Now cancel the printed text as far as page 48...

An uncertainty quantification study is carried out for the problem of the frontal collision of two elastic bodies. The time of contact and the resultant force function involved during the collision are the quantities of interest. If the initial conditions and the mechanical and geometrical properties were known, the response prediction would be deterministic. However, if the data contains any uncertainty, a stochastic approach becomes appropriate. Based on the Principle of Maximum Entropy (PME), and under certain restrictions on the parameter values, we derive the probability density function (PDF) for each of the stochastic parameters to construct a probabilistic model. Two cases are dealt with: one of a collision involving two spheres and another of a collision of two discs. In the first case, a parameter involving geometry and material properties is assumed stochastic. Since a functional relationship exists, the propagation of the uncertainty of the time of contact can be done symbolically. However, the interaction force function can only be computed from the solution of a nonlinear ordinary differential equation. Given the PDF of the parameter, the problem of uncertainty propagation is tackled using Monte Carlo simulations. The comparison of both approaches yields an excellent agreement. With respect to the collision of two discs...

O boletim Mercado de trabalho: conjuntura e análise tem periodicidade semestral e traz uma análise conjuntural do Mercado de trabalho, acompanhada de indicadores e seções temáticas que abordam tanto considerações mais técnicas como questões de cunho político-institucional.; n. 30, 40 p.; parte 1: Apresentação de conjuntura, arquivo pdf; parte 2: Análise do mercado de trabalho, arquivo pdf; parte 3: Nota Técnica: Desigualdade de rendimento do trabalho no Brasil no período pós-real, arquivo pdf; parte 4: Nota Técnica: O dilema do financiamento orçamentário das políticas públicas de emprego, arquivo pdf

O boletim Mercado de trabalho: conjuntura e análise tem periodicidade semestral e traz uma análise conjuntural do Mercado de trabalho, acompanhada de indicadores e seções temáticas que abordam tanto considerações mais técnicas como questões de cunho político-institucional.; n. 32, ca. 30 p.; parte 1: Apresentação da conjuntura, arquivo pdf; parte 2: Análise do mercado de trabalho, arquivo pdf; parte 3: Nota técnica: A evolução do mercado de trabalho metropolitano segundo a leitura da nova metodologia da pesquisa mensal de emprego no período de março de 2002 a dezembro de 2006, arquivo pdf; parte 4: Indicadores e previsões Ipea, em 6 arquivos pdf

We present a method for distance calibration without using standard fitting procedures. Instead we use random resampling to reconstruct the probability density function (PDF) of calibration data points in the fitting plane. The resulting PDF is then used to estimate distance-related properties. The method is applied to samples of radio surface brightness to diameter (\Sigma-D) data for the Galactic supernova remnants (SNRs) and planetary nebulae (PNe), and period-luminosity (PL) data for the Large Magellanic Cloud (LMC) fundamental mode classical Cepheids. We argue that resulting density maps can provide more accurate and more reliable calibrations than those obtained by standard linear fitting procedures. For the selected sample of the Galactic SNRs, the presented PDF method of distance calibration results in a smaller average distance fractional error of up to $\approx 16$ percentage points. Similarly, the fractional error is smaller for up to $\approx 8$ and $\approx 0.5$ percentage points, for the samples of Galactic PNe and LMC Cepheids, respectively. In addition, we provide a PDF-based calibration data for each of the samples.; Comment: 11 pages, 3 figures, corrected for mistakenly considering working data as absolute instead of apparent magnitude...

The probability density function (PDF) of the roughness, i.e., of the temporal variance, of 1/f^alpha noise signals is studied. Our starting point is the generalization of the model of Gaussian, time-periodic, 1/f noise, discussed in our recent Letter [T. Antal et al., PRL, vol. 87, 240601 (2001)], to arbitrary power law. We investigate three main scaling regions, distinguished by the scaling of the cumulants in terms of the microscopic scale and the total length of the period. Various analytical representations of the PDF allow for a precise numerical evaluation of the scaling function of the PDF for any alpha. A simulation of the periodic process makes it possible to study also non-periodic signals on short intervals embedded in the full period. We find that for alpha=<1/2 the scaled PDF-s in both the periodic and the non-periodic cases are Gaussian, but for alpha>1/2 they differ from the Gaussian and from each other. Both deviations increase with growing alpha. That conclusion, based on numerics, is reinforced by analytic results for alpha=2 and alpha->infinity. We suggest that our theoretical and numerical results open a new perspective on the data analysis of 1/f^alpha processes.; Comment: 12 pages incl. 6 figures, with RevTex4...

Kinetic energy stored in ISM bulk/turbulent motions is a crucial ingredient to properly describe most properties of observed galaxies. By using Monte Carlo simulations, we investigate how this energy is injected by supernovae and dissipated via cloud collisions and derive the corresponding ISM velocity probability distribution function (PDF). The functional form of the PDF for the modulus of the velocity dispersion is $$p(v) \propto v^2 \exp[-(v/\sigma)^\beta].$$ The power-law index of the PDF depends only on the value of the average cloud collision elasticity < \epsilon > as \beta = 2\exp(<\epsilon > -1). If \beta and the gas velocity dispersion \sigma are known, the specific kinetic energy dissipated by collisions is found to be \propto \sigma^2 \ln (2 / \beta)/(\beta-0.947); in steady state, this is equal to the energy input from SNe. We predict that in a multiphase, low metallicity (Z \approx 5 \times 10^{-3} Z_\odot) ISM the PDF should be close to a Maxwellian (\beta = 2) with velocity dispersion \sigma \simgt 11$ km s\m; in more metal rich systems (Z \simgt 5 \times 10^{-2} Z_\odot), instead, we expect to observe almost exponential PDFs. This is in good agreement with a number of observations that we review and might explain the different star formation modes seen in dwarfs and spiral galaxies.; Comment: Accepted for publication of MNRAS. 10 pages including 7 figures

Weak gravitational lensing changes the angular power spectra of the cosmic microwave background (CMB) temperature and polarization in a characteristic way containing valuable information for cosmological parameter estimation and weak lensing reconstructions. So far, analytical expressions for the lensed CMB power spectra assume the probability density function (PDF) of the lensing excursion angle to be Gaussian. However, coherent light deflection by nonlinear structures at low redshifts causes deviations from a pure Gaussian PDF. Working in the flat-sky limit we develop a method for computing the lensed CMB power spectra which takes these non-Gaussian features into account. Our method does not assume any specific PDF but uses instead an expansion of the characteristic function of the lensing excursion angle into its moments. Measuring these in the CMB lensing deflection field obtained from the Millennium Simulation we show that the change in the lensed power spectra is only at the 0.1% - 0.4% level on very small scales (below 4 arcmin) and demonstrate that the assumption of a Gaussian lensing excursion angle PDF is well applicable.; Comment: 9 pages, 2 figures, submitted to MNRAS

Many financial variables are found to exhibit multifractal nature, which is usually attributed to the influence of temporal correlations and fat-tailedness in the probability distribution (PDF). Based on the partition function approach of multifractal analysis, we show that there is a marked finite-size effect in the detection of multifractality, and the effective multifractality is the apparent multifractality after removing the finite-size effect. We find that the effective multifractality can be further decomposed into two components, the PDF component and the nonlinearity component. Referring to the normal distribution, we can determine the PDF component by comparing the effective multifractality of the original time series and the surrogate data that have a normal distribution and keep the same linear and nonlinear correlations as the original data. We demonstrate our method by taking the daily volatility data of Dow Jones Industrial Average from 26 May 1896 to 27 April 2007 as an example. Extensive numerical experiments show that a time series exhibits effective multifractality only if it possesses nonlinearity and the PDF has impact on the effective multifractality only when the time series possesses nonlinearity. Our method can also be applied to judge the presence of multifractality and determine its components of multifractal time series in other complex systems.; Comment: 9 RevTex pages including 9 eps figures. Comments and suggestions are warmly welcome

The analysis of the Lyman-alpha forest of absorption lines in quasar spectra has emerged as a potentially powerful technique to constrain the linear matter power spectrum. In most previous work, the amplitude of the ionizing background was fixed by calibrating simulations to match the observed mean transmitted flux in the Lyman-alpha forest. This procedure is undesirable in principle as it requires the estimation of the unabsorbed quasar continuum level, a difficult undertaking subject to various sources of systematic error and bias. We suggest an alternative approach based on measuring the one-point probability distribution function (pdf) of the fluctuations in the flux about the mean, relative to the mean, i.e. the pdf of delta_f = (f - )/. This statistic, while sensitive to the amplitude of the ionizing background, has the virtue that its measurement does not require an estimate of the unabsorbed continuum level. We present a measurement of the pdf of delta_f from seven Keck HIRES spectra, spanning a redshift range of z = 2.2 - 4.4. To illustrate that our method is useful, we compare our measurements of the pdf of delta_f, and measurements of the flux power spectrum from Croft et al. (2002) at z = 2.72, with cosmological simulations. From this comparison...

Traditionally, single realizations of the turbulent state have been the object of study in shear flow turbulence. When a statistical quantity was needed it was obtained from a spatial, temporal or ensemble average of sample realizations of the turbulence. However, there are important advantages to studying the dynamics of the statistical state (the SSD) directly. In highly chaotic systems statistical quantities are often the most useful and the advantage of obtaining these statistics directly from a state variable is obvious. Moreover, quantities such as the probability density function (pdf) are often difficult to obtain accurately by sampling state trajectories even if the pdf is stationary. In the event that the pdf is time dependent, solving directly for the pdf as a state variable is the only alternative. However, perhaps the greatest advantage of the SSD approach is conceptual: adopting this perspective reveals directly the essential cooperative mechanisms among the disparate spatial and temporal scales that underly the turbulent state. While these cooperative mechanisms have distinct manifestation in the dynamics of realizations of turbulence both these cooperative mechanisms and the phenomena associated with them are not amenable to analysis directly through study of realizations as they are through the study of the associated SSD. In this review a selection of example problems in the turbulence of planetary and laboratory flows is examined using recently developed SSD analysis methods in order to illustrate the utility of this approach to the study of turbulence in shear flow.; Comment: 25 pages...

We describe the implementation of Quantum Electrodynamic (QED) evolution at Leading Order (LO) along with Quantum Chromodynamic (QCD) evolution at Next-to-Leading Order (NLO) in the CTEQ-TEA Global analysis package. The photon Parton Distribution Function (PDF) is described by a two-parameter ansatz, coming from radiation off the valence quarks, and based on the CT14 NLO PDFs. Setting the two parameters equal, allows us to completely specify the photon PDF in terms of the momentum fraction carried by the photon, $p_0^\gamma$, at the initial scale $Q_0=1.295$ GeV. We obtain constraints on the photon PDF by comparing with ZEUS data~\cite{Chekanov:2009dq} on the production of isolated photons in deep inelastic scattering, $ep\rightarrow e\gamma+X$. For this comparison we present a new perturbative calculation of the process that consistently combines the photon-initiated contribution with the quark-initiated contribution. Comparison with the data allows us to put a constraint at the 90% confidence level of $p_0^\gamma\lesssim0.14\%$ for the photon PDF at the initial scale of $Q_0=1.295$ GeV in the one-parameter radiative ansatz. The resulting CT14QED PDFs will be made available to the public.; Comment: 26 pages, 13 figures

For a collection of distributions over a countable support set, the worst case universal compression formulation by Shtarkov attempts to assign a universal distribution over the support set. The formulation aims to ensure that the universal distribution does not underestimate the probability of any element in the support set relative to distributions in the collection. When the alphabet is uncountable and we have a collection $\cal P$ of Lebesgue continuous measures instead, we ask if there is a corresponding universal probability density function (pdf) that does not underestimate the value of the density function at any point in the support relative to pdfs in $\cal P$. Analogous to the worst case redundancy of a collection of distributions over a countable alphabet, we define the \textit{attenuation} of a class to be $A$ when the worst case optimal universal pdf at any point $x$ in the support is always at least the value any pdf in the collection $\cal P$ assigns to $x$ divided by $A$. We analyze the attenuation of the worst optimal universal pdf over length-$n$ samples generated \textit{i.i.d.} from a Gaussian distribution whose mean can be anywhere between $-\alpha/2$ to $\alpha/2$ and variance between $\sigma_m^2$ and $\sigma_M^2$. We show that this attenuation is finite...

We investigated the evolution of interacting disk galaxies using high-resolution $N$-body/SPH simulations, taking into account the multiphase nature of the interstellar medium (ISM). In our high-resolution simulations, a large-scale starburst occurred naturally at the collision interface between two gas disks at the first encounter, resulting in the formation of star clusters. This is consistent with observations of interacting galaxies. The probability distribution function (PDF) of gas density showed clear change during the galaxy-galaxy encounter. The compression of gas at the collision interface between the gas disks first appears as an excess at $n_{\rm H} \sim 10{\rm cm^{-3}}$ in the PDF, and then the excess moves to higher densities ($n_{\rm H} \gtrsim 100{\rm cm^{-3}}$) in a few times $10^7$ years where starburst takes place. After the starburst, the PDF goes back to the quasi-steady state. These results give a simple picture of starburst phenomena in galaxy-galaxy encounters.; Comment: 6 pages, 6 figures, accepted to PASJ. For high resolution figures, see http://www.cfca.nao.ac.jp/~saitoh/Papers/2009/Saitoh+2009a.pdf

We report the investigation of the 3s <- 2p transition in the BAr2 cluster. In a supersonic expansion of B atoms entrained in Ar, at high beam source backing pressures we observe several features in the fluorescence excitation spectrum which cannot be assigned to the BAr diatom. Using BAr(X, B) potential energy curves which reproduce our experimental observations on this molecule and an Ar-Ar interaction potential, we employ a pairwise additive model, along with variational and diffusion Monte-Carlo treatments of the nuclear motion, to determine the lowest vibrational state of the BAr2 cluster. A subsequent simulation of the fluorescence excitation spectrum reproduces nearly quantitatively the strongest feature in our experimental spectrum not assignable to BAr. Because of the barrier in the BAr(B 2Sigma+) potential energy curve, the 3s <- 2p transition in the BAr2 cluster is predicted to have an asymmetric profile, as is found experimentally.; Comment: a pdf file (5 kB) containing the abstract can be retrieved as ftp://mha-ibm2.umd.edu/pub/publications/BAr2.abs.pdf a pdf file (325 kB) containing the entire manuscript can be retrieved as ftp://mha-ibm2.umd.edu/pub/publications/BAr2.ms.pdf To appear in J. Chem. Phys. 106 (1997) 8 April issue.

Context. Whenever correlation functions are used for inference about cosmological parameters in the context of a Bayesian analysis, the likelihood function of correlation functions needs to be known. Usually, it is approximated as a multivariate Gaussian, though this is not necessarily a good approximation. Aims. We show how to calculate a better approximation for the probability distribution of correlation functions, which we call "quasi-Gaussian". Methods. Using the exact univariate PDF as well as constraints on correlation functions previously derived, we transform the correlation functions to an unconstrained variable for which the Gaussian approximation is well justified. From this Gaussian in the transformed space, we obtain the quasi-Gaussian PDF. The two approximations for the probability distributions are compared to the "true" distribution as obtained from simulations. Additionally, we test how the new approximation performs when used as likelihood in a toy-model Bayesian analysis. Results. The quasi-Gaussian PDF agrees very well with the PDF obtained from simulations; in particular, it provides a significantly better description than a straightforward copula approach. In a simple toy-model likelihood analysis, it yields noticeably different results than the Gaussian likelihood...

This is a review of ground-state features of the s=1/2 Heisenberg antiferromagnet on two-dimensional lattices. A central issue is the interplay of lattice topology (e.g. coordination number, non-equivalent nearest-neighbor bonds, geometric frustration) and quantum fluctuations and their impact on possible long-range order. This article presents a unified summary of all 11 two-dimensional uniform Archimedean lattices which include e.g. the square, triangular and kagome lattice. We find that the ground state of the spin-1/2 Heisenberg antiferromagnet is likely to be semi-classically ordered in most cases. However, the interplay of geometric frustration and quantum fluctuations gives rise to a quantum paramagnetic ground state without semi-classical long-range order on two lattices which are precisely those among the 11 uniform Archimedean lattices with a highly degenerate ground state in the classical limit. The first one is the famous kagome lattice where many low-lying singlet excitations are known to arise in the spin gap. The second lattice is called star lattice and has a clear gap to all excitations. Modification of certain bonds leads to quantum phase transitions which are also discussed briefly. Furthermore, we discuss the magnetization process of the Heisenberg antiferromagnet on the 11 Archimedean lattices...

High angular resolution diffusion imaging data is the observed characteristic function for the local diffusion of water molecules in tissue. This data is used to infer structural information in brain imaging. Nonparametric scalar measures are proposed to summarize such data, and to locally characterize spatial features of the diffusion probability density function (PDF), relying on the geometry of the characteristic function. Summary statistics are defined so that their distributions are, to first-order, both independent of nuisance parameters and also analytically tractable. The dominant direction of the diffusion at a spatial location (voxel) is determined, and a new set of axes are introduced in Fourier space. Variation quantified in these axes determines the local spatial properties of the diffusion density. Nonparametric hypothesis tests for determining whether the diffusion is unimodal, isotropic or multi-modal are proposed. More subtle characteristics of white-matter microstructure, such as the degree of anisotropy of the PDF and symmetry compared with a variety of asymmetric PDF alternatives, may be ascertained directly in the Fourier domain without parametric assumptions on the form of the diffusion PDF. We simulate a set of diffusion processes and characterize their local properties using the newly introduced summaries. We show how complex white-matter structures across multiple voxels exhibit clear ellipsoidal and asymmetric structure in simulation...

Weak lensing measurements are starting to provide statistical maps of the distribution of matter in the universe that are increasingly precise and complementary to cosmic microwave background maps. The probability distribution (PDF) provides a powerful tool to test non-Gausian features in the convergence field and to discriminate the different cosmological models. In this letter, we present a new PDF space Wiener filter approach to reconstruct the probability density function of the convergence from the noisy convergence field. We find that for parameters comparable to the CFHT legacy survey, the averaged PDF of the convergence in a 3 degree field can be reconstructed with an uncertainty of about 10%, even though the pointwise PDF is noise dominated.; Comment: 21 pages, 8 figures, accepted for publication in ApJ, added some discussions

The Arecibo Galaxy Environments Survey (AGES) is a 2000-hour neutral hydrogen (HI) survey using the new Arecibo L-band Feed Array (ALFA) multibeam instrument at Arecibo Observatory. It will cover 200 square degrees of sky, sampling a range of environments from the Local Void through to the Virgo Cluster with higher sensitivity, spatial resolution and velocity resolution than previous neutral hydrogen surveys.; Comment: IAU Symposium 235 - Galaxy Evolution across the Hubble Time. 3 pages (only 1 st to appear in printed proceedings), 3 figures. Uses iaus.cls. Full resolution PDF is available from http://www2.naic.edu/alfa/ealfa/AGES-IAUS235-Minchin.pdf and a PDF of the poster is available from http://www2.naic.edu/alfa/ealfa/AGES-IAU-Minchin.pdf