Consistency of f(R)=R2−R02f(R)=\sqrt{R^{2}-R_{0}^2} Gravity with the Cosmological Observations in Palatini Formalism

In this work we study the dynamics of universe in $f(R)=\sqrt{R^2-R_{0}^2}$ modified gravity with Palatini formalism. We use data from recent observations as Supernova Type Ia (SNIa) Gold sample and Supernova Legacy Survey (SNLS) data, size of baryonic acoustic peak from Sloan Digital Sky Survey (SDSS), the position of the acoustic peak from the CMB observations and large scale structure formation (LSS) from the 2dFGRS survey to put constraint on the parameters of the model. To check the consistency of this action, we compare the age of old cosmological objects with the age of universe. In the combined analysis with the all the observations, we find the parameters of model as $R_0=6.192_{-0.177}^{+0.167}\times H_0^2$ and $\Omega_m=0.278_{-0.278}^{+0.273}$.Comment: 12 pages, 7 figure

Uncertainty in the Fluctuations of the Price of Stocks

We report on a study of the Tehran Price Index (TEPIX) from 2001 to 2006 as an emerging market that has been affected by several political crises during the recent years, and analyze the non-Gaussian probability density function (PDF) of the log returns of the stocks' prices. We show that while the average of the index did not fall very much over the time period of the study, its day-to-day fluctuations strongly increased due to the crises. Using an approach based on multiplicative processes with a detrending procedure, we study the scale-dependence of the non-Gaussian PDFs, and show that the temporal dependence of their tails indicates a gradual and systematic increase in the probability of the appearance of large increments in the returns on approaching distinct critical time scales over which the TEPIX has exhibited maximum uncertainty.Comment: 5 pages, 5 figures. Accepted to appear in IJMP

Power-law Parameterized Quintessence Model

We introduce a power-law parameterized quintessence model for the dark energy which accelerate universe at the low redshifts while behaves as an ordinary matter for the early universe. We construct a unique scalar potential for this parameterized quintessence model. As the observational test, the Supernova Type Ia (SNIa) Gold sample data, size of baryonic acoustic peak from Sloan Digital Sky Survey (SDSS), the position of the acoustic peak from the CMB observations and structure formation from the 2dFGRS survey are used to constrain the parameters of the quintessence model. The best fit parameters indicates that the equation of state of this model at the present time is less than one $(w_0<-1)$ which violates the energy condition in General Relativity. Finally we compare the age of old objects with age of universe in this model.Comment: 11 pages, 17 figures, submitted to Phys. Rev.

Quantitative features of multifractal subtleties in time series

Based on the Multifractal Detrended Fluctuation Analysis (MFDFA) and on the Wavelet Transform Modulus Maxima (WTMM) methods we investigate the origin of multifractality in the time series. Series fluctuating according to a qGaussian distribution, both uncorrelated and correlated in time, are used. For the uncorrelated series at the border (q=5/3) between the Gaussian and the Levy basins of attraction asymptotically we find a phase-like transition between monofractal and bifractal characteristics. This indicates that these may solely be the specific nonlinear temporal correlations that organize the series into a genuine multifractal hierarchy. For analyzing various features of multifractality due to such correlations, we use the model series generated from the binomial cascade as well as empirical series. Then, within the temporal ranges of well developed power-law correlations we find a fast convergence in all multifractal measures. Besides of its practical significance this fact may reflect another manifestation of a conjectured q-generalized Central Limit Theorem

Long range correlation in cosmic microwave background radiation

We investigate the statistical anisotropy and Gaussianity of temperature fluctuations of Cosmic Microwave Background radiation (CMB) data from {\it Wilkinson Microwave Anisotropy Probe} survey, using the multifractal detrended fluctuation analysis, rescaled range and scaled windowed variance methods. The multifractal detrended fluctuation analysis shows that CMB fluctuations has a long range correlation function with a multifractal behavior. By comparing the shuffled and surrogate series of CMB data, we conclude that the multifractality nature of temperature fluctuation of CMB is mainly due to the long-range correlations and the map is consistent with a Gaussian distribution.Comment: 10 pages, 7 figures, V2: Added comments, references and major correction

Long-range correlation and multifractality in Bach's Inventions pitches

We show that it can be considered some of Bach pitches series as a stochastic process with scaling behavior. Using multifractal deterend fluctuation analysis (MF-DFA) method, frequency series of Bach pitches have been analyzed. In this view we find same second moment exponents (after double profiling) in ranges (1.7-1.8) in his works. Comparing MF-DFA results of original series to those for shuffled and surrogate series we can distinguish multifractality due to long-range correlations and a broad probability density function. Finally we determine the scaling exponents and singularity spectrum. We conclude fat tail has more effect in its multifractality nature than long-range correlations.Comment: 18 page, 6 figures, to appear in JSTA

Mona Lisa, the stochastic view and fractality in color space

A painting consists of objects which are arranged in specific ways. The art of painting is drawing the objects, which can be considered as known trends, in an expressive manner. Detrended methods are suitable for characterizing the artistic works of the painter by eliminating trends. It means that we study the paintings, regardless of its apparent purpose, as a stochastic process. We apply multifractal detrended fluctuation analysis to characterize the statistical properties of Mona Lisa, as an instance, to exhibit the fractality of the painting. Our results show that Mona Lisa is long range correlated and almost behaves similar in various scales.Comment: 16 pages, 5 figures, to appear in Int. J. Mod. Phys.

The Nucleotide Exchange Factor Ric-8A is a Chaperone for the Conformationally Dynamic Nucleotide-Free State of G Alpha I1

Heterotrimeric G protein alpha subunits are activated upon exchange of GDP for GTP at the nucleotide binding site of G alpha, catalyzed by guanine nucleotide exchange factors (GEFs). In addition to transmembrane G protein-coupled receptors (GPCRs), which act on G protein heterotrimers, members of the family cytosolic proteins typified by mammalian Ric-8A are GEFs for Gi/q/12/13-class G alpha subunits. Ric-8A binds to G alpha.GDP, resulting in the release of GDP. The Ric-8A complex with nucleotide-free G alpha i1 is stable, but dissociates upon binding of GTP to G alpha i1. To gain insight into the mechanism of Ric-8A-catalyzed GDP release from G alpha i1, experiments were conducted to characterize the physical state of nucleotide-free G alpha i1 (hereafter referred to as G alpha i1[]) in solution, both as a monomeric species, and in the complex with Ric-8A. We found that Ric-8A-bound, nucleotide-free G alpha i1 is more accessible to trypsinolysis than G alpha i1.GDP, but less so than G alpha i1[] alone. The TROSY-HSQC spectrum of [N-15]G alpha i1[] bound to Ric-8A shows considerable loss of peak intensity relative to that of [N-15]G alpha i1.GDP. Hydrogen-deuterium exchange in G alpha i1[] bound to Ric-8A is 1.5-fold more extensive than in G alpha i1.GDP. Differential scanning calorimetry shows that both Ric-8A and G alpha i1.GDP undergo cooperative, irreversible unfolding transitions at 47 degrees and 52 degrees, respectively, while nucleotide-free G alpha i1 shows a broad, weak transition near 35 degrees. The unfolding transition for Ric-8A: G alpha i1[] is complex, with a broad transition that peaks at 50 degrees, suggesting that both Ric-8A and G alpha i1[] are stabilized within the complex, relative to their respective free states. The C-terminus of G alpha i1 is shown to be a critical binding element for Ric-8A, as is also the case for GPCRs, suggesting that the two types of GEF might promote nucleotide exchange by similar mechanisms, by acting as chaperones for the unstable and dynamic nucleotide-free state of G alpha

Interacting Ghost Dark Energy in Non-Flat Universe

A new dark energy model called "ghost dark energy" was recently suggested to explain the observed accelerating expansion of the universe. This model originates from the Veneziano ghost of QCD. The dark energy density is proportional to Hubble parameter, $\rho_D=\alpha H$, where $\alpha$ is a constant of order $\Lambda_{\rm QCD}^3$ and $\Lambda_{\rm QCD}\sim 100 MeV$ is QCD mass scale. In this paper, we extend the ghost dark energy model to the universe with spatial curvature in the presence of interaction between dark matter and dark energy. We study cosmological implications of this model in detail. In the absence of interaction the equation of state parameter of ghost dark energy is always $w_D > -1$ and mimics a cosmological constant in the late time, while it is possible to have $w_D < -1$ provided the interaction is taken into account. When $k = 0$, all previous results of ghost dark energy in flat universe are recovered. To check the observational consistency, we use Supernova type Ia (SNIa) Gold sample, shift parameter of Cosmic Microwave Background radiation (CMB) and the Baryonic Acoustic Oscillation peak from Sloan Digital Sky Survey (SDSS). The best fit values of free parameter at $1\sigma$ confidence interval are: $\Omega_m^0= 0.35^{+0.02}_{-0.03}$, $\Omega_D^0=0.75_{-0.04}^{+0.01}$ and $b^2=0.08^{+0.03}_{-0.03}$. Consequently the total energy density of universe at present time in this model at 68% level equates to $\Omega_{\rm tot}^0=1.10^{+0.02}_{-0.05}$.Comment: 19 pages, 9 figures. V2: Added comments, observational consequences, references, figures and major corrections. Accepted for publication in General Relativity and Gravitatio

Exact Analysis of Level-Crossing Statistics for (d+1)-Dimensional Fluctuating Surfaces

We carry out an exact analysis of the average frequency $\nu_{\alpha x_i}^+$ in the direction $x_i$ of positive-slope crossing of a given level $\alpha$ such that, $h({\bf x},t)-\bar{h}=\alpha$, of growing surfaces in spatial dimension $d$. Here, $h({\bf x},t)$ is the surface height at time $t$, and $\bar{h}$ is its mean value. We analyze the problem when the surface growth dynamics is governed by the Kardar-Parisi-Zhang (KPZ) equation without surface tension, in the time regime prior to appearance of cusp singularities (sharp valleys), as well as in the random deposition (RD) model. The total number $N^+$ of such level-crossings with positive slope in all the directions is then shown to scale with time as $t^{d/2}$ for both the KPZ equation and the RD model.Comment: 22 pages, 3 figure