Spectral Analysis of Multi-dimensional Self-similar Markov Processes

In this paper we consider a discrete scale invariant (DSI) process $\{X(t), t\in {\bf R^+}\}$ with scale $l>1$. We consider to have some fix number of observations in every scale, say $T$, and to get our samples at discrete points $\alpha^k, k\in {\bf W}$ where $\alpha$ is obtained by the equality $l=\alpha^T$ and ${\bf W}=\{0, 1,...\}$. So we provide a discrete time scale invariant (DT-SI) process $X(\cdot)$ with parameter space $\{\alpha^k, k\in {\bf W}\}$. We find the spectral representation of the covariance function of such DT-SI process. By providing harmonic like representation of multi-dimensional self-similar processes, spectral density function of them are presented. We assume that the process $\{X(t), t\in {\bf R^+}\}$ is also Markov in the wide sense and provide a discrete time scale invariant Markov (DT-SIM) process with the above scheme of sampling. We present an example of DT-SIM process, simple Brownian motion, by the above sampling scheme and verify our results. Finally we find the spectral density matrix of such DT-SIM process and show that its associated $T$-dimensional self-similar Markov process is fully specified by $\{R_{j}^H(1),R_{j}^H(0),j=0, 1,..., T-1\}$ where $R_j^H(\tau)$ is the covariance function of $j$th and $(j+\tau)$th observations of the process.Comment: 16 page

Coupling running through the Looking-Glass of dimensional Reduction

The dimensional reduction, in a form of transition from four to two dimensions, was used in the 90s in a context of HE Regge scattering. Recently, it got a new impetus in quantum gravity where it opens the way to renormalizability and finite short-distance behavior. We consider a QFT model $g\,\varphi^4\,$ with running coupling defined in both the two domains of different dimensionality; the \gbar(Q^2)\, evolutions being duly conjugated at the reduction scale $\,Q\sim M.$ Beyond this scale, in the deep UV 2-dim region, the running coupling does not increase any more. Instead, it {\it slightly decreases} and tends to a finite value \gbar_2(\infty) \,< \, \gbar_2(M^2)\, from above. As a result, the global evolution picture looks quite peculiar and can propose a base for the modified scenario of gauge couplings behavior with UV fixed points provided by dimensional reduction instead of leptoquarks.Comment: 8 pages, 4 figures,Version to match the one which (besides the Appendix) will appear in "Particles and Nuclei (PEPAN), Letters", v.7, No 6(162) 2010 pp 625-631. Slightly edited, one more reference and related numerical estimate adde

Non-universal gaugino masses: a signal-based analysis for the Large Hadron Collider

We discuss the signals at the Large Hadron Collider (LHC) for scenarios with non-universal gaugino masses in supersymmetric (SUSY) theories. We perform a multichannel analysis, and consider the ratios of event rates in different channels such as $jets + {E}_T/$, $same$ - and $opposite$-$sign dileptons$ $+jets+ {E}_T/$, as well as $single-lepton$ and $trilepton$ final states together with $jets + {E}_T/$ . Low-energy SUSY spectra corresponding to high-scale gaugino non-universality arising from different breaking schemes of SU(5) as well as SO(10) Grand Unified (GUT) SUSY models are considered, with both degenerate low-energy sfermion masses and those arising from a supergravity scenario. We present the numerical predictions over a wide range of the parameter space using the event generator {\tt Pythia}, specifying the event selection criteria and pointing out regions where signals are likely to be beset with backgrounds. Certain broad features emerge from the study, which may be useful in identifying the signatures of different GUT breaking schemes and distinguishing them from a situation with a universal gaugino mass at high scale. The absolute values of the predicted event rates for different scenarios are presented together with the various event ratios, so that these can also be used whenever necessary.Comment: 54 pages, 18 figure

Fast optical variability of SS 433

We study the optical variability of the peculiar Galactic source SS 433 using the observations made with the Russian Turkish 1.5-m telescope (RTT150). A simple technique which allows to obtain high-quality photometric measurements with 0.3-1 s time resolution using ordinary CCD is described in detail. Using the test observations of nonvariable stars, we show that the atmospheric turbulence introduces no significant distortions into the measured light curves. Therefore, the data obtained in this way are well suited for studying the aperiodic variability of various objects. The large amount of SS 433 optical light curve measurements obtained in this way allowed us to obtain the power spectra of its flux variability with a record sensitivity up to frequencies of ~0.5 Hz and to detect its break at frequency =~2.4e-3 Hz. We suggest that this break in the power spectrum results from the smoothing of the optical flux variability due to a finite size of the emitting region. Based on our measurement of the break frequency in the power spectrum, we estimated the size of the accretion-disk photosphere as 2e12 cm. We show that the amplitude of the variability in SS 433 decreases sharply during accretion-disk eclipses, but it does not disappear completely. This suggests that the size of the variable optical emission source is comparable to that of the normal star whose size is therefore R_O \approx 2e12 cm \approx 30 R_sun. The decrease in flux variability amplitude during eclipses suggests the presence of a nonvariable optical emission component with a magnitude m_R=~13.2.Comment: 12 pages, 11 figures. Accepted for publication in Astronomy Letters. The original version in Russian is available at http://hea.iki.rssi.ru/rtt150/ru/ss433_pazh10/pss433_fast.pd

Unit roots in periodic autoregressions

Abstract. This paper analyzes the presence and consequences of a unit root in periodic autoregressive models for univariate quarterly time series. First, we consider various representations of such models, including a new parametrization which facilitates imposing a unit root restriction. Next, we propose a class of likelihood ratio tests for a unit root, and we derive their asymptotic null distributions. Likelihood ratio tests for periodic parameter variation are also proposed. Finally, we analyze the impact on unit root inference of misspecifying a periodic process by a constant-parameter model

Adiabatic compression and indirect detection of supersymmetric dark matter

Recent developments in the modelling of the dark matter distribution in our Galaxy point out the necessity to consider some physical processes to satisfy observational data. In particular, models with adiabatic compression, which include the effect of the baryonic gas in the halo, increase significantly the dark matter density in the central region of the Milky Way. On the other hand, the non-universality in scalar and gaugino sectors of supergravity models can also increase significantly the neutralino annihilation cross section. We show that the combination of both effects gives rise to a gamma-ray flux arising from the Galactic Center largely reachable by future experiments like GLAST. We also analyse in this framework the EGRET excess data above 1 GeV, as well as the recent data from CANGAROO and HESS. The analysis has been carried out imposing the most recent experimental constraints, such as the lower bound on the Higgs mass, the \bsg branching ratio, and the muon $g-2$. In addition, the recently improved upper bound on $B(B_s \to \mu^+ \mu^-)$ has also been taken into account. The astrophysical (WMAP) bounds on the dark matter density have also been imposed on the theoretical computation of the relic neutralino density through thermal production.Comment: 32 pages, 11 figures, final version to appear in JCA

Two photon annihilation of Kaluza-Klein dark matter

We investigate the fermionic one-loop cross section for the two photon annihilation of Kaluza-Klein (KK) dark matter particles in a model of universal extra dimensions (UED). This process gives a nearly mono-energetic gamma-ray line with energy equal to the KK dark matter particle mass. We find that the cross section is large enough that if a continuum signature is detected, the energy distribution of gamma-rays should end at the particle mass with a peak that is visible for an energy resolution of the detector at the percent level. This would give an unmistakable signature of a dark matter origin of the gamma-rays, and a unique determination of the dark matter particle mass, which in the case studied should be around 800 GeV. Unlike the situation for supersymmetric models where the two-gamma peak may or may not be visible depending on parameters, this feature seems to be quite robust in UED models, and should be similar in other models where annihilation into fermions is not helicity suppressed. The observability of the signal still depends on largely unknown astrophysical parameters related to the structure of the dark matter halo. If the dark matter near the galactic center is adiabatically contracted by the central star cluster, or if the dark matter halo has substructure surviving tidal effects, prospects for detection look promising.Comment: 17 pages, 3 figures; slightly revised versio

Oscillatory Fractional Brownian Motion and Hierarchical Random Walks

We introduce oscillatory analogues of fractional Brownian motion, sub-fractional Brownian motion and other related long range dependent Gaussian processes, we discuss their properties, and we show how they arise from particle systems with or without branching and with different types of initial conditions, where the individual particle motion is the so-called c-random walk on a hierarchical group. The oscillations are caused by the discrete and ultrametric structure of the hierarchical group, and they become slower as time tends to infinity and faster as time approaches zero. We also give other results to provide an overall picture of the behavior of this kind of systems, emphasizing the new phenomena that are caused by the ultrametric structure as compared with results for analogous models on Euclidean space

Stable Isotope Composition of Fatty Acids in Organisms of Different Trophic Levels in the Yenisei River

We studied four-link food chain, periphytic microalgae and water moss (producers), trichopteran larvae (consumers I), gammarids (omnivorous – consumers II) and Siberian grayling (consumers III) at a littoral site of the Yenisei River on the basis of three years monthly sampling. Analysis of bulk carbon stable isotopes and compound specific isotope analysis of fatty acids (FA) were done. As found, there was a gradual depletion in 13C contents of fatty acids, including essential FA upward the food chain. In all the trophic levels a parabolic dependence of δ13C values of fatty acids on their degree of unsaturation/chain length occurred, with 18:2n-6 and 18:3n-3 in its lowest point. The pattern in the δ13C differences between individual fatty acids was quite similar to that reported in literature for marine pelagic food webs. Hypotheses on isotope fractionation were suggested to explain the findings