The effects of observational correlated noises on multifractal detrended fluctuation analysis

We have numerically investigated the effects that observational correlated noises have on the generalized Hurst exponents, h(q)$h\left(q\right)$, estimated by using the multifractal generalization of detrended fluctuation analysis (MF-DFA). More precisely, artificially generated stochastic binomial multifractals with increased amount of colored noises were analyzed via MF-DFA. It has been recently shown that for moderate additions of white noise, the generalized Hurst exponents are significantly underestimated for q<2$q<2$ and they are nearly unchanged for q≥2$q\ge 2$ [J. Ludescher, M.I. Bogachev, J.W. Kantelhardt, A.Y. Schumann, A. Bunde, On spurious and corrupted multifractality: the effects of additive noise, short- term memory and periodic trends, Physica A 390 (2011) 2480–2490]. In this paper, we have found that h(q)$h\left(q\right)$ with q≥2$q\ge 2$ are also affected when correlated noises are considered. This is due to the fact that the spurious correlations influence the scaling behaviors associated to large fluctuations. The results obtained are significant for practical situations, where noises with different correlations are inherently present.     

Multifractal behavior of wild-land and forest fire time series in Brazil

We examine statistical properties of a daily hot pixel time series recorded in Brazil during the period 1998–2006, using Multifractal Detrended Fluctuation Analysis (MF-DFA). We find that generalized scaling exponent h(q)$h\left(q\right)$ is a decreasing function of q$q$, indicating multifractal behavior of hot pixel dynamics. We also calculate multifractal spectra f(α)$f\left(\alpha \right)$ and use fourth-degree polynomial regression to estimate complexity parameters that describe the degree of multifractality of the underlying process. After July 2002, when a significant increase of the number of hot pixel observations is recorded, the complexity of the series is reduced (manifested by the reduction of width of the f(α)$f\left(\alpha \right)$ spectrum), while small fluctuations increase their dominance over large scale fluctuations (manifested by the increase of skew parameter r$r$). These results should be taken into account when devising ecological and climatic models for Brazil, that contemplate the phenomena of wild-land and forest fires.     

On the length of stabilograms: A study performed with detrended fluctuation analysis

The effects associated to the length of stabilograms, a measure of the time dependence of the center of pressure of an individual standing up, are analyzed. The fractal characteristics of 27 signals with a length of 2¹⁴$2^{14}$ points, each one corresponding to a different individual, are studied by using the Detrended Fluctuation Analysis technique. The properties of the complete signals are compared to those of various subsignals extracted from them. No differences have been found between the characteristic exponents found for x$x$ and y$y$ signals. The relation between the exponents of the position and velocity signals is accomplished by the 2¹⁴$2^{14}$ point signals, while subsignals with up to 2¹²$2^{12}$ points do not verify it. Using artificial signals with 2¹⁴$2^{14}$ points, generated for α$\alpha$ values given, it has been demonstrated that the exponents obtained from these signals take values larger than expected for α<0.3$\alpha <0.3$, while the exponents of the accumulated series are smaller than expected for 0.7<α$0.7<\alpha$. For CoP trajectories this indicates that DFA-1 provides feasible exponents for the short τ$\tau$-end region of the velocity signal and the large τ$\tau$-end region of the accumulated (position) one. It has been found that the characteristic exponents vary along the series. A slightly larger persistence is found in the last part of the signal for large frequencies in the x$x$ direction.     

Efficiency and multifractality analysis of CSI 300 based on multifractal detrending moving average algorithm

We apply the multifractal detrending moving average (MFDMA) to investigate and compare the efficiency and multifractality of 5-min high-frequency China Securities Index 300 (CSI 300). The results show that the CSI 300 market becomes closer to weak-form efficiency after the introduction of CSI 300 future. We find that the CSI 300 is featured by multifractality and there are less complexity and risk after the CSI 300 index future was introduced. With the shuffling, surrogating and removing extreme values procedures, we unveil that extreme events and fat-distribution are the main origin of multifractality. Besides, we discuss the knotting phenomena in multifractality, and find that the scaling range and the irregular fluctuations for large scales in the _Fq(s)$F_q\left(s\right)$ vs s$s$ plot can cause a knot.     

Is space-time symmetry a suitable generalization of parity-time symmetry?

We discuss space-time symmetric Hamiltonian operators of the form H=H₀+igH^′$H=H_0+ig{H}^{\prime }$, where H₀$H_0$ is Hermitian and g$g$ real. H₀$H_0$ is invariant under the unitary operations of a point group G$G$ while H^′$H^{\prime }$ is invariant under transformation by elements of a subgroup G^′$G^{\prime }$ of G$G$. If G$G$ exhibits irreducible representations of dimension greater than unity, then it is possible that H$H$ has complex eigenvalues for sufficiently small nonzero values of g$g$. In the particular case that H$H$ is parity-time symmetric then it appears to exhibit real eigenvalues for all 0<g<g_c$0<g<g_c$, where g_c$g_c$ is the exceptional point closest to the origin. Point-group symmetry and perturbation theory enable one to predict whether H$H$ may exhibit real or complex eigenvalues for g>0$g>0$. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries.     

Lifshitz-point correlation length exponents from the large-n expansion

The large-n expansion is applied to the calculation of thermal critical exponents describing the critical behavior of spatially anisotropic d-dimensional systems at m  -axial Lifshitz points. We derive the leading non-trivial 1/n$1/n$ correction for the perpendicular correlation-length exponent _νL2${\nu }_{L2}$ and hence several related thermal exponents to order O(1/n)$O(1/n)$. The results are consistent with known large-n expansions for d  -dimensional critical points and isotropic Lifshitz points, as well as with the second-order epsilon expansion about the upper critical dimension d^?=4+m/2$d^{?}=4+m/2$ for generic m∈[0,d]$m\in [0,d]$. Analytical results are given for the special case d=4$d=4$, m=1$m=1$. For uniaxial Lifshitz points in three dimensions, 1/n$1/n$ coefficients are calculated numerically. The estimates of critical exponents at d=3$d=3$, m=1$m=1$ and n=3$n=3$ are discussed.     

The first Chevalley–Eilenberg Cohomology group of the Lie algebra on the transverse bundle of a decreasing family of foliations

In [L. Lebtahi, Lie algebra on the transverse bundle of a decreasing family of foliations, J. Geom. Phys. 60 (2010), 122–133], we defined the transverse bundle V^k$V^k$ to a decreasing family of k$k$ foliations _Fi$F_i$ on a manifold M$M$. We have shown that there exists a (1,1)$(1,1)$ tensor J$J$ of V^k$V^k$ such that J^k≠0$J^k\ne 0$, J^k+1=0$J^{k+1}=0$ and we defined by _LJ(V^k)$L_J\left(V^k\right)$ the Lie Algebra of vector fields X$X$ on V^k$V^k$ such that, for each vector field Y$Y$ on V^k$V^k$, [X,JY]=J[X,Y]$[X,JY]=J[X,Y]$.     

Weak mirror symmetry of complex symplectic Lie algebras

A complex symplectic structure on a Lie algebra h$\mathfrak{h}$ is an integrable complex structure J$J$ with a closed non-degenerate (2,0)$(2,0)$-form. It is determined by J$J$ and the real part Ω$\Omega$ of the (2,0)$(2,0)$-form. Suppose that h$\mathfrak{h}$ is a semi-direct product g?V$\mathfrak{g}?V$, and both g$\mathfrak{g}$ and V$V$ are Lagrangian with respect to Ω$\Omega$ and totally real with respect to J$J$. This note shows that g?V$\mathfrak{g}?V$ is its own weak mirror image in the sense that the associated differential Gerstenhaber algebras controlling the extended deformations of Ω$\Omega$ and J$J$ are isomorphic.     

The Bethe lattice treatment of sound attenuation for a spin- 3/2 Ising model

The sound attenuation phenomena is investigated for a spin- 3/2 Ising model on the Bethe lattice in terms of the recursion relations by using the Onsager theory of irreversible thermodynamics. The dependencies of sound attenuation on the temperature (T$T$), frequency (w$w$), Onsager coefficient (γ$\gamma$) and external magnetic field (H$H$) near the second-order (_Tc)$\left(T_c\right)$ and first-order (_Tt)$\left(T_t\right)$ phase transition temperatures are examined for given coordination numbers q$q$ on the Bethe lattice. It is assumed that the sound wave couples to the order-parameter fluctuations which decay mainly via the order-parameter relaxation process, thus two relaxation times are obtained and which are used to obtain an expression for the sound attenuation coefficient (α)$\left(\alpha \right)$. Our investigations revealed that only one peak is obtained near _Tt$T_t$ and three peaks are found near _Tc$T_c$ when the Onsager coefficient is varied at a given constant frequency for q=3$q=3$. Fixing the Onsager coefficient and varying the frequency always leads to two peaks for q=3,4$q=3,4$ and 6 near _Tc$T_c$. The sound attenuation peaks are observed near _Tt$T_t$ at lower values of external magnetic field, but as it increases the sound attenuation peaks decrease and eventually disappear.     

On the solvability of the transvection group of extrinsic symplectic symmetric spaces

Let M$M$ be a symplectic symmetric space, and let ?:M→V$?:M\to V$ be an extrinsic symplectic symmetric immersion in the sense of Krantz and Schwachhöfer (2010) [7], i.e., (V,Ω)$(V,\Omega )$ is a symplectic vector space and ?$?$ is an injective symplectic immersion such that for each point p∈M$p\in M$, the geodesic symmetry in p$p$ is compatible with the reflection in the affine normal space at ?(p)$?\left(p\right)$.     

A separation property for magnetic Schrödinger operators on Riemannian manifolds

We consider a Schrödinger differential expression L=_ΔA+q$L={\Delta }_A+q$ on a complete Riemannian manifold (M,g)$(M,g)$ with metric g$g$, where _ΔA${\Delta }_A$ is the magnetic Laplacian on M$M$ and q≥0$q\ge 0$ is a locally square integrable function on M$M$. In the terminology of W.N. Everitt and M. Giertz, the differential expression L$L$ is said to be separated in L²(M)$L^2\left(M\right)$ if for all u∈L²(M)$u\in L^2\left(M\right)$ such that Lu∈L²(M)$Lu\in L^2\left(M\right)$, we have qu∈L²(M)$qu\in L^2\left(M\right)$. We give sufficient conditions for L$L$ to be separated in L²(M)$L^2\left(M\right)$.     

Minimal hypersurfaces in a nearly Kaehler 6-sphere

In this paper we show that for a compact minimal hypersurface M$M$ of constant scalar curvature in the unit sphere S⁶$S^6$ with the shape operator A$A$ satisfying ‖A‖²>5${\Vert A\Vert }^2>5$, there exists an eigenvalue λ>10$\lambda >10$ of the Laplace operator of the hypersurface M$M$ such that ‖A‖²=λ−5${\Vert A\Vert }^2=\lambda -5$. This gives the next discrete value of ‖A‖²${\Vert A\Vert }^2$ greater than 0 and 5.     

Tsallis non-extensive statistics,intermittent turbulence,SOC and chaos in the solar plasma,Part one: Sunspot dynamics

In this study, the non-linear analysis of the sunspot index is embedded in the non-extensive statistical theory of Tsallis (1988, 2004, 2009) ,  and . The q$q$-triplet of Tsallis, as well as the correlation dimension and the Lyapunov exponent spectrum were estimated for the SVD components of the sunspot index timeseries. Also the multifractal scaling exponent spectrum f(a)$f\left(a\right)$, the generalized Renyi dimension spectrum D(q)$D\left(q\right)$ and the spectrum J(p)$J\left(p\right)$ of the structure function exponents were estimated experimentally and theoretically by using the q$q$-entropy principle included in Tsallis non-extensive statistical theory, following Arimitsu and Arimitsu (2001, 2000)  and . Our analysis showed clearly the following: (a) a phase transition process in the solar dynamics from high dimensional non-Gaussian SOC state to a low dimensional non-Gaussian chaotic state, (b) strong intermittent solar turbulence and anomalous (multifractal) diffusion solar process, which is strengthened as the solar dynamics makes a phase transition to low dimensional chaos in accordance to Ruzmaikin, Zeleny and Milovanov’s studies (Zelenyi and Milovanov (1991) [21]); Milovanov and Zelenyi (1993) [22]; Ruzmakin et al. (1996) [26]) (c) faithful agreement of Tsallis non-equilibrium statistical theory with the experimental estimations of (i) non-Gaussian probability distribution function P(x)$P\left(x\right)$, (ii) multifractal scaling exponent spectrum f(a)$f\left(a\right)$ and generalized Renyi dimension spectrum _Dq$D_q$, (iii) exponent spectrum J(p)$J\left(p\right)$ of the structure functions estimated for the sunspot index and its underlying non equilibrium solar dynamics.     

New limits on radiative sterile neutrino decays from a search for single photons in neutrino interactions

It has been recently shown that excess events observed by the LSND and MiniBooNE neutrino experiments could be interpreted as a signal from the radiative decay of a heavy sterile neutrino _νh${\nu }_h$ produced in _νμ${\nu }_{\mu }$ neutral-current-like neutrino interactions. If the _νh${\nu }_h$ exist, it would be also produced by the _νμ${\nu }_{\mu }$ beam from the CERN SPS in the neutrino beam line shielding. The _νh${\nu }_h$?s would penetrate the shielding and be observed through the _νh→γν${\nu }_h\to \gamma \nu$ decay followed by the photon conversion into e⁺e⁻$e^{+}{e}^{-}$ pair in the active target of the NOMAD detector. The _νh${\nu }_h$?s could be also produced in the iron of the magnetic spectrometer of the CHORUS detector, located just in front of NOMAD. Considering these two sources of _νh${\nu }_h$?s we set new constraints on _νh${\nu }_h$ properties and exclude part of the LSND/MiniBooNE _νh${\nu }_h$ parameter space using bounds on single photons production in neutrino reactions recently reported by the NOMAD Collaboration. We find that broad bands in the parameter space are still open for more sensitive searches for the _νh${\nu }_h$ in future neutrino experiments.     

On leafwise conformal diffeomorphisms

For every diffeomorphism φ:M→N$\phi :M\to N$ between 3-dimensional Riemannian manifolds M$M$ and N$N$, there are locally two 2-dimensional distributions _D±$D_{\pm }$ such that φ$\phi$ is conformal on both of them. We state necessary and sufficient conditions for a distribution to be one of _D±$D_{\pm }$. These are algebraic conditions expressed in terms of the self-adjoint and positive definite operator induced from _φ∗${\phi }_{\ast }$. We investigate the integrability condition of _D+$D_{+}$ and _D−$D_{-}$. We also show that it is possible to choose coordinate systems in which leafwise conformal diffeomorphism is holomorphic on leaves.     

Uniqueness of balanced metrics on holomorphic vector bundles

Let E→M$E\to M$ be a holomorphic vector bundle over a compact Kähler manifold (M,ω)$(M,\omega )$. We prove that if E$E$ admits a ω$\omega$-balanced metric (in X. Wang’s terminology (Wang, 2005 [3])) then it is unique. This result together with Biliotti and Ghigi (2008) [14] implies the existence and uniqueness of ω$\omega$-balanced metrics of certain direct sums of irreducible homogeneous vector bundles over rational homogeneous varieties. We finally apply our result to show the rigidity of ω$\omega$-balanced Kähler maps into Grassmannians.