on the estimation of the large deviations spectrum we propose an estimation algorithm for large deviations spectra of measures and functions the algorithm converges for natural examples of multifractals

dcca cross correlation coefficient quantifying level of cross correlation abstract in this paper a new coefficient is proposed with the objective of quantifying the level of cross correlation between nonstationary time series this cross correlation coefficient is defined in terms of the dfa method and the dcca method the implementation of this cross correlation coefficient will be illustrated with selected time series

multifractal detrended cross correlation analysis for two nonstationary signals we propose a method called multifractal detrended cross correlation analysis to investigate the multifractal behaviors in the power law cross correlations between two time series or higher dimensional quantities recorded simultaneously which can be applied to diverse complex systems such as turbulence finance ecology physiology geophysics and so on the method is validated with cross correlated one and two dimensional binomial measures and multifractal random walks as an example we illustrate the method by analyzing two financial time series

a local estimate for vectorial total variation minimization in one dimension abstract let u be the minimizer of vectorial total variation v t v with l 2 data fidelity term on an interval i we show that the total variation of u over any subinterval of i is bounded by that of the datum over the same subinterval we deduce analogous statement for the vectorial total variation flow on i

measuring correlations between non stationary series with dcca coefficient abstract in this short report we investigate the ability of the dcca coefficient to measure correlation level between non stationary series based on a wide monte carlo simulation study we show that the dcca coefficient can estimate the correlation coefficient accurately regardless the strength of non stationarity measured by the fractional differencing parameter d for a comparison we also report the results for the standard pearson correlation coefficient the dcca coefficient dominates the pearson coefficient for non stationary series

some qualitative properties for the total variation flow we prove the existence of a finite extinction time for the solutions of the dirichlet problem for the total variation flow for the neumann problem we prove that the solutions reach the average of its initial datum in finite time the asymptotic profile of the solutions of the dirichlet problem is also studied it is shown that the profiles are nonzero solutions of an eigenvalue type problem that seems to be unexplored in the previous literature the propagation of the support is analyzed in the radial case showing a behaviour entirely different to the case of the problem associated with the p laplacian operator finally the study of the radially symmetric case allows us to point out other qualitative properties that are peculiar of this special class of quasilinear equations

the total variation flow in rn the purpose of this chapter is to prove existence and uniqueness of the minimizing total variation flow in n frac partial u partial t div left frac du left du right right in left 0 infty right times mathbb r n 3 1 coupled with the initial condition u 0 x u 0 x text x in mathbb r n 3 2 when u0 l loc 1 l n

a well posed problem in singular fickian diffusion we prove that the problem of solving u t u m 1 u x x text for 1 m leqq 0 with initial conditionu x 0 x and flux conditions at infinity mathop lim limits x to infty u m 1 u x f t mathop lim limits x to infty u m 1 u x g t admits a unique solution u in c infty infty x infty 0 t t for every el1 r 0 0 and every pair of nonnegative flux functionsf g e l loc 0 the maximal existence time is given by t sup left t smallint phi x dx int limits 0 t f s g s ds right this mixed problem is ill posed for anym outside the above specified range

multifractal detrended fluctuation analysis of nonstationary time series abstract we develop a method for the multifractal characterization of nonstationary time series which is based on a generalization of the detrended fluctuation analysis dfa we relate our multifractal dfa method to the standard partition function based multifractal formalism and prove that both approaches are equivalent for stationary signals with compact support by analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series by comparing the multifractal dfa results for original series with those for shuffled series we can distinguish multifractality due to long range correlations from multifractality due to a broad probability density function we also compare our results with the wavelet transform modulus maxima method and show that the results are equivalent

mixed correlated arfima processes for power law cross correlations abstract we introduce a general framework of the mixed correlated arfima mc arfima processes which allows for various specifications of univariate and bivariate long term memory apart from a standard case when h x y 1 2 h x h y mc arfima also allows for processes with h x y 1 2 h x h y but also for long range correlated processes which are either short range cross correlated or simply correlated the major contribution of mc arfima lies in the fact that the processes have well defined asymptotic properties for h x h y and h x y which are derived in the paper so that the processes can be used in simulation studies comparing various estimators of the bivariate hurst exponent h x y moreover the framework allows for modeling of processes which are found to have h x y 1 2 h x h y

modified multifractal large deviation spectrum based on cid for financial market system abstract we modify the basic roughness grain exponent only available for application of one single series to complexity invariant distance c i d for studying multifractal features between two time series c i d is taken into consideration as a new roughness grain exponent with the large deviation spectrum to detect the similarity and correlation between different stock markets in this work the new method is firstly applied to artificial series in order to test the scale invariance hypothesis with both the legendre spectrum and large deviation spectrum results show that the large deviation spectrum is better in the detection of multifractal analysis between two time series as it exhibit plentiful scaling structures then we investigate the scaling behavior between financial time series so as to test whether there is scale invariance of stock markets in china and the us besides from the values responding to the maximal f in the 5 pair series and the widths of the spectrum a new way of measurement of the similarity and correlation has been found to overcome the limitation of q we then compute the surface area of the large deviation spectrum under each scale and further detect the evolution of the slope by a scaling non scaling criterion which helps in the measurement of scaling behavior moreover the proposed method can give us more information between different markets and distinguish them from different angles

total variation flow and sign fast diffusion in one dimension abstract we consider the dynamics of the total variation flow tvf u t div d u d u and of the sign fast diffusion equation sfde u t sign u in one spatial dimension we find the explicit dynamic and sharp asymptotic behaviour for the tvf and we deduce the one for the sfde by an explicit correspondence between the two equations

modeling long range cross correlations in two component arfima and fiarch processes we investigate how simultaneously recorded long range power law correlated multivariate signals cross correlate to this end we introduce a two component arfima stochastic process and a two component fiarch process to generate coupled fractal signals with long range power law correlations which are at the same time long range cross correlated we study how the degree of cross correlations between these signals depends on the scaling exponents characterizing the fractal correlations in each signal and on the coupling between the signals our findings have relevance when studying parallel outputs of multiple component of physical physiological and social systems

detrended fluctuation analysis as a regression framework estimating dependence at different scales we propose a framework combining detrended fluctuation analysis with standard regression methodology the method is built on detrended variances and covariances and it is designed to estimate regression parameters at different scales and under potential nonstationarity and power law correlations the former feature allows for distinguishing between effects for a pair of variables from different temporal perspectives the latter ones make the method a significant improvement over the standard least squares estimation theoretical claims are supported by monte carlo simulations the method is then applied on selected examples from physics finance environmental science and epidemiology for most of the studied cases the relationship between variables of interest varies strongly across scales

a nonlinear parabolic equation with discontinuity in the highest order and applications abstract in this paper we establish a viscosity solution theory for a class of nonlinear parabolic equations with discontinuities of the sign function type in the second derivatives of the unknown function we modify the definition of classical viscosity solutions and show uniqueness and existence of the solutions these results are related to the limit behavior for the motion of a curve by a very small power of its curvature which has applications in image processing we also discuss the relation between our equation and the total variation flow in one space dimension

cross correlations between volume change and price change in finance one usually deals not with prices but with growth rates r defined as the difference in logarithm between two consecutive prices here we consider not the trading volume but rather the volume growth rate r the difference in logarithm between two consecutive values of trading volume to this end we use several methods to analyze the properties of volume changes r and their relationship to price changes r we analyze 14 981 daily recordings of the standard and poor s s p 500 index over the 59 year period 1950 2009 and find power law cross correlations between r and r by using detrended cross correlation analysis dcca we introduce a joint stochastic process that models these cross correlations motivated by the relationship between r and r we estimate the tail exponent of the probability density function p r r 1 for both the s p 500 index as well as the collection of 1819 constituents of the new york stock exchange composite index on 17 july 2009 as a new method to estimate we calculate the time intervals q between events where r q we demonstrate that q the average of q obeys q q we find 3 furthermore by aggregating all q values of 28 global financial indices we also observe an approximate inverse cubic law

1 f behavior in cross correlations between absolute returns in a us market abstract employing detrended fluctuation analysis dfa and detrended cross correlations analysis dcca we analyze auto correlations in the absolute returns for each of 30 dow jones industrial average djia constituents s i and cross correlations in the absolute returns between the djia and each s i we find that each djia member follows the djia in absolute returns since the dcca curve for each pair s i djia i exhibits strong cross correlations with average dcca exponent 1 03 0 04 this value for implies that the power law cross correlations are of the 1 f functional form for the financial firms comprising the djia we also find that the dfa and dcca exponents controlling the duration of firm risk are somewhat larger than the corresponding values for the rest of the us financial industry

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

vibration of annular sector mindlin plates with internal radial line and circumferential arc supports an energy approach is presented for the free vibration analysis of thick annular sector plates with internal line arc supports this has been a topic of practical interest but there appears to have been no previous work reported based on the stationary energy principle and the recently proposed pb 2 rayleigh ritz method the governing eigenvalue equation is derived for internally supported thick annular sector plates of different radii relative thickness ratios sector angles and with various end conditions along the radial and circumferential edges the proposed solution algorithm involves 1 sets of mathematically complete two dimensional polynomials p 2 used as the admissible displacement and rotational functions and 2 a basic function b formed from the piecewise expressions for the boundary and internal line arc supports these functions automatically satisfy all the kinematic boundary conditions of the four edges and internal supports the numerical procedure has been demonstrated by several example plate problems convergence and comparison studies for simple examples are used to verify the accuracy of the present method

obstructions to existence in fast diffusion equations abstract the study of nonlinear diffusion equations produces a number of peculiar phenomena not present in the standard linear theory thus in the sub field of very fast diffusion it is known that the cauchy problem can be ill posed either because of non uniqueness or because of non existence of solutions with small data the equations we consider take the general form u t d u u x u x x or its several dimension analogue fast diffusion means that d at some values of the arguments typically as u 0 or u x 0 here we describe two different types of non existence phenomena some fast diffusion equations with very singular d do not allow for solutions with sign changes while other equations admit only monotone solutions no oscillations being allowed the examples we give for both types of anomaly are closely related the most typical examples are v t v x v x and u t u xx u x for these equations we investigate what happens to the cauchy problem when we take incompatible initial data and perform a standard regularization it is shown that the limit gives rise to an initial layer where the data become admissible positive or monotone respectively followed by a standard evolution for all t 0 once the obstruction has been removed

asymptotic analysis of a doubly nonlinear diffusion equation abstract we investigate the doubly nonlinear diffusion equation u t 1 n u m u n 1 u and the same equation expressed in terms of a pressure variable we classify various classes of compacted supported solutions as well as finite mass solutions that decay algebraically at infinity a number of novel phenomena are identified particularly for n 0 that seem to us worthy of further mathematical investigation

regularization by noise for stochastic hamilton jacobi equations we study regularizing effects of nonlinear stochastic perturbations for fully nonlinear pde more precisely path by path l infty bounds for the second derivative of solutions to such pde are shown these bounds are expressed as solutions to reflected sde and are shown to be optimal

detrending moving average cross correlation coefficient measuring cross correlations between non stationary series abstract in the paper we introduce a new measure of correlation between possibly non stationary series as the measure is based on the detrending moving average cross correlation analysis dmca we label it as the dmca coefficient d m c a with a moving average window length we analytically show that the coefficient ranges between 1 and 1 as a standard correlation does in the simulation study we show that the values of d m c a very well correspond to the true correlation between the analyzed series regardless the non stationarity level dependence of the newly proposed measure on other parameters correlation level moving average window length and time series length is discussed as well

evolving graphs by singular weighted curvature a new notion of solutions is introduced to study degenerate nonlinear parabolic equations in one space dimension whose diffusion effect is so strong at particular slopes of the unknowns that the equation is no longer a partial differential equation by extending the theory of viscosity solutions a comparison principle is established for periodic continuous initial data a unique global continuous solution periodic in space is constructed the theory applies to motion of interfacial curves by crystalline energy or more generally by anisotropic interfacial energy with corners when the curves are the graphs of functions even if the driving force term homogeneous in space exists the initial value problem is solvable for general nonadmissible continuous periodic initial data

finite time extinction for stochastic sign fast diffusion and self organized criticality we prove finite time extinction for stochastic sign fast diffusion equations driven by linear multiplicative space time noise corresponding to the bak tang wiesenfeld model for self organized criticality this solves a problem posed and left open in several works barbu methods appl sci 36 1726 1733 2013 rockner and wang j lond math soc 2 87 545 560 2013 barbu et al j math anal appl 389 147 164 2012 barbu and rockner comm math phys 311 539 555 2012 barbu et al comm math phys 285 901 923 2009 c r math acad sci paris 347 1 2 81 84 2009 the highly singular degenerate nature of the drift in interplay with the stochastic perturbation causes the need for new methods in the analysis of mass diffusion and several new estimates and techniques are introduced

randomness and degrees of irregularity the fundamental question are sequential data random arises in myriad contexts often with severe data length constraints furthermore there is frequently a critical need to delineate nonrandom sequences in terms of closeness to randomness e g to evaluate the efficacy of therapy in medicine we address both these issues from a computable framework via a quantification of regularity apen approximate entropy defining maximal randomness for sequences of arbitrary length indicating the applicability to sequences as short as n 5 points an infinite sequence formulation of randomness is introduced that retains the operational and computable features of the finite case in the infinite sequence setting we indicate how the foundational definition of independence in probability theory and the definition of normality in number theory reduce to limit theorems without rates of convergence from which we utilize apen to address rates of convergence of a deficit from maximal randomness refining the aforementioned concepts in a computationally essential manner representative applications among many are indicated to assess i random number generation output ii well shuffled arrangements and iii the quality of bootstrap replicates

an analytical solution for vibrations of a polarly orthotropic mindlin sectorial plate with simply supported radial edges abstract this paper presents the first known analytical solution for vibrations of a polarly orthotropic mindlin sectorial plate with simply supported radial edges the solution is a series solution constructed using the frobenius method and exactly satisfies not only the boundary conditions along the radial and circular edges but also the regularity conditions at the vertex of the radial edges the moment and shear force singularities at the vertex are exactly considered in the solution the correctness of the proposed solution is confirmed by comparing non dimensional frequencies of isotropic plates obtained from the present solution with published data obtained from a closed form solution this paper also investigates the effects of elastic and shear moduli on the vibration frequencies of the sectorial plates with free or fix boundary conditions along the circumferential edge a study is also carried out about the influence of elastic and shear moduli on the moment and shear force singularities at the plate origin r 0 for different vertex angles