complex network based time series analysis abstract recent works show that complex network theory may be a powerful tool in time series analysis we propose in this paper a reliable procedure for constructing complex networks from the correlation matrix of a time series an original stock time series the corresponding return series and its amplitude series are considered the degree distribution of the original series can be well fitted with a power law while that of the return series can be well fitted with a gaussian function the degree distribution of the amplitude series contains two asymmetric gaussian branches reconstruction of networks from time series is a common problem in diverse research the proposed strategy may be a reasonable solution to this problem

a note on the sturmian theorem for singular boundary value problems in this paper we study properties of the eigenfunctions of singular boundary value problems the main results show that for a class of singular boundary value problems the sturmian oscillation theorem holds it is a generalization of the standard case to the singular case

long range correlation and predictability of chinese stock prices abstract it is well known that the price time series of an efficient market display a brownian motion in such a case the best prediction of a future price is the last known price thus no arbitrage is possible a real market is however possibly not perfectly efficient in this paper we apply an error back propagation neural network to tick by tick high frequency time series of chinese a share stock prices and try to predict their future values the performance of the predictions varies largely for different stocks in order to seek for the dependence of the performance we study the long range correlation lrc of the data by the conventional detrended fluctuation analysis dfa and its generalization the multifractal detrended fluctuation analysis mfdfa clear relevance between the performance and the lrc is observed the prediction is particularly good when the time series are strongly anti persistent

investigation on gait time series by means of factorial moments abstract by means of factorial moments fm the fractal structures embedded in gait time series are investigated intermittency is found in records for healthy objects and this kind of intermittency is much sensitive to disease or outside influences it is found that fm is an effective tool to deal with this kind of time series

incomplete data problems in x ray computerized tomography i singular value decomposition of the limited angle transform etude des problemes intrinseques relatifs aux donnees incompletes dans la tomographie aux rayons x assistee par ordinateur decomposition de la transformation de radon

some global generalizations of the birkhoff kellogg theorem and applications on etudie certaines generalisations globales du theoreme de birkhoff kellogg et on donne des applications

hurst exponents for short time series a concept called balanced estimator of diffusion entropy is proposed to detect quantitatively scalings in short time series the effectiveness is verified by detecting successfully scaling properties for a large number of artificial fractional brownian motions calculations show that this method can give reliable scalings for short time series with length 10 2 it is also used to detect scalings in the shanghai stock index five stock catalogs and a total of 134 stocks collected from the shanghai stock exchange market the scaling exponent for each catalog is significantly larger compared with that for the stocks included in the catalog selecting a window with size 650 the evolution of scaling for the shanghai stock index is obtained by the window s sliding along the series global patterns in the evolutionary process are captured from the smoothed evolutionary curve by comparing the patterns with the important event list in the history of the considered stock market the evolution of scaling is matched with the stock index series we can find that the important events fit very well with global transitions of the scaling behaviors

the existence of solutions to second order singular boundary value problems abstract this article analyzes qualitative properties of solutions to two point boundary value problems for singular ordinary differential equations in particular we form new approaches that ensure that all possible solutions satisfy certain a priori bounds the methods involve differential inequalities the ideas are then applied to generate new existence results for solutions to the boundary value problems under consideration many of the results are novel for both the singular and the nonsingular cases the main concepts are further illustrated via applications to various equations arising in modeling such as the poisson boltzmann equation and the thomas fermi equation with an ionized atom

unbiased detrended fluctuation analysis long range correlations in very short time series abstract detrended fluctuation analysis dfa is a standard method to evaluate long range correlations embedded in non stationary time series to obtain a reliable estimation of scaling behavior it requires the length of a time series is long enough at least 10 000 which is not always the case in reality how to evaluate long range correlation behavior in a very short time series is still an open problem in the present paper we propose an improvement of dfa by correcting the bias in estimation of variance called unbiased detrended fluctuation analysis udfa extensive calculations show its high performance for instance from a fractional brownian motion fbm series with length 500 the estimated long range correlation exponent has negligible bias and acceptable confidence region standard deviation less than 0 05 as a typical example the proposed method is used to monitor evolution of fractal gait rhythm of a volunteer rich patterns are found in the evolutionary process

a note on existence uniqueness results for a class of doubly singular boundary value problems abstract in this paper we establish the existence and uniqueness of solution for nonlinear singular boundary value problem p x y x q x f x y for 0 x b and lim x 0 p x y x 0 1 y b 1 p b y b 1 here p 0 0 and also q is not assumed to be continuous at 0 so the problem may be doubly singular in this note we discuss the cases when y 0 0 at the singular end is not possible but lim x 0 p x y x 0 regions for multiple solutions have also been determined

singular value decompositions and inversion methods for the exterior radon transform and a spherical transform abstract the classical radon transform r maps an integrable function in rn to its integrals over all n 1 dimensional hyperplanes and the exterior radon transform is the transform r restricted to hyperplanes that do not intersect a given disc a singular value decomposition for the exterior transform is given for spaces of square integrable functions on the exterior of the disc this decomposition in orthogonal functions explicitly produces the null space and range of the exterior transform and gives a new method for inverting the transform modulo the null space a modification of this method is given that will exactly invert functions of compact support these results generalize theorems of r m perry and the author a singular value decomposition for the radon transform that integrates over spheres in rn containing the origin is also given this follows from the singular value decomposition for r and yields the null space and a new inversion method for this transform

evaluation of scale invariance in physiological signals by means of balanced estimation of diffusion entropy by means of the concept of the balanced estimation of diffusion entropy we evaluate the reliable scale invariance embedded in different sleep stages and stride records segments corresponding to waking light sleep rapid eye movement rem sleep and deep sleep stages are extracted from long term electroencephalogram signals for each stage the scaling exponent value is distributed over a considerably wide range which tell us that the scaling behavior is subject and sleep cycle dependent the average of the scaling exponent values for waking segments is almost the same as that for rem segments 0 8 the waking and rem stages have a significantly higher value of the average scaling exponent than that for light sleep stages 0 7 for the stride series the original diffusion entropy de and the balanced estimation of diffusion entropy bede give almost the same results for detrended series the evolutions of local scaling invariance show that the physiological states change abruptly although in the experiments great efforts have been made to keep conditions unchanged the global behavior of a single physiological signal may lose rich information on physiological states methodologically the bede can evaluate with considerable precision the scale invariance in very short time series 10 2 while the original de method sometimes may underestimate scale invariance exponents or even fail in detecting scale invariant behavior the bede method is sensitive to trends in time series the existence of trends may lead to an unreasonably high value of the scaling exponent and consequent mistaken conclusions

some existence principles and some general results for singular nonlinear two point boundary value problems abstract existence results for singular second order nonlinear two point boundary value problems of the form 1 p t p t y q t f t y 0 0 where limy 0 f t y are presented here we may allow singularities at y 0 t 0 and or t 1 also existence principles are presented for the general two point boundary value problem 1 p py qf t y py 0 0 where f 0 1 r 2 r is continuous the proof uses the nonlinear alternative of leray and schauder

existence theorems for certain classes of singular boundary value problems abstract existence results for nonlinear singular second order two point boundary value problems of the form 1 p py f t y 0 satisfies appropriate boundary conditions are presented the class of problems considered includes both the thomas fermi and singular emden fowler equations

the ill conditioned nature of the limited angle tomography problem the instability of inverting the limited angle radon transform is studied by constructing the singular value decomposition of this operator connections are established with previously known series expansions and with the discrete prolate spheroidal wave functions mollification methods are shown to delay but not prevent the onset of instability as the angular range of projections is decreased

biorthogonal decompositions of the radon transform the concept of singular value decompositions is a valuable tool in the examination of ill posed inverse problems af g such as the inversion of the radon transform a singular value decomposition depends on the determination of suitable orthogonal systems of eigenfunctions of the operators a a a a in this paper we consider a new approach which generalizes this concept by application of biorthogonal instead of orthogonal functions we are able to apply a larger class of function sets in order to account for the structure of the eigenfunction spaces although it is preferable to use eigenfunctions it is still possible to consider biorthogonal function systems which are not eigenfunctions of the operator with respect to the radon transform for functions with support in the unit ball we apply the system of appell polynomials which is a natural generalization of the univariate system of gegenbauer ultraspherical polynomials to the multivariate case the corresponding biorthogonal decompositions show some advantages in comparison with the known singular value decompositions vice versa by application of our decompositions we are able to prove new properties of the appell polynomials

incomplete data problems in x ray computerized tomography in the present paper we study truncated projections for the fanbeam geometry in computerized tomography first we derive consistency conditions for the divergent beam transform then we study a singular value decomposition for the case where only the interior rays in the fan are provided as for example in region of interest tomography we show that the high angular frequency components of the searched for densities are well determined and we present reconstructions from real data where the missing information is approximated based on the singular value decomposition