ambiguities in estimates of critical exponents for long range dependent processes abstract in this article we show that the hurst parameter and a well known wavelet estimator fail to distinguish on off models with substantially different distributions of on times we identify the problem as arising when standard power spectrum techniques which are well defined for commonly considered processes are applied to processes with extremely heavy tailed on times we provide an elementary mechanism whereby such extremely heavy tailed on time processes arise in a simple queuing model

multifractal properties of the indian financial market abstract we investigate the multifractal properties of the logarithmic returns of the indian financial indices bse nse by applying the multifractal detrended fluctuation analysis the results are compared with that of the us s p 500 index numerically we find that q th order generalized hurst exponents h q and q change with the moments q the nonlinear dependence of these scaling exponents and the singularity spectrum f show that the returns possess multifractality by comparing the mf dfa results of the original series to those for the shuffled series we find that the multifractality is due to the contributions of long range correlations as well as the broad probability density function the financial markets studied here are compared with the binomial multifractal model bmfm and have a smaller multifractal strength than the bmfm

detrending fluctuation analysis based on moving average filtering abstract detrended fluctuation analysis dfa is a scaling method commonly used for detecting long range correlations in nonstationary time series applications range from financial time series to physiological data however as the removal of trends in dfa is based on discontinuous polynomial fitting oscillations in the fluctuation function and significant errors in crossover locations can be introduced to reduce the problems induced by discontinuous fitting moving average ma methods have been proposed previously by alesio et al eur j phys b 27 2002 197 in this work a variant of such ma methods is studied specifically the performance and characteristics of a ma method based on central differences is studied some important properties of this ma method are analyzed and illustrated with several artificial and real time series

temporal series analysis approach to spectra of complex networks the spacing of nearest levels of the spectrum of a complex network can be regarded as a time series joint use of the multifractal detrended fluctuation approach mf dfa and diffusion entropy de is employed to extract characteristics from this time series for the watts strogatz small world model there exists a critical point at rewiring probability p r 0 32 for a network generated in the range 0l p r l0 32 the correlation exponent is in the range of 1 0 char21 1 64 above this critical point all the networks behave similar to that at p r 1 for the erdos renyi model the time series behaves like fractional brownian motion noise at p text er 1 n for the growing random network grn model the values of the long range correlation exponent are in the range of 0 74 char21 0 83 for most of the grn networks the probability distribution function of a constructed time series obeys a gaussian form in the joint use of mf dfa and de the shuffling procedure in de is essential to obtain a reliable result

a nonconservative lagrangian framework for statistical fluid registration safira in this paper we used a nonconservative lagrangian mechanics approach to formulate a new statistical algorithm for fluid registration of 3 d brain images this algorithm is named safira acronym for statistically assisted fluid image registration algorithm a nonstatistical version of this algorithm was implemented where the deformation was regularized by penalizing deviations from a zero rate of strain in the terms regularizing the deformation included the covariance of the deformation matrices and the vector fields q here we used a lagrangian framework to reformulate this algorithm showing that the regularizing terms essentially allow nonconservative work to occur during the flow given 3 d brain images from a group of subjects vector fields and their corresponding deformation matrices are computed in a first round of registrations using the nonstatistical implementation covariance matrices for both the deformation matrices and the vector fields are then obtained and incorporated separately or jointly in the nonconservative terms creating four versions of safira we evaluated and compared our algorithms performance on 92 3 d brain scans from healthy monozygotic and dizygotic twins 2 d validations are also shown for corpus callosum shapes delineated at midline in the same subjects after preliminary tests to demonstrate each method we compared their detection power using tensor based morphometry tbm a technique to analyze local volumetric differences in brain structure we compared the accuracy of each algorithm variant using various statistical metrics derived from the images and deformation fields all these tests were also run with a traditional fluid method which has been quite widely used in tbm studies the versions incorporating vector based empirical statistics on brain variation were consistently more accurate than their counterparts when used for automated volumetric quantification in new brain images this suggests the advantages of this approach for large scale neuroimaging studies

smoothing and matching of 3 d space curves we present a new approach to the problem of matching 3 d curves the approach has a low algorithmic complexity in the number of models and can operate in the presence of noise and partial occlusions our method builds upon the seminal work of kishon et al 1990 where curves are first smoothed using b splines with matching based on hashing using curvature and torsion measures however we introduce two enhancements we present experimental results using synthetic data and also using characteristic curves extracted from 3 d medical images an earlier version of this article was presented at the 2nd european conference on computer vision in italy

characterization of sleep stages by correlations in the magnitude and sign of heartbeat increments we study correlation properties of the magnitude and the sign of the increments in the time intervals between successive heartbeats during light sleep deep sleep and rapid eye movement rem sleep using the detrended fluctuation analysis method we find short range anticorrelations in the sign time series which are strong during deep sleep weaker during light sleep and even weaker during rem sleep in contrast we find long range positive correlations in the magnitude time series which are strong during rem sleep and weaker during light sleep we observe uncorrelated behavior for the magnitude during deep sleep since the magnitude series relates to the nonlinear properties of the original time series while the sign series relates to the linear properties our findings suggest that the nonlinear properties of the heartbeat dynamics are more pronounced during rem sleep thus the sign and the magnitude series provide information which is useful in distinguishing between the sleep stages

long range correlations in the electric signals that precede rupture further investigations the correlations within the time series of the seismic electric signal ses activities have been studied in a previous paper p varotsos n sarlis and e skordas phys rev e 66 011902 2002 here we analyze the time series of successive high and low level states durations the existence of correlation between the states is investigated by means of hurst and detrended fluctuation analysis dfa the multifractal dfa mf dfa is also employed the results point to a stronger correlation and hence longer memory in the series of the high level states furthermore an analysis in the natural time domain reveals that certain power spectrum characteristics seem to distinguish ses activities from artificial man made electric noises more precisely for natural frequencies 0 f 0 5 the curves of the ses activities and artificial noises lie above and below respectively that of the uniform distribution ud a classification of these two types of electric signals ses activities artificial noises cannot be achieved on the basis of the values of the power law exponents alone if the hurst analysis dfa and mf dfa are applied to the original time series the latter two methods however seem to allow a distinction between the ses activities and artificial noises when treating them not in conventional the time frame but in the natural time domain to further test the techniques a time series produced by another system was examined we chose a signal of ion current fluctuations in membrane channels icfmcs the following conclusions among others have been obtained first the power spectrum analysis in the natural time domain shows that the icfmc curve almost coincides in the range 0 f 0 5 with that of the ud and hence icfmc lies just in the boundary between the ses activities and artificial noises second mf dfa indicates monofractality for the icfmcs with a generalized hurst exponent h 50 8460 03 in the range 7 70 ms

finite state incompressible infinite sequences in this paper we define and study finite state complexity of finite strings and infinite sequences as well as connections between these complexity notions to randomness and normality we show that the finite state complexity does not only depend on the codes for finite transducers but also on how the codes are mapped to transducers as a consequence we relate the finite state complexity to the plain kolmogorov complexity to the process complexity and to prefix free complexity working with prefix free sets of codes we characterise martin lof random sequences in terms of finite state complexity the weak power of finite transducers is compensated by the high complexity of enumeration of finite transducers we also prove that every finite state incompressible sequence is normal but the converse implication is not true these results also show that our definition of finite state incompressibility is stronger than all other known forms of finite automata based incompressibility in particular the notion related to finite automaton based betting systems introduced by schnorr and stimm the paper concludes with a discussion of open questions

extraction of backgrounds in fluctuating systems we undertake an extensive analytical study on the generalized detrended fluctuation analysis method designed to detect the scaling behaviors of fluctuating systems but exclude out the influences of the backgrounds or the trends through our extensive studies we systematically extract out the exact backgrounds or the trends of the fluctuating systems to any order expressed in terms of the legendre polynomial our results are exact and can be applied to any 1 1 dimensional continuous fluctuating systems

recognition of an organism from fragments of its complete genome this paper considers the problem of matching a fragment to an organism using its complete genome our method is based on the probability measure representation of a genome we first demonstrate that these probability measures can be modeled as recurrent iterated function systems rifs consisting of four contractive similarities our hypothesis is that the multifractal characteristics of the probability measure of a complete genome as captured by the rifs is preserved in its reasonably long fragments we compute the rifs of fragments of various lengths and random starting points and compare with that of the original sequence for recognition using the euclidean distance a demonstration on five randomly selected organisms supports the above hypothesis

a riemannian framework for tensor computing tensors are nowadays a common source of geometric information in this paper we propose to endow the tensor space with an affine invariant riemannian metric we demonstrate that it leads to strong theoretical properties the cone of positive definite symmetric matrices is replaced by a regular and complete manifold without boundaries null eigenvalues are at the infinity the geodesic between two tensors and the mean of a set of tensors are uniquely defined etc we have previously shown that the riemannian metric provides a powerful framework for generalizing statistics to manifolds in this paper we show that it is also possible to generalize to tensor fields many important geometric data processing algorithms such as interpolation filtering diffusion and restoration of missing data for instance most interpolation and gaussian filtering schemes can be tackled efficiently through a weighted mean computation linear and anisotropic diffusion schemes can be adapted to our riemannian framework through partial differential evolution equations provided that the metric of the tensor space is taken into account for that purpose we provide intrinsic numerical schemes to compute the gradient and laplace beltrami operators finally to enforce the fidelity to the data either sparsely distributed tensors or complete tensors fields we propose least squares criteria based on our invariant riemannian distance which are particularly simple and efficient to solve

long range correlations in the electric signals that precede rupture the smoluchowski chapman kolmogorov functional equation is applied to the electric signals that precede rupture the results suggest a non markovian character of the analyzed data the rescaled range hurst and detrended fluctuation analyses as well as that related with the mean distance a walker spanned lead to power law exponents which are consistent with the existence of long range correlations a universality in the power spectrum characteristics of these signals emerges if an analysis is made not in the conventional time frame but in the natural time domain within this frame it seems that certain power spectrum characteristics of ion current fluctuations in membrane channels distinguish them from the electric signals preceding rupture the latter exhibit a behavior compatible with that expected from a model based on the random field ising hamiltonian at the critical point

the scaling properties of stock markets based on modified multiscale multifractal detrended fluctuation analysis abstract here we propose the new method dh mma based on multiscale multifractal detrended fluctuation analysis mma to investigate the scaling properties in stock markets it is demonstrated that our approach can provide a more stable and faithful description of the scaling properties in comprehensive range rather than fixing the window length and slide length it allows the assessment of more universal and subtle scaling characteristics we illustrate dh mma by selecting power law artificial data sets and six stock markets from us and china the us stocks exhibit very strong multifractality for positive values of q however the chinese stocks show stronger multifractality for negative q than positive q in general the us stock markets show similar behaviors but chinese stock markets display distinguishing characteristics

compositional segmentation and long range fractal correlations in dna sequences a segmentation algorithm based on the jensen shannon entropic divergence is used to decompose long range correlated dna sequences into statistically significant compositionally homogeneous patches by adequately setting the significance level for segmenting the sequence the underlying power law distribution of patch lengths can be revealed some of the identified dna domains were uncorrelated but most of them continued to display long range correlations even after several steps of recursive segmentation thus indicating a complex multi length scaled structure for the sequence on the other hand by separately shuffling each segment or by randomly rearranging the order in which the different segments occur in the sequence shuffled sequences preserving the original statistical distribution of patch lengths were generated both types of random sequences displayed the same correlation scaling exponents as the original dna sequence thus demonstrating that neither the internal structure of patches nor the order in which these are arranged in the sequence is critical therefore long range correlations in nucleotide sequences seem to rely only on the power law distribution of patch lengths textcopyright 1996 the american physical society

scaling analysis of trends using dfa we study two aspects of the detrended uctuation analysis dfa method namely the scaling behavior of the leading terms of the best 0t polynomials and the detection of trends we show analytically and numerically that the standard deviation of the leading terms of the best 0t polynomials used in dfa displays scaling behavior furthermore we demonstrate that the distribution of these terms can be used to reveal the presence of trends in the data we also argue that this distribution can be used as a sensitive tool for identifying weak trends c 2001 elsevier science b v all rights reserved

automatic extraction of sulcal lines on cortical surfaces based on anisotropic geodesic distance analyzing cortical sulci is important for studying cortical morphology and brain functions although sulcal lines on cortical surfaces can be defined in various ways it is critical in a neuroimaging study to define a sulcal line along the valley of a cortical surface with a high curvature within a sulcus to extract the sulcal lines automatically we present a new geometric algorithm based on the computation of anisotropic skeletons of sulcal regions because anisotropic skeletons are highly adaptive to the anisotropic nature of the surface shape the resulting sulcal lines lie accurately on the valleys of the sulcal areas our sulcal lines remain unchanged under local shape variabilities in different human brains through experiments we show that the errors of the sulcal lines for both synthetic data and real cortical surfaces were nearly as constant as the function of random noise by measuring the changes in sulcal shape in alzheimer s disease ad patients we further investigated the effectiveness of the accuracy of our sulcal lines using a large sample of mri data this study involved 70 normal controls n men women 29 41 age mean sd 71 7 4 9 years and 100 ad subjects 37 63 72 3 5 5 we observe significantly lower absolute average mean curvature and shallower sulcal depth in ad subjects where the group difference becomes more significant if we measure the quantities along the sulcal lines rather than over the entire sulcal area the most remarkable difference in the ad patients was the average sulcal depth control 11 70 and ad 11 34

large deformation diffeomorphic metric curve mapping we present a matching criterion for curves and integrate it into the large deformation diffeomorphic metric mapping lddmm scheme for computing an optimal transformation between two curves embedded in euclidean space d curves are first represented as vector valued measures which incorporate both location and the first order geometric structure of the curves then a hilbert space structure is imposed on the measures to build the norm for quantifying the closeness between two curves we describe a discretized version of this in which discrete sequences of points along the curve are represented by vector valued functionals this gives a convenient and practical way to define a matching functional for curves we derive and implement the curve matching in the large deformation framework and demonstrate mapping results of curves in 2 and 3 behaviors of the curve mapping are discussed using 2d curves the applications to shape classification is shown and experiments with 3d curves extracted from brain cortical surfaces are presented

a continuous staple for scalar vector and tensor images an application to dti analysis the comparison of images of a patient to a reference standard may enable the identification of structural brain changes these comparisons may involve the use of vector or tensor images i e 3 d images for which each voxel can be represented as an rn vector such as diffusion tensor images dti or transformations the recent introduction of the log euclidean framework for diffeomorphisms and tensors has greatly simplified the use of these images by allowing all the computations to be performed on a vector space however many sources can result in a bias in the images including disease or imaging artifacts in order to estimate and compensate for these sources of variability we developed a new algorithm called continuous staple that estimates the reference standard underlying a set of vector images this method based on an expectation maximization method similar in principle to the validation method staple also estimates for each image a set of parameters characterizing their bias and variance with respect to the reference standard we demonstrate how to use these parameters for the detection of atypical images or outliers in the population under study we identified significant differences between the tensors of diffusion images of multiple sclerosis patients and those of control subjects in the vicinity of lesions

measuring brain variability by extrapolating sparse tensor fields measured on sulcal lines modeling and understanding the variability of brain structures is a fundamental problem in neurosciences improved mathematical representations of structural brain variation are needed to help detect and understand genetic or disease related sources of abnormality as well as to improve statistical power when integrating functional brain mapping data across subjects in this paper we develop a new mathematical model of normal brain variation based on a large set of cortical sulcal landmarks 72 per brain delineated in each of 98 healthy human subjects scanned with 3d mri age 51 8 6 2 years we propose an original method to compute an average representation of the sulcal curves which constitutes the mean anatomy after affine alignment of the individual data across subjects the second order moment distribution of the sulcal position is modeled as a sparse field of covariance tensors symmetric positive definite matrices to extrapolate this information to the full brain one has to overcome the limitations of the standard euclidean matrix calculus we propose an affine invariant riemannian framework to perform computations with tensors in particular we generalize radial basis function rbf interpolation and harmonic diffusion partial differential equations pdes to tensor fields as a result we obtain a dense 3d variability map that agrees well with prior results on smaller subject samples moreover leave one sulcus out tests show that our model is globally able to recover the missing information on brain variation when there is a consistent neighboring pattern of variability finally we propose an innovative method to analyze the asymmetry of brain variability as expected the greatest asymmetries are found in regions that includes the primary language areas interestingly any such asymmetries in anatomical variance if it remains after anatomical normalization could explain why there may be greater power to detect group activation in one hemisphere versus the other in fmri studies

statistical properties of the yuan exchange rate index abstract we choice the yuan exchange rate index based on a basket of currencies as the effective exchange rate of the yuan and investigate the statistical properties of the yuan exchange rate index after china s exchange rate system reform on the 21st july 2005 after dividing the time series into two parts according to the change in the yuan exchange rate regime in july 2008 we compare the statistical properties of the yuan exchange rate index during these two periods we find that the distribution of the two return series has the exponential form we also perform the detrending moving average analysis dma and the multifractal detrending moving average analysis mfdma the two periods possess different degrees of long range correlations and the multifractal nature is also unveiled in these two time series significant difference is found in the scaling exponents q and singularity spectra f of the two periods obtained from the mfdma analysis besides in order to detect the sources of multifractality shuffling and phase randomization procedures are applied to destroy the long range temporal correlation and fat tailed distribution of the yuan exchange rate index respectively we find that the fat tailedness plays a critical role in the sources of multifractality in the first period while the long memory is the major cause in the second period the results suggest that the change in china s exchange rate regime in july 2008 gives rise to the different multifractal properties of the yuan exchange rate index in these two periods and thus has an effect on the effective exchange rate of the yuan after the exchange rate reform on the 21st july 2005

hurst exponents for interacting random walkers obeying nonlinear fokker planck equations abstract anomalous diffusion of random walks has been extensively studied for the case of non interacting particles here we study the evolution of nonlinear partial differential equations by interpreting them as fokker planck equations arising from interactions among random walkers we extend the formalism of generalized hurst exponents to the study of nonlinear evolution equations and apply it to several illustrative examples they include an analytically solvable case of a nonlinear diffusion constant and three nonlinear equations which are not analytically solvable the usual fisher equation which contains a quadratic nonlinearity a generalization of the fisher equation with density dependent diffusion constant and the nagumo equation which incorporates a cubic rather than a quadratic nonlinearity we estimate the generalized hurst exponents

characterizing volume and surface deformations in an atlas framework theory applications and implementation given deformations for mapping images or surfaces into an atlas configuration methods are described for characterizing the mean deformation and deviations from this mean jacobian matrices are used to characterize the deformations locally and the method can be applied to any image warping method for which jacobian matrices can be computed the method makes use of the fact that each matrix descriptor of the local deformation required to match an image to the atlas corresponds to a point on a semi riemannian manifold by assuring that the mean matrix lies within this manifold fundamental geometric properties common to all of the images can be preserved local deviations from the mean can be characterized in a euclidean space tangent to the semi riemannian manifold at the mean and can be accumulated globally across multiple sampling locations within the atlas to generate a global multivariate characterization of how each image deviates from the mean

natural halting probabilities partial randomness and zeta functions we introduce the zeta number natural halting probability and natural complexity of a turing machine and we relate them to chaitin s omega number halting probability and program size complexity a classification of turing machines according to their zeta numbers is proposed divergent convergent and tuatara we prove the existence of universal convergent and tuatara machines various results on algorithmic randomness and partial randomness are proved for example we show that the zeta number of a universal tuatara machine is c e and random a new type of partial randomness asymptotic randomness is introduced finally we show that in contrast to classical algorithmic randomness which cannot be naturally characterised in terms of plain complexity asymptotic randomness admits such a characterisation

universal scaling behaviors of meteorological variables volatility and relations with original records abstract volatility series defined as the magnitude of the increments between successive elements of five different meteorological variables over china are analyzed by means of detrended fluctuation analysis dfa for short universal scaling behaviors are found in all volatility records whose scaling exponents take similar distributions with similar mean values and standard deviations to reconfirm the relation between long range correlations in volatility and nonlinearity in original series dfa is also applied to the magnitude records defined as the absolute values of the original records the results clearly indicate that the nonlinearity of the original series is more pronounced in the magnitude series

effects of non stationarity on the magnitude and sign scaling in the multi scale vertical velocity increment abstract we study the scaling properties of multi scale increment series from the stationary and non stationary vertical velocity records by the detrended fluctuation analysis dfa and series decomposition methods and show the impact of non stationarity on the magnitude and sign scaling properties firstly we show it is difficult to define a significant scaling range for stationary records themselves secondly for increment series with lag one the nonlinear correlation found in magnitude fluctuation i e volatility fluctuation is obvious for both cases and over the smaller scale range the linear correlation found usually in the sign series is the same for both cases however over the larger scale range the difference is sharp and marked nonlinear correlation is also incorporated for the non stationary sign series thirdly with the lags in increment increasing there exist two scaling ranges in both the magnitude and sign fluctuations the nonlinear correlation in the magnitude series over both small and large scale ranges decreases with the lags increasing for the sign series the linear correlation is dominant over both small and large scale ranges for stationary case however the nonlinear correlation can be found over the large scale ranges for non stationary case and will decrease with lags increasing the nonlinear correlation found in the sign series over large scale range is resulted from the modulation of the large scale structures found in the non stationary data which will incorporate parts of the magnitude information into the sign series

diffeomorphic sulcal shape analysis on the cortex we present a diffeomorphic approach for constructing intrinsic shape atlases of sulci on the human cortex sulci are represented as square root velocity functions of continuous open curves in r 3 and their shapes are studied as functional representations of an infinite dimensional sphere this spherical manifold has some advantageous properties it is equipped with a riemannian l 2 metric on the tangent space and facilitates computational analyses and correspondences between sulcal shapes sulcal shape mapping is achieved by computing geodesics in the quotient space of shapes modulo scales translations rigid rotations and reparameterizations the resulting sulcal shape atlas preserves important local geometry inherently present in the sample population the sulcal shape atlas is integrated in a cortical registration framework and exhibits better geometric matching compared to the conventional euclidean method we demonstrate experimental results for sulcal shape mapping cortical surface registration and sulcal classification for two different surface extraction protocols for separate subject populations

statistical sulcal shape comparisons application to the detection of genetic encoding of the central sulcus shape principal component analysis allows a quantitative description of shape variability with a restricted num ber of parameters or modes which can be used to quantify the difference between two shapes through the computation of a modal distance a statistical test can then be applied to this set of measurements in order to detect a statistically significant difference between two groups we have applied this methodol ogy to highlight evidence of genetic encoding of the shape of neuroanatomical structures to investigate genetic constraint we studied if shapes were more similar within 10 pairs of monozygotic twins than within interpairs and compared the results with those obtained from 10 pairs of dizygotic twins the statis tical analysis was performed using a mantel permuta tion test we show using simulations that this statis tical test applied on modal distances can detect a possible genetic encoding when applied to real data this study highlighted genetic constraints on the shape of the central sulcus we found from 10 pairs of monozygotic twins that the intrapair modal distance of the central sulcus was significantly smaller than the interpair modal distance for both the left central sul cus z 52 2 66 p 0 005 and the right central sulcus z 52 2 26 p 0 05 genetic constraints on the defi nition of the central sulcus shape were confirmed by applying the same experiment to 10 pairs of normal young individuals z 52 1 39 z 52 0 63 i e values not significant at the p 0 05 level and 10 pairs of dizy gotic twins z 5 0 47 z 5 0 03 i e values not signifi cant at the p 0 05 level 2000 academic press

long range correlation properties of coding and noncoding dna sequences genbank analysis an open question in computational molecular biology is whether long range correlations are present in both coding and noncoding dna or only in the latter to answer this question we consider all 33301 coding and all 29453 noncoding eukaryotic sequences each of length larger than 512 base pairs bp in the present release of the genbank to dtermine whether there is any statistically significant distinction in their long range correlation properties standard fast fourier transform fft analysis indicates that coding sequences have practically no correlations in the range from 10 bp to 100 bp spectral exponent beta 0 00 0 04 where the uncertainty is two standard deviations in contrast for noncoding sequences the average value of the spectral exponent beta is positive 0 16 0 05 which unambiguously shows the presence of long range correlations we also separately analyze the 874 coding and the 1157 noncoding sequences that have more than 4096 bp and find a larger region of power law behavior we calculate the probability that these two data sets coding and noncoding were drawn from the same distribution and we find that it is less than 10 10 we obtain independent confirmation of these findings using the method of detrended fluctuation analysis dfa which is designed to treat sequences with statistical heterogeneity such as dna s known mosaic structure patchiness arising from the nonstationarity of nucleotide concentration the near perfect agreement between the two independent analysis methods fft and dfa increases the confidence in the reliability of our conclusion

dimensions of points in self similar fractals self similar fractals arise as the unique attractors of iterated function systems ifss consisting of finitely many contracting similarities satisfying an open set condition each point x in such a fractal f arising from an ifs s is naturally regarded as the outcome of an infinite coding sequence t which need not be unique over the alphabet sigma k 0 ldots k 1 where k is the number of contracting similarities in s a classical theorem of moran 1946 and falconer 1989 states that the hausdorff and packing dimensions of a self similar fractal coincide with its similarity dimension which depends only on the contraction ratios of the similarities the theory of computing has recently been used to provide a meaningful notion of the dimensions of individual points in euclidean space in this paper we use and extend this theory to analyze the dimensions of individual points in fractals that are computably self similar meaning that they are unique attractors of ifss that are computable and satisfy the open set condition our main theorem states that if f subseteq mathbb r n is any computably self similar fractal and s is any ifs testifying to this fact then the dimension identities operatorname dim x operatorname sdim f operatorname dim pi s t and operatorname dim x operatorname sdim f operatorname dim pi s t hold for all x in f and all coding sequences t for x in these equations operatorname sdim f denotes the similarity dimension of the fractal f operatorname dim x and operatorname dim x denote the dimension and strong dimension respectively of the point x in euclidean space and operatorname dim pi s t and operatorname dim pi s t denote the dimension and strong dimension respectively of the coding sequence t relative to a probability measure pi s that the ifs s induces on the alphabet sigma k the above mentioned theorem of moran and falconer follows easily from our main theorem by relativization along the way to our main theorem we develop the elements of the theory of constructive dimensions relative to general probability measures the proof of our main theorem uses kolmogorov complexity characterizations of these dimensions

stochastic origins of the long range correlations of ionic current fluctuations in membrane channels an explicit stochastic representation of a stationary ionic current signal recorded from a single channel of a biological membrane is presented in the framework of the proposed approach we show how the dichotomous time structure of the signal leads to the non markovian character of the channel current the rescaled range hurst and detrended fluctuation analyses confirm the theoretical result to investigate the ionic current fluctuations we introduce the orey index as a statistical method providing additional information on the properties of stochastic processes in order to reveal any differences between the experimental and reconstructed signals we apply also the statistical tests to the model based simulations of the channel action

registration atlas estimation and variability analysis of white matter fiber bundles modeled as currents this paper proposes a generic framework for the registration the template estimation and the variability analysis of white matter fiber bundles extracted from diffusion images this framework is based on the metric on currents for the comparison of fiber bundles this metric measures anatomical differences between fiber bundles seen as global homologous structures across subjects it avoids the need to establish correspondences between points or between individual fibers of different bundles it can measure differences both in terms of the geometry of the bundles like its boundaries and in terms of the density of fibers within the bundle it is robust to fiber interruptions and reconnections in addition a recently introduced sparse approximation algorithm allows us to give an interpretable representation of the fiber bundles and their variations in the framework of currents first we used this metric to drive the registration between two sets of homologous fiber bundles of two different subjects a dense deformation of the underlying white matter is estimated which is constrained by the bundles seen as global anatomical landmarks by contrast the alignment obtained from image registration is driven only by the local gradient of the image second we propose a generative statistical model for the analysis of a collection of homologous bundles this model consistently estimates prototype fiber bundles called template which capture the anatomical invariants in the population a set of deformations which align the geometry of the template to that of each subject and a set of residual perturbations the statistical analysis of both the deformations and the residuals describe the anatomical variability in terms of geometry stretching torque etc and texture fiber density etc third this statistical modeling allows us to simulate new synthetic bundles according to the estimated variability this gives a way to interpret the anatomical features that the model detects consistently across the subjects this may be used to better understand the bias introduced by the fiber extraction methods and eventually to give anatomical characterization of the normal or pathological variability of fiber bundles

trace a topological graph representation for automatic sulcal curve extraction a proper geometric representation of the cortical regions is a fundamental task for cortical shape analysis and landmark extraction however a significant challenge has arisen due to the highly variable convoluted cortical folding patterns in this paper we propose a novel topological graph representation for automatic sulcal curve extraction trace in practice the reconstructed surface suffers from noise influences introduced during image acquisition surface reconstruction in the presence of noise on the surface trace determines stable sulcal fundic regions by employing the line simplification method that prevents the sulcal folding pattern from being significantly smoothed out the sulcal curves are then traced over the connected graph in the determined regions by the dijkstra s shortest path algorithm for validation we used the state of the art surface reconstruction pipelines on a reproducibility data set the experimental results showed higher reproducibility and robustness to noise in trace than the existing method li et al 2010 with over 20 relative improvement in error for both surface reconstruction pipelines in addition the extracted sulcal curves by trace were well aligned with manually delineated primary sulcal curves we also provided a choice of parameters to control quality of the extracted sulcal curves and showed the influences of the parameter selection on the resulting curves

interindividual functional mapping a nonlinear local approach within the scope of three dimensional brain imaging we propose an interindividual fusion scheme to register functional activations according to anatomical cortical structures the sulci this paper is based on the assumption that an important part of functional intersubject variability is encoded in anatomical variability the aim of this paper is therefore to propose a generic framework to register functional activations according to the relevant anatomical landmarks compared to classical interindividual fusion schemes this approach is local it relies on a statistical sulci shape model accounting for the interindividual variability of a population of subjects and providing deformation modes relative to a reference shape a mean sulcus the deformation field obtained between a given sulcus and the reference sulcus is extended to a neighborhood of the given sulcus by using the thin plate spline interpolation it is then applied to functional activations located in the vicinity of this sulcus this approach is compared with rigid and nonrigid registration methods in this paper we present results on meg somatosensory data acquired on 18 subjects we show that the nonlinear local fusion scheme significantly reduces the observed functional variability

spectral based automatic labeling and refining of human cortical sulcal curves using expert provided examples we present a spectral based method for automatically labeling and refining major sulcal curves of a human cerebral cortex given a set of input unlabeled sulcal curves automatically extracted from a cortical surface and a collection of expert provided examples labeled sulcal curves our objective is to identify the input major sulcal curves and assign their neuroanatomical labels and then refines these curves based on the expert provided example data without employing any atlas based registration scheme as preprocessing in order to construct the example data neuroanatomists manually labeled a set of 24 major sulcal curves 12 each for the left and right hemispheres for each individual subject according to a precise protocol we collected 30 sets of such curves from 30 subjects given the raw input sulcal curve set of a subject we choose the most similar example curve to each input curve in the set to label and refine the latter according to the former we adapt a spectral matching algorithm to choose the example curve by exploiting the sulcal curve features and their relationship the high dimensionality of sulcal curve data in spectral matching is addressed by using their multi resolution representations which greatly reduces time and space complexities our method provides consistent labeling and refining results even under high variability of cortical sulci across the subjects through experiments we show that the results are comparable in accuracy to those done manually most output curves exhibited accuracy values higher than 80 and the mean accuracy values of the curves in the left and the right hemispheres were 84 69 and 84 58 respectively

automatic sulcal line extraction on cortical surfaces using geodesic path density maps abstract we present here a method that is designed to automatically extract sulcal lines on the mesh of any cortical surface the method is based on the definition of a new function the geodesic path density map gpdm within each sulcal basin i e regions with a negative mean curvature gpdm indicates at each vertex the likelihood that a shortest path between any two points of the basins boundary goes through that vertex if the distance used to compute shortest path is anisotropic and constrained by a geometric information such as the depth the gpdm indicates the likelihood that a vertex belongs to the sulcal line in the basin an automatic gpdm adaptive thresholding procedure is proposed and sulcal lines are then defined the process has been validated on a set of 25 subjects by comparing results to the manual segmentation from an expert and showed an average error below 2 mm it is also compared to our previous reference method in the context of inter subject cortical surface registration and shows an significant improvement in performance

revealing competitive behaviours in music by means of the multifractal detrended fluctuation analysis application to bach s sinfonias the one two and three dimensional multifractal detrended fluctuation analysis mfdfa was applied to bach s sinfonias which are characterized by the superposition of three different voices each voice represented as a time series can be considered as a component of a one two or three dimensional vector the one dimensional mf dfa was applied to any single voice while the two and three dimensional mf dfa was applied to the couples of voices and to the triple respectively each voice is characterized by a multifractal degree md indicated by the range of the generalized hurst exponents the higher the md the larger the amount of heterogeneity and irregularity competitive scaling multifractal behaviours in bach s sinfonias were revealed although one or two voices showed a relatively high md the other two voices or voice are characterized by a low md nevertheless the overall effect of the sinfonia measured by the md of the triple tends towards homogeneity or at least to an average between the different competitive scaling behaviour shown by the different voices

superroughening by linear growth equations with spatiotemporally correlated noise we give an extensive study on a class of interfacial superroughening processes with finite lateral system size in 1 1 dimensions described by linear growth equations with spatiotemporally power law decaying correlated noise since some of these processes have an extremely long relaxation time we first develop a very efficient method capable of simulating the interface morphology of these growth processes even in very late time we numerically observe that this class of superrough growth processes indeed gradually develops macroscopic structures with the lateral size comparable to the lateral system size through the rigorous analytical study of the equal time height difference correlation function the different time height difference correlation function and the local width we explicitly evaluate not only the leading anomalous dynamic scaling term but also all the subleading anomalous dynamic scaling terms which dominate over the ordinary dynamic scaling term moreover the relation between the macroscopic structure formation and anomalous interfacial roughening of the superrough growth processes is analytically investigated in detail

measure representation and multifractal analysis of complete genomes this paper introduces the notion of measure representation of dna sequences spectral analysis and multifractal analysis are then performed on the measure representations of a large number of complete genomes the main aim of this paper is to discuss the multifractal property of the measure representation and the classification of bacteria from the measure representations and the values of the dq spectra and related cq curves it is concluded that these complete genomes are not random sequences in fact spectral analyses performed indicate that these measure representations considered as time series exhibit strong long range correlation here the long range correlation is for the k strings with dictionary ordering and it is different from the base pair correlations introduced by other people for substrings with length k58 the dq spectra of all organisms studied are multifractal like and sufficiently smooth for the cq curves to be meaningful with the decreasing value of k the multifractality lessens the cq curves of all bacteria resemble a classical phase transition at a critical point but the analogous phase transitions of chromosomes of nonbacteria organisms are different apart from chromosome 1 of c elegans they exhibit the shape of double peaked specific heat function a classification of genomes of bacteria by assigning to each sequence a point in two dimensional space d21 d1 and in three dimensional space d21 d1 d22 was given bacteria that are close phylogenetically are almost close in the spaces d21 d1 and d21 d1 d22

long range correlation measures for quantifying patchiness deviations from uniform power law scaling in genomic dna abstract we introduce and develop new techniques to quantify dna patchiness and characteristics of their mosaic structure these techniques which involve calculating two functions l and l measure correlation exponents at length scale l and detect distinct characteristic patch sizes embedded in scale invariant patch size distributions using these methods it is possible to address a number of issues relating to the mosaic structure of genomic dna we find several distinct characteristic patch sizes in yeast human and prokaryotic sequences we also find that the distinct patch sizes in all 16 yeast chromosomes are similar

treadmill belt width but not feedback from the lower visual field influences the noise characteristics of step width time series abstract step kinematic variability which has been associated with gait related fall risk is thought to be attributed to neuromotor noise altered neuromotor control of step kinematics would be expected to manifest as changes in the noise related characteristics of the step kinematic time series this study determined the effects of eliminating feedback from the lower visual field and reducing treadmill belt width on the noise characteristics of step width time series and statistical measures of step width variability during treadmill walking we hypothesized that eliminating feedback from the lower visual field and reducing treadmill belt width would both alter the noise characteristics of step width time series reflected by decreased fractal scaling and increase statistical measures of step width variability eighteen young adults performed four randomly ordered walking trials during which we manipulated visual feedback from the lower visual field normal and obstructed and treadmill belt width wide and narrow reducing treadmill belt width but not eliminating feedback from the lower visual field significantly reduced the fractal scaling of step width time series indicating a shift towards white uncorrelated noise these results suggest that accounting for the influence of treadmill belt width on step width time series may be an important consideration in both laboratory and clinical settings further work is needed to clarify the effects of vision on measures of step width identify the mechanism s underlying the observed shift towards white uncorrelated noise associated with reduced treadmill belt width and to assess the potential relationship between the noise characteristics of step width time series and fall risk

detecting long range correlations in time series of neuronal discharges abstract we have studied the discharge dynamics of dorsal horn neurons dhn by applying the detrended fluctuation analysis dfa and the wavelet transform wt technique we have adopted that discharge dynamics is manifested by the random time series of the interspike intervals isi that is by intervals between two consecutive neuronal electrical activities in all cases studied we found two different power law type behaviors across isi enumeration scale that are separated by a crossover region our results reveal that complex neuronal dynamics may change in the presence of external stimulation which is manifested by changing the noise characteristics that appear before the crossover region the noise after the crossover region is of the 1 f type

mass exponent spectrum analysis of human ecg signals and its application to complexity detection abstract the complexity of electrocardiogram ecg signal may reflect the physiological function and healthy status of the heart in this paper we introduced two novel intermediate parameters of multifractality the mass exponent spectrum curvature and area to characterize the nonlinear complexity of ecg signal these indicators express the nonlinear superposition of the discrepancies of singularity strengths from all the adjacent points of the spectrum curve and thus overall subsets of original fractal structure the evaluation of binomial multifractal sets validated these two variables were entirely effective in exploring the complexity of this time series we then studied the ecg mass exponent spectra taken from the cohorts of healthy ischemia and myocardial infarction mi sufferer based on a large sets of 12 leads recordings and took the statistical averages among each crowd experimental results suggest the two values from healthy ecg are apparently larger than those from the heart diseased while the values from ecg of mi sufferer are much smaller than those from the other two groups as for the ischemia sufferer they are almost of moderate magnitude afterward we compared these new indicators with the nonlinear parameters of singularity spectrum the classification indexes and results of total separating ratios tsr defined in the paper both indicated that our method could achieve a better effect these conclusions may be of some values in early diagnoses and clinical applications

long correlations and truncated levy walks applied to the study latin american market indices abstract this work is devoted to the study of long correlations and other statistical properties of latin american market indices we concluded that the behavior of the return is compatible with a slow convergence to a gaussian distribution we also detected long range correlations in the absolute value of the return analyzing the effects of working with short data series this fact has relevant consequences in the volatility dynamics

1 f noise structures in pollocks s drip paintings abstract the fractality and scaling properties of luminance patterns in pollock s drip paintings are studied in this paper the painting is represented as a matrix array where each entry represents the luminance at the corresponding canva position detrended fluctuation analysis dfa is used to characterize fractality and the results show that the whole luminance pattern is indeed fractal interestingly the fractality is associated to 1 f noise structures which can be inducing the aesthetic properties of the artistic object in fact for spatial scales below 30 cm pollock s drip painting are organized as 1 f noise structures which presumably are attuned for pleasant i e aesthetic perception

brain surface conformal parameterization using riemann surface structure in medical imaging parameterized 3 d surface models are useful for anatomical modeling and visualization statistical comparisons of anatomy and surface based registration and signal processing here we introduce a parameterization method based on riemann surface structure which uses a special curvilinear net structure conformal net to partition the surface into a set of patches that can each be conformally mapped to a parallelogram the resulting surface subdivision and the parameterizations of the components are intrinsic and stable their solutions tend to be smooth functions and the boundary conditions of the dirichlet problem can be enforced conformal parameterization also helps transform partial differential equations pdes that may be defined on 3 d brain surface manifolds to modified pdes on a two dimensional parameter domain since the jacobian matrix of a conformal parameterization is diagonal the modified pde on the parameter domain is readily solved to illustrate our techniques we computed parameterizations for several types of anatomical surfaces in 3 d magnetic resonance imaging scans of the brain including the cerebral cortex hippocampi and lateral ventricles for surfaces that are topologically homeomorphic to each other and have similar geometrical structures we show that the parameterization results are consistent and the subdivided surfaces can be matched to each other finally we present an automatic sulcal landmark location algorithm by solving pdes on cortical surfaces the landmark detection results are used as constraints for building conformal maps between surfaces that also match explicitly defined landmarks

the kolmogorov complexity of real numbers we consider for a real number the kolmogorov complexities of its expansions with respect to different bases in the paper it is shown that for usual and self delimiting kolmogorov complexity the complexity of the prefixes of their expansions with respect to different bases r and b are related in a way that depends only on the relative information of one base with respect to the other more precisely we show that the complexity of the length l logrb prefix of the base r expansion of is the same up to an additive constant as the logrb fold complexity of the length l prefix of the base b expansion of then we consider the classes of reals of maximum and minimum complexity for maximally complex reals we use our result to derive a further complexity theoretic proof for the base independence of the randomness of real numbers finally we consider liouville numbers as a natural class of low complex real numbers

scaling features of texts images and time series in the given paper we consider the scaling features of long letter sequences like human writings discretized images and discretized 3nancial data using several approaches we show that the symbolic strings and time series being analyzed have a complex multiscale structure and demonstrate di5erent scalings for large and small 6uctuations we discuss complex phenomena in the scaling behavior of partition functions in the case of high frequency dax future data c 2001 elsevier science b v all rights reserved

kolmogorov complexity and hausdorff dimension abstract in this paper various relationships between the kolmogorov complexity of infinite strings and measures of information content are given the general approach taken here is to bound the complexity of a maximally complex string in a given set of strings by the hausdorff dimension or the entropy of that set it turns out that hausdorff dimension yields lower bounds to the kolmogorov complexity whereas under certain recursiveness constraints on the structure of the respective sets their entropy yields upper bounds more detailed investigations result in a generalization of p martin lof s theorems on the kolmogorov complexity of random strings to maximally complex strings in regularly structured sets of infinite strings

price volume multifractal analysis of the moroccan stock market abstract in this paper we analyzed price volume multifractal cross correlations of moroccan stock exchange we chose the period from january 1st 2000 to january 20th 2017 to investigate the multifractal behavior of price change and volume change series then we used multifractal detrended cross correlations analysis method mf dcca and multifractal detrended fluctuation analysis mf dfa to analyze the series we computed bivariate generalized hurst exponent renyi exponent and spectrum of singularity for each pair of indices to measure quantitatively cross correlations furthermore we used detrended cross correlations coefficient dcca and cross correlation test q m to analyze cross correlation quantitatively and qualitatively by analyzing results we found existence of price volume multifractal cross correlations the spectrum width has a strong multifractal cross correlation we remarked that volume change series is anti persistent when we analyzed the generalized hurst exponent for all moments q the cross correlation test showed the presence of a significant cross correlation however dcca coefficient had a small positive value which means that the level of correlation is not very significant finally we analyzed sources of multifractality and their degree of contribution in the series

bifractality of human dna strand asymmetry profiles results from transcription we use the wavelet transform modulus maxima method to investigate the multifractal properties of strand asymmetry dna walk profiles in the human genome this study reveals the bifractal nature of these profiles which involve two competing scale invariant up to repeat masked distances ensuremath lesssim 40 phantom rule 0 3em 0ex mathrm kbp components characterized by h older exponents h 1 0 78 and h 2 1 respectively the former corresponds to the long range correlated homogeneous fluctuations previously observed in dna walks generated with structural codings the latter is associated with the presence of jumps in the original strand asymmetry noisy signal s we show that a majority of upward downward jumps colocate with gene transcription start end sites here 7228 human gene transcription start sites from the refgene database are found within 2 phantom rule 0 3em 0ex mathrm kbp from an upward jump of amplitude ensuremath delta s ensuremath geqslant 0 1 which suggests that about 36 of annotated human genes present significant transcription induced strand asymmetry and very likely high expression rate

deviations from uniform power law scaling in nonstationary time series a classic problem in physics is the analysis of highly nonstationary time series that typically exhibit long range correlations here we test the hypothesis that the scaling properties of the dynamics of healthy physiological systems are more stable than those of pathological systems by studying beat to beat fluctuations in the human heart rate we develop techniques based on the fano factor and allan factor functions as well as on detrended fluctuation analysis for quantifying deviations from uniform power law scaling in nonstationary time series by analyzing extremely long data sets of up to n 10 5 beats for 11 healthy subjects we find that the fluctuations in the heart rate scale approximately uniformly over several temporal orders of magnitude by contrast we find that in data sets of comparable length for 14 subjects with heart disease the fluctuations grow erratically indicating a loss of scaling stability