coupling detrended fluctuation analysis for analyzing coupled nonstationary signals when many variables are coupled to each other a single case study could not give us thorough and precise information when these time series are stationary different methods of random matrix analysis and complex networks can be used but in nonstationary cases the multifractal detrended cross correlation analysis mf dxa method was introduced for just two coupled time series in this article we have extended the mf dxa to the method of coupling detrended fluctuation analysis cdfa for the case when more than two series are correlated to each other here we have calculated the multifractal properties of the coupled time series and by comparing cdfa results of the original series with those of the shuffled and surrogate series we can estimate the source of multifractality and the extent to which our series are coupled to each other we illustrate the method by selected examples from air pollution and foreign exchange rates

a note on anderson s theorem in the infinite dimensional setting abstract anderson s theorem states that if the numerical range w a of an n by n matrix a is contained in the unit disk d and intersects with the unit circle at more than n points then w a d an analogue of this result for compact a in an infinite dimensional setting was established by gau and wu we consider here the case of a being the sum of a normal and compact operator

a characterization of complex plane poncelet curves abstract we consider algebraic curves in the complex affine plane a natural extension of the existing definition of poncelet curves in the real plane to the complex plane is presented three equivalent polynomial equations in tangent coordinates are given for complex plane poncelet curves a the polynomial which generates the bezoutian form with parameters the foci of the curve b the darboux equation with parameters the vertices of a poncelet polygon c the determinant equation involving matrices having certain specific properties we use these polynomials in order to solve poncelet type problems namely criteria are proved for real poncelet curves to be generated by matrices that admit unitary bordering these criteria answer the question when a convex poncelet curve which is inscribed in a convex polygon is the boundary of a numerical range of a matrix we also demonstrate that the general theorems of the first three sections may shorten the proofs of some known results

stability of semiclassical bound states of nonlinear schrodinger equations with potentials in this paper we study the lyapunov stabilities of some semiclassical bound states of the nonhomogeneous nonlinear schrodinger equation we prove that among those bound states those which are concentrated near local minima respectively maxima of the potentialv are stable respectively unstable we also prove that those bound states are positive if is sufficiently small

detection of changes in the fractal scaling of heart rate and speed in a marathon race abstract the aim of this study was to detect changes in the fractal scaling behavior of heart rate and speed fluctuations when the average runner s speed decreased with fatigue scaling analysis in heart rate hr and speed s dynamics of marathon runners was performed using the detrended fluctuation analysis dfa and the wavelet based structure function we considered both the short range 1 and the long range 2 scaling exponents for the dfa method separated by a change point n 0 64 5 3 min box length the same for all the races the variability of hr and s decreased in the second part of the marathon race while the cardiac cost time series i e the number of cardiac beats per meter increased due to the decreasing speed behavior the scaling exponents 1 and 2 of hr and 1 of s increased during the race p 0 01 as did the hr wavelet scaling exponent these findings provide evidence of the significant effect of fatigue induced by long exercise on the heart rate and speed variability

stability of solitary waves for nonlinear schrodinger equations with inhomogeneous nonlinearities we show that the ground state solitary waves of the critical nonlinear schrodinger equation i t t r v 4 d 0 in dimension d 2 are orbitally stable as 0i f v 0 v 4 0 g d v 0 2 where gd is a constant that depends only on d 2002 elsevier science b v all rights reserved

on matrices whose numerical ranges have circular or weak circular symmetry in 18 among other equivalent conditions it is proved that a square complex matrix a is permutationally similar to a block shift matrix if and only if for any complex matrix b with the same zero pattern as a w b the numerical range of b is a circular disk centered at the origin in this paper we add a long list of further new equivalent conditions the corresponding result for the numerical range of a square complex matrix to be invariant under a rotation about the origin through an angle of 2 m where m 2 is a given positive integer is also proved many interesting by products are obtained in particular on the numerical range of a square nonnegative matrix a the following unexpected results are established i when the undirected graph of a is connected if w a is a circular disk centered at the origin then so is w b for any complex matrix b with the same zero pattern as a ii when a is irreducible if is an eigenvalue in the peripheral spectrum of a that lies on the boundary of w a then is a sharp point of w a we also obtain results on the numerical range of an irreducible square nonnegative matrix which strengthen or clarify the work of issos 9 and nylen and tam 14 on this topic open questions are posed at the end

equality of numerical ranges of matrix powers abstract for an n by n matrix a we determine when the numerical ranges w a k k 1 of powers of a are all equal to each other more precisely we show that this is the case if and only if a is unitarily similar to a direct sum b c where b is idempotent and c satisfies w c k w b for all k 1 we then consider for each n 1 the smallest integer k n for which every n by n matrix a with w a w a k for all k 1 k k n has an idempotent direct summand for each n 1 let p n be the largest prime less than or equal to n 1 we show that 1 k n p n for all n 2 if a is normal of size n then w a w a k for all k 1 k p n implies a having an idempotent summand and 3 k 1 2 and k 2 k 3 3 these lead us to ask whether k n p n holds for all n 1

numerical ranges poncelet curves invariant measures abstract a class of closed algebraic curves circuits is considered these circuits have the property of poncelet quadrics the circuits are generated by matrices which admit unitary bordering the link between spectral properties of the matrices and geometrical properties of the circuits is studied

randomness and changes of heart rate and respiratory frequency during high altitude mountain ascent without acclimatization abstract the aim of this study was to detect and compare the changes in the time frequency and fractal scaling behaviors of heart rate hr and respiratory frequency rf recorded simultaneously during a high altitude mountain ascent the time frequency analysis was performed using the local cosine4 orthonormal bases of coifman malvar and meyer whose spectrum is not redundant as those computed with the short fourier transform the fractal scaling behavior was obtained using the detrended fluctuation dfa and the wavelet leaders wl analysis results showed that the high altitude mountain ascent differently affected hr and rf variability rf average values increased p 0 0003 while hr average values did not change the scaling variability of hr was altered during the mountain ascent which was detected by the increasing hr short range dfa exponents with altitude p 0 03 rf scaling variability remained unchanged these differences between hr and rf alterations were also observed for the local cosine4 power law behavior since power law exponents in absolute values increased for hr p 0 003 while those of rf did not change furthermore the ratio of low over the whole local spectrum energy of rf decreased with altitude p 0 04 in contrast to hr in most of these hr and rf analyses one of the two time series was significantly modified but not both moreover the rf local cosine4 spectrum had higher entropy compared to hr p 0 01 the difference between the rf and the hr entropy increased p 0 04 during the mountain ascent in consequence rf had more randomness than hr and altitude increased this difference

structures and numerical ranges of power partial isometries abstract we derive a matrix model under unitary similarity of an n by n matrix a such that a a 2 a k k 1 are all partial isometries which generalizes the known fact that if a is a partial isometry then it is unitarily similar to a matrix of the form 0 b 0 c with b b c c i using this model we show that if a has ascent k and a a 2 a k 1 are partial isometries then the numerical range w a of a is a circular disc centered at the origin if and only if a is unitarily similar to a direct sum of jordan blocks whose largest size is k as an application this yields that for any s n matrix a w a resp w a a is a circular disc centered at the origin if and only if a is unitarily similar to the jordan block j n finally examples are given to show that for a general matrix a the conditions that w a and w a a are circular discs at 0 are independent of each other

mobius transformations and blaschke products the geometric connection abstract let b be a degree n blaschke product and for t let z 1 z n ordered according to increasing argument denote the distinct solutions to b z 0 then there is a smooth curve c such that for each the line segments joining z j and z j 1 are tangent to c we study the situation in which c is an ellipse and describe the relation to the action of the points z j under elliptic disk automorphisms these results provide a condition for the numerical range of a compressed shift operator with finite blaschke symbol to be an elliptical disk we also consider infinite blaschke products and the action of parabolic and hyperbolic disk automorphisms

the upper numerical range of a quaternionic matrix is not a complex numerical range abstract a recent result is that the quaternionic numerical range of a matrix with quaternion entries has a convex intersection with the upper half complex plane this intersection is now shown to be generally not achievable as the upper half plane part of the complex numerical range of any complex matrix a key step in the proof is that if a complex matrix has an elliptical arc as part of the boundary of its complex numerical range then the full ellipse defined by the arc is also in its complex numerical range

nonlinear schrodinger equations and sharp interpolation estimates a sharp sufficient condition for global existence is obtained for the nonlinear schrodinger equation begin array 20 c nls 2i phi t delta phi left phi right 2 sigma phi 0 x in mathbb r n t in mathbb r end array in the case 2 n this condition is in terms of an exact stationary solution nonlinear ground state of nls it is derived by solving a variational problem to obtain the best constant for classical interpolation estimates of nirenberg and gagliardo

orbital stability of bound states of nonlinear schrodinger equations with linear and nonlinear optical lattices abstract we study the orbital stability and instability of single spike bound states of semi classical nonlinear schrodinger nls equations with critical exponent linear and nonlinear optical lattices ols these equations may model two dimensional bose einstein condensates in linear and nonlinear ols when linear ols are switched off we derive the asymptotic expansion formulas and obtain necessary conditions for the orbital stability and instability of single spike bound states respectively when linear ols are turned on we consider three different conditions of linear and nonlinear ols to develop mathematical theorems which are most general on the orbital stability problem

positive solutions for a weakly coupled nonlinear schrodinger system abstract existence of a nontrivial solution is established via variational methods for a system of weakly coupled nonlinear schrodinger equations the main goal is to obtain a positive solution of minimal action if possible with all vector components not identically zero generalizations for nonautonomous systems are considered

minimal penalties for gaussian model selection this paper is mainly devoted to a precise analysis of what kind of penalties should be used in order to perform model selection via the minimiza tion of a penalized least squares type criterion within some general gaussian framework including the classical ones as compared to our previous paper on this topic birge and massart in j eur math soc 3 203 268 2001 more elaborate forms of the penalties are given which are shown to be in some sense optimal we indeed provide more precise upper bounds for the risk of the penalized estimators and lower bounds for the penalty terms showing that the use of smaller penalties may lead to disastrous results these lower bounds may also be used to design a practical strategy that allows to estimate the penalty from the data when the amount of noise is unknown we provide an illustra tion of the method for the problem of estimating a piecewise constant signal in gaussian noise when neither the number nor the location of the change points are known

humans are able to self paced constant running accelerations until exhaustion abstract although it has been experimentally reported that speed variations is the optimal way of optimizing his pace for achieving a given distance in a minimal time we still do not know what the optimal speed variations i e accelerations are at first we have to check the hypothesis that human is able to accurately self pacing its acceleration and this even in a state of fatigue during exhaustive self pacing ramp runs for that purpose 3 males and 2 females middle aged recreational runners ran in random order three exhaustive acceleration trials we instructed the five runners to perform three self paced acceleration trials based on three acceleration intensity levels soft medium and hard we chose a descriptive modelling approach to analyse the behaviour of the runners once we knew that the runners were able to perceive three acceleration intensity levels we proposed a mean reverting process ornstein uhlenbeck to describe those accelerations d a t a t a d t d w t where a is the mean acceleration a t is the measured acceleration at each time interval t the ability of the runner to correct the variations around a mean acceleration and the human induced variations the goodness of fit of the ornstein uhlenbeck process highlights the fact that humans are able to maintain a constant acceleration and are able to precisely regulate their acceleration regardless of its intensity in a run leading to exhaustion in the range from 1 min 36 s to 20 min

numerical ranges and gersgorin discs abstract for a complex matrix a a ij i j 1 n let w a be its numerical range and let g a be the convex hull of i 1 n z c z a ii i j a ij a ji 2 and g a g u au u n by n unitary it is known that w a is always contained in g a and hence in g a in this paper we consider conditions for w a to be equal to g a or g a we show that if w a g a then the boundary of w a consists only of circular arcs and line segments if moreover a is unitarily irreducible then w a is a circular disc almost complete characterizations of 2 by 2 and 3 by 3 matrices a for which w a g a are obtained we also give criteria for the equality of w a and g a in particular such a s among the permutationally irreducible ones must have even sizes we also characterize those a s with size 2 or 4 which satisfy w a g a

structural break estimation for nonstationary time series models this article considers the problem of modeling a class of nonstationary time series using piecewise autoregressive ar processes the number and locations of the piecewise ar segments as well as the orders of the respective ar processes are assumed unknown the minimum description length principle is applied to compare various segmented ar fits to the data the goal is to find the best combination of the number of segments the lengths of the segments and the orders of the piecewise ar processes such a best combination is implicitly defined as the optimizer of an objective function and a genetic algorithm is implemented to solve this difficult optimization problem numerical results from simulation experiments and real data analyses show that the procedure has excellent empirical properties the segmentation of multivariate time series is also considered assuming that the true underlying model is a segmented autoregression this procedure is shown to be consistent for estimating the location of

numerical ranges and poncelet curves abstract convex circuits which have the property of circles of the great poncelet theorem are introduced the circuits are generated as boundaries of numerical ranges of specially constructed matrices algebraic and geometric properties of such matrices and their numerical ranges are obtained these properties lead to a new proof of the poncelet theorem the proposed approach illustrates the fact that complex relations between geometrical figures in a plane may have simple interpretation in a space of higher dimension

stability theory of solitary waves in the presence of symmetry ii abstract consider an abstract hamiltonian system which is invariant under a group of operators we continue to study the effect of the group invariance on the stability of solitary waves applications are given to bound states and traveling wave solutions of nonlinear wave equations

wavelet based estimators of scaling behavior various wavelet based estimators of self similarity or long range dependence scaling exponent are studied extensively these estimators mainly include the bi orthogonal wavelet estimators and the wavelet transform modulus maxima wtmm estimator this study focuses both on short and long time series in the framework of fractional autoregressive integrated moving average farima processes we advocate the use of approximately adapted wavelet estimators for these ideal processes the scaling behavior actually extends down to the smallest scale i e the sampling period of the time series if an adapted decomposition is used but in practical situations there generally exists a cutoff scale below which the scaling behavior no longer holds we test the robustness of the set of wavelet based estimators with respect to that cutoff scale as well as to the specific density of the underlying law of the process in all situations the wtmm estimator is shown to be the best or among the best estimators in terms of the mean squared error mse we also compare the wavelet estimators with the detrended fluctuation analysis dfa estimator which was previously proved to be among the best estimators which are not wavelet based estimators the wtmm estimator turns out to be a very competitive estimator which can be further generalized to characterize multiscaling behavior

decomposing finite blaschke products abstract we present four algorithms to determine whether or not a blaschke product is a composition of two non trivial blaschke products and if it is the algorithms suggest what the composition must be the initial algorithm is a naive counting argument the second considers critical values and the counting argument the third is a geometric argument that exploits the relationship between blaschke products and curves with the poncelet property and it can also be expressed in terms of a group associated with the blaschke product the final algorithm looks at inverse images under the blaschke product our algorithms are accompanied by an applet that implements them

effect of trends on detrended fluctuation analysis scaling behavior we find that crossovers result from the competition between the scaling of the noise and the apparent scaling of the trend we study how the characteristics of these crossovers depend on i the slope of the linear trend ii the amplitude and period of the periodic trend iii the amplitude and power of the power law trend and iv the length as well as the correlation properties of the noise surprisingly we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws i e long range power law dependence of the position of the crossover on the parameters of the trends we show that the dfa result of noise with a trend can be exactly determined by the superposition of the separate results of the dfa on the noise and on the trend assuming that the noise and the trend are not correlated if this superposition rule is not followed this is an indication that the noise and the superposed trend are not independent so that removing the trend could lead to changes in the correlation properties of the noise in addition we show how to use dfa appropriately to minimize the effects of trends how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation or if the crossover is due to a trend without any transition in the dynamical properties of the noise

detecting the marathon asymmetry with a statistical signature abstract lately the sub two hour marathon attempt in monza was still based on the belief that constant speed is the best way of running this idea is relayed by marathon organizers who offer pace group leaders to help the runners to maintain a target race speed the purposes of this study are to verify the hypotheses that 1 the mass runners try to maintain a constant speed without succeeding 2 marathoners run in an asymmetric way and this turns out to be visible in the speed time series those two points are independent of the gender the level of performance 2h30 3h40 and the profile of the race paris vs berlin before considering a predictive running strategy for optimizing personal marathon running performance here we shed light on some significant statistical features by analyzing speed time series data recorded by 273 runners gps we started with looking for a trend in the speed time series by means of kendall s non parametric rank correlation coefficient we exhibited a decreasing trend in speed data whichever the level of performance gender male and female and race profile berlin and paris marathons going deeper in the study we applied a systematic analysis of the asymmetry of speed via classical statistical measures of skewness among them the quantiles of the average speed i e the proportion of the race run above or below the final average the combination of the trend and the asymmetry lead to building up a statistical signature for the speed time series which is identical regardless the level of performance gender and race profile

multiscale aspects of cardiac control abstract we report some recent attempts to understand the dynamics of complex physiologic fluctuations by adapting and extending concepts and methods developed very recently in statistical physics we first review recent progress using wavelet based multifractal analysis magnitude and sign decomposition analysis and a new segmentation algorithm to quantify multiscale features of heartbeat interval series we then investigate how heartbeat dynamics change with circadian influences and under pathologic conditions and we discuss their possible relation to the underlaying cardiac control mechanisms the analytic tools we discuss may be used on a wider range of physiologic signals

extremality of numerical radii of matrix commutators and jordan products abstract it is known that the numerical radius of the commutator resp jordan product a b b a resp a b b a of two n by n matrices a and b is related to those of a and b by w a b b a 4 w a w b in this paper we give complete characterizations of a and b for which the equality is attained the matrices involved can be considered as elaborate generalizations of the equality attaining a 0 a 0 0 and b 0 0 b 0

detecting long range correlations with detrended fluctuation analysis abstract we examine the detrended fluctuation analysis dfa which is a well established method for the detection of long range correlations in time series we show that deviations from scaling which appear at small time scales become stronger in higher orders of dfa and suggest a modified dfa method to remove them the improvement is necessary especially for short records that are affected by non stationarities furthermore we describe how crossovers in the correlation behavior can be detected reliably and determined quantitatively and show how several types of trends in the data affect the different orders of dfa

on numerical ranges of the compressions of normal matrices abstract for an n n normal matrix a whose numerical range nr a is a k polygon k n an n k 1 isometry matrix p is constructed by a unit vector c n and nr p ap is inscribed to nr a in this paper using the notations of nr p ap and some properties from projective geometry an n n diagonal matrix b and an n k 2 isometry matrix q are proposed such that nr p ap and nr q bq have as common support lines the edges of the k polygon and share the same boundary points with the polygon it is proved that the boundary of nr p ap is a differentiable curve and the boundary of the numerical range of a 3 3 matrix p ap is an ellipse when the polygon is a quadrilateral

numerical ranges of weighted shift matrices with periodic weights abstract let a be an n by n n 2 matrix of the form 0 a 1 0 a n 1 a n 0 we show that if the a j s are nonzero and their moduli are periodic then the boundary of its numerical range contains a line segment we also prove that w a contains a noncircular elliptic arc if and only if the a j s are nonzero n is even a 1 a 3 a n 1 a 2 a 4 a n and a 1 a 2 finally we give a criterion for a to be reducible and completely characterize the numerical ranges of such matrices

minimizing the effect of trends on detrended fluctuation analysis of long range correlated noise abstract detrended fluctuation analysis dfa has been proposed as a robust technique to determine possible long range correlations in power law processes phys rev e 49 1994 1685 1989 however recent studies have reported the susceptibility of dfa to trends phys rev e 64 2001 011114 011133 which give rise to spurious crossovers and prevent reliable estimation of the scaling exponents inspired by these reports we propose a technique based on singular value decomposition svd of the trajectory matrix to minimize the effect of linear power law periodic and also quasi periodic trends superimposed on long range correlated power law noise the effectiveness of the technique is demonstrated on publicly available data sets phys rev e 64 2001 011114 011133

numerical ranges of reducible companion matrices abstract in this paper we show that a reducible companion matrix is completely determined by its numerical range that is if two reducible companion matrices have the same numerical range then they must equal to each other we also obtain a criterion for a reducible companion matrix to have an elliptic numerical range put more precisely we show that the numerical range of an n by n reducible companion matrix c is an elliptic disc if and only if c is unitarily equivalent to a b where a m n 2 b m 2 with b a 1 a 2 1 n 2 n 1 1 2 and a 1 2 1 2 2 4 1 2 cos n 2

perron frobenius type results on the numerical range we present results connecting the shape of the numerical range to intrinsic properties of a matrix a w hena is a nonnegative matrix these results are to a large extent analogous to the perron frobenius theory especially as it pertains to irreducibility and cyclicity in the combinatorial sense special attention is given to polygonal circular and elliptic numerical ranges the main vehicles for obtaining these results are the hermitian and skew hermitian parts of a as well as levinger s transformation aa 1 a a 2002 elsevier science

ellipses and compositions of finite blaschke products abstract we provide a new proof of a theorem of fujimura characterizing blaschke products of degree 4 that are compositions of two degree 2 blaschke products connect this result to the numerical ranges of certain operators and characterize poncelet ellipses that are inscribed in quadrilaterals geometrically and algebraically

extremality of numerical radii of matrix products for two n by n matrices a and b it was known before that their numerical radii satisfy the inequality w ab 4w a w b and the equality is attained by the 2 by 2 matrices a 0100 and b 0010 moreover the constant 4 here can be reduced to 2 if a and b commute and the corresponding equality is attained by a i2 0100 and b 0100 i2 in this paper we give a complete characterization of a and b for which the equality holds in each case more precisely it is shown that w ab 4w a w b resp w ab 2w a w b for commuting a and b if and only if either a or b is the zero matrix or a and b are simultaneously unitarily similar to matrices of the form 0a00 a and 00b0 b resp a and b with w a a 2 and w b b 2 an analogous characterization for the extremal equality for tensor products is also proven for doubly commuting matrices we use their unitary similarity model to obtain the corresponding result for commuting 2 by 2 matrices a and b we show that w ab w a w b if and only if either a or b is a scalar matrix or a and b are simultaneously unitarily similar to a100a2 and b100b2 with a1 a2 and b1 b2

geometry of the numerical range of matrices abstract some techniques for the study of the algebraic curve c a which generates the numerical range w a of an n n matrix a as its convex hull are developed these enable one to give an explicit point equation of c a and a formula for the curvature of c a at a boundary point of w a applied to the case of a nonnegative matrix a a simple relation is found between the curvature of the function a p 1 a a t p being the perron root at 1 2 and the curvature of w a at the perron root of 1 2 a a t a connection with 2 dimensional pencils of hermitian matrices is mentioned and a conjecture formulated

condition for the numerical range to contain an elliptic disc for an n by n matrix a and an elliptic disc e in the plane we show that the sum of the number of common supporting lines and the number of common intersection points to e and the numerical range w a of a should be at least 2n 1 in order to guarantee that e be contained in w a this generalizes previous results of anderson and thompson as an application our result is used to verify a special case of the poncelet property conjecture 2003 elsevier science inc all rights reserved

scaling and universality in heart rate variability distributions we find that a universal homogeneous scaling form describes the distribution of cardiac variations for a group of healthy subjects which is stable over a wide range of time scales however a similar scaling function does not exist for a group with a common cardiopulmonary instability associated with sleep apnea subtle differences in the distributions for the day and night phase dynamics for healthy subjects are detected