gamma convergence of gradient flows with applications to ginzburg landau we present a method to prove convergence of gradient flows of families of energies that converge to a limiting energy it provides lower bound criteria to obtain the convergence that correspond to a sort of c1 order convergence of functionals we then apply this method to establish the limiting dynamical law of a finite number of vortices for the heat flow of the ginzburg landau energy in dimension 2 retrieving in a different way the existing results for the case without magnetic field and obtaining new results for the case with magnetic field 2004 wiley periodicals inc

modified multiscale cross sample entropy for complex time series we introduce the cmcse and further propose the rcmcse method mcse cmcse and rcmcse methods are employed to artificial and financial time series rcmcse reduces standard deviation and the probability of inducing undefined entropy rcmcse can provide better robustness and more accurate entropies rcmcse is more applicable for the study between us and chinese stock markets in this paper we introduce the composite multiscale cross sample entropy cmcse which may induce undefined entropies and then further propose the refined composite multiscale cross sample entropy rcmcse which modifies cmcse first we apply multiscale cross sample entropy mcse cmcse and rcmcse methods to three types of artificial time series in order to test the validity and accuracy of these methods results show that rcmcse reduces not only standard deviation but also the probability of inducing undefined entropy effectively which can provide better robustness and more accurate entropies then these three methods are employed to investigate financial time series including us and chinese stock indices for the study between stock indices in the same region some conclusions which are consistent with previous study are drawn by the rcmcse results meanwhile it can be found that undefined entropies are induced and the numbers of inducing undefined entropy by three methods for investigation between three us stock indices and two chinese mainland stock indices are given compared with mcse and cmcse rcmcse method is capable of reducing the number of undefined entropy and providing more accurate entropies moreover the differences on inducing undefined entropy between results for us stock indices two chinese mainland stock indices and results for us stock indices hsi demonstrate a much closer relation between us stock markets and hsi than between us stock markets and two chinese mainland stock markets hence it can be concluded that rcmcse is more applicable for the study between us and chinese stock markets

collisions and phase vortex interactions in dissipative ginzburg landau dynamics in this paper we describe a natural framework for the vortex dynamics in the parabolic complex ginzburg landau equation in r this general setting does not rely on any assumption of well preparedness and has the advantage to be valid even after collision times we analyze carefully collisions leading to annihilation a new phenomenon is identified the phase vortex interaction related to persistence of low frequency oscillations and leading to an unexpected drift in the motion of vortices

mixed normal superconducting states in the presence of strong electric currents we study the ginzburg landau equations in the presence of large electric currents that are smaller than the critical current where the normal state loses its stability for steady state solutions in the large kappa limit we prove that the superconductivity order parameter is exponentially small in a significant part of the domain and simply small in the rest of it similar results are obtained for the time dependent problem in continuation of the paper by the two first authors 3 we conclude by obtaining some weaker results albeit similar for steady state solutions in the large domain limit

complexity analysis of time series based on generalized fractional order cumulative residual distribution entropy abstract based on the theory of cumulative residual entropy and distribution entropy this paper proposes a new model cumulative residual distribution entropy crde which is more suitable for the complexity and risk analysis of time series the new model makes full use of the known information including not only the information of probability but also the information about the value of random variables additionally the crde considers the potential inherent information of vector to vector distance in the state space by combining theoretical analysis with empirical research this paper verifies that the new model has more advantages in measuring extreme events and small probability events with higher consistency stability and practicability in this paper the cumulative residual distribution entropy model is extended to the fractional order the generalized fractional cumulative residual distribution entropy gcrde can better capture the tiny evolution of time series which is more advantageous for studying the dynamic characteristics of complex systems the new model makes up for some shortcomings of traditional models and it can play a guiding role in the study of complex systems in the real world

weighted multiscale renyi permutation entropy of nonlinear time series abstract in this paper based on renyi permutation entropy rpe which has been recently suggested as a relative measure of complexity in nonlinear systems we propose multiscale renyi permutation entropy mrpe and weighted multiscale renyi permutation entropy wmrpe to quantify the complexity of nonlinear time series over multiple time scales first we apply mpre and wmpre to the synthetic data and make a comparison of modified methods and rpe meanwhile the influence of the change of parameters is discussed besides we interpret the necessity of considering not only multiscale but also weight by taking the amplitude into account then mrpe and wmrpe methods are employed to the closing prices of financial stock markets from different areas by observing the curves of wmrpe and analyzing the common statistics stock markets are divided into 4 groups 1 dji s p500 and hsi 2 nasdaq and ftse100 3 dax40 and cac40 and 4 shangzheng and shencheng results show that the standard deviations of weighted methods are smaller showing wmrpe is able to ensure the results more robust besides wmpre can provide abundant dynamical properties of complex systems and demonstrate the intrinsic mechanism

a product estimate for ginzburg landau and corollaries abstract we prove a new inequality for the jacobian or vorticity associated to the ginzburg landau energy in any dimension it allows to retrieve existing lower bounds on the energy to extend them to the case of unbounded vorticity and to get a few other corollaries it also provides a new estimate on the time variation for time dependent families which has applications for the study of ginzburg landau dynamics

refined composite multiscale weighted permutation entropy of financial time series abstract for quantifying the complexity of nonlinear systems multiscale weighted permutation entropy mwpe has recently been proposed mwpe has incorporated amplitude information and been applied to account for the multiple inherent dynamics of time series however mwpe may be unreliable because its estimated values show large fluctuation for slight variation of the data locations and a significant distinction only for the different length of time series therefore we propose the refined composite multiscale weighted permutation entropy rcmwpe by comparing the rcmwpe results with other methods results on both synthetic data and financial time series rcmwpe method shows not only the advantages inherited from mwpe but also lower sensitivity to the data locations more stable and much less dependent on the length of time series moreover we present and discuss the results of rcmwpe method on the daily price return series from asian and european stock markets there are significant differences between asian markets and european markets and the entropy values of hang seng index hsi are close to but higher than those of european markets the reliability of the proposed rcmwpe method has been supported by simulations on generated and real data it could be applied to a variety of fields to quantify the complexity of the systems over multiple scales more accurately

binary indices of time series complexity measures and entropy plane abstract complexity of time series is an important feature of dynamical systems such as financial systems in order to bring out the complete non linear behavior of financial time series non linear tools of complexity measurement like entropy measures are indispensable sample entropy sampen and distribution entropy disten are popular methods of assessing the complexity in various fields however both sample entropy and distribution entropy show some limitations in detecting the complexity of stock markets therefore we use two entropies as binary indices to analyze the complexity of time series and structure the entropy plane in order to further improve the accuracy of the research results we take the embedding dimension m as the variable expand the entropy point into the entropy curve for further research furthermore considering the shortcomings of sample entropy and distribution entropy in practical application we generalize them by i replacing sample entropy and distribution entropy with multi scale sample entropy and multi scale distribution entropy ii generalizing shannon entropy as tsallis entropy also scale factor and entropic index q are taken respectively as variables to get the entropy curves by using the artificial data we confirm the rationality of using entropy points and entropy curves to study the complexity of time series finally we apply this method to measure the complexity of real world financial time series the results show that the entropy curves plotted by the financial time series obtained from different areas have significant differences

intrinsic chaos and external noise in population dynamics abstract we address the problem of the relative importance of the intrinsic chaos and the external noise in determining the complexity of population dynamics we use a recently proposed method for studying the complexity of nonlinear random dynamical systems the new measure of complexity is defined in terms of the average number of bits per time unit necessary to specify the sequence generated by the system this measure coincides with the rate of divergence of nearby trajectories under two different realizations of the noise in particular we show that the complexity of a nonlinear time series model constructed from sheep populations comes completely from the environmental variations however in other situations intrinsic chaos can be the crucial factor this method can be applied to many other systems in biology and physics

chaotic and stochastic functions abstract we study chaotic functions that are exact solutions to nonlinear maps a generalization of these functions which cannot be expressed as a recursive procedure anymore can produce truly random sequences even if the initial conditions are known exactly the next values are in principle unpredictable we present a mathematical formulation of an elementary stochastic process several applications are discussed

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

blind source separation using temporal predictability a measure of temporal predictability is defined and used to separate linear mixtures of signals given any set of statistically independent source signals it is conjectured here that a linear mixture of those signals has the following property the temporal predictability of any signal mixture is less than or equal to that of any of its component source signals it is shown that this property can be used to recover source signals from a set of linear mixtures of those signals by finding an un mixing matrix that maximizes a measure of temporal predictability for each recovered signal this matrix is obtained as the solution to a generalized eigenvalue problem such problems have scaling characteristics of o n3 where n is the number of signal mixtures in contrast to independent component analysis the temporal predictability method requires minimal assumptions regarding the probability density functions of source signals it is demonstrated that the method can separate signal mixtures in which each mixture is a linear combination of source signals with supergaussian subgaussian and gaussian probability density functions and on mixtures of voices and music

the resistive state in a superconducting wire bifurcation from the normal state we study formally and rigorously the bifurcation to steady and time periodic states in a model for a thin superconducting wire in the presence of an imposed current exploiting the pt symmetry of the equations at both the linearized and nonlinear levels and taking advantage of the collision of real eigenvalues leading to complex spectrum we obtain explicit asymptotic formulas for the stationary solutions for the amplitude and period of the bifurcating periodic solutions and for the location of their zeros or phase slip centers as they are known in the physics literature in so doing we construct a center manifold for the flow and give a complete description of the associated finite dimensional dynamics

complex ginzburg landau equations and dynamics of vortices filaments and codimension 2 submanifolds here we study the asymptotic behavior of solutions to the complex ginzburg landau equations and their associated heat flows in arbitrary dimensions when the ginzburg landau parameter tends to infinity we prove that the energies of solutions in the flow are concentrated at vortices in two dimensions filaments in three dimensions and codimension 2 submanifolds in higher dimensions moreover we show the dynamical laws for the motion of these vortices filaments and codimension 2 submanifolds away from the energy concentration sets we use some measure theoretic arguments to show the strong convergence of solutions in both static and heat flow cases 1998 john wiley sons inc

preseismic electromagnetic signals in terms of complexity there is a recent thesis in the literature that an important organization of a physical system precedes a catastrophic event in this context one can search for signatures that imply the transition from a normal state to a main catastrophic event e g earthquake experimental techniques are thus useful in corroborating theories from observed data for example recent results indicate that preseismic electromagnetic time series contain information characteristic of an ensuing earthquake event hereby we attempt to demonstrate that an easily computable complexity measure such as t complexity or approximate entropy gives evidence of state changes leading to the point of global instability the appearance of a precatastrophic state is characterized by significant lower complexity in terms of t complexity and approximate entropy the present study confirms the conclusions of previous works based on an independent linear fractal spectral analysis this convergence between nonlinear and linear analysis provides a more reliable detection concerning the emergence of the last phase of the earthquake preparation process more precisely we claim that our results suggest an important principle significant complexity decrease and accession of persistency in electromagnetic em time series can be confirmed at the tail of the preseismic em emission which could be used as diagnostic tools for the earth s impending crust failure direct laboratory and field experimental data as well as theoretical arguments support the conclusions of the present analysis 2006 the american physical society

a zoo of computable binary normal sequences historically there has been a virtual absence of constructive methods to produce broad classes of certifiably random infinite sequences despite considerable interest in this endeavor previously we proved a theorem that yielded explicit algorithms to produce diverse sets of normal numbers reasonable candidates for random sequences given their limiting equidistribution of subblocks of all lengths herein we develop this algorithmic approach much further systematizing the normal number generation process in several ways we construct delineated distinct sets of normal numbers classified by the extent to which initial segments deviate from maximal irregularity with virtually any allowable specified rate of convergence to 0 of this deviation encompassing arbitrarily fast and slow rates and accommodating asymmetric behavior above or below a centered median as a corollary we provide an explicit construction of a normal number that satisfies the law of the iterated logarithm we also produce distinct families of biased normal numbers with virtually any specified rate of convergence of the bias to 0 this latter theory is in part motivated by the remarkable observation that the binary version of champernowne s number which is also normal is biased any initial segment has more 1s than 0s finally we construct an interesting normal sequence with arbitrarily fast convergence to equidistribution of singleton blocks yet arbitrarily slow convergence of pairs which has profound implications both for probability theory and for metrics to evaluate the near randomness of sequences

quantization and motion law for ginzburg landau vortices we study the vortex trajectories for the two dimensional complex parabolic ginzburg landau equation without a well preparedness assumption we prove that the trajectory set is rectifiable and satisfies a weak motion law in the case of degree 1 vortices the motion law is satisfied in the classical sense moreover dissipation occurs only at a finite number of times away from these times possible collisions and splittings of vortices are constrained by algebraic equations involving their topological degrees

a recipe for randomness despite many diverse theories that address closely related themes e g probability theory algorithmic complexity cryptoanalysis and pseudorandom number generation a near void remains in constructive methods certified to yield the desired random output herein we provide explicit techniques to produce broad sets of both highly irregular finite and normal infinite sequences based on constructions and properties derived from approximate entropy apen a computable formulation of sequential irregularity furthermore for infinite sequences we considerably refine normality by providing methods for constructing diverse classes of normal numbers classified by the extent to which initial segments deviate from maximal irregularity

numerical approximations of the ginzburg landau models for superconductivity in this paper we review various methods for the numerical approximations of the ginzburg landau models of superconductivity particular attention is given to the different treatment of gauge invariance in both the finite element finite difference and finite volume settings representative theoretical results typical numerical simulations and computational challenges are presented generalizations to other relevant models are also discussed

what is a statistical model this paper addresses two closely related questions what is a statistical model and what is a parameter the notions that a model must make sense and that a parameter must have a well defined meaning are deeply ingrained in applied statistical work reasonably well understood at an instinctive level but absent from most formal theories of modelling and inference in this paper these concepts are defined in algebraic terms using morphisms functors and natural transformations it is argued that inference on the basis of a model is not possible unless the model admits a natural extension that includes the domain for which inference is required for example prediction requires that the domain include all future units subjects or time points although it is usually not made explicit every sensible statistical model admits such an extension examples are given to show why such an extension is necessary and why a formal theory is required in the definition of a subparameter it is shown that certain parameter functions are natural and others are not inference is meaningful only for natural parameters this distinction has important consequences for the construction of prior distributions and also helps to resolve a controversy concerning the box cox model

efficient approximation concepts using second order information the primary goal of this paper is to show how second derivative information can be used in an effective way in structural optimization problems the basic idea is to generate such an information at the expense of only one more virtual load case in the sensitivity analysis part of the finite element code to achieve this goal a primal dual approach is employed that can also be interpreted as a sequential quadratic programming method another objective is to relate the proposed method to the well known family of approximation concepts techniques where the primary optimization problem is transformed into a sequence of non linear explicit subproblems when restricted to diagonal second derivatives the new approach can be viewed as a recursive convex programming method similar to the convex linearization method conlin and to its recent generalization the method of moving asymptotes mma this new method has been successfully tested on simple problems that can be solved in closed form as well as on sizing optimization of trusses in all cases the method converges faster than conlin mma or other approximation techniques based on reciprocal variables

determining the complexity of fh ss sequence by approximate entropy high complexity of frequency hopping fh spreadspectrum ss sequence is of great importance to high security multiple access communication systems for it makes fh ss sequence difficult to be analyzed with the growing development in the design of fh ss sequence in much wider fields the wellknown complexity measuresiquestthe linear complexity lc the linear complexity profile lcp and the k error linear complexity k error lc iquestare widely used but not sufficient to evaluate the complexities of the sequences available such as the cryptographical sequence and the chaotic sequence families in this paper a new complexity metric to evaluate the unpredictability of fh ss sequence based on the approximate entropy apen is proposed in the view of the maximal randomness of the sequences with arbitrary length and the theoretical bounds of the apen are derived from a probabilistic point of view simulations and analysis results show that the proposed apen works effectively to discern the changing complexities of the fh ss sequences with small number of samples which provide superior performance over its candidates

ginzburg landau vortex dynamics driven by an applied boundary current in this paper we study the time dependent ginzburg landau equations on a smooth bounded domain c 2 subject to an electrical current applied on the boundary the dynamics with an applied current are nondissipative but via the identification of a special structure in an interaction energy we are able to derive a precise upper bound for the energy growth we then turn to the study of the dynamics of the vortices of the solutions in the limit e 0 we first consider the original time scale in which the vortices do not move and the solutions undergo a phase relaxation then we study an accelerated time scale in which the vortices move according to a derived dynamical law in the dynamical law we identify a novel lorentz force term induced by the applied boundary current 2010 wiley periodicals inc

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

stochastic model for heart rate fluctuations a normal human heart rate shows complex fluctuations in time which is natural because the heart rate is controlled by a large number of different feedback control loops these unpredictable fluctuations have been shown to display fractal dynamics long term correlations and 1 f noise these characterizations are statistical and they have been widely studied and used but much less is known about the detailed time evolution dynamics of the heart rate control mechanism here we show that a simple one dimensional langevin type stochastic difference equation can accurately model the heart rate fluctuations in a time scale from minutes to hours the model consists of a deterministic nonlinear part and a stochastic part typical to gaussian noise and both parts can be directly determined from the measured heart rate data studies of 27 healthy subjects reveal that in most cases the deterministic part has a form typically seen in bistable systems there are two stable fixed points and one unstable one

convergence of the parabolic ginzburg landau equation to motion by mean curvature for the complex parabolic ginzburg landau equation we prove that asymptotically vorticity evolves according to motion by mean curvature in brakke s weak formulation the only assumption is a natural energy bound on the initial data in some cases we also prove convergence to enhanced motion in the sense of ilmanen