multiscale analysis of financial time series by renyi distribution entropy abstract it is of great interests to analyze the complexity or dependence of time series of the daily stock closing price in different regions entropy is typically a fundamental technique to explore the complexity of time series the well studied irregularity measure sample entropy sampen and a more recently proposed complexity measure distribution entropy disten are treated as classification features in our study based on renyi entropy which has been recently suggested as a measure of complexity in nonlinear systems we propose multiscale renyi distribution entropy mrde to research the complexity of nonlinear time series over multiple time scales considering the validity and accuracy renyi entropy obtains more information than the shannon entropy for time series mingled with much noise like financial time series which is mainly reflected in the choice of parameters for frequent events and rare events both the simulated signals logistic map and gaussian noise and the financial time series with three different stock markets are calculated and compared using an innovative method in different situations for different stock markets the entropy decreases as the scale factor increases except when the parameter is the maximum in the special case meanwhile we illustrate the necessity and advantage of renyi distribution entropy rde method by comparing rde results with the sampen results about stability and consistency on synthetic data and financial time series it is applied to measure the dependence by detecting the length of the time series and special algorithm parameters

inference and sample size calculation for clinical trials with incomplete observations of paired binary outcomes we investigate the estimation of intervention effect and sample size determination for experiments where subjects are supposed to contribute paired binary outcomes with some incomplete observations we propose a hybrid estimator to appropriately account for the mixed nature of observed data paired outcomes from those who contribute complete pairs of observations and unpaired outcomes from those who contribute either pre intervention or post intervention outcomes we theoretically prove that if incomplete data are evenly distributed between the pre intervention and post intervention periods the proposed estimator will always be more efficient than the traditional estimator a numerical research shows that when the distribution of incomplete data is unbalanced the proposed estimator will be superior when there is moderate to strong positive within subject correlation we further derive a closed form sample size formula to help researchers determine how many subjects need to be enrolled in such studies simulation results suggest that the calculated sample size maintains the empirical power and type i error under various design configurations we demonstrate the proposed method using a real application example copyright 2016 john wiley sons ltd

on multiscale entropy analysis for physiological data abstract we perform an analysis of cardiac data using multiscale entropy as proposed in costa et al multiscale entropy analysis of complex physiological time series phys rev lett 89 2002 068102 we reproduce the signatures of the multiscale entropy for the three cases of young healthy hearts atrial fibrillation and congestive heart failure we show that one has to be cautious how to interpret these signatures in terms of the underlying dynamics in particular we show that different dynamical systems can exhibit the same signatures depending on the sampling time and that similar systems may have different signatures depending on the time scales involved besides the total amount of data we identify the sampling time the correlation time and the period of possible nonlinear oscillations as important time scales which have to be involved in a detailed analysis of the signatures of multiscale entropies we illustrate our ideas with the lorenz equation as a simple deterministic chaotic system

a meshless method for solving an inverse spacewise dependent heat source problem in this paper an effective meshless and integration free numerical scheme for solving an inverse spacewise dependent heat source problem is proposed due to the use of the fundamental solution as basis functions the method leads to a global approximation scheme in both spatial and time domains the standard tikhonov regularization technique with the generalized cross validation criterion for choosing the regularization parameter is adopted for solving the resulting ill conditioned system of linear algebraic equations the effectiveness of the algorithm is illustrated by several numerical examples

undirected connectivity in log space we present a deterministic log space algorithm that solves st connectivity in undirected graphs the previous bound on the space complexity of undirected st connectivity was log4 3 obtained by armoni ta shma wigderson and zhou jacm 2000 as undirected st connectivity is complete for the class of problems solvable by symmetric nondeterministic log space computations the class sl this algorithm implies that sl e l where l is the class of problems solvable by deterministic log space computations independent of our work and using different techniques trifonov stoc 2005 has presented an o log n log log n space deterministic algorithm for undirected st connectivity our algorithm also implies a way to construct in log space a fixed sequence of directions that guides a deterministic walk through all of the vertices of any connected graph specifically we give log space constructible universal traversal sequences for graphs with restricted labeling and log space constructible universal exploration sequences for general graphs

cumulative tsallis entropy based on multi scale permuted distribution of financial time series abstract a method based on multi scale permuted distribution cumulative tsallis entropy mpdcte is proposed in this paper to measure the complexity and dissimilarity between sequences it avoids the influence of permutation on spatial distribution and uses the calculation of spatial distance matrix in distributed entropy to effectively measure the complexity of time series we apply the mpdcte method to the simulation data verify the effectiveness of the method discuss the influence of the parameters and compare it with the traditional entropy metric the results show that this method is insensitive to parameter changes and has a low dependence on data length the dependencies all show superiority finally it was applied to the real financial market and we selected 9 stocks in the world to analyze the mpdcte method clearly divided the stocks by analyzing the sequence which is consistent with the phenomenon of the financial market

comment on multiscale entropy analysis of complex physiologic time series a comment on the letter by madalena costa ary l goldberger and c k peng phys rev lett 89 068102 2002 the authors of the letter offer a reply

classifying the complexity of constraints using finite algebras many natural combinatorial problems can be expressed as constraint satisfaction problems this class of problems is known to be np complete in general but certain restrictions on the form of the constraints can ensure tractability here we show that any set of relations used to specify the allowed forms of constraints can be associated with a finite universal algebra and we explore how the computational complexity of the corresponding constraint satisfaction problem is connected to the properties of this algebra hence we completely translate the problem of classifying the complexity of restricted constraint satisfaction problems into the language of universal algebra we introduce a notion of tractable algebra and investigate how the tractability of an algebra relates to the tractability of the smaller algebras which may be derived from it including its subalgebras and homomorphic images this allows us to reduce significantly the types of algebras which need to be classified using our results we also show that if the decision problem associated with a given collection of constraint types can be solved efficiently then so can the corresponding search problem we then classify all finite strictly simple surjective algebras with respect to tractability obtaining a dichotomy theorem which generalizes schaefer s dichotomy for the generalized satisfiability problem finally we suggest a possible general algebraic criterion for distinguishing the tractable and intractable cases of the constraint satisfaction problem

on testing the equality of proportions in the paired case with incomplete data the problem of testing two correlated proportions with incomplete data is considered by means of monte carlo simulations studies a test proposed in this paper which can be regarded as a generalization of mcnemar s test is recommended in all cases with incomplete data and not too small samples

a dichotomy theorem for constraint satisfaction problems on a 3 element set the constraint satisfaction problem csp provides a common framework for many combinatorial problems the general csp is known to be np complete however certain restrictions on a possible form of constraints may affect the complexity and lead to tractable problem classes there is therefore a fundamental research direction aiming to separate those subclasses of the csp that are tractable and those which remain np complete schaefer gave an exhaustive solution of this problem for the csp on a 2 element domain in this article we generalise this result to a classification of the complexity of the csp on a 3 element domain the main result states that every subproblem of the csp is either tractable or np complete and the criterion separating them is that conjectured in bulatov et al 2005 and bulatov and jeavons 2001b we also characterize those subproblems for which standard constraint propagation techniques provide a decision procedure finally we exhibit a polynomial time algorithm which for a given set of allowed constraints outputs if this set gives rise to a tractable problem class to obtain the main result and the algorithm we extensively use the algebraic technique for the csp developed in jeavons 1998b bulatov et al 2005 and bulatov and jeavons 2001b

dual reciprocity hybrid boundary node method for free vibration analysis abstract as a truly meshless method of boundary type the hybrid boundary node method hbnm has the advantages of both boundary element method bem and meshless method the main problem is that it is only suitable for the homogeneous problems now the dual reciprocity method drm is introduced into hbnm to deal with the integral for the inhomogeneous terms of the governing equations and the rigid body motion approach is employed to solve the hyper singular integrations a new meshless method named dual reciprocity hybrid boundary node method drhbnm is proposed and applied to solve free vibration problems in this method the solution composes into two parts i e the general solution and the particular solution the general solution is solved by hbnm and the particular one is obtained by drm drhbnm is a true boundary type meshless method it does not require the boundary element mesh either for the purpose of interpolation of the variables or for the integration of energy the points in the domain are only used to interpolate particular solution by the radial basis function finally the boundary variables are interpolated by the independent smooth boundary segments the q r algorithm and householder algorithm are applied to solve the eigenvalues and eigenvectors of the transformed matrix numerical examples for free vibration problems show that a good convergence with mesh refinement is achievable and the computational results for the natural circular frequencies and free vibration modes are very accurate furthermore the computation parameters have little influence on the results and can be chosen in a wide range it is shown that the present method is effective and can be widely applied in practical engineering

quantified equality constraints an equality template is a relational structure with infinite universe whose relations can be defined by boolean combinations of equalities we prove a complexity classification for quantified constraint satisfaction problems qcsps over equality templates these problems are in l decidable in logarithmic space np hard or conp hard to establish our classification theorem we combine methods from universal algebra with concepts from model theory

average entropy measurement of disorder for cardiac rr interval signals abstract we introduce average entropy ae as a disorder measure of heart rate time series the ae measurement reflects both the probability distribution of all discrete values in a time series and the randomness of the series the ae analysis is able to differentiate the congestive heart failure chf the healthy and the atrial fibrillation af subjects for both short and long heart rate time series the differentiation accuracy of ae is higher than 90 in addition since the meaning of disorder is easily confused with complexity we explore the relation between them by analyzing heart rate time series specifically we demonstrate that the complexity measured by entropy of entropy eoe versus the disorder measured by ae plot of heart rate time series exhibits a distinct inverted u relation

on tests for correlated proportions in the presence of incomplete data this paper proposes test statistics based on the likelihood ratio principle for testing equality of proportions in correlated data with additional incomplete samples powers of these tests are compared through monte carlo simulation with those of tests proposed recently by ekbohm based on an unbiased estimator and campbell based on a pearson chi squared type statistic even though tests based on the maximum likelihood principle are theoretically expected to be superior to others at least asymptotically results from our simulations show that the gain in power could only be slight

diversity analysis based on ordered patterns abstract diversity index based on entropy such as emlen index e i is suggested as a highly effective algorithm to detect complexity in nonlinear systems in this paper a method considering the amplitude information called weighted emlen index w e i is proposed to extract the amplitude information and track the signal changes and then we expand e i w e i methods to multiple time scales thus multiscale emlen index m s e i and multiscale weighted emlen index m s w e i will be used to discuss the complexity of traffic time series under different scales results show that there are differences between the complexity of weekend traffic time series and workday time series which gives a better classification of traffic systems for making prediction

the complexity of counting quantifiers on equality languages an equality language is a relational structure with infinite domain whose relations are first order definable in equality we classify the extensions of the quantified constraint satisfaction problem over equality languages in which the native existential and universal quantifiers are augmented by some subset of counting quantifiers in doing this we find ourselves in various worlds in which dichotomies or trichotomies subsist

adaptive spatial decomposition in fast multipole method this work presents a new adaptive node cluster algorithm for fast multipole method in the algorithm we use rectangular boxes instead of cubes subdivide a box based on its shape and tighten the child boxes at each subdivision step more importantly we determine the number of expansion terms in multipole to local translations according to the distance between the two interaction boxes our method is tested using benchmark examples for three dimensional potential problems the results obtained show that the new algorithm can solve a problem with 100 thousands nodes in about 20 min and runs nearly three times faster than the standard algorithm the proposed algorithm is especially suitable for treating slender and shell like structures

the complexity of constraint satisfaction games and qcsp we study the complexity of two person constraint satisfaction games an instance of such a game is given by a collection of constraints on overlapping sets of variables and the two players alternately make moves assigning values from a finite domain to the variables in a specified order the first player tries to satisfy all constraints while the other tries to break at least one constraint the goal is to decide whether the first player has a winning strategy we show that such games can be conveniently represented by a logical form of quantified constraint satisfaction where an instance is given by a first order sentence in which quantifiers alternate and the quantifier free part is a conjunction of positive atomic formulas the goal is to decide whether the sentence is true while the problem of deciding such a game is pspace complete in general by restricting the set of allowed constraint predicates one can obtain infinite classes of constraint satisfaction games of lower complexity we use the quantified constraint satisfaction framework to study how the complexity of deciding such a game depends on the parameter set of allowed predicates with every predicate one can associate certain predicate preserving operations called polymorphisms we show that the complexity of our games is determined by the surjective polymorphisms of the constraint predicates we illustrate how this result can be used by identifying the complexity of a wide variety of constraint satisfaction games

reshape scale method a novel multi scale entropic analysis approach abstract the reshape scale rs method was introduced in this article as a novel approach to perform multi scale transition of sample entropy this method was able to quantify the orderliness in the signal by determining the distance over which the subsequent data points can remain affiliated to one another entropic half life enhl was introduced to characterize such an affiliation the method was tested for 1 f processes for different values furthermore the dependency of the multi scale entropy analysis developed by costa et al 2002 6 to the probability density function and the standard deviation of autoregressive signals was studied and discussed

testing equality of correlated proportions with incomplete data on both responses two test statistics are proposed for testing the equality of two correlated proportions when some observations are missing on both responses the performance of these tests in terms of size and power is compared with other tests by means of monte carlo simulations the proposed tests are easily computed and compare favorably with other tests

non inferiority and superiority tests for partially matched data when a constraint is placed on the number of new tests studies for assessing non inferiority or superiority of a new diagnostic or screening test relative to a standard test use a complete matched pairs design in which results for both tests are obtained for all subjects we present alternative tests for the situation where results on the standard test are obtained for all subjects but results on the new test are obtained for a subset of those subjects only this situation is common when results for the standard test are available from a large biobank we present a stratified random sampling procedure for drawing the subsample of subjects that receive the new diagnostic test with strata defined by the two outcome categories of the standard test we derive appropriate statistical tests for non inferiority and superiority of the new diagnostic test we will show how the number of subjects that receive the new test can be minimized by non proportional stratified random sampling

towards 3 query locally decodable codes of subexponential length a q query locally decodable code ldc encodes an n bit message x as an n bit codeword c x such that one can probabilistically recover any bit xi of the message by querying only q bits of the codeword c x even after some constant fraction of codeword bits has been corrupted we give new constructions of three query ldcs of vastly shorter length than that of previous constructions specifically given any mersenne prime p e 2t 1 we design three query ldcs of length n e exp o n1 t for every n based on the largest known mersenne prime this translates to a length of less than exp o n10 7 compared to exp o n1 2 in the previous constructions it has often been conjectured that there are infinitely many mersenne primes under this conjecture our constructions yield three query locally decodable codes of length n e exp no 1 log log n for infinitely many n we also obtain analogous improvements for private information retrieval pir schemes we give 3 server pir schemes with communication complexity of o n10 7 to access an n bit database compared to the previous best scheme with complexity o n1 5 25 assuming again that there are infinitely many mersenne primes we get 3 server pir schemes of communication complexity no 1 log logn for infinitely many n previous families of ldcs and pir schemes were based on the properties of low degree multivariate polynomials over finite fields our constructions are completely different and are obtained by constructing a large number of vectors in a small dimensional vector space whose inner products are restricted to lie in an algebraically nice set

event and time scale characteristics of heart rate dynamics the cardiac system shows various scale dynamic activities from secondly to yearly therefore multiple time scale characteristics of heart dynamics have received much attention for understanding and distinguishing healthy and pathological cardiac systems in this paper we expand the multiple time scale analysis into event and time scales to investigate scale characteristics in healthy and pathologic cardiac systems to do this we define a measure based on symbolic dynamics which calculates complexity at each time and event scale called the unit time block entropy utbe this measure allows a reliable comparison of experimental data through matching the number of words and the total measurement time at the same time for all rr interval sequences which are composed of the time durations between consecutive r waves of electrocardiograms we apply the utbe to the healthy heart rate hr group and pathological hr groups and find that the rr interval acceleration is more effective than the rr interval in distinguishing each group and we also find that the normal and pathological hr groups are clearly distinguished in some specific event and time scale regions

multiscale entropy analysis of complex physiologic time series there has been considerable interest in quantifying the complexity of physiologic time series such as heart rate however traditional algorithms indicate higher complexity for certain pathologic processes associated with random outputs than for healthy dynamics exhibiting long range correlations this paradox may be due to the fact that conventional algorithms fail to account for the multiple time scales inherent in healthy physiologic dynamics we introduce a method to calculate multiscale entropy mse for complex time series we find that mse robustly separates healthy and pathologic groups and consistently yields higher values for simulated long range correlated noise compared to uncorrelated noise

the complexity of temporal constraint satisfaction problems a temporal constraint language is a set of relations that has a first order definition in q an extended abstract of this article appeared in the proceedings of stoc 08

schaefer s theorem for graphs schaefer s theorem is a complexity classification result for so called boolean constraint satisfaction problems it states that every boolean constraint satisfaction problem is either contained in one out of six classes and can be solved in polynomial time or is np complete we present an analog of this dichotomy result for the propositional logic of graphs instead of boolean logic in this generalization of schaefer s result the input consists of a set w of variables and a conjunction of statements constraints about these variables in the language of graphs where each statement is taken from a fixed finite set of allowed quantifier free first order formulas the question is whether is satisfiable in a graph we prove that either is contained in one out of 17 classes of graph formulas and the corresponding problem can be solved in polynomial time or the problem is np complete this is achieved by a universal algebraic approach which in turn allows us to use structural ramsey theory to apply the universal algebraic approach we formulate the computational problems under consideration as constraint satisfaction problems csps whose templates are first order definable in the countably infinite random graph our method for classifying the computational complexity of those csps is based on a ramsey theoretic analysis of functions acting on the random graph and we develop general tools suitable for such an analysis which are of independent mathematical interest

regularized moving least square method and regularized improved interpolating moving least square method with nonsingular moment matrices abstract the moving least square mls method has been popular applied in surface construction and meshless methods however the moment matrix in mls method may be singular for ill quality point sets and the computation of the inverse of the singular moment matrix is difficult to overcome this problem a regularized moving least square method with nonsingular moment matrix is proposed the shape functions obtained from the regularized mls method still do not have the delta function property and may result in difficulty for imposing boundary conditions in regularized mls based meshless method to overcome this problem a regularized improved interpolating moving least square iimls method based on the iimls method is also proposed compared with the regularized mls method the regularized iimls not only has nonsingular moment matrices but also obtains shape functions with delta function property shape functions of the proposed methods are compared in 1d and 2d cases and the methods have been applied in curve fitting surface fitting and meshless method in numerical examples

the computational structure of monotone monadic snp and constraint satisfaction a study through datalog and group theory this paper starts with the project of finding a large subclass of np which exhibits a dichotomy the approach is to find this subclass via syntactic prescriptions while the paper does not achieve this goal it does isolate a class of problems specified by monotone monadic snp without inequality which may exhibit this dichotomy we justify the placing of all these restrictions by showing essentially using ladner s theorem that classes obtained by using only two of the above three restrictions do not show this dichotomy we then explore the structure of this class we show that all problems in this class reduce to the seemingly simpler class csp we divide csp into subclasses and try to unify the collection of all known polytime algorithms for csp problems and extract properties that make csp problems np hard this is where the second part of the title a study through datalog and group theory comes in we present conjectures about this class which would end in showing the dichotomy

the csp dichotomy holds for digraphs with no sources and no sinks a positive answer to a conjecture of bang jensen and hell bang jensen and hell conjectured in 1990 using the language of graph homomorphisms a constraint satisfaction problem csp dichotomy for digraphs with no sources or sinks the conjecture states that the csp for such a digraph is tractable if each component of its core is a cycle and is np complete otherwise in this paper we prove this conjecture and as a consequence a conjecture of bang jensen hell and macgillivray from 1995 classifying hereditarily hard digraphs further we show that the csp dichotomy for digraphs with no sources or sinks agrees with the algebraic characterization conjectured by bulatov jeavons and krokhin in 2005

novel meshless method for solving the potential problems with arbitrary domain in this article a non singular and boundary type meshless method in two dimensions is developed to solve the potential problems the solution is represented by a distribution of the kernel functions of double layer potentials by using the desingularization technique to regularize the singularity and hypersingularity of the kernel functions the source points can be located on the real boundary and therefore the diagonal terms of influence matrices are determined the main difficulty of the coincidence of the source and collocation points then disappears by employing the two point function the off diagonal coefficients of influence matrices are easily obtained the numerical evidences of the proposed meshless method demonstrate the accuracy of the solutions after comparing with the results of exact solution conventional mfs and bem for the dirichlet neumann and mix type boundary conditions bcs of interior and exterior problems with simple and complicated boundaries good agreements with exact solutions are observed

meshless analysis of potential problems in three dimensions with the hybrid boundary node method combining a modified functional with the moving least squares mls approximation the hybrid boundary node method hybrid bnm is a truly meshless boundary only method the method may have advantages from the meshless local boundary integral equation mlbie method and also the boundary node method bnm in fact the hybrid bnn requires only the discrete nodes located on the surface of the domain the hybrid bnm has been applied to solve 2d potential problems in this paper the hybrid bnm is extended to solve potential problems in three dimensions formulations of the hybrid bnm for 3d potential problems and the mls approximation on a generic surface are developed a general computer code of the hybrid bnm is implemented in c the main drawback of the boundary layer effect in the hybrid bnm in the 2d case is circumvented by an adaptive face integration scheme the parameters that influence the performance of this method are studied through three different geometries and known analytical fields numerical results for the solution of the 3d laplace s equation show that high convergence rates with mesh refinement and high accuracy are achievable copyright 2004 john wiley sons ltd

reconstructing the topology of clones function clones are sets of functions on a fixed domain that are closed under composition and contain the projections they carry a natural algebraic structure provided by the laws of composition which hold in them as well as a natural topological structure provided by the topology of pointwise convergence under which composition of functions becomes continuous inspired by recent results indicating the importance of the topological ego of function clones even for originally algebraic problems we study questions of the following type in which situations does the algebraic structure determine the topological structure of a functional clone we pay particular attention to function clones which contain an oligomorphic permutation group and discuss applications of this situation in model theory and theoretical computer science

the hybrid boundary node method accelerated by fast multipole expansion technique for 3d potential problems this paper presents a fast formulation of the hybrid boundary node method hybrid bnm for solving problems governed by laplace s equation in 3d the preconditioned gmres is employed for solving the resulting system of equations at each iteration step of the gmres the matrix vector multiplication is accelerated by the fast multipole method green s kernel function is expanded in terms of spherical harmonic series an oct tree data structure is used to hierarchically subdivide the computational domain into well separated cells and to invoke the multipole expansion approximation formulations for the local and multipole expansions and also conversion of multipole to local expansion are given and a binary tree data structure is applied to accelerate the moving least square approximation on surfaces all the formulations are implemented in a computer code written in c numerical examples demonstrate the accuracy and efficiency of the proposed approach copyright 2005 john wiley sons ltd

infinite permutation groups ii subgroups of small index it was shown by dixon neumann and thomas 3 that if 52 is a countably infinite set and h is a subgroup of the full symmetric group sym sz on q of index less than 2no then h contains the pointwise stabilizer in sym q of a finite subset of 52 referring to the analogous statement for an arbitrary group g which will usually be a subgroup of sym q for some 52 with iszj n as the conjecture on subgroups of small index for g it was shown by evans s that the conjecture holds for the general linear group of a vector space of dimension k over a countable or finite division ring and bruyns z obtained partial information about the conjecture in the case where g aut q the group of homeomorphisms of q to itself the conjecture was formulated in 3 for two particularly interesting cases aut q and a q the latter being the group of order preserving permutations of q macpherson s was more ambitious and suggested that the conjecture should hold for the automorphism group of any nocategorical structure though he weakened the hypothesis ig hi 2 o to ig hi k and evans 6 showed how to reformulate the conjecture using ideas about closed subgroups of g recently hrushovski has found a counter example to the general case of the conjecture though it still seems likely that it will hold in a wide class of instances the object here is to establish the truth of the conjecture in the two main cases raised in 3 we shall prove it in some other cases too principally the group of automorphisms of the countable atomless boolean algebra this is isomorphic as a graq to aut c where c is the cantor discontinuum though not as a permutation group in fact aut c has degree 2 thus although we work mainly with aut c or rather aut 2 the statement of the result comes out rather differently when expressed in this group namely it says if h is a subgroup of aut c of index less than 2x0 494 0021 8693 89 3 00