quantum spectrum as a time series fluctuation measures the fluctuations in the quantum spectrum could be treated like a time series in this framework we explore the statistical self similarity in the quantum spectrum using the detrended fluctuation analysis dfa and random matrix theory rmt we calculate the hausdorff measure for the spectra of atoms and gaussian ensembles and study their self affine properties we show that dfa is equivalent to the delta3 statistics of rmt unifying two different approaches we exploit this connection to obtain theoretical estimates for the hausdorff measure

quantifying signals with power law correlations a comparative study of detrended fluctuation analysis and detrended moving average techniques detrended fluctuation analysis dfa and detrended moving average dma are two scaling analysis methods designed to quantify correlations in noisy nonstationary signals we systematically study the performance of different variants of the dma method when applied to artificially generated long range power law correlated signals with an a priori known scaling exponent alpha 0 and compare them with the dfa method we find that the scaling results obtained from different variants of the dma method strongly depend on the type of the moving average filter further we investigate the optimal scaling regime where the dfa and dma methods accurately quantify the scaling exponent alpha 0 and how this regime depends on the correlations in the signal finally we develop a three dimensional representation to determine how the stability of the scaling curves obtained from the dfa and dma methods depends on the scale of analysis the order of detrending and the order of the moving average we use as well as on the type of correlations in the signal

wavelet based fractal analysis of dna sequences abstract the fractal scaling properties of dna sequences are analyzed using the wavelet transform mapping nucleotide sequences onto a dna walk produces fractal landscapes that can be studied quantitatively by applying the so called wavelet transform modulus maxima method this method provides a natural generalization of the classical box counting techniques to fractal signals the wavelets playing the role of generalized oscillating boxes from the scaling behavior of partition functions that are defined from the wavelet transform modulus maxima this method allows us to determine the singularity spectrum of the considered signal and thereby to achieve a complete multifractal analysis moreover by considering analyzing wavelets that make the wavelet transform microscope blind to patches of different nucleotide composition that are observed in genomic sequences we demonstrate and quantify the existence of long range correlations in the noncoding regions although the fluctuations in the patchy landscape of the dna walks reconstructed from both noncoding and protein coding regions are found homogeneous with gaussian statistics our wavelet based analysis allows us to discriminate unambiguously between the fluctuations of the former which behave like fractional brownian motions from those of the latter which cannot be distinguished from uncorrelated random brownian walks we discuss the robustness of these results with respect to various legitimate codings of the dna sequences finally we comment about the possible understanding of the origin of the observed long range correlations in noncoding dna sequences in terms of the nonequilibrium dynamical processes that produce the isochore structre of the genome

quasipolynomial generalization of lotka volterra mappings in recent years it has been shown that lotka volterra mappings constitute a valuable tool from both the theoretical and the applied points of view with developments in very diverse fields such as physics population dynamics chemistry and economy the purpose of this work is to demonstrate that many of the most important ideas and algebraic methods that constitute the basis of the quasipolynomial formalism originally conceived for the analysis of ordinary differential equations can be extended into the mapping domain the extension of the formalism into the discrete time context is remarkable as far as the quasipolynomial methodology had never been shown to be applicable beyond the differential case it will be demonstrated that lotka volterra mappings play a central role in the quasipolynomial formalism for the discrete time case moreover the extension of the formalism into the discrete time domain allows a significant generalization of lotka volterra mappings as well as a whole transfer of algebraic methods into the discrete time context the result is a novel and more general conceptual framework for the understanding of lotka volterra mappings as well as a new range of possibilities that become open not only for the theoretical analysis of lotka volterra mappings and their generalizations but also for the development of new applications

quantitative analysis for covering based rough sets through the upper approximation number coverings are a useful form of data while covering based rough sets provide an effective tool for dealing with this data covering based rough sets have been widely used in attribute reduction and rule extraction however few quantitative analyses for covering based rough sets have been conducted while many advances for classical rough sets have been obtained through quantitative tools in this paper the upper approximation number is defined as a measurement to quantify covering based rough sets and a pair of upper and lower approximation operators are constructed using the approximation number the operators not only inherit some important properties of existing approximation operators but also exhibit some new quantitative characteristics it is interesting to note that the upper approximation number of a covering approximation space is similar to the dimension of a vector space or the rank of a matrix

oscillatory behavior of the specific heat at low temperature in quasiperiodic structures we investigate the thermodynamical properties of plasmon polaritons that propagate in multiple semiconductor layers arranged in a quasi periodical fashion of fibonacci and thue morse types we have chosen these two types of quasi periodic structures for the following reasons i both were realized experimentally so they are not mere academic examples of a quasi crystal ii it is believed that the thue morse chain is more disordered than the fibonacci one i e it has a degree of aperiodicity intermediate between the fibonacci chain and the random systems more precisely the fourier amplitude spectrum of the thue morse sequence is singular continuous while for the fibonacci case we found function peaks not arranged periodically both analytical and numerical studies on the temperature dependence of the excitation s specific heat associated with the generation number n 1 2 3 for their multiscale fractal energy spectra are presented we show that when t tends to zero the specific heat displays oscillations and when t tends to infinity the specific heat goes to zero as t 2 because the energy spectrum considered is bounded

an application of rough sets to graph theory this paper studies the testing bipartiteness of simple undirected graphs based on generalized rough sets a new binary relation induced from a simple undirected graph is first defined the concept of quasi outer definable sets is then introduced and some of its important properties are investigated finally based on the quasi outer definable set a new algorithm is designed for testing bipartiteness of a simple undirected graph experiments show that the proposed algorithm is more efficient than the traditional one when the graph is represented by an adjacency matrix

characterizing multi scale self similar behavior and non statistical properties of fluctuations in financial time series abstract we make use of wavelet transform to study the multi scale self similar behavior and deviations thereof in the stock prices of large companies belonging to different economic sectors the stock market returns exhibit multi fractal characteristics with some of the companies showing deviations at small and large scales the fact that the wavelets belonging to the daubechies db basis enables one to isolate local polynomial trends of different degrees plays the key role in isolating fluctuations at different scales one of the primary motivations of this work is to study the emergence of the k 3 behavior x gabaix p gopikrishnan v plerou h stanley a theory of power law distributions in financial market fluctuations nature 423 2003 267 270 of the fluctuations starting with high frequency fluctuations we make use of db4 and db6 basis sets to respectively isolate local linear and quadratic trends at different scales in order to study the statistical characteristics of these financial time series the fluctuations reveal fat tail non gaussian behavior unstable periodic modulations at finer scales from which the characteristic k 3 power law behavior emerges at sufficiently large scales we further identify stable periodic behavior through the continuous morlet wavelet

a new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets traditional rough set theory is mainly used to extract rules from and reduce attributes in databases in which attributes are characterized by partitions while the covering rough set theory a generalization of traditional rough set theory does the same yet characterizes attributes by covers in this paper we propose a way to reduce the attributes of covering decision systems which are databases characterized by covers first we define consistent and inconsistent covering decision systems and their attribute reductions then we state the sufficient and the necessary conditions for reduction finally we use a discernibility matrix to design algorithms that compute all the reducts of consistent and inconsistent covering decision systems numerical tests on four public data sets show that the proposed attribute reductions of covering decision systems accomplish better classification performance than those of traditional rough sets

relationships among generalized rough sets in six coverings and pure reflexive neighborhood system rough set is a useful tool to deal with partition related uncertainty granularity and incompleteness of knowledge although the classical rough set is constructed on the basis of an indiscernibility relation it can also be generalized by using some weaker binary relations in this paper a systematic approach is used to study the generalized rough sets in six coverings and pure reflexive neighborhood system after two steps relationships among generalized rough sets in six coverings and pure reflexive neighborhood system are obtained the first step is to study the generalized rough sets in six coverings and to get relationships between every two covering rough set models the second step is to study the relationships between generalized rough sets in each covering and in pure reflexive neighborhood system the inclusion relations or equivalence relations among the seven upper lower approximations could be acquired finally the accuracy measures of generalized rough sets in six coverings and that in pure reflexive neighborhood system are compared the relationships among seven accuracy measures are also obtained some illustrative examples are employed to demonstrate our arguments

relationship between generalized rough sets based on binary relation and covering rough set theory is a powerful tool for dealing with uncertainty granularity and incompleteness of knowledge in information systems this paper systematically studies a type of generalized rough sets based on covering and the relationship between this type of covering based rough sets and the generalized rough sets based on binary relation firstly we present basic concepts and properties of this kind of rough sets then we investigate the relationships between this type of generalized rough sets and other five types of covering based rough sets the major contribution in this paper is that we establish the equivalency between this type of covering based rough sets and a type of binary relation based rough sets through existing results in binary relation based rough sets we present axiomatic systems for this type of covering based lower and upper approximation operations in addition we explore the relationships among several important concepts such as minimal description reduction representative covering exact covering and unary covering in covering based rough sets investigation of this type of covering based will benefit to our understanding of other types of rough sets based on covering and binary relation

attribute reduction of data with error ranges and test costs in data mining applications we have a number of measurement methods to obtain a data item with different test costs and different error ranges test costs refer to time money or other resources spent in obtaining data items related to some object observational errors correspond to differences in measured and true value of a data item in supervised learning we need to decide which data items to obtain and which measurement methods to employ so as to minimize the total test cost and help in constructing classifiers this paper studies this problem in four steps first data models are built to address error ranges and test costs second error range based covering rough set is constructed to define lower and upper approximations positive regions and relative reducts a closely related theory deals with neighborhood rough set which has been successfully applied to heterogeneous attribute reduction the major difference between the two theories is the definition of neighborhood third the minimal test cost attribute reduction problem is redefined in the new theory fourth both backtrack and heuristic algorithms are proposed to deal with the new problem the algorithms are tested on ten uci university of california irvine datasets experimental results show that the backtrack algorithm is efficient on rational sized datasets the weighting mechanism for the heuristic information is effective and the competition approach can improve the quality of the result significantly this study suggests new research trends concerning attribute reduction and covering rough set

double quantitative decision theoretic rough set the probabilistic rough set prs and the graded rough set grs are two quantification models that measure relative and absolute quantitative information between the equivalence class and a basic concept respectively as a special prs model the decision theoretic rough set dtrs mainly utilizes the conditional probability to express relative quantification however it ignores absolute quantitative information of the overlap between equivalence class and the basic set and it cannot reflect the distinctive degrees of information and extremely narrow their applications in real life in order to overcome these defects this paper proposes a framework of double quantitative decision theoretic rough set dq dtrs based on bayesian decision procedure and grs two kinds of dq dtrs model are constructed which essentially indicate the relative and absolute quantification after further studies to discuss decision rules and the inner relationship between these two models we introduce an illustrative case study about the medical diagnosis to interpret and express the theories which is valuable for applying these theories to deal with practical issues

connection between energy spectrum self similarity and specific heat log periodicity as a first step towards the understanding of the thermodynamical properties of quasiperiodic structures we have performed both analytical and numerical calculations of the specific heats associated with successive hierarchical approximations to multiscale fractal energy spectra we show that in a certain range of temperatures the specific heat displays log periodic oscillations as a function of the temperature we exhibit scaling arguments that allow for relating the mean value as well as the amplitude and the period of the oscillations to the characteristic scales of the spectrum

misleading signatures of quantum chaos the main signature of chaos in a quantum system is provided by spectral statistical analysis of the nearest neighbor spacing distribution p s and the spectral rigidity given by the delta 3 l statistic it is shown that some standard unfolding procedures such as local unfolding and gaussian broadening lead to a spurious saturation of delta 3 l that spoils the relationship of this statistic with the regular or chaotic motion of the system this effect can also be misinterpreted as berry s saturation

constructive and axiomatic approaches of fuzzy approximation operators this paper presents a general framework for the study of rough set approximation operators in fuzzy environment in which both constructive and axiomatic approaches are used in constructive approach a pair of lower and upper generalized fuzzy rough and rough fuzzy respectively approximation operators is first defined the representations of both fuzzy rough approximation operators and rough fuzzy approximation operators are then presented the connections between fuzzy and crisp respectively relations and fuzzy rough and rough fuzzy respectively approximation operators are further established in axiomatic approach various classes of fuzzy approximation operators are characterized by different sets of axioms the minimal axiom sets of fuzzy approximation operators guarantee the existence of certain types of fuzzy or crisp relations producing the same operators

some phase transitions in coupled map lattices we study finite coupled map lattices of size d 2 with individual maps 0 1 0 1 and constant diffuse coupling for x 2x mod 1 we give sufficient conditions that the coupled system has a continuum of ergodic components in the case d 2 we determine the number of ergodic components for all coupling strengths if is a mixing tent map close to the transition from mixing to a periodic interval with period 2 the uncoupled system is mixing whereas numerical studies suggest that coupling with a suitable strength breaks up the phase space into domains which are interchanged with period 2 in case d 2 we prove this rigorously

attribute reduction in decision theoretic rough set models rough set theory can be applied to rule induction there are two different types of classification rules positive and boundary rules leading to different decisions and consequences they can be distinguished not only from the syntax measures such as confidence coverage and generality but also the semantic measures such as decision monotocity cost and risk the classification rules can be evaluated locally for each individual rule or globally for a set of rules both the two types of classification rules can be generated from and interpreted by a decision theoretic model which is a probabilistic extension of the pawlak rough set model as an important concept of rough set theory an attribute reduct is a subset of attributes that are jointly sufficient and individually necessary for preserving a particular property of the given information table this paper addresses attribute reduction in decision theoretic rough set models regarding different classification properties such as decision monotocity confidence coverage generality and cost it is important to note that many of these properties can be truthfully reflected by a single measure c in the pawlak rough set model on the other hand they need to be considered separately in probabilistic models a straightforward extension of the c measure is unable to evaluate these properties this study provides a new insight into the problem of attribute reduction

parameterized attribute reduction with gaussian kernel based fuzzy rough sets fuzzy rough sets are considered as an effective tool to deal with uncertainty in data analysis and fuzzy similarity relations are used in fuzzy rough sets to calculate similarity between objects on the other hand in kernel tricks a kernel maps data into a higher dimensional feature space where the resulting structure of the learning task is linearly separable while the kernel is the inner product of this feature space and can also be viewed as a similarity function it has been reported there is an overlap between family of kernels and collection of fuzzy similarity relations this fact motivates the idea in this paper to use some kernels as fuzzy similarity relations and develop kernel based fuzzy rough sets first we consider gaussian kernel and propose gaussian kernel based fuzzy rough sets second we introduce parameterized attribute reduction with the derived model of fuzzy rough sets structures of attribute reduction are investigated and an algorithm with discernibility matrix to find all reducts is developed finally a heuristic algorithm is designed to compute reducts with gaussian kernel fuzzy rough sets several experiments are provided to demonstrate the effectiveness of the idea

study of the log periodic oscillations of the specific heat of cantor energy spectra energy spectra with fractal structure are known to lead to a specific heat with log periodic oscillations as a function of temperature in this paper we present a systematic study of the properties of these oscillations for both monoscale and multiscale energy spectra obtained from cantor sets we obtain how the amplitude of the oscillations depends on the structure of the spectrum we also find that the amplitude of the oscillations above the specific heat mean value behaves differently to the amplitude of the oscillations below the mean value the amplitudes of the latter oscillations has a limiting value given by a characteristic dimension of the spectrum this asymmetry in the amplitudes produces strong non harmonic behavior of the oscillatory regime when energy spectra with fractal structure characterized by small fractal dimension are considered in addition we also study the behavior of the specific heat when the energy spectrum has unity fractal dimension i e corresponding to an energy spectrum without energy gaps which are more similar to natural fractal energy spectra than usual cantor sets in this case we also find oscillatory behavior of the specific heat if certain conditions are satisfied

probabilistic model criteria with decision theoretic rough sets in dealing with risk in real decision problems decision theoretic rough sets with loss functions aim to obtain optimization decisions by minimizing the overall risk with bayesian decision procedures two parameters generated by loss functions divide the universe into three regions as the decision of acceptance deferment and rejection in this paper we discuss the semantics of loss functions and utilize the differences of losses replace actual losses to construct a new four level approach of probabilistic rules choosing criteria ten types of probabilistic rough set models can be generated by the four level approach and form two groups of models two way probabilistic decision models and three way probabilistic decision models a reasonable decision with these criteria is demonstrated by an illustration of oil investment

an expanded double quantitative model regarding probabilities and grades and its hierarchical double quantitative attribute reduction a double quantitative model on probabilities and grades is proposed by integration the model with quantitative semantics expands dtrs model grs model pawlak model model regions are hierarchically and optimally calculated via two algorithms three reduct types srp reduct crp reduct app reduct are hierarchically studied the double quantitative reducts expand basic qualitative and quantitative reducts probabilities and grades serve as relative and absolute measures respectively they are used to establish the decision theoretic rough set dtrs and graded rough set grs two basic quantitative models the double quantification of probabilities and grades exhibits systematicness and completeness in view of the two dimensional feature of the approximate space however double quantitative construction becomes a problem and double quantitative reduction is rarely reported thus this paper mainly constructs an expanded double quantitative model by logically integrating probabilities and grades it further studies relevant double quantitative reduction by hierarchically preserving specific regions 1 first a novel model is established via the logic integration and expansion requirement and its regional system and granular hierarchy are studied via granular computing thus regional semantics is extracted via basic semantics granules regional calculation is realized by two algorithms and the algorithm regarding calculation granules exhibits optimization according to algorithm analyses 2 second three types of model regional preservation reducts and their hierarchy are discussed in the two category case thus srp reduct crp reduct and app reduct are studied by exploring four region preservation properties constructing two region classification regions and preserving four original approximations respectively furthermore a relevant reduction hierarchy is thoroughly achieved 3 moreover the model and its reduction are illustrated by two examples of decision tables the constructional model conducts double quantification regarding probabilities and grades thus it exhibits double quantitative semantics and benignly expands dtrs model grs model and pawlak model furthermore its hierarchical reduction reflects some double quantitative reduction essence thus its reduction expands qualitative pawlak reduction while guides quantitative dtrs reduction and grs reduction

correlation structure of the deltan statistic for chaotic quantum systems the existence of a formal analogy between quantum energy spectra and discrete time series has been recently pointed out when the energy level fluctuations are described by means of the statistic it is found that chaotic quantum systems are characterized by noise while regular systems are characterized by in order to investigate the correlation structure of the statistic we study the order height height correlation function which measures the momentum of order i e the average power of the signal change after a time delay it is shown that this function has a logarithmic behavior for the spectra of chaotic quantum systems modeled by means of random matrix theory on the other hand since the power spectrum of chaotic energy spectra considered as time series exhibit noise we investigate whether the order height height correlation function of other time series with noise exhibits the same properties a time series of this kind can be generated as a linear combination of cosine functions with arbitrary phases we find that the logarithmic behavior arises with great accuracy for time series generated with random phases

double quantitative rough fuzzy set based decisions as two important expanded quantification rough set models the probabilistic rough set prs model and the graded rough set grs model are used to measure relative quantitative information and absolute quantitative information between the equivalence classes and a basic concept respectively the decision theoretic rough set dtrs model is a special case of prs model which mainly utilizes the conditional probability to express relative quantification since the fuzzy concept is more general than classical concept in real life how to make decision for a fuzzy concept using relative and absolute quantitative information is becoming a hot topic in this paper a couple of double quantitative decision theoretic rough fuzzy set dq dtrfs models based on logical conjunction and logical disjunction operation are proposed furthermore we discuss decision rules and the inner relationship between these two models then an experiment in the medical diagnosis is studied to support the theories finally to apply our methods to solve a pattern recognition problem in big data experiments on data sets downloaded from uci are conducted to test the proposed models in addition we also offer a comparative analysis using two non rough set based methods from the results obtained one finds that the proposed method is efficient for dealing with practical issues

comparison of the probabilistic approximate classification and the fuzzy set model abstract it is shown that the generalized notion probabilistic approximate classification of rough sets can be conveniently described by the concept of fuzzy sets a discussion of the proper choice of the definition for the membership function of the intersection union of fuzzy sets is also presented however from the point of view of the probabilistic approximation space it is argued that there does not exist a universal definition for the fuzzy intersection union operation

topological characterizations of covering for special covering based upper approximation operators the relationships among properties of covering approximation operators and their corresponding coverings have attracted intensive research in recent years in particular those among topological properties have drawn special attention because of their important applications in rough set theory in this paper we give topological characterizations of covering c for covering based upper approximation operators fh sh th and rh to be closure operators we also give intuitive characterizations of covering c and describe covering based approximation space u c as certain types of information exchange systems when sh or rh is a closure operator by applying our new characterizations we give inequalities about the relationship between the number of members in c and the number of elements in u and discuss relationships among conditions for different covering based upper approximation operators to be closure operators to the best of our knowledge it is the first time that such characterizations descriptions inequalities and discussions are systematically considered in the literature of rough set theory furthermore in this paper we also give several characterizations of unary coverings an important type of coverings in studying relationships among basic concepts in covering based rough sets by the relationships among different types of covering base approximation operators

exact evaluation of the causal spectrum and localization properties of electronic states on a scale free network abstract a deterministic network with tree structure is considered for which the spectrum of its adjacency matrix can be exactly evaluated by a recursive renormalization approach it amounts to successively increasing number of contributions at any finite step of construction of the tree resulting in a causal chain the resulting eigenvalues can be related the full energy spectrum of a nearest neighbor tight binding model defined on this structure given this association it turns out that further properties of the eigenvectors can be evaluated like the degree of quantum localization of the tight binding eigenstates expressed by the inverse participation ratio ipr it happens that for the current model the ipr s are also suitable to be analytically expressed in terms in corresponding eigenvalue chain the resulting ipr scaling behavior is expressed by the tails of eigenvalue chains as well

symmetry breaking bifurcation for coupled chaotic attractors the authors consider transitions from synchronous to asynchronous chaotic motion in two identical dissipatively coupled one dimensional mappings they show that the probability density of the asymmetric component satisfies a scaling law the exponent in this scaling law varies continuously with the distance from the bifurcation point and is determined by the spectrum of local lyapunov exponents of the uncoupled map finally they show that the topology of the invariant set is rather unusual though the attractor for supercritical coupling is a line it is surrounded by a strange invariant set which is dense in a two dimensional neighbourhood of the attractor

computational explorations into the dynamics of rings of coupled oscillators this paper deals with the response of homogeneous and inhomogeneous rings of coupled oscillators where each individual oscillator when uncoupled from the others is chaotic it is shown that coupling can bring about a wide variety of global responses and that there is a significant range of coupling values when the response of the ring is periodic despite the fact that each oscillator is chaotic in fact numerous periodic solutions can be found depending on the initial conditions the response of a coupled set of homogeneous and non homogeneous rings is also investigated showing that the behavior of such coupled compartmental models can be quite counterintuitive and sensitive to the parameters that describe the extent and nature of coupling

spectral fluctuations of billiards with mixed dynamics from time series to superstatistics a statistical analysis of the eigenfrequencies of two sets of superconducting microwave billiards one with mushroomlike shape and the other from the family of the limacon billiards is presented these billiards have mixed regular chaotic dynamics but different structures in their classical phase spaces the spectrum of each billiard is represented as a time series where the level order plays the role of time two most important findings follow from the time series analysis first the spectra can be characterized by two distinct relaxation lengths this is a prerequisite for the validity of the superstatistical approach which is based on the folding of two distribution functions second the shape of the resulting probability density function of the so called superstatistical parameter is reasonably approximated by an inverse chi2 distribution this distribution is used to compute nearest neighbor spacing distributions and compare them with those of the resonance frequencies of billiards with mixed dynamics within the framework of superstatistics the obtained spacing distribution is found to present a good description of the experimental ones and is of the same or even better quality as a number of other spacing distributions including the one from berry and robnik however in contrast to other approaches toward a theoretical description of spectral properties of systems with mixed dynamics superstatistics also provides a description of properties of the eigenfunctions in terms of a superstatistical generalization of the porter thomas distribution indeed the inverse chi2 parameter distribution is found suitable for the analysis of experimental resonance strengths in the limacon billiards within the framework of superstatistics

on rough set and fuzzy sublattice let l be a lattice with the least element 0 and the greatest element 1 and let be a full congruence relation on l in this paper the notion of upper and lower approximations of a fuzzy subset of l is introduced and some important properties will be studied

on the coverings by tolerance classes a tolerance is a reflexive and symmetric but not necessarily transitive binary relation contrary to what happens with equivalence relations when dealing with tolerances one must distinguish between blocks maximal subsets where the tolerance is a total relation and classes the class of an element is the set of those elements tolerable with it both blocks and classes of a tolerance on a set define coverings of this set but not every covering of a set is defined in this way the characterization of those coverings that are families of blocks of some tolerance has been known for more than a decade now in this paper we give a characterization of those coverings of a finite set that are families of classes of some tolerance

the δn statistic for the β hermite ensemble abstract the fluctuation n of the n th unfolded eigenvalue was recently characterized for the classical gaussian ensembles of n n random matrices goe gue gse it is investigated here for the hermite ensemble as a function of the reciprocal of the temperature by monte carlo simulations the ensemble averaged fluctuation n 2 and the autocorrelation function vary logarithmically with n for any 0 1 n n the simple logarithmic behavior of the higher order moments of n reported in the literature for the goe 1 and the gue 2 holds for any 0 and is accounted for by gaussian distributions whose variances depend linearly on ln n

the fourth type of covering based rough sets as a technique for granular computing rough sets deal with the vagueness and granularity in information systems covering based rough sets have been proposed to generalize this theory for wider application three types of covering based rough sets have been studied for different situations to make the theory more complete this paper proposes a fourth type of covering based rough sets compared with the existing ones the new type shows its special characteristic in the interdependency between its lower and upper approximations we carry out a systematical study of this new theory first we discuss basic properties such as normality contraction and monotone then we investigate the conditions for this type of covering based rough sets to satisfy the properties of pawlak s rough sets and study the interdependency between the lower and upper approximation operations in addition axiomatic systems for the lower and upper approximation operations are established lastly we address the relationships between this type of covering based rough sets and the three existing ones

wavelet analysis and scaling properties of time series we propose a wavelet based method for the characterization of the scaling behavior of nonstationary time series it makes use of the built in ability of the wavelets for capturing the trends in a data set in variable window sizes discrete wavelets from the daubechies family are used to illustrate the efficacy of this procedure after studying binomial multifractal time series with the present and earlier approaches of detrending for comparison we analyze the time series of averaged spin density in the 2d ising model at the critical temperature along with several experimental data sets possessing multifractal behavior

multifractal detrended cross correlation analysis of coding and non coding dna sequences through chaos game representation abstract we propose a new approach combining the chaos game representation and the two dimensional multifractal detrended cross correlation analysis methods to examine multifractal behavior in power law cross correlation between any pair of nucleotide sequences of unequal lengths in this work we analyzed the characteristic behavior of coding and non coding dna sequences of eight prokaryotes the results show the presence of strong multifractal nature between coding and non coding sequences of all data sets we found that this integrative approach helps us to consider complete dna sequences for characterization and further it may be useful for classification clustering identification of class affiliation of nucleotide sequences etc with high precision

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

local reduction of decision system with fuzzy rough sets one important and valuable topic in fuzzy rough sets is attribute reduction of decision system the existing attribute reductions with fuzzy rough sets consider all decision classes together and cannot identify key conditional attributes explicitly for special decision class in this paper we introduce the concept of local reduction with fuzzy rough sets for decision system the local reduction can identify key conditional attribute and offer a minimal description for every single decision class approach of discernibility matrix is employed to investigate the structure of local reduction at last several experiments are performed to show that the idea of local reduction is feasible and valid

rough set theory applied to lattice theory in this paper we intend to study a connection between rough sets and lattice theory we introduce the concepts of upper and lower rough ideals filters in a lattice then we offer some of their properties with regard to prime ideals filters the set of all fixed points compact elements and homomorphisms

invertible approximation operators of generalized rough sets and fuzzy rough sets this paper studies the classes of rough sets and fuzzy rough sets we discuss the invertible lower and upper approximations and present the necessary and sufficient conditions for the lower approximation to coincide with the upper approximation in both rough sets and fuzzy rough sets we also study the mathematical properties of a fuzzy rough set induced by a cyclic fuzzy relation

topological approaches to covering rough sets rough sets a tool for data mining deal with the vagueness and granularity in information systems this paper studies covering based rough sets from the topological view we explore the topological properties of this type of rough sets study the interdependency between the lower and the upper approximation operations and establish the conditions under which two coverings generate the same lower approximation operation and the same upper approximation operation lastly axiomatic systems for the lower approximation operation and the upper approximation operation are constructed

multiresolution analysis of fluctuations in non stationary time series through discrete wavelets abstract we illustrate the efficacy of a discrete wavelet based approach to characterize fluctuations in non stationary time series the present approach complements the multifractal detrended fluctuation analysis mf dfa method and is quite accurate for small size data sets as compared to polynomial fits in the mf dfa a single daubechies wavelet is used here for detrending purposes the natural built in variable window size in wavelet transforms makes this procedure well suited for non stationary data we illustrate the working of this method through the analysis of binomial multifractal model for this model our results compare well with those calculated analytically and obtained numerically through mf dfa to show the efficacy of this approach for finite data sets we also do the above comparison for gaussian white noise time series of different sizes in addition we analyze time series of three experimental data sets of tokamak plasma and also spin density fluctuations in 2d ising model

multifractal formalism for fractal signals the structure function approach versus the wavelet transform modulus maxima method several attempts have been made recently to generalize the multifractal formalism originally introduced for singular measures to fractal signals we report on a systematic comparison between the structure function approach pioneered by parisi and frisch in 2 proceedings of the international school on turbulence and predictability in geophysical fluid dynamics and climate dynamics edited by m ghil r benzi and g parisi north holland amsterdam 1985 p 84 to account for the multifractal nature of fully developed turbulent signals and an alternative method we have developed within the framework of the wavelet transform analysis we comment on the intrinsic limitations of the structure function approach this technique has fundamental drawbacks and does not provide a full characterization of the singularities of a signal in many cases we demonstrate that our method based on the wavelet transform modulus maxima representation works in most situations and is likely to be the ground of a unified multifractal description of self affine distributions our theoretical considerations are both illustrated on pedagogical examples and supported by numerical simulations

wavelet transform of multifractals we present the wavelet transform as a mathematical microscope which is well suited for studying the local scaling properties of fractal objects we apply this technique to probability measures on self similar cantor sets and to the golden mean trajectories on two tori at the onset of chaos

three layer granular structures and three way informational measures of a decision table abstract attribute reduction in rough set theory serves as a fundamental topic for information processing and its basis is usually a decision table d table d table attribute reduction concerns three hierarchical types and only classification based reduction is related to information theoretic representation aiming at inducing comprehensive d table attribute reduction with hierarchies and information this paper concretely constructs a d table s three layer granular structures and three way informational measures via granular computing and bayes theorem with regard to the d table the micro bottom meso middle and macro top are hierarchically organized according to the formal structure and systematic granularity then different layers produce different three way informational measures by developing bayes theorem thus three way weighted entropies originate from three way probabilities at the micro bottom and further evolve from the meso middle to the macro top and their granulation monotonicity and evolution systematicness are acquired furthermore three way informational measures are analyzed by three layer granular structures to achieve their hierarchical evolution superiority and algorithms finally structural and informational results are effectively illustrated by a d table example this study establishes d table s hierarchical structures to reveal constructional mechanisms and systematic relationships of informational measures the obtained results underlie the d table s hierarchical systematic and informational attribute reduction and they also enrich the three way decisions theory

dynamics of coupled nonlinear maps and its application to ecological modeling this paper investigates the behavior of coupled nonlinear dynamical systems we take two such dynamical systems or units couple them together and study the effect of coupling on the dynamics we demonstrate that coupling two chaotic units can indeed stabilize both of them several results describing the global dynamics of the coupled nonlinear system are established using them we show that by and large the presence of coupling appears to increase the orderliness of the coupled system s response producing periodicity synchronicity and quasi symmetry using exponential maps which are commonly used to simulate population dynamics we establish the applicability of our results to population dynamics

quantitative information architecture granular computing and rough set models in the double quantitative approximation space of precision and grade because precision and grade act as fundamental quantitative information in approximation space they are used in relative and absolute quantifications respectively at present the double quantification regarding precision and grade is a novel and valuable subject but quantitative information fusion has become a key problem thus this paper constructs the double quantitative approximation space of precision and grade pg approx space and tackles the fusion problem using normal logical operations it further conducts double quantification studies on granular computing and rough set models 1 first for quantitative information organization and storage we construct space and plane forms of pg approx space using the cartesian product and for quantitative information extraction and fusion we establish semantics construction and semantics granules of pg approx space 2 second by granular computing we investigate three primary granular issues quantitative semantics complete system and optimal calculation accordingly six types of fundamental granules are proposed based on the semantic microscopic and macroscopic descriptions their semantics forms structures calculations and relationships are studied and the granular hierarchical structure is achieved 3 finally we investigate rough set models in pg approx space accordingly model regions are proposed by developing the classical regions model expansion is systematically analyzed some models are constructed as their structures are obtained and a concrete model is provided based on the quantitative information architecture this paper systematically conducts and investigates double quantification and establishes a fundamental and general exploration framework

reduction and axiomization of covering generalized rough sets this paper investigates some basic properties of covering generalized rough sets and their comparison with the corresponding ones of pawlak s rough sets a tool for data mining the focus here is on the concepts and conditions for two coverings to generate the same covering lower approximation or the same covering upper approximation the concept of reducts of coverings is introduced and the procedure to find a reduct for a covering is given it has been proved that the reduct of a covering is the minimal covering that generates the same covering lower approximation or the same covering upper approximation so this concept is also a technique to get rid of redundancy in data mining furthermore it has been shown that covering lower and upper approximations determine each other finally a set of axioms is constructed to characterize the covering lower approximation operation

thermodynamics of fractal spectra cantor sets and quasiperiodic sequences we study the properties of the specific heat derived from fractal spectra for which we extend and generalize some previous known results concerning the log periodic oscillations of the specific heat c t for the monoscale case we obtain analytically the behavior of c t for a two branch general spectrum and we show that the oscillatory regime becomes nonharmonic if there exist different gap sizes in the multiscale case we connect the role of the spectral dimension as the average value of c t with the multifractal properties of the sets and we give a condition for which the oscillatory regime disappears finally we study the thermodynamics of tight binding fibonacci spectra which are not strictly invariant under changes of scale and then many of the properties found in cantor sets become in this case just approximated

scaling of the distribution of fluctuations of financial market indices up to more than one month we find that the distributions for dt 4d 1560 min are consistent with a power law asymptotic behavior characterized by an exponent a 3 well outside the stable levy regime 0 a 2 to test the robustness of the s p result we perform a parallel analysis on two other financial market indices database iv contains 3560 daily records of the nikkei index for the 14 year period 1984 1997 and database v contains 4649 daily records of the hang seng index for the 18 year period 1980 1997 we find estimates ofa consistent with those describing the distribution of s p 500 daily returns one possible reason for the scaling of these distributions is the long persistence of the autocorrelation function of the volatility for time scales longer than dt 3 4 d our results are consistent with a slow convergence to gaussian behavior s1063 651x 99 11211 x pacs number s 05 40 fb 05 45 tp 89 90 1n

specific heat properties of electrons in generalized fibonacci quasicrystals abstract the purpose of this paper is to investigate the specific heat properties of electrons in one dimensional quasiperiodic potentials arranged in accordance with the generalized fibonacci sequence the electronic energy spectra are calculated using the one dimensional schrodinger equation in a tight binding approximation both analytical and numerical results on the temperature dependence of the electron s specific heat associated with their multiscale fractal energy spectra are presented we compare our numerical results with those found for the ordinary fibonacci structure a rich and varied behavior is found for the specific heat oscillations when t 0 with interesting physical consequences

decision theoretic rough fuzzy set model and application this article investigates the rough approximation of a fuzzy concept on a probabilistic approximation space we propose the probabilistic rough fuzzy set by defining the conditional probability of a fuzzy event then we establish the model of probabilistic rough fuzzy set and discuss several properties in detail furthermore three generalizations of probabilistic rough fuzzy set namely 0 5 probabilistic rough fuzzy set variable precision probabilistic rough fuzzy set and bayesian rough fuzzy set are reported in order to give a systematic method of selecting parameters for the probabilistic rough fuzzy set we propose a decision theoretic rough fuzzy set that is we formulate a non parametric definition of the probabilistic rough fuzzy set moreover we illustrate the motivation and verify the validity of the decision theoretic rough fuzzy set by using a credit card applicant decision making problem furthermore the interrelationship between the decision theoretic rough fuzzy set and the probabilistic rough fuzzy set is explained the main contribution of this paper is twofold one is to extend the probabilistic rough set to fuzzy environment i e the probabilistic rough fuzzy set model another is to present an approach to select parameters needed in probabilistic rough fuzzy set modeling by using the process of decision making under conditions of risk

relationship among basic concepts in covering based rough sets uncertainty and incompleteness of knowledge are widespread phenomena in information systems rough set theory is a tool for dealing with granularity and vagueness in data analysis rough set method has already been applied to various fields such as process control economics medical diagnosis biochemistry environmental science biology chemistry psychology and conflict analysis covering based rough set theory is an extension to classical rough sets in covering based rough sets there exist several basic concepts such as reducible elements of a covering minimal descriptions unary coverings and the property that the intersection of any two elements is the union of finite elements in this covering these concepts appeared in the literature of covering based rough sets separately in this paper we study the relationships between them in particular we establish the equivalence of the unary covering and the covering with the property that the intersection of any two elements is the union of finite elements in this covering we also investigate the relationship between the covering lower approximation operation and the interior operator a characterization of the interior operator by the covering lower approximation operation is presented in this paper correspondingly we study the relationship between the covering upper approximation operation and the closure operator in addition we explore the conditions under which the covering upper approximation operation is monotone the study of the relationships between these concepts will help us have a better understanding of covering based rough sets

three way decisions with probabilistic rough sets the rough set theory approximates a concept by three regions namely the positive boundary and negative regions rules constructed from the three regions are associated with different actions and decisions which immediately leads to the notion of three way decision rules a positive rule makes a decision of acceptance a negative rule makes a decision of rejection and a boundary rule makes a decision of abstaining this paper provides an analysis of three way decision rules in the classical rough set model and the decision theoretic rough set model the results enrich the rough set theory by ideas from bayesian decision theory and hypothesis testing in statistics the connections established between the levels of tolerance for errors and costs of incorrect decisions make the rough set theory practical in applications

the superiority of three way decisions in probabilistic rough set models three way decisions provide a means for trading off different types of classification error in order to obtain a minimum cost ternary classifier this paper compares probabilistic three way decisions probabilistic two way decisions and qualitative three way decisions of the standard rough set model it is shown that under certain conditions when considering the costs of different types of miss classifications probabilistic three way decisions are superior to the other two

effect of nonstationarities on detrended fluctuation analysis detrended fluctuation analysis dfa is a scaling analysis method used to quantify long range power law correlations in signals many physical and biological signals are noisy heterogeneous and exhibit different types of nonstationarities which can affect the correlation properties of these signals we systematically study the effects of three types of nonstationarities often encountered in real data specifically we consider nonstationary sequences formed in three ways i stitching together segments of data obtained from discontinuous experimental recordings or removing some noisy and unreliable parts from continuous recordings and stitching together the remaining parts a cutting procedure commonly used in preparing data prior to signal analysis ii adding to a signal with known correlations a tunable concentration of random outliers or spikes with different amplitudes and iii generating a signal comprised of segments with different properties e g different standard deviations or different correlation exponents we compare the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types of nonstationarities we find that introducing nonstationarities to stationary correlated signals leads to the appearance of crossovers in the scaling behavior and we study how the characteristics of these crossovers depend on a the fraction and size of the parts cut out from the signal b the concentration of spikes and their amplitudes c the proportion between segments with different standard deviations or different correlations and d the correlation properties of the stationary signal we show how to develop strategies for preprocessing raw data prior to analysis which will minimize the effects of nonstationarities on the scaling properties of the data and how to interpret the results of dfa for complex signals with different local characteristics

covering based rough set approximations we propose a framework for the study of covering based rough set approximations three equivalent formulations of the classical rough sets are examined by using equivalence relations partitions and s algebras respectively they suggest the element based the granule based and the subsystem based definitions of approximation operators covering based rough sets are systematically investigated by generalizing these formulations and definitions a covering of universe of objects is used to generate different neighborhood operators neighborhood systems coverings and subsystems of the power set of the universe they are in turn used to define different types of generalized approximation operators within the proposed framework we review and discuss covering based approximation operators according to the element granule and subsystem based definitions

difference in nature of correlation between nasdaq and bse indices abstract we apply a recently developed wavelet based approach to characterize the correlation and scaling properties of non stationary financial time series this approach is local in nature and it makes use of wavelets from the daubechies family for detrending purpose the built in variable windows in wavelet transform makes this procedure well suited for the non stationary data we analyze daily price of nasdaq composite index for a period of 20 years and bse sensex index over a period of 15 years it is found that the long range correlation as well as fractal behavior for both the stock index values differ from each other significantly strong non statistical long range correlation is observed in bse index whose removal revealed a gaussian random noise character for the corresponding fluctuation the nasdaq index on the other hand showed a multifractal behavior with long range statistical correlation

comparison of multifractal and thermodynamical properties of fractal and natural spectra in this paper we explain the multifractal and thermodynamical properties of deterministic fractal spectra and compare the most relevant behaviors with those obtained for some natural spectra with multifractal properties in particular we compare the heat capacity c t derived from cantor set type spectra with the ones obtained from several atomic spectra we nd that although many of the properties of deterministic fractals previously reported are also reproduced in natural fractals oscillations of c t in log scale new features appear in the natural case the mean value of c t is not always related to the multifractal properties and the oscillations are present in cases for which they disappear in deterministic fractals c 2000 elsevier science b v all rights reserved

spectral fluctuation characterization of random matrix ensembles through wavelets a recently developed wavelet based approach is employed to characterize the scaling behaviour of spectral fluctuations of random matrix ensembles as well as complex atomic systems our study clearly reveals anti persistent behaviour and supports the fourier power spectral analysis it also finds evidence for multi fractal nature in the atomic spectra the multi resolution and localization nature of the discrete wavelets ideally characterizes the fluctuations in these time series some of which are not stationary

positive approximation an accelerator for attribute reduction in rough set theory feature selection is a challenging problem in areas such as pattern recognition machine learning and data mining considering a consistency measure introduced in rough set theory the problem of feature selection also called attribute reduction aims to retain the discriminatory power of original features many heuristic attribute reduction algorithms have been proposed however quite often these methods are computationally time consuming to overcome this shortcoming we introduce a theoretic framework based on rough set theory called positive approximation which can be used to accelerate a heuristic process of attribute reduction based on the proposed accelerator a general attribute reduction algorithm is designed through the use of the accelerator several representative heuristic attribute reduction algorithms in rough set theory have been enhanced note that each of the modified algorithms can choose the same attribute reduct as its original version and hence possesses the same classification accuracy experiments show that these modified algorithms outperform their original counterparts it is worth noting that the performance of the modified algorithms becomes more visible when dealing with larger data sets

rough fuzzy functions in classification this paper generalizes the concept of rough membership functions in pattern classification tasks to rough fuzzy membership functions and rough fuzzy ownership functions unlike the rough membership value of a pattern which is sensitive only towards the rough uncertainty associated with the pattern the rough fuzzy membership or ownership value of the pattern signifies the rough uncertainty as well as the fuzzy uncertainty associated with the pattern in this paper various set theoretic properties of the rough fuzzy functions are exploited to characterize the concept of rough fuzzy sets these properties are also used to measure the rough fuzzy uncertainty associated with the given output class finally a few possible applications of the rough fuzzy functions are mentioned

approaches to knowledge reduction of covering decision systems based on information theory in this paper we propose some new approaches for attribute reduction in covering decision systems from the viewpoint of information theory firstly we introduce information entropy and conditional entropy of the covering and define attribute reduction by means of conditional entropy in consistent covering decision systems secondly in inconsistent covering decision systems the limitary conditional entropy of the covering is proposed and attribute reductions are defined and finally by the significance of the covering some algorithms are designed to compute all the reducts of consistent and inconsistent covering decision systems we prove that their computational complexity are polynomial numerical tests show that the proposed attribute reductions accomplish better classification performance than those of traditional rough sets in addition in traditional rough set theory mibark algorithm g y wang h hu d yang decision table reduction based on conditional information entropy chinese j comput 25 2002 1 8 cannot ensure the reduct is the minimal attribute subset which keeps the decision rule invariant in inconsistent decision systems here we solve this problem in inconsistent covering decision systems

a multi objective decision making model with fuzzy rough coefficients and its application to the inventory problem in this paper we concentrate on developing a fuzzy rough multi objective decision making model according to uncertainty theory we present some equivalent models and a traditional algorithm based on an interactive fuzzy satisfying method which is similar to the interactive fuzzy rough satisfying method in order to obtain a satisfying solution for the decision maker in addition the technique of fuzzy rough simulation is applied to deal with general fuzzy rough objective functions and fuzzy rough constraints which are usually difficult to convert into their equivalents furthermore combined with the techniques of fuzzy rough simulation a genetic algorithm using the compromise approach is designed for solving a fuzzy rough multi objective programming problem finally a model is applied to an inventory problem to illustrate the usefulness of the proposed model and algorithm and then a sensitivity analysis is made

approaches to knowledge reduction based on variable precision rough set model this paper deals with approaches to knowledge reduction based on variable precision rough set model the concepts of lower distribution reduct and upper distribution reduct based on variable precision rough sets vprs are first introduced their equivalent definitions are then given and the relationships among lower and upper distribution reducts and alternative types of knowledge reduction in inconsistent systems are investigated it is proved that for some special thresholds lower distribution reduct is equivalent to the maximum distribution reduct whereas upper distribution reduct is equivalent to the possible reduct the judgement theorems and discernibility matrices associated with the lower and upper distribution reducts are also established from which we can obtain the approaches to knowledge reduction in vprs