modeling the searching behavior of social monkeys we discuss various features of the trajectories of spider monkeys lookingfor food in a tropical forest as observed recently in an extensive in situ study some of the features observed can be interpreted as the result of social interactions in addition a simple model of deterministic walk in a random environment reproduces the observed angular correlations between successive steps and in some cases the emergence of l evy distributions for the length of the steps c

approach to an irregular time series on the basis of the fractal theory we present a technique to measure the fractal dimension of the set of points t f t forming the graph of a function f defined on the unit interval first we apply it to a fractional brownian function 1 which has a property of self similarity for all scales and we can get the stable and precise fractal dimension this technique is also applied to the observational data of natural phenomena it does not show self similarity all over the scale but has a different self similarity across the characteristic time scale the present method gives us a stable characteristic time scale as well as the fractal dimension

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

statistical properties of daily ensemble variables in the chinese stock markets abstract we study dynamical behavior of the chinese stock markets by investigating the statistical properties of daily ensemble return and variety defined respectively as the mean and the standard deviation of the ensemble daily price return of a portfolio of stocks traded in china s stock markets on a given day the distribution of the daily ensemble return has an exponential form in the center and power law tails while the variety distribution is lognormal in the bulk followed by a power law tail for large variety based on detrended fluctuation analysis r s analysis and modified r s analysis we find evidence of long memory in the ensemble return and strong evidence of long memory in the evolution of variety

a wavelet based joint estimator of the parameters of long range dependence a joint estimator is presented for the two parameters that define the long range dependence phenomenon in the simplest case the estimator is based on the coefficients of a discrete wavelet decomposition improving a wavelet based estimator of the scaling parameter abry and veitch 1998 as well as extending it to include the associated power parameter an important feature is its conceptual and practical simplicity consisting essentially in measuring the slope and the intercept of a linear fit after a discrete wavelet transform is performed a very fast o n operation under well justified technical idealizations the estimator is shown to be unbiased and of minimum or close to minimum variance for the scale parameter and asymptotically unbiased and efficient for the second parameter through theoretical arguments and numerical simulations it is shown that in practice even for small data sets the bias is very small and the variance close to optimal for both parameters closed form expressions are given for the covariance matrix of the estimator as a function of data length and are shown by simulation to be very accurate even when the technical idealizations are not satisfied comparisons are made against two maximum likelihood estimators in terms of robustness and computational cost the wavelet estimator is found to be clearly superior and statistically its performance is comparable we apply the tool to the analysis of ethernet teletraffic data completing an earlier study on the scaling parameter alone

tensor product of quantum logics a quantum logic is the couple l m where l is an orthomodular lattice and m is a strong set of states on l the jauch piron property in the form is also supposed for any state of m a tensor product of quantum logics is defined this definition is compared with the definition of a free orthodistributive product of orthomodular lattices the existence and uniqueness of the tensor product in special cases of hilbert space quantum logics and one quantum and one classical logic are studied

optimal cycles for low dissipation heat engines we consider the optimization of a finite time carnot engine characterized by small dissipations we bound the power with a simple inequality and show that the optimal strategy is to perform small cycles around a given working point which can be thus chosen optimally remarkably this optimal point is independent of the figure of merit combining power and efficiency that is being maximized furthermore for a general class of dissipative dynamics the maximal power output becomes proportional to the heat capacity of the working substance since the heat capacity can scale supraextensively with the number of constituents of the engine this enables us to design optimal many body carnot engines reaching maximum efficiency at finite power per constituent in the thermodynamic limit

a connection between distributivity and locality in compound p lattices a p lattice is a complete orthomodular atomic lattice l which is formed by the set of propositions of a physical system a composition of physical systems is considered and some concept of locality in a compound physical system is represented in terms of p lattices we give a remark toward necessary and sufficient conditions for it to hold which have been provided implicitly in antecedent studies and we show that it can be provided under weaker conditions

detrending moving average algorithm for multifractals the detrending moving average dma algorithm is a widely used technique to quantify the long term correlations of nonstationary time series and the long range correlations of fractal surfaces which contains a parameter ensuremath theta determining the position of the detrending window we develop multifractal detrending moving average mfdma algorithms for the analysis of one dimensional multifractal measures and higher dimensional multifractals which is a generalization of the dma method the performance of the one dimensional and two dimensional mfdma methods is investigated using synthetic multifractal measures with analytical solutions for backward ensuremath theta 0 centered ensuremath theta 0 5 and forward ensuremath theta 1 detrending windows we find that the estimated multifractal scaling exponent ensuremath tau q and the singularity spectrum f ensuremath alpha are in good agreement with the theoretical values in addition the backward mfdma method has the best performance which provides the most accurate estimates of the scaling exponents with lowest error bars while the centered mfdma method has the worse performance it is found that the backward mfdma algorithm also outperforms the multifractal detrended fluctuation analysis the one dimensional backward mfdma method is applied to analyzing the time series of shanghai stock exchange composite index and its multifractal nature is confirmed

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

comparison of detrending methods for fluctuation analysis abstract we examine several recently suggested methods for the detection of long range correlations in data series based on similar ideas as the well established detrended fluctuation analysis dfa in particular we present a detailed comparison between the regular dfa and two recently suggested methods the centered moving average cma method and a modified detrended fluctuation analysis mdfa we find that cma performs the same as dfa in long data with weak trends and is slightly superior to dfa in short data with weak trends when comparing standard dfa to mdfa we observe that dfa performs slightly better in almost all examples we studied we also discuss how several types of trends affect different types of dfa for weak trends in the data the new methods are comparable with dfa in these respects however if the functional form of the trend in data is not a priori known dfa remains the method of choice only a comparison of dfa results using different detrending polynomials yields full recognition of the trends a comparison with independent methods is recommended for proving long range correlations

golden mean arithmetic in the fractal branching of diffusion limited aggregates we use the wavelet transform microscope to explore the intricate fractal geometry of witten and sander s diffusion limited aggregates we report on the discovery of fibonacci sequences in the internal hierarchical structure of these clusters we discuss the relevance of the golden mean arithmetic to the numerically well established statistical self similarity of these aggregates

coefficient of performance and its bounds for general refrigerators with nonisothermal processes an analysis of the coefficient of performance cop and its bounds at maximum figure of merit for refrigerators is conducted and the heat transfer processes are described using newton s law of cooling with a time dependent heat conductance the upper bound of the cop is independent of the time duration completing either process or the heat conductance the optimal temperature profiles in the heat exchanging processes are analyzed under different dimensionless contact time limits provided the dimensionless contact times satisfy certain relations the endoreversible model is recovered furthermore numerical calculations are conducted to investigate the effect of different heat conductances on temperature profiles under the maximum criterion this work can guide design and operation of actual refrigerators

the thermodynamics of fractals revisited with wavelets abstract the multifractal formalism originally introduced to describe statistically the scaling properties of singular measures is revisited using the wavelet transform this new approach is based on the definition of partition functions from the wavelet transform modulus maxima we demonstrate that very much like thermodynamic functions the generalized fractal dimensions d q and the f singularity spectrum can be readily determined from the scaling behavior of these partition functions we show that this method provides a natural generalization of the classical box counting techniques to fractal signals the wavelets playing the role of generalized boxes we illustrate our theoretical considerations on pedagogical examples e g devil s staircases and fractional brownian motions we also report the results of some recent application of the wavelet transform modulus maxima method to fully developed turbulence data that we emphasize the wavelet transform as a mathematical microscope that can be further used to extract microscopic informations about the scaling properties of fractal objects in particular we show that a dynamical system which leaves invariant such an object can be uncovered form the space scale arrangement of its wavelet transform modulus maxima we elaborate on a wavelet based tree matching algorithm that provides a very promising tool for solving the inverse fractal problem this step towards a statistical mechanics of fractals is illustrated on discrete period doubling dynamical systems where the wavelet transform is shown to reveal the renormalization operation which is essential to the understanding of the universal properties of this transition to chaos finally we apply our technique to analyze the fractal hierarchy of dla azimuthal cantor sets defined by intersecting the inner frozen region of large mass off lattice diffusion limited aggregates dla wit a circle this study clearly lets out the existence of an underlying multiplicative process that is likely to account for the fibonacci structural ordering recently discovered in the apparently disordered arborescent dla morphology

low dissipation carnot like heat engines at maximum efficient power we study the optimal performance of carnot like heat engines working in the low dissipation regime using the product of the efficiency and the power output also known as the efficient power as our objective function efficient power function represents a trade off between power and efficiency of a heat engine we find lower and upper bounds on the efficiency in the case of extreme asymmetric dissipation when the ratio of dissipation coefficients at the cold and the hot contacts approaches respectively zero or infinity in addition we obtain the form of efficiency for the case of symmetric dissipation we also discuss the universal features of efficiency at maximum efficient power and derive the bounds on the efficiency using a global linear irreversible framework introduced recently by one of the authors

estimation of fractal signals from noisy measurements using wavelets the role of the wavelet transformation as a whitening filter for 1 f processes is exploited to address problems of parameter and signal estimations for 1 f processes embedded in white background noise robust computationally efficient and consistent iterative parameter estimation algorithms are derived based on the method of maximum likelihood and cramer rao bounds are obtained included among these algorithms are optimal fractal dimension estimators for noisy data algorithms for obtaining bayesian minimum mean square signal estimates are also derived together with an explicit formula for the resulting error these smoothing algorithms find application in signal enhancement and restoration the parameter estimation algorithms find application in signal enhancement and restoration the parameter estimation algorithms in addition to solving the spectrum estimation problem and to providing parameters for the smoothing process are useful in problems of signal detection and classification results from simulations are presented to demonstrated the viability of the algorithms

universality of efficiency at unified trade off optimization we calculate the efficiency at the unified trade off optimization criterion the so called maximum criterion representing a compromise between the useful energy and the lost energy of heat engines operating between two reservoirs at different temperatures and chemical potentials and demonstrate that the linear coefficient 3 4 and quadratic coefficient 1 32 of the efficiency at maximum are universal for heat engines under strong coupling and symmetry conditions it is further proved that the conclusions obtained here also apply to the ecological optimization criterion

ecological optimization and coefficient of performance bounds of general refrigerators abstract an analysis of cop and its bounds at maximum ecological criterion for general refrigerators is conducted for generality both the non isothermal heat transfer processes and the internal dissipations are considered under different situations the cop under the maximum ecological criterion have been studied systematically and the general upper and lower bounds of the optimal cop have been obtained furthermore under maximum ecological criterion the cop of general endoreversible refrigerators have also been studied and the cop bounds of different kinds of refrigerators have been analyzed as actual refrigerators may not operate under the condition of maximum cop or maximum cooling load but operate under the maximum ecological condition which indicates the best compromise between the refrigeration rate and the loss of refrigeration rate this paper could provide a practical insight for designing and operating actual refrigerators

correlation structure of the discrete wavelet coefficients of fractional brownian motion it is shown that the discrete wavelet coefficients of fractional brownian motion at different scales are correlated and that their auto and cross correlation functions decay hyperbolically fast at a rate much faster than that of the autocorrelation of the fractional brownian motion itself the rate of decay of the correlation function in the wavelet domain is primarily determined by the number of vanishing moments of the analyzing wavelet

minimal dissipation in processes far from equilibrium a central goal of thermodynamics is to identify optimal processes during which the least amount of energy is dissipated into the environment generally even for simple systems such as the parametric harmonic oscillator optimal control strategies are mathematically involved and contain peculiar and counterintuitive features we show that optimal driving protocols determined by means of linear response theory exhibit the same step and ensuremath delta peak like structures that were previously found from solving the full optimal control problem however our method is significantly less involved since only a minimum of a quadratic form has to be determined in addition our findings suggest that optimal protocols from linear response theory are applicable far outside their actual range of validity

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

locality and orthomodular structure of compound systems a p lattice is defined as a complete orthomodular atomic lattice l which is formed by the set of propositions of a physical system a composition of physical systems in the framework of p lattices is considered and some notions of locality are given it is shown that the following statements about compound systems are equivalent a all atoms of a compound system are reducible to those of its subsystems b all pure states of a compound system are separable into those of its subsystems c a compound system has statistical property independence d at least one of the subsystems is classical e bell type inequalities hold

heat engines at optimal power low dissipation versus endoreversible model the low dissipation model and the endoreversible model of heat engines are two of the most commonly studied models of machines in finite time thermodynamics in this paper we compare the performance characteristics of these two models under optimal power output we point out a basic equivalence between them in the linear response regime

optimization induced by stability and the role of limited control near a steady state a relationship between stability and self optimization is found for weakly dissipative heat devices the effect of limited control on operation variables around an steady state is such that after instabilities the paths toward relaxation are given by trajectories stemming from restitution forces which improve the system thermodynamic performance power output efficiency and entropy generation statistics over random trajectories for many cycles shows this behavior as well two types of dynamics are analyzed one where an stability basin appears and another one where the system is globally stable under both dynamics there is an induced trend in the control variables space due to stability in the energetic space this behavior translates into a preference for better thermodynamic states and thus stability could favor self optimization under limited control this is analyzed from the multiobjective optimization perspective as a result the statistical behavior of the system is strongly influenced by the pareto front the set of points with the best compromise between several objective functions and the stability basin additionally endoreversible and irreversible behaviors appear as very relevant limits the first one is an upper bound in energetic performance connected with the pareto front and the second one represents an attractor for the stochastic trajectories

fractional brownian motion a maximum likelihood estimator and its application to image texture fractals have been shown to be useful in characterizing texture in a variety of contexts use of this methodology normally involves measurement of a parameter h which is directly related to fractal dimension in this work the basic theory of fractional brownian motion is extended to the discrete case it is shown that the power spectral density of such a discrete process is only approximately proportional to f a instead of in direct proportion as in the continuous case an asymptotic cramer rao bound is derived for the variance of an estimate of h subsequently a maximum likelihood estimator mle is developed to estimate h it is shown that the variance of this estimator nearly achieves the minimum bound a generation algorithm for discrete fractional motion is presented and used to demonstrate the capabilities of the mle when the discrete fractional brownian process is contaminated with additive gaussian noise the results show that even at signal to noise ratios of 30 db significant errors in estimation of h can result when noise is present the mle is then applied to x ray images of the human calcaneus to demonstrate how the line to line formulation can be applied to the two dimensional case these results indicate that it has strong potential for quantifying texture

determination of the hurst exponent by use of wavelet transforms we propose a method for global hurst exponent determination based on wavelets using this method we analyze synthetic data with predefined hurst exponents fracture surfaces and data from economy the results are compared to those obtained with fourier spectral analysis when many samples are available the wavelet and fourier methods are comparable in accuracy however when one or only a few samples are available the wavelet method outperforms the fourier method by a large margin

estimating performance of feynman s ratchet with limited information we estimate the performance of feynman s ratchet at given values of the ratio of cold to hot reservoir temperatures and the figure of merit efficiency in the case of engine and coefficienct of performance in the case of refrigerator the latter implies that only the ratio of two intrinsic energy scales is known to the observer but their exact values are completely uncertain the prior probability distribution for the uncertain energy parameters is argued to be jeffreys prior we define an average measure for performance of the model by averaging over the prior distribution the power output heat engine or the criterion refrigerator which is the product of rate of heat absorbed from the cold reservoir and the coefficient of performance cop we observe that the figure of merit at optimal performance close to equilibrium is reproduced by the prior averaging procedure further we obtain the well known expressions of finite time thermodynamics for the efficiency at optimal power and the cop at optimal criterion given by and respectively this analogy is explored further and we point out that the expected heat flow from and to the reservoirs behaves as an effective newtonian flow we also show in a class of quasi static models of quantum heat engines how curzon ahlborn efficiency emerges in asymptotic limit with the use of jeffreys prior

a quantum logical and geometrical approach to the study of improper mixtures we study improper mixtures from a quantum logical and geometrical point of view taking into account the fact that improper mixtures do not admit an ignorance interpretation and must be considered as states in their own right we do not follow the standard approach which considers improper mixtures as measures over the algebra of projections instead of it we use the convex set of states in order to construct a new lattice whose atoms are all physical states pure states and improper mixtures this is done in order to overcome one of the problems which appear in the standard quantum logical formalism namely that for a subsystem of a larger system in an entangled state the conjunction of all actual properties of the subsystem does not yield its actual state in fact its state is an improper mixture and cannot be represented in the von neumann lattice as a minimal property which determines all other properties as is the case for pure states or classical systems the new lattice also contains all propos

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

singularity spectrum of fractal signals from wavelet analysis exact results the multifractal formalism for singular measures is revisited using the wavelet transform for bernoulli invariant measures of some expanding markov maps the generalized fractal dimensions are proved to be transition points for the scaling exponents of some partition functions defined from the wavelet transform modulus maxima the generalization of this formalism to fractal signals is established for the class of distribution functions of these singular invariant measures it is demonstrated that the hausdorff dimensiond h of the set of singularities of holder exponenth can be directly determined from the wavelet transform modulus maxima the singularity spectrum so obtained is shown to be not disturbed by the presence in the signal of a superimposed polynomial behavior of ordern provided one uses an analyzing wavelet that possesses at leastn n vanishing moments however it is shown that ac behavior generally induces a phase transition in thed h singularity spectrum that somewhat masks the weakest singularities this phase transition actually depends on the numbern of vanishing moments of the analyzing wavelet its observation is emphasized as a reliable experimental test for the existence of nonsingular behavior in the considered signal these theoretical results are illustrated with numerical examples they are likely to be valid for a large class of fractal functions as suggested by recent applications to fractional brownian motions and turbulent velocity signals

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

estimation of farima parameters in the case of negative memory and stable noise in this paper we extend a method of estimation of parameters of the fractional autoregressive integrated moving average farima process with stable noise to the case of negative memory parameter d we construct an estimator that is a modification of that of kokoszka and taqqu and prove its consistency for 1 2 we show that the estimator is accurate and possesses a low variance for farima time series with both light and heavy tailed noises it is illustrated by means of monte carlo simulations finally we compare the introduced method of estimation of d with classical methods like the r s modified r s and variance the results show that the proposed estimator is vastly superior to them

coefficient of performance at maximum figure of merit and its bounds for low dissipation carnot like refrigerators the figure of merit for refrigerators performing finite time carnot like cycles between two reservoirs at temperature t h and t c t h is optimized it is found that the coefficient of performance at maximum figure of merit is bounded between 0 and sqrt 9 8e c 3 2 for the low dissipation refrigerators where e c t c t h t c is the carnot coefficient of performance for reversible refrigerators these bounds can be reached for extremely asymmetric low dissipation cases when the ratio between the dissipation constants of the processes in contact with the cold and hot reservoirs approaches to zero or infinity respectively the observed coefficients of performance for real refrigerators are located in the region between the lower and upper bounds which is in good agreement with our theoretical estimation

efficiency at and near maximum power of low dissipation heat engines a universality in optimization of trade off between power and efficiency for low dissipation carnot cycles is presented it is shown that any trade off measure expressible in terms of efficiency and the ratio of power to its maximum value can be optimized independently of most details of the dynamics and of the coupling to thermal reservoirs the result is demonstrated on two specific trade off measures the first one is designed for finding optimal efficiency for a given output power and clearly reveals diseconomy of engines working at maximum power as the second example we derive universal lower and upper bounds on the efficiency at maximum trade off given by the product of power and efficiency the results are illustrated on a model of a diffusion based heat engine such engines operate in the low dissipation regime given that the used driving minimizes the work dissipated during the isothermal branches the peculiarities of the corresponding optimization procedure are reviewed and thoroughly discussed

testing for the source of multifractality in water level records abstract the multifractality in hydrologic data has been studied in many literatures but few literatures focus on its source which is helpful for understanding the underlying mechanisms that generate hydrologic data we propose a hypothesis testing procedure for the source of multifractality in water level records based on the empirical distributions of generalized hurst exponent estimated from a set of shuffled or surrogate series the proposed hypothesis testing procedure can show more details about the source of multifractality than previous methods with some statistics especially about the effects of large and small fluctuations on multifractality the generalized hurst exponents are estimated via multifractal detrended fluctuation analysis the data set contains about two million high frequency water level records of a northern china river at its 10 observation stations the testing results show that the multifractality in water levels is mainly caused by nonlinear correlations in small fluctuations and linear correlations in small and large fluctuations and is also related to the probability distribution of small fluctuations this conclusion is validated via some constructed semi surrogate series and values of statistics for source testing

ignorance is a bliss mathematical structure of many box models we show that the propositional system of a many box model is always a set representable effect algebra in particular cases of 2 box and 1 box models it is an orthomodular poset and an orthomodular lattice respectively we discuss the relation of the obtained results with the so called local orthogonality principle we argue that non classical properties of box models are the result of a dual enrichment of the set of states caused by the impoverishment of the set of propositions on the other hand quantum mechanical models always have more propositions as well as more states than the classical ones consequently we show that the box models cannot be considered as generalizations of quantum mechanical models and seeking additional principles that could allow us to recover quantum correlations in box models are at least from the fundamental point of view pointless

the fractal energy measurement and the singularity energy spectrum analysis abstract the singularity exponent se is the characteristic parameter of fractal and multifractal signals based on se the fractal dimension reflecting the global self similar character the instantaneous se reflecting the local self similar character the multifractal spectrum mfs reflecting the distribution of se and the time varying mfs reflecting pointwise multifractal spectrum were proposed however all the studies were based on the depiction of spatial or differentiability characters of fractal signals taking the se as the independent dimension this paper investigates the fractal energy measurement fem and the singularity energy spectrum ses theory firstly we study the energy measurement and the energy spectrum of a fractal signal in the singularity domain propose the conception of fem and ses of multifractal signals and investigate the hausdorff measure and the local direction angle of the fractal energy element then we prove the compatibility between fem and traditional energy and point out that ses can be measured in the fractal space finally we study the algorithm of ses under the condition of a continuous signal and a discrete signal and give the approximation algorithm of the latter and the estimations of fem and ses of the gaussian white noise fractal brownian motion and the multifractal brownian motion show the theoretical significance and application value of fem and ses

structural five fold symmetry in the fractal morphology of diffusion limited aggregates abstract the statistical self similarity of the geometry of diffusion limited aggregates and the multifractal nature of the growth probability distribution on the surface of the growing clusters are investigated using the wavelet transform this study reveals the existence of a predominant structural five fold symmetry in the internal frozen region as well as in the active outer region of the interface this observation is corroborated by a statistical analysis of the screening effects that govern diffusion limited aggregation dla growth in linear and sector shaped cells the existence of this symmetry is likely to be a clue to a hierarchichal fractal ordering we report on the discovery of fibonacci sequences in the inner extinct region of large mass off lattice dla clusters with a branching ratio which converges asymptotically to the golden mean we suggest an interpretation of the dla morphology as a quasifractal counterpart of the well ordered snowflake fractal architecture

entropy generation and unified optimization of carnot like and low dissipation refrigerators the connection between carnot like and low dissipation refrigerators is proposed by means of their entropy generation and the optimization of two unified compromise based figures of merit their optimization shows that only a limited set of heat transfer laws in the carnot like model are compatible with the results stemming from the low dissipation approximation even though there is an agreement of the related physical spaces of variables a comparison between two operation regimes and relations among entropy generation efficiency cooling power and power input are obtained with emphasis on the role of dissipation symmetries the results extend previous findings for heat engines at maximum power conditions

optimal protocols for slowly driven quantum systems the design of efficient quantum information processing will rely on optimal nonequilibrium transitions of driven quantum systems building on a recently developed geometric framework for computing optimal protocols for classical systems driven in finite time we construct a general framework for optimizing the average information entropy for driven quantum systems geodesics on the parameter manifold endowed with a positive semidefinite metric correspond to protocols that minimize the average information entropy production in finite time we use this framework to explicitly compute the optimal entropy production for a simple two state quantum system coupled to a heat bath of bosonic oscillators which has applications to quantum annealing

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed