bandt pompe approach to the classical quantum transition abstract by regarding the celebrated classical quantum transition problem as one pertaining to the domain of dynamic systems theory we present a discussion that exhibits the superiority of the bandt pompe approach to the extraction of a probability distribution from time series values

handling borders in systolic architectures for the 1 d discrete wavelet transform for perfect reconstruction we propose a modified systolic architecture that implements the 1 d discrete wavelet transform dwt on the basis of the recursive pyramid algorithm rpa while correctly managing the border problem and obtaining perfect reconstruction all the architectures so far described in the literature do not explicitly address the handling of borders and usually assume a zero padding extension the rpa makes heavy use of this assumption which produces very efficient systolic architectures it is however well known that the zero padding extension does not allow perfect recovery of the original signal if we compute exactly n coefficients more coefficients are required either in the forward or in the inverse transform and their production within the rpa scheme lowers the efficiency of the systolic architecture to a minimum we introduce a modified rpa working on an extended transform with a compressed schedule that restores good values of efficiency ec rpa we also propose a second version of rpa based on a periodic extension of the signal and of the transform pe rpa that achieves perfect reconstruction by computing exactly n dwt coefficients a reduced version of the second algorithm r pe rpa is tailored to the efficient computations of a fixed number of levels in the transform the vlsi complexity of the management of borders is analyzed through synthesis from a vhdl description of the three algorithms synthesis results show that the controller required for pe rpa can be as large as a ten tap array r pe rpa instead requires half this area in both cases the controller complexity scales sublinearly with the length of the input

on the implementation of nonseparable two dimensional haar wavelet transforms we introduce a transformation to localize the equations defining the successive levels of the mallat 1989 pyramid for two dimensional 2 d haar wavelets we propose a methodology for implementing these wavelet transforms in parallel architectures like systolic arrays more specifically we show that there is a perfect match between the wavelet algorithms and the multiphase multirate array mpra architectures

simple measure for complexity a measure of complexity is proposed based on appropriately defined notions of order and disorder which has a considerable degree of flexibility in its dependence on these concepts the possible functional dependencies which result encompass those of many earlier definitions of complexity the proposed measure is in principle easy to calculate and has the property of an intensive thermodynamic quantity with appropriate choices of parameters it behaves similarly to effective measure complexity for the logistic map it is also a generalization of the normalized complexity of lopez ruiz et al but does not suffer from over universality

characterization of time dynamical evolution of electroencephalographic epileptic records abstract since traditional electrical brain signal analysis is mostly qualitative the development of new quantitative methods is crucial for restricting the subjectivity in the study of brain signals these methods are particularly fruitful when they are strongly correlated with intuitive physical concepts that allow a better understanding of the brain dynamics the processing of information by the brain is reflected in dynamical changes of the electrical activity in time frequency and space therefore the concomitant studies require methods capable of describing the qualitative variation of the signal in both time and frequency the entropy defined from the wavelet functions is a measure of the order disorder degree present in a time series in consequence this entropy evaluates over eeg time series gives information about the underlying dynamical process in the brain more specifically of the synchrony of the group cells involved in the different neural responses the total wavelet entropy results independent of the signal energy and becomes a good tool for detecting dynamical changes in the system behavior in addition the total wavelet entropy has advantages over the lyapunov exponents because it is parameter free and independent of the stationarity of the time series in this work we compared the results of the time evolution of the chaoticity lyapunov exponent as a function of time with the corresponding time evolution of the total wavelet entropy in two different eeg records one provide by depth electrodes and other by scalp ones

the recursive pyramid algorithm for the discrete wavelet transform the recursive pyramid algorithm rpa is a reformulation of the classical pyramid algorithm pa for computing the discrete wavelet transform dwt the rpa computes the n point dwt in real time running dwt using just l log n spl minus 1 words of storage as compared with o n words required by the pa l is the length of the wavelet filter the rpa is combined with the short length fir filter algorithms to reduce the number of multiplications and additions

tsallis deformation parameter q quantifies the classical quantum transition abstract we investigate the classical limit of a type of semiclassical evolution the pertinent system representing the interaction between matter and a given field on using tsallis q entropy as a quantifier of the ensuing dynamics we find that it not only appropriately describes the quantum classical transition but that the associated deformation parameter q itself characterizes the different regimes involved in the process detecting the most salient fine details of the changeover

fast algorithms for discrete and continuous wavelet transforms several algorithms are reviewed for computing various types of wavelet transforms the mallat algorithm 1989 the a trous algorithm and their generalizations by shensa the goal of this work is to develop guidelines for implementing discrete and continuous wavelet transforms efficiently and to compare the various algorithms obtained and give an idea of possible gains by providing operation counts most wavelet transform algorithms compute sampled coefficients of the continuous wavelet transform using the filter bank structure of the discrete wavelet transform although this general method is already efficient it is shown that noticeable computational savings can be obtained by applying known fast convolution techniques such as the fft fast fourier transform in a suitable manner the modified algorithms are termed fast because of their ability to reduce the computational complexity per computed coefficient from l to log l within a small constant factor for large filter lengths l for short filters smaller gains are obtained fast running fir finite impulse response filtering techniques allow one to achieve typically 30 savings in computations

brain electrical activity analysis using wavelet based informational tools ii tsallis non extensivity and complexity measures the processing of information by the brain is reflected in dynamical changes of the electrical activity in i time ii frequency and iii space therefore the concomitant studies require methods capable of describing the qualitative variation of the signal in both time and frequency the present work complements the efforts described in rosso et al physica a 313 2002 587 devoted to non extensive information measures a la tsallis here we show that the notion of complexity using 1 appropriate information theory tools adapted to a non extensive scenario and 2 scalp eeg data provides one with valuable insights into the dynamics of neural activity in particular using different complexity measures we detect the presence of states characterized by both order and maximal complexity

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

generalized boltzmann factors and the maximum entropy principle entropies for complex systems abstract we generalize the usual exponential boltzmann factor to any reasonable and potentially observable distribution function b e by defining generalized logarithms as inverses of these distribution functions we are led to a generalization of the classical boltzmann gibbs entropy s bg d e e b e ln b e to the expression s d e e 0 b e d x x which contains the classical entropy as a special case we show that this is the unique modification of entropy which is compatible with the maximum entropy principle for arbitrary non exponential distribution functions we demonstrate that this entropy has two important features first it describes the correct thermodynamic relations of the system and second the observed distributions are straightforward solutions to the jaynes maximum entropy principle with the ordinary not escort constraints tsallis entropy is recovered as a further special case

complete to overcomplete discrete wavelet transforms theory and applications a new transform is proposed that derives the overcomplete discrete wavelet transform odwt subbands from the critically sampled dwt subbands complete representation this complete to overcomplete dwt codwt has certain advantages in comparison to the conventional approach that performs the inverse dwt to reconstruct the input signal followed by the a spl grave trous or the lowband shift algorithm specifically the computation of the input signal is not required as a result the minimum number of downsampling operations is performed and the use of upsampling is avoided the proposed codwt computes the odwt subbands by using a set of prediction filter matrices and filtering and downsampling operators applied to the dwt this formulation demonstrates a clear separation between the single rate and multirate components of the transform this can be especially significant when the codwt is used in resource constrained environments such as resolution scalable image and video codecs to illustrate the applicability of the proposed transform in these emerging applications a new scheme for the transform calculation is proposed and existing coding techniques that benefit from its usage are surveyed the analysis of the proposed codwt in terms of arithmetic complexity and delay reveals significant gains as compared with the conventional approach

two fast architectures for the direct 2 d discrete wavelet transform we propose two architectures for the direct two dimensional 2 d discrete wavelet transform dwt the first one is based on a modified recursive pyramid algorithm mrpa and performs a nonstandard decomposition i e mallat s 1989 tree of an n spl times n image in approximately 2n sup 2 3 clock cycles ccs this result consistently speeds up other known architectures that commonly need approximately n sup 2 ccs furthermore the proposed architecture is simpler than others in terms of hardware complexity subsequently we show how symmetric anti symmetric properties of linear phase wavelet filter bases can be exploited in order to further reduce the vlsi area this is used to design a second architecture that provides one processing unit for each level of decomposition pipelined approach and performs a decomposition in approximately n sup 2 2 ccs in many practical cases even this architecture is simpler than general mrpa based devices having only one processing unit

tsallis entropy and cortical dynamics the analysis of eeg signals abstract we undertake the study of eeg signals by recourse to a wavelet based multiresolution analysis as adapted to an information measure scenario different information measures are employed it is shown that non extensive ones seem to be of particular usefulness

algorithms for scheduling a single machine to minimize the weighted number of late jobs this paper considers the problem of scheduling n jobs each having a processing time a due date and a weight on a single machine to minimize the weighted number of late jobs an o n log n algorithm is given for solving the linear programming problem obtained by relaxing the integrality constraints in a zero one programming formulation of the problem this linear programming lower bound is used in a reduction algorithm that eliminates jobs from the problem also a branch and bound algorithm that uses the linear programming lower bound is proposed computational results with branch and bound algorithms that use this and other lower bounds and with a dynamic programming algorithm for problems with up to 1000 jobs are given

nonextensive statistical mechanics and economics abstract ergodicity this is to say dynamics whose time averages coincide with ensemble averages naturally leads to boltzmann gibbs bg statistical mechanics hence to standard thermodynamics this formalism has been at the basis of an enormous success in describing among others the particular stationary state corresponding to thermal equilibrium there are however vast classes of complex systems which accommodate quite badly or even not at all within the bg formalism such dynamical systems exhibit in one way or another nonergodic aspects in order to be able to theoretically study at least some of these systems a formalism was proposed 14 years ago which is sometimes referred to as nonextensive statistical mechanics we briefly introduce this formalism its foundations and applications furthermore we provide some bridging to important economical phenomena such as option pricing return and volume distributions observed in the financial markets and the fascinating and ubiquitous concept of risk aversion one may summarize the whole approach by saying that bg statistical mechanics is based on the entropy s bg k i p i ln p i and typically provides exponential laws for describing stationary states and basic time dependent phenomena while nonextensive statistical mechanics is instead based on the entropic form s q k 1 i p i q q 1 with s 1 s bg and typically provides for the same type of description asymptotic power laws

the advanced oca for 2 d discrete periodized wavelet transformation we develop a novel computation method for the 2 d discrete periodized wavelet transformation dpwt the new algorithm is based on the operator correlation algorithm oca compared with the classical 2 d pyramid algorithm the new advanced operator correlation algorithm aoca has two major advantages it requires half the number of multiplications and can yield the same output snr with half the precision of the dpwt filter coefficients furthermore the modular structure of the adca makes it particularly suitable for a vlsi implementation

multivalued mappings in generalized chaos synchronization the onset of generalized synchronization of chaos in directionally coupled systems corresponds to the formation of a continuous mapping that enables one to persistently define the state of the response system from the trajectory of the drive system a recently developed theory of generalized synchronization of chaos deals only with the case where this synchronization mapping is a single valued function in this paper we explore generalized synchronization in a regime where the synchronization mapping can become a multivalued function specifically we study the properties of the multivalued mapping that occurs between the drive and response systems when the systems are synchronized with a frequency ratio other than one to one and address the issues of the existence and continuity of such mappings the basic theoretical framework underlying the considered synchronization regimes is then developed

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