equivalent continuous and discrete realizations of levy flights a model of one dimensional motion of an inertial particle abstract the paper is devoted to the relationship between the continuous markovian description of levy flights developed previously see e g i a lubashevsky truncated levy flights and generalized cauchy processes eur phys j b 82 2011 189 195 and references therein and their equivalent representation in terms of discrete steps of a wandering particle a certain generalization of continuous time random walks to simplify understanding the key points of the technique to be created our consideration is confined to the one dimensional model for continuous random motion of a particle with inertia its dynamics governed by stochastic self acceleration is described as motion on the phase plane x v comprising the position x and velocity v d x d t of the given particle a notion of random walks inside a certain neighborhood l of the line v 0 the x axis and outside it is developed it enables us to represent a continuous trajectory of particle motion on the plane x v as a collection of the corresponding discrete steps each of these steps matches one complete fragment of the velocity fluctuations originating and terminating at the boundary of l as demonstrated the characteristic length of particle spatial displacement is mainly determined by velocity fluctuations with large amplitude which endows the derived random walks along the x axis with the characteristic properties of levy flights using the developed classification of random trajectories a certain parameter free core stochastic process is constructed its peculiarity is that all the characteristics of levy flights similar to the exponent of the levy scaling law are no more than the parameters of the corresponding transformation from the particle velocity v to the related variable of the core process in this way the previously found validity of the continuous markovian model for all the regimes of levy flights is explained based on the obtained results an efficient single peak approximation is constructed in particular it enables us to calculate the basic characteristics of levy flights using the probabilistic properties of extreme velocity fluctuations and the shape of the most probable trajectory of particle motion within such extreme fluctuations

a generalized fluctuation dissipation theorem for the one dimensional diffusion process the langevin equation describes the time evolution of a real stationary process witht positivity reflection positivity originating in the axiomatic quantum field theory for this langevin equation a generalized fluctuation dissipation theorem is proved we shall obtain as its application a generalized fluctuation dissipation theorem for the one dimensional non linear diffusion process which presents one solution of ryogo kubo s problem in physics

advanced information of parity bits for decoding short linear block codes using the a algorithm the a algorithm for decoding linear block codes is known to be an efficient tree search method for decoding short linear block codes we propose to employ the early acquired information of some parity bits to speed up the tree search analysis for the number of required information bits for obtaining the parity bits is provided in addition two versions of the modified a algorithm which take advantage of the advanced information of parity bits are provided simulation results show that there is advantage in reducing the number of search tree edges in each proposed version as compared with two existing a algorithms which do not consider the early information of parity bits

statistical properties of a turbulent cascade abstract statistical properties of a turbulent cascade are evaluated by considering the joint probability distribution p 1 l1 2 l2 for two velocity increments 1 2 of different length scales l1 l2 we present experimental evidence that the conditional probability distribution p 2 l2 1 l1 obeys a chapman kolmogorov equation we evaluate the kramers moyal coefficient and show evidence that higher order coefficients vanish except for the drift and diffusion coefficient as a result the joint probability distributions obeys a fokker planck equation we calculate drift and diffusion coefficients and discuss their relationship to universal behaviour in the scaling region and to intermittency of the turbulent cascade

maximum likelihood soft decoding of binary block codes and decoders for the golay codes maximum likelihood soft decision decoding of linear block codes is addressed a binary multiple check generalization of the wagner rule is presented and two methods for its implementation one of which resembles the suboptimal forney chase algorithms are described besides efficient soft decoding of small codes the generalized rule enables utilization of subspaces of a wide variety thereby yielding maximum likelihood decoders with substantially reduced computational complexity for some larger binary codes more sophisticated choice and exploitation of the structure of both a subspace and the coset representatives are demonstrated for the 24 12 golay code yielding a computational gain factor of about 2 with respect to previous methods a ternary single check version of the wagner rule is applied for efficient soft decoding of the 12 6 ternary golay code

computationally efficient soft decision decoding of linear block codes based on ordered statistics soft decision decoding of a linear block code using the most reliable basis corresponding to each received word is investigated based either on probabilistic properties or on the structure of the code considered three improvements to the algorithm devised by fossorier and lin see ibid vol 41 no 9 p 1379 1396 1995 are presented these modifications allow large computation savings or significant decoding speedup with little error performance degradation first a reduced probabilistic list of codeword candidates is associated with order i reprocessing of a given code it results in a large reduction of the maximum number of computations with a very small degradation in performance then a probabilistic stopping criterion is introduced for order 0 reprocessing this new test significantly decreases the average number of computations when appropriately implemented finally the application of the algorithm to coset decoding is considered for u u v constructed codes in addition to the conventional coset decoding a new adaptive practically optimum coset decoding method is presented where at each reprocessing stage the number of surviving cosets decreases suboptimum closest coset decoding is also investigated it is shown that two stage decoding with the algorithm of fossorier and lin offers a large variety of choices since the reprocessing order of each stage can be determined independently

long range anticorrelations and non gaussian behavior of the heartbeat we find that the successive increments in the cardiac beat to beat interals of healthy subjects display scale invariant long range anticorrelations up to 10 4 heart beats furthermore we find that the histogram for the heartbeat intervals increments is well described by a l evy stable distribution for a group of subjects with severe heart disease we find that the distribution is unchanged but the long range correlations vanish therefore the different scaling behavior in health and disease must relate to the underlying dynamics of the heartbeat

efficient heuristic search algorithms for soft decision decoding of linear block codes efficient new algorithms are presented for maximum likelihood and suboptimal soft decision decoding algorithms for linear block codes the first algorithm ma improves the efficiency of the a decoding algorithm conducting the heuristic search through a code tree while exploiting code specific properties the second algorithm h reduces search space by successively estimating the cost of the minimum cost codeword with a fixed value at each of the most reliable and linearly independent components of the received message the third algorithm directed search finds the codeword closest to the received vector by exploring a continuous search space the strengths of these three algorithms are combined in a hybrid algorithm applied to the 128 64 the 256 131 and the 256 139 binary extended bose chaudhuri hocquenghem bch codes simulation results show that this hybrid algorithm can efficiently decode the 128 64 code for any signal to noise ratio with near optimal performance previously no practical decoder could have decoded this code with such a performance for all ranges of signal to noise ratio

a new adaptive two stage maximum likelihood decoding algorithm for linear block codes in this paper we propose a new two stage ts structure for computationally efficient maximum likelihood decoding mld of linear block codes with this structure near optimal mld performance can be achieved at low complexity through ts processing the first stage of processing estimates a minimum sufficient set mss of candidate codewords that contains the optimal codeword while the second stage performs optimal or suboptimal decoding search within the estimated mss of small size based on the new structure we propose a decoding algorithm that systematically trades off between the decoding complexity and the bounded block error rate performance a low complexity complementary decoding algorithm is developed to estimate the mss followed by an ordered algebraic decoding oad algorithm to achieve flexible system design since the size of the mss changes with the signal to noise ratio the overall decoding complexity adaptively scales with the quality of the communication link theoretical analysis is provided to evaluate the potential complexity reduction enabled by the proposed decoding structure

optimal soft decision block decoders based on fast hadamard transform an approach for efficient utilization of fast hadamard transform in decoding binary linear block codes is presented computational gain is obtained by employing various types of concurring codewords and memory reduction is also achieved by appropriately selecting rows for the generator matrix the availability of these codewords in general and particularly in some of the most frequently encountered codes is discussed

probability distributions for one component equations with multiplicative noise abstract systems described by equations involving both multiplicative and additive noise are common in nature examples include convection of a passive scalar field polymers in turbulent flow and noise in dye lasers in this paper the one component version of this problem is studied the steady state probability distribution is classified into two different types of behavior one class has power law tails and the other is of the form of an exponential to a power law the value of the power law exponent is determined analytically for models having colored gaussian noise it is found to only depend on the power spectrum of the noise at zero frequency when non gaussian noise is considered it is shown that stretched exponential tails are possible an intuitive understanding of the results is found and makes use of the lyapunov exponents for these systems

publisher s note stationary and dynamical properties of information entropies in nonextensive systems phys rev e 77 031133 2008 we have discussed dynamical properties of the tsallis entropy and the generalized fisher information in nonextensive systems described by the langevin model subjected to additive and multiplicative noise analytical expressions for the timedependent tsallis entropy and generalized fisher information have been obtained with the use of the q moment approach to the fokker planck equation developed in a previous study h hasegawa phys rev e 77 031133 2008 model calculations of the information entropies in response to an applied pulse and sinusoidal inputs have been presented

coset codes ii binary lattices and related codes for pt i see ibid vol 34 no 5 p 1123 51 1988 the family of barnes wall lattices including d sub 4 and e sub 8 of lengths n 2 sup n and their principal sublattices which are useful in constructing coset codes are generated by iteration of a simple construction called the squaring construction the closely related reed muller codes are generated by the same construction the principal properties of these codes and lattices are consequences of the general properties of iterated squaring constructions which also exhibit the interrelationships between codes and lattices of different lengths an extension called the cubing construction generates good codes and lattices of lengths n 3 2 sup n including the golay code and leech lattice with the use of special bases for 8 space another related construction generates the nordstrom robinson code and an analogous 16 dimensional nonlattice packing these constructions are represented by trellis diagrams that display their structure and interrelationships and that lead to efficient maximum likelihood decoding algorithms

decoding linear block codes using a priority first search performance analysis and suboptimal version an efficient maximum likelihood soft decision decoding algorithm for linear block codes using a generalized dijkstra s algorithm was proposed by han hartmann and chen 1993 we prove that this algorithm is efficient for most practical communication systems where the probability of error is less than 10 sup 3 by finding an upper bound of the computational effort of the algorithm a suboptimal decoding algorithm is also proposed the performance of this suboptimal decoding algorithm is within 0 25 db of the performance of an optimal decoding algorithm for the 104 52 binary extended quadratic residue code and within 0 5 db of the optimal performance for the 128 64 binary bch code respectively

reliability based soft decision decoding with multiple biases in this paper a new reliability based soft decision decoding algorithm is presented this algorithm repeatedly uses biased reliability values to construct the most reliable basis mrb as a result this new method makes use of multiple information sets in a stochastic way compared to previously proposed competitive approaches this new method produces a more efficient mrb reprocessing type algorithm to achieve near maximum likelihood decoding mld performance with a proper choice of the bias value it can be combined with any mrb reprocessing type algorithm and in each case a tight performance analysis can be derived

critical scale invariance in a healthy human heart rate we demonstrate the robust scale invariance in the probability density function pdf of detrended healthy human heart rate increments which is preserved not only in a quiescent condition but also in a dynamic state where the mean level of the heart rate is dramatically changing this scale independent and fractal structure is markedly different from the scale dependent pdf evolution observed in a turbulentlike cascade heart rate model these results strongly support the view that a healthy human heart rate is controlled to converge continually to a critical state

traveling salesman problem and tsallis statistics a generalization of the stochastic method of simulated annealing algorithm based on tsallis statistics is proposed this algorithm is considerably faster than the traditional ones in solving the traveling salesman problem acceptable solutions are found in fewer steps and higher temperatures than both the classical and the fast simulated annealings recent developments in solving np complete problems can be incorporated and improve the performance even more

bit level soft decision decoding of reed solomon codes a reed solomon decoder that makes use of bit level soft decision information is presented a reed solomon generator matrix that possesses a certain inherent structure in gf 2 is derived this structure allows the code to be represented as a union of cosets each coset being an interleaver of several binary bch codes such partition into cosets provides a clue for efficient bit level soft decision decoding two decoding algorithms are derived in the development of the first algorithm a memoryless channel is assumed making the value of this algorithm more conceptual than practical the second algorithm which is obtained as a modification of the first does account for channel memory and thus accommodates a bursty channel both decoding algorithms are in many cases orders of magnitude more efficient than conventional techniques

fractional generalized cauchy process this paper presents a fractional generalized cauchy process fgcp with an additive and a multiplicative gaussian white noise for describing subordinated anomalous fluctuations the fgcp displays intermittent dynamics on random time durations whose analytical representation is given by the ito over stochastic integral the associated probability density function is given by a generalized cauchy distribution at the stationary state a fractional feynman kac formula is utilized to show that weak ergodicity breaking of the fgcp depends on the existence of the subordinator and or the divergence of variance

asymptotic power law of moments in a random multiplicative process with weak additive noise it is well known that a random multiplicative process with weak additive noise generates a power law probability distribution it has recently been recognized that this process exhibits another type of power law the moment of the stochastic variable scales as a function of the additive noise strength we clarify the mechanism for this power law behavior of moments by treating a simple langevin type model both approximately and exactly and argue this mechanism is universal we also discuss the relevance of our findings to noisy on off intermittency and to singular spatio temporal chaos recently observed in systems of non locally coupled elements

low dimensional chaos in a driven damped nonlinear schro dinger equation abstract we study bifurcations of attractors in a driven damped nonlinear schrodinger equation which models nonlinear responses of a plasma driven by a rf field and a sequence of period doubling bifurcations is shown to lead to a chaotic attractor in a low dimensional subspace spanned by a soliton and long wavelength radiation

analogs of renormalization group transformations in random processes abstract we review the properties of a real space renormalization group transformation of the free energy including the existence of oscillatory terms multiplying the non analytic part of the free energy we then construct stochastic processes which incorporate into probability distributions the features of the free energy scaling equation the essential information is obtainable from the scaling equation and a direct solution for a probability is not necessary these random processes are shown to be generated directly from cantor sets in a spatial representation the ensuing random process exhibits a transition between gaussian and fractal behavior in the fractal regime the trajectories will in an average sense form self similar clusters in a temporal representation the random process exhibits a transition between an asymptotically constant renewal rate and fractal behavior the fractal regime represents a frozen state with only transient effects allowed and is related to charge transport in glasses

on a ast algorithms for decoding short linear block codes the a ast algorithm for decoding linear block codes is an efficient tree search method for decoding short linear block codes the information contained in the parity bits are potentially useful for reducing the edges needed in the tree search we propose to extract the information embedded in the parity bits by considering sums of parity bits which can be decided by part of the message bits analysis for the number of required message bits for obtaining sums of parity bits is provided the information contained in the parity bits can help to reduce the number of search tree edges

twofold fuzzy sets and rough sets some issues in knowledge representation abstract this paper deals with the representation of sets where the membership of some elements may be ill known rather than just a matter of degree as in a fuzzy set the notion of a twofold fuzzy set is introduced when the relevant information for determining the membership status is incomplete a twofold fuzzy set is made of a nested pair of fuzzy sets the one which gathers the elements which more or less necessarily belong and the one which gathers the elements which more or less possibly belong twofold fuzzy sets are compared from a frontal and from a semantical point of view with other proposals and particularly with the notion of a rough set recently introduced by pawlak set operations of twofold fuzzy sets are discussed and the cardinality of a twofold fuzzy set is defined twofold fuzzy relations are also introduced finally various applications of twofold fuzzy sets in knowledge representation are briefly discussed

a self organizing state space model a self organizing filter and smoother for the general nonlinear non gaussian state space model is proposed an expanded state space model is defined by augmenting the state vector with the unknown parameters of the original state space model the state of the augmented state space model and hence the state and the parameters of the original state space model are estimated simultaneously by either a non gaussian filter smoother or a monte carlo filter smoother in contrast to maximum likelihood estimation of model parameters in ordinary state space modeling for which the recursive filter computation has to be done many times model parameter estimation in the proposed self organizing filter smoother is achieved with only two passes of the recursive filter and smoother operations examples such as automatic tuning of dispersion and the shape parameters adaptation to changes of the amplitude of a signal in seismic data state estimation for a nonlinear state space model with unknown parameters and seasonal adjustment with a nonlinear model with changing variance parameters are shown to exemplify the usefulness of the proposed method

reduced lists of error patterns for maximum likelihood soft decoding a method whereby a substantially reduced family of error patterns called survivors may be created for maximum likelihood soft decoding is introduced the family of survivor depends on the received word a decoder based on this approach first forms the survivors then scores them rather than obtaining the survivors by online elimination of error patterns the use of predetermined lists that represent all families of survivors is proposed

on off intermittency power spectrum and fractal properties of time series abstract some dynamical systems possess invariant submanifolds such that the dynamics restricted to the invariant submanifold is chaotic this situation arises in systems with a spatial symmetry or in the synchronization of chaotic oscillators the invariant submanifold could become unstable to perturbations in the transverse directions when a parameter of the system is changed through a critical blow out value this could result in an extreme form of temporally intermittent bursting called on off intermittency we propose a model that incorporates the universal features of systems that display on off intermittency we study this model both with and without additive noise and we derive scaling results for the power spectral density of the on off intermittent process and for the box counting dimension for the set of time intervals when the process takes on values above a given threshold we then present numerical simulations realizing these results

maximum likelihood estimators for generalized cauchy processes maximum likelihood estimator mle for a generalized cauchy process gcp is studied with the aid of the method of information geometry in statistics our gcp is described by the langevin equation with multiplicative and additive noises the exact expressions of mles are given for the two cases that the two types of noises are uncorrelated and mutually correlated it is shown that the mles for these two gcps are free from divergence even in the parameter region wherein the ordinary moments diverge the mle relations can be regarded as a generalized fluctuation dissipation theorem for the present langevin equation availability of them and of some other higher order statistics is demonstrated theoretically and numerically