the construction of preconditioners for elliptic problems by substructuring i in earlier parts of this series of papers we constructed preconditioners for the discrete systems of equations arising from the numerical approximation of elliptic boundary value problems the resulting algorithms are well suited for implementation on computers with parallel architecture in this paper we will develop a technique which utilizes these earlier methods to derive even more efficient preconditioners the iterative algorithms using these new preconditioners converge to the solution of the discrete equations with a rate that is independent of the number of unknowns these preconditioners involve an incomplete chebyshev iteration for boundary interface conditions which results in a negligible increase in the amount of computational work theoretical estimates and the results of numerical experiments are given which demonstrate the effectiveness of the methods

the normalized correlation accounting for binaural detection across center frequency bernstein and trahiotis l r bernstein and c trahiotis j acoust soc am 100 1754 1763 1996 recently reported the results of experiments designed to determine the form of interaural correlation that accounts for listeners sensitivities to interaural disparities within high frequency stimuli overall those results demonstrated that listeners abilities to discriminate changes in the interaural correlation of the envelope from a base correlation of 1 0 were well accounted for by the use of the normalized correlation the purpose of this study was to determine how well the normalized correlation computed subsequent to half wave rectification and low pass filtering could account for binaural detection data at low intermediate and high frequencies respectively in a four interval two alternative task listeners detected which interval contained a tone between 500 hz and 2 khz added antiphasically to diotic 100 hz wide noise nos nonsignal intervals contained the tone added homophasically noso performance was measured for signal to noise ratios between 30 and 30 db results indicated that a low pass filter function based on physiological measures of synchrony in cochlear nerve fibers in conjunction with the assumption of half wave square law rectification accounted for typically 80 of the variance in the behavioral data

lateralization of bands of noise as a function of combinations of interaural intensitive differences interaural temporal differences and bandwidth listeners indicated the intracranial position of bands of noise from 50 to 400 hz in width for several combinations of interaural intensitive differences iid and interaural temporal differences itd and or interaural phase differences ipd all itd and ipd combinations produced an interaural delay of 1500 s at the center frequency of the noise the interaural phase spectra were constructed to produce several patterns of putative cross correlation functions potency of iids depended greatly on particular combinations of bandwidth itd and ipd for some combinations changing the iid by only 3 db resulted in large shifts in laterality sometimes moving the image from near one ear to near the other the complex interactions observed make the results incompatible with the traditional notion that iids simply act as weights or scalars rather iids act in two distinct manners 1 as independent scalar quantities and 2 by interacting with specific combinations of bandwidth and itd ipd which is believed to reflect an action within the cross correlation surface

lateralization of complex binaural stimuli a weighted image model this article describes a new model that predicts the subjective lateral position of bandpass stimuli it is assumed as in other models that stimuli are bandpass filtered and rectified and that the rectified outputs of filters with matching center frequencies undergo interaural cross correlation the model specifies and utilizes the shape and location of assumed patterns of neural activity that describe the cross correlation function individual modes of this function receive greater weighting if they are straighter describing consistent interaural delay over frequency and or more central describing interaural delays of smaller magnitude this weighting of straightness and centrality is used by the model to predict the perceived laterality of several types of low frequency bandpass stimuli with interaural time delays and or phase shifts including bandpass noise amplitude modulated stimuli with time delayed envelopes and bandpass filtered clicks this model is compared to other theories that describe lateralization in terms of the relative contributions of information in the envelopes and fine structures of binaural stimuli

incidence of nonextensive thermodynamics in temporal scaling at feigenbaum points abstract recently in phys rev lett 95 2005 140601 grassberger addresses the interesting issue of the applicability of q statistics to the renowned feigenbaum attractor he concludes there is no genuine connection between the dynamics at the critical attractor and the generalized statistics and argues against its usefulness and correctness yet several points are not in line with our current knowledge nor are his interpretations we refer here only to the dynamics on the attractor to point out that a correct reading of recent developments invalidates his basic claim

on the definition of temperature using time averages abstract this paper is a natural continuation of a previous one by the author which was concerned with the foundations of statistical thermodynamics far from equilibrium one of the problems left open in that paper was the correct definition of temperature in the literature temperature is in general defined through the mean kinetic energy of the particles of a given system in this paper instead temperature is defined a la caratheodory the system being coupled to a heat bath and temperature being singled out as the right integrating factor of the exchanged heat as a byproduct the right expression for the entropy is also obtained in particular in the case of a q distribution the entropy turns out to be that of tsallis

asymmetric unimodal maps at the edge of chaos we numerically investigate the sensitivity to initial conditions of asymmetric unimodal maps x t 1 1 a x t z i i 1 2 correspond to x t 0 and x t 1 0 a or 2 t 0 1 2 at the edge of chaos we employ three distinct algorithms to characterize the power law sensitivity to initial conditions at the edge of chaos namely direct measure of the divergence of initially nearby trajectories the computation of the rate of increase of generalized non extensive entropies s q and multi fractal analysis the first two methods provide consistent estimates for the exponent governing the power law sensitivity in addition to this we verify that the multi fractal analysis does not provide precise estimates of the singularity spectrum f alpha especially near its extremal points such feature prevents to perform a fine check of the accuracy of the scaling relation between f alpha and the entropic index q thus restricting the applicability of the multi fractal analysis for studying the sensitivity to initial conditions in this class of asymmetric maps

the effects of randomizing values of interaural disparities on binaural detection and on discrimination of interaural correlation the purpose of this study was to assess whether randomizing roving baseline interaural parameters of binaural stimuli would adversely affect performance in masking level difference and in interaural correlation discrimination paradigms listeners detection thresholds were measured in noso and nos configurations for both broadband 100 3000 hz and narrow band 450 550 hz maskers centered at 500 hz in addition thresholds of interaural decorrelation from a reference correlation of 1 0 were measured for 100 hz wide bands of noise centered at 500 hz data were obtained under conditions in which either values of itd or values of iid were roved both within and across trials data were also collected in the absence of a rove the range of the rove was 500 s for itds and was 6 db for iids the duration of the stimuli was varied between 17 and 310 ms overall the results indicate that independent of duration roving the interaural cues produced small degradations of performance as compared to data ob

block monotone iterative methods for elliptic variational inequalities this paper discusses some important block iterative methods for solving variational inequalities with a nonlinear operator and proves their monotone convergence properties and comparison theorems these results extend c v pao s research work in numer math 72 1995 239 to variational inequalities

temporal extensivity of tsallis entropy and the bound on entropy production rate the tsallis entropy which is a generalization of the boltzmann gibbs entropy plays a central role in nonextensive statistical mechanics of complex systems a lot of efforts have recently been made on establishing a dynamical foundation for the tsallis entropy they are primarily concerned with nonlinear dynamical systems at the edge of chaos here it is shown by generalizing a formulation of thermostatistics based on time averages recently proposed by carati a carati physica a 348 110 2005 that whenever relevant the tsallis entropy indexed by q is temporally extensive linear growth in time i e finite entropy production rate then the universal bound on the entropy production rate is shown to be 1 absolute value 1 q the property of the associated probabilistic process i e the sojourn time distribution determining randomness of motion in phase space is also analyzed

convergence rate analysis of a multiplicative schwarz method for variational inequalities this paper derives a linear convergence for the schwarz overlapping domain decomposition method when applied to constrained minimization problems the convergence analysis is based on a minimization approach to the corresponding functional over a convex set a general framework of convergence is established for some multiplicative schwarz algorithm the abstract theory is particularly applied to some obstacle problems which yields a linear convergence for the corresponding schwarz overlapping domain decomposition method of one and two levels numerical experiments are presented to confirm the convergence estimate derived in this paper

criticality in nonlinear one dimensional maps rg universal map and nonextensive entropy abstract we consider the period doubling and intermittency transitions in iterated nonlinear one dimensional maps to corroborate unambiguously the validity of tsallis nonextensive statistics at these critical points we study the map x n 1 x n u x n z z 1 as it describes generically the neighborhood of all of these transitions the exact renormalization group rg fixed point map and perturbation static expressions match the corresponding expressions for the dynamics of iterates the time evolution is universal in the rg sense and the nonextensive entropy s q associated to the fixed point map is maximum with respect to that of the other maps in its basin of attraction the degree of nonextensivity the index q in s q and the degree of nonlinearity z are equivalent and the generalized lyapunov exponent q q 2 q 1 is the leading map expansion coefficient u the corresponding deterministic diffusion problem is similarly interpreted we discuss our results

chaos edges of z logistic maps connection between the relaxation and sensitivity entropic indices chaos thresholds of the z logistic maps x t 1 1 a xt z z 1 t 0 1 2 are numerically analyzed at accumulation points of cycles 2 3 and 5 three different cycles 5 we verify that the nonextensive q generalization of a pesin like identity is preserved through averaging over the entire phase space more precisely we computationally verify lim t infinity formula see text where the entropy s q formula see text the sensitivity to the initial conditions xi triple bond lim deltax 0 0 deltax t deltax 0 and ln q x triple bond x 1 q 1 1 q ln 1 x ln x the entropic index formula see text and the coefficient formula see text depend on both z and the cycle we also study the relaxation that occurs if we start with an ensemble of initial conditions homogeneously occupying the entire phase space the associated lebesgue measure asymptotically decreases as 1 t 1 q rel 1 q rel 1 these results i illustrate the connection conjectured by one of us between sensitivity and relaxation entropic indices namely formula see text where the positive numbers alpha n alpha n depend on the cycle ii exhibit an unexpected scaling namely formula see text

monotone multigrid methodsfor elliptic variational inequalities ii we derive globally convergent multigrid methods for discrete elliptic variational inequalities of the second kind as obtained from the approximation of related continuous problems by piecewise linear finite elements the coarse grid corrections are computed from certain obstacle problems the actual constraints are fixed by the preceding nonlinear fine grid smoothing this new approach allows the implementation as a classical v cycle and preserves the usual multigrid efficiency we give 1 o j 3 estimates for the asymptotic convergence rates the numerical results indicate a significant improvement as compared with previous multigrid approaches

localization of sound in rooms v binaural coherence and human sensitivity to interaural time differences in noise binaural recordings of noise in rooms were used to determine the relationship between binaural coherence and the effectiveness of the interaural time difference itd as a cue for human sound localization experiments showed a strong monotonic relationship between the coherence and a listener s ability to discriminate values of itd the relationship was found to be independent of other widely varying acoustical properties of the rooms however the relationship varied dramatically with noise band center frequency the ability to discriminate small itd changes was greatest for a mid frequency band to achieve sensitivity comparable to mid band the binaural coherence had to be much larger at high frequency where waveform itd cues are imperceptible and also at low frequency where the binaural coherence in a room is necessarily large rivalry experiments with opposing interaural level differences ilds found that the trading ratio between itd and ild increasingly favored the ild as coherence decreased suggesting that the perceptual weight of the itd is decreased by increased reflections in rooms

a convergent overlapping domain decomposition method for total variation minimization in this paper we are concerned with the analysis of convergent sequential and parallel overlapping domain decomposition methods for the minimization of functionals formed by a discrepancy term with respect to the data and a total variation constraint to our knowledge this is the first successful attempt of addressing such a strategy for the nonlinear nonadditive and nonsmooth problem of total variation minimization we provide several numerical experiments showing the successful application of the algorithm for the restoration of 1d signals and 2d images in interpolation inpainting problems respectively and in a compressed sensing problem for recovering piecewise constant medical type images from partial fourier ensembles

thermodynamics and time averages abstract for a dynamical system far from equilibrium one has to deal with empirical probabilities defined through time averages and the main problem then is how to formulate an appropriate statistical thermodynamics the common answer is that the standard functional expression of boltzmann gibbs for the entropy should be used the empirical probabilities being substituted for the gibbs measure other functional expressions have been suggested but apparently with no clear mechanical foundation here it is shown how a natural extension of the original procedure employed by gibbs and khinchin in defining entropy with the only proviso of using the empirical probabilities leads to a functional expression for the entropy which is in general different from that of boltzmann gibbs in particular the gibbs entropy is recovered for empirical probabilities of the poisson type while the tsallis entropies are recovered for a deformation of the poisson distribution

the normalized interaural correlation accounting for nospi thresholds obtained with gaussian and low noise masking noise recently j acoust soc am 103 2578 2589 1998 and j acoust soc am 103 2573 2577 1998 independently reported that greater masking of interaurally phase reversed s tones was produced by diotic low noise noise than by diotic gaussian noise based on quantitative analyses eddins and barber suggested that their results could not be accounted for by assuming that listeners judgments were based on constant criterion changes in the normalized interaural correlation produced by adding the s signal to the diotic masker in particular they showed that a model like the one previously employed by j acoust soc am 100 3774 3784 1996 predicted an ordering of thresholds between the conditions of interest that was opposite to that observed bernstein and trahiotis computed the normalized interaural correlation subsequent to half wave square law rectification and low pass filtering the parameters of which were chosen to mimic peripheral auditory processing in this report it is demonstrat

on the linear convergence of descent methods for convex essentially smooth minimization consider the problem of minimizing over a polyhedral set the composition of an affine mapping with a strictly convex essentially smooth function a general result on the linear convergence of descent methods for solving this problem is presented by applying this result the linear convergence of both the gradient projection algorithm of goldstein and levitin and polyak and a matrix splitting algorithm using regular splitting is established the results do not require that the cost function be strongly convex or that the optimal solution set be bounded the key to the analysis lies in a new error bound for estimating the distance from a feasible point to the optimal solution set

rate of convergence for some constraint decomposition methods for nonlinear variational inequalities some general subspace correction algorithms are proposed for a convex optimization problem over a convex constraint subset one of the nontrivial applications of the algorithms is the solving of some obstacle problems by multilevel domain decomposition and multigrid methods for domain decomposition and multigrid methods the rate of convergence for the algorithms for obstacle problems is of the same order as the rate of convergence for jump coefficient linear elliptic problems in order to analyse the convergence rate we need to decompose a finite element function into a sum of functions from the subspaces and also satisfying some constraints a special nonlinear interpolation operator is introduced for decomposing the functions

on the use of the normalized correlation as an index of interaural envelope correlation the purpose of the present study was to obtain new empirical observations that would help determine the form of interaural envelope correlation that accounts for listeners sensitivity to binaural information conveyed by high frequency stimuli in a four interval two alternative task listeners detected which interval contained a 4 khz tone added antiphasically to diotic 200 hz wide noise nos the nonsignal intervals contained the tone added homophasically noso discriminability d was measured as a function of s n for values between 30 and 30 db for all s ns overall level was 70 db spl using a similar procedure listeners were also tested in direct discrimination tasks where changes in envelope correlations were produced in one of two manners first changes in the normalized interaural envelope correlation were produced by varying the degree to which the envelopes covaried this was accomplished by mixing two independent gaussian noises second changes in the normalized interaural envelope correlation were produced by adding dc values to the envelopes of the stimuli overall in both experiments listeners ability to discriminate changes in interaural envelope correlation from a base correlation of 1 0 was well accounted for by the normalized correlation it is also shown that the normalized correlation of the envelope accounts for classic data concerning discriminability of interaural time differences at high frequencies as a function of depth of modulation

the infinite number of generalized dimensions of fractals and strange attractors abstract we show that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions dq q 0 to this aim we develop a rescaling transformation group which yields analytic expressions for all the quantities dq we prove that lim q 0 dq fractal dimension d limq 1dq information dimension and dq 2 correlation exponent v dq with other integer q s correspond to exponents associated with ternary quaternary and higher correlation functions we prove that generally dq dq for any q q for homogeneous fractals dq dq a particularly interesting dimension is dq for two examples feigenbaum attractor generalized baker s transformation we calculate the generalized dimensions and find that d is a non trivial number all the other generalized dimensions are bounded between the fractal dimension and d

on monotone and geometric convergence of schwarz methods for two sided obstacle problems convergence of schwarz methods is discussed for certain discretizations of two sided obstacle problems monotone and especially geometrical convergence are established if the stiffness matrix is a kind of m matrix and an h independent convergence rate is proved for uniformly overlapping decomposition

partially asynchronous parallel algorithms for network flow and other problems the problem of computing a fixed point of a nonexpansive function f is considered sufficient conditions are provided under which a parallel partially asynchronous implementation of the iteration x f x converges these results are then applied to i quadratic programming subject to box constraints ii strictly convex cost network flow optimization iii an agreement and a markov chain problem iv neural network optimization and v finding the least element of a polyhedral set determined by a weakly diagonally dominant leontief system finally simulation results illustrating the attainable speedup and the effects of asynchronism are presented

convergence rate of a schwarz multilevel method for the constrained minimization of nonquadratic functionals in l badea convergence rate of a multiplicative schwarz method for strongly nonlinear inequalities v barbu i lasiecka d tiba and c varsan eds kluwer academic publishers boston 2003 the convergence of a subspace correction method applied to the constrained minimization of a functional in a general reflexive banach space has been proved provided that the convex set verifies a certain assumption this assumption is weaker than that in which the convex set is decomposed according to the space decomposition as a sum of subsets in the sobolev spaces the proposed method becomes a multiplicative schwarz method for the solution of the variational inequalities coming from the minimization of nonquadratic functionals we prove in this paper that this assumption holds for the one two and multilevel multiplicative schwarz methods in the finite element space and we explicitly write the constants in the error estimations depending on the overlapping and mesh parameters our error estimates are similar with those obtained for the minimization of quadratic functionals in l badea x c tai and j wang siam j numer anal 2003 pp 1052 1073 or with those obtained for the one obstacle problem in x c tai numer math 93 2003 pp 755 786

analysis of a damped nonlinear multilevel method in this paper we present a new algorithm that is obtained by introducing a damping parameter in the classical nonlinear multilevel method we analyse this damped nonlinear multilevel method in particular we prove global convergence and local efficiency for a suitable class of problems

overlapping domain decomposition methods for total variation denoising alternating and parallel overlapping domain decomposition methods for the minimization of the total variation are presented their derivation is based on the predual formulation of the total variat

stability of tsallis entropy and instabilities of renyi and normalized tsallis entropies a basis for q exponential distributions the q exponential distributions which are generalizations of the zipf mandelbrot power law distribution are frequently encountered in complex systems at their stationary states from the viewpoint of the principle of maximum entropy they can apparently be derived from three different generalized entropies the renyi entropy the tsallis entropy and the normalized tsallis entropy accordingly mere fittings of observed data by the q exponential distributions do not lead to identification of the correct physical entropy here stabilities of these entropies i e their behaviors under arbitrary small deformation of a distribution are examined it is shown that among the three the tsallis entropy is stable and can provide an entropic basis for the q exponential distributions whereas the others are unstable and cannot represent any experimentally observable quantities

on multi grid methods for variational inequalities we consider here a general class of algorithms for the numerical solution of variational inequalities a convergence proof is given and in particular a multi grid method is described numerical results are presented for the finite difference discretization of an obstacle problem for minimal surfaces

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

binaural detection as a function of interaural correlation and bandwidth of masking noise implications for estimates of spectral resolution detection thresholds were measured for an antiphasic s 500 hz tone masked by a binaural noise as a function of the bandwidth of the noise several values of interaural correlation of the masking noise were used ranging from 1 to 1 the bandwidth dependence of the thresholds showed a pattern consistent with a 100 hz wide critical band for most values of interaural correlation even for those values which resulted in a considerable binaural release of masking only when the interaural correlation of the masking noise was very close to or equal to unity was the bandwidth dependence of the thresholds in accord with an approximately 300 hz wide binaural critical band measured in previous studies our analysis of the data calls into question the commonly stated notion that binaural processing is characterized by a wider critical band than is monaural processing

monotone multigrid methods for elliptic variational inequalities i we derive fast solvers for discrete elliptic variational inequalities of the first kind obstacle problems as resulting from the approximation of related continuous problems by piecewise linear finite elements using basic ideas of successive subspace correction we modify well known relaxation methods by extending the set of search directions extended underrelaxations are called monotone multigrid methods if they are quasioptimal in a certain sense by construction all monotone multigrid methods are globally convergent we take a closer look at two natural variants the standard monotone multigrid method and a truncated version for the considered model problems the asymptotic convergence rates resulting from the standard approach suffer from insufficient coarse grid transport while the truncated monotone multigrid method provides the same efficiency as in the unconstrained case

interaural correlation discrimination i bandwidth and level dependence measurements of interaural cross correlation jnds from two reference correlations at several bandwidths were obtained for constant total power and constant spectral power gaussian noise at a reference correlation of 1 the results indicate that for bandwidths less than or equal to 115 hz the jnd remains at a constant value of approximately 0 004 and monotonically increases discrimination performance degrades to approximately 0 04 as bandwidth increases above 115 hz at a reference correlation of 0 the jnd decreases discrimination performance improves from approximately 0 7 to 0 35 as the bandwidth increases from 3 to 115 hz and remains at a constant value of approximately 0 35 for bandwidths greater than 115 hz a decrease in the spectral level causes an increase in the jnds at a reference correlation of 1 and no change in the jnds at a reference correlation of 0 of the three models tested none is able to completely describe all of the empirical results

an additive schwarz method for variational inequalities this paper proposes an additive schwarz method for variational inequalities and their approximations by finite element methods the schwarz domain decomposition method is proved to converge with a geometric rate depending on the decomposition of the domain the result is based on an framework of convergence analysis established for general variational inequalities in hilbert spaces

adaptive multilevel methods for obstacle problems the authors consider the discretization of obstacle problems for second order elliptic differential operators by piecewise linear finite elements assuming that the discrete problems are reduced to a sequence of linear problems by suitable active set strategies the linear problems are solved iteratively by preconditioned conjugate gradient iterations the proposed preconditioners are treated theoretically as abstract additive schwarz methods and are implemented as truncated hierarchical basis preconditioners to allow for local mesh refinement semilocal and local a posteriors error estimates are derived providing lower and upper estimates for the discretization error the theoretical results are illustrated by numerical computations

perceptual fusion and fragmentation of complex tones made inharmonic by applying different degrees of frequency shift and spectral stretch global pitch depends on harmonic relations between components but the perceptual coherence of a complex tone cannot be explained in the same way instead it has been proposed that the auditory system responds to a common pattern of equal spacing between components but is only sensitive to deviations from this pattern over a limited range roberts and brunstrom j acoust soc am 104 2326 2338 1998 this hypothesis predicts that spectral fusion will be largely unaffected either by frequency shifting a harmonic stimulus because equal spacing is preserved or by small degrees of spectral stretch because significant deviations from equal spacing only cumulate over large spectral distances complex tones were either shifted by 0 50 of f0 200 hz 10 or stretched by 0 12 of f0 100 hz 10 subjects heard a complex followed by a pure tone in a continuous loop one of the components 2 11 was mistuned by 4 and subjects adjusted the pure tone to match its pitch broadly consistent with our hypothesis frequency shifts had relatively little effect on hit rates and only large degrees of stretch reduced them substantially the implications for simultaneous grouping are explored with reference to an autocorrelation model of auditory processing

enhancing interaural delay based extents of laterality at high frequencies by using transposed stimuli an acoustic pointing task was used to determine whether interaural temporal disparities itds conveyed by high frequency transposed stimuli would produce larger extents of laterality than itds conveyed by bands of high frequency gaussian noise the envelopes of transposed stimuli are designed to provide high frequency channels with information similar to that conveyed by the waveforms of low frequency stimuli lateralization was measured for low frequency gaussian noises the same noises transposed to 4 khz and high frequency gaussian bands of noise centered at 4 khz extents of laterality obtained with the transposed stimuli were greater than those obtained with bands of gaussian noise centered at 4 khz and in some cases were equivalent to those obtained with low frequency stimuli in a second experiment the general effects on lateral position produced by imposed combinations of bandwidth itd and interaural phase disparities ipds on low frequency stimuli remained when those stimuli were transposed to 4 khz overall the data were fairly well accounted for by a model that computes the cross correlation subsequent to known stages of peripheral auditory processing augmented by low pass filtering of the envelopes within the high frequency channels of each ear

global and uniform convergence of subspace correction methods for some convex optimization problems this paper gives some global and uniform convergence estimates for a class of subspace correction based on space decomposition iterative methods applied to some unconstrained convex optimization problems some multigrid and domain decomposition methods are also discussed as special examples for solving some nonlinear elliptic boundary value problems

some properties of q logarithm and q exponential functions in tsallis statistics we present some formulae which q logarithmic and q exponential functions introduced in tsallis statistics satisfy exact expression of the mellin transform of q exponential function is given moreover the q generalization of the digamma function is presented

asymptotically scale invariant occupancy of phase space makes the entropy sq extensive phase space can be constructed for n equal and distinguishable subsystems that could be probabilistically either weakly correlated or strongly correlated if they are locally correlated we expect the boltzmann gibbs entropy s bg k i p i ln p i to be extensive i e s bg n n for n in particular if they are independent s bg is strictly additive i e s bg n ns bg 1 n however if the subsystems are globally correlated we expect for a vast class of systems the entropy s q k 1 i p q i q 1 with s 1 s bg for some special value of q 1 to be the one which is extensive i e s q n n for n another concept which is relevant is strict or asymptotic scale freedom or scale invariance defined as the situation for which all marginal probabilities of the n system coincide or asymptotically approach for n the joint probabilities of the n 1 system if each subsystem is a binary one scale freedom is guaranteed by what we hereafter refer to as the leibnitz rule i e the sum of two successive joint probabilities of the n system coincides or asymptotically approaches the corresponding joint probability of the n 1 system the kinds of interplay of these various concepts are illustrated in several examples one of them justifies the title of this paper we conjecture that these mechanisms are deeply related to the very frequent emergence in natural and artificial complex systems of scale free structures and to their connections with nonextensive statistical mechanics summarizing we have shown that for asymptotically scale invariant systems it is s q with q 1 and not s bg the entropy which matches standard clausius like prescriptions of classical thermodynamics

the lateralization of simple dichotic pitches a simple dichotic pitch arises when a single narrow band possesses a different interaural configuration from a surrounding broadband noise whose interaural configuration is uniform and correlated such pitches were created by interaurally decorrelating a narrow band experiment 1 or by giving a narrow band a different interaural time difference from the noise experiment 2 using an adaptive forced choice procedure listeners adjusted the interaural intensity difference of pointers to match their lateralization to that of the dichotic pitches the primary determinants of lateralization were the interaural configuration of the broadband noise experiment 1 the center frequency of the narrow band experiment 1 and its interaural configuration experiment 2 the ability of two computational models to predict these results was evaluated a version of the central spectrum model j raatgever and f a bilsen j acoust soc am 80 429 441 1986 incorporating realistic frequency selectivity accounted for the main results of experiment 1 but not experiment 2 a new reconstruction comparison model accounted for the main results of both experiments to accommodate the variables shown to influence lateralization this model segregates evidence of the dichotic pitch from the noise reconstructs the cross correlogram of the noise and compares it with the cross correlogram of the original stimulus

convergence estimates for product iterative methods with applications to domain decomposition in this paper we consider iterative methods for the solution of symmetric positive definite problems on a space which are defined in terms of products of operators defined with respect to a number of subspaces the simplest algorithm of this sort has an error reducing operator which is the product of orthogonal projections onto the complement of the subspaces new normreduction estimates for these iterative techniques will be presented in an abstract setting applications are given for overlapping schwarz algorithms with many subregions for finite element approximation of second order elliptic problems

subspace correction methods for nonsymmetric parabolic problems abstract a convergence proof for general subspace correction techniques applied to an abstract nonsymmetric parabolic equation is given one of the main concerns is to give a unified convergence analysis for domain decomposition and multigrid methods for parabolic problems the analysis is also valid for nonsymmetric problems for second order parabolic problems the convection can dominate the diffusion the algorithms can be applied to domain decomposition methods with or without the coarse mesh for applications to multigrid methods the coarsest mesh does not need to be very coarse a relation between the coarse mesh size and the time step is needed to get a convergence rate independent of the mesh the number of iterations at each time step for the algorithms is also estimated some numerical experiments are presented for domain decomposition methods with minimum overlap which support the theoretical predictions the algorithms are able to capture the sharp traveling shocks for convection dominated problems

stabilities of generalized entropies the generalized entropic measure which is maximized by a given arbitrary distribution under the constraints on normalization of the distribution and the finite ordinary expectation value of a physical random quantity is considered to examine if it can be of physical relevance its experimental robustness is discussed in particular lesche s criterion is analysed which states that an entropic measure is stable if its change under an arbitrary weak deformation of the distribution representing fluctuations of experimental data remains small it is essential to note the difference between this criterion and thermodynamic stability a general condition under which the generalized entropy becomes stable is derived examples known in the literature including the entropy for the stretched exponential distribution the quantum group entropy and the entropy are discussed

lateralization produced by envelope based interaural temporal disparities of high frequency raised sine stimuli empirical data and modeling an acoustic pointing task was used to measure extents of laterality produced by ongoing interaural temporal disparities itds conveyed by the envelopes of 4 khz centered raised sine stimuli while varying parametrically their peakedness depth of modulation and frequency of modulation one purpose of the study was to determine whether such manipulations would produce changes in laterality logically consistent with those found for itd discrimination thresholds reported by bernstein and trahiotis j acoust soc am 125 3234 3242 2009 the data obtained revealed that they did in that 1 increasing depth of modulation peakedness or frequency of modulation between 32 and 128 hz produced smaller threshold itds and greater laterality and 2 increasing frequency of modulation to 256 hz produced modest increases in threshold itds and modest decreases in laterality the extents of laterality measured were successfully accounted for via an augmentation of the cross correlation based position variable modeling approach developed by stern and shear j acoust soc am 100 2278 2288 1996 to account for itd based extents of laterality obtained at low spectral frequencies

path integral approach to the nonextensive canonical density matrix abstract feynman s path integral is herein generalized to the nonextensive canonical density matrix based on tsallis entropy this generalization is done in two ways by using unnormalized and normalized constraints firstly we consider the path integral formulation with unnormalized constraints and this generalization is worked out through two different ways which are shown to be equivalent these formulations with unnormalized constraints are solutions to the two generalized bloch equations proposed in this work the first form of the generalized bloch equation is linear but with a temperature dependent effective hamiltonian the second form is nonlinear and resembles the anomalous correlated diffusion equation porous medium equation furthermore we can extend these results to the prescription of field theory using integral representations the second development is dedicated to analyzing the path integral formulation with normalized constraints to illustrate the methods introduced here we analyze the free particle case and a non interacting scalar field the results herein obtained are expected to be useful in the discussion of generic nonextensive contexts

domain decomposition method for image deblurring as a fundamental problem in image processing image deblurring has still attracted a lot of research attention due to the large computational cost especially for high resolution images it becomes challenging to solve the deblurring minimization problem and the underlying partial differential equations the domain decomposition method dd as one of the most efficient algorithms for solving large scale problems had not been applied directly to image deblurring because of the global characteristic of the blur operator in this paper in order to avoid separating the blur operator we propose an algorithm for directly solving the total variational based minimization problems with dd various numerical experiments and comparisons demonstrate that the larger the image size is the more efficient the proposed method is in saving running time the parallelization has also been realized by using the parallel computing toolbox of matlab

on multilevel iterative methods for optimization problems this paper is concerned with multilevel iterative methods which combine a descent scheme with a hierarchy of auxiliary problems in lower dimensional subspaces the construction of auxiliary problems as well as applications to elasto plastic model and linear programming are described the auxiliary problem for the dual of a perturbed linear program is interpreted as a dual of perturbed aggregated linear program coercivity of the objective function over the feasible set is sufficient for the boundedness of the iterates equivalents of this condition are presented in special cases

fractal structure with a typical scale in order to understand the characteristics common to distributions which have both fractal and non fractal scale regions in a unified framework we introduce the concept of a typical scale we employ a model of 2d gravity modified by the r2 term as a tool to understand such distributions through the typical scale this model is obtained by adding an interaction term with a typical scale to a scale invariant system a distribution derived in the model provides power law one in the large scale region but weibull like one in the small scale region as examples of distributions which have both fractal and non fractal regions we take those of personal income and citation number of scientific papers we show that these distributions are fitted fairly well by the distribution curves derived analytically in the r2 2d gravity model as a result we consider that the typical scale is a useful concept to understand various distributions observed in the real world in a unified way we also point out that the r2 2d gravity model provides us with an effective tool to read the typical scales of various distributions in a systematic way

the normalized correlation accounting for nosπ thresholds with gaussian and low noise masking noise recently both eddins and barber j acoust soc am 103 2578 2589 1998 and hall et al j acoust soc am 103 2573 2577 1998 demonstrated that low noise noise produced more masking of antipha sic tones than did gaussian noise eddins and barber could not account for this finding by considering changes in the normalized interaural correlation produced by adding antiphasic signals to the diotic maskers they calculated the normalized correlation subsequent to half wave square law rectification and low pass filtering that approach was used successfully by bernstein and trahiotis j acoust soc am 100 3774 3784 1996 to account for binaural detection performance as a function of frequency in this presentation it will be shown that one can account quantitatively for thresholds obtained with low noise noise and with gaussian noise by incorporating a stage of compression prior to rectification and low pass filtering the compressive function employed produces effects similar to tho

convergence rate analysis of an asynchronous space decomposition method for convex minimization we analyze the convergence rate of an asynchronous space decomposition method for constrained convex minimization in a reflexive banach space this method includes as special cases parallel domain decomposition methods and multigrid methods for solving elliptic partial differential equations in particular the method generalizes the additive schwarz domain decomposition methods to allow for asynchronous updates it also generalizes the bpx multigrid method to allow for use as solvers instead of as preconditioners possibly with asynchronous updates and is applicable to nonlinear problems applications to an overlapping domain decomposition for obstacle problems are also studied the method of this work is also closely related to relaxation methods for nonlinear network flow accordingly we specialize our convergence rate results to the above methods the asynchronous method is implementable in a multiprocessor system allowing for communication and computation delays among the processors

multi grid solutions to the elastic plastic torsion problem in multiply connected domains the elastic plastic torsion problem for an elastic perfectly plastic cylinder with multiply connected cross section twisted around its longitudinal axis is formulated as an obstacle problem for an associated stress potential the obstacle being defined in terms of a generalized distance function based upon the reformulation of the obstacle problem as an equivalent linear complementarity problem the latter is discretized by means of finite difference techniques and a monotonically convergent iterative scheme for its numerical solution is developed at each step of the iteration the solution of a reduced system of discrete poisson equations is required which is done by applying multi grid techniques with respect to a hierarchy of grid point sets combined with a suitably chosen nested iteration process this results in a computationally very efficient algorithm for the approximate solution of the elastic plastic torsion problem

a unified analysis of hoffman s bound via fenchel duality in 1952 hoffman showed that the distance from any point to the solution set of a linear system is bounded above by a constant times the norm of the residual subsequently this bound has been studied extensively and has found many practical uses in this paper we consider an extension of hoffman s bound to a partially infinite dimensional setting in which the norm defining the distance is replaced by a positively homogeneous convex function and the linear system is replaced by a convex inclusion of the form ax a in k where a is a continuous linear operator from some normed linear space into mathbf r m a is an element of the range space of a and k is a nonempty closed convex cone in mathbf r m when specialized to the finite dimensional case we unify and extend many existing results on hoffman s bound our analysis is based on the use of fenchel duality to express the distance as the supremum of a certain concave function over a bounded subset of the polar of k much of our analysis als

on the fractal dimension of orbits compatible with tsallis statistics abstract in a previous paper a carati physica a 348 2005 110 120 it was shown how for a dynamical system the probability distribution function of sojourn times in phase space defined in terms of the dynamical orbits up to a given observation time induces unambiguously a statistical ensemble in phase space in the present paper the p d f of the sojourn times corresponding to a tsallis ensemble is obtained this by the way requires the solution of a problem of a general character disregarded in paper a carati physica a 348 2005 110 120 in particular some qualitative properties such as the fractal dimension of the dynamical orbits compatible with the tsallis ensembles are indicated

manipulating the straightness and curvature of patterns of interaural cross correlation affects listeners sensitivity to changes in interaural delay the purpose of this study was to test the hypothesis that stimuli characterized by straight trajectories of their patterns of cross correlation foster greater sensitivity to changes in interaural temporal disparities itds than do stimuli characterized by more curved trajectories of their patterns of cross correlation to do so sensitivity to changes in itd was measured as a function of duration using a set of reference stimuli that yielded differing relative amounts of straightness within their patterns of cross correlation while keeping the dominant trajectory at or near midline the relative amounts of straightness were manipulated by employing specific combinations of bandwidth itd and interaural phase disparity ipd of gaussian noises centered at 500 hz the results were consistent with expectations in that the patterning of the threshold itds revealed increasingly poorer sensitivity as greater and greater curvature was imposed on the dominant midline trajectory the variations in threshold itd across the stimulus conditions can be accounted for quite well quantitatively by assuming either that the listeners based their judgments on changes in the position of the most central peak of the cross correlation function or that they based their judgments on changes in the centroid of a second level cross correlation function in a second experiment binaural detection was measured using a subset of the reference stimuli as maskers as expected sensitivity was poorest with the maskers characterized by the greatest curvature which were also those having the lowest interaural correlation

analysis of a multilevel iterative method for nonlinear finite element equations the multilevel iterative technique is a powerful technique for solving the systems of equations associated with discretized partial differential equations we describe how this technique can be combined with a globally convergent approximate newton method to solve nonlinear partial differential equations we show that asymptotically only one newton iteration per level is required thus the complexity for linear and nonlinear problems is essentially equal

a novel two grid method for semilinear elliptic equations a new finite element discretization technique based on two coarse and fine subspaces is presented for a semilinear elliptic boundary value problem the solution of a nonlinear system on the fine space is reduced to the solution of two small one linear and one nonlinear systems on the coarse space and a linear system on the fine space it is shown both theoretically and numerically that the coarse space can be extremely coarse and still achieve asymptotically optimal approximation as a result the numerical solution of such a nonlinear equation is not significantly more expensive than the solution of one single linearized equation

rate of convergence of some space decomposition methods for linear and nonlinear problems convergence of a space decomposition method is proved for a class of convex programming problems a space decomposition refers to a method that decomposes a space into a sum of subspaces which could be a domain decomposition or a multilevel method when applied to partial differential equations two algorithms are proposed both can be used for linear as well as nonlinear elliptic problems and they reduce to the standard additive and multiplicative schwarz methods for linear elliptic problems

on the rate of convergence of a partially asynchronous gradient projection algorithm recently bertsekas and tsitsiklis proposed a partially asynchronous implementation of the gradient projection algorithm of goldstein and levitin and polyak for the problem of minimizing a differentiable function over a closed convex set in this paper the rate of convergence of this algorithm is analyzed it is shown that if the standard assumptions hold that is the solution set is nonempty and the gradient of the function is lipschitz continuous and i the isocost surfaces of the objective function restricted to the solution set are properly separated and ii a certain multifunction associated with the problem is locally upper lipschitzian then this algorithm attains a linear rate of convergence

measures of extents of laterality for high frequency transposed stimuli under conditions of binaural interference our purpose in this study was to determine whether across frequency binaural interference would occur if itd based extents of laterality were measured using high frequency transposed stimuli as targets the results of an earlier study l r bernstein and c trahiotis j acoust soc am 116 3062 3069 2004 which focused on threshold itds rather than extents of laterality suggested that high frequency transposed stimuli might be immune to binaural interference effects resulting from the addition of a spectrally remote low frequency interferer in contrast to the earlier findings the data from this study indicate that high frequency transposed targets are susceptible to binaural interference nevertheless high frequency transposed targets even when presented along with an interferer yielded greater extents of itd based laterality than did high frequency gaussian noise targets presented in isolation that is the enhanced potency of itds conveyed by transposed stimuli persisted even in the

subspace correction methods for total variation and ell_1 minimization this paper is concerned with the numerical minimization of energy functionals in hilbert spaces involving convex constraints coinciding with a seminorm for a subspace the optimization is realized by alternating minimizations of the functional on a sequence of orthogonal subspaces on each subspace an iterative proximity map algorithm is implemented via oblique thresholding which is the main new tool introduced in this work we provide convergence conditions for the algorithm in order to compute minimizers of the target energy analogous results are derived for a parallel variant of the algorithm applications are presented in domain decomposition methods for degenerate elliptic pdes arising in total variation minimization and in accelerated sparse recovery algorithms based on ell 1 minimization we include numerical examples which show efficient solutions to classical problems in signal and image processing