statistical complexity measure of pseudorandom bit generators abstract pseudorandom number generators prng are extensively used in monte carlo simulations gambling machines and cryptography as substitutes of ideal random number generators rng each application imposes different statistical requirements to prngs as l ecuyer clearly states the main goal for monte carlo methods is to reproduce the statistical properties on which these methods are based whereas for gambling machines and cryptology observing the sequence of output values for some time should provide no practical advantage for predicting the forthcoming numbers better than by just guessing at random in accordance with different applications several statistical test suites have been developed to analyze the sequences generated by prngs in a recent paper a new statistical complexity measure phys lett a 311 2003 126 has been defined here we propose this measure as a randomness quantifier of a prngs the test is applied to three very well known and widely tested prngs available in the literature all of them are based on mathematical algorithms another prngs based on lorenz 3d chaotic dynamical system is also analyzed prngs based on chaos may be considered as a model for physical noise sources and important new results are recently reported all the design steps of this prng are described and each stage increase the prng randomness using different strategies it is shown that the mpr statistical complexity measure is capable to quantify this randomness improvement the prng based on the chaotic 3d lorenz dynamical system is also evaluated using traditional digital signal processing tools for comparison

distinguishing chaotic and stochastic dynamics from time series by using a multiscale symbolic approach in this paper we introduce a multiscale symbolic information theory approach for discriminating nonlinear deterministic and stochastic dynamics from time series associated with complex systems more precisely we show that the multiscale complexity entropy causality plane is a useful representation space to identify the range of scales at which deterministic or noisy behaviors dominate the system s dynamics numerical simulations obtained from the well known and widely used mackey glass oscillator operating in a high dimensional chaotic regime were used as test beds the effect of an increased amount of observational white noise was carefully examined the results obtained were contrasted with those derived from correlated stochastic processes and continuous stochastic limit cycles finally several experimental and natural time series were analyzed in order to show the applicability of this scale dependent symbolic approach in practical situations

harnack inequalities and discrete continuous error estimates for a chain of atoms with two body interactions we consider deformations in r 3 of an infinite linear chain of atoms where each atom interacts with all others through a two body potential we compute the effect of an external force applied to the chain at equilibrium the positions of the particles satisfy an euler lagrange equation for large classes of potentials we prove that every solution is well approximated by the solution of a continuous model we establish an error estimate between the discrete and the continuous solution based on a harnack lemma of indepen dent interest finally we apply our results to some lennard jones potentials

rigorous properties and uncertainty like relationships on product complexity measures application to atomic systems most of research on complexities and the corresponding conclusions have been obtained by numerically quantifying their values and little attention has been paid to their theoretical properties and the exact meaning within an statistical framework valid for any arbitrary n dimensional distribution in the present work different product complexities constructed as a product of two relevant information quantities associated to the concepts of uncertainty and localization are investigated different results on product complexities such as rigorous bounds uncertainty like inequalities relationships among themselves and also statistical interpretations are given for the sake of completeness some of these analytical results on product complexities are numerically checked for the one particle densities of atomic systems in both conjugated spaces

effective cohesive behavior of layers of interatomic planes a simple model of cleavage in brittle crystals consists of a layer of material containing n atomic planes separating in accordance with an interplanar potential under the action of an opening displacement prescribed on the boundary of the layer the problem addressed in this work concerns the characterization of the constrained minima of the energy en of the layer as a function of as n becomes large these minima determine the effective or macroscopic cohesive law of the crystal the main results presented in this communication are i the computation of the limit e0 of en as n ii the characterization of the minimum values of e0 as a function of the macroscopic opening displacement iii a proof of uniform convergence of the minima of en for the case of nearest neighbor interactions and iv a proof of uniform convergence of the derivatives of en or tractions in the same case the scaling on which the present convergence analysis is based has the effect of separating the bulk and surface contributions to the energy it differs crucially from other scalings employed in the past in that it renders both contributions of the same order

multigrid tomographic inversion with variable resolution data and image spaces a multigrid inversion approach that uses variable resolutions of both the data space and the image space is proposed since the computational complexity of inverse problems typically increases with a larger number of unknown image pixels and a larger number of measurements the proposed algorithm further reduces the computation relative to conventional multigrid approaches which change only the image space resolution at coarse scales the advantage is particularly important for data rich applications where data resolutions may differ for different scales applications of the approach to bayesian reconstruction algorithms in transmission and emission tomography with a generalized gaussian markov random field image prior are presented both with a poisson noise model and with a quadratic data term simulation results indicate that the proposed multigrid approach results in significant improvement in convergence speed compared to the fixed grid iterative coordinate descent method and a multigrid method with fixed data resolution

a method to discern complexity in two dimensional patterns generated by coupled map lattices complex patterns generated by the time evolution of a one dimensional digitalized coupled map lattice are quantitatively analyzed a method for discerning complexity among different patterns is implemented the quantitative results indicate two zones in parameter space where the dynamics show the most complex patterns these zones are located on the two edges of an absorbent region where the system displays spatio temporal intermittency

the interior radon transform the interior radon transform arises from a limited data problem in computerized tomography when only rays travelling through a specified region of interest are measured this problem occurs due to technical restrictions of the sampling apparatus or in an endeavour to reduce the x ray dose the corresponding operator mathcal r i is investigated as a mapping between weighted l 2 spaces the main result is a singular value decomposition svd for this operator for functions of unbounded support in mathbb r 2 the proof is based on the construction of intertwining differential operators the techniques used are unified in the sense that svds for other radon transforms with rotational symmetry can easily be derived in the same way consistency conditions are also obtained for mathcal r i for functions of bounded and unbounded support many of the results generalize to higher dimensions they are stated whenever they follow directly from the two dimensional case

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

intensive entropic non triviality measure abstract we discuss a way of characterizing probability distributions complementing that provided by the celebrated notion of information measure with reference to a measure of complexity that we call a nontriviality measure our starting point is the lmc measure of complexity advanced by lopez ruiz et al phys lett a 209 1995 321 and its analysis by anteneodo and plastino phys lett a 223 1997 348 an improvement of some of their troublesome characteristics is thereby achieved basically we replace the euclidean distance to equilibrium by the jensen shannon divergence the resulting measure turns out to be i an intensive quantity and ii allows one to distinguish between different degrees of periodicity we apply the cured measure to the logistic map so as to clearly exhibit its advantages

a comparison of shannon kullback leibler and renormalized entropies within successive bifurcations abstract an issue in the context of self organization is the existence of bifurcation processes that are often observed in dissipative dynamical systems the first bifurcation occurs when a stable fixed point becomes unstable as the parameter set of the system slightly changes then the system eventually paves their way to new stable branches when the most ordered spatial patterns emerge the system implies a high level of self organization in the phase space exchange of energy matter with its surroundings is allowed for in such open systems open systems cannot be analyzed in terms of usual h theorem of boltzmann since it is only valid for isolated systems thereby the boltzmann gibbs bg entropy or shannon is not able to explain such systems which increase their order as a signature of self organization however klimontovich showed that the bg entropy can still be used in such systems after a renormalization procedure and he also introduced the renormalized entropy as a measure of the relative degree of order by using his s theorem in this paper we analyze the henon map and the rossler oscillator as high dimensional dissipative systems we show that the renormalized entropy detects transition points of the systems and explains changes in relative order through successive bifurcations or chaotic band mergings the correlation analysis also shows that the renormalized entropy is a better measure than the shannon or kullback leibler k l entropies

a comparison of lmc and sdl complexity measures on binomial distributions abstract the concept of complexity has been widely discussed in the last forty years with a lot of thinking contributions coming from all areas of the human knowledge including philosophy linguistics history biology physics chemistry and many others with mathematicians trying to give a rigorous view of it in this sense thermodynamics meets information theory and by using the entropy definition lopez ruiz mancini and calbet proposed a definition for complexity that is referred as lmc measure shiner davison and landsberg by slightly changing the lmc definition proposed the sdl measure and the both lmc and sdl are satisfactory to measure complexity for a lot of problems here sdl and lmc measures are applied to the case of a binomial probability distribution trying to clarify how the length of the data set implies complexity and how the success probability of the repeated trials determines how complex the whole set is

characterization of gaussian self similar stochastic processes using wavelet based informational tools efficient tools to characterize stochastic processes are discussed quantifiers originally proposed within the framework of information theory like entropy and statistical complexity are translated into wavelet language which renders the above quantifiers into tools that exhibit the important localization advantages provided by wavelet theory two important and popular stochastic processes fractional brownian motion and fractional gaussian noise are studied using these wavelet based informational tools exact analytical expressions are obtained for the wavelet probability distribution finally numerical simulations are used to validate our analytical results

binary indices of time series complexity measures and entropy plane abstract complexity of time series is an important feature of dynamical systems such as financial systems in order to bring out the complete non linear behavior of financial time series non linear tools of complexity measurement like entropy measures are indispensable sample entropy sampen and distribution entropy disten are popular methods of assessing the complexity in various fields however both sample entropy and distribution entropy show some limitations in detecting the complexity of stock markets therefore we use two entropies as binary indices to analyze the complexity of time series and structure the entropy plane in order to further improve the accuracy of the research results we take the embedding dimension m as the variable expand the entropy point into the entropy curve for further research furthermore considering the shortcomings of sample entropy and distribution entropy in practical application we generalize them by i replacing sample entropy and distribution entropy with multi scale sample entropy and multi scale distribution entropy ii generalizing shannon entropy as tsallis entropy also scale factor and entropic index q are taken respectively as variables to get the entropy curves by using the artificial data we confirm the rationality of using entropy points and entropy curves to study the complexity of time series finally we apply this method to measure the complexity of real world financial time series the results show that the entropy curves plotted by the financial time series obtained from different areas have significant differences

macroscopic behavior of microscopic oscillations in harmonic lattices via wigner husimi transforms we consider the dynamics of infinite harmonic lattices in the limit of the lattice distance tending to 0 we allow for general polyatomic crystals but assume exact periodicity such that the system can be solved in principle by fourier transform and linear algebra methods

a statistical complexity measure with nonextensive entropy and quasi multiplicativity the properties of a statistical complexity measure that are characterized by nonextensivity in entropy have been investigated which is of so called disequilibrium type considering the composition law for two systems with different nonextensivities quasi multiplicativity a nontrivial relation between the nonextensive parameters and the fluctuating bit number in information theory has been mentioned to see the time evolution of the nonextensive complexity measure we examine systems having a lognormal distribution the underlying dynamics for which is known to obey a random multiplicative process in the presence of a boundary constraint

complexity entropy causality plane a useful approach for distinguishing songs nowadays we are often faced with huge databases resulting from the rapid growth of data storage technologies this is particularly true when dealing with music databases in this context it is essential to have techniques and tools able to discriminate properties from these massive sets in this work we report on a statistical analysis of more than ten thousand songs aiming to obtain a complexity hierarchy our approach is based on the estimation of the permutation entropy combined with an intensive complexity measure building up the complexity entropy causality plane the results obtained indicate that this representation space is very promising to discriminate songs as well as to allow a relative quantitative comparison among songs additionally we believe that the here reported method may be applied in practical situations since it is simple robust and has a fast numerical implementation

complex and composite entropy fluctuation behaviors of statistical physics interacting financial model abstract in an attempt to investigate and reproduce the fluctuation dynamics of price changes in financial markets a novel complex random interacting financial price model is developed by combining voter interacting system with compound poisson process in this model the dissemination of investors investment attitudes can simulate normal and frequent small price fluctuations of financial markets while the random drastic jumps can capture undue and rare large price fluctuations as results of sudden economic events and political events in the markets in order to verify the rationality of the model some statistical characteristics of the model returns including fat tail power law scaling complexity and multifractal are compared with real returns by probability density functions composite distance fuzzy entropy c fuzzyen matching energy and multifractal detrended fluctuation analysis the c fuzzyen is a new entropy based approach based on fuzzy entropy and complexity invariant to measure the complexity behaviors of return series the effectiveness analysis of c fuzzyen indicates that it has a higher estimation accuracy and stronger robustness than fuzzy entropy the empirical results show that the price model is able to reproduce some important statistical properties of financial markets to a certain extent and the complexity of returns for the proposed model increases when infection intensity or jump intensity increases

evidence of self organization in brain electrical activity using wavelet based informational tools abstract in the present work we show that appropriate information theory tools based on the wavelet transform relative wavelet energy normalized total wavelet entropy h generalized wavelet complexity c w when applied to tonic clonic epileptic eeg data provide one with valuable insights into the dynamics of neural activity twenty tonic clonic secondary generalized epileptic records pertaining to eight patients have been analyzed if the electromyographic activity is excluded the difference between the ictal and pre ictal mean entropic values h h ictal h pre ictal is negative in 95 of the cases p 0 0001 and the mean complexity variation c w c w ictal c w pre ictal is positive in 85 of the cases p 0 0002 thus during the seizure entropy diminishes while complexity grows this is construed as evidence supporting the conjecture that an epileptic focus in this kind of seizures triggers a self organized brain state characterized by both order and maximal complexity

new sampling scheme for region of interest tomography the wavelet localization technique was previously applied to the study of region of interest roi tomography it achieves a significant saving in the required projections if only a small region of a tomographic image is of interest in this paper we first show that with the same sampling scheme a simple interpolation applied to the samples can give a result at least as good as that using the original wavelet localization approach it implies that the use of the wavelet transform is not the key to the reduction of the sampling requirement in fact the quality of the reconstructed roi is largely determined by the structure of the sampling scheme rather than directly reducing the projection number the use of the wavelet theory permits a clear understanding of how to achieve a good sampling pattern based on an error analysis using the wavelet theory we further suggest a new sampling scheme such that the number of required projections in each angle is reduced in a multiresolution form a new multiresolution interpolation algorithm is then used to interpolate the missing samples to obtain the full projections as a result more than 84 of projections are saved as compared with the traditional approach in reconstructing an roi of 32 spl times 32 pixels in an image of 256 spl times 256 pixels a series of simulations was performed to reconstruct different sizes of the roi all results show that the signal to error ratios of the reconstructed roi are comparable with that using full projection data set

classical ground states in one dimension we give conditions on an interaction sufficient to guarantee that in one dimension it yield a periodic ground state with one or two particles per unit cell

a proof of crystallization in two dimensions many materials have a crystalline phase at low temperatures the simplest example where this fundamental phenomenon can be studied are pair interaction energies of the type where y x 2 is the position of particle x and v r is the pair interaction energy of two particles which are placed at distance r due to the mermin wagner theorem it can t be expected that at finite temperature this system exhibits long range ordering we focus on the zero temperature case and show rigorously that under suitable assumptions on the potential v which are compatible with the growth behavior of the lennard jones potential the ground state energy per particle converges to an explicit constant e where e is the minimum of a simple function on 0 furthermore if suitable dirichlet or periodic boundary conditions are used then the minimizers form a triangular lattice to the best knowledge of the author this is the first result in the literature where periodicity of ground states is established for a physically relevant model which is invariant under the euclidean symmetry group consisting of rotations and translations

ordinal analysis of time series abstract in order to develop fast and robust methods for extracting qualitative information from non linear time series bandt and pompe have proposed to consider time series from the pure ordinal viewpoint on the basis of counting ordinal patterns which describe the up and down in a time series they have introduced the concept of permutation entropy for quantifying the complexity of a system behind a time series the permutation entropy only provides one detail of the ordinal structure of a time series here we present a method for extracting the whole ordinal information

incomparability entropy and mixing dynamics abstract boltzmann states are considered in a fundamentally new way specifically their mixing character the mixing character of these states is known to be partially ordered by majorization and thus contains information regarding their incomparability previously we showed that boltzmann entropy states had a huge range in the number of incomparable states here we phase average incomparability across boltzmann states we propose the consequent function as a new state variable complimentary to entropy that provides new insights to boltzmann systems this function can be related to a traditional complexity viewpoint and so we call it average boltzmann complexity abc the evolution of boltzmann complexity is explored via a monte carlo lattice dynamics approach and is shown to be consistent with the view of entropy as the arrow of time our report concludes with a discussion of the information contained in boltzmann complexity and offers suggestions for further studies

forbidden patterns permutation entropy and stock market inefficiency abstract in this paper we introduce two new quantifiers for the stock market inefficiency the number of forbidden patterns and the normalized permutation entropy they are model independent measures thus they have more general applicability we find robust evidence that degree of market inefficiency is positively correlated with the number of forbidden patterns and negatively correlated with the permutation entropy our empirical results suggest that these two physical tools are useful to discriminate the stage of stock market development and can be easily implemented

permutation entropy and statistical complexity quantifier of nonstationarity effect in the vertical velocity records how the nonstationarity in the atmosphere turbulent vertical velocity series affects its organization degree of multiscale structures is quantified by permutation entropy pe and complexity entropy causality plane cecp and marked pe and cecp differences are detected between the nonstationary and stationary series we find that the value of pe is lower in the nonstationary vertical velocity series than the stationary counterparts both types of series locate near the region of the higher complexity value in the cecp as chaotic systems but the pe is smaller and the complexity degree is larger in the nonstationary series than the stationary with smaller time delays due to the close relationship between pe and the multiscale shannon entropy we show that the pe and cecp can be also taken as an indicator to quantify the different organization degrees of the multiscale structures existing between the stationary and nonstationary surface vertical velocity records

from molecular models to continuum mechanics we present here a limiting process allowing us to write some continuum mechanics models as a natural asymptotic of molecular models the approach is based on the hypothesis that the macroscopic displacement is equal to the microscopic one we carry out the corresponding calculations in the case of two body energies including higher order terms and also in the case of thomas fermi type models

a model for competitiveness level analysis in sports competitions application to basketball abstract the degree of overall competitiveness of a sport league is a complex phenomenon it is difficult to assess and quantify all elements that yield the final standing in this paper we analyze the general behavior of the result matrices of each season and we use the corresponding results as a probably density thus the results of previous seasons are a way to investigate the probability that each team has to reach a certain number of victories we developed a model based on shannon entropy using two extreme competitive structures a hierarchical structure and a random structure and applied this model to investigate the competitiveness of two of the best professional basketball leagues the nba usa and the acb spain both leagues entropy levels are high nba mean 0 983 acb mean 0 980 indicating high competitiveness although the entropy of the acb from 0 986 to 0 972 demonstrated more seasonal variability than that of the nba from 0 985 to 0 990 a possible result of greater sporting gradients in the acb the use of this methodology has proven useful for investigating the competitiveness of sports leagues as well as their underlying variability across time

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

generalized entropy plane based on large deviations theory for financial time series abstract complexity entropy causality plane analysis and large deviations spectrums theory are proposed to study time series the entropy plane analysis depicts the complexity of a system in two dimensional plane while large deviations theory shows the spectral structure of time series in the way of multifractal in this paper we combine the characteristics of these two popular methods and propose a generalized entropy plane model based on the large deviation theory the methodology is applied to both synthetic data and financial markets we discuss the impact of the parameters on the results in detail besides the modified model can distinguish different time series meanwhile we compare our results with the original complexity entropy causality plane and large deviations spectrums and the consistency of these results is confirmed the method can provide abundant dynamical properties of complex systems

generalized entropy plane based on permutation entropy and distribution entropy analysis for complex time series abstract entropy is an accessible way to work as a measure of the irregularity and the uncertainty between the predicting knowledge and the given time series statistical complexity measure scm combining shannon entropy and the extensive jensen shannon divergence provides important additional information regarding the peculiarities of the underlying probability distribution not already detected by the entropy in this paper we extend the traditional complexity entropy causality plane which applies the diagram of scm versus normalized shannon entropy to two generalized complexity entropy plane based on permutation entropy pe and permuted distribution entropy pedisen moreover as the important extension of the shannon entropy the tsallis entropy and renyi entropy are used to construct the plane we discuss the parameter selection for the pe plane and pedisen plane respectively outlier detection is recently a heated point focusing on discovering patterns that occur infrequently in the time series in data mining however there exists few entropy plane based methods in outlier detection we apply the proposed procedure to the real world data for outlier detection it turns out that the generalized entropy plane is robust to the type of original series and is efficient for detecting outliers

entropic descriptor of a complex behaviour abstract we propose a new type of entropic descriptor that is able to quantify the statistical complexity a measure of complex behaviour by taking simultaneously into account the average departures of a system s entropy s from both its maximum possible value s max and its minimum possible value s min when these two departures are similar to each other the statistical complexity is maximal we apply the new concept to the variability over a range of length scales of spatial or grey level pattern arrangements in simple models the pertinent results confirm the fact that a highly non trivial length scale dependence of the entropic descriptor makes it an adequate complexity measure able to distinguish between structurally distinct configurational macrostates with the same degree of disorder a feature that makes it a good tool for discerning structures in complex patterns

complexity of dynamics as variability of predictability we construct a complexity measure from first principles as an average over the obstruction against prediction of some observable that can be chosen by the observer our measure evaluates the variability of the predictability for characteristic system behaviors which we extract by means of the thermodynamic formalism using theoretical and experimental applications we show that complex and chaotic are different notions of perception in comparison to other proposed measures of complexity our measure is easily computable non divergent for the classical 1 d dynamical systems and has properties of non overuniversality the measure can also be computed for higher dimensional and experimental systems including systems composed of different attractors moreover the results of the computations made for classical 1 d dynamical systems imply that it is not the nonhyperbolicity but the existence of a continuum of characteristic system length scales that is at the heart of complexity

using permutations to detect dependence between time series abstract in this paper we propose an independence test between two time series which is based on permutations the proposed test can be carried out by means of different common statistics such as pearson s chi square or the likelihood ratio we also point out why an exact test is necessary simulated and real data return exchange rates between several currencies reveal the capacity of this test to detect linear and nonlinear dependences

measuring randomness by leave one out prediction error analysis of eeg after painful stimulation abstract a parametric approach to measure randomness in time series is presented time series are modelled by a kernel machine performing regularized least squares and the leave one out loo error is used to quantify unpredictability on analyzing simulated data sets we find that structure in data leads to a minimum of the loo error as the regularizing parameter is varied we consider electroencephalographic signals from migraineurs and healthy humans after painful stimulation and use the proposed approach to detect changes of physiological state and to find differences between the response from patients and healthy subjects as painful stimulus causes organization of the local activity in the cortex eeg series become more predictable after stimulation this phenomenon is less evident in patients the inadequate cortical response to pain in migraineurs separates patients from controls with a probability close to 0 005

incomplete data problems in x ray computerized tomography in the present paper we study truncated projections for the fanbeam geometry in computerized tomography first we derive consistency conditions for the divergent beam transform then we study a singular value decomposition for the case where only the interior rays in the fan are provided as for example in region of interest tomography we show that the high angular frequency components of the searched for densities are well determined and we present reconstructions from real data where the missing information is approximated based on the singular value decomposition

a kalman filtering approach to stochastic global and region of interest tomography we define two forms of stochastic tomography in global tomography the goal is to reconstruct an object from noisy observations of all of its projections in region of interest roi tomography the goal is to reconstruct a small portion of an object an roi from noisy observations of its projections densely sampled in and near the roi and sparsely sampled away from the roi we solve both problems by expanding the object and its projections in a circular harmonic fourier series in the angular variable so that the radon transform becomes abel transforms of integer orders applied to the harmonics the algorithm has three major components first we fit state space models to each order of abel transform and thus represent the radon transform operation as a parallel bank of systems each of which computes the appropriate abel transform of a circular harmonic a variable transformation here allows either the global or roi problem to be solved second the object harmonics are modeled as a brownian branch this is a two point boundary value system which is markovianized into a form suitable for the kalman filter finally a parallel bank of kalman smoothing filters independently estimates each circular harmonic from the noisy projection data numerical examples illustrate the proposed procedure

on the material symmetry group of elastic crystals and the born rule the aim of this paper is to investigate the extent to which non linear elasticity theory can be used for describing the behavior of crystalline solids the results we obtain show that some strict and definite boundaries must be set to the possibility of actually doing so specifically we address here a twofold problem on one hand we pose the question of the validity of the socalled born rule a fundamental hypothesis due to cauchy and in a weaker form to born by means of which continuum theories of crystal mechanics are formulated on the other hand we explore the possibility of developing an effective elastic model independently of the rule in those cases in which the rule itself does not work our results are based on a close study of the implications of the phenomenon of mechanical twinning with regard to the symmetry properties of the energy function of an elastic crystal these are summarized by the choice of a material symmetry group g the main experimental features of twinning lead one to consider a class of twinning subgroups of g that are particular reflection groups in fact particular linear representations possibly unfaithful of abstract coxeter groups in the generic case the properties of such groups prevent the born rule from holding only when some very special non generic conditions are met by the twinning modes of a crystalline substance is the rule valid the development of an elastic model is then possible by following a well known procedure the analysis of relevant experimental data confirms that while basically all crystals exhibit twins most of them do exhibit generic twinning modes for which the hypothesis of born is violated we also show that in such generic cases any tentative thermoelastic approach developed independently of the rule does not give physically sound results and thus cannot be usefully adopted because some quite undesirable conclusions regarding the symmetry of the energy can be drawn that definitely make elasticity inadequate for our purposes experimental data point out nonetheless two quite remarkable classes of nongeneric materials for which the born rule is never violated and to which an elastic model safely applies

extremum complexity distribution of a monodimensional ideal gas out of equilibrium abstract the extremum complexity momentum distribution for an isolated monodimensional ideal gas out of equilibrium is analytically approximated in a first approximation it consists of a double non overlapping gaussian distribution in good agreement with this result the numerical simulations of a particular isolated monodimensional gas which is abruptly pushed far from equilibrium shows the extremum complexity distribution in the decay of the system toward equilibrium

gas liquid two phase flow structure in the multi scale weighted complexity entropy causality plane abstract the multi scale weighted complexity entropy causality plane ms wcecp is proposed for characterizing the physical structure of complex system firstly we use the method to investigate typical nonlinear time series compared with the multi scale complexity entropy causality plane ms cecp the ms wcecp can not only uncover the dynamic information loss of complex system with the increase of scale but also can characterize the complexity of nonlinear dynamic system in particular the algorithm of ms wcecp performs strong anti noise ability then we calculate the ms wcecp for the conductance fluctuating signals measured from vertical upward gas liquid two phase flow experiments in a small diameter pipe the results demonstrate that the ms wcecp is a useful approach for exploring the stability and complexity in gas liquid two phase flows

atomic to continuum passage for nanotubes a discrete saint venant principle and error estimates we consider general infinite nanotubes of atoms in mathbb r 3 where each atom interacts with all the others through a two body potential at the equilibrium the positions of the atoms satisfy a euler lagrange equation when there are no exterior forces and for a suitable geometry a particular family of nanotubes is the set of perfect nanotubes at the equilibrium when exterior forces are applied on the nanotube we compare the nanotube to nanotubes of the previous family in part i of the paper this quantitative comparison is formulated in our first main result as a discrete saint venant principle as a corollary we also give a liouville classification result our saint venant principle can be derived for a large class of potentials including the lennard jones potential when the perfect nanotubes at the equilibrium are stable the approach is designed to be applicable to nanotubes that can have general shapes like for instance carbon nanotubes or dna under the oversimplified assumption that all the atoms are identical in part ii of the paper we derive from our saint venant principle a macroscopic mechanical model for general nanotubes we prove that every solution is well approximated by the solution of a continuum model involving stretching and twisting but no bending we establish error estimates between the discrete and the continuous solution more precisely we give two error estimates one at the microscopic level and one at the macroscopic level

the experimental signals analysis for bubbly oil in water flow using multi scale weighted permutation entropy abstract we firstly combine multi scale method ms and weighted permutation entropy wpe to analyze chaotic noisy and fractal time series and find that mswpe can distinguish different nonlinear time series and exhibit a better robustness in the presence of higher levels of noise a task that multi scale permutation entropy mspe fails to work we then apply mswpe to analyze the signals from vertical upward oil in water two phase flow experiments our results suggest that the change rate of mswpe enables to characterize the transition of flow patterns and multi scale weighted permutation entropy allows indicating the discrepancy of complexity of oil in water two phase flow

determination of the noise level of chaotic time series we propose a method to determine the amount of measurement noise present in a chaotic time series if the data are embedded in a space of higher dimension than that strictly required to reconstruct the dynamics the extra dimensions are dominated by the noise which results in a certain shape of the correlation integral for the case in which only gaussian noise is present this shape can be calculated analytically as a function of the noise level thus the noise level can be obtained from a simple function fit the analytical result also shows that a noise level of more than 2 will obscure any possible scaling of the correlation integral and thus makes it impossible to estimate the correlation dimension

a statistical measure of complexity with nonextensive entropy abstract a statistical measure of complexity utilising the concept of entropy or information is proposed our way in this study is to use a nonextensive entropy instead of an extensive additive shannon entropy in the definition but can be characterised as a difference between the qth order renyi entropy and the second one furthermore we devise a conditional joint and mutual complexity measure as a coherent possibility the behavior of the measure for the logistic map shows that it is more sensitive to nonextensivity at the transition point ac 3 8284 than any other values when 0

variational formulation of softening phenomena in fracture mechanics the one dimensional case we show that discrete models of atoms subject to nearest neighbour non linear interactions approximate continua allowing for softening and fracture a detailed study of local minima and stationary points is carried out scale effects are discussed

comment i on simple measure for complexity we critique the measure of complexity introduced by shiner davison and landsberg phys rev e 59 1459 1999 in particular we point out that it is over universal in the sense that it has the same dependence on disorder for structurally distinct systems we then give counterexamples to the claim that complexity is synonymous with being out of equilibrium equilibrium systems can be structurally complex and nonequilibrium systems can be structurally simple we also correct a misinterpretation of a result given by two of the present authors j p crutchfield and d p feldman phys rev e 55 r1239 1997

multiscale entropy analysis of complex physiologic time series there has been considerable interest in quantifying the complexity of physiologic time series such as heart rate however traditional algorithms indicate higher complexity for certain pathologic processes associated with random outputs than for healthy dynamics exhibiting long range correlations this paradox may be due to the fact that conventional algorithms fail to account for the multiple time scales inherent in healthy physiologic dynamics we introduce a method to calculate multiscale entropy mse for complex time series we find that mse robustly separates healthy and pathologic groups and consistently yields higher values for simulated long range correlated noise compared to uncorrelated noise

wavelet localization of the radon transform the authors develop an algorithm which significantly reduces radiation exposure in x ray tomography when a local region of the body is to be imaged the algorithm uses the properties of wavelets to essentially localize the radon transform this algorithm differs from previous algorithms for doing local tomography because it recovers an approximation to the original image not the image module the nullspace of the local tomography operator or the lambda transform of the image this is possible because the authors do not truly invert the interior radon transform but rather sample the radon transform sparsely away from the local region of interest much attention in the field has been directed towards localized tomography the authors believe that this technique represents a significant contribution towards this effort

inhomogeneity and complexity measures for spatial patterns abstract in this work we examine two different measures for inhomogeneity and complexity that are derived from non extensive considerations a la tsallis their performance is then tested on theoretically generated patterns all measures are found to exhibit a most sensitive behaviour for sierpinski carpets the procedures here introduced provide us with new powerful tsallis tools for analysing the inhomogeneity and complexity of spatial patterns

cauchy born rule and the stability of crystalline solids static problems we study the connection between atomistic and continuum models for the elastic deformation of crystalline solids at zero temperature we prove under certain sharp stability conditions that the correct nonlinear elasticity model is given by the classical cauchy born rule in the sense that elastically deformed states of the atomistic model are closely approximated by solutions of the continuum model with stored energy functionals obtained from the cauchy born rule the analysis is carried out for both simple and complex lattices and for this purpose we develop the necessary tools for performing asymptotic analysis on such lattices our results are sharp and they also suggest criteria for the onset of instabilities of crystalline solids

a hankel transform approach to tomographic image reconstruction a relatively unexplored algorithm is developed for reconstructing a two dimensional image from a finite set of its sampled projections the algorithm referred to as the hankel transform reconstruction htr algorithm is polar coordinate based the algorithm expands the polar form fourier transform f r theta of an image into a fourier series in theta calculates the appropriately ordered hankel transform of the coefficients of this series giving the coefficients for the fourier series of the polar form image f p phi resolves this series giving a polar form reconstruction and interpolates this reconstruction to a rectilinear grid the htr algorithm is outlined and it is shown that its performance compares favorably to the popular convolution backprojection algorithm

extracting features of gaussian self similar stochastic processes via the bandt pompe approach by recourse to appropriate information theory quantifiers normalized shannon entropy and martin plastino rosso intensive statistical complexity measure we revisit the characterization of gaussian self similar stochastic processes from a bandt pompe viewpoint we show that the ensuing approach exhibits considerable advantages with respect to other treatments in particular clear quantifiers gaps are found in the transition between the continuous processes and their associated noises

region of interest tomography using exponential radial sampling the authors combine several ideas including nonuniform sampling and circular harmonic expansions into a new procedure for reconstructing a small region of interest roi of an image from a set of its projections that are densely sampled in the roi and coarsely sampled outside the roi specifically the radial sampling density of both the projections and the reconstructed image decreases exponentially with increasing distance from the roi the problem and data are reminiscent of the recently formulated local tomography problem however the authors algorithm reconstructs the roi of the image itself not the filtered version of it obtained using local tomography the new algorithm has the added advantages of speed it can be implemented entirely using the fft and parallelizability each image harmonic is computed independently numerical examples compare the new algorithm to filtered backprojection

an information based tool for inferring the nature of deterministic sources in real data the scope of the paper is to find signatures of the forces controlling complex systems modeled by langevin equations by recourse to information theory quantifiers we evaluate in detail the permutation entropy pe and the permutation statistical complexity psc measures for two similarity classes of stochastic models characterized by either drifting or reversion properties and employ them as a reference basis for the inspection of real series new relevant model parameters arise as compared to standard entropy measures we determine the normalized pe and psc curves according to them over a range of permutation orders n and infer the limiting measures for arbitrary large order we found that the psc measure is strongly scale dependent with systems of the drifting class showing crossovers as n increases this result gives warning signs about the proper interpretation of finite scale analysis of complexity in general processes conversely a key n invariant outcome arises that is the normalized pe values for both classes of models keep complementary for any n we argue that both pe and psc measures enable one to unravel the nature drifting or restoring of the deterministic sources underlying complexity we conclude by investigating the presence of local trends in stock price series