a practical guide to heavy tails statistical techniques and applications part 1 applications heavy tailed probability distributions in the world wide web m e crovella et al self similarity and heavy tails structural modelling of network traffic w willinger et al heavy tails in high frequency financial data u a muller et al stable paretian modelling in finance some empirical and theoretical aspects s mittnik et al risk management and quantile estimation f bassi et al part 2 time series analyzing stable time series r j adler et al inference for linear processes with stable noise m calder r a davis on estimating the intensity of long range dependence in finite and infinite variance time series m s taqqu v teverovsky why non linearities can ruin the heavy tailed modeller s day s i resnick periodogram estimates from heavy tailed data t mikosch bayesian inference for time series with infinite variance stable innovations n ravishanker z qiou part 3 heavy tail estimation hill bootstrap and jackknife estimators for heavy tails o v pictet et al characteristic function based estimation of stable distribution parameters s m kogan d b williams part 4 regression bootstrapping signs and permutations for regression with heavy tailed errors a robust resampling r lepage et al linear regression with stable disturbances j h mcculloch part 5 signal processing deviation from normality in statistical signal processing parameter estimation with alpha stable distributions p tsakalides c l nikias statistical modelling and receiver design for multi user communication networks g a tsihrintzis part 6 model structures subexponential distributions c m goldie c kluppelberg structure of stationary stable processes j rosinski tail behaviour of some shot noise processes g samorodnitsky part 7 numerical procedures numerical approximation of the symmetric stable distribution and density j h mcculloch table of the maximally skewed stable distributions j h mcculloch d b panton multivariate stable distributions approximation estimation simulation and identification j p nolan univariate stable distributions parametrizations and software j p nolan

dct domain watermarking techniques for still images detector performance analysis and a new structure a spread spectrum like discrete cosine transform dct domain watermarking technique for copyright protection of still digital images is analyzed the dct is applied in blocks of 8 spl times 8 pixels as in the jpeg algorithm the watermark can encode information to track illegal misuses for flexibility purposes the original image is not necessary during the ownership verification process so it must be modeled by noise two tests are involved in the ownership verification stage watermark decoding in which the message carried by the watermark is extracted and watermark detection which decides whether a given image contains a watermark generated with a certain key we apply generalized gaussian distributions to statistically model the dct coefficients of the original image and show how the resulting detector structures lead to considerable improvements in performance with respect to the correlation receiver which has been widely considered in the literature and makes use of the gaussian noise assumption as a result of our work analytical expressions for performance measures such as the probability of errors in watermark decoding and the probabilities of false alarms and of detection in watermark detection are derived and contrasted with experimental results

a table of elliptic integrals cubic cases forty one integrands that are rational except for the square root of a cubic polynomial with known real zeros are integrated in terms of ital r functions for which fortran codes are available in cotrast to conventional tables the interval of integration is not required to begin or end at a singular point of the integrand the table contains one elliptic integral of the first kind 26 of the second kind and 14 of the third kind only 10 of the integrals are treated in standard tables which list a large number of special cases that are unified here

when is a periodic discrete time system equivalent to a time invariant one we give the precise conditions under which a periodic discrete time linear state space system can be transformed into a time invariant one by a change of basis thus our theory is the discrete time counterpart of the classical theory of floquet transforms developed by floquet and lyapunov in the 1800s for continuous time systems we state and prove a necessary and sufficient condition for a discrete time floquet transform to exist and give a construction for the transform when it does exist our results also extend to generalized state space or descriptor systems

lqg optimal control of multirate sampled data systems an lqg control synthesis technique for multirate sampled data systems where each input has its own frequency of updating and each output has its own frequency of measurement is presented the skew of the output sampling mechanism renders the prediction problem singular for the lack of measures at some time instants an ad hoc prediction algorithm is derived by enlarging the dimension of the state vector to be estimated and feeding the state filter with a combination of measured outputs over a past and finite interval of time the constraints on the input updating mechanism are dealt with by inserting a dynamical system corresponding to a zero order hold into the loop

a table of elliptic integrals of the second kind by evaluating elliptic integrals in terms of standard r functions instead of legendre s integrals many in one case 144 formulas in previous tables are unified the present table includes only integrals of the first and second kinds having integrands with real singular points the 216 integrals of this type listed in gradshteyn and ryzhik s table constitute a small fraction of the special cases of 13 integrals evaluated here the interval of integration is not required as it is in previous table to begin or end at a singular point of the integrand fortran codes for the standard r functions are included in a supplement

analysis of multiresolution image denoising schemes using generalized gaussian and complexity priors research on universal and minimax wavelet shrinkage and thresholding methods has demonstrated near ideal estimation performance in various asymptotic frameworks however image processing practice has shown that universal thresholding methods are outperformed by simple bayesian estimators assuming independent wavelet coefficients and heavy tailed priors such as generalized gaussian distributions ggds in this paper we investigate various connections between shrinkage methods and maximum a posteriori map estimation using such priors in particular we state a simple condition under which map estimates are sparse we also introduce a new family of complexity priors based upon rissanen s universal prior on integers one particular estimator in this class outperforms conventional estimators based on earlier applications of the minimum description length mdl principle we develop analytical expressions for the shrinkage rules implied by ggd and complexity priors this allows us to show the equivalence between universal hard thresholding map estimation using a very heavy tailed ggd and mdl estimation using one of the new complexity priors theoretical analysis supported by numerous practical experiments shows the robustness of some of these estimates against mis specifications of the prior a basic concern in image processing applications

some applications of the lambert w function to classical statistical mechanics we apply the recently defined lambert w function to some problems of classical statistical mechanics i e the tonks gas and a fluid of classical particles interacting via repulsive pair potentials the latter case is considered both from the point of view of the standard theory of liquids and in the framework of a field theoretical description some new mathematical properties of the lambert w function are obtained by passing

lyapunov methods for time invariant delay difference inclusions motivated by the fact that delay difference inclusions ddis form a rich modeling class that includes for example uncertain time delay systems and certain types of networked control systems this paper provides a comprehensive collection of lyapunov methods for ddis first the lyapunov krasovskii approach which is an extension of the classical lyapunov theory to time delay systems is considered it is shown that a ddi is mathcal kl stable if and only if it admits a lyapunov krasovskii function lkf second the lyapunov razumikhin method which is a type of small gain approach for time delay systems is studied it is proved that a ddi is mathcal kl stable if it admits a lyapunov razumikhin function lrf moreover an example of a linear delay difference equation which is globally exponentially stable but does not admit an lrf is provided thus it is established that the existence of an lrf is not a necessary condition for mathcal kl stability of a ddi then it is shown that the existence of an lrf is a sufficient condition for the existence of an lkf and that only under certain additional assumptions is the converse true furthermore it is shown that an lrf induces a family of sets with certain contraction properties that are particular to time delay systems on the other hand an lkf is shown to induce a type of contractive set similar to those induced by a classical lyapunov function the class of quadratic candidate functions is used to illustrate the results derived in this paper in terms of both lkfs and lrfs respectively both stability analysis and stabilizing controller synthesis methods for linear ddis are proposed

statistical field theory for simple fluids the collective variables representation abstract an alternative representation of an exact statistical field theory for simple fluids based on the method of collective variables is presented the results obtained are examined from the point of another version of theory that was developed recently by performing a hubbard stratonovich transformation of the configurational boltzmann factor j m caillol mol phys 101 2003 1617 the analytical expressions for the pressure and the free energy are derived in two loop approximation for both versions of theory and it is shown that they are indeed equivalent the results yield a new type approximation within an untested approximation scheme

isotropic finite volume discretization finite volume methods traditionally employ dimension by dimension extension of the one dimensional reconstruction and averaging procedures to achieve spatial discretization of the governing partial differential equations on a structured cartesian mesh in multiple dimensions this simple approach based on tensor product stencils introduces an undesirable grid orientation dependence in the computed solution the resulting anisotropic errors lead to a disparity in the calculations that is most prominent between directions parallel and diagonal to the grid lines in this work we develop isotropic finite volume discretization schemes which minimize such grid orientation effects in multidimensional calculations by eliminating the directional bias in the lowest order term in the truncation error explicit isotropic expressions that relate the cell face averaged line and surface integrals of a function and its derivatives to the given cell area and volume averages are derived in two and three dimensions respectively it is found that a family of isotropic approximations with a free parameter can be derived by combining isotropic schemes based on next nearest and next next nearest neighbors in three dimensions use of these isotropic expressions alone in a standard finite volume framework however is found to be insufficient in enforcing rotational invariance when the flux vector is nonlinear and or spatially non uniform the rotationally invariant terms which lead to a loss of isotropy in such cases are explicitly identified and recast in a differential form various forms of flux correction terms which allow for a full recovery of rotational invariance in the lowest order truncation error terms while preserving the formal order of accuracy and discrete conservation of the original finite volume method are developed numerical tests in two and three dimensions attest the superior directional attributes of the proposed isotropic finite volume method prominent anisotropic errors such as spurious asymmetric distortions on a circular reaction diffusion wave that feature in the conventional finite volume implementation are effectively suppressed through isotropic finite volume discretization furthermore for a given spatial resolution a striking improvement in the prediction of kinetic energy decay rate corresponding to a general two dimensional incompressible flow field is observed with the use of an isotropic finite volume method instead of the conventional discretization c 2014 elsevier inc all rights reserved

the density functional theory of classical fluids revisited we reconsider the density functional theory of nonuniform classical fluids from the point of view of convex analysis from the observation that the logarithm of the grand partition function log xi phi is a convex functional of the external potential phi it is shown that the kohn sham free energy cal a rho is a convex functional of the density rho log xi phi and cal a rho constitute a pair of legendre transforms and each of these functionals can therefore be obtained as the solution of a variational principle the convexity ensures the unicity of the solution in both cases the variational principle which gives log xi phi as the maximum of a functional of rho is precisely that considered in the density functional theory while the dual principle which gives cal a rho as the maximum of a functional of phi seems to be a new result

anomalous scaling and lee yang zeros in self organized criticality we show that the generating functions of probability distributions in self organized criticality soc models exhibit a lee yang phenomenon phys rev 87 404 1952 namely their zeros pinch the real axis at z 1 as the system size goes to infinity this establishes a new link between the classical theory of critical phenomena and soc a scaling theory of the lee yang zeros is proposed in this setting

precise and fast computation of the general complete elliptic integral of the second kind we developed an efficient procedure to evaluate two auxiliary complete elliptic integrals of the second kind b m and d m by using their taylor series expansions the definition of jacobi s nome and legendre s relation the developed procedure is more precise than the existing ones in the sense that the maximum relative errors are 1 3 machine epsilons and it runs drastically faster around 5 times faster than bulirsch s cel2 and 16 times faster than carlson s rf and rd

fast computation of a general complete elliptic integral of third kind by half and double argument transformations we developed a novel method to calculate an associate complete elliptic integral of the third kind j n m p n m k m n the key idea is the double argument formula of j n m with respect to n we derived it from the not so popular addition theorem of jacobi s complete elliptic integral of the third kind p 1 a m with respect to a which is a real or pure imaginary argument connected with n and m as n msn 2 a m repeatedly using the half argument transformation fukushima 2010 28 of a new variable y n m or its complement x m n m we reduce y sufficiently small say less than 0 3 or so then we evaluate the integral for the reduced variable by its maclaurin series expansion the coefficients of the series expansion are recursively computed from two other associate complete elliptic integrals b m e m 1 m k m m and d m k m e m m the precise and fast computation of these two integrals is found in our previous work fukushima 2011 17 finally we recover the integral value for the original n by successively applying the double argument formula of j n m the new method is sufficiently precise in the sense that the maximum errors are less than around 10 machine epsilons for the sole computation of j n m the new method runs 1 2 1 5 and 4 7 5 5 times faster than bulirsch s cel and carlson s r j respectively in the simultaneous computation of three associate complete integrals the new method runs 1 6 1 7 and 5 3 8 0 times faster than cel and carlson s r d and r j respectively

solutions of neutral delay differential equations using a generalized lambert w function abstract the lambert w function is defined by w a e w a a 0 one of the many applications of the lambert w function is in solving delay differential equations ddes in 2003 asl and ulsoy provided a solution of some ddes in terms of the lambert w functions asl et al 2003 1 however the solutions are limited to differential equations with delay in the state variable scott et al 2006 2 introduced a generalized lambert function which was further studied by mez and baricz 2017 3 in our work we show that this generalization of the lambert w function provides an analytical solution to neutral delay differential equations nddes nddes are ddes with time delay not only in the state variables but also in the derivative terms this analytical solution is advantageous such that it is similar to the general solutions of linear odes also one can identify how the parameters affect the solution of the equation since our proposed solution is written in terms of these parameters we then propose a new numerical method to solve linear nddes using the generalized lambert w function we test our method to examples with known solutions we also provide a real world application by solving an ndde model of the population growth of an e coli culture using our proposed approach

computation of a general integral of fermi dirac distribution by mcdougall stoner method abstract we extended the method of mcdougall and stoner 1938 15 to the computation of a general integral of the fermi dirac distribution f when 0 the new method splits f into a sum of three parts a b and c and integrates them exactly and or numerically by means of the double exponential quadrature rules as increases b f damps algebraically while c f decays exponentially thus they can be ignored when exceeds certain threshold values depending on the input error tolerance when a is exactly computable and is sufficiently large such that b and c are negligible the new method was 60 1000 times faster than the numerical integration of f even if b and or c are not negligible their smallness and rapid decay significantly accelerate their numerical quadrature so that the speed up factor becomes 3 20 unless is less than 2 0 4 5 on the other hand when a is numerically integrated the speed up factor diminishes to 2 5 still the superiority of the new method to the numerical integration of f is unchanged

fast switch and spline scheme for accurate inversion of nonlinear functions the new first choice solution to kepler s equation abstract numerically obtaining the inverse of a function is a common task for many scientific problems often solved using a newton iteration method here we describe an alternative scheme based on switching variables followed by spline interpolation which can be applied to monotonic functions under very general conditions to optimize the algorithm we designed a specific ultra fast spline routine we also derive analytically the theoretical errors of the method and test it on examples that are of interest in physics in particular we compute the real branch of lambert s w y function which is defined as the inverse of xexp x and we solve kepler s equation in all cases our predictions for the theoretical errors are in excellent agreement with our numerical results and are smaller than what could be expected from the general error analysis of spline interpolation by many orders of magnitude namely by an astonishing 3 10 22 factor for the computation of w in the range w y 0 10 and by a factor 2 10 4 for kepler s problem in our tests this scheme is much faster than newton raphson method by a factor in the range 10 4 10 3 for the execution time in the examples when the values of the inverse function over an entire interval or for a large number of points are requested for kepler s equation and tolerance 10 6 rad the algorithm outperforms newton s method for all values of the number of points n 2

on asymptotic stability of discrete time linear time varying systems this note is concerned with asymptotic stability analysis of discrete time linear time varying dltv systems the contribution can be summarized as follows first the difference between nonuniformly exponential stability es which was not well recognized in the literature and uniformly es ues was revealed and illustrated by numerical examples second some state transition matrices and difference lyapunov inequalities dlis based necessary and sufficient conditions were derived for testing different stability concepts including asymptotic stability as es and ues of general dltv systems the main feature of the dlis based criteria is that the time difference of the lyapunov function is not required to be negative definite finally the es concept was utilized for analysis stability of a class of upper triangular dltv systems and perturbated dltv systems the effectiveness of the proposed results was demonstrated by some examples

supplement to a table of elliptic integrals of the second kind c c double precision function rf x y z errtol ierr c c this function subroutine computes the incomplete elliptic c integral of the first kind c rf x y z integral from zero to infinity of c c 1 2 1 2 1 2 c 1 2 t x t y t z dt c c where x y and z are nonnegative and at most one of them c is zero if one of them is zero the integral is complete c the duplication theorem is iterated until the variables are c nearly equal and the function is then expanded in taylor c series to fifth order c references b c carlson and e m notis algorithms for c incomplete elliptic integrals acm transactions on mathemac tical software 7 1981 398 403 b c carlson computing c elliptic integrals by duplication numer math 33 1979 c 1 16 c authors b c carlson and elaine m notis ames laboratoryc doe iowa state university ames ia 50011 and r l pexton c lawrence livermore national laboratory livermore ca 94550 c aug 1 1979 revised jan 15 1987 c c check value rf 0 1 2 1 31102 87771 46059 90523 24198 c check by addition theorem rf xx z x w rf y y z y w c rf o z w where x y z w are positive and x y z w c integer ierr printr double precision c1 c2 c3 e2 e3 epslon errtol lamda double precision lolim mu s uplimx xn xndev xnroot double precision yyn yndev ynroot z zn zndev znroot c intrinsic functions used dabs dmax1 dmin1 dsqrt c c printr is the unit number of the printer data printr 6 c

dissipativity of t periodic linear systems it is proved that the existence of a positive definite storage function is necessary and sufficient for strict dissipativity of linear systems with periodic coefficients the connection between strict dissipativity of the system and a nonoscillatory property of an associated hamiltonian system is established

constrained robust model predictive control based on periodic invariance in this paper a receding horizon control method for input state constrained systems with polyhedral uncertainties is proposed the dual mode prediction strategy is adopted to deal with the constraints and periodically invariant sets are used to derive a target invariant set of the dual mode prediction strategy the proposed control method is shown to have novel characteristics earlier approaches do not have i e i the convex hull of all the periodically invariant sets are invariant in the sense that there are feasible feedback gains guaranteeing invariance for any elements of the convex hull and it provides larger target sets than other methods based on ordinary invariant sets ii a particular convex hull of periodically invariant sets that is computable off line can be used as an invariant target set in this case the number of on line variables is only equal to the period of invariance and thus the proposed algorithm is computationally very efficient these on line variables provide interpolation between different feedback gains to yield best performance

sufficient conditions for stabilization of sampled data nonlinear systems via discrete time approximations given a parameterized by sampling period t family of approximate discrete time models of a sampled nonlinear plant and given a family of controllers stabilizing the family of plant models for all t sufficiently small we present conditions which guarantee that the same family of controllers semi globally practically stabilizes the exact discrete time model of the plant for sufficiently small sampling periods when the family of controllers is locally bounded uniformly in the sampling period the inter sample behavior can also be uniformly bounded so that the time varying sampled data model of the plant is uniformly semi globally practically stabilized the result justifies controller design for sampled data nonlinear systems based on the approximate discrete time model of the system when sampling is sufficiently fast and the conditions we propose are satisfied our analysis is applicable to a wide range of time discretization schemes and general plant models

state space solution to the periodic multirate h sub spl infin control problem a lifting approach a two riccati equation solution to the h sub spl infin control problem for periodic multirate systems is derived via the lifting method the solution is expressed in terms of two algebraic riccati equations the causality constraints are represented by a set of positive definiteness conditions and coupling criteria as a by product the study shows that there is a close connection between the solution of the causally constrained lifted problem and the solution obtained by solving the problem directly as a periodic h sub spl infin problem defined for the multirate system

precise and fast computation of lambert w functions without transcendental function evaluations we have developed a new method to compute the real valued lambert w functions w 0 z and w 1 z the method is a composite of 1 the series expansions around the branch point w 1 and around zero w 0 and 2 the numerical solution of the modified defining equation w ze w in the latter process we 1 repeatedly duplicate a test interval until it brackets the solution 2 conduct bisections to find an approximate solution and 3 improve it by a single application of the fifth order formula of schroder s method the first two steps are accelerated by preparing auxiliary numerical constants beforehand and utilizing the addition theorem of the exponential function as a result the new method requires no call of transcendental functions such as the exponential function or the logarithm this makes it around twice as fast as existing methods 1 7 and 2 0 times faster than the methods of fritsch et al 1973 and veberic 2012 16 14 for w 0 z and 1 8 and 2 0 times faster than the methods of veberic 2012 14 and chapeau blondeau and monir 2002 13 for w 1 z

numerical evaluation of the lambert w function and application to generation of generalized gaussian noise with exponent 1 2 we address the problem of synthesizing a generalized gaussian noise with exponent 1 2 by means of a nonlinear memoryless transformation applied to a uniform noise we show that this transformation is expressable in terms of a special function known under the name of the lambert w function we review the main methods for numerical evaluation of the relevant branch of the multivalued lambert w function with controlled accuracy and complement them with an original rational function approximation based on these methods synthesis of the generalized gaussian noise can be performed with arbitrary accuracy we construct a simple and fast evaluation algorithm with prescribed accuracy which is especially suited for monte carlo simulation requiring large numbers of realizations of the generalized gaussian noise

on stability and stabilization of periodic discrete time systems with an application to satellite attitude control an alternative stability analysis theorem for nonlinear periodic discrete time systems is presented the developed theorem offers a trade off between conservatism and complexity of the corresponding stability test in addition it yields a tractable stabilizing controller synthesis method for linear periodic discrete time systems subject to polytopic state and input constraints it is proven that in this setting the proposed synthesis method is strictly less conservative than available tractable synthesis methods the application of the derived method to the satellite attitude control problem results in a large region of attraction

relative entropy fuzzy c means clustering pattern recognition is a collection of computer techniques to classify various observations into different clusters of similar attributes in either supervised or unsupervised manner application of fuzzy logic to unsupervised classification or clustering methods has resulted in many wildly used techniques such as fuzzy c means fcm method however when the observations are too noisy the performance of such methods might be reduced thus in this paper a new fuzzy clustering method based on fcm is presented and the relative entropy is added to its objective function as a regularization function to maximize the dissimilarity between clusters several examples are provided to examine the performance of the proposed clustering method the obtained results show that the proposed method has a very good ability in detecting noises and assignment of suitable membership degrees to the observations

a table of elliptic integrals one quadratic factor integration in terms of real quantities is accomplished for 33 integrands that are rational except for the square root of a cubic or quartic polynomial with exactly one pair of conjugate complex zeros formulas are provided by which 45 more integrals of the same type can be expressed in terms of real quantities with the help of earlier papers neither limit of integration is assumed to be a singular point of the integrand all the integrals are reduced to r functions for which fortran programs are available most of the integrals are not listed in other tables

numerical computation of inverse complete elliptic integrals of first and second kinds we developed the numerical procedures to evaluate the inverse functions of the complete elliptic integrals of the first and the second kind k m and e m with respect to the parameter m the evaluation is executed by inverting eight sets of the truncated taylor series expansions of the integrals in terms of m or of log 1 m the developed procedures are 1 so precise that the maximum absolute errors are less than 3 5 machine epsilons and 2 30 40 faster than the evaluation of the integrals themselves by the fastest procedures fukushima 2009a 2011

brief paper predictive control of hybrid systems input to state stability results for sub optimal solutions this article presents a novel model predictive control mpc scheme that achieves input to state stabilization of constrained discontinuous nonlinear and hybrid systems input to state stability iss is guaranteed when an optimal solution of the mpc optimization problem is attained special attention is paid to the effect that sub optimal solutions have on iss of the closed loop system this issue is of interest as firstly the infimum of mpc optimization problems does not have to be attained and secondly numerical solvers usually provide only sub optimal solutions an explicit relation is established between the deviation of the predictive control law from the optimum and the resulting deterioration of the iss property of the closed loop system by imposing stronger conditions on the sub optimal solutions iss can even be attained in this case

dissipation additions to flux difference splitting abstract although the flux difference splitting methods for solving the euler equations are generally very robust and no explicit dissipation is required there are situations where explicit dissipation is needed two cases a slowly moving shock problem and a blunt body calculation are discussed in this paper the slowly moving shock problem is tested extensively by roe s riemann solver and a cure for roe s riemann solver is proposed for the second order scheme it is found necessary to reduce the second order accuracy to first order accuracy inside the shock layer for the supersonic blunt body calculation adding dissipation in the linear waves in roe s riemann solver can prevent numerical instability in the subsonic pocket the drawback of yee s formula to cure the instability when used on viscous flow calculation is demonstrated a better solution based on the pressure gradient is proposed

numerical perturbative and chebyshev inversion of the incomplete elliptic integral of the second kind abstract the incomplete elliptic integral of the second kind e sin t m 0 t 1 m sin 2 t dt where m 0 1 is the elliptic modulus can be inverted with respect to angle t by solving the transcendental equation e sin t m z 0 we show that newton s iteration t n 1 t n e sin t m z 1 m sin 2 t always converges to t z m e 1 z m within a relative error of less than 10 10 in three iterations or less from the first guess t 0 z m 2 r 2 where defining 1 z e 1 m r 1 m 2 2 and atan 1 m we briefly discuss three alternative initialization strategies homotopy initialization t 0 z m 1 m z 0 mt z m m 1 perturbation series in powers of m and inversion of the chebyshev interpolant of the incomplete elliptic integral although all work well and are general strategies applicable to a very wide range of problems none of these three alternatives is as efficient as the empirical initialization which is completely problem specific this illustrates tai tsun wu s maxim usefulness is often inversely proportional to generality

dichotomy and absolute stability of nonlinear systems with periodically nonstationary linear part abstract systems with periodically nonstationary linear part are considered inputs and outputs of nonlinearities satisfy a certain integral quadratic constraint the conditions necessary and sufficient of dichotomy and absolute stability are obtained

precise and fast computation of a general incomplete elliptic integral of second kind by half and double argument transformations this is a continuation of our works to compute the incomplete elliptic integrals of the first and second kind fukushima 2010 2011 21 23 we developed a method to compute an associate incomplete elliptic integral of the third kind j f n m p f n m f f m n by the half argument formulas of the sine and cosine amplitude functions and the double argument transformation of the integral the relative errors of j f n m computed by the new method are sufficiently small as less than 20 machine epsilons meanwhile the simplicity of the adopted algorithm makes the new method run 1 5 to 3 7 times faster than carlson s duplication method the combination of the new method and that to compute simultaneously two other associate incomplete elliptic integrals of the second kind b f m e f m 1 m f f m m and d f m f f m e f m m which we established recently 23 enables a precise and fast computation of arbitrary linear combination of legendre s incomplete elliptic integrals of all three kinds f f m e f m and p f n m these new procedures share the same device the half argument transformations while the double argument transformation of j f n m includes those of b f m and d f m as its sub component as a result the simultaneous computation of the three associate integrals is significantly faster than computing them separately in fact our combined procedure is 2 7 to 5 9 times faster than the combination of carlson s duplication method to compute r d and r j

on q non extensive statistics with non tsallisian entropy we combine an axiomatics of renyi with the qq deformed version of khinchin axioms to obtain a measure of information i e entropy which accounts both for systems with embedded self similarity and non extensivity we show that the entropy thus obtained is uniquely solved in terms of a one parameter family of information measures the ensuing maximal entropy distribution is phrased in terms of a special function known as the lambert w function we analyze the corresponding high and low temperature asymptotics and reveal a non trivial structure of the parameter space salient issues such as concavity and schur concavity of the new entropy are also discussed

stability of periodically time varying systems this paper proposes a novel approach to stability analysis of discrete time nonlinear periodically time varying systems the contributions are as follows firstly a relaxation of standard lyapunov conditions is derived this leads to a less conservative lyapunov function that is required to decrease at each period rather than at each time instant secondly for linear periodic systems with constraints it is shown that compared to standard lyapunov theory the novel concept of periodic lyapunov functions allows for the calculation of a larger estimate of the region of attraction an example illustrates the effectiveness of the developed theory

structural properties of multirate sampled data systems a complete analysis of the structural properties of multirate sampled data systems is considered in this paper necessary and sufficient conditions for the reachability controllability and stabilizability and for the dual notions are given in terms of simple rank tests these results obtained by the structural theory of periodic systems generalize to the multirate case the well known conditions of the single rate case

further remarks on strict input to state stable lyapunov functions for time varying systems we study the stability properties of a class of time varying non linear systems we assume that non strict input to state stable iss lyapunov functions for our systems are given and posit a mild persistency of excitation condition on our given lyapunov functions which guarantee the existence of strict iss lyapunov functions for our systems next we provide simple direct constructions of explicit strict iss lyapunov functions for our systems by applying an integral smoothing method we illustrate our constructions using a tracking problem for a rotating rigid body

lattice vector quantization of generalized gaussian sources many important sources of data including sub band image and speech coefficients are highly peaked and can be well modeled by the family of generalized gaussian gg pdfs parameterized by a shape parameter spl nu we present here algorithms for defining and quantizing to a z lattice in which the boundary is optimized to the characteristics of gg sources and show that these techniques lead to high performance and low complexity for bit rates and dimensions that are of interest in a number of practical coding applications we derive an analytical description of the granular and overload distortion valid for low and moderate bit rates and also provide a description of quantizer performance in the limit of high rate and dimension

on the structure of the solution set of a generalized euler lambert equation abstract the transcendental equation x e x z and its solutions described by the lambert w function often occur in physics and mathematics in the last decades it turned out that the study of similar but more general equations is necessary in molecular physics in the theory of general relativity and also in the description of bose fermi mixtures as well as in some combinatorial problems in this paper we offer a full description for the solution set of a one parameter generalization of the above mentioned equation

noise enhanced performance for an optimal bayesian estimator a novel instance of a stochastic resonance effect under the form of a noise improved performance is shown to be possible for an optimal bayesian estimator estimation of the frequency of a periodic signal corrupted by a phase noise is considered the optimal bayesian estimator achieving the minimum of the mean square estimation error is explicitly derived conditions are exhibited where this minimal error is reduced when the noise level is raised over some ranges where this occurs essentially with non gaussian noise in the tested configurations these results contribute a new step in the exploration of stochastic resonance and its potentialities for signal processing

on the modeling of dct and subband image data for compression image subband and discrete cosine transform coefficients are modeled for efficient quantization and noiseless coding quantizers and codes are selected based on laplacian fixed generalized gaussian and adaptive generalized gaussian models the quantizers and codes based on the adaptive generalized gaussian models are always superior in mean squared error distortion performance but generally by no more than 0 08 bit pixel compared with the much simpler laplacian model based quantizers and noiseless codes this provides strong motivation for the selection of pyramid codes for transform and subband image coding

smooth lyapunov functions for hybrid systems part i existence is equivalent to robustness hybrid systems are dynamical systems where the state is allowed to either evolve continuously flow on certain subsets of the state space or evolve discontinuously jump from other subsets of the state space for a broad class of such systems characterized by mild regularity conditions on the data we establish the equivalence between the robustness of stability with respect to two measures and a characterization of such stability in terms of a smooth lyapunov function this result unifies and generalizes previous results for differential and difference inclusions with outer semicontinuous and locally bounded right hand sides furthermore we give a description of forward completeness of a hybrid system in terms of a smooth lyapunov like function

statistical texture characterization from discrete wavelet representations we conjecture that texture can be characterized by the statistics of the wavelet detail coefficients and therefore introduce two feature sets 1 the wavelet histogram signatures which capture all first order statistics using a model based approach and 2 the wavelet co occurrence signatures which reflect the coefficients second order statistics the introduced feature sets outperform the traditionally used energy best performance is achieved by combining histogram and co occurrence signatures

brief paper razumikhin type stability theorems for discrete delay systems in this paper by employing the razumikhin technique and lyapunov functions razumikhin type theorems that guarantee the uniform stability uniformly asymptotic stability and uniformly exponential stability for the general discrete delay systems are established respectively moreover razumikhin type uniformly exponential stability theorem gives the estimation of the convergence speed as theoretic application the razumikhin type uniformly exponential stability result is further studied and used to show some well known stability results for some kinds of discrete delay systems finally examples are also worked through to illustrate our results

smooth lyapunov functions for hybrid systems part ii pre asymptotically stable compact sets it is shown that pre asymptotic stability which generalizes asymptotic stability of a compact set for a hybrid system satisfying mild regularity assumptions is equivalent to the existence of a smooth lyapunov function this result is achieved with the intermediate result that asymptotic stability of a compact set for a hybrid system is generically robust to small state dependent perturbations as a special case we state a converse lyapunov theorem for systems with logic variables and use this result to establish input to state stabilization using hybrid feedback control the converse lyapunov theorems are also used to establish semiglobal practical robustness to slowly varying weakly jumping parameters to temporal regularization to the insertion of jumps according to an ldquoaverage dwell timerdquo rule and to the insertion of flow according to a ldquoreverse average dwell timerdquo rule

recursive computation of derivatives of elliptic functions and of incomplete elliptic integrals presented are the recurrence formulas to compute the derivatives of a general elliptic function weierstrass s function the jacobian elliptic functions and the incomplete elliptic integrals in the forms of jacobi and legendre with respect to the argument or the amplitude the double precision computation by the formulas is correct with 15 digits or so for the first 10 orders of differentiation at least

a table of elliptic integrals of the third kind as many as 72 elliptic integrals of the third kind in previous tables are unified by evaluation in terms of r functions instead of legendre s integrals the present table includes only integrals having integrands with real singular points in addition to 31 integrals of the third kind most of them unavailable elsewhere 10 integrals of the first and second kinds from an earlier table are listed again in new notation in contrast to conventional tables the interval of integration is not required to begin or end at a singular point of the integrand fortran codes for the standard r functions r sub c and r sub j revised to include their cauchy principal values are listed in a supplement

numerical inversion of a general incomplete elliptic integral we present a numerical method to invert a general incomplete elliptic integral with respect to its argument and or amplitude the method obtains a solution by bisection accelerated by half argument formulas and addition theorems to evaluate the incomplete elliptic integrals and jacobian elliptic functions required in the process if faster execution is desirable at the cost of complexity of the algorithm the sequence of bisection is switched to allow an improvement by using newton s method halley s method or higher order schroder methods in the improvement process the elliptic integrals and functions are computed by using maclaurin series expansion and addition theorems based on the values obtained at the end of the bisection also the derivatives of the elliptic integrals and functions are recursively evaluated from their values by adopting 0 2 as the critical value of the length of the solution interval to shift to the improvement process we suppress the expected number of bisections to be as low as four on average the typical number of applications of update formulas in the double precision environment is three for newton s method and two for halley s method or higher order schroder methods whether the improvement process is added or not our method requires none of the procedures to compute the incomplete elliptic integrals and jacobian elliptic functions but only those to evaluate the complete elliptic integrals once at the beginning as a result it runs fairly quickly in general for example when using the improvement process it is around 2 5 times faster than newton s method using boyd s starter boyd 2012 25 in inverting e f m legendre s incomplete elliptic integral of the second kind

a new asymptotic stability criterion for nonlinear time variant differential equations a new sufficient condition for asymptotic stability of ordinary differential equations is proposed unlike classical lyapunov theory the time derivative along solutions of the lyapunov function may have positive and negative values the classical lyapunov approach may be regarded as an infinitesimal version of the present theorem verification in practical problems is harder than in the classical case an example is included in order to indicate how the present theorem may be applied

brief strict lyapunov functions for time varying systems uniformly asymptotically stable periodic time varying systems for which is known a lyapunov function with a derivative along the trajectories non positive and negative definite in the state variable on non empty open intervals of the time are considered for these systems strict lyapunov functions are constructed

fast computation of incomplete elliptic integral of first kind by half argument transformation we developed a new method to calculate the incomplete elliptic integral of the first kind f varphi m by using the half argument formulas of jacobian elliptic functions the method reduces the magnitude of varphi by repeated usage of the formulas while fixing m the method is sufficiently precise in the sense that the maximum relative error is 3 5 machine epsilons at most thanks to the simplicity of the half argument formulas the new procedure is significantly faster than the existing procedures for example it runs 20 60 faster than bulirsch function el1 and 1 9 2 2 times faster than the method using carlson s function r f

precise and fast computation of fermi dirac integral of integer and half integer order by piecewise minimax rational approximation piecewise quadruple precision approximations of the fermi dirac integral of integer order 0 1 10 and half integer order 9 2 1 21 2 are developed by combining i the optimally truncated sommerfeld expansion ii the piecewise truncated chebyshev series expansion and or iii the reflection formula they are used in constructing the double precision piecewise minimax rational approximations of the integral of the same orders the relative errors of the new minimax approximations which are all due to rounding off are 3 13 machine epsilons at most and less than 4 machine epsilons typically while their cpu times are only 0 44 1 1 times that of the exponential function when 5 45 as a result the new approximations run 16 31 times faster than the piecewise chebyshev polynomial approximations macleod 1998 for the physically important orders 1 2 1 5 2 and 330 720 and 50 93 times faster than the combined series expansions goano 1995 for the half integer orders 1 2 1 21 2 and the integer orders 1 1 9 respectively a file of the fortran codes of the obtained approximations and their test program and sample output is named xfdh txt and located at https www researchgate net profile toshio fukushima

the schwarzian newton method for solving nonlinear equations with applications the author acknowledges financial support from ministerio de economia y competitividad project mtm2012 34787