exploring estimator bias variance tradeoffs using the uniform cr bound we introduce a plane which we call the delta sigma plane that is indexed by the norm of the estimator bias gradient and the variance of the estimator the norm of the bias gradient is related to the maximum variation in the estimator bias function over a neighborhood of parameter space using a uniform cramer rao cr bound on estimator variance a delta sigma tradeoff curve is specified that defines an unachievable region of the delta sigma plane for a specified statistical model in order to place an estimator on this plane for comparison with the delta sigma tradeoff curve the estimator variance bias gradient and bias gradient norm must be evaluated we present a simple and accurate method for experimentally determining the bias gradient norm based on applying a bootstrap estimator to a sample mean constructed from the gradient of the log likelihood we demonstrate the methods developed in this paper for linear gaussian and nonlinear poisson inverse problems

stability boundary and collisions of two dimensional solitons in pt symmetric couplers with the cubic quintic nonlinearity we introduce one and two dimensional 1d and 2d models of parity time mathcal pt symmetric couplers with the mutually balanced linear gain and loss applied to the two cores and cubic quintic cq nonlinearity acting in each one the 2d and 1d models may be realized in dual core optical wave guides in the spatiotemporal and spatial domains respectively stationary solutions for mathcal pt symmetric solitons in these systems reduce to their counterparts in the usual coupler the most essential problem is the stability of the solitons which become unstable against symmetry breaking with the increase of the energy norm and retrieve the stability at still larger energies the boundary value of the intercore coupling constant above which the solitons are completely stable is found by means of an analytical approximation based on the cw zero dimensional counterpart of the system the approximation demonstrates good agreement with numerical findings for the 1d and 2d solitons numerical results for the stability limits of the 2d solitons are obtained by means of the computation of eigenvalues for small perturbations and verified in direct simulations although large parts of the soliton families are unstable the instability is quite weak collisions between 2d solitons in the mathcal pt symmetric coupler are studied by means of simulations outcomes of the collisions are inelastic but not destructive as they do not break the mathcal pt symmetry

targeting characteristic wave properties in reaction diffusion systems by optimization of external forcing we consider the targeted manipulation of reaction diffusion waves by optimization of an external forcing parameter as an example we present numerical results for the fitzhugh nagumo system exploiting model based optimization capable of targeting characteristic wave properties such as wavelength shape and propagation speed by spatiotemporally controlling electric current the conceptual basis of our approach is optimal control of periodic orbits in a wave variable coordinate system the results are transferred back to the partial differential equation context and validated in numerical simulations the whole procedure is applicable to any reaction diffusion model

detecting shocks outliers and breaks in time series abstract a single outlier in a regression model can be detected by the effect of its deletion on the residual sum of squares an equivalent procedure is the simple intervention in which an extra parameter is added for the mean of the observation in question similarly for unobserved components or structural time series models the effect of elaborations of the model on inferences can be investigated by the use of interventions involving a single parameter such as trend or level changes because such time series models contain more than one variance the effect of the intervention is measured by the change in individual variances we examine the effect on the estimated parameters of moving various kinds of intervention along the series the horrendous computational problems involved are overcome by the use of score statistics combined with recent developments in filtering and smoothing interpretation of the resulting time series plots of diagnostics is aided by simulation envelopes our procedures illustrated with four example permit keen insights into the fragility of inferences to specific shocks such as outliers and level breaks although the emphasis is mostly on parameter estimation forecast are also considered possible extensions include seasonal adjustment and detrending of series

feedback control of the kuramoto sivashinsky equation abstract this work focuses on linear finite dimensional output feedback control of the kuramoto sivashinsky equation kse with periodic boundary conditions under the assumption that the linearization of the kse around the zero solution is controllable and observable linear finite dimensional output feedback controllers are synthesized that achieve stabilization of the zero solution for any value of the instability parameter the controllers are synthesized on the basis of finite dimensional approximations of the kse which are obtained through galerkin s method the performance of the controllers is successfully tested through computer simulations

control of rare intense events in spatiotemporally chaotic systems we address the problem of using feedback control for the purpose of suppressing rare intense events in spatially extended systems as an example we investigate the use of control to suppress turbulent spikes in the complex ginzburg landau equation in the limit of small dissipation we explore how information obtained by forecasting can be used to implement spatially and temporally localized control parameter changes and how control strength and cost are related to effectiveness in this framework the effects of model error and imperfect state measurement are also considered

bootstrap multiple tests applied to sensor location a method for finding optimal locations of vibration sensors within a group of sensors for detecting knock in combustion engines is proposed it differs from other techniques in that only signal processing and statistical tests are used the method is based on linearly predicting the in cylinder pressure in a combustion chamber from the output signals of a group of vibration sensors being distributed on the engine wall the irrelevancy of a sensor in the group is characterized by the closeness to zero of a coherence gain explained by this sensor at some frequencies of interest we formulate multiple hypotheses define suitable statistics approximate their sampling distributions by the nonparametric bootstrap method and construct the generalized sequentially rejective bonferroni multiple test the level of accuracy of bootstrap tests is superior to that of asymptotic tests provided the test statistic used is asymptotically pivotal to achieve pivoting we transform the test statistic into a variance stable scale where we use a bootstrap technique to approximate the variance stabilizing transformation simulations results as well as results of an experiment performed on a test bed with a four cylinder engine emphasize the applicability of the method

hole solutions in the 1d complex ginzburg landau equation abstract the cubic complex ginzburg landau equation cgle has a one parameter family of traveling localized source solutions these so called nozaki bekki holes are dynamically stable in some parameter range but always structurally unstable a perturbation of the equation in general leads to a positive or negative monotonic acceleration or an oscillation of the holes this confirms that the cubic cgle has an inner symmetry as a consequence small perturbations change some of the qualitative dynamics of the cubic cgle and enhance or suppress spatio temporal intermittency in some parameter range an analytic stability analysis of holes in the cubic cgle and a semianalytical treatment of the acceleration instability in the perturbed equation is performed by using matching and perturbation methods furthermore we treat the asymptotic hole shock interaction the results which can be obtained fully analytically in the nonlinear schro dinger limit are also used for the quantitative description of modulated solutions made up of periodic arrangements of traveling holes and shocks

a recursive algorithm for computing cramer rao type bounds on estimator covariance we give a recursive algorithm to calculate submatrices of the cramer rao cr matrix bound on the covariance of any unbiased estimator of a vector parameter spl theta our algorithm computes a sequence of lower bounds that converges monotonically to the cr bound with exponential speed of convergence the recursive algorithm uses an invertible splitting matrix to successively approximate the inverse fisher information matrix we present a statistical approach to selecting the splitting matrix based on a complete data incomplete data formulation similar to that of the well known em parameter estimation algorithm as a concrete illustration we consider image reconstruction from projections for emission computed tomography

anomalous lyapunov spectrum in globally coupled oscillators abstract numerical experiments of a globally coupled oscillator system show that one type of collective chaos of high dimension has discrete and continuous parts in its lyapunov spectrum this occurs in a scattered state i e a state in which no two oscillators behave identically it is argued from a consideration of the phase space structure that the discrete exponents are related to in a sense the macroscopic dynamics while the continuous part reflects the microscopic dynamics this type of high dimensional chaos is compared to a second type possessing an apparently continuous part only preceding the appearance of the first type we found a sequence of bifurcations of collective low dimensional behavior in scattered states and their investigation reveals the route to the first type of the high dimensional chaos

monte carlo evaluation of resampling based hypothesis tests abstract monte carlo estimation of the power of tests that require resampling can be very computationally intensive it is possible to reduce the size of the inner resampling loop as long as the resulting estimator of power can be corrected for bias a simple linear extrapolation method is shown to perform well in correcting for bias and thus reduces computation time in monte carlo power studies

constrained realization monte carlo method for hypothesis testing abstract we compare two theoretically distinct approaches to generate artificial or surrogate data for testing hypotheses about a given data set the first and more straightforward approach is to fit a single best model to the original data and then to generate surrogate data sets that are typical realizations of that model the second approach concentrates not on the model but directly on the original data it attempts to constrain the surrogate data sets so that they exactly agree with the original data for a specified set of sample statistics examples of these two approaches are provided for two simple cases a test for deviations from a gaussian distribution and a test for serial dependence in a time series additionally we consider test for nonlinearity in time series based on a fourier transform ft method and on more conventional autoregressive moving average arma fits to the data the comparative performance of hypothesis testing schemes based on these two approaches is found to depend on whether or not the discriminating statistic is pivotal a statistic is pivotal if its distribution is the same for all processes consistent with the null hypothesis the typical realization method requires that the discriminating statistic satisfy this property the constrained realization approach on the other hand does not share this requirement and can provide an accurate and powerful test without having to sacrifice flexibility in the choice of discriminating statistic

feedback control of subcritical oscillatory instabilities feedback control of a subcritical oscillatory instability is investigated in the framework of a globally controlled complex ginzburg landau equation that describes the nonlinear dynamics near the instability threshold the control is based on a feedback loop between the system linear growth rate and the maximum of the amplitude of the emerging pattern it is shown that such control can suppress the blow up and result in the formation of spatially localized pulses similar to oscillons in the one dimensional case depending on the values of the linear and nonlinear dispersion coefficients several types of the pulse dynamics are possible in which the computational domain contains i a single stationary pulse ii several coexisting stationary pulses iii competing pulses that appear one after another at random locations so that at each moment of time there is only one pulse in the domain iv spatiotemporally chaotic system of short pulses v spatially synchronized pulses similar dynamic behavior is found also in the two dimensional case the effect of the feedback delay is also studied it is shown that the increase of the delay leads to an oscillatory instability of the pulses and the formation of pulses with oscillating amplitude

beyond the odd number limitation a bifurcation analysis of time delayed feedback control we investigate the normal form of a subcritical hopf bifurcation subjected to time delayed feedback control bifurcation diagrams which cover time dependent states as well are obtained by analytical means the computations show that unstable limit cycles with an odd number of positive floquet exponents can be stabilized by time delayed feedback control contrary to incorrect claims in the literature the model system constitutes one of the few examples where a nonlinear time delay system can be treated entirely by analytical means

blow up profile for the complex ginzburg landau equation abstract we construct a solution to the complex ginzburg landau equation which blows up in finite time t only at one blow up point we also give a sharp description of its blow up profile the proof relies on the reduction of the problem to a finite dimensional one and the use of index theory to conclude two major difficulties arise in the proof the linearized operator around the profile is not self adjoint and it has a second neutral mode in the last section the interpretation of the parameters of the finite dimensional problem in terms of the blow up time and the blow up point gives the stability of the constructed solution with respect to perturbations in the initial data

global feedback control for pattern forming systems global feedback control of pattern formation in a wide class of systems described by the swift hohenberg sh equation is investigated theoretically by means of stability analysis and numerical simulations two cases are considered i feedback control of the competition between hexagon and roll patterns described by a supercritical sh equation and ii the use of feedback control to suppress the blowup in a system described by a subcritical sh equation in case i it is shown that feedback control can change the hexagon and roll stability regions in the parameter space as well as cause a transition from up to down hexagons and stabilize a skewed mixed mode hexagonal pattern in case ii it is demonstrated that feedback control can suppress blowup and lead to the formation of spatially localized patterns in the weakly nonlinear regime the effects of a delayed feedback are also investigated for both cases and it is shown that delay can induce temporal oscillations as well as blowup

from collective oscillations to collective chaos in a globally coupled oscillator system abstract various types of collective behaviors are discovered in globally coupled ginzburg landau oscillators when the coupling is sufficiently weak the oscillators are either in complete synchrony or their phases are scattered completely randomly for finite coupling new collective behaviors emerge such as splitting of the population into a small number of clusters or their fusion into a continuous stringlike distribution in the phase plane low dimensional chaotic dynamics arises from the coupled motion of 3 point clusters chaotic motion is also exhibited by fused clusters which is of extremely high dimension possibly proportional to the system size as is implied from its lyapunov analysis in the latter type of chaos the motion of the string is in some cases characterized by repeated stretching and foldings it is argued how this kind of coherent behavior seen on a collective level does not contradict the high dimensionality of the corresponding chaotic attractor

stability and nonlinear dynamics of solitary waves generated by subcritical oscillatory instability under the action of feedback control we consider the influence of global feedback control which acts on an oscillatory system governed by a subcritical ginzburg landau equation exact solutions corresponding to solitary wave solutions are obtained a generalized variational approach is applied for the simplification of the whole problem and its reduction to a finite dimensional dynamical model the finite dimensional evolution model is used for studying the indirect interaction between solitary waves caused by the global control the stability analysis is held in the framework of the finite dimensional model the boundaries of monotonic and oscillatory instabilities are obtained the basic types of dynamics provided by the finite dimensional model are described and compared with the results of a direct numerical simulation of the original equation

control of pattern formation by time delay feedback with global and local contributions we consider the suppression of spatiotemporal chaos in the complex ginzburglandau equation by a combined global and local time delay feedback feedback terms are implemented as a control scheme i e they are proportional to the difference between the time delayed state of the system and its current state we perform a linear stability analysis of uniform oscillations with respect to space dependent perturbations and compare with numerical simulations similarly for the fixed point solution that corresponds to amplitude death in the spatially extended system a linear stability analysis with respect to space dependent perturbations is performed and complemented by numerical simulations

nonparametric monte carlo tests for multivariate distributions summary in this paper nonparametric monte carlo test procedures are proposed for composite hypotheses in which the multivariate distribution belongs to a nonparametric family when a random variable is in distribution equal to a product of two independent variables monte carlo simulations can be performed conditionally on one of the variables they can be applied to testing several commonly used distributions including elliptically symmetric reflectively symmetric liouville dirichlet and symmetric scale mixture distributions the tests are exactly valid when the hypothetical distributions are without nuisance location parameters finite sample simulations show that the monte carlo tests outperform bootstrap tests the method is illustrated with analysis of a real dataset

a modified uniform cramer rao bound for multiple pinhole aperture design this paper presents a modified uniform cramer rao bound ucrb for studying estimator spatial resolution and variance tradeoffs we proposed to use a resolution constraint that is imposed on mean gradient vectors of achieved estimators and derived the minimum achievable variance for any estimator satisfies this resolution constraint this approach partially overcomes the limitations of the former ucrb approach based on a bias gradient norm constraint we applied this method in a feasibility study of using multiple pinhole apertures for small animal spect imaging applications the spect system studied was based on an existing gamma camera the achievable spatial resolution and variance tradeoffs for systems with different design parameters such as number of pinholes and pinhole size were studied

dynamical models for dissipative localized waves of the complex ginzburg landau equation finite dimensional dynamical models for solitons of the cubic quintic complex ginzburg landau equation cgle are derived the models describe the evolution of the pulse parameters such as the maximum amplitude pulse width and chirp a clear correspondence between attractors of the finite dimensional dynamical systems and localized waves of the continuous dissipative system is demonstrated it is shown that stationary solitons of the cgle correspond to fixed points while pulsating solitons are associated with stable limit cycles the models show that a transformation from a stationary soliton to a pulsating soliton is the result of a hopf bifurcation in the reduced dynamical system the appearance of moving fronts kinks in the cgle is related to the loss of stability of the limit cycles bifurcation boundaries and pulse behavior in the regions between the boundaries for a wide range of system parameters are found from analysis of the reduced dynamical models we also provide a comparison between various models and their correspondence to the exact results

lorentzian type soliton solutions of ac driven complex ginzburg landau equation abstract fractional transform solutions of modified complex ginzburg landau equation phase locked to a time dependent force have been found the reported solutions are necessarily of the lorentzian type containing trigonometric hyperbolic and pure cnoidal functions numerical simulations indicated that the periodic solutions and soliton solutions are quite stable against finite perturbations

evolution of nonsoliton and quasi classical wavetrains in nonlinear schro dinger and korteweg de vries equations with dissipative perturbations abstract nonlinear schrodinger equations with attraction and with repulsion nse and nse and the korteweg de vries equation perturbed by small dissipative terms are considered near the linear instability threshold where nonlinear and spatially nonuniform dissipations dominate explicit solutions expressing the local amplitude and occupation numbers of a nonsoliton dispersive wavetrain in terms of arbitrary initial data are obtained at sufficiently large times in the logarithmic approximation for nse the particular case of the wavetrain near the soliton birth threshold is also considered the influence of the dissipation on the evolution of a quasi classical strongly nonlinear wavetrain is studied it is demonstrated that for nse the dissipation can be taken into account within the framework of the eikonal approximation while for the nse a perturbation theory based on the inverse scattering transform is relevant

spillover stabilization in finite dimensional control and observer design for dissipative evolution equations we consider the problem of global stabilization of a semilinear dissipative evolution equation by finite dimensional control with finite dimensional outputs coupling between the system modes occurs directly through the nonlinearity and also through the control influence functions similar modal coupling occurs in the infinite dimensional error dynamics through the nonlinearity and measurements for both the control and observer designs rather than decompose the original system into fourier modes we consider lyapunov functions based on the infinite dimensional dynamics of the state and error systems respectively the inner product terms of the lyapunov derivative are decomposed into fourier modes upper bounds on the terms representing control and observation spillover are obtained linear quadratic regulator lqr designs are used to stabilize the state and error systems with these upper bounds relations between system and lqr design parameters are given to ensure global stability of the state and error dynamics with robustness with respect to control and observation spillover respectively it is shown that the control and observer designs can be combined to yield a globally stabilizing compensator the control and observer designs are numerically demonstrated on the problem of controlling stall in a model of axial compressors

exact soliton solutions of the one dimensional complex swift hohenberg equation abstract using painleve analysis the hirota multi linear method and a direct ansatz technique we study analytic solutions of the 1 1 dimensional complex cubic and quintic swift hohenberg equations we consider both standard and generalized versions of these equations we have found that a number of exact solutions exist to each of these equations provided that the coefficients are constrained by certain relations the set of solutions include particular types of solitary wave solutions hole dark soliton solutions and periodic solutions in terms of elliptic jacobi functions and the weierstrass function although these solutions represent only a small subset of the large variety of possible solutions admitted by the complex cubic and quintic swift hohenberg equations those presented here are the first examples of exact analytic solutions found thus far

numerical analysis of the rescaling method for parabolic problems with blow up in finite time abstract in this work we study the numerical solution for parabolic equations whose solutions have a common property of blowing up in finite time and the equations are invariant under the following scaling transformation u u x t 2 p 1 u x 2 t for that purpose we apply the rescaling method proposed by berger and kohn 1988 to such problems the convergence of the method is proved under some regularity assumption some numerical experiments are given to derive the blow up profile verifying henceforth the theoretical results

the local and global existence of solutions for a time fractional complex ginzburg landau equation abstract we study the following time fractional complex nonlinear ginzburg landau equation e i 0 c d t u u e i u p 1 u x r n t 0 u 0 x u 0 x x r n where 0 1 r 2 2 p 1 u 0 l q r n q q c n p 1 2 and q 1 is a complex valued function and d t 0 c u t 0 i t 1 u t x u 0 x where i t 1 0 denotes a left riemann liouville fractional integral of order 1 by defining two operators and establishing some estimates of them we prove the well posedness of the mild solution for this problem in c 0 t l q r n and l 2 r q n r q 0 t l r r n where r satisfies 1 q 1 r 2 n moreover we also obtain the existence of global solutions when u 0 l q c r n is sufficiently small

numerical approximation of relative equilibria for equivariant pdes we prove convergence results for the numerical approximation of relative equilibria of parabolic systems in one space dimension these systems are special examples of equivariant evolution equations we use finite differences on a large interval with appropriately chosen boundary conditions moreover we consider the approximation of isolated eigenvalues of finite multiplicity of the linear operator which arises from linearization at the equilibrium as well as the approximation of the corresponding invariant subspace the results in this paper which are a generalization of the results in v thummler numerical analysis of the method of freezing traveling waves ph d thesis bielefeld university 2005 are illustrated by numerical computations for the cubic quintic ginzburg landau equation

controlling spatiotemporal chaos in oscillatory reaction diffusion systems by time delay autosynchronization abstract diffusion induced turbulence in spatially extended oscillatory media near a supercritical hopf bifurcation can be controlled by applying global time delay autosynchronization we consider the complex ginzburg landau equation in the benjamin feir unstable regime and analytically investigate the stability of uniform oscillations depending on the feedback parameters we show that a noninvasive stabilization of uniform oscillations is not possible in this type of system the synchronization diagram in the plane spanned by the feedback parameters is derived numerical simulations confirm the analytical results and give additional information on the spatiotemporal dynamics of the system close to complete synchronization

computer simulation of wave collapses in the nonlinear schro dinger equation abstract the self tuning numerical scheme for simulation of collapse phenomena in the framework of the nonlinear schrodinger equation is developed the scheme allows to reach extremely high field amplitudes 2 0 2 10 15 without lack of validity numerical results are compared with analytical predictions

influence of dirichlet boundary conditions on dissipative solitons in the cubic quintic complex ginzburg landau equation we investigate the influence of dirichlet boundary conditions on various types of localized solutions of the cubic quintic complex ginzburg landau equation as it arises as an envelope equation near the weakly inverted onset of traveling waves we find that various types of nonmoving pulses and holes can accommodate dirichlet boundary conditions by having for holes two halves of a ensuremath pi hole at each end of the box moving pulses of fixed shape as they arise for periodic boundary conditions are replaced by a nonmoving asymmetric pulse which has half a ensuremath pi hole at the end of the box in the original moving direction to guarantee that dirichlet boundary conditions are met moving breathing pulses as they arise for periodic boundary conditions propagate toward one end of the container and stop moving while the breathing persists indefinitely finally breathing and moving holes are replaced by two nonbreathing half ensuremath pi holes at each end of the container and one hump in the bulk

feedback control of subcritical turing instability with zero mode a global feedback control of a system that exhibits a subcritical monotonic instability at a nonzero wave number short wave or turing instability in the presence of a zero mode is investigated using a ginzburg landau equation coupled to an equation for the zero mode this system is studied analytically and numerically it is shown that feedback control based on measuring the maximum of the pattern amplitude over the domain can stabilize the system and lead to the formation of localized unipulse stationary states or traveling solitary waves it is found that the unipulse traveling structures result from an instability of the stationary unipulse structures when one of the parameters characterizing the coupling between the periodic pattern and the zero mode exceeds a critical value that is determined by the zero mode damping coefficient

on exact solutions of modified complex ginzburg landau equation abstract the one dimensional modified complex ginzburg landau equation has been studied by the use of the conte and musette method this method permits us to derive all the known exact solutions in a unified natural scheme these solutions are expressed in terms of solitary wave periodic unbounded wave and shock type wave we also find previously unknown exact propagating hole the degeneracies of modified complex ginzburg landau equation have also been examined as well as several of their solutions

singularities in a modified kuramoto sivashinsky equation describing interface motion for phase transition abstract phase transitions can be modeled by the motion of an interface between two locally stable phases a modified kuramoto sivashinsky equation h t 2 h 4 h 1 h 2 2 h 2 h xx h yy h xy 2 describes near planar interfaces which are marginally long wave unstable we study the question of finite time singularity formation in this equation in one and two space dimensions on a periodic domain such singularity formation does not occur in the kuramoto sivashinsky equation 0 for all 1 0 we provide sufficient conditions on the initial data and size of the domain to guarantee a finite time blow up in which a second derivative of h becomes unbounded using a bifurcation theory analysis we show a parallel between the stability of steady periodic solutions and the question of finite time blow up in one dimension finally we consider the local structure of the blow up in the one dimensional case via similarity solutions and numerical simulations that employ a dynamically adaptive self similar grid the simulations resolve the singularity to over 25 decades in h xx l and indicate that the singularities are all locally described by a unique self similar profile in h xx we discuss the relevance of these observations to the full intrinsic equations of motion and the associated physics

on the number of bootstrap simulations required to construct a confidence interval abstract the purpose of this document is to make two points about the effect of the number of bootstrap simulations b on percentile t bootstrap confidence intervals the first point concerns coverage probability the second distance of the simulated critical point form the true critical point derived with b infinity in both cases the author has in mind applications to smooth statistics such as the studentized mean of a sample drawn from a continuous distribution he indicates the change that have to be made if the distribution of the statistic is not smooth additional keywords exponentive functions

stability of bright solitary wave solutions to perturbed nonlinear schrodinger equations abstract the propagation of pulses in ideal nonlinear optical fibers without loss is governed by the nonlinear schrodinger equation nls when considering realistic fibers one must examine perturbed nls equations with the particular perturbation depending on the physical situation that is being modeled a common example is the complex ginzburg landau equation cgl which is a dissipative perturbation it is known that some of the stable bright solitons of the nls survive a dissipative perturbation such as the cgl given that a wave persists it is then important to determine its stability with respect to the perturbed nls a major difficulty in analyzing the stability of solitary waves upon adding dissipative terms is that eigenvalues may bifurcate out of the essential spectrum since the essential spectrum of the nls is located on the imaginary axis such eigenvalues may lead to an unstable wave in fact eigenvalues can pop out of the essential spectrum even if the unperturbed problem has no eigenvalue embedded in the essential spectrum here we present a technique which can be used to track these bifurcating eigenvalues as a consequence we are able to locate the spectrum for bright solitary wave solutions to various perturbed nonlinear schrodinger equations and determine precise conditions on parameters for which the waves are stable in addition we show that a particular perturbation the parametrically forced nls equation supports stable multi bump solitary waves the technique for tracking eigenvalues which bifurcate from the essential spectrum is very general and should therefore be applicable to a larger class of problems than those presented here

who cares about integrability abstract problems that admit solitons and are completely integrable have been analyzed in detail since their discovery by zabusky and kruskal 25 years ago their study has influenced the development of both mathematics and physics during that time the questions addressed here are 1 i has this subject run its natural course 2 ii will it significantly influence the nonlinear science that develops over the next decade supporting examples will be chosen from several disciplines but especially from the study of water waves

stability criterion for bright solitary waves of the perturbed cubic quintic schro dinger equation abstract the stability of the bright solitary wave solution to the perturbed cubic quintic schrodinger equation is considered it is shown that in a certain region of parameter space these solutions are unstable with the instability being manifested as a small positive eignevalue furthermore it is shown that in the complimentary region of parameter space there are no small unstable eigenvalues the proof involves a novel calculation of the evans function which is of interest in its own right as a consequence of the eigenvalue calculation it is additionally shown that n bump bright solitary waves bifurcate from the primary wave

monte carlo tests with nuisance parameters a general approach to finite sample inference and nonstandard asymptotics abstract the technique of monte carlo mc tests dwass 1957 annals of mathematical statistics 28 181 187 barnard 1963 journal of the royal statistical society series b 25 294 provides a simple method for building exact tests from statistics whose finite sample distribution is intractable but can be simulated when no nuisance parameter is involved we extend this method in two ways first by allowing for mc tests based on exchangeable possibly discrete test statistics second by generalizing it to statistics whose null distribution involves nuisance parameters maximized mc mmc tests simplified asymptotically justified versions of the mmc method are also proposed these provide a simple way of improving standard asymptotics and dealing with nonstandard asymptotics

exact solutions of the one dimensional quintic complex ginzburg landau equation abstract exact solitary wave solutions of the one dimensional quintic complex ginzburg landau equations are obtained using a method derived from the painleve test for integrability these solutions are expressed in terms of hyperbolic functions and include the pulses and fronts found by van saarloos and hohenberg we also find previously unknown sources and sinks the emphasis is put on the systematic character of the method which breaks away from approaches involving somewhat ad hoc ansatze

theoretical comparison of bootstrap confidence intervals we develop a unified framework within which many commonly used bootstrap critical points and confidence intervals may be discussed and compared in all seven different bootstrap methods are examined each being usable in both parametric and nonparametric contexts emphasis is on the way in which the methods cope with first and second order departures from normality percentile t and accelerated bias correction emerge as the most promising of existing techniques certain other methods are shown to lead to serious errors in coverage and position of critical point an alternative approach based on shortest bootstrap confidence intervals is developed we also make several more technical contributions in particular we confirm efron s conjecture that accelerated bias correction is second order correct in a variety of multivariate circumstances and give a simple interpretation of the acceleration constant

recursive algorithms for computing the cramer rao bound computation of the cramer rao bound crb on estimator variance requires the inverse or the pseudo inverse fisher information matrix fim direct matrix inversion can be computationally intractable when the number of unknown parameters is large in this correspondence we compare several iterative methods for approximating the crb using matrix splitting and preconditioned conjugate gradient algorithms for a large class of inverse problems we show that nonmonotone gauss seidel and preconditioned conjugate gradient algorithms require significantly fewer flops for convergence than monotone bound preserving algorithms

construction of a blow up solution for the complex ginzburg landau equation in a critical case we construct a solution for the complex ginzburg landau equation in some critical case which blows up in finite time t only at one blow up point we also give a sharp description of its profile the proof relies on the reduction of the problem to a finite dimensional one and the use of index theory to conclude the interpretation of the parameters of the finite dimension problem in terms of the blow up point and time allows to prove the stability of the constructed solution

spatial and temporal feedback control of traveling wave solutions of the two dimensional complex ginzburg landau equation previous work has shown that benjamin feir unstable traveling waves of the complex ginzburg landau equation cgle in two spatial dimensions cannot be stabilized using a particular time delayed feedback control mechanism known as time delay autosynchronization in this paper we show that the addition of similar spatial feedback terms can be used to stabilize such waves this type of feedback is a generalization of the time delay method of pyragas k pyragas continuous control of chaos by self controlling feedback phys lett a 170 1992 421 428 and has been previously used to stabilize waves in the one dimensional cgle by montgomery and silber k montgomery m silber feedback control of traveling wave solutions of the complex ginzburg landau equation nonlinearity 17 6 2004 2225 2248 we consider two cases in which the feedback contains either one or two spatial terms we focus on how the spatial terms may be chosen to select the direction of travel of the plane waves numerical linear stability calculations demonstrate the results of our analysis c 2007 elsevier b v all rights reserved

invariant painleve analysis and coherent structures of two families of reaction diffusion equations exact closed form coherent structures pulses fronts domain walls having the form of complicated traveling waves are constructed for two families of reaction diffusion equations by the use of invariant painleve analysis these analytical solutions which are derived directly from the underlying pde s are investigated in the light of restrictions imposed by the ode that any traveling wave reduction of the corresponding pde must satisfy in particular it is shown that the coherent structures a asymptotically satisfy the ode governing traveling wave reductions and b are accessible to the pde from compact support initial conditions the solutions are compared with each other and with previously known solutions of the equations

the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

controlling turbulence in the complex ginzburg landau equation abstract we suggest that diffusion induced turbulence in distributed dynamical systems near a supercritical hopf bifurcation can be controlled by means of global delayed feedback analytical and numerical investigations of this method for a system described by the complex ginzburg landau equation are performed suppression of phase and amplitude turbulence is found inside a window of delay times under increasing the intensity of the control signal

sources sinks and wavenumber selection in coupled cgl equations and experimental implications for counter propagating wave systems we study the coupled complex ginzburg landau cgl equations for traveling wave systems and show that sources and sinks are the important coherent structures that organize much of the dynamical properties of traveling wave systems we focus on the regime in which sources and sinks separate patches of left and right traveling waves i e the case that these modes suppress each other we present in detail the framework to analyze these coherent structures and show that the theory predicts a number of general properties which can be tested directly in experiments our counting arguments for the multiplicities of these structures show that independently of the precise values of the coefficients in the equations there generally exists a symmetric stationary source solution which sends out waves with a unique frequency and wave number sinks on the other hand occur in two parameter families and play an essentially passive role being sandwiched between the sources these simple but general results imply that sources are important in organizing the dynamics of the coupled cgl equations simulations show that the consequences of the wavenumber selection by the sources is reminiscent of a similar selection by spirals in the 2d complex ginzburg landau equations sources can send out stable waves convectively unstable waves or absolutely unstable waves we show that there exists an additional dynamical regime where both single and bimodal states are unstable the ensuing chaotic states have no counterpart in single amplitude equations a third dynamical mechanism is associated with the fact that the width of the sources does not show simple scaling with the growth rate e this is related to the fact that the standard coupled cgl equations are not uniform in e in particular when the group velocity term dominates over the linear growth term no stationary source can exist however sources displaying nontrivial dynamics can often survive here our results for the existence multiplicity wavelength selection dynamics and scaling of sources and sinks and the patterns they generate are easily accessible by experiments we therefore advocate a study of the sources and sinks as a means to probe traveling wave systems and compare theory and experiment in addition they bring up a large number of new research issues and open problems which are listed explicitly in the concluding section

linearity inside nonlinearity exact solutions to the complex ginzburg landau equation abstract systems of two linear partial differential equations pdes with constant coefficients define a natural basis of elementary functions to build some exact solutions to nonlinear pdes for the one dimensional complex ginzburg landau equation the usual representations of the complex field re a or a are multivalued which makes difficult the search for exact solutions in this manner fortunately the painleve analysis naturally introduces an elementary single valued like representation of a by two fields z grad respectively complex abd real uniquely defined by an explicit expression for and a ze i another important feature is the invariance by parity on a which increases the class of expected solutions this allows to retrieve quite easily the four famous solutions of nozaki and bekki represented by the constant coefficients of two linear partial differential equations and a finite set of constants

the stability test for symmetric alpha stable distributions symmetric alpha stable distributions are a popular statistical model for heavy tailed phenomena encountered in communications radar biomedicine and econometrics the use of the symmetric alpha stable model is often supported by empirical evidence where qualitative criteria are used to judge the fit leading to subjective decisions objective decisions can only be made through quantitative statistical tests here a goodness of fit hypothesis test for symmetric alpha stable distributions is developed based on their unique stability property critical values for the test are found using both asymptotic theory and from bootstrap estimates experiments show that the stability test using bootstrap estimates of the critical values is better able to discriminate between symmetric alpha stable distributions and other heavy tailed distributions than classical tests such as the kolmogorov smirnov test

information theoretic image formation the emergent role of information theory in image formation is surveyed unlike the subject of information theoretic communication theory information theoretic imaging is far from a mature subject the possible role of information theory in problems of image formation is to provide a rigorous framework for defining the imaging problem for defining measures of optimality used to form estimates of images for addressing issues associated with the development of algorithms based on these optimality criteria and for quantifying the quality of the approximations the definition of the imaging problem consists of an appropriate model for the data and an appropriate model for the reproduction space which is the space within which image estimates take values each problem statement has an associated optimality criterion that measures the overall quality of an estimate the optimality criteria include maximizing the likelihood function and minimizing mean squared error for stochastic problems and minimizing squared error and discrimination for deterministic problems the development of algorithms is closely tied to the definition of the imaging problem and the associated optimality criterion algorithms with a strong information theoretic motivation are obtained by the method of expectation maximization related alternating minimization algorithms are discussed in quantifying the quality of approximations global and local measures are discussed global measures include the mean squared error and discrimination between an estimate and the truth and probability of error for recognition or hypothesis testing problems local measures include fisher information

confidence intervals from monte carlo tests abstract monte carlo tests have exact level when the distribution of the test statistic is free of nuisance parameters confidence sets obtained by inverting such tests are also exact but may have a complicated structure the sets reduce to intervals if the sampling can be organized in a special way a sufficient condition is that the test statistic is monotone in the parameter of interest when all random drawings are kept fixed examples given include models from the one parameter exponential class a simple theory quantifying the impact of monte carlo uncertainty is also developed

on the principle of pseudo linearized stability applications to some delayed nonlinear parabolic equations ut u t 0 to the associated equilibria w d a d b x such that aw bw f where c c 0 x is the function which takes constant values equal to w our main goal is to extend to a broad class of nonlinear operators a the usual linearized stability principle saying roughly speaking that for the special case of a linear single valued and b and f are differentiable the asymptotic stability of the zero solution of the

characterization of dispersive chaos and related states of binary fluid convection abstract we describe an extensive series of experiments on traveling wave convection in an ethanol water mixture with separation ratio 0 020 in a long narrow annular container as the stress parameter is quasi statically increased through the range 0 2 above onset this system evolves through a series of complex spatiotemporal states before settling into an extended pattern of steady spatially uniform convective rolls much of the dynamical behavior is influenced by strong nonlinear dispersion which causes the repeated and often irregular appearance and sudden collapse of spatially localized bursts of traveling waves small amplitude states seen very close to onset are analyzed quantitatively using a complex ginzburg landau equation complex dynamical states encountered further above onset are analyzed using a number of classical statistical techniques focusing mainly on correlation functions and fourier spectra in addition we use the technique of biorthogonal decomposition in an effort to extract the basic structures of the patterns and to characterize the complexty of their dynamics

elliptic solutions of the quintic complex one dimensional ginzburg landau equation the conte musette method has been modified for the search of only elliptic solutions to systems of differential equations a key idea of this a prior restriction is to simplify calculations by means of the use of a few laurent series solutions instead of one and the use of the residue theorem the application of this approach to the quintic complex one dimensional ginzburg landau equation cgle5 allows us to find elliptic solutions in the wave form restrictions on coefficients which are necessary conditions for the existence of elliptic solutions for the cgle5 have been found as well we demonstrate that to find elliptic solutions the analysis of a system of differential equations is preferable to the analysis of the equivalent single differential equation

front motion metastability and subcritical bifurcations in hydrodynamics metastability occurs whenever under given external conditions as defined by the reynolds number in hydrodynamics more than one linearly stable solution may exist in variational problems the preferred state is usually claimed to be the one with the lowest energy but in hydrodynamics and except for very special conditions no energy functional exists from an analogy between amplitude and reaction diffusion equations it is argued that the border separating in space two possible solutions of the flow equations as turbulent and laminar in pipe flows or boundary layers moves with a constant mean velocity depending on the control parameter the sign of this velocity allows to decide which state is stable and which is metastable possible physical implications of these ideas for various problems of hydrodynamics are discussed

fronts pulses sources and sinks in generalized complex ginzberg landau equations an important clement in the long time dynamics of pattern forming systems is a class of solutions we will call coherent structures these are states that are either themselves localized or that consist of domains of regular patterns connected by localized defects or interfaces this paper summarizes and extends recent work on such coherent structures in the one dimensional complex ginzburg landau equation and its generalizations for which rather complete information can be obtained on the existence and competition of fronts pulses sources and sinks for the special subclass of uniformly translating structures the solutions are derived from a set of ordinary differential equations that can be interpreted as a flow in a three dimensional phase space fixed points of the flow correspond to the two basic building blocks of coherent structures uniform amplitude states and evanescent waves whose amplitude decreases smoothly to zero a study of the stability of the fixed points under the flow leads to results on the existence and multiplicity of the different coherent structures the dynamical analysis of the original partial differential equation focusses on the competition between pulses and fronts and is expressed in terms of a set of conjectures for front propagation that generalize the marginal stability and pinch point approaches of earlier authors these rules together with an exact front solution whose dynamics plays an important role in the selection of patterns yield an analytic expression for the upper limit of the range of existence of pulse solutions as well as a determination of the regions of parameter space where uniformly translating fron t solutions can exist extensive numerical simulations show consistency with these rules and conjectures for the existence of fronts and pulses in the parameter ranges where no uniformly translating fronts can exist examples are shown of irregularly spreading fronts that generate strongly chaotic regions as well as nonuniformly translating fronts that lead to uniform amplitude states recent perturbative treatments based on expansions about the nonlinear schr6dinger equation are generalized to perturbations of the cubic quintic and derivative schr idinger equations for which both pulses and fronts exist in the unperturbed system comparison of the results with the exact solutions shows that the perturbation theory only yields a subset of the relevant solutions nevertheless those that are obtained are found to be consistent with the general conjectures and in particular they provide an analytic demonstration of front pulse competition while the discussion of the competition between fronts and pulses focusses on the complex ginzburg landau equation with quintic terms and a subcritical bifurcation a number of results are also presented for the cubic equation in particular the existence of a family of moving source solutions derived by bekki and nozaki for this equation contradicts the naive counting arguments we attribute this contradiction to a hidden symmetry of the solution but have not been able to show explicitly how this symmetry affects the phase space orbits

spatiotemporal chaos in the one dimensional complex ginzburg landau equation the dynamical behavior of a large one dimensional system obeying the cubic complex ginzburg landau equation is studied numerically as a function of parameters near a supercritical bifurcation two types of chaotic behavior can be distinguished beyond the benjamin feir instability a phase turbulence regime with a conserved phase winding number and no phase dislocations space time defects and a defect regime with a nonzero density of defects the transition between the two can either be continuous or discontinuous hysteretic depending on parameters the spatial decay of the phase correlation function is inferred to be exponential in both regimes with a sharp decrease of the correlation length upon entering the defect phase the temporal decay of correlations is exponential in the defect regime

global feedback control of a long wave morphological instability abstract nonlinear dynamics of a long wave morphological instability of a crystallization front during directional solidification in the presence of feedback control is investigated feedback control is applied by varying the pulling speed and the temperature gradient according to the measured maximum depressions of the crystal melt interface for the case of small segregation coefficient a long scale nonlinear evolution equation for the shape of the interface is derived in the frozen temperature approximation the equation contains a nonlocal global control term and describes the near threshold nonlinear dynamics of the morphological instability in the presence of the feedback control this equation is studied analytically and numerically both for 1 1 and 2 1 interfaces it is shown that the chosen global feedback control can prevent the blow up of subcritical and supercritical solutions i e the formation of deep cells it leads to the formation of stationary periodic patterns or spatially localized structures

a perturbative painleve approach to nonlinear differential equations abstract we further improve the painleve test so that negative indices resonances can be treated we demand single valuedness not only for any pole like expansion as in the usual painleve test but also for every solution close to it represented as a perturbation series in a small parameter e order zero is the usual test order one already treated in a preliminary paper reduces to a linear fuchs analysis near a regular singularity and allows the introduction of all missing arbitrary coefficients higher orders lead to the analysis of a linear fuchsian type inhomogeneous equation we obtain an infinite sequence of necessary conditions for the absence of movable logarithmic branch points arising at every integer index whether positive or negative and at every order those arising at negative indices including 1 are new while some conditions may not arise before some high perturbation order we present several illustrative examples we discuss the understanding of negative indices and conclude that they are indistinguishable from positive indices just as in the fuchs theory in particular negative indices give rise to doubly infinite laurent series

bootstrapping nonparametric density estimators with empirically chosen bandwidths we examine the way in which empirical bandwidth choice affects distributional properties of nonparametric density estimators two bandwidth selection methods are considered in detail local and global plug in rules particular attention is focussed on whether the accuracy of distributional bootstrap approximations is appreciably influenced by using the resample version hat h rather than the sample version hat h of an empirical bandwidth it is shown theoretically that in marked contrast to similar problems in more familiar settings no general first order theoretical improvement can be expected when using the resampling version in the case of local plug in rules the inability of the bootstrap to accurately reflect biases of the components used to construct the bandwidth selector means that the bootstrap distribution of hat h is unable to capture some of the main properties of the distribution of hat h if the second derivative component is slightly undersmoothed then some improvements are possible through using hat h but they would be difficult to achieve in practice on the other hand for global plug in methods both hat h and hat h are such good approximations to an optimal deterministic bandwidth that the variations of either can be largely ignored at least at a first order level thus for quite different reasons in the two cases the computational burden of varying an empirical bandwidth across resamples is difficult to justify

dynamics of one and two dimensional fronts in a bistable equation with time delayed global feedback propagation failure and control mechanisms we study the evolution of fronts in a bistable equation with time delayed global feedback in the fast reaction and slow diffusion regime this equation generalizes the hodgkin grafstein and allen cahn equations we derive a nonlinear equation governing the motion of fronts which includes a term with delay in the one dimensional case this equation is linear we study the motion of one and two dimensional fronts finding a much richer dynamics than for the previously studied cases without time delayed global feedback we explain the mechanism by which localized fronts created by inhibitory global coupling loose stability in a hopf bifurcation as the delay time increases we show that for certain delay times the prevailing phase is different from that corresponding to the system in the absence of global coupling numerical simulations of the partial differential equation are in agreement with the analytical predictions

periodic spatio temporal oscillations governed by a globally controlled ginzburg landau equation abstract a new type of periodic oscillations in a globally controlled subcritical cubic complex ginzburg landau equation formerly observed in numerical simulations is explained and investigated analytically by means of a multiscale perturbation theory using an appropriate class of solutions of the nonlinear schrodinger equation as a starting point we construct a new class of asymptotic solutions of the cubic complex ginzburg landau equation in the limit of large dispersion and nonlinear frequency shift

generalized monte carlo significance tests summary simple monte carlo significance testing has many applications particularly in the preliminary analysis of spatial data the method requires the value of the test statistic to be ranked among a random sample of values generated according to the null hypothesis however there are situations in which a sample of values can only be conveniently generated using a markov chain initiated by the observed data so that independence is violated this paper describes two methods that overcome the problem of dependence and allow exact tests to be carried out the methods are applied to the rasch model to the finite lattice ising model and to the testing of association between spatial processes power is discussed in a simple case

soliton solutions and backlund transformation for the complex ginzburg landau equation abstract symbolically investigated in this paper is the complex ginzburg landau cgl equation with the hirota method both bright and dark soliton solutions for the cgl equation are obtained simultaneously new backlund transformation in the bilinear form is derived relevant properties and features are discussed solitons can be compressed amplified when the nonlinear linear dispersion effect is enhanced meanwhile central frequency of the soliton can be affected by the nonlinear and linear dispersion effects besides directions of the movement for the soliton central frequency can be adjusted results of this paper would be of certain value to the studies on the soliton compression and amplification

improvements of jackknife confidence limit methods summary edgeworth expansion is applied to studentized parameter estimates when the standard error has been computed by a jackknife method adjustments to the usual jackknife confidence limit formulae are obtained this approach is contrasted with a bootstrap approach in numerical illustrations for estimation of a ratio jackknife methods are nonparametric methods for estimating the bias and standard error of an estimate t approximate confidence limits for the estimand can be found by using a large sample normal approximation for t somewhat curiously little is known about possible improvements to the normal approximation in this context although improvements based on edgeworth expansions are familiar in other problems in this paper we show that edgeworth expansion methods can be applied in the jackknife context numerical results for a particular application raise the possibility that the resulting improvements of jackknife methods can be matched by a suitable use of bootstrap methods efron 1982

stability on time dependent domains convective and dilution effects abstract we explore near critical behavior of spatially extended systems on time dependent spatial domains with convective and dilution effects due to domain flow as a paradigm we use the swift hohenberg equation which is the simplest nonlinear model with a non zero critical wavenumber to study dynamic pattern formation on time dependent domains a universal amplitude equation governing weakly nonlinear evolution of patterns on time dependent domains is derived and proves to be a generalization of the standard ginzburg landau equation its key solutions identified here demonstrate a substantial variety spatially periodic states with a time dependent wavenumber steady spatially non periodic states and pulse train solutions in contrast to extended systems on time fixed domains the effects of domain flow such as bifurcation delay due to domain growth and destabilization due to oscillatory domain flow on the eckhaus instability responsible for phase slips in spatially periodic states are analyzed with the help of both local and global stability analyses a nonlinear phase equation describing the approach to a phase slip event is derived detailed analysis of a phase slip using multiple time scale methods demonstrates different mechanisms governing the wavelength changing process at different stages

exact goodness of fit tests for markov chains goodness of fit tests are useful in assessing whether a statistical model is consistent with available data however the usual asymptotics often fail either because of the paucity of the data or because a nonstandard test statistic is of interest in this article we describe exact goodness of fit tests for first and higher order markov chains with particular attention given to time reversible ones the tests are obtained by conditioning on the sufficient statistics for the transition probabilities and are implemented by simple monte carlo sampling or by markov chain monte carlo they apply both to single and to multiple sequences and allow a free choice of test statistic three examples are given the first concerns multiple sequences of dry and wet january days for the years 1948 1983 at snoqualmie falls washington state and suggests that standard analysis may be misleading the second one is for a four state dna sequence and lends support to the original conclusion that a second order markov chain provides an adequate fit to the data the last one is six state atomistic data arising in molecular conformational dynamics simulation of solvated alanine dipeptide and points to strong evidence against a first order reversible markov chain at 6 picosecond time steps

breaking the hidden symmetry in the ginzburg landau equation in this paper we study localised traveling solutions to a ginzburg landau equation to which we have added a small o e 0 e 1 quintic term we consider this term as a model for the higher order nonlinearities which appear in the derivation of the ginzburg landau equation by a combination of a geometrical approach and an explicit perturbation analysis we are able to relate the family of bekki nozaki solutions of the cubic equation n bekki and b nozaki 1985 phys lett a 110 133 135 to a curve of co dimension 2 homoclinic bifurcations in parameter space thus we are able to interpret the hidden symmetry which has been conjectured to explain the existence of the bekki nozaki solutions from the point of view of bifurcation theory we show that the quintic term breaks this hidden symmetry and that the one parameter family of bekki nozaki solutions is embedded in a two parameter family of homoclinic solutions which exist at a co dimension 1 homoclinic bifurcation furthermore we show mainly by geometrical arguments that the addition of the small quintic term can create large families of traveling localised structures that cannot exist in the cubic case these solutions exist in open subsets of the parameter space and correspond to structurally stable multi or n circuit heteroclinic orbits in an ode reduction and have a monotonically decreasing increasing amplitude except for a number n of relatively fast jumps

the cubic complex ginzburg landau equation for a backward bifurcation abstract the one dimensional complex ginzburg landau equation cgle with a destabilizing cubic nonlinearity and no saturating higher order terms has stable bounded solutions we consider a simple pedagogical model exhibiting qualitatively the mechanism which may suppress the divergence of the solutions then we investigate the functional form of the blow up collapse solutions immediately before the divergence from this analysis we find analytic boundaries for the existence of collapse solutions in the parameter space of the cgle a comparison with numerical simulations demonstrates that for parameters without collapse solutions the solutions of the cgle remain bounded for all times finally we discuss the implications of our results for the solutions of the cgle when saturating higher order terms are included

on solitary wave solutions of ac driven complex ginzburg landau equation a new class of periodic solutions of modified complex ginzburg landau equation phase locked to a time dependent force by applying a nonfeedback mechanism for chaos control have been found the reported solutions are necessarily of the rational form containing trigonometric and hyperbolic functions

on the level error after bartlett adjustment of the likelihood ratio statistic summary it is well known that bartlett adjustment reduces level error of the likelihood ratio statistic from order n l to order n3 2 in the present note we show that level error of the adjusted statistic is actually order n2

the effect of simulation order on level accuracy and power of monte carlo tests we discuss the effect of simulation order on level accuracy and power of monte carlo tests in a very general setting both parametric problems with or without nuisance parameters and nonparametric problems are treated by a single unifying argument it is shown that if the level of a monte carlo test is known only nominally not precisely then the level error of a monte carlo test is an order of magnitude less than that of the corresponding asymptotic test this result is available whenever the test statistic is asymptotically pivotal even if the number of simulations is held fixed as the sample size n increases it implies that monte carlo methods are a real alternative to asymptotic methods we also show that even if the number of simulations is held fixed a monte carlo test is able to distinguish between the null hypothesis and alternative hypotheses distant n 12 from the null

dynamics of solitary waves generated by subcritical instability under the action of delayed feedback control abstract we consider the influence of a global delayed feedback control which acts on a system governed by a subcritical ginzburg landau equation the method based on a variational principle is applied for the derivation of a low dimensional evolution model in the framework of this model a one pulse solution is found and its linear and nonlinear stability analysis is carried out the existence region for a stable time periodic pulse solution is found between the boundaries in the parameter space corresponding to a hopf bifurcation and a saddle node bifurcation the obtained results are compared with the results of an analytical linear theory and direct numerical simulations of the original problem

strong resonances of spatially distributed oscillators a laboratory to study patterns and defects abstract this paper describes phenomena which arise in a continuous system of coupled oscillators subject to a strongly resonant forcing we show that the temporal forcing induces a new type of instability leading to the formation of spatial patterns such as stripes hexagons and spatio temporal intermittent states reminiscent of chemical and magnetical systems we also report the existence of localized states where the instability is confined in the core of a defect leading to an increased mobility and diffusive behaviour of the defect

spatiotemporal lattice boltzmann model for the three dimensional cubic quintic complex ginzburg landau equation abstract a spatiotemporal lattice boltzmann model for solving the three dimensional cubic quintic complex ginzburg landau equation cqcgle is proposed different from the classic lattice boltzmann models this lattice boltzmann model is based on uniformly distributed lattice points in a three dimensional spatiotemporal space and the evolution of the model is about a spatial axis rather than time the algorithm possesses advantages similar to the lattice boltzmann method in that it is easily adapted to complex ginzburg landau equations examples show that the model reproduces the phenomena in the cqcgle accurately

bootstrap recycling a monte carlo alternative to the nested bootstrap abstract a monte carlo algorithm is described that can be used in place of the nested bootstrap it is particularly advantageous when there is a premium on the number of bootstrap samples either because samples are hard to generate or because expensive computations are applied to each sample this recycling algorithm is useful because it enables inference procedures like prepivoting and bootstrap iteration in models where nested bootstrapping is computationally impractical implementation of the recycling algorithm is quite straightforward as a replacement of the double bootstrap for example bootstrap recycling involves two stages of sampling as does the double bootstrap the first stage of both algorithms is the same simulate from the fitted model in the second stage of recycling one batch of samples is simulated from one measure a measure dominating all the first stage fits these samples are recycled with each first stage sample to yield estimated adjustments to the original inference procedur