on the equivalence of time and frequency domain maximum likelihood estimation maximum likelihood estimation has a rich history it has been successfully applied to many problems including dynamical system identification different approaches have been proposed in the time and frequency domains in this paper we discuss the relationship between these approaches and we establish conditions under which the different formulations are equivalent for finite length data a key point in this context is how initial and final conditions are considered and how they are introduced in the likelihood function

analytical and numerical studies of the variable coefficient gardner equation the gardner or extended korteweg de vries equation with the variable sign cubic non linear term is studied this equation occurred in the theory of interfacial waves in the stratified shear flow at some certain conditions on the medium stratification an asymptotic method is applied to study the solitary wave transformation when the coefficient of the cubic non linear term is varied slowly it is found the one branch of the solitary waves destroys in the vicinity of the bifurcation point where the exponential soliton transforms into the breather through algebraic soliton other solitary waves change their amplitude accordingly to the cubic non linear term variation the structure of the tail formed behind the solitary wave is determined direct numerical simulation of the gardner equation is performed to analyze the transformation and breaking of the solitary wave it confirms most of the theoretical results the calculated dynamics of the table top soliton due to the large values of the mass and momentum integrals differs from the asymptotic prediction because the characteristic time of the variation of the cubic non linear term has the same order as the duration of table top soliton

performance analysis of multi innovation gradient type identification methods it is well known that the stochastic gradient sg identification algorithm has poor convergence rate in order to improve the convergence rate we extend the sg algorithm from the viewpoint of innovation modification and present multi innovation gradient type identification algorithms including a multi innovation stochastic gradient misg algorithm and a multi innovation forgetting gradient mifg algorithm because the multi innovation gradient type algorithms use not only the current data but also the past data at each iteration parameter estimation accuracy can be improved finally the performance analysis and simulation results show that the proposed misg and mifg algorithms have faster convergence rates and better tracking performance than their corresponding sg algorithms

a combinatorial particle swarm optimization for solving multi mode resource constrained project scheduling problems the particle swarm optimization pso has been widely used to solve continuous problems the discrete problems have just begun to be also solved by the discrete pso however the combinatorial problems remain a prohibitive area to the pso mainly in case of integer values in this paper we propose a combinatorial pso cpso algorithm that we take up challenge to use in order to solve a multi mode resource constrained project scheduling problem mrcpsp the results that have been obtained using a standard set of instances after extensive experiments prove to be very competitive in terms of number of problems solved to optimality by comparing average deviations and percentages of optima found our cpso algorithm outperforms the simulated annealing algorithm and it is close to the pso algorithm

bell polynomial approach applied to the seventh order sawada kotera ito equation in this paper the bell polynomial approach is extended to the seventh order sawada kotera ito equation which is regarded as a higher order integrable one in the korteweg de vries hierarchy through several combinations of the constructed bell polynomials the bilinear form with an auxiliary independent variable introduced backlund transformation lax pair and infinite conservation laws for such an equation are derived by means of symbolic computation

improved bell polynomial procedure for the higher order korteweg de vries equations in fluid dynamics korteweg de vries kdv typed equations are seen in fluid dynamics plasma physics and other fields by means of the bell polynomial procedure we take two higher order members of the kdv hierarchy the seventh and ninth order lax s kdv equations in fluid dynamics as the examples for studying the integrable properties of the higher order equations different from lower order equations two new partial differential operators in the bell polynomial procedure are introduced to construct the multi dimensional bilinear forms of such equations with several auxiliary independent variables through the procedure simplified via the algebraic operation of the polynomials the backlund transformations lax pairs and infinite conservation laws of such equations are deduced

wave group dynamics in weakly nonlinear long wave models abstract the dynamics of wave groups is studied for long waves using the framework of the extended korteweg de vries equation it is shown that the dynamics is much richer than the corresponding results obtained just from the korteweg de vries equation first a reduction to a nonlinear schrodinger equation is obtained for weakly nonlinear wave packets and it is demonstrated that either the focussing or the defocussing case can be obtained this is in contrast to the corresponding reduction for the korteweg de vries equation where only the defocussing case is obtained next the condition for modulational instability is obtained it is shown that wave packets are unstable only for a positive sign of the coefficient of the cubic nonlinear term in the extended korteweg de vries equation and for a high carrier frequency at the boundary of this parameter space a modified nonlinear schrodinger equation is derived and its steady state solutions including an algebraic soliton are found the exact breather solution of the extended korteweg de vries equation is analysed it is shown that in the limit of weak nonlinearity it transforms to a wave group with an envelope described by soliton solutions of the nonlinear schrodinger equation and its modification as described above numerical simulations demonstrate the main features of wave group evolution and show some differences in the behaviour of the solutions of the extended korteweg de vries equation compared with those of the nonlinear schrodinger equation

the effect of transfer function estimation errors on the filtered x lms algorithm the filtered x lms algorithm which is commonly implemented in active noise and vibration control systems requires an estimate of the cancellation path transfer function to maintain algorithm stability this correspondence considers the effect of errors in this estimate on the stability of the algorithm implemented in the time domain concluding that while a maximum phase error of spl plusmn 90 spl deg is a bound for stability there is no simple relationship between error and stability within this region

maximum likelihood least squares identification method for active noise control systems with autoregressive moving average noise maximum likelihood methods are significant for parameter estimation and system modeling this paper derives a maximum likelihood principle based least squares identification algorithm for online secondary path modeling in feed forward active noise control systems with autoregressive moving average noise this derivation proves that minimizing the cost function of least squares is equivalent to the maximum of likelihood function proposed method requires tuning of only one parameter in comparison with other recognized methods simulation tests show that proposed algorithm has better estimation accuracy and noise reduction capability than the current state of the art methods in the presence and absence of disturbance at the error microphone

solitary wave transformation on the underwater step asymptotic theory and numerical experiments abstract the transformation of a solitary wave on an underwater step is studied analytically and numerically the theoretical model includes the linear potential description of the wave transformation on a step and the weakly nonlinear theory of long waves based on the korteweg de vries equation for reflected and transmitted waves far from a step numerical simulation of solitary wave transformation on an underwater step is performed in the framework of an extended 1d boussinesq like system and fully nonlinear fully dispersive 2d navier stokes equations the results of numerical simulations for the incident solitary wave of weak amplitude are in agreement with the theoretical predictions for the wave shapes of the secondary solitons but not with the predictions for travel times

brief paper accuracy analysis of time domain maximum likelihood method and sample maximum likelihood method for errors in variables and output error identification for identifying errors in variables models the time domain maximum likelihood tml method and the sample maximum likelihood sml method are two approaches both methods give optimal estimation accuracy but under different assumptions in the tml method an important assumption is that the noise free input signal is modelled as a stationary process with rational spectrum for sml the noise free input needs to be periodic it is interesting to know which of these assumptions contain more information to boost the estimation performance in this paper the estimation accuracy of the two methods is analyzed statistically for both errors in variables eiv and output error models oem numerical comparisons between these two estimates are also done under different signal to noise ratios snrs the results suggest that tml and sml have similar estimation accuracy at moderate or high snr for eiv for oem identification these two methods have the same accuracy at any snr

two dimensional leaps in near critical flow over isolated orography this paper describes steady two dimensional disturbances forced oil the interface of a two layer fluid by flow over an isolated obstacle the oncoming flow speed is close to the linear longwave speed and the layer densities layer depths and obstacle height are chosen so that the equations of motion reduce to the forced two dimensional korteweg de vries equation with cubic nonlinearity i e the forced extended kadomtsev petviashvili equation the distinctive feature noted here is the appearance in the far lee wave wake behind obstacles in subcritical flow of a table top wave extending almost one dimensionally for many obstacles widths across the flow numerical integrations show that the most important parameter determining whether this wave appears is the departure from criticality with the wave appearing in slightly subcritical flows but being destroyed by two dimensional effects behind even quite long ridges in even moderately subcritical flow the wave appears after the flow has passed through a transition from subcritical to supercritical over the obstacle and its leading and trailing edges resemble dissipationless leaps standing in supercritical flow two dimensional steady supercritical flows are related to one dimensional unsteady flows with time in the unsteady flow associated with a slow cross stream variable in the two dimensional flows thus the wide cross stream extent of the table top wave appears to derive from the combination of its occurrence in a supercritical region embedded in the subcritical flow and the propagation without change of form of table top waves in one dimensional unsteady flow the table top wave here is associated with a resonant steepening of the transition above the obstacle and a consequent twelvefold increase in drag remarkably the table top wave is generated equally strongly and extends laterally equally as far behind an axisymmetric obstacle as behind a ridge and so leads to subcritical flows differing significantly from linear predictions

fractional brownian motion a maximum likelihood estimator and its application to image texture fractals have been shown to be useful in characterizing texture in a variety of contexts use of this methodology normally involves measurement of a parameter h which is directly related to fractal dimension in this work the basic theory of fractional brownian motion is extended to the discrete case it is shown that the power spectral density of such a discrete process is only approximately proportional to f a instead of in direct proportion as in the continuous case an asymptotic cramer rao bound is derived for the variance of an estimate of h subsequently a maximum likelihood estimator mle is developed to estimate h it is shown that the variance of this estimator nearly achieves the minimum bound a generation algorithm for discrete fractional motion is presented and used to demonstrate the capabilities of the mle when the discrete fractional brownian process is contaminated with additive gaussian noise the results show that even at signal to noise ratios of 30 db significant errors in estimation of h can result when noise is present the mle is then applied to x ray images of the human calcaneus to demonstrate how the line to line formulation can be applied to the two dimensional case these results indicate that it has strong potential for quantifying texture

solitary wave transformation in a medium with sign variable quadratic nonlinearity and cubic nonlinearity abstract solitary wave transformation in a zone with a sign variable coefficient for the quadratic nonlinear term is studied in the framework of the variable coefficient extended korteweg de vries equation this situation can be realised for internal waves in a stratified ocean when the pycnocline lies midway between the sea bed and the sea surface the effects of the cases when the coefficient of the cubic nonlinear term can be either positive or negative are investigated for small amplitude solitary waves previous results when the cubic nonlinear term is ignored are confirmed the initial solitary wave is destroyed and solitary waves of the opposite polarity are generated after passage through the turning point i e the location where the coefficient of the quadratic nonlinear term is zero for large amplitude solitary waves the cubic nonlinear term and particularly its sign influence significantly both the polarity and amplitude of the resulting solitary waves if the cubic nonlinear term has a negative coefficient the amplitude of the large terminal wave is comparable with the initial value it is less than 50 when the cubic nonlinear term is ignored if the cubic nonlinear term has a positive coefficient the result depends on the initial wave amplitude large amplitude solitary waves pass through the transition zone keeping the solitary wave shape and its polarity moderate amplitude solitary wave are destroyed and transformed to a strongly pulsating wave packet breather

lax pair backlund transformation and n soliton like solution for a variable coefficient gardner equation from nonlinear lattice plasma physics and ocean dynamics with symbolic computation abstract in this paper a generalized variable coefficient gardner equation arising in nonlinear lattice plasma physics and ocean dynamics is investigated with symbolic computation the lax pair and backlund transformation are explicitly obtained when the coefficient functions obey the painleve integrable conditions meanwhile under the constraint conditions two transformations from such an equation either to the constant coefficient gardner or modified korteweg de vries mkdv equation are proposed via the two transformations the investigations on the variable coefficient gardner equation can be based on the constant coefficient ones the n soliton like solution is presented and discussed through the figures for some sample solutions it is shown in the discussions that the variable coefficient gardner equation possesses the right and left travelling soliton like waves which involve abundant temporally inhomogeneous features

nonlinear disintegration of sine wave in the framework of the gardner equation abstract internal tidal wave entering shallow waters transforms into an undular bore and this process can be described in the framework of the gardner equation extended version of the korteweg de vries equation with both quadratic and cubic nonlinear terms our numerical computations demonstrate the features of undular bore developing for different signs of the cubic nonlinear term if cubic nonlinear term is negative and initial wave amplitude is large enough two undular bores are generated from the two breaking points formed on both crest slopes within dispersionless gardner equation undular bore consists of one table top soliton and a group of small soliton like waves passing through the table top soliton if the cubic nonlinear term is positive and again the wave amplitude is large enough the breaking points appear on crest and trough generating groups of positive and negative soliton like pulses this is the main difference with respect to the classic korteweg de vries equation where the breaking point is single it is shown also that nonlinear interaction of waves happens similarly to one of scenarios of two soliton interaction of exchange or overtake types with a phase shift if small amplitude pulses interact with large amplitude soliton like pulses their speed in average is negative in the case when free velocity is positive nonlinear interaction leads to the generation of higher harmonics and spectrum width increases with amplitude increase independently of the sign of cubic nonlinear term the breaking asymptotic k 4 3 predicted within the dispersionless gardner equation emerges during the process of undular bore development the formation of soliton like perturbations leads to appearance of several spectral peaks which are downshifting with time

a hybrid rank based evolutionary algorithm applied to multi mode resource constrained project scheduling problem abstract we consider the multi mode resource constrained project scheduling problem mrcpsp where a task has different execution modes characterized by different resource requirements due to the nonrenewable resources and the multiple modes this problem is np hard therefore we implement an evolutionary algorithm looking for a feasible solution minimizing the makespan in this paper we propose and investigate two new ideas on the one hand we transform the problem of single objective mrcpsp to bi objective one to cope with the potential violation of nonrenewable resource constraints relaxing the latter constraints allows to visit a larger solution set and thus to simplify the evolutionary operators on the other hand we build the fitness function not on a priori grid of the bi objective space but on an adaptive one relying on clustering techniques this proposed idea aims at more relevant fitness values we show that a clustering based fitness function can be an appealing feature in multi objective evolutionary algorithms since it may promote diversity and avoid premature convergence of the algorithms clustering heuristics require certainly computation time but they are still competitive with respect to classical niche formation multi objective genetic algorithm

mean weight behavior of the filtered x lms algorithm a new stochastic analysis is presented for the filtered x lms fxlms algorithm the analysis does not use independence theory an analytical model is derived for the mean behavior of the adaptive weights the model is valid for white or colored reference inputs and accurately predicts the mean weight behavior even for large step sizes the constrained wiener solution is determined as a function of the input statistics and the impulse responses of the adaptation loop filters effects of secondary path estimation error are studied monte carlo simulations demonstrate the accuracy of the theoretical model

a particle swarm optimization algorithm for makespan and total flowtime minimization in the permutation flowshop sequencing problem abstract in this paper a particle swarm optimization algorithm pso is presented to solve the permutation flowshop sequencing problem pfsp with the objectives of minimizing makespan and the total flowtime of jobs for this purpose a heuristic rule called the smallest position value spv borrowed from the random key representation of bean j c bean genetic algorithm and random keys for sequencing and optimization orsa journal of computing 6 2 1994 154 160 was developed to enable the continuous particle swarm optimization algorithm to be applied to all classes of sequencing problems in addition a very efficient local search called variable neighborhood search vns was embedded in the pso algorithm to solve the well known benchmark suites in the literature the pso algorithm was applied to both the 90 benchmark instances provided by taillard e taillard benchmarks for basic scheduling problems european journal of operational research 64 1993 278 285 and the 14 000 random narrow random and structured benchmark instances provided by watson et al j p watson l barbulescu l d whitley a e howe contrasting structured and random permutation flowshop scheduling problems search space topology and algorithm performance orsa journal of computing 14 2 2002 98 123 for makespan criterion the solution quality was evaluated according to the best known solutions provided either by taillard or watson et al the total flowtime criterion was evaluated with the best known solutions provided by liu and reeves j liu c r reeves constructive and composite heuristic solutions to the p ci scheduling problem european journal of operational research 132 2001 439 452 and rajendran and ziegler c rajendran h ziegler ant colony algorithms for permutation flowshop scheduling to minimize makespan total flowtime of jobs european journal of operational research 155 2 2004 426 438 for the total flowtime criterion 57 out of the 90 best known solutions reported by liu and reeves and rajendran and ziegler were improved whereas for the makespan criterion 195 out of the 800 best known solutions for the random and narrow random problems reported by watson et al were improved by the vns version of the pso algorithm

finding numerical solutions of diophantine equations using ant colony optimization the paper attempts to find numerical solutions of diophantine equations a challenging problem as there are no general methods to find solutions of such equations it uses the metaphor of foraging habits of real ants the ant colony optimization based procedure starts with randomly assigned locations to a fixed number of artificial ants depending upon the quality of these positions ants deposit pheromone at the nodes a successor node is selected from the topological neighbourhood of each of the nodes based on this stochastic pheromone deposit if an ant bumps into an already encountered node the pheromone is updated correspondingly a suitably defined pheromone evaporation strategy guarantees that premature convergence does not take place the experimental results which compares with those of other machine intelligence techniques validate the effectiveness of the proposed method

numerical solution of certain exponential and non linear diophantine systems of equations by using a discrete particle swarm optimization algorithm this article proposes the numerical solution of some non linear systems of diophantine equations including some exponential cases by its transformation into an optimization problem for the first example the implemented algorithm is able to find all the non negative integer roots in a given region of the domain of the objective function when compared to the analytic solution systems of different sizes are solved as an example for these their answers were found being them of excellent quality in terms of accuracy and precision even though there is no way of being certain that they are the only ones following matiyasevich theorem however and for systems of modest size the computation time increased considerably when the search space was increased