the wigner transform and some exact properties of linear operators the wigner transform of an integral kernel on the full line generalizes the fourier transform of a translation kernel the eigenvalue spectra of hermitian kernels are related to the topographic features of their wigner transforms two kernels whose wigner transforms are equivalent under the unimodular afline group have the same spectrum of eigenvalues and have eigenfunctions related by an explicit linear transformation any kernel whose wigner transform has concentric ellipses as contour lines yields an eigenvalue problem which may be solved exactly

contributions to the eigenvalue problem for slowly varying operators we consider hermitian operators with kernels which exhibit a slow variation k x y varepsilon x y 2 the wigner transform of such a kernel is tilde k p q int k u q exp iup du it has been shown sirovich and knight quart appl math 38 1981 pp 469 488 that eigenvalues follow an area rule lambda n is approximately an eigenvalue if the locus of lambda n tilde k p q encloses an area 2n 1 pi varepsilon in this paper we illustrate this construction along with the associated eigenfunctions for a class of operators which model retinal organization in addition the eigenvalue problem for small values of the index n principal eigenfunctions and eigenvalues is considered in detail modified eigenfunctions are obtained in this limit also considered is the splitting of degenerate eigenvalues and related nonuniformities

multi objectivization via decomposition an analysis of helper objectives and complete decomposition abstract multi objectivization has been used to solve several single objective problems with improved results over traditional genetically inspired optimization methods multi objectivization reformulates the single objective problem into a multiple objective problem the reformulated problem is then solved with a multiple objective method to obtain a resulting solution to the original problem multi objectivization via decomposition mvd and the addition of novel objectives are the two major approaches used in multi objectivization this paper focuses on analysis of two major mvd methods helper objectives and complete decomposition helper objectives decomposition methods identify one or more decomposed objectives that are used simultaneously with the main objective to focus attention on components of the decomposed objectives complete decomposition unlike helper objectives does not explicitly use the main objective and instead uses decomposed objectives that exhaustively cover all portions of the main objective this work examines the relationship between helper objective decompositions and complete decomposition using both an analytic and experimental methodology pareto dominance relationships are examined analytically to clarify the relationship between dominant solutions in both types of decompositions these results more clearly characterize how solutions from the two approaches rank in pareto frontier based fitness algorithms such as nsga ii an empirical study on job shop scheduling problems shows how fitness signal and fitness noise are affected by the balance of decomposition size additionally we provide evidence that for the settings and instances studied complete decompositions have a better on average performance when compared to analogous helper objective decompositions lastly we examine the underlying forces that determine effective decomposition size we argue that it is advantageous to use less balanced decompositions as within decomposition conflict increases and as heuristic strength increases

a look ahead levinson algorithm for general toeplitz systems the authors present an extension of levinson s algorithm that is guaranteed to be weakly stable for a large class of general toeplitz matrices namely those that do not have many consecutive ill conditioned leading principal submatrices the new algorithm adapts itself to the given toeplitz matrix by skipping over all the ill conditioned leading principal submatrices encountered during the solution process this is done by a look ahead strategy that monitors the condition of the leading principal submatrices and if necessary switches to a block step of suitable size the overhead of the look ahead algorithm is typically small compared to the classical levinson algorithm and in addition a reliable condition number estimate is produced

a new algorithm for solving toeplitz systems of equations abstract we present some recurrences that are the basis for an algorithm to invert an n n toeplitz system of linear equations with computational complexity o n log 2 n the recurrences used are closely related to the zohar trench and bareiss algorithms but do not have any obvious connection with other asymptotically fast algorithms for the inversion of toeplitz systems

a hybrid immune multiobjective optimization algorithm in this paper we develop a hybrid immune multiobjective optimization algorithm himo based on clonal selection principle in himo a hybrid mutation operator is proposed with the combination of gaussian and polynomial mutations gp hm operator the gp hm operator adopts an adaptive switching parameter to control the mutation process which uses relative large steps in high probability for boundary individuals and less crowded individuals with the generation running the probability to perform relative large steps is reduced gradually by this means the exploratory capabilities are enhanced by keeping a desirable balance between global search and local search so as to accelerate the convergence speed to the true pareto optimal front in the global space with many local pareto optimal fronts when comparing himo with various state of the art multiobjective optimization algorithms developed recently simulation results show that himo performs better evidently

recursive partial realization from the combined sequence of markov parameters and moments abstract in this paper we develop the recursive structure of partial realization from a two sided sequence of markov parameters and moments the specific feature of this recursive structure is that it accommodates sequences growing in two directions like in the two point pade approximation we present a recursive algorithm for the minimal partial realization from a sequence of markov parameters and moments that amounts to recursive lu factorization of a toeplitz behavior matrix leaping over nongeneric sections it turns out that this algorithm reveals a new continued fraction expansion which extends the classical cauer third form as a corollary various results related to toeplitz matrices two point pade approximations continued fractions etc are unified within this partial realization setting

a stabilized superfast solver for indefinite hankel systems abstract we present a stabilized superfast solver for indefinite hankel systems whose size is a power of 2 the hankel system is transformed into a loewner system which is solved by using an inversion formula for loewner matrices this explicit formula for the inverse of a loewner matrix contains certain parameters that are computed by solving two linearized rational interpolation problems on the unit circle the heart of our hankel solver is a superfast algorithm to solve these interpolation problems this algorithm is stabilized via pivoting iterative improvement and by giving the so called difficult interpolation points an adequate treatment we have implemented our algorithm in fortran 90 numerical examples illustrate the effectiveness of our approach

the pareto fitness genetic algorithm test function study evolutionary algorithms have shown some success in solving multiobjective optimization problems the methods of fitness assignment are mainly based on the information about the dominance relation between individuals we propose a pareto fitness genetic algorithm pfga in which we introduce a modified ranking procedure and a promising way of sharing a new fitness function based on the rank of the individual and its density value is designed this is considered as our main contribution the performance of our algorithm is evaluated on six multiobjective benchmarks with different pareto front features computational results quality of the approximation of the pareto optimal set and the number of fitness function evaluations proving its efficiency are reported

regularized fast recursive least squares algorithms for adaptive filtering fast recursive least squares frls algorithms are developed by using factorization techniques which represent an alternative way to the geometrical projections approach or the matrix partitioning based derivations the estimation problem is formulated within a regularization approach and priors are used to achieve a regularized solution which presents better numerical stability properties than the conventional least squares one the numerical complexity of the presented algorithms is explicitly related to the displacement rank of the a priori covariance matrix of the solution it then varies between o 5m and that of the slow rls algorithms to update the kalman gain vector m being the order of the solution an important advantage of the algorithms is that they admit a unified formulation such that the same equations may equally treat the prewindowed and the covariance cases independently from the used priors the difference lies only in the involved numerical complexity which is modified through a change of the dimensions of the intervening variables simulation results are given to illustrate the performances of these algorithms

an improved multiobjective differential evolution based on pareto adaptive dominance and orthogonal design abstract evolutionary multiobjective optimization has become a very popular topic in the last few years since the 1980s various evolutionary approaches that are capable of searching for multiple solutions simultaneously in a single run have been developed to solve multiobjective optimization problems mops however to find a uniformly distributed near complete and near optimal pareto front in a small number of fitness function evaluations nffes is a challenging task for any multiobjective optimization evolutionary algorithm moea in this paper we present an improved differential evolution algorithm to mops that combines several features of previous evolutionary algorithms in a unique manner it is characterized by a employing the orthogonal design method with quantization technique to generate the initial population b adopting an archive to store the nondominated solutions and employing the new pareto adaptive dominance method to update the archive at each generation c storing the extreme points and inserting them into the final archive in order to remedy one of the limitations of dominance the loss of the extreme points in the final archive and d using a hybrid selection mechanism in which a random selection and an elitist selection are alternated in order to allow using the archive solution to guide the search towards the pareto optimal front experiments have been conducted on a number of unconstrained real valued artificial functions of two and three objectives the results prove the efficiency of our approach with respect to the quality of the approximation of the pareto optimal front and the considerable reduction of nffes in these test problems by examining the selected performance metrics our approach is found to be statistically competitive with five state of the art moeas in terms of keeping the diversity of the individuals along the tradeoff surface finding a well approximated pareto optimal front and reducing the computational effort

parallel complexity of computations with general and toeplitz like matrices filled with integers and extensions computations with toeplitz and toeplitz like matrices are fundamental for many areas of algebraic and numerical computing the list of computational problems reducible to toeplitz and toeplitz like computations includes in particular the evaluation of the greatest common divisor gcd the least common multiple lcm and the resultant of two polynomials computing pade approximation and the berlekamp massey recurrence coefficients as well as numerous problems reducible to these transition to toeplitz and toeplitz like computations is currently the basis for the design of the parallel randomized nc rnc algorithms for these computational problems our main result is in constructing nearly optimal randomized parallel algorithms for toeplitz and toeplitz like computations and consequently for numerous related computational problems including the computational problems listed above where all the input values are integers and all the output values are computed exactly this includes randomized parallel algorithms for computing the rank the determinant and a basis for the null space of an n n toeplitz or toeplitz like matrix a filled with integers as well as a solution x to a linear system a x f if the system is consistent our algorithms use o log n log n log a parallel time and o n log n processors each capable of performing in unit time an arithmetic operation a comparision or a rounding of a rational number to a closest integer the cost bounds cover the cost of the verification of the correctness of the output the computations by these algorithms can be performed with the precision of o n log a bits which matches the precision required in order to represent the output except for the rank computation where the precision of the computation decreases the algorithms involve either a single random parameter or at most 2n 1 parameters the cited processor bounds are less by roughly factor n than ones supported by the known algorithms that run in polylogarithmic arithmetic time and do not use rounding to the closest integers technically we first devise new algorithms supporting our old nearly optimal complexity estimates for parallel computations with general matrices filled with integers then we decrease dramatically by roughly factor n1 376 the processor bounds required in these algorithms in the case where the input matrix is toeplitz like our algorithms exploit and combine some new techniques which may be of independent interest e g in the study of parallel and sequential computation of recursive factorization of integer matrices as well as our earlier techniques of variable diagonal relating to each other several known algebraic and numerical methods stream contraction and the truncation of displacement generators in toeplitz like computations our development and application of these techniques may be of independent

an exact recursion for the composite nearest neighbor degeneracy for a 2 n lattice space a set theoretic argument is utilized to develop a recursion relation that yields exactly the composite nearest neighbor degeneracy for simple indistinguishable particles distributed on a 2 n lattice space the associated generating functions as well as the expectation of the resulting statistics are also treated

periodic quasi orthogonal spline bases and applications to least squares curve fitting of digital images presents a new covariant basis dubbed the quasi orthogonal q spline basis for the space of n degree periodic uniform splines with k knots this basis is obtained analogously to the b spline basis by scaling and periodically translating a single spline function of bounded support the construction hinges on an important theorem involving the asymptotic behavior in the dimension of the inverse of banded toeplitz matrices the authors show that the gram matrix for this basis is nearly diagonal hence the name quasi orthogonal the new basis is applied to the problem of approximating closed digital curves in 2d images by least squares fitting since the new spline basis is almost orthogonal the least squares solution can be approximated by decimating a convolution between a resolution dependent kernel and the given data the approximating curve is expressed as a linear combination of the new spline functions and new control points another convolution maps these control points to the classical b spline control points a generalization of the result has relevance to the solution of regularized fitting problems

generalized app detection of continuous phase modulation over unknown isi channels techniques for computing soft information in the presence of unknown intersymbol interference are presented with a particular focus on iterative detection of serially concatenated continuous phase modulation the techniques are centered around the recursive least squares algorithm thus enabling unsupervised detection in particular we employ bidirectional estimation

a frequency domain state space approach to ls estimation and its application in turbo equalization a frequency domain state space approach to the least squares ls estimation for finite impulse response fir system identification is proposed by exploiting the toeplitz structure of the data matrix leading to two low complexity fft fast fourier transform based unbiased recursive estimators the proposed recursive estimators are applied to the smoothing estimation of time varying frequency selective channels in turbo equalization systems and channel estimation approaches with complexity o logl per symbol are developed where l is the number of channel taps

a multiobjective immune algorithm based on a multiple affinity model abstract this paper presents a new multiobjective immune algorithm based on a multiple affinity model inspired by immune system mam moia the multiple affinity model builds the relationship model among main entities and concepts in multiobjective problems mops and multiobjective evolutionary algorithms moeas including feasible solution variable space objective space pareto optimal set ranking and crowding distance in the model immune operators including clonal proliferation hypermutation and immune suppression are designed to proliferate superior antibodies and suppress the inferiors mam moia is compared with nsga ii spea2 and nnia in solving the zdt and dtlz standard test problems the experimental study based on three performance metrics including coverage of two sets convergence and spacing proves that mam moia is effective for solving mops

a turbo fde technique for reduced cp sc based block transmission systems for conventional cyclic prefix cp assisted block transmission systems the cp length is selected on the basis of the expected maximum delay spread with regard to single carrier sc based block transmission implementations a full length cp is recommendable since it allows good performances through the use of simple frequency domain equalization fde techniques in this letter a soft decision directed correction sddc aided turbo fde technique is presented for reduced cp sc based block transmission systems using conventional frame structures the relations with some already known iterative fde techniques are established and a set of performance results is reported and discussed the advantages of the proposed approach are emphasized namely the possibility of approximately achieving besides the obvious bandwidth efficiency gain the maximum power efficiency gain that a strong cp reduction allows

a novel elitist multiobjective optimization algorithm multiobjective extremal optimization abstract recently a general purpose local search heuristic method called extremal optimization eo has been successfully applied to some np hard combinatorial optimization problems this paper presents an investigation on eo with its application in numerical multiobjective optimization and proposes a new novel elitist 1 multiobjective algorithm called multiobjective extremal optimization moeo in order to extend eo to solve the multiobjective optimization problems the pareto dominance strategy is introduced to the fitness assignment of the proposed approach we also present a new hybrid mutation operator that enhances the exploratory capabilities of our algorithm the proposed approach is validated using five popular benchmark functions the simulation results indicate that the proposed approach is highly competitive with the state of the art multiobjective evolutionary algorithms thus moeo can be considered a good alternative to solve numerical multiobjective optimization problems