a geometrical method for removing edge effects from kernel type nonparametric regression estimators abstract we introduce a simple geometric method for removing edge effects from kernel type nonparametric regression estimators it involves reflecting the data set in two estimated points thereby generating a new data set with three times the range of the original data the usual kernel type estimator may be applied to the new enlarged data set without any danger of edge effects this technique is applicable generally to both regularly spaced and randomly spaced designs and admits a natural analog of leave one out cross validation the new cross validation algorithm may be extended to the very ends of the design interval unlike its more conventional counterpart which must be downweighted at the ends of the interval to avoid edge effects

computing the minimum construction cost of a building s external wall taking into account its energy efficiency abstract the construction of a building s external wall is subject to many restrictions such as budget workforce availability of materials thickness maintenance cost time limit and specially energy efficiency legislation intended at mitigating the negative effects of the energy consumption and obtaining a more sustainable and healthier indoor environment the choice of the appropriate material and thickness composing each layer of an external wall can significantly reduce the energy consumption of the building without adversely affecting the cost of the wall by using integer linear programming ilp the aim of this paper is to obtain this best choice of materials and thicknesses to minimize the construction cost of an external wall while complying with the abovementioned restrictions a case study is presented with more than 5 5 million combinations of different selected materials and their thicknesses for the different layers of the wall the ilp problem has been solved for 165 scenarios that take into account different maximal allowed thermal transmittances and a range of the most usual thicknesses and material options of an external wall

fast recognition of alternating groups of unknown degree abstract we present a constructive recognition algorithm to decide whether a given black box group is isomorphic to an alternating or a symmetric group without prior knowledge of the degree this eliminates the major gap in known algorithms as they require the degree as additional input our methods are probabilistic and rely on results about proportions of elements with certain properties in alternating and symmetric groups these results are of independent interest for instance we establish a lower bound for the proportion of involutions with small support

computing in groups of lie type we describe two methods for computing with the elements of untwisted groups of lie type using the steinberg presentation and using highest weight representations we give algorithms for element arithmetic within the steinberg presentation conversion between this presentation and linear representations is achieved using a new generalisation of row and column reduction

possibilistic mean variance models and efficient frontiers for portfolio selection problem in this paper it is assumed that the rates of return on assets can be expressed by possibility distributions rather than probability distributions we propose two kinds of portfolio selection models based on lower and upper possibilistic means and possibilistic variances respectively and introduce the notions of lower and upper possibilistic efficient portfolios we also present an algorithm which can derive the explicit expression of the possibilistic efficient frontier for the possibilistic mean variance portfolio selection problem dealing with lower bounds on asset holdings

a capable neural network model for solving the maximum flow problem this paper presents an optimization technique for solving a maximum flow problem arising in widespread applications in a variety of settings on the basis of the karush kuhn tucker kkt optimality conditions a neural network model is constructed the equilibrium point of the proposed neural network is then proved to be equivalent to the optimal solution of the original problem it is also shown that the proposed neural network model is stable in the sense of lyapunov and it is globally convergent to an exact optimal solution of the maximum flow problem several illustrative examples are provided to show the feasibility and the efficiency of the proposed method in this paper

a dynamic model to solve the absolute value equations abstract in this paper the analytic solution of the absolute value equations ave is investigated as far as we know there are some numerical methods to obtain the solution of the ave however there is not a study on exact solution of the ave here we try to obtain the exact solution of the ave based on a dynamical system model constructed by the projection function finally the simulation results show the effectiveness and the accuracy of the method

a novel neural network for variational inequalities with linear and nonlinear constraints variational inequality is a uniform approach for many important optimization and equilibrium problems based on the sufficient and necessary conditions of the solution this paper presents a novel neural network model for solving variational inequalities with linear and nonlinear constraints three sufficient conditions are provided to ensure that the proposed network with an asymmetric mapping is stable in the sense of lyapunov and converges to an exact solution of the original problem meanwhile the proposed network with a gradient mapping is also proved to be stable in the sense of lyapunov and to have a finite time convergence under some mild conditions by using a new energy function compared with the existing neural networks the new model can be applied to solve some nonmonotone problems has no adjustable parameter and has lower complexity thus the structure of the proposed network is very simple since the proposed network can be used to solve a broad class of optimization problems it has great application potential the validity and transient behavior of the proposed neural network are demonstrated by several numerical examples

nonparametric kernel algorithm for recovery of functions from noisy measurements with applications this note presents a kernel algorithm for recovery of a regression function from noisy data conditions are provided that assure pointwise convergence in the mean square and almost sure senses an application to a class of linear system identification problems is discussed

application of projection neural network in solving convex programming problems in this paper we present that solution of convex programming problems is equivalent with solution of projection formulation then we introduce neural network models for solving projection formulation and analysis stability conditions and convergence simulation shows that the introduced neural network is effective in solving convex programming problems

nonlinearity estimation in hammerstein systems based on ordered observations the nonlinear subsystem of a hammerstein system is identified i e its characteristic is recovered from input output ohservations of the whole system the input and disturbance are white stochastic processes the identified characteristic satisfies a piecewise lipschitz condition only algorithms presented in the paper are calculated from ordered input output observations i e from pairs of observations arranged in a sequence in which input measurements increase in value the mean integrated square error converges to zero as the number of observations tends to infinity convergence rates are insensitive to the shape of the probability density of the input signal results of numerical simulation are also shown

effective black box constructive recognition of classical groups abstract we describe a black box las vegas algorithm to construct standard generators for classical groups defined over finite fields we assume that the field has size at least 4 and that oracles to solve certain problems are available subject to these assumptions the algorithm runs in polynomial time a practical implementation of our algorithm is distributed with the computer algebra system magma

a possibilistic approach to selecting portfolios with highest utility score the mean variance methodology for the portfolio selection problem originally proposed by markowitz has been one of the most important research fields in modern finance in this paper we will assume that i each investor can assign a welfare or utility score to competing investment portfolios based on the expected return and risk of the portfolios and ii the rates of return on securities are modelled by possibility distributions rather than probability distributions we will present an algorithm of complexity o n3 for finding an exact optimal solution in the sense of utility scores to the n asset portfolio selection problem under possibility distributions

presentations on standard generators for classical groups abstract for each family of finite classical groups and their associated simple quotients we provide an explicit presentation on a specific generating set of size at most 8 since there exist efficient algorithms to construct this generating set in any copy of the group our presentations can be used to verify claimed isomorphisms between representations of the classical group the presentations are available in magma

dynamic system identification with order statistics systems consisting of linear dynamic and memory less nonlinear subsystems are identified the paper deals with systems in which the nonlinear element is followed by a linear element as well as systems in which the subsystems are connected in parallel the goal of the identification is to recover the nonlinearity from noisy input output observations of the whole system signals interconnecting the elements are not measured observed values of the input signal are rearranged in increasing order and coefficients for the expansion of the nonlinearity in trigonometric series are estimated from the new sequence of observations obtained in this way two algorithms are presented and their mean integrated square error is examined conditions for pointwise convergence are also established for the nonlinearity satisfying the lipschitz condition the error converges to zero the rate of convergence derived for differentiable nonlinear characteristics is insensitive to the roughness of the probability density of the input signal results of numerical simulation are also presented

a robbins monro procedure for estimation in semiparametric regression models this paper is devoted to the parametric estimation of a shift together with the nonparametric estimation of a regression function in a semiparametric regression model we implement a robbins monro procedure very efficient and easy to handle on the one hand we propose a stochastic algorithm similar to that of robbins monro in order to estimate the shift parameter a preliminary evaluation of the regression function is not necessary for estimating the shift parameter on the other hand we make use of a recursive nadaraya watson estimator for the estimation of the regression function this kernel estimator takes in account the previous estimation of the shift parameter we establish the almost sure convergence for both robbins monro and nadaraya watson estimators the asymptotic normality of our estimates is also provided

an efficient dynamic model for solving a portfolio selection with uncertain chance constraint models this paper presents a neural network model for solving maximization programming model with chance constraint in which the security returns are uncertain variables the main idea is to replace the portfolio selection models when the uncertain returns are chosen as some special cases such as linear uncertain variables trapezoidal uncertain variables and normal uncertain variables with a linear programming lp problem according to the saddle point theorem optimization theory convex analysis theory lyapunov stability theory and lasalle invariance principle the equilibrium point of the proposed neural network is proved to be equivalent to the optimal solution of the original problem it is also shown that the proposed neural network model is stable in the sense of lyapunov and it is globally convergent to an exact optimal solution of the portfolio selection problem with uncertain returns two illustrative examples are provided to show the feasibility and the efficiency of the proposed method in this paper

expected value of fuzzy variable and fuzzy expected value models this paper will present a novel concept of expected values of fuzzy variables which is essentially a type of choquet integral and coincides with that of random variables in order to calculate the expected value of general fuzzy variable a fuzzy simulation technique is also designed finally we construct a spectrum of fuzzy expected value models and integrate fuzzy simulation neural network and genetic algorithms to produce a hybrid intelligent algorithm for solving general fuzzy expected value models

nonparametric output prediction for nonlinear fading memory systems the authors construct a class of elementary nonparametric output predictors of an unknown discrete time nonlinear fading memory system their algorithms predict asymptotically well for every bounded input sequence every disturbance sequence in certain classes and every linear or nonlinear system that is continuous and asymptotically time invariant causal and with fading memory the predictor is based on k sub n nearest neighbor estimators from nonparametric statistics it uses only previous input and noisy output data of the system without any knowledge of the structure of the unknown system the bounds on the input or the properties of noise under additional smoothness conditions the authors provide rates of convergence for the time average errors of their scheme finally they apply their results to the special case of stable linear time invariant lti systems

neural network models and its application for solving linear and quadratic programming problems in this paper we consider two recurrent neural network model for solving linear and quadratic programming problems the first model is derived from an unconstraint minimization reformulation of the program the second model directly is obtained of optimality condition for an optimization problem by applying the energy function and the duality gap we will compare the convergence these models we also explore the existence and the convergence of the trajectory and stability properties for the neural networks models finally in some numerical examples the effectiveness of the methods is shown

nonparametric identification of hammerstein systems a discrete time nonlinear hammerstein system is identified and the correlation and frequency domain methods for identification of its linear subsystem are presented the main results concern the estimation of the nonlinear memoryless subsystem no conditions concerning the functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is given the algorithm is simply a nonparametric kernel estimate of the regression function calculated from dependent data it is shown that the algorithm converges to the characteristic of the subsystem regardless of the probability distribution of the input variable pointwise as well as global consistencies are established for lipschitz characteristics the rate of the convergence in probability is o n sup 1 3

writing projective representations over subfields let g x be an absolutely irreducible subgroup of gl d k and let f be a proper subfield of the finite field k we present a practical algorithm to decide constructively whether or not g is conjugate to a subgroup of gl d f k where k denotes the centre of gl d k if the derived group of g also acts absolutely irreducibly then the algorithm is las vegas and costs o x d3 d2log f arithmetic operations in k this work forms part of a recognition project based on aschbacher s classification of maximal subgroups of gl d k

fuzzy chance constrained portfolio selection abstract this paper selects the portfolio with fuzzy returns by criteria of chance represented by credibility measure in the paper two types of credibility based portfolio selection model are provided according to two types of chance criteria by one chance criterion the objective is to maximize the investor s return at a given threshold confidence level by another chance criterion the objective is to maximize the credibility of achieving a specified return level subject to the constraints to provide a general method to solve the new models a hybrid intelligent algorithm integrating fuzzy simulation and genetic algorithm is designed in the paper two numerical examples with security returns taking different types of membership function are also given to illustrate the modelling idea of the paper and to demonstrate the effectiveness of the proposed algorithm

identification of miso nonlinear regressions in the presence of a wide class of disturbances a nonparametric algorithm based on multiple fourier series for identification of miso multidimensional input single output systems is investigated it is shown that the algorithm converges for a wide class of noise

adjoint representations of black box groups psl2 fq abstract given a black box group y encrypting psl 2 f over an unknown field f of unknown odd characteristic p and a global exponent e for y that is an integer e such that y e 1 for all y y we present a las vegas algorithm which constructs a unipotent element in y the running time of our algorithm is polynomial in log e this answers the question posed by babai and beals in 1999 we also find the characteristic of the underlying field in time polynomial in log e and linear in p all our algorithms are randomized furthermore we construct in time polynomial in log e a black box group x encrypting pgl 2 f so 3 f over the same field as y its subgroup y of index 2 isomorphic to y and a polynomial in log e time isomorphism y y a black box field k and polynomial time in log e isomorphisms so 3 k x so 3 k if in addition we know p and the standard explicitly given finite field f q isomorphic to the field on which y is defined then we construct in time polynomial in log e isomorphism so 3 f q so 3 k unlike many papers on black box groups our algorithms make no use of additional oracles other than the black box group operations moreover our result acts as an sl 2 oracle in the black box group theory we implemented our algorithms in gap and tested them for groups such as psl 2 f for f 115756986668303657898962467957 a prime number

nonparametric density estimation the l 1 view differentiation of integrals consistency lower bounds for rates of convergence rates of convergence in l1 the automatic kernel estimate l1 and pointwise convergence estimates related to the kernel estimate and the histogram estimate simulation inequalities and random variate generation the transformed kernel estimate applications in discrimination operations on density estimates estimators based on orthogonal series index

on estimation of a class of nonlinear systems by the kernel regression estimate the estimation of a multiple input single output discrete hammerstein system is studied such a system contains a nonlinear memoryless subsystem followed by a dynamic linear subsystem the impulse response of the dynamic linear subsystem is obtained by the correlation method the main results concern the estimation of the nonlinear memoryless subsystem no conditions are imposed on the functional form of the nonlinear subsystem and the nonlinearity is recovered using the kernel regression estimate the distribution free pointwise and global convergence of the estimate is demonstrated that is no conditions are imposed on the input distribution and convergence is proven for virtually all nonlinearities the rates of pointwise as well as global convergence are obtained for all input distributions and for lipschitz type nonlinearities

a law of the iterated logarithm for kernel estimators of regression functions for fixed design regression data kernel estimation is widely used to estimate v t thev th derivative of t denoting such an estimator by hat mu nv t this paper is concerned with the almost sure convergence of hat mu nv t e hat mu nv t it is shown that under several inserting procedures a law of iterated logarithm holds

portfolio selection under independent possibilistic information this paper deals with a portfolio selection problem with independently estimated possibilistic return rates under such a circumstance a distributive investment has been regarded as a good solution in the traditional portfolio theory however the conventional possibilistic approach yields a concentrated investment solution considering the reason why a distributive investment is advocated a new approach to the possibilistic portfolio selection is proposed

an estimation model of value at risk portfolio under uncertainty a value at risk portfolio model under uncertainty is discussed in the proposed model randomness and fuzziness are evaluated respectively by the probabilistic expectation and the mean values with evaluation weights and l mean functions the means the variances and the measurements of imprecision for fuzzy numbers fuzzy random variables are evaluated in the possibility case and the necessity case and the rate of return in portfolio is estimated regarding the both random factors and imprecise factors by analytical approach we derive a solution of the value at risk portfolio problem a numerical example is given to illustrate our idea

recursive nonparametric estimation for time series this paper considers online kernel estimation for both short and long range dependent time series data utilizing the predictive dependence measure of wu we carefully study the asymptotic properties of recursive kernel density and regression estimators for a general class of stationary processes in particular we prove that the proposed estimators have the asymptotic normality and the corresponding central limit theorems are provided in addition we establish the sharp laws of the iterated logarithms that precisely characterize the asymptotic almost sure behavior of the proposed estimators

a one layer recurrent neural network with a discontinuous hard limiting activation function for quadratic programming in this paper a one layer recurrent neural network with a discontinuous hard limiting activation function is proposed for quadratic programming this neural network is capable of solving a large class of quadratic programming problems the state variables of the neural network are proven to be globally stable and the output variables are proven to be convergent to optimal solutions as long as the objective function is strictly convex on a set defined by the equality constraints in addition a sequential quadratic programming approach based on the proposed recurrent neural network is developed for general nonlinear programming simulation results on numerical examples and support vector machine svm learning show the effectiveness and performance of the neural network

possibilistic linear programming a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem in this paper we review some fuzzy linear programming methods and techniques from a practical point of view in the rst part the general history and the approach of fuzzy mathematical programming are introduced using a numerical example some models of fuzzy linear programming are described in the second part of the paper fuzzy mathematical programming approaches are compared to stochastic programming ones the advantages and disadvantages of fuzzy mathematical programming approaches are exemplied in the setting of an optimal portfolio selection problem finally some newly developed ideas and techniques in fuzzy mathematical programming are briey reviewed c 2000 elsevier science b v all rights reserved

kernels for nonparametric curve estimation summary the choice of kernels for the nonparametric estimation of regression functions and of their derivatives is investigated explicit expressions are obtained for kernels minimizing the asymptotic variance or the asymptotic integrated mean square error imse the present proof of the optimality of the latter kernels is restricted up to order k 5 these kernels are also of interest for the nonparametric estimation of probability densities and spectral densities a finite sample study indicates that higher order kernels asymptotically improving the rate of convergence may become attractive for realistic finite sample size suitably modified kernels are considered for estimating at the extremities of the data in a way which allows to retain the order of the bias found for interior points

fuzzy mean variance skewness portfolio selection models by interval analysis in portfolio selection problem the expected return risk liquidity etc cannot be predicted precisely the investor generally makes his portfolio decision according to his experience and his economic wisdom so deterministic portfolio selection is not a good choice for the investor in most of the recent works on this problem fuzzy set theory is widely used to model the problem in uncertain environments this paper utilizes the concept of interval numbers in fuzzy set theory to extend the classical mean variance mv portfolio selection model into mean variance skewness mvs model with consideration of transaction cost in addition some other criteria like short and long term returns liquidity dividends number of assets in the portfolio and the maximum and minimum allowable capital invested in stocks of any selected company are considered three different models have been proposed by defining the future financial market optimistically pessimistically and in the combined form to model the fuzzy mvs portfolio selection problem in order to solve the models fuzzy simulation fs and elitist genetic algorithm ega are integrated to produce a more powerful and effective hybrid intelligence algorithm hia finally our approaches are tested on a set of stock data from bombay stock exchange bse

multi objective possibilistic model for portfolio selection with transaction cost in this paper we introduce the possibilistic mean value and variance of continuous distribution rather than probability distributions we propose a multi objective portfolio based model and added another entropy objective function to generate a well diversified asset portfolio within optimal asset allocation for quantifying any potential return and risk portfolio liquidity is taken into account and a multi objective non linear programming model for portfolio rebalancing with transaction cost is proposed the models are illustrated with numerical examples

constructing composition factors for a linear group in polynomial time abstract we present a las vegas polynomial time algorithm that takes as input a subgroup of gl d f q and subject to the existence of certain oracles determines its composition factors provided that none of those factors is isomorphic to one of b 2 2 2 2 k 1 f 4 2 2 2 k 1 d 4 3 2 k or g 2 2 3 2 k 1 for any k

a unifying approach to nonparametric regression estimation abstract there exists a variety of nonparametric regression estimators with cubic smoothing splines k nearest neighbor k nn estimators and various types of kernel estimators among the most popular a class of kernel estimators with local bandwidth depending on the density of the design points is introduced where the degree of design adaptation may be expressed by a single parameter in 0 1 the adaptation to the design is such that the bandwidth is made larger to a degree depending on where the design is thin special values of this parameter correspond approximately to the ordinary fixed width kernel estimator the smoothing spline and the k nn estimator hence this method offers a synthesis of some classical methods the same method allows estimation of derivatives by using appropriate kernels the influence of this degree of design adaptation on the integrated mean squared error is investigated there is no uniformly optimal solution the optimal solution depends in a complex way on de

recovering band limited signals under noise we consider the problem of recovering a band limited signal f t from noisy data yk f k spl tau spl gt epsilon sub k where spl tau is the sampling rate starting from the truncated whittaker shannon cardinal expansion with or without sampling windows both cases yield inconsistent estimates of f t we propose estimators that are convergent to f t in the pointwise and uniform sense the basic idea is to cut down high frequencies in the data and to use suitable oversampling spl tau spl les spl pi spl omega spl omega being the bandwidth maximum frequency of f t the simplest estimator we propose is given by f spl circ sub n t spl tau spl sigma t k spl tau spl les n spl tau yksin spl omega t k spl tau spl pi t k spl tau t spl les n spl tau generalizations of f spl circ sub n including sampling windows are also examined the main aim is to examine the mean squared error mse properties of such estimators in order to determine the optimal choice of the sampling rate spl tau yielding the fastest possible rate of convergence the best rate for the mse we obtain is o in n n

portfolio adjusting optimization under credibility measures this paper discusses portfolio adjusting problems for an existing portfolio the returns of risky assets are regarded as fuzzy variables and a class of credibilistic mean variance adjusting models with transaction costs are proposed on the basis of credibility theory under the assumption that the returns of risky assets are triangular fuzzy variables the optimization models are converted into crisp forms furthermore we employ the sequential quadratic programming method to work out the optimal strategy numerical examples illustrate the effectiveness of the proposed models and the influence of the transaction costs in portfolio selection

fast management of permutation groups i we present new algorithms for permutation group manipulation our methods result in an improvement of nearly an order of magnitude in the worst case analysis for the fundamental problems of finding strong generating sets and testing membership the normal structure of the group is brought into play even for such elementary issues an essential element is the recognition of large alternating composition factors of the given group and subsequent extension of the permutation domain to display the natural action of these alternating groups further new features include a novel fast handling of alternating groups and the sifting of defining relations in order to link these and other analyzed factors with the rest of the group the analysis of the algorithm depends on the classification of finite simple groups in a sequel to this paper using an enhancement of the present method we shall achieve a further order of magnitude improvement

black box groups isomorphic to pgl 2 2e abstract a deterministic polynomial time algorithm constructs an isomorphism between pgl 2 2 e and a black box group to which it is isomorphic

some contributions to fixed distribution learning theory we consider some problems in learning with respect to a fixed distribution we introduce two new notions of learnability these are probably uniformly approximately correct puac learnability which is a stronger requirement than the widely studied pac learnability and minimal empirical risk mer learnability which is a stronger requirement than the previously defined notions of solid or potential learnability it is shown that although the motivations for defining these two notions of learnability are entirely different these two notions are in fact equivalent to each other and in turn equivalent to a property introduced here referred to as the shrinking width property it is further shown that if the function class to be learned has the property that empirical means converge uniformly to their true values then all of these learnability properties hold in the course of proving conditions for these forms of learnability we also obtain a new estimate for the vc dimension of a collection of sets obtained by performing boolean operations on a given collection this result is of independent interest we consider both the case in which there is an underlying target function as well as the case of model free or agnostic learning finally we consider the issue of representation of a collection of sets by its subcollection of equivalence classes it is shown by example that by suitably choosing representatives of each equivalence class it is possible to affect the property of uniform convergence of empirical probabilities

short presentations for alternating and symmetric groups we construct two kinds of presentations for the alternating and symmetric groups of degree n the first are on two generators in which the number of relations is o logn and the presentation length is o log 2 n the second have a bounded number of generators and relations and length o logn

on the series expansion approach to the identification of hammerstein systems a polynomial identification algorithm for recovering a nonlinearity in the hammerstein system is proposed the estimate employs the legendre orthogonal system with adaptively selected number of terms the global consistency along with rates of convergence are established no assumptions concerning continuity of the nonlinearity or its functional form are made a data driven method using the cross validation technique for selecting the number of terms in the estimate is presented

a dynamical model for solving degenerate quadratic minimax problems with constraints this paper presents a new neural network model for solving degenerate quadratic minimax dqm problems on the basis of the saddle point theorem optimization theory convex analysis theory lyapunov stability theory and lasalle invariance principle the equilibrium point of the proposed network is proved to be equivalent to the optimal solution of the dqm problems it is also shown that the proposed network model is stable in the sense of lyapunov and it is globally convergent to an exact optimal solution of the original problem several illustrative examples are provided to show the feasibility and the efficiency of the proposed method in this paper

memoryless nonlinear system identification with unknown model order the problem of identifying a general memoryless input output system from measurements of inputs and the corresponding outputs is considered the measured output is sought to be represented as the linear combination of known functions of the input with some additive noise the choice of model order to be used to fit the data is the main issue addressed and a cost function involving the prediction error and the model order is derived the cost function under certain approximations is shown to be similar to one obtained by h akaike 1969 1970 if there is a real system generating the data it is shown that the expected value of this cost function is always minimized at the true value of the order as long as the noise variance satisfies certain conditions asymptotic results for some cases are derived an efficient algorithm is proposed for identifying the model order some simulation results using the proposed algorithm are also presented

nonparametric identification of wiener systems a wiener system i e a system in which a linear dynamic part is followed by a nonlinear and memoryless one is identified no parametric restriction is imposed on the functional form of the nonlinear characteristic of the memoryless subsystem and a nonparametric algorithm recovering the characteristic from input output observations of the whole system is proposed its consistency is shown and the rate of convergence is given an idea for identification of the impulse response of the linear subsystem is proposed results of numerical simulation are also presented

nonparametric estimation of a regression function consider the regression model y i g x i e i i 1 2 n where x i s denote unordered design variables and g is an unknown function defined on the interval 0 1 assume e i are iid random variables with zero mean and finite variance priestley and chao 1972 and clark 1977 proposed estimators g 2n and g 3n respectively for g in this paper the asymptotic behavior of g 2n and g 3n is studied utilizing the properties of the new estimator g 1n it is shown that g 1n g 2n g 3n are asymptotically equivalent in various senses moreover consistency results are established and rates of uniform convergence obtained for example if e e 3 if g is lipschitz of order 1 and if n is any sequence of constants tending to as n then for all 0 a leqq b 1 n 1 mathord left vphantom 1 3 right kern nulldelimiterspace 3 mathord left vphantom n 1 mathord left vphantom 1 3 right kern nulldelimiterspace 3 beta n log n mathop sup limits a leqq x leqq b g 1n x g x xrightarrow w p 1 0 right kern nulldelimiterspace beta n log n mathop sup limits a leqq x leqq b g 1n x g x xrightarrow w p 1 0 as n finally when g is monotone a strong consistent isotonic estimator g n is considered

constructive recognition of mathrm psl 2 q existing black box and other algorithms for explicitly recognising groups of lie type over gf q have asymptotic running times which are polynomial in q whereas the input size involves only log q this has represented a serious obstruction to the efficient recognition of such groups recently brooksbank and kantor devised new explicit recognition algorithms for classical groups these run in time that is polynomial in the size of the input given an oracle that recognises psl 2 q explicitly the present paper in conjunction with an earlier paper by the first two authors provides such an oracle the earlier paper produced an algorithm for explicitly recognising sl 2 q in its natural representation in polynomial time given a discrete logarithm oracle for gf q the algorithm presented here takes as input a generating set for a subgroup g of gl d f that is isomorphic modulo scalars to psl 2 q where f is a finite field of the same characteristic as gf q it returns the natural representation of g modulo scalars since a faithful projective representation of psl 2 q in cross characteristic or a faithful permutation representation of this group is necessarily of size that is polynomial in q rather than in log q elementary algorithms will recognise psl 2 q explicitly in polynomial time in these cases given a discrete logarithm oracle for gf q our algorithm thus provides the required polynomial time oracle for recognising psl 2 q explicitly in the remaining case namely for representations in the natural characteristic this leads to a partial solution of a question posed by babai and shalev if g is a matrix group in characteristic p determine in polynomial time whether or not op g is trivial

a hybrid intelligent algorithm for portfolio selection problem with fuzzy returns portfolio selection theory with fuzzy returns has been well developed and widely applied within the framework of credibility theory several fuzzy portfolio selection models have been proposed such as mean variance model entropy optimization model chance constrained programming model and so on in order to solve these nonlinear optimization models a hybrid intelligent algorithm is designed by integrating simulated annealing algorithm neural network and fuzzy simulation techniques where the neural network is used to approximate the expected value and variance for fuzzy returns and the fuzzy simulation is used to generate the training data for neural network since these models are used to be solved by genetic algorithm some comparisons between the hybrid intelligent algorithm and genetic algorithm are given in terms of numerical examples which imply that the hybrid intelligent algorithm is robust and more effective in particular it reduces the running time significantly for large size problems

hammerstein system identification with the nearest neighbor algorithm the nonlinear characteristic in a hammerstein system i e a system in which a nonlinear memoryless subsystem and a linear dynamic are connected in a cascade is recovered with the nonparametric nearest neighbor regression estimate the a priori information is nonparametric both the nonlinear characteristic and the impulse response are completely unknown and can be of any form local and global properties of the estimate are examined whatever the probability density of the input signal the estimate converges at every continuity point of the characteristic as well as in the global sense we derive the asymptotic bias and variance of the proposed estimate as a result the optimal rate of convergence is established that additionally is independent of the shape of the input density results of numerical simulations are also presented

black box exceptional groups of lie type ii abstract if a black box group g is known to be isomorphic to an exceptional simple group g of lie type of twisted rank 1 other than any f 4 2 2 e or d 4 3 2 e over a field of known size q and if suitable sl 2 and discrete log oracles are available when q is odd then a polynomial time las vegas algorithm is given that produces a constructive isomorphism between g and g

mean variance skewness model for portfolio selection with fuzzy returns numerous empirical studies show that portfolio returns are generally asymmetric and investors would prefer a portfolio return with larger degree of asymmetry when the mean value and variance are same in order to measure the asymmetry of fuzzy portfolio return a concept of skewness is defined as the third central moment in this paper and its mathematical properties are studied as an extension of the fuzzy mean variance model a mean variance skewness model is presented and the corresponding variations are also considered in order to solve the proposed models a genetic algorithm integrating fuzzy simulation is designed finally several numerical examples are given to illustrate the modelling idea and the effectiveness of the proposed algorithm

computing matrix group decompositions with respect to a normal subgroup abstract we describe an algorithm which can be used to investigate whether a matrix group defined over a finite field decomposes with respect to a normal subgroup defined as the normal closure of a given set of matrices the possible decompositions correspond to classes in aschbacher s classification of subgroups of the general linear group

risk curve and fuzzy portfolio selection in stochastic environment variance semivariance and probability of a bad outcome are three popular definitions of risk for portfolio selection in fuzzy environment variance is carried on as the definition of risk however in real life risk is understood in many different ways in this paper we propose a new definition of risk for portfolio selection in fuzzy environment based on this new definition a new type of model is provided to give a general solution to the new model problem a hybrid intelligent algorithm is designed one numerical example is also presented to illustrate the optimization idea and the effectiveness of the designed algorithm

portfolio selection problems with random fuzzy variable returns this paper considers several portfolio selection problems including probabilistic future returns with ambiguous expected returns assumed as random fuzzy variables random fuzzy portfolio selection problems are formulated as nonlinear programming problems based on both stochastic and fuzzy programming approaches since there is no efficient solution method to solve these problems directly main problems are transformed into equivalent deterministic quadratic programming problems using probabilistic chance constraints possibility measure and fuzzy goals and their efficient solution methods to find a global optimal solution of each problem is constructed furthermore numerical examples of portfolio selection problems are provided to illustrate our proposed models and solution methods compared with several previous basic models and to show that our proposed model is a versatile model to be applicable to various unexpected conditions

nonparametric identification of a particular nonlinear time series system a nonlinear time series system is identified the system has a cascade structure that is it consists of a nonlinear memoryless element followed by a dynamic linear system given a gaussian input a hermite series based method for recovering the system nonlinearity is presented the proposed identification procedure is nonparametric since it is able to be consistent for a broad class of nonpolynomial characteristics the consistency and rate of convergence of the procedure are established also some data driven methods for selecting the optimal number of terms in the procedure are proposed the results are illustrated by a numerical example

recognising the small ree groups in their natural representations we present las vegas algorithms for constructive recognition and constructive membership testing of the ree groups g22 q ree q where q 32m 1 for some m 0 in their natural representations of degree 7 the input is a generating set x gl 7 q the constructive recognition algorithm is polynomial time given a discrete logarithm oracle the constructive membership testing consists of a pre processing step that only needs to be executed once for a given x and a main step the latter is polynomial time and the former is polynomial time given a discrete logarithm oracle implementations of the algorithms are available for the computer algebra system magma

recognition of finite exceptional groups of lie type let q be a prime power and let g be an absolutely irreducible subgroup of gld f where f is a finite field of the same characteristic as fq the field of q elements assume that g g q a quasisimple group of exceptional lie type over fq which is neither a suzuki nor a ree group we present a las vegas algorithm that constructs an isomorphism from g to the standard copy of g q if g 6 3d4 q with q even then the algorithm runs in polynomial time subject to the existence of a discrete log oracle

the choice of weights in kernel regression estimation summary for kernel regression estimation a weighting scheme due to nadaraya and watson has been associated with random design and a convolution type weighting scheme with fixed design based on integrated mean square error none of the estimators is uniformly optimal in either design however the convolution type weights are minimax optimal further advantages of this estimator can be seen in the structure of the bias

a new method for recognising suzuki groups abstract we present a new algorithm for constructive recognition of the suzuki groups in their natural representations the algorithm runs in las vegas polynomial time given a discrete logarithm oracle an implementation is available in the magma computer algebra system

asymptotic optimality for c_p c_l cross validation and generalized cross validation discrete index set c p c l cross validation and generalized cross validation are useful data driven techniques for selecting a good estimate from a proposed class of linear estimates the asymptotic behaviors of these procedures are studied some easily interpretable conditions are derived to demonstrate the asymptotic optimality it is argued that cross validation and generalized cross validation can be viewed as some special ways of applying c l applications in nearest neighbor nonparametric regression and in model selection are discussed in detail

a feedback neural network for solving convex constraint optimization problems in this paper a feedback neural network model is presented by two steps firstly a convex sub optimization problem with bound constraints is established by introducing an energy function and the neural subnetwork for solving the sub optimization problem is constructed based on the projection method secondly a feedback neural network is proposed by using the subnetwork and can converge to an exact optimal solution of primal optimization problem the distinguishing features of the proposed feedback network are no lagrange multipliers no dual variables and no penalty parameters it has the least number of state variables simple structure and is suitable for hardware implementation two simulation examples are provided to show the feasibility and efficiency of proposed method in the paper