construction of nonlinear resilient boolean functions using small affine functions in this correspondence we use affine functions on a small number of variables to construct resilient functions on a large number of variables we show that by properly combining these functions it is possible to achieve high nonlinearity and high algebraic degree an important contribution of the correspondence is to show that for each order of resiliency m it is possible to find infinitely many odd and even positive integers n such that it is possible to construct maximum degree n variable m resilient functions having nonlinearity strictly greater than 2 sup n 1 2 sup spl lfloor n 2 spl rfloor we also present construction of some important functions on a small number of variables

on the existence of 10 2 7 488 resilient functions using a heuristic search combined with some algebraic techniques several examples for 10 variable boolean functions with nonlinearity 488 algebraic degree 7 and resiliency degree 2 were constructed this construction affirmatively answers the open problem about the existence of such functions

on the existence of 9 3 5 240 resilient functions using a heuristic search technique several examples for 9 variable boolean functions with nonlinearity 240 algebraic degree 5 and resiliency degree 3 were constructed this construction affirmatively answers the open problem about the existence of such functions

a spectral characterization of correlation immune combining functions it is shown that a boolean combining function f x of n variables is mth order correlation immune if and only if its walsh transform f omega vanishes for all omega with hamming weight between 1 and m inclusive this result is used to extend slightly siegenthaler s ieee trans comput vol c 34 pp 81 85 jan 1985 characterization of the algebraic normal form of correlation immune combining functions

correlation immunity of nonlinear combining functions for cryptographic applications corresp pseudonoise generators for cryptographic applications consisting of several linear feedback shift registers with a nonlinear combining function have been proposed as running key generators in stream ciphers these running key generators eau sometimes be broken by ciphertext only correlation attacks on individual subsequences a new class of combining functions is presented which provides better security against such attacks the security is quantified by the smallest number m 1 of subsequences that must be simultaneously considered in a correlation attack a necessary condition for such m th order correlation immunity is proved a recursive construction is given that permits the construction of an m th order immune combining function for n subsequences for any m and n with 1 leq m finally the trade off between the length of the linear equivalent of the nonlinear generator and the order m of its immunity against correlation attacks is considered

on parameter estimation for normal mixtures based on fuzzy clustering algorithms described here are three approaches to estimate the parameters of a mixture of normal distributions one approach is based on a modification of the expectation maximization algorithm to compute maximum likelihood estimates another makes use of the fuzzy c means clustering algorithms and the third is based on the penalized fuzzy c means clustering algorithms the accuracy and computational efficiency of algorithms of these three types to estimate parameters of normal mixtures are compared with samples drawn from univariate normal mixtures of two classes

generalized lexicographic multiobjective combinatorial optimization application to cryptography this paper formalizes a family of prioritized multicriteria optimization problems and assesses the corresponding up to date known suboptimal solutions the resulting framework is then employed to characterize and search for boolean functions which are valuable for a robust symmetric mainly block cipher design the proposed optimality definitions generalize the lexicographic method by establishing an ordered sequence of multiobjective combinatorial optimization problems which in turn gathers the relative relevance of the criteria so that the optimal solutions can be obtained from a sequential application of the pareto efficiency the relationship among the different formulable problems is characterized in terms of both their respective solutions sets and computing costs since in practice only a limited set of functions can be evaluated i e are known the best known pareto efficient functions are also defined finally this framework is employed to obtain new functions having known pareto max

clustering of clusters abstract an algorithm for the clustering of existing clusters is introduced in this paper the algorithm was adopted from fuzzy c mean and modifications made to take into account the extra information i e some data samples already form clusters partition coefficients together with some other criteria are used for testing cluster validity the method was applied on chinese character recognition and an encouraging result was obtained

convergence properties of the generalized fuzzy c means clustering algorithms fuzzy c means fcm clustering algorithms have been widely used to solve clustering problems yang and yu 1 extended these to optimization procedures with respect to any probability distribution they showed that the optimal cluster centers are the fixed points of these generalized fcm clustering algorithms the convergence properties of algorithms are the important theoretical issue in this paper we present convergence properties of the generalized fcm clustering algorithms these are global convergence local convergence and its rate of convergence

on a class of fuzzy classification maximum likelihood procedures classification maximum likelihood cml procedure is a remarkable mixture of maximum likelihood approach to clustering this has been well documented in the book of mclachlan and basford in this paper we make the fuzzy extension of the cml procedure based on this class of fuzzy cml procedures we extend the fuzzy clustering algorithms of trauwaert kaufman and rousseeuw by adding a penalty term especially we derive a generalized type of fuzzy c means fcm clustering algorithms called the penalized fcm clustering algorithms then we create some asymptotic behaviors of these penalized fcm procedures by doing some numerical examples we find that the penalized fcm is more meaningful and effective than fcm

optimal design of radial basis function neural networks for fuzzy rule extraction in high dimensional data abstract the design of an optimal radial basis function neural network rbfnf is not a straightforward procedure in this paper we take advantage of the functional equivalence between rbfn and fuzzy inference systems to propose a novel efficient approach to rbfn design for fuzzy rule extraction the method is based on advanced fuzzy clustering techniques solutions to practical problems are proposed by combining these different solutions a general methodology is derived the efficiency of our method is demonstrated on challenging synthetic and real world data sets

search for boolean functions with excellent profiles in the rotation symmetric class for the first time boolean functions on 9 variables having nonlinearity 241 are discovered that remained as an open question in literature for almost three decades such functions are found by heuristic search in the space of rotation symmetric boolean functions rsbfs this shows that there exist boolean functions on n odd variables having nonlinearity 2n 1 2n 1 2 if and only if n 7 using similar search technique balanced boolean functions on 9 10 and 11 variables are attained having autocorrelation spectra with maximum absolute value 2lceiln 2rceil on odd number of variables earlier such functions were known for 15 21 variables there was no evidence of such functions at all on even number of variables in certain cases our functions can be affinely transformed to obtain first order resiliency or first order propagation characteristics moreover 10 variable functions having first order resiliency and nonlinearity 492 are presented that had been posed as an open question at crypto 2000 the functions reported in this paper are discovered using a suitably modified steepest descent based iterative heuristic search in the rsbf class along with proper affine transformations it seems elusive to get a construction technique to match such functions

constructions of almost optimal resilient boolean functions on large even number of variables in this paper a technique on constructing nonlinear resilient boolean functions is described by using several sets of disjoint spectra functions on a small number of variables an almost optimal resilient function on a large even number of variables can be constructed it is shown that given any m one can construct infinitely many re variable n even m resilient functions with nonlinearity 2n 1 2n 2 a large class of highly nonlinear resilient functions which were not known are obtained then one method to optimize the degree of the constructed functions is proposed last an improved version of the main construction is given

further constructions of resilient boolean functions with very high nonlinearity one well known method of generating key stream sequences for stream ciphers is to combine the outputs of several linear feedback shift registers lfsr using a combining boolean function here we concentrate on the design of good combining boolean functions we provide resilient boolean functions with currently best known nonlinearity these functions were not known earlier and the issues related to their existence were posed as open questions in the literature some of the functions we construct here achieve the provable upper bound on nonlinearity for resilient boolean functions our technique interlinks mathematical results with classical computer search

ncm neutrosophic c means clustering algorithm abstract in this paper a new clustering algorithm neutrosophic c means ncm is introduced for uncertain data clustering which is inspired from fuzzy c means and the neutrosophic set framework to derive such a structure a novel suitable objective function is defined and minimized and the clustering problem is formulated as a constrained minimization problem whose solution depends on the objective function in the objective function two new types of rejection have been introduced the ambiguity rejection which concerns the patterns lying near the cluster boundaries and the distance rejection dealing with patterns that are far away from all the clusters these measures are able to manage uncertainty due to imprecise and or incomplete definition of the clusters we conducted several experiments with synthetic and real data sets the results are encouraging and compared favorably with results from other methods as fcm pcm and fpcm algorithms on the same data sets finally the proposed method was applied into image segmentation algorithm the experimental results show that the proposed algorithm can be considered as a promising tool for data clustering and image processing

local convergence of the fuzzy c means algorithms abstract much understanding has recently been gained concerning global convergence properties of the fuzzy c means fcm family of clustering algorithms these global convergence properties which hold for all iteration sequences guarantee that every fcm iteration sequence converges at least along a subsequence to a stationary point of an fcm objective function in this paper we prove a local convergence property that is a property pertaining to iteration sequences started near a solution specifically a simple result is proved which shows that whenever an fcm algorithm is started sufficiently near a minimizer of the corresponding objective function then the iteration sequence must converge to that particular minimizer the result guarantees that once captured by the local neighborhood of a minimizer the succeeding iterate sequence will not escape thus infinite oscillation of such a sequence cannot occur the rate of convergence of the sequence to such a point is also discussed

parameter estimation for finite mixture distributions abstract in this paper we compare numerically two approaches to the estimation of the parameters of the component densities in a univariate mixture of normal distributions one approach is based on a constrained maximum likelihood ml algorithm the other on the fuzzy c means fcm clustering algorithm our study indicates that i the ml method produces superior estimates when the component densities are well mixed while either algorithm provides good estimates for well separated distributions ii the fcm approach is almost always faster than the ml method and iii initialization of the ml method with the output of fcm almost always improves both the run time and accuracy of the statistical estimates

on a class of fuzzy c numbers clustering procedures for fuzzy data this paper describes a class of fuzzy clustering procedures for fuzzy data most fuzzy clustering techniques are designed for handling crisp data with their class memberships using the idea of fuzzy set theory here we derive new types of fuzzy clustering procedures in dealing with fuzzy data these procedures are called fuzzy c numbers fcn clusterings specially we construct these fcns for u type triangular trapezoidal and normal fuzzy numbers k jwoy s cluster analysis fuzzy clustering fuzzy data analysis fuzzy numbers fuzzy intervals fuzzy c means clustering fuzzy c numbers clustering

orthogonal central composite designs of the third order in the evaluation of sensitivity and plant growth simulation models abstract the u s department of agriculture has used response surface techniques as applied by baker and bargmann 1981 to plant process simulation models as an aid in the identification of interrelationships among yield and various single valued and functional parameters orthogonal cubic surfaces have provided insight into higher order relationships as well as a measure of the relative sensitivity of yield to experimentally determined parameter values several examples investigate the effectiveness of those higher order surfaces and illustrate how less precise and less costly measurements may be possible in building and using these simulation models