fractional extreme value adaptive training method fractional steepest descent approach the application of fractional calculus to signal processing and adaptive learning is an emerging area of research a novel fractional adaptive learning approach that utilizes fractional calculus is presented in this paper in particular a fractional steepest descent approach is proposed a fractional quadratic energy norm is studied and the stability and convergence of our proposed method are analyzed in detail the fractional steepest descent approach is implemented numerically and its stability is analyzed experimentally

variable step size lms algorithm for fractal signals this paper presents a novel variable step size lms vslms algorithm for tracking signals from the gaussian 1 fbeta family of fractal signals that are inherently nonstationary the proposed algorithm differs from the existing vslms algorithms in the following ways 1 it deals with a specific class of nonstationary signals 2 it utilizes a nondiagonal step size matrix which is simultaneously diagonalizable with the auto covariance matrix of the input signal 3 in the decoupled weight vector space one of the step size parameters requires time varying constraints for the algorithm to converge to the optimal weights whereas the constraints on the remaining step size parameters are time invariant and 4 it computes the step size matrix by estimating the hurst exponent required to characterize the statistical properties of the signal at the input of the adaptive filter the experimental setup of an adaptive channel equalizer is considered for equalization of fractal signals transmitted over stationary awgn channel the performance of the proposed fractal based variable step size least mean square fb vslms algorithm is compared with the unsigned vslms algorithm and is observed to be better for the class of nonstationary signals considered

dimension estimation of discrete time fractional brownian motion with applications to image texture classification fractional brownian motion fbm is a suitable description model for a large number of natural shapes and phenomena in applications it is imperative to estimate the fractal dimension from sampled data namely discrete time fbm dfbm to this aim the increment of dfbm referred to as discrete time fractional gaussian noise dfgn is invoked as an auxiliary tool the regular part of dfgn is first filtered out via levinson s algorithm the power spectral density of the regular process is found to satisfy a power law that its exponent can be well fitted by a quadratic function of fractal dimension a new method is then proposed to estimate the fractal dimension of dfbm from the given data set the computational complexity and statistical properties are investigated moreover the proposed algorithm is robust with respect to amplitude scaling and shifting as well as time shifting on the data finally the effectiveness of this estimator is demonstrated via a classification problem of natural texture images

the transitive closure convergence of powers and adjoint of generalized fuzzy matrices generalized fuzzy matrices are considered as matrices over a special type of semiring which is called an incline and their transitive closure powers determinant and adjoint matrices are studied an expression for the transitive closure of a matrix a as a sum of its powers and some su2cient conditions for powers of a matrix to converge are given if the incline is commutative a su2cient condition for nilpotency of a matrix is obtained namely the determinants of the principal submatrices of the matrix are all equal to zero element in addition it is proved that a n 1 is equal to the adjoint matrix of a if the matrix a satis5es a in

on the calculation of fractal features from images fractal geometry is becoming increasingly more important in the study of image characteristics there are numerous methods available to estimate parameters from images of fractal surfaces a very general technique to calculate numerous fractal features involves the estimation of the mass density function by box counting the authors analyze the box counting method establish a lower bound for the box size and indicate how algorithms can be improved to give better estimates of fractal features of images this provides a theoretical basis for a heuristic approach used by c a pickover and a l khorasani 1986

an adaptive conscientious competitive learning algorithm and its applications abstract an adaptive conscientious competitive learning accl algorithm is proposed in this paper the accl algorithm can adjust the conscience parameter itself according to the feedback information about the practical winning situation of all neurons during the learning process the a priori information about the distribution range of the input patterns which is required for the conventional conscientious competitive learning ccl algorithm is no longer required in the accl algorithm the neurons get stuck problem of the competitive learning cl algorithm and conscientious competitive learning ccl algorithm with small conscience parameter is overcome at the same time neurons will not be tangled together as in the case of the ccl algorithm with large conscience parameter the accl algorithm is applied to vector quantization vq and probability density function estimation pdfe it can generate better results than the conventional cl and ccl algorithms experimental results are also included to demonstrate its effectiveness

fuzzy subinclines ideals of incline algebras the fuzzification of subinclines ideals in inclines are considered and some related properties are investigated we also state the product of fuzzy subinclines ideals and the projections of fuzzy subinclines ideals we discuss fuzzy relations fuzzy characteristic subinclines ideals

reduction of quantum systems with arbitrary first class constraints and hecke algebras we propose a method for reduction of quantum systems with arbitrary first class constraints an appropriate mathematical setting for the problem is the homology of associative algebras for every such algebra a and subalgebra b with augmentation there exists a cohomological complex which is a generalization of the brst one its cohomology is an associative graded algebra hk a b which we call the hecke algebra of the triple a b it acts in the cohomology space h b v for every left a module v in particular the zeroth graded component hk 0 a b acts in the space of b invariants of v and provides the reduction of the quantum system

an application of incline matrices in dynamic analysis of generalized fuzzy bidirectional associative memories this paper studies an application of the incline matrix theory in the dynamic analysis of incline valued fuzzy bidirectional associative memories l fbams for short it is proved that the strong convergence and the strong stability of an l fbam are equivalent to the existence of indices and the convergence in finite steps of the product matrices of connection incline matrices of the l fbam respectively it is shown that the convergence index the period of limit cycles the stable states and equilibria of a strongly convergent l fbam are expressed by the indices the periods and the standard eigenvectors of the product matrices of connection incline matrices of the l fbam respectively

an adaptive hybrid pattern for noise robust texture analysis local binary patterns lbp achieve great success in texture analysis however they are not robust to noise the two reasons for such disadvantage of lbp schemes are 1 they encode the texture spatial structure based only on local information which is sensitive to noise and 2 they use exact values as the quantization thresholds which make the extracted features sensitive to small changes in the input image in this paper we propose a noise robust adaptive hybrid pattern ahp for noised texture analysis in our scheme two solutions from the perspective of texture description model and quantization algorithm have been developed to reduce the feature s noise sensitiveness first a hybrid texture description model is proposed in this model the global texture spatial structure which is depicted by a global description model is encoded with the primitive microfeature for texture description second we develop an adaptive quantization algorithm in which equal probability quantization is utilized to achieve the maximum partition entropy higher noise tolerance can be obtained with the minimum lost information in the quantization process the experimental results of texture classification on two texture databases with three different types of noise show that our approach leads significant improvement in noised texture analysis furthermore our scheme achieves state of the art performance in noisy face recognition highlightsa hybrid texture description model is proposed for noise robust texture modeling an adaptive quantization algorithm is designed for robust angular space quantization based on the new description model and quantization algorithm we develop the ahp experimental results demonstrate the significant improvement achieved by our scheme

the wavelet transform of stochastic processes with stationary increments and its application to fractional brownian motion the wavelet transform of random processes with wide sense stationary increments is shown to be a wide sense stationary process whose correlation function and spectral distribution are determined the second order properties of the coefficients in the wavelet orthonormal series expansion of such processes is obtained applications to the spectral analysis and to the synthesis of fractional brownian motion are given

fractional differential mask a fractional differential based approach for multiscale texture enhancement in this paper we intend to implement a class of fractional differential masks with high precision thanks to two commonly used definitions of fractional differential for what are known as grumwald letnikov and riemann liouville we propose six fractional differential masks and present the structures and parameters of each mask respectively on the direction of negative x coordinate positive x coordinate negative y coordinate positive y coordinate left downward diagonal left upward diagonal right downward diagonal and right upward diagonal moreover by theoretical and experimental analyzing we demonstrate the second is the best performance fractional differential mask of the proposed six ones finally we discuss further the capability of multiscale fractional differential masks for texture enhancement experiments show that for rich grained digital image the capability of nonlinearly enhancing complex texture details in smooth area by fractional differential based approach appears obvious better than by traditional integral based algorithms

correlation structure of the discrete wavelet coefficients of fractional brownian motion it is shown that the discrete wavelet coefficients of fractional brownian motion at different scales are correlated and that their auto and cross correlation functions decay hyperbolically fast at a rate much faster than that of the autocorrelation of the fractional brownian motion itself the rate of decay of the correlation function in the wavelet domain is primarily determined by the number of vanishing moments of the analyzing wavelet

conjugacy classes in weyl groups and q w algebras abstract we define noncommutative deformations w q s g of algebras of regular functions on certain transversal slices to the set of conjugacy classes in an algebraic group g which play the role of slodowy slices in algebraic group theory the algebras w q s g called q w algebras are labeled by conjugacy classes of elements s of the weyl group of g the algebra w q s g is a quantization of a poisson structure defined on the corresponding transversal slice in g with the help of poisson reduction of a poisson bracket associated to a poisson lie group g dual to a quasitriangular poisson lie group we also define a quantum group counterpart of the category of generalized gelfand graev representations and establish an equivalence between this category and the category of representations of the corresponding q w algebra the algebras w q s g can be regarded as quantum group counterparts of w algebras however in general they are not deformations of the usual w algebras

an improved box counting method for image fractal dimension estimation fractal dimension fd is a useful feature for texture segmentation shape classification and graphic analysis in many fields the box counting approach is one of the frequently used techniques to estimate the fd of an image this paper presents an efficient box counting based method for the improvement of fd estimation accuracy a new model is proposed to assign the smallest number of boxes to cover the entire image surface at each selected scale as required thereby yielding more accurate estimates the experiments using synthesized fractional brownian motion images real texture images and remote sensing images demonstrate this new method can outperform the well known differential boxing counting dbc method

maximum order index of matrices over commutative inclines an answer to an open problem abstract this paper proves that the maximum order index of n n matrices over an arbitrary commutative incline equals n 1 2 1 this is an answer to an open problem compute the maximum order index of a member of m n l proposed by cao kim and roush in a monograph incline algebra and applications 1984 where m n l is the set of all n n matrices over an incline l

fractional order anisotropic diffusion for image denoising this paper introduces a new class of fractional order anisotropic diffusion equations for noise removal these equations are euler lagrange equations of a cost functional which is an increasing function of the absolute value of the fractional derivative of the image intensity function so the proposed equations can be seen as generalizations of second order and fourth order anisotropic diffusion equations we use the discrete fourier transform to implement the numerical algorithm and give an iterative scheme in the frequency domain it is one important aspect of the algorithm that it considers the input image as a periodic image to overcome this problem we use a folded algorithm by extending the image symmetrically about its borders finally we list various numerical results on denoising real images experiments show that the proposed fractional order anisotropic diffusion equations yield good visual effects and better signal to noise ratio

on the spectrum of fractional brownian motions fractional brownian motions fbms provide useful models for a number of physical phenomena whose empirical spectra obey power laws of fractional order however due to the nonstationary nature of these processes the precise meaning of such spectra remains generally unclear two complementary approaches are proposed which are intended to clarify this point the first one based on a time frequency analysis takes into account the nonstationary nature of fbm and puts emphasis on time averaged measurements the second one based on a time scale analysis is matched to self similarity properties of fbm and reveals an underlying stationary structure relative to each time scaling

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

multiple resolution texture analysis and classification textures are classified based on the change in their properties with changing resolution the area of the gray level surface is measured at serveral resolutions this area decreases at coarser resolutions since fine details that contribute to the area disappear fractal properties of the picture are computed from the rate of this decrease in area and are used for texture comparison and classification the relation of a texture picture to its negative and directional properties are also discussed

maximum likelihood estimation of the parameters of discrete fractionally differenced gaussian noise process a maximum likelihood estimation procedure is constructed for estimating the parameters of discrete fractionally differenced gaussian noise from an observation set of finite size n the procedure does not involve the computation of any matrix inverse or determinant it requires n sup 2 2 o n operations the expected value of the loglikelihood function for estimating the parameter d of fractionally differenced gaussian noise which corresponds to a parameter of the equivalent continuous time fractional brownian motion related to its fractal dimension is shown to have a unique maximum that occurs at the true value of d a cramer rao bound on the variance of any unbiased estimate of d obtained from a finite sized observation set is derived it is shown experimentally that the maximum likelihood estimate of d is unbiased and efficient when finite size data sets are used in the estimation procedure the proposed procedure is extended to deal with noisy observations of discrete fractionally differenced gaussian noise

fractal feature analysis and classification in medical imaging following b b mandelbrot s fractal theory 1982 it was found that the fractal dimension could be obtained in medical images by the concept of fractional brownian motion an estimation concept for determination of the fractal dimension based upon the concept of fractional brownian motion is discussed two applications are found 1 classification 2 edge enhancement and detection for the purpose of classification a normalized fractional brownian motion feature vector is defined from this estimation concept it represented the normalized average absolute intensity difference of pixel pairs on a surface of different scales the feature vector uses relatively few data items to represent the statistical characteristics of the medial image surface and is invariant to linear intensity transformation for edge enhancement and detection application a transformed image is obtained by calculating the fractal dimension of each pixel over the whole medical image the fractal dimension value of each pixel is obtained by calculating the fractal dimension of 7 7 pixel block centered on this pixel

measuring the fractal dimension of signals morphological covers and iterative optimization fractals can model many classes of time series data the fractal dimension is an important characteristic of fractals that contains information about their geometrical structure at multiple scales the covering methods are a class of efficient approaches to measure the fractal dimension of an arbitrary fractal signal by creating multiscale covers around the signal s graph in this paper we develop a general method that uses multiscale morphological operations with varying structuring elements to unify and extend the theory and digital implementations of covering methods it is theoretically estab lished that for the fractal dimension computation covering one dimensional signals with planar sets is equivalent to mor phologically transforming the signal by one dimensional func tions which reduces the computational complexity from quad ratic in the signal s length to linear then a morphological covering algorithm is developed and applied to discrete time signals synthesized from weierstrass functions fractal inter polation functions and fractional brownian motion further for deterministic parametric fractals depending on a single pa rameter related to their dimension we develop an optimization method that starts from an initial estimate and iteratively con verges to the true fractal dimension by searching in the param eter space and minimizing a distance between the original sig nal and all such signals from the same class experimental results are also provided to demonstrate the good performance of the developed methods

semi infinite cohomology and hecke algebras abstract this paper provides a homological algebraic foundation for generalizations of classical hecke algebras introduced in 1999 a sevostyanov comm math phys 204 137 these new hecke algebras are associated to triples of the form a a 0 e where a is an associative algebra over a field k containing subalgebra a 0 with augmentation e a 0 k these algebras are connected with cohomology of associative algebras in the sense that for every left a module v and right a module w the hecke algebra associated to triple a a 0 e naturally acts in the a 0 cohomology and a 0 homology spaces of v and w respectively we also introduce the semi infinite cohomology functor for associative algebras and define modifications of hecke algebras acting in semi infinite cohomology spaces we call these algebras semi infinite hecke algebras as an example we realize the w algebra w k g associated to a complex semisimple lie algebra g as a semi infinite hecke algebra using this realization we explicitly calculate the algebra w k g avoiding the bosonization technique used in 1992 b feigin and e frenkel internat j mod phys a 7 suppl 1a 197 215

a fast estimation algorithm on the hurst parameter of discrete time fractional brownian motion the purpose of this paper is to demonstrate that the discrete time fractional gaussian noise dfgn is a regular process based on this property a fast algorithm with low computational cost is proposed to estimate the hurst parameter h which is an important parameter in fractional brownian motion fbm this algorithm is robust under amplitude shift invariant to time shift and unaffected by a scaling factor in power spectral density psd finally the computational complexity is also investigated

dioids and semirings links to fuzzy sets and other applications besides the classical algebraic structures of groups rings and fields which have long been the almost exclusive reference concepts used in mathematical modelling other algebraic structures such as dioids and semirings have emerged in the last two or three decades in connection with modelling and solving a rich variety of non classical problems e g in decision analysis fuzzy set theory operations research automatic control and mathematical physics the present paper aims at providing an overview of applications of dioid and semiring structures stressing links with fuzzy sets and emphasizing linear algebraic problems solving linear systems computing eigenvalues and eigenvectors non classical path finding problems using algebras of endomorphisms and connections between dioid structure and nonlinear analysis in view of solving problems in mathematical physics

inclines of algebraic structures an incline is a generalization of a boolean algebra or fuzzy algebra consisting of a semiring satisfying additive idempotence and the incline axiom xy x x xy y y the ideals in a ring or semigroup form an incline as do the topologizing filters in a ring we generalize the latter result to semirings and obtain the structure of these inclines in specific cases

wavelet analysis and synthesis of fractional brownian motion fractional brownian motion fbm offers a convenient modeling for nonstationary stochastic processes with long term dependencies and 1 f type spectral behavior over wide ranges of frequencies statistical self similarity is an essential feature of fbm and makes natural the use of wavelets for both its analysis and its synthesis a detailed second order analysis is carried out for wavelet coefficients of fbm it reveals a stationary structure at each scale and a power law behavior of the coefficients variance from which the fractal dimension of fbm can be estimated conditions for using orthonormal wavelet decompositions as approximate whitening filters are discussed consequences of discretization are considered and some connections between the wavelet point of view and previous approaches based on length measurements analysis or dyadic interpolation synthesis are briefly pointed out

unsupervised segmentation of ultrasonic liver images by multiresolution fractal feature vector the feasibility of selecting fractal feature vector based on multiresolution analysis to segment suspicious abnormal regions of ultrasonic liver images is described in this paper the proposed feature extraction algorithm is based on the spatial frequency decomposition and fractal geometry segmentation of various liver diseases reveals that the fractal feature vector based on multiresolution analysis is trustworthy a quantitative characterization based on the proposed unsupervised segmentation algorithm can be utilized to establish an automatic computer aided diagnostic system as well to increase the visual interpretation capability of ultrasonic liver image for junior physicians off line learning software is developed to investigate the visual criteria