an information theoretic fuzzy c spherical shells clustering algorithm in this paper we shall investigate source compression coding theorem from the perspective of robust fuzzy clustering that is derived from the basic fuzzy c spherical shells fcss algorithm the proposed information fuzzy c spherical shells ifcss algorithm tackles the intertwined robust fuzzy clustering problems of outlier detection prototype initialization and cluster validity in a unified framework of information clustering the ifcss addresses fuzzy membership and typicality issues separately through the minimum number and the sensitivity of hyper parameters in the clustering objective function we use the basic fcss algorithm for the clustering phase to minimize the number of hyper parameters and reduce the difficulty of prototype initialization especially for spherical shells data the robustness of ifcss against noisy points outliers is obtained by the maximizing the mutual information mi which also provides a good criterion for prototype initialization the clustering validity criterion for the ifcss is proposed based on the structural risk minimization principle to achieve an optimal trade off between the empirical risk clustering and model complexity control cluster number the effectiveness of the proposed algorithms for clustering spherical shells is supported by experimental results

boundedness of automorphic l functions in vertical strips the purpose of this paper is to prove the boundedness in vertical strips of finite width for all the l functions that appear in constant terms of eisenstein series under a certain natural assumption on local normalized intertwining operators as a corollary we prove the boundedness for a number of important l functions among them the symmetic cube and triple product l functions attached to cusp forms on gl 2 as well as several rankin selberg product l functions where the local assumption was alredy proved to be valid in each case under the same assumption the finiteness of poles on all of c for all of these l functions is also proved a necessary step in the proof of boundedness in vertical strips

a robust real time ellipse detector abstract in this paper we present an improved ellipse detector that may be used in real time face detection in this algorithm we first extract edges from the image using a robust edge detector which is then followed by a rule based method finally we decompose the parameter space of the hough transform to achieve computational efficiency our extensive experimental results show indeed that the proposed detector is capable of detecting ellipse features with an excellent accuracy under various image conditions at a high speed 10 frames per second on a pentium iii 500 mhz pc

general c means clustering model partitional clustering is an important part of cluster analysis based on various theories numerous clustering algorithms have been developed and new clustering algorithms continue to appear in the literature it is known that occam s razor plays a pivotal role in data based models and partitional clustering is categorized as a data based model however no relation had previously been discovered between occam s razor and partitional clustering as we discuss in this paper the three main contributions of this paper can be summarized as follows 1 according to a novel definition of the mean a unifying generative framework for partitional clustering algorithms called a general c means clustering model gcm is presented and studied and 2 based on the local optimality test of the gcm the connection between occam s razor and partitional clustering is established for the first time as its application a comprehensive review of the existing objective function based clustering algorithms is presented based on gcm 3 under a common assumption about partitional clustering a theoretical guide for devising and implementing clustering algorithm is discovered these conclusions are verified by numerical experimental results

fuzzy shell clustering algorithms in image processing fuzzy c rectangular and 2 rectangular shells objective function based clustering has been generalized recently to detect contours of circles and ellipses or even hyperbolas in a set of binary data vectors although there are special algorithms to discover lines the detection of rectangles needs further treatment a simple line detection algorithm is not sufficient for rectangles since for identifying four lines as one rectangle additional information such as the length of the lines and whether they are parallel or meet at a right angle is necessary in this paper a special fuzzy shell clustering algorithm for rectangular contours is developed the principal idea behind it can be generalized for other polygons so we also derive an algorithm that is capable of detecting rectangles and other polygons as well as approximating circles ellipses and lines

on moments of twisted l functions we study the average of the product of the central values of two l functions of modular forms f and g twisted by dirichlet characters to a large prime modulus q as our principal tools we use spectral theory to develop bounds on averages of shifted convolution sums with differences ranging over multiples of q and we use the theory of deligne and katz to prove new bounds on bilinear forms in kloosterman sums with power savings when both variables are near the square root of q when at least one of the forms f and g is non cuspidal we obtain an asymptotic formula for the mixed second moment of twisted l functions with a power saving error term in particular when both are non cuspidal this gives a significant improvement on m young s asymptotic evaluation of the fourth moment of dirichlet l functions in the general case the asymptotic formula with a power saving is proved under a conjectural estimate for certain bilinear forms in kloosterman sums

connection between fuzzy theory simulated annealing and convex duality abstract simulated annealing is a well known heuristic method in which the basic notions of statistical mechanics are used as an analogy for treating optimization problems the physical term of energy is regarded as an objective criterion which has to be minimized in this context also the terms of temperature free energy and entropy have been involved the present paper generalizes this formalism in order to make it available as a basic tool for fuzzy theory and multicriteria analysis therefore the formula of free energy is generalized in order to introduce a new aggregation operator the main feature of this operator is the compensatory property of aggregation it fills the gap between the maximum operator the minimum operator and the weighted sum by a coherent mathematical formalism which is connected with a large mathematical background the aggregation operator plays the same peculiar part as the shannon entropy does in information theory this is verified by means of convex duality in this formalism the fuzzy decisions that correspond to the boltzmann distribution are involved from there we derive a fuzzy extension principle which can be applied to developing new algorithms moreover we discover a bridge between the boltzmann distribution and the fuzzy c means approach across this bridge some help arises for both of the two sides thus we derive new and generalized versions of the fuzzy c means algorithm and we establish a fuzzy version of simulated annealing which is more efficient than the original simulated annealing

on extrapolation of rearrangement invariant spaces abstract we study extrapolation spaces generated by the banach scales of l p and l p spaces defined on 0 1 we give new extrapolatory descriptions for the marcinkiewicz and the orlicz lorentz spaces using interpolation of sublinear positive operators we also prove interpolation embeddings for extrapolation spaces

cuspidality of symmetric powers with applications the purpose of this paper is to prove that the symmetric fourth power of a cusp form on rm gl 2 whose existence was proved earlier by the first author is cuspidal unless the corresponding automorphic representation is of dihedral tetrahedral or octahedral type as a consequence we prove a number of results toward the ramanujan petersson and sato tate conjectures in particular we establish the bound q sp 1 9 sb v for unramified hecke eigenvalues of cusp forms on rm gl 2 over an arbitrary number field this is the best bound available at present

the quantum unique ergodicity conjecture for thin sets abstract we consider some analogs of the quantum unique ergodicity conjecture for geodesics and shrinking families of sets in particular we prove the analog of the que conjecture for eisenstein series restricted to the infinite geodesic connecting 0 and inside the modular surface

fcm based model selection algorithms for determining the number of clusters clustering is an important research topic that has practical applications in many fields it has been demonstrated that fuzzy clustering using algorithms such as the fuzzy c means fcm has clear advantages over crisp and probabilistic clustering methods like most clustering algorithms however fcm and its derivatives need the number of clusters in the given data set as one of their initializing parameters the main goal of this paper is to develop an effective fuzzy algorithm for automatically determining the number of clusters after a brief review of the relevant literature we present a new algorithm for determining the number of clusters in a given data set and a new validity index for measuring the goodness of clustering experimental results and comparisons are given to illustrate the performance of the new algorithm

on the local langlands conejcture mathrm gl n the cyclic case let f be a locally compact nonarchimedean field and p its residue characteristic let f be a separable algebraic closure of f wf the weil group of f over f e a character of fx of order n and e the corresponding character of wf then there exists a canonical map from the set of equivalence classes a of irreducible degree n representations of wf such that e a a to the set of equivalence classes 7r of admissible irreducible supercuspidal representations of gl n f verifying odet x 7t this map is shown to be bijective and to preserve e factors for pairs

une preuve simple des conjectures de langlands pour gl n sur un corps p adique let f be a finite extension of p for each integer n 1 we construct a bijection from the set f 0 n of isomorphism classes of irreducible degree n representations of the absolute weil group of f onto the set f 0 n of isomorphism classes of smooth irreducible supercuspidal representations of gl n f those bijections preserve epsilon factors for pairs and hence we obtain a proof of the langlands conjectures for gl n over f which is more direct than harris and taylor s our approach is global and analogous to the derivation of local class field theory from global class field theory we start with a result of kottwitz and clozel on the good reduction of some shimura varieties and we use a trick of harris who constructs non galois automorphic induction in certain cases

a time domain constrained fuzzy clustering method and its application to signal analysis this paper introduces a new fuzzy clustering method with time domain constraints which is used to signal analysis proposed method makes it possible to include natural constraints for signal analysis using fuzzy clustering that is the neighboring samples of signal belong to the same cluster this method can be called time domain constrained fuzzy clustering this paper introduces two approaches to include the above kind of constraints the first approach leads to the time domain constrained fuzzy c regression models method the second approach leads to the insensitive version of the above method which results in additional robustness for outliers and non gaussian noise finally simulations on synthetic as well as real life signals are realized to evaluate the performance of the time domain constrained fuzzy clustering methods a comparison with the traditional fuzzy c regression models is also made large scale simulations demonstrate the competitiveness of the proposed methods for signal analysis with respect to the traditional fuzzy clustering methods

unsupervised optimal fuzzy clustering this study reports on a method for carrying out fuzzy classification without a priori assumptions on the number of clusters in the data set assessment of cluster validity is based on performance measures using hypervolume and density criteria an algorithm is derived from a combination of the fuzzy k means algorithm and fuzzy maximum likelihood estimation the unsupervised fuzzy partition optimal number of classes algorithm performs well in situations of large variability of cluster shapes densities and number of data points in each cluster the algorithm was tested on different classes of simulated data and on a real data set derived from sleep eeg signal

adaptive fuzzy c shells clustering and detection of ellipses several generalizations of the fuzzy c shells fcs algorithm are presented for characterizing and detecting clusters that are hyperellipsoidal shells an earlier generalization the adaptive fuzzy c shells afcs algorithm is examined in detail and is found to have global convergence problems when the shapes to be detected are partial new formulations are considered wherein the norm inducing matrix in the distance metric is unconstrained in contrast to the afcs algorithm the resulting algorithm called the afcs u algorithm performs better for partial shapes another formulation based on the second order quadrics equation is considered these algorithms can detect ellipses and circles in 2d data they are compared with the hough transform ht based methods for ellipse detection existing ht based methods for ellipse detection are evaluated and a multistage method incorporating the good features of all the methods is used for comparison numerical examples of real image data show that the afcs algorithm requires less memory than the ht based methods and it is at least an order of magnitude faster than the ht approach

on the ramanujan conjecture and finiteness of poles for certain l functions in this paper we prove a number of general results about automorphic l functions which appear in the constant terms of eisenstein series for an arbitrary quasi split connected reductive algebraic group over a number field these l functions were first introduced by langlands for chevalley groups 20 and through them he was led to make some of his deep conjectures 21 one significance of these l functions is that all the automorphic l functions studied so far are among them there are three general results first we obtain a uniform line of absolute convergence for all of these l functions theorem 5 1 a uniform estimate for the hecke eigenvalues of generic cusp forms on many absolutely simple quasi split connected reductive algebraic groups over number fields corollary 5 4 and an improvement on the best available estimate for the fourier coefficients of maass wave forms corollary 5 5 also follow next we establish a meromorphic continuation and functional equation for each of these l functions theorem 6 1 finally in theorem 6 2 we prove finiteness of poles on the whole complex plane for an important class of these l functions corollaries 6 6 through 6 10 more precisely let g be a quasi split connected reductive algebraic group over a number field f set g g a f where a f is the ring of adeles of f fix a borel subgroup b of g over f and let u be its unipotent radical let p be a maximal f parabolic subgroup of g with p d b in the context of the problems studied here nothing new will be obtained if one drops the maximality condition on p write p mn a levi decomposition n c u and let b u p m and n be the corresponding groups of adelic points for every place v of f let gv g fj similarly we have bv us pv me and nv let x xv be a generic character of u f u cf section 3 then each xv is generic let r ov 7tv be a cusp form on m we shall say 7t is

extrapolation methods and rubio de francia s extrapolation theorem we develop a general framework to study extrapolation of inequalities 2005 elsevier inc all rights reserved msc primary 47b38 46m35 secondary 42b25 42b20

the fourth moment of individual dirichlet l functions on the critical line we prove an asymptotic formula for the second moment of a product of two dirichlet l functions on the critical line which has a power saving in the error term and which is uniform with respect to the involved dirichlet characters as special cases we give uniform asymptotic formulae for the fourth moment of individual dirichlet l functions and for the second moment of dedekind zeta functions of quadratic number fields on the critical line

demography of cirsium vulgare in a grazing experiment the complete demographies of 16 populations of cirsium vulgare were followed in a replicated experiment the experiment was a factorial combination of two intensities of sheep grazing in each of three seasons winter grazed or ungrazed spring grazed or ungrazed and summer light or heavy grazing giving eight treatments in two blocks for 6 years from 1987 to 1992 the population sizes of c vulgare were monitored in each of the 16 paddocks after 1989 grazing in spring or winter or increased grazing in summer all increased population sizes population sizes fluctuated widely between years the effects of the grazing treatments and plant sizes on the transitions between nine life history stages were determined

an integrated approach to fuzzy learning vector quantization and fuzzy c means clustering derives an interpretation for a family of competitive learning algorithms and investigates their relationship to fuzzy c means and fuzzy learning vector quantization these algorithms map a set of feature vectors into a set of prototypes associated with a competitive network that performs unsupervised learning derivation of the new algorithms is accomplished by minimizing an average generalized distance between the feature vectors and prototypes using gradient descent a close relationship between the resulting algorithms and fuzzy c means is revealed by investigating the functionals involved it is also shown that the fuzzy c means and fuzzy learning vector quantization algorithms are related to the proposed algorithms if the learning rate at each iteration is selected to satisfy a certain condition

unsupervised fuzzy clustering with multi center clusters a new unsupervised fuzzy clustering algorithm is provided in this paper to cluster the data patterns without a priori information about the number of clusters the initial guesses of the locations of the cluster centers or the initial guesses of the membership values are not necessary with the minimization of a new objective function cluster centers are generated one by one related centers are defined to belong to the same cluster multi centers are adopted to represent the non spherical shape of clusters thus the clustering algorithm with multi center clusters can handle non traditional curved clusters the proposed algorithm is tested on different data sets with a variety of cluster shapes cluster densities and number of points in each cluster also the results are compared with some other clustering algorithms to show the effectiveness of the algorithm moreover the designed unsupervised fuzzy clustering algorithm is applied to cluster the pixels in a color image to show the efficiency of the algorithm

fuzzy and possibilistic shell clustering algorithms and their application to boundary detection and surface approximation ii shell clustering algorithms are ideally suited for computer vision tasks such as boundary detection and surface approximation particularly when the boundaries have jagged or scattered edges and when the range data is sparse this is because shell clustering is insensitive to local aberrations it can be performed directly in image space and unlike traditional approaches it does assume dense data and does not use additional features such as curvatures and surface normals the shell clustering algorithms introduced in part i of this paper assume that the number of clusters is known however which is not the case in many boundary detection and surface approximation applications this problem can be overcome by considering cluster validity we introduce a validity measure called surface density which is explicitly meant for the type of applications considered in this paper we show through theoretical derivations that surface density is relatively invariant to size and partiality incompleteness of the clusters we describe unsupervised clustering algorithms that use the surface density measure and other measures to determine the optimum number of shell clusters automatically and illustrate the application of the proposed algorithms to boundary detection in the case of intensity images and to surface approximation in the case of range images

enhancement of fuzzy clustering by mechanisms of partial supervision semi supervised or partial fuzzy clustering plays an important and unique role in discovering hidden structure in data realized in presence of a certain quite limited fraction of labeled patterns the objective of this study is to investigate and quantify the effect of various distance functions distances on the performance of the clustering mechanisms the underlying goal of endowing the clustering algorithms with a higher level of flexibility is done via the use of various distances the enhancement of this character is evaluated by means of a comprehensive assessment of quality of clusters their ensuing discrimination abilities and the accuracy of clusters themselves in addition to the standard euclidean distance being commonly exploited in fuzzy clustering three more versatile and adaptive distance measures are considered such as its weighted version a full adaptive distance and a kernel based distance using fuzzy c means fcm coming in its generic format we show its semi supervised enhancements derive detailed formulas and analyze their effectiveness the improvements of semi supervised clustering are empirically evaluated and numerically quantified with the use of several machine learning data sets

possibilistic shell clustering of template based shapes in this paper we present a new type of alternating optimization based possibilistic c shell algorithm for clustering template based shapes a cluster prototype consists of a copy of the template after translation scaling rotation and or affine transformations this extends the capability of shell clustering beyond a few standard geometrical shapes that have been in the literature so far we use a number of 2 d datasets consisting of both synthetic and real world images to illustrate the capability of our algorithm in detecting generic template based shapes in images we also describe a progressive clustering procedure aimed to relax the requirements for a known number of clusters and good initialization as well as new performance measures of shell clustering algorithms

a proof of langland s conjecture on plancherel measures complementary series of p adic groups analysis of p adic reductive groups our first result theorem 7 9 proves a conjecture of langlands on normalization of intertwining operators by means of local langlands root numbers and l functions at least when the group is quasi split and the inducing representation is generic assuming two natural conjectures in harmonic analysis of p adic groups we also prove the validity of the conjecture in general theorem 9 5 as our second result we obtain all the complementary series and special representations of quasi split p adic groups coming from rank one parabolic subgroups and generic supercuspidal represen

gaps a clustering method using a new point symmetry based distance measure in this paper an evolutionary clustering technique is described that uses a new point symmetry based distance measure the algorithm is therefore able to detect both convex and non convex clusters kd tree based nearest neighbor search is used to reduce the complexity of finding the closest symmetric point adaptive mutation and crossover probabilities are used the proposed ga with point symmetry gaps distance based clustering algorithm is able to detect any type of clusters irrespective of their geometrical shape and overlapping nature as long as they possess the characteristic of symmetry gaps is compared with existing symmetry based clustering technique sbkm its modified version and the well known k means algorithm sixteen data sets with widely varying characteristics are used to demonstrate its superiority for real life data sets anova and manova statistical analyses are performed

convex set based fuzzy clustering prototype based methods are commonly used in cluster analysis and the results may be highly dependent on the prototype used we propose a two level fuzzy clustering method that involves adaptively expanding and merging convex polytopes where the convex polytopes are considered as a flexible prototype therefore the dependency on the use of a specified prototype can be eliminated also the proposed method makes it possible to effectively represent an arbitrarily distributed data set without a priori knowledge of the number of clusters in the data set in the first level of our proposed method each cluster is represented by a convex polytope which is described by its set of vertices specifically nonlinear membership functions are utilized to determine whether an input pattern creates a new cluster or whether an existing cluster should be modified in the second level the expandable clusters that are selected by an intercluster distance measure are merged to improve clustering efficiency and to reduce the order dependency of the incoming input patterns several experimental results are given to show the validity of our method

the multisynapse neural network and its application to fuzzy clustering in this paper a new neural architecture the multisynapse neural network is developed for constrained optimization problems whose objective functions may include high order logarithmic and sinusoidal forms etc unlike the traditional hopfield networks which can only handle quadratic form optimization meanwhile based on the application of this new architecture a fuzzy bidirectional associative clustering network fbacn which is composed of two layers of recurrent networks is proposed for fuzzy partition clustering according to the objective functional method it is well known that fuzzy c means is a milestone algorithm in the area of fuzzy c partition clustering all of the following objective functional based fuzzy c partition algorithms incorporate the formulas of fuzzy c means as the prime mover in their algorithms however when an application of fuzzy c partition has sophisticated constraints the necessity of analytical solutions in a single iteration step becomes a fatal issue of the existing algorithms the largest advantage of fbacn is that it does not need analytical solutions for the problems on which some prior information is known we bring a combination of part crisp and part fuzzy clustering in the third optimization problem

robust clustering methods a unified view clustering methods need to be robust if they are to be useful in practice in this paper we analyze several popular robust clustering methods and show that they have much in common we also establish a connection between fuzzy set theory and robust statistics and point out the similarities between robust clustering methods and statistical methods such as the weighted least squares technique the m estimator the minimum volume ellipsoid algorithm cooperative robust estimation minimization of probability of randomness and the epsilon contamination model by gleaning the common principles upon which the methods proposed in the literature are based we arrive at a unified view of robust clustering methods we define several general concepts that are useful in robust clustering state the robust clustering problem in terms of the defined concepts and propose generic algorithms and guidelines for clustering noisy data we also discuss why the generalized hough transform is a suboptimal solution to the robust clustering problem

relative entropy fuzzy c means clustering pattern recognition is a collection of computer techniques to classify various observations into different clusters of similar attributes in either supervised or unsupervised manner application of fuzzy logic to unsupervised classification or clustering methods has resulted in many wildly used techniques such as fuzzy c means fcm method however when the observations are too noisy the performance of such methods might be reduced thus in this paper a new fuzzy clustering method based on fcm is presented and the relative entropy is added to its objective function as a regularization function to maximize the dissimilarity between clusters several examples are provided to examine the performance of the proposed clustering method the obtained results show that the proposed method has a very good ability in detecting noises and assignment of suitable membership degrees to the observations

intermediate spaces between 2 τ lτ and l abstract in this paper we introduce an intermediate space l t between 2 l t and l t where l t are the l subspaces of a nonatomic finite measure space t and study its properties in particular this space is banach and rearrangement invariant with respect to the measure our main result states that under some conditions l t coincides with a special marcinkiewicz space in addition we obtain zygmund type weak and integral estimates for functions from l t and apply them to estimate the norms of the conjugate fourier and littlewood paley operators from l t to l t where t is the unit circle in c relationships between l t and bmo t are discussed as well

bilinear forms with kloosterman sums and applications we prove nontrivial bounds for general bilinear forms in hyper kloosterman sums when the sizes of both variables may be below the range controlled by fourier analytic methods polya vinogradov range we then derive applications to the second moment of cusp forms twisted by characters modulo primes and to the distribution in arithmetic progressions to large moduli of certain eisenstein hecke coefficients on gl 3 our main tools are new bounds for certain complete sums in three variables over finite fields proved using methods from algebraic geometry especially l adic cohomology and the riemann hypothesis

competitive algorithms for the clustering of noisy data abstract in this paper we consider the issue of clustering when outliers exist the outlier set is defined as the complement of the data set following this concept a specially designed fuzzy membership weighted objective function is proposed and the corresponding optimal membership is derived unlike the membership of fuzzy c means the derived fuzzy membership does not reduce with the increase of the cluster number with the suitable redefinition of the distance metric we demonstrate that the objective function could be used to extract c spherical shells a hard clustering algorithm alleviating the prototype under utilization problem is also derived artificially generated data are used for comparisons

a multiresolution image segmentation technique based on pyramidal segmentation and fuzzy clustering in this paper an unsupervised image segmentation technique is presented which combines pyramidal image segmentation with the fuzzy c means clustering algorithm each layer of the pyramid is split into a number of regions by a root labeling technique and then fuzzy c means is used to merge the regions of the layer with the highest image resolution a cluster validity functional is used to find the optimal number of objects automatically segmentation of a number of synthetic as well as clinical images is illustrated and two fully automatic segmentation approaches are evaluated which determine the left ventricular volume lv in 140 cardiovascular magnetic resonance mr images first fuzzy c means is applied without pyramids in the second approach the regions generated by pyramidal segmentation are merged by fuzzy c means the correlation coefficients of manually and automatically defined lv lumen of all 140 and 20 end diastolic images were equal to 0 86 and 0 79 respectively when images were segmented with fuzzy c means alone these coefficients increased to 0 90 and 0 93 when the pyramidal segmentation was combined with fuzzy c means this method can be applied to any dimensional representation and at any resolution level of an image series the evaluation study shows good performance in detecting lv lumen in mr images

local coefficients as artin factors for real groups introduction the purpose of this paper is to prove the equality of certain local coefficients of arithmetic significance which were attached to representations of quasi split real reductive algebraic groups in 27 with their corresponding artin factors attached by local class field theory 21 as a consequence we establish an identity satisfied by certain normalized intertwining operators it seems to be useful in applications of the trace formula 1 29 more precisely let g be the group of real points of a quasi split reductive algebraic group over r let a be the set of simple roots defined by a fixed minimal parabolic subgroup po m0a0u of g fix 6 c a and let p p9 be the corresponding standard parabolic subgroup of g and write p man for its langlands decomposition fix a nondegenerate character x f u i a h o be an irreducible admissible x gic banach in particular x generic unitary representation of m cf section 1 given v g a the complex dual of the lie algebra of a let i v o 0 be the continuously quasi unitarily if o is unitary induced representation indp ga e v 9 and let v v o 0 be its space section 0 then f a vfoo o now let w be the weyl group of ao in g choose w g w such that w 0 c a let n be the unipotent group opposite to n define n u c wn w where w is a representative of w in g for g f a 00 define

rederivation of the fuzzypossibilistic clustering objective function through bayesian inference unsupervised clustering of a set of datums into homogeneous groups is a primitive operation required in many signal and image processing applications in fact different incarnations and hybrids of fuzzy c means fcm and possibilistic c means pcm have been suggested which address additional requirements such as accepting weighted sets and being robust to the presence of outliers nevertheless arriving at a general framework which is independent of the datum model and the notion of homogeneity of a particular problem class is a challenge however this process has not been followed organically and clustering algorithms are generally based on exogenous objective functions which are heuristically engineered and are believed to lead to the satisfaction of a required behavior these techniques also commonly depend on regularization coefficients which are to be set prudently by the user or through separate processes in contrast in this work we utilize bayesian inference and derive a robustified objective function for a fuzzypossibilistic clustering algorithm by assuming a generic datum model and a generic notion of cluster homogeneity we utilize this model for the purpose of cluster validity assessment as well we emphasize the epistemological importance of the theoretical basis on which the developed methodology rests at the end of this paper we present experimental results to exhibit the utilization of the developed framework in the context of four different problem classes

mollification of the fourth moment of automorphic l functions and arithmetic applications we compute the asymptotics of twisted fourth power moments of modular l functions of large prime level near the critical line this allows us to prove some new non vanishing results on the central values of automorphic l functions in particular those obtained by base change from gl 2 q to gl 2 k for k a cyclic field of low degree

invariant distributions and time averages for horocycle flows there are infinitely many obstructions to existence of smooth solutions of the cohomological equation uu f where u is the vector field generating the horocycle flow on the unit tangent bundle sm of a riemann m surface of finite area and f is a given function on sm we study the sobolev regularity of these obstructions construct smooth solutions of the cohomological equation and derive asymptotics for the ergodic averages of horocycle flows

template based shell clustering using a line segment representation of data this paper presents the algorithms and experimental results for template based shell clustering when the datasets are represented by line segments compared with point datasets such representations have several advantages which include better scalability and noise immunity as well as the availability of orientation information using both synthetic and real world image datasets we have experimentally demonstrated that line segment based representations result in both better accuracy and better efficiency in shell clustering

modularity of the rankin selberg l series and multiplicity one for sl 2 let f g be primitive cusp forms holomorphic or otherwise on the upper half plane h of levels n m respectively with unitarily normalized l functions l s f equation and l s g equation when p does not divide n resp m the inverse roots p p resp p p are nonzero with sum ap resp bp for every p prime to nm set lp s f g 1 p pp s 1 p pp s 1 p pp s 1 p pp s 1 let l s f g denote the incomplete euler product of lp s f g over all p not dividing nm this is closely related to the convolution l series sum over n 1 a sub n b sub n n s whose miraculous properties were first studied by rankin and selberg

real zeros and size of rankin selberg l functions in the level aspect in this paper some asymptotic formulas are proved for the harmonic mollified second moment of a family of rankin selberg l functions one of the main new input is a substantial improvement of the admissible length of the mollifier which is done by solving a shifted convolution problem by a spectral method on average a first consequence is a new subconvexity bound for rankin selberg l functions in the level aspect moreover infinitely many rankin selberg l functions having at most eight non trivial real zeros are produced and some new non trivial estimates for the analytic rank of the family studied are obtained

integral moments of l functions we give a new heuristic for all of the main terms in the integral moments of various families of primitive l functions the results agree with previous conjectures for the leading order terms our conjectures also have an almost identical form to exact expressions for the corresponding moments of the characteristic polynomials of either unitary orthogonal or symplectic matrices where the moments are defined by the appropriate group averages this lends support to the idea that arithmetical l functions have a spectral interpretation and that their value distributions can be modelled using random matrix theory numerical examples show good agreement with our conjectures

on the arithmetic of shalika models and the critical values of l functions for gl2n let pi be a cohomological cuspidal automorphic representation of rm gl 2n bbb a over a totally real number field f suppose that pi has a shalika model we define a rational structure on the shalika model of pi f comparing it with a rational structure on a realization of pi f in cuspidal cohomology in top degree we define certain periods omega epsilon pi f we describe the behavior of such top degree periods upon twisting pi by algebraic hecke characters chi of f then we prove an algebraicity result for all the critical values of the standard l functions l s pi otimes chi here we use the recent work of b sun on the non vanishing of a certain quantity attached to pi infty as applications we obtain algebraicity results in the following cases firstly for the symmetric cube l functions attached to holomorphic hilbert modular cusp forms we also discuss the situation for higher symmetric powers secondly for certain self dual of symplectic type rankin selberg l functions for rm gl 3 times rm gl 2 assuming langlands functoriality this generalizes to certain rankin selberg l functions of rm gl n times rm gl n 1 thirdly for the degree four l functions attached to siegel modular forms of genus 2 and full level moreover we compare our top degree periods with periods defined by other authors we also show that our main theorem is compatible with conjectures of deligne and gross

breaking the 12 barrier for the twisted second moment of dirichlet l functions abstract we study the second moment of dirichlet l functions to a large prime modulus q twisted by the square of an arbitrary dirichlet polynomial we break the 1 2 barrier in this problem and obtain an asymptotic formula provided that the length of the dirichlet polynomial is less than q 51 101 q 1 2 1 202 as an application we obtain an upper bound of the correct order of magnitude for the third moment of dirichlet l functions we give further results when the coefficients of the dirichlet polynomial are more specialized

on fuzzy cluster validity indices cluster analysis aims at identifying groups of similar objects and helps to discover distribution of patterns and interesting correlations in large data sets especially fuzzy clustering has been widely studied and applied in a variety of key areas and fuzzy cluster validation plays a very important role in fuzzy clustering this paper introduces the fundamental concepts of cluster validity and presents a review of fuzzy cluster validity indices available in the literature we conducted extensive comparisons of the mentioned indices in conjunction with the fuzzy c means clustering algorithm on a number of widely used data sets and make a simple analysis of the experimental results

the fourth moment of dirichlet l functions we compute the fourth moment of dirichlet l functions at the central point for prime moduli with a power savings in the error term

the fuzzy c spherical shells algorithm a new approach the fuzzy c spherical shells fcss algorithm is specially designed to search for clusters that can be described by circular arcs or generally by shells of hyperspheres a new approach to the fcss algorithm is presented this algorithm is computationally and implementationally simpler than other clustering algorithms that have been suggested for this purpose an unsupervised algorithm which automatically finds the optimum number of clusters is not known it uses a cluster validity measure to identify good clusters merges all compatible clusters and eliminates spurious clusters to achieve the final results experimental results on several data sets are presented

fuzzy c varieties elliptotypes clustering in reproducing kernel hilbert space abstract fuzzy clustering algorithms are successfully applied to a wide variety of problems such as pattern recognition image analysis modeling and so on the fuzzy c means fcm method is one of the most popular clustering methods based on the minimization of a criterion function however the performance of the fcm method is good only when a data set contains clusters that are approximately the same size and shape in this paper a simple idea will be used to overcome this problem the original input data space will be mapped into the high possibly infinite dimensional feature space f through some nonlinear mapping in this space the data structures will be modeled by the linear varieties or elliptotypes this method is called kernel fuzzy c varieties elliptotypes clustering algorithm performance of the new clustering algorithm is experimentally compared with fcm and fuzzy c varieties elliptotypes methods using synthetic datasets and real life datasets

twisted endoscopy and reducibility of induced representations for p adic groups 1 introduction this is the first in a series of papers in which we study the reducibility of representations induced from discrete series representations of the levi factors ofmaximal parabolic subgroups of p adic groups on the unitary axis the problem is equivalent to determining certain local langlands l functions which are of arithmetic significance by themselves one of the main aims of this paper is to interpret our results in the direction of the parametrization problem by means of the theory of twisted endoscopy for which our method seems to be very suitable when the representation is supercuspidal we also study the reducibility of the induced representations off the unitary axis let f be a p adic field of characteristic zero fix a positive integer n 1 and let g be either of the groups sp2n s02n or s02n l in all three cases there is a conjugacy class of maximal parabolic subgroups which has gl as its levi factor let p mn be the standard parabolic subgroup ofg in this conjugacy class then m gl let tr be a discrete series representation of m gln f and given s c let i s tr be the representation of g g f induced from tr r idet ls let i tr i 0 tr

a cluster validity index for fuzzy clustering a new cluster validity index is proposed for the validation of partitions of object data produced by the fuzzy c means algorithm the proposed validity index uses a variation measure and a separation measure between two fuzzy clusters a good fuzzy partition is expected to have a low degree of variation and a large separation distance testing of the proposed index and nine previously formulated indices on well known data sets shows the superior effectiveness and reliability of the proposed index in comparison to other indices and the robustness of the proposed index in noisy environments

self organization of pulse coupled oscillators with application to clustering we introduce an efficient synchronization model that organizes a population of integrate and fire oscillators into stable and structured groups each oscillator fires synchronously with all the others within its group but the groups themselves fire with a constant phase difference the structure of the synchronized groups depends on the choice of the coupling function we show that by defining the interaction between oscillators according to the relative distance between them our model can be used as a general clustering algorithm unlike existing models our model incorporates techniques from relational and prototype based clustering methods and results in a clustering algorithm that is simple efficient robust unbiased by the size of the clusters and that can find an arbitrary number of clusters in addition to helping the model self organize into stable groups the synergy between clustering and synchronization reduces the computational complexity significantly the resulting clustering algorithm has several advantages over conventional clustering techniques in particular it can generate a nested sequence of partitions and it can determine the optimum number of clusters in an efficient manner moreover since our approach does not involve optimizing an objective function it is not sensitive to initialization and it can incorporate nonmetric similarity measures we illustrate the performance of our algorithms with several synthetic and real data sets

uncertain fuzzy clustering interval type 2 fuzzy approach to c means in many pattern recognition applications it may be impossible in most cases to obtain perfect knowledge or information for a given pattern set uncertain information can create imperfect expressions for pattern sets in various pattern recognition algorithms therefore various types of uncertainty may be taken into account when performing several pattern recognition methods when one performs clustering with fuzzy sets fuzzy membership values express assignment availability of patterns for clusters however when one assigns fuzzy memberships to a pattern set imperfect information for a pattern set involves uncertainty which exist in the various parameters that are used in fuzzy membership assignment when one encounters fuzzy clustering fuzzy membership design includes various uncertainties e g distance measure fuzzifier prototypes etc in this paper we focus on the uncertainty associated with the fuzzifier parameter m that controls the amount of fuzziness of the final c partition in the fuzzy c means fcm algorithm to design and manage uncertainty for fuzzifier m we extend a pattern set to interval type 2 fuzzy sets using two fuzzifiers m1 and m2 which creates a footprint of uncertainty fou for the fuzzifier m then we incorporate this interval type 2 fuzzy set into fcm to observe the effect of managing uncertainty from the two fuzzifiers we also provide some solutions to type reduction and defuzzification i e cluster center updating and hard partitioning in fcm several experimental results are given to show the validity of our method