integral complete multipartite graphs abstract we give counterexamples to a result in f esser and f harary 2 theorem 3 asserting that two nonisomorphic complete r partite graphs with the same number of vertices have different spectral radii we then derive some results on invariant factors and apply them to obtain relationship between the parameters of integral complete multipartite graphs and their integer eigenvalues necessary conditions for complete multipartite graphs to be integral are obtained

personalized mode transductive spanning svm classification tree personalized transductive learning ptl builds a unique local model for classification of individual test samples and is therefore practically neighborhood dependant i e a specific model is built in a subspace spanned by a set of samples adjacent to the test sample while existing ptl methods usually define the neighborhood by a predefined dis similarity measure this paper introduces a new concept of a knowledgeable neighborhood and a transductive support vector machine svm classification tree t svmt for ptl the neighborhood of a test sample is constructed over the classification knowledge modelled by regional svms and a set of such svms adjacent to the test sample is systematically aggregated into a t svmt compared to a regular svm and other svmts a t svmt by virtue of the aggregation of svms has an inherent superiority in classifying class imbalanced datasets the t svmt has also solved the over fitting problem of all previous svmts since it aggregates neighborhood knowledge and thus significantly reduces the size of the svm tree the properties of the t svmt are evaluated through experiments on a synthetic dataset eight bench mark cancer diagnosis datasets as well as a case study of face membership authentication

the universal r matrix for u_q rm sl 3 and beyond ther matrices for the quantised lie algebrasa n are constructed through the quantum double procedure given by drinfel d 6 the case ofu q sl 3 is thoroughly analysed initially to demonstrate the more subtle points of the calculation the ease of the calculation fora n is very dependent on a choice of generators for the borel subalgebrau q b and its dual and a certain ordering imposed on these generators which is related to the length of a certain word in the weyl group

classical solutions of the quantum yang baxter equation the classical analogue is developed here for part of the construction in which knot and link invariants are produced from representations of quantum groups whereas previous work begins with a quantum group obtained by deforming the multiplication of functions on a poisson lie group we work directly with a poisson lie groupg and its associated symplectic groupoid the classical analog of the quantumr matrix is a lagrangian submanifold open image in new window in the cartesian square of the symplectic groupoid for any symplectic leafs ing open image in new window induces a symplectic automorphism ofs s which satisfies the set theoretic yang baxter equation when combined with the flip map exchanging components and suitably implanted in each cartesian powers n generates a symplectic action of the braid groupb n ons n application of a symplectic trace formula to the fixed point set of the action of braids should lead to link invariants but work on this last step is still in progress

complex quantum groups and their quantum enveloping algebras we construct complexified versions of the quantum groups associated with the lie algebras of typean 1 bn cn anddn following the ideas of faddeev reshetikhin and takhtajan we obtain the hopf algebras of regular functionals u on these complexified quantum groups in the special examplea1 we derive theq deformed enveloping algebrauq sl 2 in the limitq 1 the undeformeduq sl 2 is recovered

relating p adic eigenvalues and the local smith normal form abstract conditions are established under which the p adic valuations of the invariant factors diagonal entries of the smith form of an integer matrix are equal to the p adic valuations of the eigenvalues it is then shown that this correspondence is the typical case for most matrices density counts are given for when this property holds as well as easy transformations to this typical case

quantum deformation of lorentz group a one parameter quantum deformations l 2 ofsl 2 is introduced and investigated an analog of the iwasawa decomposition is proved the compact part of this decomposition coincides withs u 2 whereas the solvable part is identified as a pontryagin dual ofs u 2 it shows thats l 2 is the result of the dual version of drinfeld s double group construction applied tos u 2 the same construction applied to any compact quantum groupgc is discussed in detail in particular the explicit formulae for the haar measures on the pontryagin dualgd ofgc and on the double groupg are given we show that there exists remarkable 1 1 correspondence between representations ofg and bicovariant bimodules tensor bundles overgc the theory of smooth representations ofs l 2 is the same as that ofsl 2 clebsh gordon coefficients are however modified the corresponding tame bicovariant bimodules ons u 2 are classified an application to 4d differential calculus is presented the nonsmooth case is also discussed

optimal partitioning for classification and regression trees an iterative algorithm that finds a locally optimal partition for an arbitrary loss function in time linear in n for each iteration is presented the algorithm is a k means like clustering algorithm that uses as its distance measure a generalization of kullback s information divergence moreover it is proven that the globally optimal partition must satisfy a nearest neighbour condition using divergence as the distance measure these results generalize similar results of l breiman et al 1984 to an arbitrary number of classes or regression variables and to an arbitrary number of bills experimental results on a text to speech example are provided and additional applications of the algorithm including the design of variable combinations surrogate splits composite nodes and decision graphs are suggested

comparison of texture analysis schemes under nonideal conditions several recent advancements in the field of texture analysis prompt some fundamental questions for instance what is the true impact of these novel advancements under real world environments when do these novel advancements fail to perform which methods perform better and under what conditions in this work we investigate these and other issues under nonideal image acquisition environments specifically environments with changing conditions due to illumination variations and those caused by both affine and nonaffine transformations we study the performance of nine popular texture analysis algorithms using three different datasets with varying levels of difficulty experiments are performed on nonideal texture datasets under five different setups we find that most state of the art techniques do not perform well under these conditions to a large extent their performance under nonideal conditions depends critically on the nature of the textural surface moreover most techniques fail to perform reliably when the number of classes in the dataset is increased significantly over the regular size datasets used in previous work multiscale features performed reasonably well against variations caused by illumination and rotation but are prone to fail under changes in scale surprisingly the performance for most of the algorithms is generally stable on structured or periodic textures even with variations in illumination or affine transformations

eigenvalues and the smith normal form abstract we compare the smith normal form snf over the integers of an integral nonsingular matrix with its spectrum when its eigenvalues are integers our results include tight bounds on the size of the largest element of the snf when the matrix is diagonalizable with nonzero integer eigenvalues with no assumptions on the diagonalizing matrices

integer invariants of abelian cayley graphs let g be a finite abelian group let e be a subset of g and form the cayley directed graph of g with connecting set e we explain how for various matrices associated to this graph the spectrum can be used to give information on the smith normal form this technique is applied to several interesting examples including matrices in the bose mesner algebra of the hamming association scheme h n q we also recover results of bai and jacobson niedermaier reiner on the critical group of a cartesian product of complete graphs

face membership authentication using svm classification tree generated by membership based lle data partition this paper presents a new membership authentication method by face classification using a support vector machine svm classification tree in which the size of membership group and the members in the membership group can be changed dynamically unlike our previous svm ensemble based method which performed only one face classification in the whole feature space the proposed method employed a divide and conquer strategy that first performs a recursive data partition by membership based locally linear embedding lle data clustering then does the svm classification in each partitioned feature subset our experimental results show that the proposed svm tree not only keeps the good properties that the svm ensemble method has such as a good authentication accuracy and the robustness to the change of members but also has a considerable improvement on the stability under the change of membership group size

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

the linear separability problem some testing methods the notion of linear separability is used widely in machine learning research learning algorithms that use this concept to learn include neural networks single layer perceptron and recursive deterministic perceptron and kernel machines support vector machines this paper presents an overview of several of the methods for testing linear separability between two classes the methods are divided into four groups those based on linear programming those based on computational geometry one based on neural networks and one based on quadratic programming the fisher linear discriminant method is also presented a section on the quantification of the complexity of classification problems is included

t g t a toy model for conformal field theory we study a chiral operator algebra of conformal field theory and quantum deformation of the finite dimensional lie group to obtain the definition of t g t and its representation the closeness of the kac moody algebras constituting the chiral operator algebra of a typical and generic conformal field theory model namely the wznw model and quantum deformation of corresponding finite dimensional lie groupg has become more and more evident in recent years 1 5 this in particular prompts further investigation of the differential geometry of such deformations the notion of tangent and cotangent bundles is basic in classical differential geometry it is only natural that the quantum deformations oftg andt g are to be introduced alongside those forg itself physical ideas could be useful for this goal indeed thet g can be interpreted as a phase space for a kind of a top generalizing the usual top associated withg so 3 the classical mechanics is a natural language to describe differential geometry whereas the usual quantization is nothing but the representation theory in this paper we put corresponding formulas in such a fashion that their deformation becomes almost evident given the experience in this domain as a result we get the definition of t g t and its representation t is the deformation parameter to make the exposition most simple and formulas transparent we shall work on an example ofg sl 2 and present results in such a way that the generalizations become evident we shall stick to generic complex versions real and especially compact forms requiring some additional consideration not all of which are self evident

integer based constellation shaping method for papr reduction in ofdm systems in this paper the problem of reducing the peak to average power ratio papr in an orthogonal frequency division multiplexing system is considered we design a cubic constellation called the hadamard constellation whose boundary is along the bases defined by the hadamard matrix in the transform domain then we further reduce the papr by applying the selective mapping technique the encoding method following the method introduced in the work of kwok is derived from a decomposition known as the smith normal form this new technique offers a papr that is significantly lower than those of the best known techniques without any loss in terms of energy and or spectral efficiency and without any side information being transmitted moreover it has a low computational complexity

the local structure of poisson manifolds varietes de poisson et applications decomposition structures de poisson lineaires approximation lineaire systemes hamiltoniens le probleme de linearisation groupes de fonction realisations et applications impulsion paires duales et groupes de jauge existence des realisations unicite des realisations les problemes des 3 corps restreints et autres exemples

quantum deformations of certain simple modules over enveloping algebras soit f un corps soit f 0 un sous corps de f soit u l algebre enveloppante universelle sur f 0 de l algebre de lie de kac moody correspondant a la matrice a d entiers on montre qu un module integrable de poids le plus eleve v de u admet une deformation quantique

constructably laplacian integral graphs a graph is laplacian integral if the spectrum of its laplacian matrix consists entirely of integers we consider the class of constructably laplacian integral graphs those graphs that be constructed from an empty graph by adding a sequence of edges in such a way that each time a new edge is added the resulting graph is laplacian integral we characterize the constructably laplacian integral graphs in terms of certain forbidden vertex induced subgraphs and consider the number of nonisomorphic laplacian integral graphs that can be constructed by adding a suitable edge to a constructably laplacian integral graph we also discuss the eigenvalues of constructably laplacian integral graphs and identify families of isospectral nonisomorphic graphs within the class

online support vector machine based on convex hull vertices selection the support vector machine svm method as a promising classification technique has been widely used in various fields due to its high efficiency however svm cannot effectively solve online classification problems since when a new sample is misclassified the classifier has to be retrained with all training samples plus the new sample which is time consuming according to the geometric characteristics of svm in this paper we propose an online svm classifier called vs osvm which is based on convex hull vertices selection within each class the vs osvm algorithm has two steps 1 the samples selection process in which a small number of skeleton samples constituting an approximate convex hull in each class of the current training samples are selected and 2 the online updating process in which the classifier is updated with newly arriving samples and the selected skeleton samples from the theoretical point of view the first d 1 d is the dimension of the input samples selected samples are proved to be vertices of the convex hull this guarantees that the selected samples in our approach keep the greatest amount of information of the convex hull from the application point of view the new algorithm can update the classifier without reducing its classification performance experimental results on benchmark data sets have shown the validity and effectiveness of the vs osvm algorithm

bicovariant quantum algebras and quantum lie algebras a bicovariant calculus of differential operators on a quantum group is constructed in a natural way using invariant maps from fun mathfrak g q tou q g given by elements of the pure braid group these operators the reflection matrix y l sl being a special case generate algebras that linearly close under adjoint actions i e they form generalized lie algebras we establish the connection between the hopf algebra formulation of the calculus and a formulation in compact matrix form which is quite powerful for actual computations and as applications we find the quantum determinant and an orthogonality relation fory inso q n

matrices over rings of algebraic integers abstract for matrices with algebraic integer entries this paper studies i completions with prescribed determinant ii the hermite triangular form iii the schur triangular form iv the smith diagonal form and v links connecting eigenvalues and smith invariants

more on quantum groups from the quantization point of view star products on the classical double group of a simple lie group and on corresponding symplectic groupoids are given so that the quantum double and the quantized tangent bundle are obtained in the deformation description complex quantum groups and bicovariant quantum lie algebras are discussed from this point of view further we discuss the quantization of the poisson structure on the symmetric algebras g leading to the quantized enveloping algebrau h g as an example of biquantization in the sense of turaev description ofu h g in terms of the generators of the bicovariant differential calculus onf g q is very convenient for this purpose finaly we interpret in the deformation framework some well known properties of compact quantum groups as simple consequences of corresponding properties of classical compact lie groups an analogue of the classical kirillov s universal character formula is given for the unitary irreducble representation in the compact case

deforming maps for lie group covariant creation and annihilation operators any deformation of a weyl or clifford algebra a can be realized through a deforming map i e a formal change of generators in a this is true in particular if a is covariant under a lie algebra g and its deformation is induced by some triangular deformation uhg of the hopf algebra ug we propose a systematic method to construct all the corresponding deforming maps together with the corresponding realizations of the action of uhg the method is then generalized and explicitly applied to the case that uhg is the quantum group uhsl 2 a preliminary study of the status of deforming maps at the representation level shows in particular that deformed fock representations induced by a compact uhg can be interpreted as standard undeformed fock representations describing particles with ordinary bose or fermi statistics

smith forms for adjacency matrices of circulant graphs we calculate the smith normal form of the adjacency matrix of each of the following graphs or their complements or both complete graph cycle graph square of the cycle power graph of the cycle distance matrix graph of cycle andrasfai graph doob graph cocktail party graph crown graph prism graph mobius ladder the proofs operate by finding the abelianization of a cyclically presented group whose relation matrix is column equivalent to the required adjacency matrix

quantum dressing orbits on compact groups the quantum double is shown to imply the dressing transformation on quantum compact groups and the quantum iwasawa decompositon in the general case quantum dressing orbits are described explicitly as algebras the dual coalgebras consisting of differential operators are related to the quantum weyl elements besides the differential geometry on a quantum leaf allows a remarkably simple construction of irreducible representations of the algebras of quantum functions representation spaces then consist of analytic functions on classical phase spaces these representations are also interpreted in the framework of quantization in the spirit of berezin applied to symplectic leaves on classical compact groups convenient coherent states are introduced and a correspondence between classical and quantum observables is given

on the critical group of the n cube abstract reiner proposed two conjectures about the structure of the critical group of the n cube q n in this paper we confirm them furthermore we describe its p primary structure for all odd primes p the results are generalized to cartesian product of complete graphs k n 1 k n k by jacobson niedermaier and reiner

complex quantum group dual algebra and bicovariant differential calculus the method used to construct the bicovariant bimodule in ref csww is applied to examine the structure of the dual algebra and the bicovariant differential calculus of the complex quantum group the complex quantum group fun q sl n c is defined by requiring that it contains fun q su n as a subalgebra analogously to the quantum lorentz group analyzing the properties of the fundamental bimodule we show that the dual algebra has the structure of the twisted product fun q su n fun q su n reg then the bicovariant differential calculi on the complex quantum group are constructed

bicovariant differential calculus on quantum groups su q n and so q n following woronowicz s proposal the bicovariant differential calculus on the quantum groupssu q n andso q n is constructed a systematic construction of bicovariant bimodules by using the hat r q matrix is presented the relation between the hopf algebras generated by the linear functionals relating the left and right multiplication of these bicovariant bimodules and theq deformed universal enveloping algebras is given imposing the conditions of bicovariance and consistency with the quantum group structure the differential algebras and exterior derivatives are defined as an application the maurer cartan equations and theq analogue of the structure constants are formulated

the yang baxter equation and invariants of links on considere le fait que l on peut construire des invariants d isotopie p et f pour des liens en utilisant certaines solutions des equations de yang baxter

primitive ideals of c q sl 3 the primitive ideals of the hopf algebrac q sl 3 are classified in particular it is shown that the orbits in primc q sl 3 under the action of the representation grouph c c are parameterized naturally byw w wherew is the associated weyl group it is shown that there is a natural one to one correspondence between primitive ideals ofc q sl 3 and symplectic leaves of the associated poisson algebraic groupsl 3 c

face recognition using an enhanced independent component analysis approach this paper is concerned with an enhanced independent component analysis ica and its application to face recognition typically face representations obtained by ica involve unsupervised learning and high order statistics in this paper we develop an enhancement of the generic ica by augmenting this method by the fisher linear discriminant analysis lda hence its abbreviation fica the fica is systematically developed and presented along with its underlying architecture a comparative analysis explores four distance metrics as well as classification with support vector machines svms we demonstrate that the fica approach leads to the formation of well separated classes in low dimension subspace and is endowed with a great deal of insensitivity to large variation in illumination and facial expression the comprehensive experiments are completed for the facial recognition technology feret face database a comparative analysis demonstrates that fica comes with improved classification rates when compared with some other conventional approaches such as eigenface fisherface and the ica itself

face recognition using total margin based adaptive fuzzy support vector machines this paper presents a new classifier called total margin based adaptive fuzzy support vector machines taf svm that deals with several problems that may occur in support vector machines svms when applied to the face recognition the proposed taf svm not only solves the overfitting problem resulted from the outlier with the approach of fuzzification of the penalty but also corrects the skew of the optimal separating hyperplane due to the very imbalanced data sets by using different cost algorithm in addition by introducing the total margin algorithm to replace the conventional soft margin algorithm a lower generalization error bound can be obtained those three functions are embodied into the traditional svm so that the taf svm is proposed and reformulated in both linear and nonlinear cases by using two databases the chung yuan christian university cycu multiview and the facial recognition technology feret face databases and using the kernel fisher s discriminant analysis kfda algorithm to extract discriminating face features experimental results show that the proposed taf svm is superior to svm in terms of the face recognition accuracy the results also indicate that the proposed taf svm can achieve smaller error variances than svm over a number of tests such that better recognition stability can be obtained

computing hermite and smith normal forms of triangular integer matrices abstract this paper considers the problem of transforming a triangular integer input matrix to canonical hermite and smith normal form we provide algorithms and prove deterministic running times for both transformation problems that are optimal in the matrix dimension the algorithms are easily implemented assume standard integer arithmetic and admit excellent performance in practice the results presented here lead to a faster algorithm for computing the smith normal form of an arbitrary i e non triangular input matrix