maximum lq likelihood estimation via the expectation maximization algorithm a robust estimation of mixture models we introduce a maximum lq likelihood estimation mlqe of mixture models using our proposed expectation maximization em algorithm namely the em algorithm with lq likelihood em lq properties of the mlqe obtained from the proposed em lq are studied through simulated mixture model data compared with the maximum likelihood estimation mle which is obtained from the em algorithm the mlqe provides a more robust estimation against outliers for small sample sizes in particular we study the performance of the mlqe in the context of the gross error model where the true model of interest is a mixture of two normal distributions and the contamination component is a third normal distribution with a large variance a numerical comparison between the mlqe and the mle for this gross error model is presented in terms of kullback leibler kl distance and relative efficiency

numerical investigation on the obliquely incident water wave passing through the submerged breakwater by singular boundary method this short communication presents the singular boundary method sbm to solve the obliquely incident water wave passing through the submerged breakwater the sbm is a recent boundary type collocation method with the merits of being meshless integration free mathematically simple easy to program well suited for unbounded domain problems the accuracy and efficiency of the sbm is first verified in several benchmark examples in comparison with the boundary element method then the effects of the position size and geometry of the breakwater on water wave propagation are investigated through numerical experiments and some new observations are concluded

a meshless singular boundary method for transient heat conduction problems in layered materials abstract the transient heat conduction problems in layered materials are common encountered in practical application but bring great challenge to most numerical algorithms in this study the singular boundary method sbm a meshless boundary collocation technique is first employed to numerically simulate such problems based on the time dependent fundamental solution of diffusion equation taking the boundary conditions and interface conditions into account the computing system of the sbm for layered materials is established and then is solved the proposed method fully inherits the merits of conventional boundary type methods while possessing its distinctive advantages furthermore it is simple straightforward computationally efficient and stable since it does not need to discretize temporal derivative term three numerical experiments are performed to verify the efficiency and accuracy of the proposed scheme numerical results clearly indicate the efficiency accuracy and stability of the presented sbm for solving transient heat conduction problems in layered materials

derived equivalences of k3 surfaces and orientation every fourier mukai equivalence between the derived categories of two k3 surfaces induces a hodge isometry of their cohomologies viewed as hodge structures of weight two endowed with the mukai pairing we prove that this hodge isometry preserves the natural orientation of the four positive directions this leads to a complete description of the action of the group of all autoequivalences on cohomology very much like the classical torelli theorem for k3 surfaces determining all hodge isometries that are induced by automorphisms

robustness properties of k means and trimmed k means abstract the generalized k means method is based on the minimization of the discrepancy between a random variable or a sample of this random variable and a set with k points measured through a penalty function as in the m estimators setting k 1 a penalty function with unbounded derivative naturally leads to nonrobust generalized k means however surprisingly the lack of robustness extends also to the case of bounded that is generalized k means do not inherit the robustness properties of the m estimator from which they came attempting to robustify the generalized k means method the generalized trimmed k means method arises from combining k means idea with a so called impartial trimming procedure in this article study generalized k means and generalized trimmed k means performance from the viewpoint of hampel s robustness criteria that is we investigate the influence function breakdown point and qualitative robustness confirming the superiority provided by the trimming we inc

novel meshless method for solving the potential problems with arbitrary domain in this article a non singular and boundary type meshless method in two dimensions is developed to solve the potential problems the solution is represented by a distribution of the kernel functions of double layer potentials by using the desingularization technique to regularize the singularity and hypersingularity of the kernel functions the source points can be located on the real boundary and therefore the diagonal terms of influence matrices are determined the main difficulty of the coincidence of the source and collocation points then disappears by employing the two point function the off diagonal coefficients of influence matrices are easily obtained the numerical evidences of the proposed meshless method demonstrate the accuracy of the solutions after comparing with the results of exact solution conventional mfs and bem for the dirichlet neumann and mix type boundary conditions bcs of interior and exterior problems with simple and complicated boundaries good agreements with exact solutions are observed

maximum likelihood estimation via the ecm algorithm a general framework two major reasons for the popularity of the em algorithm are that its maximum step involves only complete data maximum likelihood estimation which is often computationally simple and that its convergence is stable with each iteration increasing the likelihood when the associated complete data maximum likelihood estimation itself is complicated em is less attractive because the m step is computationally unattractive in many cases however complete data maximum likelihood estimation is relatively simple when conditional on some function of the parameters being estimated

mixture densities maximum likelihood and the em algorithm the problem of estimating the parameters which determine a mixture density has been the subject of a large diverse body of literature spanning nearly ninety years during the last two decades the

robust estimation in the normal mixture model based on robust clustering summary we introduce a robust estimation procedure that is based on the choice of a representative trimmed subsample through an initial robust clustering procedure and subsequent improvements based on maximum likelihood to obtain the initial trimming we resort to the trimmed k means a simple procedure designed for finding the core of the clusters under appropriate configurations by handling the trimmed data as censored maximum likelihood estimation provides in each step the location and shape of the next trimming data driven restrictions on the parameters requiring that every distribution in the mixture must be sufficiently represented in the initial clustered region allow singularities to be avoided and guarantee the existence of the estimator our analysis includes robustness properties and asymptotic results as well as worked examples

mapping class group and a global torelli theorem for hyperkahler manifolds a mapping class group of an oriented manifold is a quotient of its diffeomorphism group by the isotopies we compute a mapping class group of a hyperkahler manifold m showing that it is commensurable to an arithmetic lattice in so 3 b2 3 a teichmuller space of m is a space of complex structures on m up to isotopies we define a birational teichmuller space by identifying certain points corresponding to bimeromorphically equivalent manifolds we show that the period map gives the isomorphism between connected components of the birational teichmuller space and the corresponding period space so b2 3 3 so 2 so b2 3 1 we use this result to obtain a torelli theorem identifying each connected component of the birational moduli space with a quotient of a period space by an arithmetic group when m is a hilbert scheme of n points on a k3 surface with n 1 a prime power our torelli theorem implies the usual hodge theoretic birational torelli theorem for other examples of hyperkahler manifolds the hodge theoretic torelli theorem is known to be false

equivalences of twisted k3 surfaces we prove that two derived equivalent twisted k3 surfaces have isomorphic periods the converse is shown for k3 surfaces with large picard number it is also shown that all possible twisted derived equivalences between arbitrary twisted k3 surfaces form a subgroup of the group of all orthogonal transformations of the cohomology of a k3 surface

the method of fundamental solutions and quasi monte carlo method for diffusion equations the laplace transform is applied to remove the time dependent variable in the diffusion equation for non harmonic initial conditions this gives rise to a non homogeneous modified helmholtz equation which we solve by the method of fundamental solutions to do this a particular solution must be obtained which we find through a method suggested by atkinson to avoid costly gaussian quadratures we approximate the particular solution using quasi monte carlo integration which has the advantage of ignoring the singularity in the integrand the approximate transformed solution is then inverted numerically using stehfest s algorithm two numerical examples are given to illustrate the simplicity and effectiveness of our approach to solving diffusion equations in 2 d and 3 d 1998 john wiley sons ltd

a q parameterized deterministic annealing em algorithm based on nonextensive statistical mechanics we propose a q parameterized deterministic annealing expectation maximization q daem algorithm for parameter estimation motivated by the concept of tsallis entropy that originates from the nonextensive statistical mechanics the q daem algorithm combines the feature of annealing algorithms to reduce initialization sensitivity and that of q em algorithms to achieve fast convergence the q em algorithm is a one parameter generalized em algorithm that has been previously proposed by the authors by interpreting the em algorithm via likelihood lower bound maximization we build the fundamental interconnections among daem q daem and statistical mechanics to illustrate the benefits of using q daem we investigate two applications finite mixture model estimation in data clustering and joint channel estimation and data detection in communication systems where we show that the q daem algorithm achieves superior performance over the em algorithm for both applications

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

free circle actions with contractible orbits on symplectic manifolds we prove that closed symplectic four manifolds do not admit any smooth free circle actions with contractible orbits without assuming that the actions preserve the symplectic forms in higher dimensions such actions by symplectomorphisms do exist and we give explicit examples based on the constructions of fgm

information ratios for validating mixture analyses abstract determining the number of components in a mixture of distributions is an important but difficult problem this article introduces a procedure called minimum information ratio estimation and validation mirev which is based on a ratio of fisher information matrices the smallest eigenvalue of the information ratio matrix is used to determine the number of components a measure of uncertainty may be obtained using a bootstrap technique simulations illustrate the effectiveness of the procedure for mixtures of exponential families an expression for the observed information ratio matrix provides insight to the success of the procedure cluster analysis attempts to identify and characterize subpopulations believed to be present in a population a wide variety of methods are available including criterion optimization hierarchical methods and various heuristic methods criterion optimization techniques such as mixture analysis fuzzy clustering and partitioning methods are popular because they

bayesian repulsive gaussian mixture model we develop a general class of bayesian repulsive gaussian mixture models that encourage well separated clusters aiming at reducing potentially redundant components produced by independent priors f