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The adaptation of the k -means algorithm to solving the multiple ellipses detection problem by using an initial approximation obtained by the DIRECT global optimization algorithm

Rudolf Scitovski, Kristian Sabo (2019)

Applications of Mathematics

We consider the multiple ellipses detection problem on the basis of a data points set coming from a number of ellipses in the plane not known in advance, whereby an ellipse E is viewed as a Mahalanobis circle with center S , radius r , and some positive definite matrix Σ . A very efficient method for solving this problem is proposed. The method uses a modification of the k -means algorithm for Mahalanobis-circle centers. The initial approximation consists of the set of circles whose centers are determined...

The ring of multisymmetric functions

Francesco Vaccarino (2005)

Annales de l’institut Fourier

We give a presentation (in terms of generators and relations) of the ring of multisymmetric functions that holds for any commutative ring R , thereby answering a classical question coming from works of F. Junker [J1, J2, J3] in the late nineteen century and then implicitly in H. Weyl book “The classical groups” [W].

Thom polynomials and Schur functions: the singularities I 2 , 2 ( - )

Piotr Pragacz (2007)

Annales de l’institut Fourier

We give the Thom polynomials for the singularities I 2 , 2 associated with maps ( , 0 ) ( + k , 0 ) with parameter k 0 . Our computations combine the characterization of Thom polynomials via the “method of restriction equations” of Rimanyi et al. with the techniques of Schur functions.

Thom polynomials and Schur functions: the singularities I I I 2 , 3 ( - )

Özer Öztürk (2010)

Annales Polonici Mathematici

We give a closed formula for the Thom polynomials of the singularities I I I 2 , 3 ( - ) in terms of Schur functions. Our computations combine the characterization of the Thom polynomials via the “method of restriction equations” of Rimányi et al. with the techniques of Schur functions.

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