In this paper, we construct a new suboptimal filter by deriving the Ito's stochastic differential equations of the estimation of higher order central moments satisfy and imposing some conditions to form a closed system. The essentially infinite-dimensional cubic sensor problem has been investigated in detail numerically to illustrate the reasonableness of the imposed conditions, and the numerical experiments support our discussion. A 2-dimensional polynomial filtering problem has also been experimented.

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We use Coulomb branch indices of Argyres-Douglas theories on S1×L(k,1) to quantize moduli spaces H of wild/irregular Hitchin systems. In particular, we obtain formulae for the "wild Hitchin characters" -- the graded dimensions of the Hilbert spaces from quantization -- for four infinite families of H, giving access to many interesting geometric and topological data of these moduli spaces. We observe that the wild Hitchin characters can always be written as a sum over fixed points in H under the U(1) Hitchin action, and a limit of them can be identified with matrix elements of the modular transform STkS in certain two-dimensional chiral algebras. Although naturally fitting into the geometric Langlands program, the appearance of chiral algebras, which was known previously to be associated with Schur operators but not Coulomb branch operators, is somewhat surprising.

In this paper, we introduce a new method to avoid zero reductions in Gröbner basis computation. We call this method LASyz, which stands for Lineal Algebra to compute Syzygies. LASyz uses exhaustively the information of both principal syzygies and non-trivial syzygies to avoid zero reductions. All computation is done using linear algebra techniques. LASyz is easy to understand and implement. The method does not require to compute Gröbner bases of subsequences of generators incrementally and it imposes no restrictions on the reductions allowed. We provide a complete theoretical foundation for the LASyz method and we describe an algorithm to compute Gröbner bases for zero dimensional ideals based on this foundation. A qualitative comparison with similar algorithms is provided and the performance of the algorithm is illustrated with experimental data.

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