We show that the pure spinor formalism proposed by Berkovits to covariantly quantize superstrings is a gauge fixed, twisted version of the complexified n = 2 superembedding formulation of the superstring. This provides the Berkovits approach with a geometrical superdiffeomorphism invariant ground. As a consequence, the absence of the worldsheet (super)diffeomorphism ghosts in the pure spinor qu...

An algorithm for obtaining the Taylor coefficients of an expansion of Feynman diagrams is proposed. It is based on recurrence relations which can be applied to the propagator as well as to the vertex diagrams. As an application, several coefficients of the Taylor series expansion for the two-loop non-planar vertex and two-loop propagator diagrams are calculated. The results of the numerical eva...

An Enhanced Two-Step Least Squared (LS) approach is proposed here for hybrid Time Difference of Arrival/Angle of Arrival (TDOA/ AOA) wireless location. Compared to the original two-step LS algorithm, the method here can provide better performance, almost the same as that of Taylor-Series estimator. Compared to the Taylor-Series solution, the method has many computational advantages, such as, li...

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Planar motion can be synthesized with two-degree-of-freedom curvature theory by using the second-order Taylor series to coordinate planar path-tracking systems. Second-order control-variable coordination generates tracking error away from the reference point, and tracking becomes erratic when the driving variable experiences a dwell in its trajectory. This paper extends the technique through an...

We propose an effective and light-weight learning algorithm, Symplectic Taylor Neural Networks (Taylor-nets), to conduct continuous, long-term predictions of a complex Hamiltonian dynamic system based on sparse, short-term observations. At the heart our algorithm is novel neural network architecture consisting two sub-networks. Both are embedded with terms in form series expansion designed symm...

Efficient recurrence relations for computing arbitrary-order Taylor coefficients for any univariate function can be directly applied to a function of n variables by fixing a direction in Rn. After a sequence of directions, the multivariate Taylor coefficients or partial derivatives can be reconstructed or “interpolated”. The sequence of univariate calculations is more efficient than multivariat...