In this paper, we apply our inversion mapping method, the trajectory mixture density network (TMDN), to a new corpus of articulatory data, recorded with a Carstens AG500 electromagnetic articulograph. This new data set, mngu0, is relatively large and phonetically rich, among other beneficial characteristics. We obtain good results, with a root mean square (RMS) error of only 0.99mm. This compar...

This paper proposes a trajectory model which is based on a mixture density network trained with target features augmented with dynamic features together with an algorithm for estimating maximum likelihood trajectories which respects constraints between the static and derived dynamic features. This model was evaluated on an inversion mapping task. We found the introduction of the trajectory mode...

We provide an error estimate for the local mean projection approximation in L p([0, τ∗]) for p ∈ [1,+∞[, in terms of the regularity of the underlying grid, and we apply it to the corresponding projection approximation of weakly singular Fredholm integral equations of the second kind. © 2004 Elsevier Ltd. All rights reserved.

For a process normally distributed and a target located at the mid-point of a twosided tolerance interval, Vännman suggests a family of indices depending on two parameters. In order to choose the parameters which allow to obtain an index that is sensitive to departures of the mean from the target, we need to take the properties of its estimator into account. For a target not located at the mid-...

Several problems involving E(T ) and E2(T ), the error terms in the mean square and mean fourth moment formula for |ζ( 1 2 + it)|, are discussed. In particular it is proved that

We study the mean square weighted L2 discrepancy of randomized digital (t,m, s)nets over Zp. The randomization method considered here is a digital shift of depth m, i.e., for each coordinate the first m digits of each point are shifted by the same shift whereas the remaining digits in each coordinate are shifted independently for each point. We also consider a simplified version of this shift. ...

Differential semblance velocity analysis flattens image gathers automatically by minimizing the mean square difference of neighboring traces in an image volume. Implementations based on normal moveout correction as “imaging” method are relatively fast, can accomodate arbitrary acquisition geometry, and can be organized to output 1D, 2D, or 3D interval velocity models. Within the limits of its i...

Let ∆(x) denote the error term in the Dirichlet divisor problem, and E(T ) the error term in the asymptotic formula for the mean square of |ζ( 1 2 + it)|. If E∗(t) = E(t) − 2π∆∗(t/2π) with ∆∗(x) = −∆(x) + 2∆(2x) − 1 2 ∆(4x), then we obtain ∫ T 0 |E(t)| dt ≪ε T 2+ε and ∫ T 0 |E∗(t)| 544 75 dt ≪ε T 601 225 . It is also shown how bounds for moments of |E∗(t)| lead to bounds for moments of |ζ( 1 2 ...

A simple proof of the classical subconvexity bound ζ( 1 2 + it) ≪ε t1/6+ε for the Riemann zeta-function is given, and estimation by more refined techniques is discussed. The connections between the Dirichlet divisor problem and the mean square of |ζ( 1 2 + it)| are analysed. 1. Convexity for the Riemann zeta-function Let as usual (1.1) ζ(s) = ∞

Weibull distributions are widely used in reliability and survival analysis. In this paper, different methods to estimate the shape and scale parameters of the two-parameter Weibull distribution have been reviewed and compared, based on the bias, mean square error and variance. Because a theoretical comparison is not possible, an extensive simulation study has been conducted to compare the perfo...