background: the accuracy and reproducibility of measurements in a locally made three dimensional (3d) simulator was assessed and compared with manual caliper measurements. materials and methods: a total of 20 casts were scanned by our laser scanner. software capabilities included dimensional measurements, transformation and rotation of the cast as a whole, separation and rotation of each tooth ...

We propose DigitHist, a histogram summary for selectivity estimation on multi-dimensional data with tight error bounds. By combining multi-dimensional and one-dimensional histograms along regular grids of different resolutions, DigitHist provides an accurate and reliable histogram approach for multi-dimensional data. To achieve a compact summary, we use a sparse representation combined with a n...

Pricing a path-dependent financial derivative, such as an Asian option, requires the computation of E[g(B(·))], the expectation of a payoff functional, g, that depends on a Brownian motion, (B(t))t=0. The expectation corresponds to an infinite dimensional integral, which is approximated by the sample average of a d-dimensional approximation to the integrand. In this article, a multilevel algori...

Error variance estimation plays an important role in statistical inference for high dimensional regression models. This paper concerns with error variance estimation in high dimensional sparse additive model. We study the asymptotic behavior of the traditional mean squared errors, the naive estimate of error variance, and show that it may significantly underestimate the error variance due to sp...

We revisit the method of Carleman linearization for systems of ordinary differential equations with polynomial right-hand sides. This transformation provides an approximate linearization in a higher-dimensional space through the exact embedding of polynomial nonlinearities into an infinite-dimensional linear system, which is then truncated to obtain a finite-dimensional representation with an a...

We present the theory and implementation for a new automatic adaptive h-re nement and -dere nement method for twoand three-dimensional elliptic problems. An exact lower error bound for dere nement is obtained theoretically in terms of the nite element solution, complementing the various known upper error bounds for re nement. These error bounds are used to determine where to insert and/or remov...

Bounded real balanced truncation for infinite-dimensional systems is considered. This provides reduced order finite-dimensional systems that retain bounded realness. We obtain an error bound analogous to the finite-dimensional case in terms of the bounded real singular values. By using the Cayley transform a gap metric error bound for positive real balanced truncation is subsequently obtained. ...