Let K be a function field in one variable over an arbitrary field F. Given a rational function φ ∈ K(z) of degree at least two, the associated canonical height on the projective line was defined by Call and Silverman. The preperiodic points of φ all have canonical height zero; conversely, if F is a finite field, then every point of canonical height zero is preperiodic. However, if F is an infin...

OBJECTIVE To establish reference charts for fetal cerebellar vermis height in an unselected population. METHODS A prospective cross-sectional study between September 2009 and December 2014 was carried out at ALTAMEDICA Fetal-Maternal Medical Centre, Rome, Italy. Of 25203 fetal biometric measurements, 12167 (48%) measurements of the cerebellar vermis were available. After excluding 1562 (12.8%...

We prove an effective Weierstrass Division Theorem for algebraic restricted power series with p-adic coefficients. The complexity of such power series is measured using a certain height function on the algebraic closure of the field of rational functions over Q. The paper includes a construction of this height function, following an idea of Kani. We apply the effective Weierstrass Division Theo...

In this paper we show several approximation results for folding networks { a generalization of partial recurrent neural networks such that not only time sequences but arbitrary trees can serve as input: Any measurable function can be approximated in probability. Any continuous function can be approximated in the maximum norm on inputs with restricted height, but the resources necessarily increa...

Body mass index (BMI), weight(kg)/ height(m)2, is a widely used measure of obesity in medical science. In economics, there appeared studies showing that BMI has a negative (or no) effect on wage. But BMI is a tightly specified function of weight and height, and there is no a priori reason to believe why this particular function is the best to combine weight and height. In this paper, we address...

In this paper, we present a novel two-step, variational and feature preserving smoothing method for terrain data. The first step computes the field of 3D normal vectors from the height map and smoothes them by minimizing a robust penalty function of curvature. This penalty function favors piecewise planar surfaces; therefore, it is better suited for processing terrain data then previous methods...