We present a method for recovering the structure of a plant directly from a small set of widely-spaced images for automated analysis of phenotype. Structure recovery is more complex than shape estimation, but the resulting structure estimate is more closely related to phenotype than is a 3D geometric model. The method we propose is applicable to a wide variety of plants, but is demonstrated on ...

We consider the invariant measure of a homogeneous continuoustime Markov process in the quarter-plane. The basic solutions of the global balance equation are the geometric distributions. We first show that the invariant measure can not be a finite linear combination of basic geometric distributions, unless it consists of a single basic geometric distribution. Second, we show that a countable li...

Setting up a symbolic algebraic system is the first step in mathematics mechanization of any branch of mathematics. In this paper, we establish a compact symbolic algebraic framework for local geometric computing in intrinsic differential geometry, by choosing only the Lie derivative and the covariant derivative as basic local differential operators. In this framework, not only geometric entiti...

Examples of geometric phases abound in many areas of physics. They offer both fundamental insights into many physical phenomena and lead to interesting practical implementations. One of them, as indicated recently, might be an inherently fault-tolerant quantum computation. This, however, requires one to deal with geometric phases in the presence of noise and interactions between different physi...

The Lorenz attractor was introduced in 1963 by E. N. Lorenz as one of the first examples of strange attractors. However Lorenz’ research was mainly based on (non-rigourous) numerical simulations and, until recently, the proof of the existence of the Lorenz attractor remained elusive. To address that problem some authors introduced geometric Lorenz models and proved that geometric Lorenz models ...

In this paper we describe and discuss a new kernel design for geometric computation in the plane. It combines different kinds of floating-point filter techniques and a lazy evaluation scheme with the exact number types provided by LEDA allowing for efficient and exact computation with rational and algebraic geometric objects. It is the first kernel design which uses floating-point filter techni...

This is a tutorial on some aspects of toric varieties related to their potential use in geometric modeling. We discuss projective toric varieties and their ideals, as well as real toric varieties. In particular, we explain the relation between linear precision and a particular linear projection we call the algebraic moment map.

A study was completed of more than 170,000 records of pediatric venous blood levels and supporting demographic information collected in New York City during 1970-1976. The geometric mean (GM) blood lead level shows a consistent cyclical variation superimposed on an overall decreasing trend with time for all ages and ethnic groups studied. The GM blood lead levels for blacks are significantly gr...