To extract useful information from high-dimensional geometric or structural data, we must find low-dimensional projections that are informative and interesting to look at. The conventional, manual-interaction methods used for this purpose are ineffective when the dimensionality of the data is high, or when the geometric models are complex. Standard methods for determining useful low-dimensional...

The local statistical and geometric structure of three-dimensional turbulent flow can be described by the properties of the velocity gradient tensor. A stochastic model is developed for the Lagrangian time evolution of this tensor, in which the exact nonlinear self-stretching term accounts for the development of well-known non-Gaussian statistics and geometric alignment trends. The nonlocal pre...

B-Reps (Boundary Representations) represent geometric objects defined as stratified point sets. This paper extends boundary representations of non-manifold geometric objects to n-dimensional stratified objects possibly having incomplete boundaries. The proposed representation has given rise to a new geometric kernel called DiX (Data in Xtratus), having been derived from a mathematical model bas...

Model-based object recognition must solve three-dimensional geometric problems involving the registration of multiple sensors and the spatial relationship of a three-dimensional model to the sensors. Observation and verification of the registration and recognition processes requires display of these geometric relationships. We have developed a prototype software system which allows a user to in...

Suppose that a geometrically distributed number of observations are available from an absolutely continuous distribution function $F$, within this set of observations denote the random number of records by $M$. This is called geometric random record model. In this paper, characterizations of $F$ are provided in terms of the subsequences entropies of records conditional on events ${M geq n}$ or ...

We discuss the systematic effects arising from the cosmological redshift-space (geometric) distortion on the statistical analysis of isodensity contour using high-redshift catalogs. Especially, we present a simple theoretical model for isodensity statistics in cosmological redshift-space, as a generalization of the work by Matsubara (1996). The statistical quantities considered here are the two...

We describe a recent program from the study of definable groups in certain o-minimal structures. A central notion of this program is that of a (geometric) lattice. We propose a definition of a lattice in an arbitrary first-order structure. We then use it to describe, uniformly, various structure theorems for o-minimal groups, each time recovering a lattice that captures some significant invaria...

We suggest that some observational features of high-energy radiation from pulsars should be explained in terms of three dimensional geometric models, e.g. the phase-resolved X-ray and γ-ray spectra and the energy dependent light curves from various pulsars. In this paper, we present a three dimensional pulsar outer-magnetospheric gap model to explain these observational features. The outer-magn...