Curved Inertia Frames: Visual Attention and Perceptual Organization Using Convexity and Symmetry

In this paper we present an approach to perceptual organization and attention based on Curved Inertia Frames (C.I.F.), a novel definition of "curved axis of inertia'' tolerant to noisy and spurious data. The definition is useful because it can find frames that correspond to large, smooth, convex, symmetric and central parts. It is novel because it is global and can detect curved axes. We discuss briefly the relation to human perception, the recognition of non-rigid objects, shape description, and extensions to finding "features", inside/outside relations, and long- smooth ridges in arbitrary surfaces.

The Bifurcation Interpreter: A Step Towards the Automatic Analysis of Dynamical Systems

The Bifurcation Interpreter is a computer program that autonomously explores the steady-state orbits of one-parameter families of periodically- driven oscillators. To report its findings, the Interpreter generates schematic diagrams and English text descriptions similar to those appearing in the science and engineering research literature. Given a system of equations as input, the Interpreter uses symbolic algebra to automatically generate numerical procedures that simulate the system. The Interpreter incorporates knowledge about dynamical systems theory, which it uses to guide the simulations, to interpret the results, and to minimize the effects of numerical error.

Automatic Analysis and Synthesis of Controllers for Dynamical Systems Based On P

I present a novel design methodology for the synthesis of automatic controllers, together with a computational environment---the Control Engineer's Workbench---integrating a suite of programs that automatically analyze and design controllers for high-performance, global control of nonlinear systems. This work demonstrates that difficult control synthesis tasks can be automated, using programs that actively exploit and efficiently represent knowledge of nonlinear dynamics and phase space and effectively use the representation to guide and perform the control design. The Control Engineer's Workbench combines powerful numerical and symbolic computations with artificial intelligence reasoning techniques. As a demonstration, the Workbench automatically designed a high-quality maglev controller that outperforms a previous linear design by a factor of 20.

A Dynamical Systems Model for Language Change

Formalizing linguists' intuitions of language change as a dynamical system, we quantify the time course of language change including sudden vs. gradual changes in languages. We apply the computer model to the historical loss of Verb Second from Old French to modern French, showing that otherwise adequate grammatical theories can fail our new evolutionary criterion.

3D Object Recognition: Symmetry and Virtual Views

Many 3D objects in the world around us are strongly constrained. For instance, not only cultural artifacts but also many natural objects are bilaterally symmetric. Thoretical arguments suggest and psychophysical experiments confirm that humans may be better in the recognition of symmetric objects. The hypothesis of symmetry-induced virtual views together with a network model that successfully accounts for human recognition of generic 3D objects leads to predictions that we have verified with psychophysical experiments.