Causes and Effects of Chaos

Most of the recent literature on chaos and nonlinear dynamics is written either for popular science magazine readers or for advanced mathematicians. This paper gives a broad introduction to this interesting and rapidly growing field at a level that is between the two. The graphical and analytical tools used in the literature are explained and demonstrated, the rudiments of the current theory are outlined and that theory is discussed in the context of several examples: an electronic circuit, a chemical reaction and a system of satellites in the solar system.

Towards Autonomous Motion Vision

Earlier, we introduced a direct method called fixation for the recovery of shape and motion in the general case. The method uses neither feature correspondence nor optical flow. Instead, it directly employs the spatiotemporal gradients of image brightness. This work reports the experimental results of applying some of our fixation algorithms to a sequence of real images where the motion is a combination of translation and rotation. These results show that parameters such as the fization patch size have crucial effects on the estimation of some motion parameters. Some of the critical issues involved in the implementaion of our autonomous motion vision system are also discussed here. Among those are the criteria for automatic choice of an optimum size for the fixation patch, and an appropriate location for the fixation point which result in good estimates for important motion parameters. Finally, a calibration method is described for identifying the real location of the rotation axis in imaging systems.

Using Special-Purpose Computing to Examine Chaotic Behavior in Nonlinear Mappings

Studying chaotic behavior in nonlinear systems requires numerous computations in order to simulate the behavior of such systems. The Standard Map Machine was designed and implemented as a special computer for performing these intensive computations with high-speed and high-precision. Its impressive performance is due to its simple architecture specialized to the numerical computations required of nonlinear systems. This report discusses the design and implementation of the Standard Map Machine and its use in the study of nonlinear mappings; in particular, the study of the standard map.

Three-Dimensional Motion Estimation Using Shading Information in Multiple Frames

A new formulation for recovering the structure and motion parameters of a moving patch using both motion and shading information is presented. It is based on a new differential constraint equation (FICE) that links the spatiotemporal gradients of irradiance to the motion and structure parameters and the temporal variations of the surface shading. The FICE separates the contribution to the irradiance spatiotemporal gradients of the gradients due to texture from those due to shading and allows the FICE to be used for textured and textureless surface. The new approach, combining motion and shading information, leads directly to two different contributions: it can compensate for the effects of shading variations in recovering the shape and motion; and it can exploit the shading/illumination effects to recover motion and shape when they cannot be recovered without it. The FICE formulation is also extended to multiple frames.

Forecasting Global Temperature Variations by Neural Networks

Global temperature variations between 1861 and 1984 are forecast usingsregularization networks, multilayer perceptrons and linearsautoregression. The regularization network, optimized by stochasticsgradient descent associated with colored noise, gives the bestsforecasts. For all the models, prediction errors noticeably increasesafter 1965. These results are consistent with the hypothesis that thesclimate dynamics is characterized by low-dimensional chaos and thatsthe it may have changed at some point after 1965, which is alsosconsistent with the recent idea of climate change.s