Active Sensing and Data Driven Algorithm Selection

IEEE KIMAS Conference, Boston, October 2003

Roger Brockett

Slides [pdf]

Making use of Hidden Symmetries in Data

IEEE International Symposium on Information Theory, Japan, July 2003

Roger Brockett

It is a cornerstone of theoretical physics that the discovery and exploitation of symmetries is basic to understanding the structure of nature. On the other hand, information theorists have come to view symmetries as both a blessing and a curse in the design of codes. In this talk we emphasize the positive aspects focusing on the use of symmetries in the algorithmic domain. Our emphasis will be on problems involving the estimation of random processes, where the symmetries are revealed by the existence of a suitable type of Lie algebra, but we will also show that the existence of symmetries lies behind a number of well known practical algorithms used in signal processing and linear algebra. Finally, we will discuss the use of approximate symmetries in the context of a problem arising in neuroscience involving place cell data.

Slides [html]

Subriemannian Geodesics, Oscillations, and a Feedback Regulator Problem

Banach Center Workshop on Geometry and Nonlinear Control, Poland, June 2003

Roger Brockett

Many important engineering systems accomplish their purpose using cyclic processes whose characteristics are under feedback control. Examples involving thermodynamic cycles and electromechanical energy conversion processes are particularly noteworthy. Likewise, cyclic processes are prevalent in nature and the idea of a pattern generator is widely used to rationalize mechanisms used for orchestrating movements such as those involved in locomotion and respiration. In this talk, we develop a linkage between the use of cyclic processes and the control of nonholonomic systems, emphasizing the problem of achieving stable regulation.

Slides [html]

The Weyl group as a symmetry group for subriemannian geodesics

Workshop on Geometry, Dynamics and Mechanics in Honour of the 60th Birthday of J.E. Marsden, Fields Institute, Toronto, August 2002

Roger Brockett

Audio [real audio]

Dynamical Systems and Computational Mechanisms

Royal Academy of Sciences, Belgium, July 2002

Roger Brockett

Developments in fields outside electrical engineering and computer science have raised questions about the possibility of carrying out computation in ways other than those based on digital logic. Quantum computing and neuro-computing are examples. When formulated mathematically, these new fields relate to dynamical systems and raise questions in signal processing whose resolution seems to require new methods. Up until now, the statement that computers are dynamical systems of the input/output type has not gotten computer scientists especially excited because it has not yet been shown to have practical consequence or theoretical power. It is my goal here to try to show that this point of view has both explanatory value and mathematical interest.

Slides-1 [pdf], Slides-2 [pdf], Slides-3 [pdf], Slides-4 [pdf]