Title: Electronic circuits verify importance of dynamics in perception and predict failure of prominent algorithms used in bioinformatics.Ruedi Stoop
This topic focuses on continued insights triggered by our paper "Real-World Existence and Origins of the Spiral Organization of Shrimp-Shaped Domains,” (PRL 105, 074102 (2010)). The talk first gives a detailed outline of this paper, emphasizing on the relation between mathematical models and their simulation, and between the two and real-world experiments. Then we will answer some questions related to, but not treated in the original work. Finally, we will emphasize and illustrate how nonlinear physics may be of key importance for difficulties encountered in various fields of bioinformatics analysis.
Areas in parameter space of dimensions higher than one on which the solutions of a smooth nonlinear dynamical system are regular, are found to be connected and to have the peculiar characteristic form of a shrimp. We give the first detailed demonstration of the emergence of shrimps in electronic systems, discuss the influence that different approximate hardware descriptions have, and clarify questions that have recently been raised about the nature of the organization of shrimps in parameter space. In particular, we demonstrate explicitly that the phenomenon was theoretically predicted by the (very unfortunately: recently passed away) Russian mathematician L.P. Shilnikov in the sixties. Moreover, we design a simpler circuit that provides the explicit proof of this fact. We then reveal the mathematical key elements that lead to the formation of shrimps.
We finally show that the phenomenon of shrimp emergence is likely to underlie a number of problems found in different fields of bioinformatics. One important example will be clustering as the fundamental process behind the modeling of neuroinformatic perception and, more generally, in most bioinformatics applications. We show how the objects to be clustered emerge from general nonlinear processes, and that they therefore have shrimps-shaped boundaries. One consequence of this is that by means of most traditional clustering approaches, they cannot properly be clustered. We demonstrate exemplarily how an electronics implementation of a simple blueprint borrowed from the mammalian brain outperforms by far the algorithms commonly used for clustering, both in time and quality of the result.
The talk will mediate between theoretical concepts of nonlinear dynamics with an emphasis on chaos, their implementation in electronics and their applications to real-world systems. It will demonstrate the importance of the underlying nonlinear concepts and the fact that we, as the specialists in this field, are now well-equipped for solving key questions in eminent fields of technology such as bioinformatics.
University of Michigan Sponsors
- Horace H. Rackham School of Graduate Studies at the University of Michigan, Ann Arbor
- Michigan Center for Theoretical Physics
- Center for Studies of Complex Systems
- Medical School
- Department of Mathematics
- Department of Physics
- Biophysics Program