Last week (January 3-7) I was an attendee at Dynamics Days, a complexity conference held this year in the Inner Harbor section of Baltimore, MD and hosted by the University of Maryland-College Park. The University of Maryland has an active research group studying chaotic systems and includes people such as Ed Ott, Wolgang Losert, and Michelle Girvan. In fact, this year's event featured a tribute to Ed Ott in honor of his 70th birthday.
I presented a poster on my own work, which was part of a very active poster session. There were also several overarching themes that were shared by a number of talks and poster presentations. One theme was using variations on Lagrangian analysis for understanding turbulent flows. One example is the calculation of finite size Lyapunov exponents (FSLEs) to understand the effects on scale in complex systems. Another example was in the use of second-order Lagrangian systems to understand the effects of turbulence on UAV aircraft. The third example involved incorporating a stochastic element into Lagrangian modeling through the use of an uncertainty estimator. In general, the use of Lagrangians to understand aggregations of particles due to flow field dynamics is currently at the cutting-edge of research in engineering and physics, most notably in the form of Lagrangian Coherent Structure (LCS) analysis.
Example of a Lorentz attractor (above) and a flow field containing Lagrangian Coherent Structures (LCSs) - (below).
A second theme was (of course) chaotic systems, or dynamical systems that are often operate far from equilibrium. Jim Yorke reminded us that there are several definitions of chaos, depending on the type of system under analysis. The best known form of chaos is "statistical regularity" chaos, the short hand of which is understood as a strange attractor. Other forms of chaos include: transient chaos, broad-band power spectra, and deterministic and bounded dynamic behavior. Chaos can be represented as either oscillatory regimes embodied in attractor maps or bifurcations and period doubling-type events embodied in Henon (horseshoe) and logistic maps. Yorke made the connection between each representation and how it relates to our understanding of chaos. He also briefly touched on an emerging application of chaos to system control, which involves a game of survival between the noise and control components of a system. In chaotic systems, where the noise is greater than the control component, the dataset first needs to be sculpted, which reveals a series of safe sets that can be further sculpted to increase controllability. A related presentation focused on the difference between "fast" and "slow" dynamics, and how they work together to define time dynamics.
Example of a Rossler attractor (above) and a logistic map (below).
A third theme was Biophysics. There were a number of posters on actin scaffoldings in cells and cell motility. In particular, actinomyosin elements in the cell are used for rigidity sensing and can be understood as a small-scale muscular machine. There was a presentation on the study of quorum sensing in bacteria using populations of magnetic dipoles as a physical analogues to biological signaling processes and spatiotemporal gradient sensing, and a related presentation on the statistical mechanics of chemotactic movements. There was also an interesting presentation by Theo Geisel on the perception of beat in music. We learned that derivations in drumbeat during the course of a song acts to "humanize" a given song, and that this information can be used to build audio editing technologies. There were several other presentations on neuroscience, including new directions in modeling the dynamical chaos of sleep/wake cycles (Victoria Booth) and the modeling of fast and slow neuronal dynamics using ion concentrations. Finally, Tomas Bohr gave a presentation on how plants are dynamical systems. In particular, the passive and active transport of water and sugars from the leaves to the root systems can be modeled using a series of mathematical techniques and predicts the growth and size limitations of plants.
Example of a Henon map, representing a horseshoe bifurcation.
A fourth theme was evolutionary game theory and the evolution of information and computation. This includes a wide range of approaches such as autonomous boolean networks, discontinuous percolation to model group selection, and encodings for regulatory networks. One notable presentation focused on a stochastic framework for understanding transcriptional dynamics. The major features of this model included relations between timescales and the role of oscillations, dampening, and excitability in the transcriptional process. Another talk involves using the rock-paper-scissors game to model the nonlinear hierarchical dynamics (where there is no dominant strategy) of viral infection and virulence. Jim Crutchfield's group had several posters on the nature of information and the role of entropy in biological complexity. One up-and-coming researcher by the name of Garrett Michener presented on his work encodings for regulatory networks that combines genetic algorithms, neural networks, regulatory networks, and computational linguistics. His models produce some interesting complex behaviors.
Example of active transport of water and sugars in a plant.
One obscure idea that interested me the most were various approaches to extreme events. While in many cases extreme events are treated as outliers, it is also known that not all data are normally-distributed. As a result, we need methods for understanding value that exhibit large variation from the mean in proper context. There was a poster than focused explicitly on how to measure extreme events in a system, and a presentation that discussed the phenomenon of rogue waves in optical systems with applications to rogue waves in other physical systems (such as the surface of the ocean). Next year's Dynamics Days (2013), obscure ideas and all, will be held in Boulder, Colorado.
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