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Jan 11 - "Objects that Make Objects: The Population Dynamics of Structural Complexity"

Jim Crutchfield, Center for Computational Science and Engineering, UC Davis

Abstract: To analyze the evolutionary emergence of structural complexity in physical processes we introduce a general, but tractable, model of objects that interact to produce new objects. Since the objects -- epsilon-machines -- have well defined structural properties, we demonstrate that complexity in the resulting population-dynamical system emerges on several distinct organizational scales during evolution -- from individuals to nested levels of mutually self-sustaining interaction. The evolution to increased organization is dominated by the spontaneous creation of structural hierarchies and this, in turn, is facilitated by the innovation and maintenance of relatively low-complexity, but general individuals.

Paper: J. P. Crutchfield and Olof Görnerup,
"Objects That Make Objects: The Population Dynamics of Structural Complexity".
Santa Fe Institute Working Paper 04-06-020. nlin.AO/0406058

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Jan 18 - "The Analysis of Pattern"

Nello Cristianini, Statistics, UC Davis

Abstract: We will informally discuss what patterns are, why we should care about them and what technology has been developed to discover and exploit them. The talk with be at an informal and intuitive level, no special algorithms will be discussed.

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Jan 25 - "Visualization tools for complex systems"

Ingrid Hotz, Institute for Data Analysis and Visualization, UC Davis

Abstract: The amount of data generated by simulations, experiments and data collections is constantly increasing. Therefore, new ways have to be found to reveal the information contained in this data. Visualization is one way to do this. It uses the human perceptual capabilities to recognize structures, irregularities and patterns contained in the data. The purpose of visualization is to translate data of all kind into pictures supporting this human ability. This means providing a qualitative overview of large complex data-sets, but also helps to find interesting regions, enhance important structures, and choosing the right perspective. In this talk I try to illustrate some goals and issues in visualization using vector and tensor fields as an example.

Feb 8 - "Exploring the Relationships between Complexity and Randomness: Complexity-Entropy Diagrams"

Dave Feldman, Physics, College of the Atlantic

Abstract: The past several decades has seen a considerable effort toward the development of measures of complexity. These measures are intended to capture, to varying degrees, our intuitive notions of pattern, regularity, memory, or structure. One of the questions motivating this work concerns the nature of the relationship between complexity and entropy. Is complexity the absence of disorder? Are maximally complex phenomena those that combine order and disorder? Is there a general relationship between complexity and entropy? These questions are often addressed by appealing to a complexity-entropy diagram: a plot of a system's complexity vs. its entropy. In this talk I will review several information-theoretic measures of randomness and structural complexity. I will then present calculations of complexity-entropy diagrams for a range of systems: one-dimensional maps of the unit interval; one- and two-dimensional Ising models; Markov chains; cellular automata; and topological languages. The main conclusion that will emerge from this survey is that there is a large range of possible complexity-entropy behaviors. In particular, there is not a universal complexity-entropy curve.

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Feb 15 - "Structural Complexity in Disordered, Layered Crystals"

Dowman Varn, Max Planck Institute for the Physics of Complex Systems

Abstract: A significant challenge in condensed matter science is the discovery and characterization of structure in complex, disordered materials directly from their x-ray diffraction spectra. A broad class of layered materials, called polytypes, can exist in a wide range of both ordered and disordered stacking configurations. Examples of polytypes include micas and kaolins, and substances of technological importance, such as the wide band gap semiconductor silicon carbide. While standard crystallographic techniques can identify most ordered stacking structures, understanding the diffuse diffraction spectra arising from disordered specimens has proven more challenging. In this talk, I will briefly discuss the phenomenon of polytypism at a level suitable for a general scientific audience. I will introduce a novel technique for detecting and characterizing disordered stacking structure directly from x-ray diffraction spectra. The resulting expression for the structure is a directed graph. I will demonstrate the technique on x-ray diffraction spectra obtained from zinc sulphide crystals and show how it provides insight into the complex stacking structure of these crystals as well as allows for the calculation of material properties of physical import. The techniques introduced here are quite general, and are applicable to the problem of inferring structure (either spacial or temporal) given an experimental signal in the form of a power spectrum.

Feb 22 - "The science of complex networks"

Raissa D'Souza, Center for Computational Science and Engineering, UC Davis

Abstract: Network structures are pervasive in the natural and engineered world, from biological networks to the Internet. What advantages do network structures offer over regular topology? How does network topology affect function, and in turn, feedback from the function affect topological change? Can we use properties observed in natural networks to steer engineering implementations? Such questions guide our thinking as we strive to build a mathematical framework for understanding network phenomena.

One common observation in many classes of networks is the existence of "scale-free" probability distributions. We introduce an underlying mathematical framework for network growth, based on optimization of tradeoffs, and show that the much studied mechanisms of Preferential Attachment (PA) and of saturation emerge from these more basic considerations. Previously these mechanisms had been assumed as fundamental axioms. Time permitting, applications to self-organizing sensor networks, and the larger issue of the interplay between statistical physics, computer simulation and probability theory will be presented.

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Mar 1 - "The UC Davis KeckCAVES project"

Oliver Kreylos, Computer Science, UC Davis

Abstract: KeckCAVES (The W.M. Keck Center for Active Visualization in the Earth Sciences) is a collaborative project between Earth scientists and computer scientists, with the goal to develop, and apply, advanced visualization techniques to Earth science research. KeckCAVES' centerpiece is a walk-in immersive visualization environment (a 4-sided CAVE). More importantly, however, KeckCAVES brings together researchers from visualization/computer science and Earth science to develop problem-specific immersive ("virtual reality") visualization software to address complex Earth science problems.

In this presentation, I will introduce the fundamentals of virtual reality, what sets it apart from "regular" visualization, and how KeckCAVES utilizes VR's benefits to investigate scientific questions.

Mar 15 - "Video Analysis of Stomatal Patch Dynamics"

Aaron Luttman, Department of Mathematical Sciences, University of Montana

Abstract: In order to engage in photosynthesis, leaves use pores on their surface - called stomata - to absorb CO₂. The opening of these pores results in the evaporation of H₂O, which is a detriment to leaf function. Thus a leaf is faced with the global optimization problem of maximizing CO₂ uptake for a fixed amount of H₂O loss. In solving this problem, stomata in spatially homogeneous patches often synchronize their apertures, even though this does not result in optimal local CO₂ uptake. In order to visualize these patches, a dye is injected into a leaf so that it fluoresces when closing its stomata. Understanding how synchronized patches of stomata results in an optimal CO₂ uptake for the entire leaf requires a thorough analysis of these fluorescence patterns. Using an experimental background model to drive video segmentation, we use a variational level-set approach for extracting the spatially synchronized stomatal patches from video taken of the leaf fluorescence. Methods of two-dimensional pattern analysis can then be used to analyze the dynamics of the stomatal patches.

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Mar 22 - "Self-organizing Microtubule Asters"

Alex Mogilner, Department of Mathematics and Center for Genetics and Development, UC Davis

Abstract: Both cell division, and cell migration, and intracellular transport depend on asters made of microtubules - dynamic cytoskeletal polymers. These asters have a remarkable ability to self-organize and find the center of the cell. I will tell about experiments with fragments of fish melanophore cells, in which pigment granules, coated with dynein molecular motors, move to minus ends of microtubules, and also alter microtubule dynamics. A positive feedback between granule transport and dyneins nucleating microtubules and stabilizing their minus ends leads to aster self-organization, while the spontaneous nucleation of microtubules causes aster centering. The main focus of the talk will be to illustrate how mathematical modeling assists experimental research in uncovering molecular mechanisms of self-organization in the cell.

Apr 5 - "Visualization of three-dimensional gene expression patterns"

Gunther Weber

Abstract: not available.

Apr 12 - "Helping Pavlov, Skinner, Tolman, Lorenz, and Tinbergen, build a robot: A behavior systems approach"

William Timberlake, Department of Psychology, Indiana University

Abstract: Research on behavior has emphasized the importance of conditioning procedures, cognition, or the contributions of evolved perceptual-motor units and adaptive motivation. All three approaches analyze and model the mechanisms and outcomes of behavior using simplified "unnatural" conditions, but disagree on how best to proceed. I suggest that starting with an ethological model provides a basis for predicting and understanding the use of conditioning procedures as analytic tools to clarify the operation of underlying systems and start to build a behaving organism.

Apr 19 - "Sparse coding and inference in visual cortex"

Bruno Olshausen, Helen Wills Neuroscience Institute and School of Optometry and Redwood Center for Theoretical Neuroscience, UC Berkeley

Abstract: Our percepts of the world are clearly *inferred*, rather than being computed directly from the available data. This means that our brains must be endowed with powerful inferential machinery - i.e., probabilistic models - for combining incoming sensory information together with prior knowledge in order to infer what's "out there" in the environment. In this talk I will present a simple version of a probabilistic model for primary visual cortex (V1) that is based on the idea of sparse coding - i.e., where images are represented by a small number of active units at any given time. I will then present the results of computational simulations showing that this idea is consistent with the receptive field properties found in V1 neurons, and I will present data supporting the idea that cortical neurons are attempting to infer sparse representations of images. Both the model and the data make clear that if we are to actually understand what is going on the cortex, we need to focus our efforts on studying how it operates under natural conditions.

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Apr 26 - "Complex behavior in aftershock sequences"

Robert Shcherbakov, Center for Computational Science and Engineering, UC Davis

Abstract: Aftershocks provide a wealth of information that can be used to better understand the physics of earthquake processes. The occurrence of aftershocks is an outcome of complex dynamics in the brittle part of the Earth's crust initiated by a main shock. This dynamics is a combined effect of different processes taking place in a highly heterogeneous media over a wide range of temporal and spatial scales. In this presentation aftershock sequences in California are studied in order to better understand their scaling properties. In the temporal domain, the decay of aftershock rates can be described by the generalized Omori's law, which incorporates three empirical laws: the Gutenberg-Richter relation for frequency-magnitude scaling, the modified Omori's law for the temporal decay of aftershocks, and the modified Bath's law for the difference between the magnitudes of a main shock and its largest aftershock. The analysis of decay rates suggests that the parameter c in the generalized Omori's law is not a constant but scales with the lower magnitude cutoff and plays the role of a characteristic time in the establishment of Gutenberg-Richter scaling. Distributions of interoccurrence times between earthquakes in aftershock sequences are also analyzed and a model based on a non-homogeneous Poisson (NHP) process is proposed to quantify the observed scaling. In this model the generalized Omori's law for the decay of aftershocks is used as a time-dependent rate in the NHP process. The analytically derived distribution of interoccurrence times is applied to several major aftershock sequences in California to confirm the validity of the proposed hypothesis. It is argued that the NHP process combined with the generalized Omori's law can be used to a good approximation to quantify the observed temporal scaling of interoccurrence times between earthquakes in aftershock sequences. The validity of these scaling laws is evidence that earthquakes exhibit self-organization and complexity.

May 3 - "Simple Rules, Morphology, and the Physical Environment: Modeling the Sensorimotor Behavior of Infant Mammals"

Jeff Schank, Psychology, UC Davis

Abstract: This talk presents an overview of a research program aimed at using autonomous robots to model infant mammals. We are investigating the development of sensorimotor behavior in infant Norway rat pups (age 7 to 10 days) both in groups and alone. We have developed physical and simulated robots that model aspects of the shape and tactile capabilities of pups. When placed in a rectangular arena, rat pups display patterns of behavior expected of thigmotactic organisms. They tend to follow walls, end up in corners, and when in groups, aggregate in corners. The patterns we observe are difficult to replicate with deterministic thigmotactic architectures instantiated in autonomous robots. However, when robots are programmed to move about randomly, alone or in groups in an arena, they display behavior that match qualitatively and quantitatively patterns observed in pups. We conclude that thigmotactic-like patterns of behavior (e.g., aggregation, wall-following) can emerge from non-thigmotactic rules, but further work is required to determine the ridged versus flexible bodies in generating these patterns.

May 10 - "Complexity in quantum dynamical systems"

Karoline Wiesner, Center for Computational Science and Engineering, UC Davis

Abstract: We are interested in the possibility that quantum systems, such as molecules, store and process information. As a first step in exploring this, we introduce a class of quantum finite-state automata. To illustrate the power of these models we analyze several prototype quantum dynamical system, emphasizing the difference between physical and computation-theoretic views of quantum behavior. The quantum automaton analysis reveals structure in behavior that the physical description fails to detect. We also compare the relative generative capabilities of quantum and classical systems.

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