A Seminar Series on Advanced Modeling Concepts for Environmental Science

Special Colloquium Series, Spring & Fall 2005

The complexity of natural systems has challenged scientists to seek new approaches to better describe, understand, and analyze environmental processes. Conceptual frameworks are sought that appropriately account for the effects of heterogeneity, patterns, hierarchies, and other complex interactions in natural systems at multiple space and time scales. Recent advances in physics and applied mathematics have led to the development of fascinating new methods that may serve this purpose in many environmental science disciplines.

This colloquium series features internationally acclaimed scientists that work at the leading edge of developing nontraditional mathematical, physical, and chemical concepts applicable to complex systems. These concepts include scaling, percolation theory, novel stochastic methods, fractals, chance, networks, cellular automata, and other aspects of nonlinear dynamical systems.

Many of these concepts are absent from the conventional palette of environmental scientists and of students in environmental sciences and geosciences. The specific purpose of these colloquia is to provide an introductory, illustrative tour of these topics at a level suitable for students and practitioners in environmental sciences, geosciences, as well as engineering and science. This Colloquium Series provides a unique opportunity to foster a dialogue between sciences, engineering, and environmental sciences.

Sponsors

This special Colloquium Series is made possible by the generous support of these sponsors:

• College of Agriculture and Environmental Sciences
• John Muir Institute of the Environment
• Computational Science and Engineering Center
• Department of Land, Air, and Water Resources
• Department of Civil and Environmental Engineering
• Department of Chemical Engineering and Materials Science
• Soil Sciences Graduate Group
• Atmospheric Sciences Graduate Group
• Hydrologic Sciences Graduate Group
• Groundwater Hydrology Program, University of California Cooperative Extension

Spring

The Effect of Connectivity of Microscopic Elements of Disordered Systems on their Macroscopic Properties: Introduction to Percolation Theory

Muhammad Sahimi (University of Southern California)

April 14, 2005 (Abstract): If the streets of Los Angeles are randomly closed (which is often seemingly the case), what is the minimum number of streets that must be open in order for a driver to start from the Pacific Ocean on the Westside and reach the USC medical school on the Eastside? In these times of high oil and gasoline prices, if we inject water into an oil reservoir in order to increase oil production, how should the water front advance in the reservoir in order to produce more oil? If a composite material is composed of conducting and nonconducting elements, what is the minimum volume fraction of the conducting elements in order for the composite as a whole to be conducting? If monomers are reacting in a reaction bath to form a large molecule, what is the minimum fraction of reacted monomers in order for the molecule to become rigid and behave like a solid material? How does people knowing each other and talking to one another affect their voting patterns? These and similar questions can be answered by using percolation theory which quantifies the effect of the connectivity of the microscopic elements (streets, pores that are filled with water, conducting elements, monomers, people, ...) of disordered systems (Los Angeles, an oil reservoirs, society, ...) on their Macroscopic properties (flow of traffic, flow of oil, flow of electric current, ...). In this seminar, the essential elements of percolation theory are described in simple terms and their applications to the above and several other important problems in science and technology are discussed.

Webcast available in real or wmv formats.

Transient Dynamics: The Key to Ecological Understanding

Alan Hastings (University of California, Davis)

April 21, 2005 (Abstract): Almost all analysis of mathematical models in ecology has focused on asymptotic behavior. I will first discuss what the relevant ecological time scales are, and therefore how relevant the asymptotic analysis may or may not be. Arguing through the use of examples, and also using ideas drawn from dynamical systems, I will both discuss the importance of transients, and how their presence may be analyzed mathematically.

Webcast available in real or wmv formats.

Some Thoughts About Stochastic Hydrologic Modeling Inspired by the Canadian Wilderness

Vit Klemes (Canadian National Hydrology Research Institute)

April 28, 2005 (Abstract): Hydrologic science starts with observations of water, continues with recording them, i.e. converting them into "data", then proceeds to fitting the patterns of these data with mathematical models, and finally uses such models to make predictions about the behavior of water in the frequency and the time domains. It is significant, though often overlooked that, on this route, hydrological science inconspicuously tends to drift ever farther from the "hydro" towards the "logic" with an implicit hope that in doing so it raises its "scientific status". The irony of this "natural process" is that the most "scientific" predictions about the behavior of the real wet water are often based on the behavior of the rather dry "logical constructs" – mathematical models fitted to pure numbers whose original "hydro" meaning does not enter the picture: the models would be exactly the same regardless of what their underlying numbers might represent. However, what is even more important, is that the main product of these models – their predictions – are usually extrapolations of their "logic" beyond – and often far beyond! – the range of the observations. And it is well known that extrapolation is bad science, except when used as a hypothesis subject to confirmation by observation – a situation seldom if ever encountered in stochastic hydrology. Based on inspirations from the Canadian wilderness (and from other natural settings), the lecture will consider possible ways of "irrigating the dry logic" of stochastic hydrological modeling.

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Nonextensive Statistical Mechanics - Introduction and Applications

Constantino Tsallis (Sante Fe Institute and Brazilian Academy of Sciences)

May 12, 2005 (Abstract): Boltzmann-Gibbs Statistical Mechanics is constructed upon hypothesis such as ergodicity. Many nonlinear dynamical systems -- typically those related to complexity -- do not satisfy this requirement. It is nevertheless possible to theoretically handle important classes of them through a generalization of the Boltzmann-Gibbs entropy. An introduction to this theory as well as to its dynamical foundations will be briefly provided. Some illustrative applications will be shown as well.

Webcast available in real or wmv formats.

Process, Pattern, Prediction: Understanding Complexity in Driven Dynamical Systems

John Rundle (Center for Computational Science and Engineering)

May 19, 2005 (Abstract): Edward N Lorenz discovered that chaos and unpredictability are hallmarks of even simple driven systems. Predicting the future evolution of a variety of driven nonlinear systems is further complicated by the fact that their dynamical processes are 1) often not amenable to direct observation; and 2) are strongly multi-scale, so that length and time scales range from very much smaller and shorter than human perception, to very much larger and longer. An example of such systems is the atmosphere, in which, from a practical standpoint, it is impossible to measure the temperatures, pressures, and humidity at all locations at all times. Other important systems include neural networks and earthquake fault systems, both of which are examples of driven threshold systems. In systems such as these, we can only observe the space-time patterns of extreme events. Using these space-time patterns, and whatever is known about the dynamics of these high-dimensional nonlinear earth systems, it often possible to construct numerical simulations that can be used to make predictions about the future space-time evolution of the system and the possible occurrence of extreme events. The accuracy of these predictions and forecasts is limited by the proximity and similarity of the model trajectory through state space, to that of the actual system. The existence of flexible new Grid computing techniques made possible by the World Wide Web has opened new avenues for the realization of sophisticated, state-of-the-art numerical simulations. Thus our ability to forecast the extreme events of the future is limited by a range of issues originating from the dynamical process of interest, the space-time patterns we can observe, and the accuracy of the predictions that are desired.

Webcast available in real or wmv formats.

Ants and Genes: Lessons from Collective Intelligence From Social Insects to Gene Regulatory Systems

Christian Jacob (University of Calgary)

May 26, 2005 (Abstract): We are surrounded by a natural world of massively parallel, decentralized biological ‘information processing’ systems, a world that exhibits fascinating emergent properties in many ways. In fact, our very own bodies are the result of emergent patterns, as the development of any multi-cellular organism is determined by localized interactions among an enormous number of cells, carefully orchestrated by enzymes, signalling proteins and other molecular ‘agents.’ What is particularly striking about these highly distributed developmental processes is that a centralized control agency is completely missing. This is also the case for many other biological systems, such as termites which build their nests – without an architect that draws a plan, or brain cells evolving into a complex 'mind machine' – without an explicit blueprint of a network layout. First, I will present examples of how to use evolutionary computing to breed swarm behaviours, which shows an easy way to program, or rather breed, collectively intelligent systems. By example of an agent-based model of a gene regulatory system, I will expand the notion of swarm intelligence to the simulation of processes within a bacterial cell, which makes highly complicated biological processes much more accessible to computer-based investigations. If time permits, we will also look at a highly visual model of the immune system reactions in response to a viral attack. The talk will be concluded by demonstrations of SwarmArt, an exploratory art project which utilizes swarm intelligence and evolution.

Webcast available in real or wmv formats.

Multiagent Dynamical Systems

James Crutchfield (Center for Computational Science and Engineering)

June 2, 2005 (Abstract): I will show how to model multiagent systems using dynamical systems theory by deriving a class of macroscopic differential equations that describe mutual adaptation in agent collectives, starting from a discrete-time stochastic (microscopic) model. The resulting dynamical systems show that the agents' adaptation is a dynamic balance between optimization of actions that achieve the highest rewards (exploitation) and randomization that chooses locally suboptimal, but novel actions (exploration). It turns out that, although individual agents interact with their environment and other agents in a purely self-interested way without sharing knowledge and ignorant of a context larger than immediate interaction, a strategic dynamic emerges naturally between agents. Under suitable assumptions, the strategic interactions can be interpreted as a game. Overall, though, the emergent strategies are determined by environment-mediated interactions and agents' local reinforcement schemes and so are not amenable to game-theoretic techniques. Application to several familiar, explicitly game-theoretic interactions shows that the adaptation dynamics exhibits a diversity of collective behaviors, including stable limit cycles, quasiperiodicity, intermittency, and deterministic chaos. The simplicity of the assumptions underlying the macroscopic equations suggests that these behaviors should be expected broadly in multiagent systems.

Webcast available in real or wmv formats.

Fall

Exploring Chemical Reaction Networks in Science and Technology

Brian Higgins (University of California, Davis)

October 6, 2005 (Abstract): In recent years the study of network architectures has become increasingly important in understanding complex systems in different branches of science and technology. Examples include metabolic networks (network of metabolites connected by chemical reactions), the Internet (a network of servers), the World Wide Web (a network of web pages), social networks. In this talk we are going to focus on chemical reaction networks in which a network of arbitrary chemical species are connected by chemical reactions. Chemical reaction networks tend to be the rule not the exception in many industrial chemical plants, where the synthesis route for producing a desirable product typically involves numerous chemical steps. I will begin the talk with an mathematical overview of stoichiometry, the foundation for understanding chemical reaction networks, and then proceed with a review of several example chemical reaction networks based on mass action kinetics that display varied dynamically properties. Then we will use concepts from stoichiometry to devise a new way to generate combinatorial libraries of reaction sequences that are chemically consistent and can be studied by graph theory. In particular, we will examine the topological structure of reaction networks, assess what properties are needed to obtain small-world or scale-free behavior, if at all.

Webcast available in real or wmv formats.

Endogenous versus Exogenous Origins of Crises

Didier Sornette (University of California, Los Angeles)

October 12, 2005 (Abstract): Are large biological extinctions such as the Cretaceous/Tertiary KT boundary due to a meteorite, extreme volcanic activity or self-organized critical extinction cascades? Are commercial successes due to a progressive reputation cascade or the result of a well orchestrated advertisement? Are financial crashes due to external shocks or to self-organized instabilities, are intermittent bursts of financial volatility resulting from external shocks or from cumulative effects of news in a long-memory system? Are earthquakes witnesses of tectonic forces or actors triggering other earthquakes close to a critical self-sustained triggering process? Determining the chain of causality for extreme events in complex systems requires disentangling interwoven exogenous and endogenous contributions with either no clear or too many signatures. Here, I review several efforts carried out with collaborators, which suggest a general strategy for understanding the organization of several complex systems under the dual effect of endogenous and exogenous fluctuations. The studied examples are: earthquake foreshocks, mainshock, aftershocks, Internet download shocks, book sale shocks, social shocks, financial volatility shocks, and financial crashes. Simple models are offered to quantitatively relate the endogenous organization to the exogenous response of the system. Suggestions for applications of these ideas toother problems including illnesses and climate are discussed. Didier Sornette graduated from Ecole Normale Superieure (ENS Ulm, Paris) and received his PhD at University of Nice on Statistical Physics of interfaces in Physical Sciences. Didier’s present fields of research interest include: social sciences, finance and economics: decision theory, behavioral decision making, societal risks, bubbles and crashes, large and extreme risks, theory of derivatives, portfolio optimization, trading strategies, insurance, macro-economics, agent-based models, market microstructures. Physics of complex systems and pattern formation in spatio-temporal structures, dynamical system theory, pattern recognition, self-organized criticality, prediction of complex systems, time series analysis; Rupture in random media, theory of earthquakes and of tectonic deformations, rupture and earthquake prediction. Didier has authored and coauthored more than 330 research papers in refereed international journals and more than 120 papers in books and conference proceedings; has been editor of two proceedings of two international conferences; and has authored two textbooks and one monograph.

Webcast available in real or wmv formats.

From Complexity to Peace

Carlos Puente (University of California, Davis)

October 20, 2005 (Abstract): The last few decades have witnessed the development of a host of ideas aimed at understanding and predicting nature's ever present complexity. It is shown that such a work provides, through its detailed study of order and disorder, a suitable framework for visualizing the dynamics and consequences of mankind's ever present divisive traits. Specifically, this talk shall explain: (a) how recent universal results pertaining to multiplicative cascades and fully developed turbulence entice all of us, in a logical way, to seek peace in a condition typified by the hypotenuse of a right-angled triangle; (b) how recent universal results pertaining to the transition from order to chaos via a cascade of bifurcations point us to a serene state, symbolized by the convergence to the origin in the root of a Feigenbaum's tree, in which we all may achieve our inherently desired condition of justice and peace; and (c) how recent universal results pertaining to power-laws, selforganized criticality and space-filling transformations provide additional and pertinent reminders that point us to unity as an essential element for us to achieve peace. Dr. Puente received his Ph. D. from the Massachusetts Institute of Technology and has been a professor at the Department of Land, Air, and Water Resources at the University of California, Davis since 1986. He is the author of over 40 refereed publications, including the book "Treasures inside the Bell. Hidden Order in Chance" and the upcoming books "The Hypotenuse. An Illustrated Scientific Parable for Turbulent Times" and "The Fig Tree and the Bell. God’s Love via Modern Science." Because of his contributions, he recently was named Fellow of the International Society for Complexity, Information, and Design.

Webcast available in real or wmv formats.

Networks, Power Laws and Phase Transitions

Raissa D'Souza (University of California, Davis)

October 27, 2005 (Abstract): We are beginning to understand how pervasive network structures are in natural and engineered systems, and to formulate mathematical theories of network growth. A common observation in technological, biological and social networks is the existence of "scale-free" probability distributions, and of phase transitions (abrupt changes in behavior, such as the emergence of a giant connected core). Mathematical models of random graphs based on the paradigm of preferential attachment (PA) have been used extensively to model network growth as they reproduce some of the observed scale-free properties. Furthermore, PA has a long tradition of use from economics to biology, where it is taken as a fundamental axiom. Rather than assuming PA, we begin with a more basic mechanism, of competition between opposing forces, and show that PA can arise as the solution to the optimization problem. In addition, certain aspects of Internet growth, that have not been captured by previous models, emerge from our framework. This talk will begin by surveying characteristic structures for different types of networks. Then our optimization model of "competition induced preferential attachment" will be presented, along with how PA emerges. Time permitting, I will digress to a discussion of phase transitions, and present a computational study of "traffic" on a lattice, which shows a sharp transition from free flowing to fully jammed. It is a simple model whose behavior remained elusive for over a decade.

Webcast available in real or wmv formats.

Natural Hazards as Self-Organizing Complex Systems

Don Turcotte (University of California, Davis)

November 3, 2005 (Abstract): A sequence of cellular automata models have been proposed as examples of "self-organized criticality". Three of these have direct applications to natural hazards: the sand-pile model to landslides, the forest-fire model to forest and wild fires, and the slider-block model to earthquakes. the relationship of these models to critical point phenomena will be discussed, in particular the relationship of the forest-fire model to the critical-point behavior of the site percolation model. An inverse cascade model that explains the behavior of both SOC and natural hazards will be shown. In addition to discussing the frequency area statistics of landslides, forest and wild fires, and earthquakes; the recurrence statistics of floods will be considered. It will be shown that the current application of log Pearson type 3 statistics to flood frequency analyses is fundamentally flawed.

Webcast available in real or wmv formats.

The Prospects and Perils of Complex Systems Modeling

Melanie Mitchell (Portland State University)

November 10, 2005 (Abstract): Scientists have studied complex systems for centuries, but only the relatively recent invention of electronic computers and subsequent dramatic increases in computing power have allowed the detailed simulation of such systems as food webs, financial markets, the immune system, and human societies. Such computational models have the potential to address questions whose study has not been accessible via more traditional mathematical and experimental techniques. However, this new approach to scientific inquiry comes with its own problems and potential pitfalls, including hidden assumptions, non-replicability of behavior, and misinterpretation of and over-reliance on results. In this talk I will review several prominent complex-systems models as examples of the prospects and perils of such modeling techniques. These examples will range from explorations of the simplest cellular automata to detailed "agent-based" simulations of food webs, economic systems, and human behavior. My hope is that an analysis of this kind will interest, assist, and possibly surprise people who are currently involved in modeling or who would like to be.

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Insights Into Complex Systems

Michelle Girvan (Cornell University)

November 17, 2005 (Abstract): Many systems take the form of networks: examples include the Internet, the World Wide Web, distribution networks, neural networks, biochemical networks, food webs, and social networks. Drawing on techniques from statistical physics and dynamical systems, researchers have begun to take a complex systems approach to characterizing and modeling these networked systems, as they cannot be well described by completely structured or completely random representations. Here, I will discuss the interplay between network structure and system dynamics in many of the aforementioned systems, reviewing recent advances in the field of complex networks.

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Nonlinear Dynamics, Modeling, and the Environmental Sciences: Ideas and Tools

Elizabeth Bradley (University of Colorado)

December 1, 2005 (Abstract): Nonlinearity and chaos are ubiquitous and fascinating. Chaotic systems, in particular, are exquisitely sensitive to small perturbations, but their behavior has a fixed and highly characteristic pattern. Understanding this somewhat counterintuitive combination of effects is important to one's ability to model the physical world. One can even exploit these effects to obtain design improvements in engineered systems: spacecraft trajectories that require less fuel, for example, or fuel injectors that mix gasoline and air more effectively. This talk will begin with a review of some of the most basic ideas and tools of the field of nonlinear dynamics, and then cover a variety of interesting examples, ranging from environmental science and engineering to dance. Most of these tools were developed for low-dimensional systems and many of them require perfect models: situations that are rare in the environmental sciences. For practitioners in these fields, then, it is important to understand how and when to use which one, how to interpret the results, and how to recognize their failure modes.

Webcast available in real or wmv formats.