The course will be divided into three parts: fundamentals, case study, and project laboratory.
The morning sessions will focus on general complex systems concepts and methods with examples drawn from a wide range of disciplines in the physical, biological and social sciences. A total of 8 one and a half hour lectures (12 hours) will be given over four days.
The afternoon sessions will be devoted to the case study on human aging. The faculty will work as a team to lecture, lead discussions and participate in discussions. Sessions will be spread over four days to presentations and discussions of applications to aging (6 hours presentation, 6 hours discussion).
Evening laboratory hours will be devoted to student projects that will involve supervision by faculty and post docs (8 hours). The final day of the program (Friday) will be devoted to summary discussions, an exam, and wrapup (6 hours). The total number of hours devoted to class time will be 38 hours.
Fundamentals in Complex Systems (Eight lectures):

 Introduction & Summary, Yaneer BarYam, NECSI

 This lecture will present an overview of complex systems emphasizing the role of multiple scales and the role of interdependence of parts in system behavior. The dynamic influence between scales will be shown to as described by chaos and nonlinear dynamics, and the existence of structure on multiple scales will be shown to be captured by the concept of fractals. The mechanisms of pattern formation creating physical structures and dynamical processes and pattern recognition that allows their representation in descriptive forms will be reviewed. How relationships between parts of a system lead to the formation of spatial structure and temporal dynamics will be examined. Discussion will cover the essential role that modeling and description of systems on multiple scales plays in our understanding of emergence, complexity, evolution, adaptation and learning.

 Nonlinear Dynamics and Nonlinear Network Dynamics, John Sterman MIT, Sloan School of Management

 This lecture will describe the basics of nonlinear systems, feedback, and the dynamics of systems with multiple feedback loops in networks of influences including methods for constructing models of real systems as networks of nonlinear influences.

 Statistical Approaches and Statistical Networks, Dan Rothman MIT, Earth and Planetary Science

 This lecture will describe the use of averaging to obtain characteristic properties of classes of systems and subsystems as an essential tool for characterizing the behavior of complex systems. The notion of relevant variables, mean field theory, microscale and macroscale variables and descriptions will be reviewed. The behavior of statistical distributions and correlations in complex systems as contrasted with standard statistics will be illustrated by examples. A review will be given of how the analysis of network properties using statistical methods reveals systematic properties relevant to understanding communication, transportation and influence networks.

 Computer modeling and computational paradigm, Larry Rudolph MIT

 This lecture will describe the concept and strategy of computer modeling to represent experimental observations, theoretical models and their logical consequences. Practical methods and common stumbling blocks of building computer simulations such as cellular automata, networks and agents will be reviewed. The basic process of model construction, simulation and analysis will be illustrated by several practical examples. Moreover, the fundamental concept of a rulebased state change system as a general framework for describing dynamic processes will be discussed in application to a wide range of complex systems.

 Information in Systems and Informatics, Temple Smith Boston University

 This lecture will discuss how, in general, patterns in physical biological and social systems have informational properties which are essential to their description. Thus, treating complex systems using informational properties and translating between informational and physical descriptions is an essential part of the study of complex systems. However, in systems such as DNA and human language where informational properties are well separated from physical properties there are important analysis tools for recognizing patterns in the information which have relevance to understanding the dynamics of information and its relationship to physical system properties. These analysis tools will be described and examples of applications will be presented.

 Time series analysis, Blake LeBaron Brandeis University, School of International Economics and Finance

 This lecture will discuss analysis and predication (possibility of and limitations of) of time series using both nonlinear dynamics and statistical analysis. The possibility as well as the limits of prediction suggested by dynamic and statistical models will be presented. The relationship of time series of complex systems to their underlying structure will be explained.

 Evolutionary paradigm Terrence Deacon, Boston University

 This lecture will describe evolution as a model of origin and change of complex systems through environmental influences, with relevance to the dynamics of complex systems on all scales and in artificial as well as natural contexts. A discussion of the essential features of evolution and the attributes of evolutionary models as well as a variety of applications will be presented.

Case Study on Aging (Four lectures and discussions):

 Introduction: The aging of complex human physiology, Lewis Lipsitz, Hebrew Rehabilitation Center for the Aged, Harvard University

 There are probably over 300 theoretical approaches which drive the current research on aging. We shall briefly examine several of the most promising (e.g. evolutionary theory; freeradical theory; gerontogene theory; dynamical systems theory) and the phenomenology of aging to which they are related and the following questions will be specifically addressed: Is senescence distinct from aging? What living organisms show senescence? Does senescence arise from one simple principleor is it inherently a complex emergent property? Is senescence predominantly a dynamic or an information failure? What are some of the chief manifestations of senescence common to most or all organisms that grow old and die? A systematic relationship (scaling law) between mammalian life span and body size will be discussed and the species which have large deviations from this law will be used to probe the origin / significance of this law. Finally, the question will be raised: Is there a theoretical basis, arising from the sciences of complexity, for intervening to delay or slow human aging?

 Physical degradation and non equilibrium dynamics, Eugene Yates, UCLA, Department of Medicine

 Living organisms do not satisfy the assumptions that are often made to simplify the discussion of inanimate systems, whether they are the assumptions of equilibrium, or the assumptions of persistent far from equilibrium dissipative structures (e.g. Taylor vortices, Benard cells, BZ reaction waves, the red spot of Jupiter). To understand the physical processes that give rise to aging, we must understand how decay due to the underlying instability of a nonequilibrium system is delayed by the quasistability of its the structure, the effects of (partially controlled) nonequilibrium flow of energy and materials through the system, and the processes that promote equilibration.

 Heart rate dynamics and physiological processes, Ary Goldberger

 This lecture will explore a paradox: individuals with a wide range of different illnesses are often characterized by strikingly periodic and predictable (ordered) dynamics, even though the disease processes themselves are referred to as disorders. Patients with certain diseases may lose aspects of their interindividual variability, appearing remarkably alike with respect to their pathologic dynamics, appearance and behavior. The main example for our purposes is the progressive reduction in dynamic complexity with aging. Additional examples include: autistic children show highly repetitive behaviors; obsessivecompulsive individuals perseverate monotonously; Parkinsonian patients exhibit virtually indistinguishable tremors; and cyclic oscillations on neutrophil counts may occur in chronic myelogenous leukemia. Such stereotypy contrasts strikingly with the variability and unpredictability that characterize healthy structure and function. A promising advance in the understanding of healthy variability (and by contrast, dynamics of some diseases) has been the introduction of nonlinear dynamics and fractal mathematics to biological systems analysis. Using these methods we can effectively demonstrate that a healthy individual has a complex dynamics, while various dynamic diseases, induce a reduced complexity. The complexity of the dynamics can be reasonably understood to be an essential part of their adaptive capability to a varying environment, while certain "dynamic" diseases cause reduced dynamic complexity and thus reduced ability to adapt to environmental changes. Thus we learn that aging also induces a reduced dynamic complexity consistent with a reduced responsiveness to environmental complexity.

 Genetic issues, Eugene Yates

 Genetic manipulations in animals whose genomes are largely, or fully defined (if not exactly "decoded"!) have demonstrated that point mutations (or deletions) can have substantial effects on both median and maximum lifespan potentials. For example, in Caenorhabditis elegans, mutations in the gene daf2 allow the worms to live for a month instead of two weeks. A "methuselah" gene mutation in Drosophila has a similar lifeprolonging effect. The lifespan of mice has also been extended by genetic manipulations. In cells that still have mitotic capability, that capacity is diminished (or lost) as telomeres shorten with each division cycle and so the gene(s) affecting telomerase levels become candidates for lifespan extensions of some cellular lines. On a broader scale, delaying onset of reproductive activity results in fruit flies that stay healthy to advanced ages – possibly the result of the experimental selection of a subset (perhaps 3 to 8) of favorable genes. Then there is the obvious fact that different mammalian species have different median lifespan expectancies, and that (in the laboratory) small animals of a species tend to live longer than large ones. Can we understand the sensitivity of lifespan to genetics in the context of a physical deterioration model or should the physical deterioration model be modified? Is the "genefor" syndrome obscuring a more broadlybased approach to senescence that attends to the possible modification of life span due to a variety of factors, environmental and dynamic? Can the common linear variance models (genes + environment) adequately express the very nonlinear interactions among genes, development, nonprogrammatic events, and fluctuations in the external environment(s)?

Project Laboratory
 Time is also allocated, primarily during the evenings, for students to access data from an online database and apply analysis packages that will be prepared in advance. A computer lab will be available to enable students during the course to access the online resource and continued access will be possible after the course ends.

 The students will conduct projects under the supervision of faculty and postdocs to familiarize themselves with a number of methodologies that can be applied to complex systems. Each project will involve a well defined question which can be addressed within the time allotted. Sample questions will be prepared in advance. The questions and analysis methods will correspond to the lectures.

 A database of aging related information will be made available to the students. A particular emphasis will be placed on a "heart rate dynamics" online resource developed in collaboration with the National Resource for Complex Biomedical Signals (a collaboration of the Beth Israel Deaconess Medical Center, MIT and Boston University).
