My research interest is to apply concepts and tools in Physics and/or Mathematics (calculus, statistics, etc)  to understand complex systems that are of great recent interests in multidisciplinary fields of studies. Complexity is characterized by the common absence of single length and/or time scale, or its exhibition of interaction of at all scales. Examples under consideration will be [1] individual entity and collective behavior of these entities (critical phenomena), [2] time series of physiological origins (e.g. heart beat variations), [3] self organized critical behaviors (SOC, earthquake or crashes in financial market), and [4] network dynamics (human behaviors). The basic and universal concept is very simple: the emergence of ubiquitous scale-free power law,  f(x)~1/x^(1+a), in many complex systems. The indices of these power laws, a, have modern implications in the interpretation of long term system behavior. These emergent features originated from the empirical data will find applications in many modern engineering, materials, biological, and even social systems. For example, is a periodic or regularly beating heart a health one?

Below is a list of general books, the contents of which, will demonstrate the diverse nature of complexity in many fields of interest to “almost” everyone.

• Complexity: A Guided Tour M. Mitchell

• Simply Complexity: A Clear Guide  N. Johnson

• Complexity: The emergent science at the edge of order and chaos M. Waldrop

• Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life S.H. Strogatz

• How nature works: the science of self-organized criticality P. Bak

• Chaos: Making a New Science J. Gleick

• The Essence Of Chaos E. Lorenz

• The Fractal Geometry of Nature B.B. Mandelbrot

• Chance and Chaos D. Ruelle

Technical books on complex systems displaying nonlinear dynamics, chaos, random walk behavior

• Complex Webs: Anticipating the Improbable B.J. West and P. Grigolini

• From Order to Chaos II: Essays : Critical, Chaotic and Otherwise (World Scientific Series on Nonlinear Science, Series a, Monographs and Treatises, Volume 32) L.P. Kadanoff

• Understanding Nonlinear Dynamics, D. Kaplan and L. Glass

• Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering (Studies in Nonlinearity) S.H. Strogatz

• From Clocks to Chaos L. Glass and M.C. Mackey

• Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge Nonlinear Science Series) A. Pikovsky, et al.

• Physiology, Promiscuity, and Prophecy at the Millennium: A Tale of Tails (Studies of Nonlinear Phenomena in Life Science) B.J. West

• Dynamics Of Complex Systems (Studies in Nonlinearity) Y. Bar-yam

• Critical Phenomena in Natural Sciences: Chaos, Fractals, Self Organization and Disorder: Concepts and Tools (Springer Series in Synergetics) D. Sornette

• Self-Organized Criticality: Emergent Complex Behavior in Physical and Biological Systems (Cambridge Lecture Notes in Physics) H.J. Jensen

• Dynamic Patterns: The Self-Organization of Brain and Behavior (Complex Adaptive Systems) J.A.S. Kelso

• Brownian Agents and Active Particles, F. Schweitzer

Finance Related

• Econophysics: An Intro (Physics Textbook) S. Sinha, et al.

• The Statistical Mechanics of Financial Markets J. Voit

• Introduction to Econophysics: Correlations and Complexity in Finance R.N. Mantegna and H. E. Stanley

• Fractals and Scaling In Finance: Discontinuity, Concentration, Risk B.B. Mandelbrot, et. al

• The Misbehavior of Markets: A Fractal View of Financial Turbulence B.B Mandelbrot, et. al

• Why Stock Markets Crash: Critical Events in Complex Financial Systems D. Sornette

• The Black Swan: The Impact of the Highly Improbable: With a new section: “On Robustness and Fragility”, 2nd Ed. N.N. Taleb

Miscellaneous

Comment on our weekly Friday 4:00pm (coffee-donuts provided) informal mini-talk series

This weekly meeting in the Biophysics Group of Prof. B. Antanaitis is opened to all curious minds. We have begun to explore relations among these ideas, scaling, universality, power laws etc, started from phase transition and critical phenomena in physics and will dip into other interdisciplinary fields with help of miscellaneous random walk models featuring fractal time and spatial dependence.

Everyone, students and faculties, in the Lafayette community is warmly welcome. Better still, if you like to share your expertise in these multidisciplinary fields, please email Prof. Antanaitis (antanaib@lafayette.edu) or me (wongym@lafayette.edu) to schedule your presentation.