A Unified Theory of Complex Systems
Recently added: Review Slides from BAST meeting (
PPT)
A surprisingly consistent view on the fundamental nature of complex systems can now be drawn
from the convergence of three distinct research themes:
- Molecular biology has provided a detailed description of much of the components of biological networks, and the organizational principles of these networks are becoming increasingly apparent. It is now clear that much of the complexity in biology is driven by its regulatory networks, however poorly understood the details remain.
- Advanced technology is creating engineering examples of networks where we do know all the details and that have complexity approaching that of biology. While the components are entirely different, there is striking convergence at the network level of the architecture and the role of protocols, layering, control, and feedback in structuring complex system modularity.
- A new mathematical framework for the study of complex networks suggests that this apparent network-level evolutionary convergence both within biology and between biology and technology is not accidental, and follows necessarily from the requirements that both biology and technology be efficient, robust, adaptive, and evolvable.
- Robust yet fragile (RYF): A crucial insight is
that both evolution and natural selection or engineering design must
produce high robustness to uncertain environments and components in order
for systems to persist. Yet this allows and even facilitates severe
fragility to novel perturbations, particularly those that exploit the very
mechanisms providing robustness, and this "robust yet fragile" (RYF)
feature must be exploited explicitly in any theory that hopes to scale to
large systems.
- HOT: The above views of "organized complexity"
contrast sharply with the view of "emergent complexity" that is preferred
within physics, and currently dominates much of the popular scientific
literature. While motivation for our research is drawn from biology and
technology, HOT (Highly Optimized/Organized Tolerance/Tradeoffs) is a
conceptual approach that aims to explain the concepts of organized
complexity, involving optimizing functional objectives of networks subject
to constraints on their components, but often using models more familiar
in the emergent complexity genre. Thus to sharpen the contrast, HOT has
often been presented in the context of lattices, cellular automata, spin
glasses, phase transitions, criticality, chaos, fractals, scale-free
networks, self-organization, and so on, that have been the inspiration for
the physics perspective.
- Complex Network Topology:
We propose a novel approach to the study of complex network topology
in which we use an optimization framework to model the mechanisms
driving network design and growth. While previous methods of topology
generation have focused on explicit replication of statistical properties,
such as node hierarchies and node degree distributions, our approach
provides a framework that reconciles the domain-specific details of
vastly different systems with general principles underlying network
evolution and growth. By investigating plausible objectives and
constraints in the design of actual networks, observed network
properties such as certain hierarchical structures and node degree
distributions can be understood as the natural by-product of an
approximately optimal solution to a network design problem.
In the process, we resolve some of the misconceptions that exist in the
complex systems literature regarding the prevalence and significance
of power law or scaling distributions.
Historical References