Universal Laws and Architectures

his talk will focus on progress towards a more “unified” theory for complex networks motivated by biology and technology, and involving several elements: hard limits on achievable robust performance ( “laws”), the organizing principles that succeed or fail in achieving them (architectures and protocols), the resulting high variability data and “robust yet fragile” behavior observed in real systems and case studies (behavior, data), and the processes by which systems evolve (variation, selection, design). We will leverage a series of case studies from neuroscience, cell biology, human physiology, and technology to illustrate the implications of recent theoretical developments. [7]

Insights into what the potential universal laws, architecture, and organizational principles are can be drawn from three converging research themes. First, detailed description of components and a growing attention to systems in biology and neuroscience, the organizational principles of organisms and evolution are becoming increasingly apparent. Biologists are articulating richly detailed explanations of biological complexity, robustness, and evolvability that point to universal principles and architectures.[2][6] Second, while the components differ and the system processes are far less integrated, advanced technology’s complexity is now approaching biology’s and there are striking convergences at the level of organization and architecture, and the role of layering, protocols, and feedback control in structuring complex multiscale modularity [4][1], Determining what is essential about this convergence and what is merely historical accident requires a deeper understanding of architecture — the most universal, high-level, persistent elements of organization — and protocols. Protocols define how diverse modules interact, and architecture defines how sets of protocols are organized.

The third research theme is new mathematical frameworks for the study of complex networks that suggests this apparent network-level evolutionary convergence within/between biology/technology is not accidental, but follows necessarily from their universal system requirements to be fast, efficient, adaptive, evolvable, and most importantly, robust to perturbations in their environment and component parts. The universal hard limits on systems and their components have until recently been studied separately in fragmented domains of physics, chemistry, biology, communications, computation, and control, but a unified theory is needed and appears feasible. We have the beginnings of the underlying mathematical framework and also a series of case studies in classical problems in complexity from statistical mechanics[5], turbulence[8], cell biology[6], human physiology and medicine, smartgrid, wildfire ecology, earthquakes, economics, the Internet, and neuroscience. The emphasis will be on the implications of the theory rather than details, but the underlying math issues will be sketched.

Hard limits on measurement, prediction, communication, computation, decision, and control, as well as the underlying physical energy and material conversion mechanism necessary to implement these abstract process are at the heart of modern mathematical theories of systems in engineering and science (often associated with names such as Shannon, Poincare, Turing, Gödel, Bode, Wiener, Heisenberg, Carnot,…). They form the foundation for rich and deep subjects that are nevertheless now introduced at the undergraduate level. Unfortunately, these subjects remain largely fragmented and incompatible, even as the tradeoffs between these limits are essential to understanding human physiology and neuroscience, and are of growing importance in building integrated and sustainable systems. Time permitting, we will give an accessible introduction to these theories, how they do and don’t relate to each other, and progress and prospects for a more integrated theory. Particular emphasis will be put on Turing’s work in honor of his 100th birthday.