The study of coupled human-natural systems has been among the increased focus of scientific investigation for the last decade. Whilst many of the theoretical foundations in the study of complexity in such systems exist for a while, our empirical evidence-based inference reveals more insights into the challenges and opportunities for deeper understanding of the complexity in the coupled systemic interactions. Going beyond simple inferences, such understanding leads us to explore collective...

There are competing schools of thought about the question of whether spacetime is fundamentally continuous or discrete. Here, we consider the possibility that spacetime could be simultaneously continuous and discrete, in the same mathematical way that information can be simultaneously continuous and discrete. The equivalence of continuous information and discrete information, which is of key importance in signal processing, is established by the Shannon sampling theory: for any band-limited...

Cellular automata (CA) were initially conceived as a formal model to study self-replication in artificial systems. Although self-replication in natural systems is characterized by exponential population increase until exhaustion of resources, after more than fifty years of research, no CA-based self-replicator has come close to exhibiting such rapid population growth. We believe this is due to an intrinsic limitation of CA's, namely, the inability to model extended structures held together by...

Our new book, "Loving and Hating Mathematics," is about the emotional, social and political aspects of mathematical life. A major chapter tells of mathematical communities, such as Gottingen in the early 20th century, Bourbaki in Paris, and the Courant Institute in New York. The creation of such a productive community often depends on the leadership and vision of a vital, charismatic figure How the community continues and endures depends on how its members internalize and develop that...

We investigate the neural mechanisms underlying decision-making by conducting electrophysiological recordings in awake monkeys while they perform a motion discrimination task

Proponents of nuclear power say that it is the only real alternative to coal-fired power plants if CO2 emissions are to be greatly reduced because wind and solar are too intermittent and unreliable. But massive alteration of the Earth’s climate and making plutonium in costly boilers called reactors turbines are not the only alternatives.

This talk is an overview of my work as a graduate fellow at the Santa Fe Institute on different aspects of the statics and dynamics of the mutual fund industry.

Today, the reconstruction of the organismal evolutionary tree is basedmainly on molecular sequence data. However, sequence data are sometimes insufficient to reliably resolve in particular deep branches.

Much of ergodic theory deals with deterministic dynamical systems, whereas this talk deals with stochastic systems.