Nearly thirty years of chaos research have shown that chaos is an ubiquitous phenomenon. Almost any dynamical system with a sufficiently large phase space described by nonlinear equations shows some kind of complexity in its time evolution, i.e. chaos. The degree of complexity is measured by topological entropy, Lyapunov exponents, decay of correlations, and, in the case of dissipative systems,...

The element of surprise and the suddenness of insight make the study of creative behavior a prime candidate for concepts and methods from nonlinear dynamical systems (NDS) theory. The first contribution in this area, as nearly as we can discern, was chance-configuration theory (Simonton, 1988), which explained how random flows of idea elements self-organize into the core of a solution to a prob...

This paper intends to provide suggestions of how sustainable building simulation might profit from mathematical models derived from chaos and complexity approaches. It notes that with the increasing complexity of building systems which are capable of intelligently adjusting buildings' performance from the environment and occupant behaviour and adapting to environmental extremes, building perfor...

We develop a novel generalization bound for learning the kernel problem. First, we show that the generalization analysis of the kernel learning problem reduces to investigation of the suprema of the Rademacher chaos process of order 2 over candidate kernels, which we refer to as Rademacher chaos complexity. Next, we show how to estimate the empirical Rademacher chaos complexity by well-establis...

Motivated by the evolution of complex bird songs, an abstract imitation game is proposed to study the increase of dynamical complexity: Artificial ”birds” display a ”song” time series to each other, and those imitate the other’s song better win the game. With the introduction of population dynamics according to the score of the game and the mutation of parameters for the song dynamics, the dyna...

In this paper we develop a novel probabilistic generalization bound for regularized kernel learning algorithms. First, we show that generalization analysis of kernel learning algorithms reduces to investigation of the suprema of homogeneous Rademacher chaos process of order two over candidate kernels, which we refer to it as Rademacher chaos complexity. Our new methodology is based on the princ...

In this paper we develop a novel probabilistic generalization bound for learning the kernel problem. First, we show that the generalization analysis of the kernel learning algorithms reduces to investigation of the suprema of the Rademacher chaos process of order two over candidate kernels, which we refer to as Rademacher chaos complexity. Next, we show how to estimate the empirical Rademacher ...

In this paper we develop a novel probabilistic generalization bound for learning the kernel problem. First, we show that the generalization analysis of the regularized kernel learning system reduces to investigation of the suprema of the Rademacher chaos process of order two over candidate kernels, which we refer to as Rademacher chaos complexity. Next, we show how to estimate the empirical Rad...