We propose a novel data delivery strategy, called Whirlpool, for efficient SHM using Wireless Sensor Networks. Whirlpool implements a rotating interrogation of a monitoring structure and provides collision-aware scheduling of the monitoring queries. The Whirlpool strategy can be tuned for the required Quality of Data (QoD). We apply Whirlpool to examine the unique properties of output signals o...

On an influential account, chaos is explained in terms of random behaviour; and random behaviour in turn is explained in terms of having positive Kolmogorov-Sinai entropy (KSE). Though intuitively plausible, the association of the KSE with random behaviour needs justification since the definition of the KSE does not make reference to any notion that is connected to randomness. I provide this ju...

We show that the coarse-grained quantum baker's map exhibits a linear entropy increase at an asymptotic rate given by the Kolmogorov-Sinai entropy of the classical chaotic baker's map. The starting point of our analysis is a symbolic representation of the map on a string of N qubits, i.e., an N-bit register of a quantum computer. To coarse grain the quantum evolution, we make use of the decoher...

We study a measure entropy for finitely generated free group actions called f-invariant entropy. The f-invariant entropy was developed by L. Bowen and is essentially a special case of his measure entropy theory for actions of sofic groups. In this paper we relate the f-invariant entropy of a finitely generated free group action to the f-invariant entropy of the restricted action of a subgroup. ...

Lempel and Ziv (1976) proposed a computable string production-complexity. In this paper, our emphasis is on providing the rigorous development, where possible, for the theoretical aspects of a more recent and contrasting measure of string complexity. We derive expressions for complexity bounds subject to certain constraints. We derive an analytic approximation to the upper bound to linearize th...

We demonstrate that discrete Lyapunov exponents are isomorphic to numeric overflows of the capacity of an arbitrary noiseless and memoryless channel in a Shannon communication model with feedback. The isomorphism allows the understanding of Lyapunov exponents in terms of Information Theory, rather than the traditional definitions in chaos theory. The result also implies alternative approaches t...

Theorem 1 (Jewett-Krieger). Let (X,A , μ, S) be an ergodic dynamical system. Then there is a compact space Y and a homeomorphism T on Y , which is uniquely ergodic and minimal, such that if ν denotes the unique T -invariant probability measure on Y and B the Borel σalgebra of Y , the ergodic dynamical system (Y,B, ν, T ) is equivalent to (X,A , μ, S). In addition, (Y,B, ν, T ) can be constructe...

In the case of ergodicity much of the structure of a one-dimensional time-discrete dynamical system is already determined by its ordinal structure. In order to explain this phenomenon more precisely, we show that ordinal patterns, which describe the up and down in the orbits of an ergodic Borel measurable map on a subset of the real numbers, are in a certain sense generating. On this base we gi...

We consider a one-parameter family of expanding interval maps {Tα}α∈[0,1] (japanese continued fractions) which include the Gauss map (α = 1) and the nearest integer and by-excess continued fraction maps (α = 1 2 , α = 0). We prove that the Kolmogorov-Sinai entropy h(α) of these maps depends continuously on the parameter and that h(α) → 0 as α → 0. Numerical results suggest that this convergence...