Related papers: An algorithmic complexity interpretation of Lin's …
There is no single universally accepted definition of "Complexity". There are several perspectives on complexity and what constitutes complex behaviour or complex systems, as opposed to regular, predictable behaviour and simple systems. In…
We study wave function structure for quantum graphs in the chaotic and disordered regime, using measures such as the wave function intensity distribution and the inverse participation ratio. The result is much less ergodicity than expected…
Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for…
It is discussed and surveyed a numerical method proposed before, that alternative to the usual compression method, provides an approximation to the algorithmic (Kolmogorov) complexity, particularly useful for short strings for which…
Signatures of chaos can be understood by studying quantum systems whose classical counterpart is chaotic. However, the concepts of integrability, non-integrability and chaos extend to systems without a classical analogue. Here, we first…
Unexpectedness is a central concept in Simplicity Theory, a theory of cognition relating various inferential processes to the computation of Kolmogorov complexities, rather than probabilities. Its predictive power has been confirmed by…
This paper is concerned with robust instability analysis for linear multi-agent dynamical systems with cyclic structure. This relates to interesting and important periodic oscillation phenomena in biology and neuronal science, since the…
I explain in what sense the structure of space and time is probably vague or indefinite, a notion I define. This leads to the mathematical representation of location in space and time by a vague interval. From this, a principle of…
We review recent progress in applying information- and computation-theoretic measures to describe material structure that transcends previous methods based on exact geometric symmetries. We discuss the necessary theoretical background for…
Biological information processing is often carried out by complex networks of interconnected dynamical units. A basic question about such networks is that of reliability: if the same signal is presented many times with the network in…
We propose a test based on the theory of algorithmic complexity and an experimental evaluation of Levin's universal distribution to identify evidence in support of or in contravention of the claim that the world is algorithmic in nature. To…
For chaotic systems there is a theory for the decay of the survival probability, and for the parametric dependence of the local density of states. This theory leads to the distinction between "perturbative" and "non-perturbative" regimes,…
We examine the stability of hierarchical triple systems using direct $N$-body simulations without adopting a secular perturbation approximation. We estimate their disruption timescales in addition to the mere stable/unstable criterion, with…
Kolmogorov complexity is a measure of the information contained in a binary string. We investigate here the notion of quantum Kolmogorov complexity, a measure of the information required to describe a quantum state. We show that for any…
The 4/5 and 2/3 laws of turbulence can emerge from a theory of 'engineered' random vector fields $\mathcal{X}_{i}(x,t) =X_{i}(x,t)+\tfrac{\theta}{\sqrt{d(d+2)}} X_{i}(x,t)\psi(x)$ existing within $\mathbf{D}\subset\mathbf{R}^{d}$. Here,…
Developing quantum technologies requires the control and understanding of the non-equilibrium dynamics of quantum information in many-body systems. Local information propagates in the system by creating complex correlations known as…
Define $\|n\|$ to be the complexity of $n$, the smallest number of ones needed to write $n$ using an arbitrary combination of addition and multiplication. Define $n$ to be stable if for all $k\ge 0$, we have $\|3^k n\|=\|n\|+3k$. In [7],…
Estimation of structure, such as in variable selection, graphical modelling or cluster analysis is notoriously difficult, especially for high-dimensional data. We introduce stability selection. It is based on subsampling in combination with…
Model selection in clustering requires (i) to specify a suitable clustering principle and (ii) to control the model order complexity by choosing an appropriate number of clusters depending on the noise level in the data. We advocate an…
The global steady state of a system in thermal equilibrium exponentially favors configurations with lesser energy. This principle is a powerful explanation of self-organization because energy is a local property of a configuration. For…