Related papers: Comment on "Simple Measure of Complexity"
Based on general and minimal properties of the {\it discrete} circuit complexity, we define the complexity in {\it continuous} systems in a geometrical way. We first show that the Finsler metric naturally emerges in the geometry of the…
We introduce amorphic complexity as a new topological invariant that measures the complexity of dynamical systems in the regime of zero entropy. Its main purpose is to detect the very onset of disorder in the asymptotic behaviour. For…
A simplified Heisenberg spin model is studied in order to examine the idea of decoherence in closed quantum systems. For this purpose, we present a quantifiable definition to quantum coherence $\Xi$, and discuss in some detail a general…
In this essay, I attempt to provide supporting evidence as well as some balance for the thesis on `Transforming socio-economics with a new epistemology' presented by Hollingworth and Mueller (2008). First, I review a personal highlight of…
Lattice data, taken since 1998 near the critical line of a 4D Ising model, have been supporting the large logarithmic rescaling of the scalar condensate predicted in the alternative description of symmetry breaking proposed by Consoli and…
We introduce a robust belief-based measure of complexity. The idea is that task A is deemed more complex than task B if the probability of solving A correctly is smaller than the probability of solving B correctly regardless of the reward.…
A general notion of information-related complexity applicable to both natural and man-made systems is proposed. The overall approach is to explicitly consider a rational agent performing a certain task with a quantifiable degree of success.…
We present a framework for selecting and developing measures of dependence when the goal is the quantification of a relationship between two variables, not simply the establishment of its existence. Much of the literature on dependence…
This article discusses two recent works by the author, one with Brown and Hurtado on Zimmer's conjecture and one with Bader, Miller and Stover on totally geodesic submanifolds of real and complex hyperbolic manifolds. The main purpose of…
We provide conditions which guarantee that ergodic measures are dense in the simplex of invariant probability measures of a dynamical system given by a continuous map acting on a Polish space. Using them we study generic properties of…
The question of how irreversibility can emerge as a generic phenomena when the underlying mechanical theory is reversible has been a long-standing fundamental problem for both classical and quantum mechanics. We describe a mechanism for the…
Complex macroscopic behaviour can arise in many-body systems with only very simple elements as a consequence of the combination of competition and inhomogeneity. This paper attempts to illustrate how statistical physics has driven this…
Asymptotic equilibrium stresses are defined for countably infinite tensegrities and generalisations of the Roth-Whiteley characterisation of first-order rigidity are obtained. Generalisations of prestress stability and second order rigidity…
A pedagogical description of a simple ungeometrical approach to General Relativity is given, which follows the pattern of well understood field theories, such as electrodynamics. This leads quickly to most of the important weak field…
Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less…
We investigate a possible unified theory of all interactions which is based only on fundamental spinor fields. The vielbein and metric arise as composite objects. The effective quantum gravitational theory can lead to a modification of…
We have recently shown that in non-equilibrium spin systems at criticality the limit $\Xin$ of the fluctuation-dissipation ratio X(t,tw) for t >> tw >> 1 can be measured using observables such as magnetization or energy [Phys. Rev.\ E {\bf…
In this comment on the work of F. Buscemi, M.J.W. Hall, M. Ozawa and M.M. Wilde [PRL 112, 050401, 2014, arXiv:1310.6603], we point out a misrepresentation of measures of error and disturbance introduced in our recent work [PRL 111, 160405,…
We study Nielsen complexity and Fubini-Study complexity for a class of exactly solvable one dimensional spin systems. Our examples include the transverse XY spin chain and its natural extensions, the quantum compass model with and without…
We introduce a novel quantity for general dynamical systems, which we call the asymptotic uniform complexity. We prove an inequality relating the asymptotic uniform complexity of a dynamical system to its mean topological matching number.…