Related papers: Comment on "Simple Measure of Complexity"
In this work, we develop a new complexity metric for an important class of low-rank matrix optimization problems in both symmetric and asymmetric cases, where the metric aims to quantify the complexity of the nonconvex optimization…
This entry in the Encyclopedia of Complexity and Systems Science, Springer present a summary of some of the concepts and calculational tools that have been developed in attempts to apply statistical physics approaches to seismology. We…
We revisit the classical concept of near-decomposability in complex systems, introduced by Herbert Simon in his foundational article The Architecture of Complexity, by developing an explicit quantitative analysis based on singular…
The LMC complexity, an indicator of complexity based on a probabilistic description, is revisited. A straightforward approach allows us to establish the time evolution of this indicator in a near-equilibrium situation and gives us a new…
This study is focused on the qualitative and quantitative characterization of chaotic systems with the use of symbolic description. We consider two famous systems: Lorenz and R\"ossler models with their iconic attractors, and demonstrate…
In classical finite-range spin systems, especially those with disorder such as spin glasses, a low-temperature Gibbs state may be a mixture of a number of pure or ordered states; the complexity of the Gibbs state has been defined in the…
The nature of concept learning is a core question in cognitive science. Theories must account for the relative difficulty of acquiring different concepts by supervised learners. For a canonical set of six category types, two distinct…
It is shown that all the known uncertainty relations are the secondary consequences of Robertson's relation. The basic idea is to use the Heisenberg picture so that the time development of quantum mechanical operators incorporate the…
Characterizing complexity and criticality in quantum systems requires diagnostics that are both computationally tractable and physically insightful. We apply a measure of quantum state complexity for n-qubit systems, defined as the…
The aim of this paper is to generalize the definition of complexity for the static self-gravitating structure in $f(R,T,Q)$ gravitational theory, where $R$ is the Ricci scalar, $T$ is the trace part of energy momentum tensor and $Q\equiv…
Complexity remains one of the central challenges in science and technology. Although several approaches at defining and/or quantifying complexity have been proposed, at some point each of them seems to run into intrinsic limitations or…
It is well-known that SRB and equilibrium measures for uniformly hyperbolic flows admit a product structure in terms of measures on stable and unstable leaves with scaling properties given by the potential function. We describe a…
We investigate the universality of multi-spin systems in architectures of various symmetries of coupling type and topology. Explicit reachability sets under symmetry constraints are provided. Thus for a given (possibly symmetric)…
Motivated on the one hand by recent results on isochronous dynamical systems, and on the other by quantum gravity applications of complex metrics, we show that, if such enlarged class of metrics is considered, one can easily obtain periodic…
Measure-theoretic slow entropy is a more refined invariant than the classical measure-theoretic entropy to characterize the complexity of dynamical systems with subexponential growth rates of distinguishable orbit types. In this paper we…
We apply the recently developed notion of complexity for field theory to a quantum quench through a critical point in 1+1 dimensions. We begin with a toy model consisting of a quantum harmonic oscillator, and show that complexity exhibits…
Information-theoretic inequalities play a fundamental role in numerous scientific and technological areas as they generally express the impossibility to have a complete description of a system via a finite number of information measures. In…
The term complexity derives etymologically from the Latin plexus, which means interwoven. Intuitively, this implies that something complex is composed by elements that are difficult to separate. This difficulty arises from the relevant…
A finite relational structure A is called compact if for any infinite relational structure B of the same type, the existence of a homomorphism from B to A is equivalent to the existence of homomorphisms from all finite substructures of B to…
Quantifying the complexity of systems consisting of many interacting parts has been an important challenge in the field of complex systems in both abstract and applied contexts. One approach, the complexity profile, is a measure of the…