Related papers: Towards a Universal Measure of Complexity
How much information a fermionic state contains? To address this fundamental question, we define the complexity of a particle-conserving many-fermion state as the entropy of its Fock space probability distribution, minimized over all Fock…
Entropy relates the fast, microscopic behaviour of the elements in a system to its slow, macroscopic state. We propose to use it to explain how, as complexity theory suggests, small scale decisions of individuals form cities. For this, we…
We seek general principles of the structure of the cellular collective activity associated with conscious awareness. Can we obtain evidence for features of the optimal brain organization that allows for adequate processing of stimuli and…
We have proposed novel measures based on the Kolmogorov complexity for use in complex system behavior studies and time series analysis. We have considered background of the Kolmogorov complexity and also we have discussed meaning of the…
We consider the number of Bowen sets which are necessary to cover a large measure subset of the phase space. This introduce some complexity indicator characterizing different kind of (weakly) chaotic dynamics. Since in many systems its…
We resolve a long-standing open question on the relationship between measure-theoretic dynamical complexity and symbolic complexity by establishing the exact word complexity at which measure-theoretic strong mixing manifests: For every…
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…
The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…
There are many methods developed to approximate a cloud of vectors embedded in high-dimensional space by simpler objects: starting from principal points and linear manifolds to self-organizing maps, neural gas, elastic maps, various types…
We analyze the subsystem size scaling of the entanglement entropy of a non-ergodic pure state that can be described by a multi-parametric Gaussian ensemble of complex matrices in a bipartite basis. Our analysis indicates, for a given set of…
We propose to quantify the entanglement of pure states of $N \times N$ bipartite quantum system by defining its Husimi distribution with respect to $SU(N)\times SU(N)$ coherent states. The Wehrl entropy is minimal if and only if the pure…
During a spontaneous change, a macroscopic physical system will evolve towards a macro-state with more realizations. This observation is at the basis of the Statistical Mechanical version of the Second Law of Thermodynamics, and it provides…
As urban critic Jane Jacobs conceived, a city is essentially the problem of organized complexity. What underlies the complexity refers to a structural factor, called living structure, which is defined as a mathematical structure composed of…
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…
There is a commonly recognized paradigm in which a multipartite quantum system described by a density matrix having no product eigenbasis is considered to possess nonclassical correlation. Supporting this paradigm, we define two entropic…
A measure for the complexity of a differentiable function f(x) on an interval is introduced. It is based on approximations of the function by piecewise constant functions. The measure takes into account the quality of the approximation and…
Assembly theory (AT) quantifies selection using the assembly equation and identifies complex objects that occur in abundance based on two measurements, assembly index and copy number, where the assembly index is the minimum number of…
Data complexity is an important concept in the natural sciences and related areas, but lacks a rigorous and computable definition. In this paper, we focus on a particular sense of complexity that is high if the data is structured in a way…
Given a dynamical system with constrained outputs, the maximal admissible set (MAS) is defined as the set of all initial conditions such that the output constraints are satisfied for all time. It has been previously shown that for…
This paper leverages linear systems theory to propose a principled measure of complexity for network systems. We focus on a network of first-order scalar linear systems interconnected through a directed graph. By locally filtering out the…