Related papers: A Statistical Measure of Complexity
We review several statistical complexity measures proposed over the last decade and a half as general indicators of structure or correlation. Recently, Lopez-Ruiz, Mancini, and Calbet [Phys. Lett. A 209 (1995) 321] introduced another…
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…
We study the build up of complexity on the example of 1 kg matter in different forms. We start on the simplest example of ideal gases, and then continue with more complex chemical, biological, life and social and technical structures. We…
A property, or statistical functional, is said to be elicitable if it minimizes expected loss for some loss function. The study of which properties are elicitable sheds light on the capabilities and limitations of point estimation and…
A weak measurement consists in coupling a system to a probe in such a way that constructive interference generates a large output. So far, only the average output of the probe and its variance were studied. Here, the characteristic function…
This work builds on a rich discourse surrounding the social brain hypothesis as well as the definition and quantification of social complexity. We believe this manuscript provides a new perspective on the topic by pairing a conceptual…
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.…
Since human randomness production has been studied and widely used to assess executive functions (especially inhibition), many measures have been suggested to assess the degree to which a sequence is random-like. However, each of them…
We present an analysis of eight measures used for quantifying morphological complexity of natural languages. The measures we study are corpus-based measures of morphological complexity with varying requirements for corpus annotation. We…
The integral with respect to a multidimensional stochastic measure, for which we assume only $\sigma$-additivity in probability, is studied. The continuity and differentiability of its realizations are established.
A stochastic dynamics framework for the study of complex systems is presented.
Several measures of non-convexity (departures from convexity) have been introduced in the literature, both for sets and functions. Some of them are of geometric nature, while others are more of topological nature. We address the statistical…
The paper presents a construction of a quantitative measure of variability for parameter estimates in the data fitting problem under interval uncertainty. It shows the degree of variability and ambiguity of the estimate, and the need for…
The problem of advancing coordinatization of mathematics is considered. The need to develop a theory for measuring value and complexity of mathematical implications and proofs is discussed including motivations, benefits and implementation…
The coupling complexity index is an information measure introduced within the framework of ordinal symbolic dynamics. This index is used to characterize the complexity of the relationship between dynamical system components. In this work,…
Complexity of patterns is a key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal…
Measuring software complexity plays an important role to meet the demands of complex software. The cyclomatic complexity is one of most used and renowned metric among the other three proposed and researched metrics that are namely: Line of…
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.…
We describe the fundamental constructions and properties of determinantal probability measures and point processes, giving streamlined proofs. We illustrate these with some important examples. We pose several general questions and…
In this paper we introduce the notions of statistical convergence and statistical Cauchyness of sequences in a metric-like space. We study some basic properties of these notions