Related papers: A Statistical Measure of Complexity
This paper introduces a qualitative measure of ambiguity and analyses its relationship with other measures of uncertainty. Probability measures relative likelihoods, while ambiguity measures vagueness surrounding those judgments. Ambiguity…
Reduce and control complexity is an essential practice in software design. Cyclomatic complexity (CC) is one of the most popular software metrics, applied for more than 40 years. Despite CC is an interesting metric to highlight the number…
The "quantum complexity" of a unitary operator measures the difficulty of its construction from a set of elementary quantum gates. While the notion of quantum complexity was first introduced as a quantum generalization of the classical…
In this exploratory note we ask the question of what a measure of performance for all tasks is like if we use a weighting of tasks based on a difficulty function. This difficulty function depends on the complexity of the (acceptable)…
New measures for the quantization of systems with constraints are discussed and applied to several examples, in particular, examples of alternative but equivalent formulations of given first-class constraints, as well as a comparison of…
Several complexity metrics are described which are related to logic structure, data structure and size of spreadsheet models. They primarily concentrate on the dispersion of cell references and cell paths. Most metrics are newly defined,…
Interpreting experimental data in high school experiments can be a difficult task for students, especially when there is large variation in the data. At the same time, calculating the standard deviation poses a challenge for students. In…
This article is a survey on the topic of polynomial amoebas. We review results of papers written on the topic with an emphasis on its computational aspects. Polynomial amoebas have numerous applications in various domains of mathematics and…
A general approach to the measurement of an observable with pre- and post-selection is presented. The limit of weak measurement is studied in detail, and it is shown that the phase of the probe, including a Hamiltonian contribution to it,…
A survey of properties of a sequence of coefficients appearing in the evaluation of a quartic definite integral is presented. These properties are of analytical, combinatorial and number-theoretical nature.
In this article we define a metric on C(S1; S1). Also, we give some density results in C(S^1; S^1).
We propose a new type of entropic descriptor that is able to quantify the statistical complexity (a measure of complex behaviour) by taking simultaneously into account the average departures of a system's entropy S from both its maximum…
We propose a measure of learning efficiency for non-finite state spaces. We characterize the complexity of a learning problem by the metric entropy of its state space. We then describe how learning efficiency is determined by this measure…
The emergence of a complex, large-scale organisation of cosmic matter into the Cosmic Web is a beautiful exemplification of how complexity can be produced by simple initial conditions and simple physical laws. In the epoch of Big Data in…
Analysis of the process of accumulation of the results of measurements shows that the success of this process substantially depends on the possibility of coordination of actions of two participants of the process - preparator who prepares…
We will review some of the theoretical progresses that have been in the study of complex systems in physics and of their applications to biology.
On account of a greater need for understanding the complexity of time series like physiological time series, financial time series, and many more that enter into picture for their inculpation with real-world problems, several complexity…
Written language is complex. A written text can be considered an attempt to convey a meaningful message which ends up being constrained by language rules, context dependence and highly redundant in its use of resources. Despite all these…
We study the problem of constructing positive representations of complex measures. In this paper we consider complex densities on a direct product of $U(1)$ groups and look for representations by probability distributions on the…
In this work the one-parameter Fisher-R\'enyi measure of complexity for general $d$-dimensional probability distributions is introduced and its main analytic properties are discussed. Then, this quantity is determined for the hydrogenic…