Related papers: Concept and Definition of Complexity
Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…
The subword complexity of a finite word $w$ of length $N$ is a function which associates to each $n\le N$ the number of all distinct subwords of $w$ having the length $n$. We define the \emph{maximal complexity} C(w) as the maximum of the…
Simplicity is held by many to be the key to general intelligence. Simpler models tend to "generalise", identifying the cause or generator of data with greater sample efficiency. The implications of the correlation between simplicity and…
We propose a more general definition of generic-case complexity, based on using a random process for generating inputs of an algorithm and using the time needed to generate an input as a way of measuring the size of that input.
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…
In this chapter, a statistical measure of complexity is introduced and some of its properties are discussed. Also, some straightforward applications are shown.
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…
This habilitation thesis is intended to be a good introduction to enumeration, the problem of listing solutions. It focuses on the different ways of measuring complexity in enumeration, with a particular emphasis on my contributions to the…
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…
Informational entropy is often identified as physical entropy. This is surprising because the two quantities are differently defined and furthermore the former is a subjective quantity while the latter is an objective one. We describe the…
Several approaches and corresponding definitions of complexity have been developed in different fields. Urban systems are the archetype of complex socio-technical systems concerned with these different viewpoints. We suggest in this chapter…
The complexity and the chaos degree can be used to examine the chaotic aspects of not only several nonlinear classical and quantum physical physics but also life sciences. We will construct a model describing the function of brain in the…
According to Brooke [1] "Usability does not exist in any absolute sense; it can only be defined with reference to particular contexts." That is, one cannot speak of usability without specifying what that particular usability is…
In this paper we give a definition for the Kolmogorov complexity of a pure quantum state. In classical information theory the algorithmic complexity of a string is a measure of the information needed by a universal machine to reproduce the…
The fast changing reality in technical and natural domains perceived by always more accurate observations has drawn attention on new and very broad class of systems with specific behaviour represented under the common wording complexity.…
Biological systems are generally complicated and/or complex. In the former approach, one sets up a model with a large number of parameters to describe the system in detail. The latter approach focuses on understanding the universal aspects…
Complexity theory provides a wealth of complexity classes for analyzing the complexity of decision and counting problems. Despite the practical relevance of enumeration problems, the tools provided by complexity theory for this important…
Even when concepts similar to emergence have been used since antiquity, we lack an agreed definition. However, emergence has been identified as one of the main features of complex systems. Most would agree on the statement ``life is…
This chapter presents a brief review of complexity research in mathematics education. We argue how research on complexity, as it pertains to mathematics education, can be viewed as an epistemological discourse, an historical discourse, a…
In classical mechanics the complexity of a dynamical system is characterized by the rate of local exponential instability which effaces the memory of initial conditions and leads to practical irreversibility. In striking contrast, quantum…