Topic
Effective complexity
About: Effective complexity is a research topic. Over the lifetime, 55 publications have been published within this topic receiving 1932 citations.
Papers published on a yearly basis
Papers
TL;DR: This article defines the concept of an information measure and shows how common information measures such as entropy, Shannon information, and algorithmic information content can be combined to solve problems of characterization, inference, and learning for complex systems.
Abstract: This article defines the concept of an information measure and shows how common information measures such as entropy, Shannon information, and algorithmic information content can be combined to solve problems of characterization, inference, and learning for complex systems. Particularly useful quantities are the effective complexity, which is roughly the length of a compact description of the identified regularities of an entity, and total information, which is effective complexity plus an entropy term that measures the information required to describe the random aspects of the entity. Mathematical definitions are given for both quantities and some applications are discussed. In particular, it is pointed out that if one compares different sets of identified regularities of an entity, the ‘best’ set minimizes the total information, and then, subject to that constraint, minimizes the effective complexity; the resulting effective complexity is then in many respects independent of the observer. © 1996 John Wiley & Sons, Inc.
341 citations
2 Dec 2009
TL;DR: Lower bounds are given on the work factor of idealized versions of code-based cryptography algorithms, taking into account all possible tweaks which could improve their practical complexity.
Abstract: Code-based cryptography is often viewed as an interesting "Post-Quantum" alternative to the classical number theory cryptography. Unlike many other such alternatives, it has the convenient advantage of having only a few, well identified, attack algorithms. However, improvements to these algorithms have made their effective complexity quite complex to compute. We give here some lower bounds on the work factor of idealized versions of these algorithms, taking into account all possible tweaks which could improve their practical complexity. The aim of this article is to help designers select durably secure parameters.
280 citations
TL;DR: In this article, the authors discuss how to define a suitable non-monetary metrics for the value of diversification and the effective complexity of products and introduce a new approach to the definition of these metrics which seems to overcome the previous problems and test it in a series of model systems.
206 citations
TL;DR: In this paper, the authors introduce a statistical measure of the effective model complexity, called the Bayesian complexity, which can be used to assess how many effective parameters a set of data can support and that it is a useful complement to the model likelihood (the evidence) in model selection questions.
Abstract: We introduce a statistical measure of the effective model complexity, called the Bayesian complexity. We demonstrate that the Bayesian complexity can be used to assess how many effective parameters a set of data can support and that it is a useful complement to the model likelihood (the evidence) in model selection questions. We apply this approach to recent measurements of cosmic microwave background anisotropies combined with the Hubble Space Telescope measurement of the Hubble parameter. Using mildly noninformative priors, we show how the 3-year WMAP data improves on the first-year data by being able to measure both the spectral index and the reionization epoch at the same time. We also find that a nonzero curvature is strongly disfavored. We conclude that although current data could constrain at least seven effective parameters, only six of them are required in a scheme based on the $\ensuremath{\Lambda}\mathrm{CDM}$ concordance cosmology.
191 citations
1 Jan 2015
TL;DR: This chapter begins with the tricky concept of randomness, and the powerful approach of the Markov chain, which leads naturally into consideration of random walks.
Abstract: This chapter begins with the tricky concept of randomness. Since a random sequence (e.g., of DNA) represents the null hypothesis for many propositions concerning purported regularities, it is of fundamental importance to master randomness—in so far as it can in principle be mastered. The chapter then moves on to random processes, and the powerful approach of the Markov chain. That leads naturally into consideration of random walks. Noise, already introduced as a disturbance in Chap. 3, is given further consideration. The second part of the chapter deals with complexity. The quantification of complexity may be useful for a number of topics within bioinformatics; for example, everybody is supposed to know that phenotypic complexity has gradually increased during the history of life on Earth, although there appears to be no comprehensive quantitative evidence for it.
73 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 5 |
| 2020 | 3 |
| 2019 | 4 |
| 2018 | 3 |
| 2017 | 2 |
| 2016 | 2 |