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Algorithmic Information Dynamics: A Computational Approach to Causality from Cells to Networks

A topical collection in Entropy (ISSN 1099-4300). This collection belongs to the section "Complexity".

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Editors


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Collection Editor
School of Biomedical Engineering and Imaging Sciences, King’s College London, London WC2R 2LS, UK
Interests: algorithmic information theory; complex systems; philosophy of algorithmic randomness; Kolmogorov complexity; computational biology; digital philosophy; programmability; natural computation; cellular automata; algorithmic probability; logical depth; measures of sophistication
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Collection Editor
1. National Laboratory for Scientific Computing (LNCC), Petropolis 25651-075, RJ, Brazil
2. Algorithmic Nature Group, Laboratoire de Recherche Scientifique (LABORES) for the Natural and Digital Sciences, 75005 Paris, France
3. Oxford Immune Algorithmics, Reading RG1 3EU, UK
Interests: algorithmic information; complexity; emergence; self-organization; evolution

Topical Collection Information

Dear Colleagues,

Classical probability theory and traditional statistics have long helped scientists to find meaningful signals amid the noise and thereby make sense of the world. However, classical approaches have proven a little threadbare in today’s landscape of large datasets and complex data, which are driving new insights in disciplines ranging from biology to ecology to economics. This is as true in biology, with the advent of new techniques of genome editing, as it is in astronomy, with telescope surveys charting the entire sky in the search for new Earth-like planets. The data have changed. Maybe it is time our data analysis tools did, too.

Algorithmic information dynamics (AID) is a new type of discrete calculus based on computer programming, employed to study complex systems by exploring the software space of models explaining a system subject to changes or perturbations. The objective is to look for computable mechanistic generating models and first principles, thereby ushering in the next generation of scientific discovery and model-driven machine learning. Following a popular online course sponsored by the Santa Fe Institute, and the publication in recent years of a number of papers (by original authors as well as independent groups) that utilize AID based on new tools such as the coding theorem and the block decomposition method (motivated by algorithmic probability) to discover new knowledge, AID is becoming a tool fully equal to the challenge of studying rich, complex systems. Whereas we had only been using weak (e.g., computable) measures to study complex systems, now it is possible to match data to models in degree of sophistication.

We encourage authors and researchers to continue exploring how AID can help us to understand new aspects of systems science by building rich causal computational models and submitting their results to this Topical Collection. They would thereby be contributing to progress in the methodological aspects of systems science, advancing it beyond its current reliance on simplistic data analysis and ad hoc measures.

Dr. Hector Zenil
Dr. Felipe S. Abrahão
Collection Editors

Manuscript Submission Information

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Published Papers (1 paper)

2024

13 pages, 406 KiB  
Article
An Additively Optimal Interpreter for Approximating Kolmogorov Prefix Complexity
by Zoe Leyva-Acosta, Eduardo Acuña Yeomans and Francisco Hernandez-Quiroz
Entropy 2024, 26(9), 802; https://doi.org/10.3390/e26090802 - 20 Sep 2024
Viewed by 402
Abstract
We study practical approximations of Kolmogorov prefix complexity (K) using IMP2, a high-level programming language. Our focus is on investigating the optimality of the interpreter for this language as the reference machine for the Coding Theorem Method (CTM). This method is [...] Read more.
We study practical approximations of Kolmogorov prefix complexity (K) using IMP2, a high-level programming language. Our focus is on investigating the optimality of the interpreter for this language as the reference machine for the Coding Theorem Method (CTM). This method is designed to address applications of algorithmic complexity that differ from the popular traditional lossless compression approach based on the principles of algorithmic probability. The chosen model of computation is proven to be suitable for this task, and a comparison to other models and methods is conducted. Our findings show that CTM approximations using our model do not always correlate with the results from lower-level models of computation. This suggests that some models may require a larger program space to converge to Levin’s universal distribution. Furthermore, we compare the CTM with an upper bound on Kolmogorov complexity and find a strong correlation, supporting the CTM’s validity as an approximation method with finer-grade resolution of K. Full article
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