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Related papers: Open, Reproducible Calculation of Assembly Indices

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The assembly index of assembly theory quantifies the minimal number of composition steps required to construct an object from elementary components. The study proves that the decision version of the assembly index problem is NP-complete,…

Computational Complexity · Computer Science 2026-04-21 Piotr Masierak

Assembly theory (AT) quantifies selection using the assembly equation and identifies complex objects that occur in abundance based on two measurements, assembly index and copy number, where the assembly index is the minimum number of…

Assembly theory has received considerable attention in the recent past. Here we analyze the formal framework of this model and show that assembly pathways coincide with certain minimal hyperpaths in B-hypergraphs. This makes it possible to…

Discrete Mathematics · Computer Science 2025-05-30 Christoph Flamm , Daniel Merkle , Peter F. Stadler

Assembly Theory, as developed by Cronin and co-workers, assigns to an object an assembly index: the minimal number of binary join operations required to build at least one copy of the object from a specified set of basic building blocks,…

Formal Languages and Automata Theory · Computer Science 2026-02-06 Piotr Masierak

Assembly Theory (AT) was developed to help distinguish living from non-living systems. The theory is simple as it posits that the amount of selection or Assembly is a function of the number of complex objects where their complexity can be…

Other Quantitative Biology · Quantitative Biology 2024-06-12 Sara I. Walker , Cole Mathis , Stuart Marshall , Leroy Cronin

This document presents a combinatorial framework for analyzing assembly systems using generating functions. We explore the theory through concrete examples, such as linear polymers, and develop recursive equations to characterize valid…

Combinatorics · Mathematics 2025-01-22 Andrés Ortiz-Muñoz

The \emph{index set} of a computable structure $\mathcal{A}$ is the set of indices for computable copies of $\mathcal{A}$. We determine the complexity of the index sets of various mathematically interesting structures, including arbitrary…

Logic · Mathematics 2008-03-25 Wesley Calvert , Valentina S. Harizanov , Julia F. Knight , Sara Miller

Quantifying the evolution and complexity of materials is of importance in many areas of science and engineering, where a central open challenge is developing experimental complexity measurements to distinguish random structures from evolved…

Materials Science · Physics 2025-02-26 Keith Y Patarroyo , Abhishek Sharma , Ian Seet , Ignas Packmore , Sara I. Walker , Leroy Cronin

Inspired by an analytic construction of Chang, Weinberger and Yu, we define an assembly map in relative geometric $K$-homology. The properties of the geometric assembly map are studied using a variety of index theoretic tools (e.g., the…

K-Theory and Homology · Mathematics 2019-03-15 Robin J. Deeley , Magnus Goffeng

Assembly Theory (AT) and its central measure, the assembly index (Ai), represent an invaluable opportunity to address some of the most persistent and widespread conflations and misconceptions about computability and complexity theory in…

We demonstrate that the assembly pathway method underlying assembly theory (AT) is an encoding scheme widely used by popular statistical compression algorithms. We show that in all cases (synthetic or natural) AT performs similarly to other…

Information Theory · Computer Science 2024-08-15 Abicumaran Uthamacumaran , Felipe S. Abrahão , Narsis A. Kiani , Hector Zenil

Binary code is pervasive, and binary analysis is a key task in reverse engineering, malware classification, and vulnerability discovery. Unfortunately, while there exist large corpora of malicious binaries, obtaining high-quality corpora of…

Cryptography and Security · Computer Science 2024-11-05 Chang Liu , Rebecca Saul , Yihao Sun , Edward Raff , Maya Fuchs , Townsend Southard Pantano , James Holt , Kristopher Micinski

We prove the full equivalence between Assembly Theory (AT) and Shannon Entropy via a method based upon the principles of statistical compression renamed `assembly index' that belongs to the LZ family of popular compression algorithms (ZIP,…

Information Theory · Computer Science 2024-04-04 Felipe S. Abrahão , Santiago Hernández-Orozco , Narsis A. Kiani , Jesper Tegnér , Hector Zenil

Developing machine learning enabled smart manufacturing is promising for composite structures assembly process. To improve production quality and efficiency of the assembly process, accurate predictive analysis on dimensional deviations and…

Machine Learning · Statistics 2020-11-24 Cheolhei Lee , Jianguo Wu , Wenjia Wang , Xiaowei Yue

In this tutorial-style review we discuss basic concepts of coupled cluster theory and recent developments that increase its computational efficiency for calculations of molecules, solids and materials in general. We will touch upon the…

Materials Science · Physics 2020-04-15 Igor Ying Zhang , Andreas Grüneis

Clustering ensemble has emerged as an important research topic in the field of machine learning. Although numerous methods have been proposed to improve clustering quality, most existing approaches overlook the need for interpretability in…

Machine Learning · Computer Science 2025-06-09 Hang Lv , Lianyu Hu , Mudi Jiang , Xinying Liu , Zengyou He

Many random combinatorial objects have a component structure whose joint distribution is equal to that of a process of mutually independent random variables, conditioned on the value of a weighted sum of the variables. It is interesting to…

Probability · Mathematics 2013-08-16 Richard Arratia , Simon Tavare

GeneralizIT is a Python package designed to streamline the application of Generalizability Theory (G-Theory) in research and practice. G-Theory extends classical test theory by estimating multiple sources of error variance, providing a more…

Applications · Statistics 2024-12-10 Tyler J. Smith , Theresa Kline , Adrienne Kline

Structural equation modeling is widely used in IS research. However, inconsistent construct definitions impede the cumulative development of knowledge. In this work, we present an approach that aims at the integration of structural equation…

Computation and Language · Computer Science 2026-05-19 Maximilian Reinhardt , Jonas Scharfenberger , Burkhardt Funk

Assembly planning is the core of automating product assembly, maintenance, and recycling for modern industrial manufacturing. Despite its importance and long history of research, planning for mechanical assemblies when given the final…

Robotics · Computer Science 2022-11-09 Yunsheng Tian , Jie Xu , Yichen Li , Jieliang Luo , Shinjiro Sueda , Hui Li , Karl D. D. Willis , Wojciech Matusik
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