Physical Sciences and Mathematics Commons^™

Reconstructability Of Epistatic Functions, Martin Zwick, Joe Fusion, Beth Wilmot

Systems Science Faculty Publications and Presentations

Background: Reconstructability Analysis (RA) has been used to detect epistasis in genomic data; in that work, even the simplest RA models (variable-based models without loops) gave performance superior to two other methods. A follow-on theoretical study showed that RA also offers higher-resolution models, namely variable-based models with loops and state-based models, likely to be even more effective in modeling epistasis, and also described several mathematical approaches to classifying types of epistasis.

Methods: The present paper extends this second study by discussing a non-standard use of RA: the analysis of epistasis in quantitative as opposed to nominal variables; such quantitative variables …

Reconstructability Analysis Of Epistasis, Martin Zwick

Systems Science Faculty Publications and Presentations

The literature on epistasis describes various methods to detect epistatic interactions and to classify different types of epistasis. Reconstructability analysis (RA) has recently been used to detect epistasis in genomic data. This paper shows that RA offers a classification of types of epistasis at three levels of resolution (variable-based models without loops, variable-based models with loops, state-based models). These types can be defined by the simplest RA structures that model the data without information loss; a more detailed classification can be defined by the information content of multiple candidate structures. The RA classification can be augmented with structures from related …

Enhancements To Crisp Possibilistic Reconstructability Analysis, Anas Al-Rabadi, Martin Zwick

Systems Science Faculty Publications and Presentations

Modified Reconstructibility Analysis (MRA), a novel decomposition within the framework of set-theoretic (crisp possibilistic) Reconstructibility Analysis, is presented. It is shown that in some cases while 3-variable NPN-classified Boolean functions are not decomposable using Conventional Reconstructibility Analysis (CRA), they are decomposable using Modified Reconstructibility Analysis (MRA). Also, it is shown that whenever a decomposition of 3-variable NPN-classified Boolean functions exists in both MRA and CRA, MRA yields simpler or equal complexity decompositions. A comparison of the corresponding complexities for Ashenhurst-Curtis decompositions, and Modified Reconstructibility Analysis (MRA) is also presented. While both AC and MRA decompose some but …

An Overview Of Reconstructability Analysis, Martin Zwick

Systems Science Faculty Publications and Presentations

This paper is an overview of reconstructability analysis (RA), a discrete multivariate modeling methodology developed in the systems literature; an earlier version of this tutorial is Zwick (2001). RA was derived from Ashby (1964), and was developed by Broekstra, Cavallo, Cellier Conant, Jones, Klir, Krippendorff, and others (Klir, 1986, 1996). RA resembles and partially overlaps log‐line (LL) statistical methods used in the social sciences (Bishop et al., 1978; Knoke and Burke, 1980). RA also resembles and overlaps methods used in logic design and machine learning (LDL) in electrical and computer engineering (e.g. Perkowski et al., 1997). Applications of RA, like …