Two topics in Tree Inference: Locating a phonological network effect in immediate recall and arborescence partitive set form

Schweickert, Richard; Han, Hye Joo

doi:10.1016/j.jmp.2016.02.001

“…1 Many of these problems have practical relevance to graphtheoretic problems encountered in mathematical psychology. Examples include, but are not necessarily limited to, (i) max-cut clustering and its relationship to minimization of the line index of balance for signed graphs (Aref, Mason, & Wilson, 2018;Brusco & Steinley, 2010;Cartwright & Harary, 1956;Harary, 1959), (ii) graph coloring and chromatic numbers (Brusco & Cradit, 2004;Doignon, Ducamp, & Falmagne, 1984;Koppen, 1987), (iii) linear ordering problems, which have relevance to maximum-likelihood paired comparison ranking (Baker & Hubert, 1977;Brusco, 2001, DeCani, 1969Remage & Thompson, 1966;Tritchler & Lockwood, 1991) and directed acyclic graphs (Davis-Stober, Doignon, Fiorini, Glineur, & Regenwetter, 2018;Schweickert & Han, 2016;Schweickert, Fisher, & Goldstein, 2010), and (iv) finding a minimum subset of points that assures a point of interest falls within the convex hull, which is relevant to the study of distribution-free random utility models (e.g., Davis-Stober et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Ising formulations of some graph-theoretic problems in psychological research: Models and methods

Brusco

¹

,

Davis‐Stober

²

,

Steinley

³

2021

Journal of Mathematical Psychology

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It is well known that many NP-hard and NP-complete graph-theoretic problems can be formulated and solved as Ising spin models. We discuss several problems that have a particular history in mathematical psychology, most notably max-cut clustering, graph coloring, a linear ordering problem related to paired comparison ranking and directed acyclic graphs, and the problem of finding a minimum subset of points necessary to contain another point within a convex hull. New Ising spin models are presented for the latter two problems. In addition, we provide MATLAB software programs for obtaining solutions via enumeration of all spin ensembles (when computationally feasible) and simulated annealing. Although we are not advocating that the Ising spin model is the preferred approach for formulation and solution of graph-theoretic problems on conventional digital computers, it does provide a unifying framework for these problems. Moreover, recent progress in the development of quantum computing architecture has shown that Ising spin models can afford enormous improvements in algorithm efficiency when implemented on these platforms, which may ultimately lead to widespread use of the methodology in the future.

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“…1 Many of these problems have practical relevance to graphtheoretic problems encountered in mathematical psychology. Examples include, but are not necessarily limited to, (i) max-cut clustering and its relationship to minimization of the line index of balance for signed graphs (Aref, Mason, & Wilson, 2018;Brusco & Steinley, 2010;Cartwright & Harary, 1956;Harary, 1959), (ii) graph coloring and chromatic numbers (Brusco & Cradit, 2004;Doignon, Ducamp, & Falmagne, 1984;Koppen, 1987), (iii) linear ordering problems, which have relevance to maximum-likelihood paired comparison ranking (Baker & Hubert, 1977;Brusco, 2001, DeCani, 1969Remage & Thompson, 1966;Tritchler & Lockwood, 1991) and directed acyclic graphs (Davis-Stober, Doignon, Fiorini, Glineur, & Regenwetter, 2018;Schweickert & Han, 2016;Schweickert, Fisher, & Goldstein, 2010), and (iv) finding a minimum subset of points that assures a point of interest falls within the convex hull, which is relevant to the study of distribution-free random utility models (e.g., Davis-Stober et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Ising formulations of some graph-theoretic problems in psychological research: models and methods

Brusco¹,

Davis‐Stober²,

Steinley³

2020

Preprint

View full text Add to dashboard Cite

It is well known that many NP-hard and NP-complete graph-theoretic problems can be formulated and solved as Ising spin models. We discuss several problems that have a particular history in mathematical psychology, most notably max-cut clustering, graph coloring, a linear ordering problem related to paired comparison ranking and directed acyclic graphs, and the problem of finding a minimum subset of points necessary to contain another point within a convex hull. New Ising spin models are presented for the latter two problems. In addition, we provide MATLAB software programs for obtaining solutions via enumeration of all spin ensembles (when computationally feasible) and simulated annealing. Although we are not advocating that the Ising spin model is the preferred approach for formulation and solution of graph-theoretic problems on conventional digital computers, it does provide a unifying framework for these problems. Moreover, recent progress in the development of quantum computing architecture has shown that Ising spin models can afford enormous improvements in algorithm efficiency when implemented on these platforms, which may ultimately lead to widespread use of the methodology in the future.

show abstract

Memory representations, tree structures, and parameter polysemy: Comment on Cooper, Greve, and Henson (2017)

Kellen

¹

,

Singmann

²

2017

Cortex

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Two topics in Tree Inference: Locating a phonological network effect in immediate recall and arborescence partitive set form

Cited by 6 publications

References 39 publications

Ising formulations of some graph-theoretic problems in psychological research: Models and methods

Ising formulations of some graph-theoretic problems in psychological research: Models and methods

Ising formulations of some graph-theoretic problems in psychological research: models and methods

Memory representations, tree structures, and parameter polysemy: Comment on Cooper, Greve, and Henson (2017)

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