*Jelena ProkiĆ and John Nerbonne*

- Published in print:
- 2009
- Published Online:
- September 2012
- ISBN:
- 9780748640300
- eISBN:
- 9780748671380
- Item type:
- chapter

- Publisher:
- Edinburgh University Press
- DOI:
- 10.3366/edinburgh/9780748640300.003.0009
- Subject:
- Linguistics, Applied Linguistics and Pedagogy

Dialectometry is a multidisciplinary field that uses various quantitative methods in the analysis of dialect data. Very often those techniques include classification algorithms such as hierarchical ...
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Dialectometry is a multidisciplinary field that uses various quantitative methods in the analysis of dialect data. Very often those techniques include classification algorithms such as hierarchical clustering algorithms used to detect groups within certain dialect area. Although known for their instability, clustering algorithms are often applied without evaluation or with only partial evaluation. Very small differences in the input data can produce substantially different grouping of dialects. This chapter evaluates algorithms used to detect groups among language dialect varieties measured at the aggregate level. The data used in this research is dialect pronunciation data that consists of various pronunciations of 156 words collected all over Bulgaria. The distances between words are calculated using Levenshtein algorithm, which also resulted in the calculation of the distances between each two sites in the data set. Seven hierarchical clustering algorithms, as well as the k-means and neighbor-joining algorithm, are applied to the calculated distances.Less

Dialectometry is a multidisciplinary field that uses various quantitative methods in the analysis of dialect data. Very often those techniques include classification algorithms such as hierarchical clustering algorithms used to detect groups within certain dialect area. Although known for their instability, clustering algorithms are often applied without evaluation or with only partial evaluation. Very small differences in the input data can produce substantially different grouping of dialects. This chapter evaluates algorithms used to detect groups among language dialect varieties measured at the aggregate level. The data used in this research is dialect pronunciation data that consists of various pronunciations of 156 words collected all over Bulgaria. The distances between words are calculated using Levenshtein algorithm, which also resulted in the calculation of the distances between each two sites in the data set. Seven hierarchical clustering algorithms, as well as the k-means and neighbor-joining algorithm, are applied to the calculated distances.

*Joseph F. Boudreau and Eric S. Swanson*

- Published in print:
- 2017
- Published Online:
- February 2018
- ISBN:
- 9780198708636
- eISBN:
- 9780191858598
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198708636.003.0020
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The thermodynamic properties of spin systems are evaluated with Monte Carlo methods. A review of classical thermodynamics is followed by a discussion of critical exponents. The Monte Carlo method is ...
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The thermodynamic properties of spin systems are evaluated with Monte Carlo methods. A review of classical thermodynamics is followed by a discussion of critical exponents. The Monte Carlo method is then applied to the two-dimensional Ising model with the goal of determining the phase diagram for magnetization. Boundary conditions, the reweighting method, autocorrelation, and critical slowing down are all explored. Cluster algorithms for overcoming critical slowing down are developed next and shown to dramatically reduce autocorrelation. A variety of spin systems that illustrate first, second, and infinite order (topological) phase transitions are explored. Finally, applications to random systems called spin glasses and to neural networks are briefly reviewed.Less

The thermodynamic properties of spin systems are evaluated with Monte Carlo methods. A review of classical thermodynamics is followed by a discussion of critical exponents. The Monte Carlo method is then applied to the two-dimensional Ising model with the goal of determining the phase diagram for magnetization. Boundary conditions, the reweighting method, autocorrelation, and critical slowing down are all explored. Cluster algorithms for overcoming critical slowing down are developed next and shown to dramatically reduce autocorrelation. A variety of spin systems that illustrate first, second, and infinite order (topological) phase transitions are explored. Finally, applications to random systems called spin glasses and to neural networks are briefly reviewed.

*Joseph F. Boudreau and Eric S. Swanson*

- Published in print:
- 2017
- Published Online:
- February 2018
- ISBN:
- 9780198708636
- eISBN:
- 9780191858598
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198708636.003.0008
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Percolation deals with global properties of random configurations of local objects. While simple to implement in models, understanding percolation requires skill in pattern recognition and analysis. ...
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Percolation deals with global properties of random configurations of local objects. While simple to implement in models, understanding percolation requires skill in pattern recognition and analysis. A cluster recognition algorithm is developed to obtain properties of percolation models. The fractal nature of a percolating system is discussed, along with general features of fractals. Scaling laws and critical exponents, which are central features of modern approaches to complex systems, are also introduced and illustrated with percolating systems. The important concept of a correlation function is also used to characterize these systems. Finally, the insensitivity of large classes of model systems with respect to short range dynamics, known as universality, is discussed in the context of percolation. This is illustrated with the modern concepts of coarse graining and the renormalization group.Less

Percolation deals with global properties of random configurations of local objects. While simple to implement in models, understanding percolation requires skill in pattern recognition and analysis. A cluster recognition algorithm is developed to obtain properties of percolation models. The fractal nature of a percolating system is discussed, along with general features of fractals. Scaling laws and critical exponents, which are central features of modern approaches to complex systems, are also introduced and illustrated with percolating systems. The important concept of a correlation function is also used to characterize these systems. Finally, the insensitivity of large classes of model systems with respect to short range dynamics, known as universality, is discussed in the context of percolation. This is illustrated with the modern concepts of coarse graining and the renormalization group.