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The SEX algorithm in
 Computer Chess, ICCA J
, 1989
"... Abstract. The neighborjoining algorithm is a popular phylogenetics method for constructing trees from dissimilarity maps. The neighbornet algorithm is an extension of the neighborjoining algorithm and is used for constructing split networks. We begin by describing the output of neighbornet in te ..."
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Abstract. The neighborjoining algorithm is a popular phylogenetics method for constructing trees from dissimilarity maps. The neighbornet algorithm is an extension of the neighborjoining algorithm and is used for constructing split networks. We begin by describing the output of neighbornet in terms of the tessellation of M n 0 by associahedra. This highlights the fact that neighbornet outputs a tree in addition to a circular ordering and we explain when the neighbornet tree is the neighborjoining tree. A key observation is that the tree constructed in existing implementations of neighbornet is not a neighborjoining tree. Next, we show that neighbornet is a greedy algorithm for finding circular split systems of minimal balanced length. This leads to an interpretation of neighbornet as a greedy algorithm for the traveling salesman problem. The algorithm is optimal for Kalmanson matrices, from which it follows that neighbornet is consistent and has optimal radius 1 2. We also provide a statistical interpretation for the balanced length for a circular split system as the length based on weighted least squares estimates of the splits. We conclude with applications of these results and demonstrate the implications of our theorems for a recently published comparison of Papuan and Austronesian languages. 1.
Generalizing Scales
"... Instead of considering scales to be linearly ordered structures, it is proposed that scales are better conceived of as metrics (dissimilarity matrices). Further, to be considered a scale of typological interest, there should be a significant correlation between a meaningscale and a formscale. This ..."
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Instead of considering scales to be linearly ordered structures, it is proposed that scales are better conceived of as metrics (dissimilarity matrices). Further, to be considered a scale of typological interest, there should be a significant correlation between a meaningscale and a formscale. This conceptualisation allows for a fruitful generalization of the concept "scale". As a handson example of the proposals put forward in this paper, the "scale of likelihood of spontaneous occurrence " (Haspelmath 1993) is reanalyzed. This scale describes the prototypical agentivity of the subject of a predicate. 1. Scales as restrictions on formfunction mapping Scales 1 of linguistic structure are one of the more promising avenues of research into the unification of the worldwide linguistic diversity. Although our growing understanding of the diversity of the world’s languages seems to put more and more doubt on many grandiose attempts on universally valid generalizations, the significance of scales for human languages (like the wellknown animacy scale) still appears to stand strong. So, what actually is a scale? A scale seems to be mostly thought of as an asymmetrical onedimensional arrangement (a “total order ” in mathematical parlance) on certain crosslinguistic categories/functions. Put differently, a scale is a linear ordering of functions with a “high end ” and a “low end”. To be a considered an interesting scale, the formal encoding of these functions in actual languages should be related to this linear ordering. In this paper, I will argue that this concept of a scale can be fruitfully generalized. In a very general sense, all linguistic structure consists of forms expressing particular functions. If we find restrictions—across languages— on the kind of forms that are used to express certain functions, then this 1 The term “scale ” is used here synonymously to what is also known as an “implicational hierarchy”, “markedness hierarchy ” or simply “hierarchy ” in linguistics.
Phylogenetic Models of Language
"... Language diversi cation is a stochastic process which presents similarities with phylogenetic evolution. Recently, there has been interest in modelling this ..."
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Language diversi cation is a stochastic process which presents similarities with phylogenetic evolution. Recently, there has been interest in modelling this
Handbook of Historical Linguistics. New York: Routledge. Trees, waves and linkages: Models of language diversification
, 2013
"... 1.1 Language extinction, language emergence The number of languages spoken on the planet has oscillated up and down throughout the history of mankind. 1 Different social factors operate in opposite ways, some resulting in the decrease of language diversity, others favouring the emergence of new lang ..."
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1.1 Language extinction, language emergence The number of languages spoken on the planet has oscillated up and down throughout the history of mankind. 1 Different social factors operate in opposite ways, some resulting in the decrease of language diversity, others favouring the emergence of new languages. Thus, languages fade away and disappear when their speakers undergo some pressure towards abandoning their heritage language and replacing it in all contexts with a new language that is in some way more socially prominent (Simpson, this volume). The process of language extinction may be rapid or slow, and varies in intensity depending on historical circumstances. While this process results in the erosion of language diversity, others bring about the opposite result: an increase in the number of spoken languages. Because no natural language appears ex nihilo, one has to explain how new languages emerge out of older ones. Some – such as pidgins and creoles (Romaine 1988, Siegel 2004) or mixed languages (Matras & Bakker 2003) – result historically from the encounter of two populations who were driven, under very special social conditions, to combine elements of their respective