The scaling of the minimum sum of edge lengths in uniformly random trees

Journal of Quantitative Linguistics

Gómez-Rodríguez

2019

Self Cite

Dependency distance minimization (DDm) is a word order principle favouring the placement of syntactically related words close to each other in sentences. Massive evidence of the principle has been reported for more than a decade with the help of syntactic dependency treebanks where long sentences abound. However, it has been predicted theoretically that the principle is more likely to be beaten in short sequences by the principle of surprisal minimization (predictability maximization). Here we introduce a simple binomial test to verify such a hypothesis. In short sentences, we find anti-DDm for some languages from different families. Our analysis of the syntactic dependency structures suggests that anti-DDm is produced by star trees.

Section: Discussionmentioning

confidence: 99%

Anti Dependency Distance Minimization in Short Sequences. A Graph Theoretic Approach

Journal of Quantitative Linguistics

Gómez-Rodríguez

2019

Self Cite

“…We have seen above that k 2 is a fundamental structural property of a tree: it determines |Q|. As k 2 determines the range of variation of |Q|, k 2 also determines the solution to the minimum linear arrangement problem: the solution is minimum for linear trees and maximum for star trees [29]. k 2 is a measure of the hubiness of a tree [25] and we have seen that its range of variation is…”

Section: A Hubiness Coefficientmentioning

confidence: 99%

“…Suppose that the vertices of a linear tree with n ≥ 2 are labelled following a depth-first traversal from one of the leaves. This is equivalent to labelling vertices according to their position in a minimum linear arrangement [29]. Fig.…”

Section: Introductionmentioning

confidence: 99%

Are crossing dependencies really scarce?

Physica A: Statistical Mechanics and its Applications

Gómez-Rodríguez

Esteban

2018

The syntactic structure of a sentence can be modelled as a tree, where vertices correspond to words and edges indicate syntactic dependencies. It has been claimed recurrently that the number of edge crossings in real sentences is small. However, a baseline or null hypothesis has been lacking. Here we quantify the amount of crossings of real sentences and compare it to the predictions of a series of baselines. We conclude that crossings are really scarce in real sentences. Their scarcity is unexpected by the hubiness of the trees. Indeed, real sentences are close to linear trees, where the potential number of crossings is maximized.

“…We pay further attention to the particular case of trees given their interest for research on edge lengths, e.g., [ V rla [D 2 ] becomes an increasing linear function of k 2 when n is also constant (recall 33)). In trees where n is given, it has been shown that [11]…”

Section: Uniformly Random Labelled Treesmentioning

confidence: 99%

The sum of edge lengths in random linear arrangements

2019

J. Stat. Mech.

Self Cite

Spatial networks are networks where nodes are located in a space equipped with a metric. Typically, the space is two-dimensional and until recently and traditionally, the metric that was usually considered was the Euclidean distance. In spatial networks, the cost of a link depends on the edge length, i.e. the distance between the nodes that define the edge. Hypothesizing that there is pressure to reduce the length of the edges of a network requires a null model, e.g., a random layout of the vertices of the network. Here we investigate the properties of the distribution of the sum of edge lengths in random linear arrangement of vertices, that has many applications in different fields. A random linear arrangement consists of an ordering of the elements of the nodes of a network being all possible orderings equally likely. The distance between two vertices is one plus the number of intermediate vertices in the ordering. Compact formulae for the 1st and 2nd moments about zero as well as the variance of the sum of edge lengths are obtained for arbitrary graphs and trees. We also analyze the evolution of that variance in Erdős-Rényi graphs and its scaling in uniformly random trees. Various developments and applications for future research are suggested.