23 research outputs found
Hubiness, length, crossings and their relationships in dependency trees
Here tree dependency structures are studied from three different perspectives: their degree variance (hubiness), the mean dependency length and the number of dependency crossings. Bounds that reveal pairwise dependencies among these three metrics are derived. Hubiness (the variance of degrees) plays a central role: the mean dependency length is bounded below by hubiness while the number of crossings is bounded above by hubiness. Our findings suggest that the online memory cost of a sentence might be determined not just by the ordering of words but also by the hubiness of the underlying structure. The 2nd moment of degree plays a crucial role that is reminiscent of its role in large complex networks.Peer ReviewedPostprint (published version
Are crossing dependencies really scarce?
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.Peer ReviewedPostprint (author's final draft
Crossings as a side effect of dependency lengths
The syntactic structure of sentences exhibits a striking regularity:
dependencies tend to not cross when drawn above the sentence. We investigate
two competing explanations. The traditional hypothesis is that this trend
arises from an independent principle of syntax that reduces crossings
practically to zero. An alternative to this view is the hypothesis that
crossings are a side effect of dependency lengths, i.e. sentences with shorter
dependency lengths should tend to have fewer crossings. We are able to reject
the traditional view in the majority of languages considered. The alternative
hypothesis can lead to a more parsimonious theory of language.Comment: the discussion section has been expanded significantly; in press in
Complexity (Wiley
Non-crossing dependencies: Least effort, not grammar
The use of null hypotheses (in a statistical sense) is common in hard sciences but not in theoretical linguistics. Here the null hypothesis that the low frequency of syntactic dependency crossings is expected by an arbitrary ordering of words is rejected. It is shown that this would require star dependency structures, which are both unrealistic and too restrictive. The hypothesis of the limited resources of the human brain is revisited. Stronger null hypotheses taking into account actual dependency lengths for the likelihood of crossings are presented. Those hypotheses suggests that crossings are likely to reduce when dependencies are shortened. A hypothesis based on pressure to reduce dependency lengths is more parsimonious than a principle of minimization of crossings or a grammatical ban that is totally dissociated from the general and non-linguistic principle of economy.Postprint (author's final draft
The risks of mixing dependency lengths from sequences of different length
Mixing dependency lengths from sequences of different length is a common
practice in language research. However, the empirical distribution of
dependency lengths of sentences of the same length differs from that of
sentences of varying length and the distribution of dependency lengths depends
on sentence length for real sentences and also under the null hypothesis that
dependencies connect vertices located in random positions of the sequence. This
suggests that certain results, such as the distribution of syntactic dependency
lengths mixing dependencies from sentences of varying length, could be a mere
consequence of that mixing. Furthermore, differences in the global averages of
dependency length (mixing lengths from sentences of varying length) for two
different languages do not simply imply a priori that one language optimizes
dependency lengths better than the other because those differences could be due
to differences in the distribution of sentence lengths and other factors.Comment: Laguage and referencing has been improved; Eqs. 7, 11, B7 and B8 have
been correcte
The sum of edge lengths in random linear arrangements
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 Erdos-Renyi
graphs and its scaling in uniformly random trees. Various developments and
applications for future research are suggested
Anti dependency distance minimization in short sequences: A graph theoretic approach
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.Peer ReviewedPostprint (author's final draft