6 research outputs found
Liberating language research from dogmas of the 20th century
A commentary on the article "Large-scale evidence of dependency length
minimization in 37 languages" by Futrell, Mahowald & Gibson (PNAS 2015 112 (33)
10336-10341).Comment: Minor correction
A commentary on "The now-or-never bottleneck: a fundamental constraint on language", by Christiansen and Chater (2016)
In a recent article, Christiansen and Chater (2016) present a fundamental
constraint on language, i.e. a now-or-never bottleneck that arises from our
fleeting memory, and explore its implications, e.g., chunk-and-pass processing,
outlining a framework that promises to unify different areas of research. Here
we explore additional support for this constraint and suggest further
connections from quantitative linguistics and information theory
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
Edge crossings in random linear arrangements
In spatial networks vertices are arranged in some space and edges may cross.
When arranging vertices in a 1-dimensional lattice edges may cross when drawn
above the vertex sequence as it happens in linguistic and biological networks.
Here we investigate the general of problem of the distribution of edge
crossings in random arrangements of the vertices. We generalize the existing
formula for the expectation of this number in random linear arrangements of
trees to any network and derive an expression for the variance of the number of
crossings in an arbitrary layout relying on a novel characterization of the
algebraic structure of that variance in an arbitrary space. We provide compact
formulae for the expectation and the variance in complete graphs, complete
bipartite graphs, cycle graphs, one-regular graphs and various kinds of trees
(star trees, quasi-star trees and linear trees). In these networks, the scaling
of expectation and variance as a function of network size is asymptotically
power-law-like in random linear arrangements. Our work paves the way for
further research and applications in 1-dimension or investigating the
distribution of the number of crossings in lattices of higher dimension or
other embeddings.Comment: Generalised our theory from one-dimensional layouts to practically
any type of layout. This helps study the variance of the number of crossings
in graphs when their vertices are arranged on the surface of a sphere, or on
the plane. Moreover, we also give closed formulae for this variance on
particular types of graphs in both linear arrangements and general layout
The optimality of syntactic dependency distances
It is often stated that human languages, as other biological systems, are
shaped by cost-cutting pressures but, to what extent? Attempts to quantify the
degree of optimality of languages by means of an optimality score have been
scarce and focused mostly on English. Here we recast the problem of the
optimality of the word order of a sentence as an optimization problem on a
spatial network where the vertices are words, arcs indicate syntactic
dependencies and the space is defined by the linear order of the words in the
sentence. We introduce a new score to quantify the cognitive pressure to reduce
the distance between linked words in a sentence. The analysis of sentences from
93 languages representing 19 linguistic families reveals that half of languages
are optimized to a 70% or more. The score indicates that distances are not
significantly reduced in a few languages and confirms two theoretical
predictions, i.e. that longer sentences are more optimized and that distances
are more likely to be longer than expected by chance in short sentences. We
present a new hierarchical ranking of languages by their degree of
optimization. The statistical advantages of the new score call for a
reevaluation of the evolution of dependency distance over time in languages as
well as the relationship between dependency distance and linguistic competence.
Finally, the principles behind the design of the score can be extended to
develop more powerful normalizations of topological distances or physical
distances in more dimensions
Liberating language research from dogmas of the 20th century
A commentary on the article “Large-scale evidence of dependency length
minimization in 37 languages” by Futrell, Mahowald & Gibson (PNAS 2015 112 (33) 10336-10341)