143 research outputs found
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
The placement of the head that minimizes online memory: a complex systems approach
It is well known that the length of a syntactic dependency determines its
online memory cost. Thus, the problem of the placement of a head and its
dependents (complements or modifiers) that minimizes online memory is
equivalent to the problem of the minimum linear arrangement of a star tree.
However, how that length is translated into cognitive cost is not known. This
study shows that the online memory cost is minimized when the head is placed at
the center, regardless of the function that transforms length into cost,
provided only that this function is strictly monotonically increasing. Online
memory defines a quasi-convex adaptive landscape with a single central minimum
if the number of elements is odd and two central minima if that number is even.
We discuss various aspects of the dynamics of word order of subject (S), verb
(V) and object (O) from a complex systems perspective and suggest that word
orders tend to evolve by swapping adjacent constituents from an initial or
early SOV configuration that is attracted towards a central word order by
online memory minimization. We also suggest that the stability of SVO is due to
at least two factors, the quasi-convex shape of the adaptive landscape in the
online memory dimension and online memory adaptations that avoid regression to
SOV. Although OVS is also optimal for placing the verb at the center, its low
frequency is explained by its long distance to the seminal SOV in the
permutation space.Comment: Minor changes (language improved; typos in Eqs. 5, 6 and 13
corrected
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 meaning-frequency law in Zipfian optimization models of communication
According to Zipf's meaning-frequency law, words that are more frequent tend
to have more meanings. Here it is shown that a linear dependency between the
frequency of a form and its number of meanings is found in a family of models
of Zipf's law for word frequencies. This is evidence for a weak version of the
meaning-frequency law. Interestingly, that weak law (a) is not an inevitable of
property of the assumptions of the family and (b) is found at least in the
narrow regime where those models exhibit Zipf's law for word frequencies
Kauffman's adjacent possible in word order evolution
Word order evolution has been hypothesized to be constrained by a word order
permutation ring: transitions involving orders that are closer in the
permutation ring are more likely. The hypothesis can be seen as a particular
case of Kauffman's adjacent possible in word order evolution. Here we consider
the problem of the association of the six possible orders of S, V and O to
yield a couple of primary alternating orders as a window to word order
evolution. We evaluate the suitability of various competing hypotheses to
predict one member of the couple from the other with the help of information
theoretic model selection. Our ensemble of models includes a six-way model that
is based on the word order permutation ring (Kauffman's adjacent possible) and
another model based on the dual two-way of standard typology, that reduces word
order to basic orders preferences (e.g., a preference for SV over VS and
another for SO over OS). Our analysis indicates that the permutation ring
yields the best model when favoring parsimony strongly, providing support for
Kauffman's general view and a six-way typology.Comment: Minor corrections (small errors concerning the parameters of model 1,
language, style,...) except for the mathematical arguments at the end of
section "Further details about Model 2" of the supplementar
Beyond description. Comment on "Approaching human language with complex networks" by Cong & Liu
Comment on "Approaching human language with complex networks" by Cong & Li
The placement of the head that maximizes predictability. An information theoretic approach
The minimization of the length of syntactic dependencies is a
well-established principle of word order and the basis of a mathematical theory
of word order. Here we complete that theory from the perspective of information
theory, adding a competing word order principle: the maximization of
predictability of a target element. These two principles are in conflict: to
maximize the predictability of the head, the head should appear last, which
maximizes the costs with respect to dependency length minimization. The
implications of such a broad theoretical framework to understand the
optimality, diversity and evolution of the six possible orderings of subject,
object and verb are reviewed.Comment: in press in Glottometric
Compression and the origins of Zipf's law for word frequencies
Here we sketch a new derivation of Zipf's law for word frequencies based on
optimal coding. The structure of the derivation is reminiscent of Mandelbrot's
random typing model but it has multiple advantages over random typing: (1) it
starts from realistic cognitive pressures (2) it does not require fine tuning
of parameters and (3) it sheds light on the origins of other statistical laws
of language and thus can lead to a compact theory of linguistic laws. Our
findings suggest that the recurrence of Zipf's law in human languages could
originate from pressure for easy and fast communication.Comment: arguments have been improved; in press in Complexity (Wiley
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
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