Searcharxiv⌕ Search

arXiv subjects

Ramon Ferrer-i-Cancho

Publications and source records attributed to Ramon Ferrer-i-Cancho.

At least 73 records · Page 4Linked to original sources
arXiv2015

Zipf's law for word frequencies: word forms versus lemmas in long texts

Zipf's law is a fundamental paradigm in the statistics of written and spoken natural language as well as in other communication systems. We raise the question of the elementary units for which Zipf's law should hold in the most natural way, studying its validity for plain word forms and for the corresponding lemma forms. In order to have as homogeneous sources as possible, we analyze some of the longest literary texts ever written, comprising four different languages, with different levels of morphological complexity. In all cases Zipf's law is fulfilled, in the sense that a power-law distribution of word or lemma frequencies is valid for several orders of magnitude. We investigate the extent to which the word-lemma transformation preserves two parameters of Zipf's law: the exponent and the low-frequency cut-off. We are not able to demonstrate a strict invariance of the tail, as for a few texts both exponents deviate significantly, but we conclude that the exponents are very similar, despite the remarkable transformation that going from words to lemmas represents, considerably affecting all ranges of frequencies. In contrast, the low-frequency cut-offs are less stable.

physics.soc-ph↗
arXiv2015

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.

cs.CL↗
arXiv2015

Reply to the commentary "Be careful when assuming the obvious", by P. Alday

Here we respond to some comments by Alday concerning headedness in linguistic theory and the validity of the assumptions of a mathematical model for word order. For brevity, we focus only on two assumptions: the unit of measurement of dependency length and the monotonicity of the cost of a dependency as a function of its length. We also revise the implicit psychological bias in Alday's comments. Notwithstanding, Alday is indicating the path for linguistic research with his unusual concerns about parsimony from multiple dimensions.

cs.CL↗
arXiv2014

A stronger null hypothesis for crossing dependencies

The syntactic structure of a sentence can be modeled as a tree where vertices are words and edges indicate syntactic dependencies between words. It is well-known that those edges normally do not cross when drawn over the sentence. Here a new null hypothesis for the number of edge crossings of a sentence is presented. That null hypothesis takes into account the length of the pair of edges that may cross and predicts the relative number of crossings in random trees with a small error, suggesting that a ban of crossings or a principle of minimization of crossings are not needed in general to explain the origins of non-crossing dependencies. Our work paves the way for more powerful null hypotheses to investigate the origins of non-crossing dependencies in nature.

cs.CL↗
arXiv2014

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.

cs.CL↗
arXiv2014

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.

cs.CL↗
arXiv2014

When is Menzerath-Altmann law mathematically trivial? A new approach

Menzerath's law, the tendency of Z, the mean size of the parts, to decrease as X, the number of parts, increases is found in language, music and genomes. Recently, it has been argued that the presence of the law in genomes is an inevitable consequence of the fact that Z = Y/X, which would imply that Z scales with X as Z ~ 1/X. That scaling is a very particular case of Menzerath-Altmann law that has been rejected by means of a correlation test between X and Y in genomes, being X the number of chromosomes of a species, Y its genome size in bases and Z the mean chromosome size. Here we review the statistical foundations of that test and consider three non-parametric tests based upon different correlation metrics and one parametric test to evaluate if Z ~ 1/X in genomes. The most powerful test is a new non-parametric based upon the correlation ratio, which is able to reject Z ~ 1/X in nine out of eleven taxonomic groups and detect a borderline group. Rather than a fact, Z ~ 1/X is a baseline that real genomes do not meet. The view of Menzerath-Altmann law as inevitable is seriously flawed.

q-bio.GN↗
arXiv2013

Why SOV might be initially preferred and then lost or recovered? A theoretical framework

Little is known about why SOV order is initially preferred and then discarded or recovered. Here we present a framework for understanding these and many related word order phenomena: the diversity of dominant orders, the existence of free words orders, the need of alternative word orders and word order reversions and cycles in evolution. Under that framework, word order is regarded as a multiconstraint satisfaction problem in which at least two constraints are in conflict: online memory minimization and maximum predictability.

cs.CL↗
arXiv2013

Networks in Cognitive Science

Networks of interconnected nodes have long played a key role in Cognitive Science, from artificial neural net- works to spreading activation models of semantic mem- ory. Recently, however, a new Network Science has been developed, providing insights into the emergence of global, system-scale properties in contexts as diverse as the Internet, metabolic reactions, and collaborations among scientists. Today, the inclusion of network theory into Cognitive Sciences, and the expansion of complex- systems science, promises to significantly change the way in which the organization and dynamics of cognitive and behavioral processes are understood. In this paper, we review recent contributions of network theory at different levels and domains within the Cognitive Sciences.

physics.soc-ph↗
arXiv2013

Constant conditional entropy and related hypotheses

Constant entropy rate (conditional entropies must remain constant as the sequence length increases) and uniform information density (conditional probabilities must remain constant as the sequence length increases) are two information theoretic principles that are argued to underlie a wide range of linguistic phenomena. Here we revise the predictions of these principles to the light of Hilberg's law on the scaling of conditional entropy in language and related laws. We show that constant entropy rate (CER) and two interpretations for uniform information density (UID), full UID and strong UID, are inconsistent with these laws. Strong UID implies CER but the reverse is not true. Full UID, a particular case of UID, leads to costly uncorrelated sequences that are totally unrealistic. We conclude that CER and its particular cases are incomplete hypotheses about the scaling of conditional entropies.

cond-mat.stat-mech↗
arXiv2013

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.

cs.CL↗
arXiv2012

The challenges of statistical patterns of language: the case of Menzerath's law in genomes

The importance of statistical patterns of language has been debated over decades. Although Zipf's law is perhaps the most popular case, recently, Menzerath's law has begun to be involved. Menzerath's law manifests in language, music and genomes as a tendency of the mean size of the parts to decrease as the number of parts increases in many situations. This statistical regularity emerges also in the context of genomes, for instance, as a tendency of species with more chromosomes to have a smaller mean chromosome size. It has been argued that the instantiation of this law in genomes is not indicative of any parallel between language and genomes because (a) the law is inevitable and (b) non-coding DNA dominates genomes. Here mathematical, statistical and conceptual challenges of these criticisms are discussed. Two major conclusions are drawn: the law is not inevitable and languages also have a correlate of non-coding DNA. However, the wide range of manifestations of the law in and outside genomes suggests that the striking similarities between non-coding DNA and certain linguistics units could be anecdotal for understanding the recurrence of that statistical law.

q-bio.GN↗
arXiv2012

The law of brevity in macaque vocal communication is not an artifact of analyzing mean call durations

Words follow the law of brevity, i.e. more frequent words tend to be shorter. From a statistical point of view, this qualitative definition of the law states that word length and word frequency are negatively correlated. Here the recent finding of patterning consistent with the law of brevity in Formosan macaque vocal communication (Semple et al., 2010) is revisited. It is shown that the negative correlation between mean duration and frequency of use in the vocalizations of Formosan macaques is not an artifact of the use of a mean duration for each call type instead of the customary 'word' length of studies of the law in human language. The key point demonstrated is that the total duration of calls of a particular type increases with the number of calls of that type. The finding of the law of brevity in the vocalizations of these macaques therefore defies a trivial explanation.

q-bio.NC↗
arXiv2012

The failure of the law of brevity in two New World primates. Statistical caveats

Parallels of Zipf's law of brevity, the tendency of more frequent words to be shorter, have been found in bottlenose dolphins and Formosan macaques. Although these findings suggest that behavioral repertoires are shaped by a general principle of compression, common marmosets and golden-backed uakaris do not exhibit the law. However, we argue that the law may be impossible or difficult to detect statistically in a given species if the repertoire is too small, a problem that could be affecting golden backed uakaris, and show that the law is present in a subset of the repertoire of common marmosets. We suggest that the visibility of the law will depend on the subset of the repertoire under consideration or the repertoire size.

q-bio.NC↗
arXiv2012

Information content versus word length in random typing

Recently, it has been claimed that a linear relationship between a measure of information content and word length is expected from word length optimization and it has been shown that this linearity is supported by a strong correlation between information content and word length in many languages (Piantadosi et al. 2011, PNAS 108, 3825-3826). Here, we study in detail some connections between this measure and standard information theory. The relationship between the measure and word length is studied for the popular random typing process where a text is constructed by pressing keys at random from a keyboard containing letters and a space behaving as a word delimiter. Although this random process does not optimize word lengths according to information content, it exhibits a linear relationship between information content and word length. The exact slope and intercept are presented for three major variants of the random typing process. A strong correlation between information content and word length can simply arise from the units making a word (e.g., letters) and not necessarily from the interplay between a word and its context as proposed by Piantadosi et al. In itself, the linear relation does not entail the results of any optimization process.

physics.data-an↗
arXiv2012

A practical recipe to fit discrete power-law distributions

Power laws pervade statistical physics and complex systems, but, traditionally, researchers in these fields have paid little attention to properly fit these distributions. Who has not seen (or even shown) a log-log plot of a completely curved line pretending to be a power law? Recently, Clauset et al. have proposed a method to decide if a set of values of a variable has a distribution whose tail is a power law. The key of their procedure is the identification of the minimum value of the variable for which the fit holds, which is selected as the value for which the Kolmogorov-Smirnov distance between the empirical distribution and its maximum-likelihood fit is minimum. However, it has been shown that this method can reject the power-law hypothesis even in the case of power-law simulated data. Here we propose a simpler selection criterion, which is illustrated with the more involving case of discrete power-law distributions.

stat.AP↗
arXiv2012

The parameters of Menzerath-Altmann law in genomes

The relationship between the size of the whole and the size of the parts in language and music is known to follow Menzerath-Altmann law at many levels of description (morphemes, words, sentences...). Qualitatively, the law states that larger the whole, the smaller its parts, e.g., the longer a word (in syllables) the shorter its syllables (in letters or phonemes). This patterning has also been found in genomes: the longer a genome (in chromosomes), the shorter its chromosomes (in base pairs). However, it has been argued recently that mean chromosome length is trivially a pure power function of chromosome number with an exponent of -1. The functional dependency between mean chromosome size and chromosome number in groups of organisms from three different kingdoms is studied. The fit of a pure power function yields exponents between -1.6 and 0.1. It is shown that an exponent of -1 is unlikely for fungi, gymnosperm plants, insects, reptiles, ray-finned fishes and amphibians. Even when the exponent is very close to -1, adding an exponential component is able to yield a better fit with regard to a pure power-law in plants, mammals, ray-finned fishes and amphibians. The parameters of Menzerath-Altmann law in genomes deviate significantly from a power law with a -1 exponent with the exception of birds and cartilaginous fishes.

q-bio.GN↗