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Ramon Ferrer-i-Cancho

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

At least 19 recordsLinked to original sources
arXiv2026

How to measure the optimality of word or gesture order with respect to the principle of swap distance minimization

The structure of all the permutations of a sequence can be represented as a permutohedron, a graph where vertices are permutations and two vertices are linked if a swap of adjacent elements in the permutation of one of the vertices produces the permutation of the other vertex. It has been hypothesized that word orders in languages minimize the swap distance in the permutohedron: given a source order, word orders that are closer in the permutohedron should be less costly and thus more likely. Here we explain how to measure the degree of optimality of word order variation with respect to swap distance minimization. We illustrate the power of our novel mathematical framework by examining spontaneous gestures produced by speakers from four languages (two SVO languages and two VSO languages, which represent two linguistic families). We show that crosslinguistic gestures are at least $77\%$ optimal. It is unlikely that the multiple times where crosslinguistic gestures hit optimality are due to chance. We establish the theoretical foundations for research on the optimality of word or gesture order with respect to swap distance minimization in communication systems. Finally, we introduce the quadratic assignment problem (QAP) into language research as an umbrella for multiple optimization problems and, accordingly, postulate a general principle of optimal assignment that unifies various linguistic principles including swap distance minimization.

cs.CL↗
arXiv2026

Swap distance minimization shapes the order of subject, object and verb in languages of the world

Languages of the world vary concerning the order of subject (S), object (O) and verb (V). The most frequent dominant orders are SOV and SVO, and researchers have tailored models to this fact. However, there are still languages whose dominant order does not conform to these expectations or even lack a dominant order. Here we approach word order variation through swap distance, namely the distance between orders in the permutohedron, a graph where the vertices are the six possible orders of S, O and V, and two orders are connected if they differ by a swap of adjacent constituents. Then word order variation becomes a problem of assigning probabilities to word orders so as to minimize the average swap distance. Although previous work suggests that swap distance minimization may influence synchronic and diachronic variation as well as word order acceptability, here we provide large-scale cross-linguistic evidence across families, macroareas and sources that word order variation within languages is shaped by the principle of swap distance minimization, even when the dominant order is not SOV/SVO and even when a dominant order is lacking.

cs.CL↗
arXiv2026

On the feasibility of dependency parsing of non-human sequences without a gold standard. Is evaluation possible in other species?

Dependency parsing consists of finding a tree representation for a sequence. Unsupervised dependency parsing aims to develop parsing methods without a gold standard during model training. In human languages, an unsupervised parser can be evaluated because some gold standard is usually available or can be created. For other species, a gold standard is unknown. Thus one may conclude that it is impossible to determine the accuracy of an unsupervised parser and, consequently, dependency parsing is unfeasible in other species. However, here we apply recent advances in network science to demonstrate that the proportion of correct edges retrieved by a parser must be high for the sequences of vocalizations or gestures that non-human primates produce due to the fast decay of the sequence length distribution. In contrast, human language sequences lack that property. Therefore, evaluation without a gold standard is feasible in non-human primates but a hard problem in humans.

cs.CL↗
arXiv2026

Maximum Linear Arrangement: exact algorithms for specific classes of graphs and approximation algorithms for wide classes of graphs

Linear arrangements of graphs are a well-known type of graph labeling and are found in many important computational problems. A linear arrangement is usually defined as a permutation of the $n$ vertices of a graph. An intuitive geometric setting is that of vertices lying on consecutive integer positions in the real line, starting at 1; edges are often drawn as semicircles above the real line. A well-known computational problem is the Minimum Linear Arrangement Problem (${\tt minLA}$) where the goal is to find an arrangement that minimizes the sum of edge lengths. In this paper we study the Maximum Linear Arrangement problem (${\tt MaxLA}$), the counterpart of ${\tt minLA}$. We devise a new characterization of maximum arrangements of general graphs, and prove that ${\tt MaxLA}$ can be solved for $k$-regular graphs ($k\le2$) in time $O(n)$, and for $k$-linear trees ($k\le2$) in time $O(n)$. We present two constrained variants of ${\tt MaxLA}$ we call ${\tt bipartite MaxLA}$ and ${\tt 1-thistle MaxLA}$. We prove that the former can be solved in time $O(n)$ for any connected bipartite graph; the latter can be solved by an algorithm that typically runs in time $O(n^3\log n)$ on unlabeled trees. We show that ${\tt bipartite MaxLA}$ is a $3/2$-approximation algorithm for ${\tt MaxLA}$ for trees.

cs.DS↗
arXiv2026

Ease of dependency distance minimization in star-like structures

The syntactic structure of a sentence can be represented as a tree where edges indicate syntactic dependencies between words. When that structure is a star, it has been demonstrated that the head should be placed in the middle of the linear arrangement according to the principle of syntactic dependency distance minimization. However, hubs of stars tend to be put at one of the ends, against that principle. Here we address two questions: (1) How difficult is it to minimize dependency distance? (2) Why anti dependency distance minimization effects have been found in star structures but not in path structures? The ease of optimization is determined by the shape of the optimization landscape. It was demonstrated that the landscape of star structures is quasiconvex (Ferrer-i-Cancho 2015, Language Dynamics and Change). As for (1), here we show that it is indeed convex (a particular case of quasiconvexity) both for star trees and quasistar trees and thus the distance-based optimization problem is simpler than previously believed. As for (2), we argue that (a) competing principles, rather than the difficulty of optimization, must be the actual reason for anti-dependency distance minimization effects and that (b) dependency distance minimization on star-like structures is less rewarding compared to other structures.

cs.CL↗
arXiv2026

The optimality of word lengths. Theoretical foundations and an empirical study

Zipf's law of abbreviation, namely the tendency of more frequent words to be shorter, has been viewed as a manifestation of compression, i.e. the minimization of the length of forms -- a universal principle of natural communication. Although the claim that languages are optimized has become trendy, attempts to measure the degree of optimization of languages have been rather scarce. Here we present two optimality scores that are dualy normalized, namely, they are normalized with respect to both the minimum and the random baseline. We analyze the theoretical and statistical advantages and disadvantages of these and other scores. Harnessing the best score, we quantify the degree of optimality of word lengths per language. This includes parallel texts in 20 languages of 9 families, written in 8 scripts, as well as spoken data for 46 languages of 12 families, two constructed languages, and one isolate. Our analyses indicate that languages are optimized to 62 or 67 percent on average (depending on the source) when word lengths are measured in characters, and to 65 percent on average when word lengths are measured in time. In general, spoken word durations are more optimized than written word lengths in characters. Our work paves the way to measure the degree of optimality of the vocalizations or gestures of other species, and to compare them against written, spoken, or signed human languages.

cs.CL↗
arXiv2026

The exponential distribution of the order of demonstrative, numeral, adjective and noun

The frequency of the preferred order for a noun phrase formed by demonstrative, numeral, adjective and noun has received significant attention over the last two decades. We investigate the actual distribution of the 24 possible orders. There is no consensus on whether it is well-fitted by an exponential or a power law distribution. We find that an exponential distribution is a much better model. This finding and other circumstances where an exponential-like distribution is found challenge the view that power-law distributions, e.g., Zipf's law for word frequencies, are inevitable. We also investigate which of two exponential distributions gives a better fit: an exponential model where the 24 orders have non-zero probability (a geometric distribution truncated at rank 24) or an exponential model where the number of orders that can have non-zero probability is variable (a right-truncated geometric distribution). When consistency and generalizability are prioritized, we find higher support for the exponential model where all 24 orders have non-zero probability. These findings strongly suggest that there is no hard constraint on word order variation and then unattested orders merely result from undersampling, consistently with Cysouw's view.

cs.CL↗
arXiv2026

Swap distance minimization beyond entropy minimization in word order variation

Consider a linguistic structure formed by $n$ elements, for instance, subject, direct object and verb ($n=3$) or subject, direct object, indirect object and verb ($n=4$). We investigate whether the frequency of the $n!$ possible orders is constrained by two principles. First, entropy minimization, a principle that has been suggested to shape natural communication systems at distinct levels of organization. Second, swap distance minimization, namely a preference for word orders that require fewer swaps of adjacent elements to be produced from a source order. We present average swap distance, a novel score for research on swap distance minimization. We find strong evidence of pressure for entropy minimization and swap distance minimization with respect to a die rolling experiment in distinct linguistic structures with $n=3$ or $n=4$. Evidence with respect to a Polya urn process is strong for $n=4$ but weaker for $n=3$. We still find evidence consistent with the action of swap distance minimization when word order frequencies are shuffled, indicating that swap distance minimization effects are beyond pressure to reduce word order entropy.

cs.CL↗
arXiv2025

Who is the root in a syntactic dependency structure?

The syntactic structure of a sentence can be described as a tree that indicates the syntactic relationships between words. In spite of significant progress in unsupervised methods that retrieve the syntactic structure of sentences, guessing the right direction of edges is still a challenge. As in a syntactic dependency structure edges are oriented away from the root, the challenge of guessing the right direction can be reduced to finding an undirected tree and the root. The limited performance of current unsupervised methods demonstrates the lack of a proper understanding of what a root vertex is from first principles. We consider an ensemble of centrality scores, some that only take into account the free tree (non-spatial scores) and others that take into account the position of vertices (spatial scores). We test the hypothesis that the root vertex is an important or central vertex of the syntactic dependency structure. We confirm the hypothesis in the sense that root vertices tend to have high centrality and that vertices of high centrality tend to be roots. The best performance in guessing the root is achieved by novel scores that only take into account the position of a vertex and that of its neighbours. We provide theoretical and empirical foundations towards a universal notion of rootness from a network science perspective.

cs.CL↗
arXiv2025

On the class of coding optimality of human languages and the origins of Zipf's law

Here we present a new class of optimality for coding systems. Members of that class are displaced linearly from optimal coding and thus exhibit Zipf's law, namely a power-law distribution of frequency ranks. Within that class, Zipf's law, the size-rank law and the size-probability law form a group-like structure. We identify human languages that are members of the class. All languages showing sufficient agreement with Zipf's law are potential members of the class. In contrast, there are communication systems in other species that cannot be members of that class for exhibiting an exponential distribution instead but dolphins and humpback whales might. We provide a new insight into plots of frequency versus rank in double logarithmic scale. For any system, a straight line in that scale indicates that the lengths of optimal codes under non-singular coding and under uniquely decodable encoding are displaced by a linear function whose slope is the exponent of Zipf's law. For systems under compression and constrained to be uniquely decodable, such a straight line may indicate that the system is coding close to optimality. We provide support for the hypothesis that Zipf's law originates from compression and define testable conditions for the emergence of Zipf's law in compressing systems.

cs.CL↗
arXiv2025

The distribution of syntactic dependency distances

The syntactic structure of a sentence can be represented as a graph, where vertices are words and edges indicate syntactic dependencies between them. In this setting, the distance between two linked words is defined as the difference between their positions. Here we wish to contribute to the characterization of the actual distribution of syntactic dependency distances, which has previously been argued to follow a power-law distribution. Here we propose a new model with two exponential regimes in which the probability decay is allowed to change after a break-point. This transition could mirror the transition from the processing of word chunks to higher-level structures. We find that a two-regime model - where the first regime follows either an exponential or a power-law decay - is the most likely one in all 20 languages we considered, independently of sentence length and annotation style. Moreover, the break-point exhibits low variation across languages and averages values of 4-5 words, suggesting that the amount of words that can be simultaneously processed abstracts from the specific language to a high degree. The probability decay slows down after the breakpoint, consistently with a universal chunk-and-pass mechanism. Finally, we give an account of the relation between the best estimated model and the closeness of syntactic dependencies as function of sentence length, according to a recently introduced optimality score.

cs.CL↗
arXiv2024

The optimal placement of the head in the noun phrase. The case of demonstrative, numeral, adjective and noun

The word order of a sentence is shaped by multiple principles. The principle of syntactic dependency distance minimization is in conflict with the principle of surprisal minimization (or predictability maximization) in single head syntactic dependency structures: while the former predicts that the head should be placed at the center of the linear arrangement, the latter predicts that the head should be placed at one of the ends (either first or last). A critical question is when surprisal minimization (or predictability maximization) should surpass syntactic dependency distance minimization. In the context of single head structures, it has been predicted that this is more likely to happen when two conditions are met, i.e. (a) fewer words are involved and (b) words are shorter. Here we test the prediction on the noun phrase when it is composed of a demonstrative, a numeral, an adjective and a noun. We find that, across preferred orders in languages, the noun tends to be placed at one of the ends, confirming the theoretical prediction. We also show evidence of anti locality effects: syntactic dependency distances in preferred orders are longer than expected by chance.

cs.CL↗
arXiv2024

Predictability maximization and the origins of word order harmony

We address the linguistic problem of the sequential arrangement of a head and its dependents from an information theoretic perspective. In particular, we consider the optimal placement of a head that maximizes the predictability of the sequence. We assume that dependents are statistically independent given a head, in line with the open-choice principle and the core assumptions of dependency grammar. We demonstrate the optimality of harmonic order, i.e., placing the head last maximizes the predictability of the head whereas placing the head first maximizes the predictability of dependents. We also show that postponing the head is the optimal strategy to maximize its predictability while bringing it forward is the optimal strategy to maximize the predictability of dependents. We unravel the advantages of the strategy of maximizing the predictability of the head over maximizing the predictability of dependents. Our findings shed light on the placements of the head adopted by real languages or emerging in different kinds of experiments.

cs.CL↗
arXiv2024

Minimum projective linearizations of trees in linear time

The Minimum Linear Arrangement problem (MLA) consists of finding a mapping $π$ from vertices of a graph to distinct integers that minimizes $\sum_{\{u,v\}\in E}|π(u) - π(v)|$. In that setting, vertices are often assumed to lie on a horizontal line and edges are drawn as semicircles above said line. For trees, various algorithms are available to solve the problem in polynomial time in $n=|V|$. There exist variants of the MLA in which the arrangements are constrained. Iordanskii, and later Hochberg and Stallmann (HS), put forward $O(n)$-time algorithms that solve the problem when arrangements are constrained to be planar (also known as one-page book embeddings). We also consider linear arrangements of rooted trees that are constrained to be projective (planar embeddings where the root is not covered by any edge). Gildea and Temperley (GT) sketched an algorithm for projective arrangements which they claimed runs in $O(n)$ but did not provide any justification of its cost. In contrast, Park and Levy claimed that GT's algorithm runs in $O(n \log d_{max})$ where $d_{max}$ is the maximum degree but did not provide sufficient detail. Here we correct an error in HS's algorithm for the planar case, show its relationship with the projective case, and derive simple algorithms for the projective and planar cases that run without a doubt in $O(n)$ time.

cs.DS↗
arXiv2023

Swap distance minimization in SOV languages. Cognitive and mathematical foundations

Distance minimization is a general principle of language. A special case of this principle in the domain of word order is swap distance minimization. This principle predicts that variations from a canonical order that are reached by fewer swaps of adjacent constituents are lest costly and thus more likely. Here we investigate the principle in the context of the triple formed by subject (S), object (O) and verb (V). We introduce the concept of word order rotation as a cognitive underpinning of that prediction. When the canonical order of a language is SOV, the principle predicts SOV < SVO, OSV < VSO, OVS < VOS, in order of increasing cognitive cost. We test the prediction in three flexible order SOV languages: Korean (Koreanic), Malayalam (Dravidian), and Sinhalese (Indo-European). Evidence of swap distance minimization is found in all three languages, but it is weaker in Sinhalese. Swap distance minimization is stronger than a preference for the canonical order in Korean and especially Malayalam.

cs.CL↗
arXiv2023

Linguistic laws in biology

Linguistic laws, the common statistical patterns of human language, have been investigated by quantitative linguists for nearly a century. Recently, biologists from a range of disciplines have started to explore the prevalence of these laws beyond language, finding patterns consistent with linguistic laws across multiple levels of biological organisation, from molecular (genomes, genes, and proteins) to organismal (animal behaviour) to ecological (populations and ecosystems). We propose a new conceptual framework for the study of linguistic laws in biology, comprising and integrating distinct levels of analysis, from description to prediction to theory building. Adopting this framework will provide critical new insights into the fundamental rules of organisation underpinning natural systems, unifying linguistic laws and core theory in biology.

cs.CL↗
arXiv2023

The expected sum of edge lengths in planar linearizations of trees. Theory and applications

Dependency trees have proven to be a very successful model to represent the syntactic structure of sentences of human languages. In these structures, vertices are words and edges connect syntactically-dependent words. The tendency of these dependencies to be short has been demonstrated using random baselines for the sum of the lengths of the edges or its variants. A ubiquitous baseline is the expected sum in projective orderings (wherein edges do not cross and the root word of the sentence is not covered by any edge), that can be computed in time $O(n)$. Here we focus on a weaker formal constraint, namely planarity. In the theoretical domain, we present a characterization of planarity that, given a sentence, yields either the number of planar permutations or an efficient algorithm to generate uniformly random planar permutations of the words. We also show the relationship between the expected sum in planar arrangements and the expected sum in projective arrangements. In the domain of applications, we derive a $O(n)$-time algorithm to calculate the expected value of the sum of edge lengths. We also apply this research to a parallel corpus and find that the gap between actual dependency distance and the random baseline reduces as the strength of the formal constraint on dependency structures increases, suggesting that formal constraints absorb part of the dependency distance minimization effect. Our research paves the way for replicating past research on dependency distance minimization using random planar linearizations as random baseline.

cs.CL↗
arXiv2023

Fast calculation of the variance of edge crossings in random arrangements

The crossing number of a graph $G$, $\mathrm{cr}(G)$, is the minimum number of edge crossings arising when drawing a graph on a certain surface. Determining $\mathrm{cr}(G)$ is a problem of great importance in Graph Theory. Its maximum variant, i.e. the maximum crossing number, $\mathrm{max-cr}(G)$, is receiving growing attention. Instead of an optimization problem on the number of crossings, here we consider the variance of the number of edge crossings, when embedding the vertices of an arbitrary graph uniformly at random in some space. In his pioneering research, Moon derived this variance on random linear arrangements of complete unipartite and bipartite graphs. Given the need of efficient algorithms to support this sort of research and given also the growing interest of the number of edge crossings in spatial networks, networks where vertices are embedded in some space, here we derive an algorithm to calculate the variance in arbitrary graphs in time $o(nm^2)$ that we transform into one that runs in time $O(nm)$ by reusing computations. We also derive one for forests that runs in time $O(n)$. These algorithms work on a wide range of random layouts (not only on Moon's) and are based on novel arithmetic expressions for the calculation of the variance that we develop from previous theoretical work. This paves the way for many applications that rely on a fast but exact calculation of the variance.

stat.CO↗