Revisión del concepto de carga mental: Evaluación, consecuencias y proceso de normalización

The introduction of modern technology in almost every human environment imposes higher cognitive demands on people pegorming everyday tasks. This is why mental workload is a topic of increasing importance. There is no agreement on the definition of mental workload, nor any unit of measurement. It is usually assessed through un array of methods that focus on items ranging from its possible sources to the opinions of the people performing a specific task. Mental fatigue (induced by infraload as well as by overload) and the mistakes that may arise from it are two of the main consequences that should be analysed fiom the perspective of their ca~ise- that is, information processing. Finally, the paper describes the current attempts to standardize the coiacept of mental workload

Linear-time calculation of the expected sum of edge lengths in random projective linearizations of trees

The syntactic structure of a sentence is often represented using syntactic dependency trees. The sum of the distances between syntactically related words has been in the limelight for the past decades. Research on dependency distances led to the formulation of the principle of dependency distance minimization whereby words in sentences are ordered so as to minimize that sum. Numerous random baselines have been defined to carry out related quantitative studies on languages. The simplest random baseline is the expected value of the sum in unconstrained random permutations of the words in the sentence, namely, when all the shufflings of the words of a sentence are allowed and equally likely. Here we focus on a popular baseline: random projective permutations of the words of the sentence, that is, permutations where the syntactic dependency structure is projective, a formal constraint that sentences satisfy often in languages. Thus far, the expectation of the sum of dependency distances in random projective shufflings of a sentence has been estimated approximately with a Monte Carlo procedure whose cost is of the order of Rn, where n is the number of words of the sentence and R is the number of samples; it is well known that the larger R is, the lower the error of the estimation but the larger the time cost. Here we present formulae to compute that expectation without error in time of the order of n. Furthermore, we show that star trees maximize it, and provide an algorithm to retrieve the trees that minimize it.LAP is supported by Secretaria d’Universitats i Recerca de la Generalitat de Catalunya and the Social European Fund. RFC is also supported by the recognition 2017SGR-856 (MACDA) from AGAUR (Generalitat de Catalunya). RFC and LAP are supported by the grant TIN2017-89244-R from MINECO (Ministerio de Economía, Industria y Competitividad).Peer ReviewedPostprint (published version

Linear-time calculation of the expected sum of edge lengths in planar linearizations of trees

Dependency graphs have proven to be a very successful model to represent the syntactic structure of sentences of human languages. In these graphs, widely accepted to be trees, vertices are words and arcs 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). It was shown that said expected value can be computed in $O(n)$ time. In this article we focus on planar orderings (where the root word can be covered) and present two main results. First, we show the relationship between the expected sum in planar arrangements and the expected sum in projective arrangements. Second, we also derive a $O(n)$-time algorithm to calculate the expected value of the sum of edge lengths. These two results stem from another contribution of the present article, namely 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. Our research paves the way for replicating past research on dependency distance minimization using random planar linearizations as random baseline.Comment: Updated with comments from a colleagu

Fast calculation of the variance of edge crossings

The crossing number, i.e. the minimum number of edge crossings arising when drawing a graph on a certain surface, is a very important problem of graph theory. The opposite problem, i.e. the maximum crossing number, is receiving growing attention. Here we consider a complementary problem of the distribution of the number of edge crossings, namely the variance of the number of crossings, when embedding the vertices of an arbitrary graph in some space at random. In his pioneering research, Moon derived that 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 algorithms to calculate the variance in arbitrary graphs in $o(nm^2)$-time, and in forests in $O(n)$-time. 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.Comment: Better connection with graph theory (crossing number). Introduction and discussion substantially rewritten. Minor corrections in other parts of the articl

Linear-time calculation of the expected sum of edge lengths in random projective linearizations of trees

The syntactic structure of a sentence is often represented using syntactic dependency trees. The sum of the distances between syntactically related words has been in the limelight for the past decades. Research on dependency distances led to the formulation of the principle of dependency distance minimization whereby words in sentences are ordered so as to minimize that sum. Numerous random baselines have been defined to carry out related quantitative studies on languages. The simplest random baseline is the expected value of the sum in unconstrained random permutations of the words in the sentence, namely when all the shufflings of the words of a sentence are allowed and equally likely. Here we focus on a popular baseline: random projective permutations of the words of the sentence, that is, permutations where the syntactic dependency structure is projective, a formal constraint that sentences satisfy often in languages. Thus far, the expectation of the sum of dependency distances in random projective shufflings of a sentence has been estimated approximately with a Monte Carlo procedure whose cost is of the order of $Zn$, where $n$ is the number of words of the sentence and $Z$ is the number of samples; the larger $Z$, the lower the error of the estimation but the larger the time cost. Here we present formulae to compute that expectation without error in time of the order of $n$. Furthermore, we show that star trees maximize it, and devise a dynamic programming algorithm to retrieve the trees that minimize it

Reappraising the distribution of the number of edge crossings of graphs on a sphere

Many real transportation and mobility networks have their vertices placed on the surface of the Earth. In such embeddings, the edges laid on that surface may cross. In his pioneering research, Moon analyzed the distribution of the number of crossings on complete graphs and complete bipartite graphs whose vertices are located uniformly at random on the surface of a sphere assuming that vertex placements are independent from each other. Here we revise his derivation of that variance in the light of recent theoretical developments on the variance of crossings and computer simulations. We show that Moon's formulae are inaccurate in predicting the true variance and provide exact formulae.Comment: Corrected mistakes in equation 31. Added new figure (7). Added acknowledgements to J. W. Moon. Other minor changes. Updated figures. Minor changes in the last updat

The linear arrangement library: A new tool for research on syntactic dependency structures

The new and growing field of Quantitative Dependency Syntax has emerged at the crossroads between Dependency Syntax and Quantitative Linguistics. One of the main concerns in this field is the statistical patterns of syntactic dependency structures. These structures, grouped in treebanks, are the source for statistical analyses in these and related areas; dozens of scores devised over the years are the tools of a new industry to search for patterns and perform other sorts of analyses. The plethora of such metrics and their increasing complexity require sharing the source code of the programs used to perform such analyses. However, such code is not often shared with the scientific community or is tested following unknown standards. Here we present a new open-source tool, the Linear Arrangement Library (LAL), which caters to the needs of, especially, inexperienced programmers. This tool enables the calculation of these metrics on single syntactic dependency structures, treebanks, and collection of treebanks, grounded on ease of use and yet with great flexibility. LAL has been designed to be efficient, easy to use (while satisfying the needs of all levels of programming expertise), reliable (thanks to thorough testing), and to unite research from different traditions, geographic areas, and research fields.LAP is supported by Secretaria d’Universitats i Recerca de la Generalitat de Catalunya and the Social European Fund. RFC and LAP are supported by the grant TIN2017-89244-R from MINECO (Ministerio de Economía, Industria y Competitividad). RFC is also supported by the recognition 2017SGR-856 (MACDA) from AGAUR (Generalitat de Catalunya). JLE is funded by the grant PID2019-109137GB-C22 from MINECO.Peer ReviewedPostprint (published version

Revisión del concepto de carga mental: evaluación, consecuencias y proceso de normalización

The introduction of modern technology in almost every human environment imposes higher cognitive demands on people pegorming everyday tasks. This is why mental workload is a topic of increasing importance. There is no agreement on the definition of mental workload, nor any unit of measurement. It is usually assessed through un array of methods that focus on items ranging from its possible sources to the opinions of thepeople performing a specific task. Mental fatigue (induced by infraload as well as by overload) and the mistakes that may arise from it are two of the main consequences that should be analysed fiom the perspective of their ca~ise- that is, information processing. Finally, the paper describes the current attempts to standardize the coiacept of mental workload.La carga mental constituye un tópico que reviste cada vez más importancia en ergonomia, a medida que la moderna tecnologia se ha ido introduciendo en la práctica totalidad de los entornos, imponiendo mayores demandas cognitivas a las personas encargadas de llevar a cabo las tareas que nos plantea la vida cotidiana. No existe consenso en su definiciónconcreta, ni posee una unidad de medida específica. Su evaluación se acostumbra a efectuar mediante una bateria de procedimientos que abarcan desde sus posibles generadores hasta la opini6n de las personas que realizan las tareas. La fatiga mental, provocada tanto por infra como por sobrecarga, y los posibles errores que pueden generarse, son dos de lasconsecuencias cruciales que conviene analizar, todo ello desde la perspectiva de la generación de la carga mental: el procesamiento de información. Finalmente, conviene considerar los procesos de normalización internacional de la temática que se están desarrollando