A local limit theorem for the critical random graph

We consider the limit distribution of the orders of the k largest components in the Erd¿os-Rényi random graph inside the critical window for arbitrary k. We prove a local limit theorem for this joint distribution and derive an exact expression for the joint probability density function

Optimality Theory as a Framework for Lexical Acquisition

This paper re-investigates a lexical acquisition system initially developed for French.We show that, interestingly, the architecture of the system reproduces and implements the main components of Optimality Theory. However, we formulate the hypothesis that some of its limitations are mainly due to a poor representation of the constraints used. Finally, we show how a better representation of the constraints used would yield better results

The bicycle-train travellers in the Netherlands: personal profiles and travel choices

The Netherlands seems to exhibit the unique conditions that allow cycling on the country level instead of only the city level. Moreover, the national transit system seemingly provides one crucial condition: citizens use the train and cycling systems in an integrated manner, with combined bicycle-train transport recently demonstrating strong growth. Relatively little is known about bicycle-train users, i.e. the people who combine the bicycle and the train in a single trip. In this paper, we investigate their profiles and travel choices, in terms of the modes they choose for access and egress travel, their choice of stations, and their choice of type of bicycles. Studying this specific group can add to our understanding of the role of the train system in the success of cycling in the Netherlands, in turn helping improve policy transfer to metropolitan areas in other countries. In 2017, in cooperation with the Dutch National Railways, researchers surveyed a sample of train travellers, ultimately resulting in more than 3000 completed questionnaires. Descriptive analyses revealed that, compared to train travellers who do not or rarely cycle to/from train stations, bicycle-train users are on average more likely to be young people who are engaged in full-time employment or entrepreneurs, commute to work and hold university degrees. As for their cycling behaviour, bicycle-train travellers use bicycles much more often on the home-end of train trips than on the activity-end. Furthermore, bicycle-train travellers infrequently use suburban stations on the home-end, preferring large stations in the centres of major cities instead. For those who use bicycles, shared bicycles claim a considerable share on the activity-end of a train trip

Monte Carlo study of the hull distribution for the q=1 Brauer model

We study a special case of the Brauer model in which every path of the model has weight q=1. The model has been studied before as a solvable lattice model and can be viewed as a Lorentz lattice gas. The paths of the model are also called self-avoiding trails. We consider the model in a triangle with boundary conditions such that one of the trails must cross the triangle from a corner to the opposite side. Motivated by similarities between this model, SLE(6) and critical percolation, we investigate the distribution of the hull generated by this trail (the set of points on or surrounded by the trail) up to the hitting time of the side of the triangle opposite the starting point. Our Monte Carlo results are consistent with the hypothesis that for system size tending to infinity, the hull distribution is the same as that of a Brownian motion with perpendicular reflection on the boundary.Comment: 21 pages, 9 figure

Pattern theorems, ratio limit theorems and Gumbel maximal clusters for random fields

We study occurrences of patterns on clusters of size n in random fields on Z^d. We prove that for a given pattern, there is a constant a>0 such that the probability that this pattern occurs at most an times on a cluster of size n is exponentially small. Moreover, for random fields obeying a certain Markov property, we show that the ratio between the numbers of occurrences of two distinct patterns on a cluster is concentrated around a constant value. This leads to an elegant and simple proof of the ratio limit theorem for these random fields, which states that the ratio of the probabilities that the cluster of the origin has sizes n+1 and n converges as n tends to infinity. Implications for the maximal cluster in a finite box are discussed.Comment: 23 pages, 2 figure

Language specificity of infant-directed speech: speaking rate and word position in word-learning contexts

Previous research indicates that infant-directed speech (IDS) is usually slower than adult-directed speech (ADS) and mothers prefer placing a focused word in isolation or utterance-final position in (English) IDS, which may benefit word learning. This study investigated the speaking rate and word position of IDS in two typologically-distinct languages: Dutch and Mandarin Chinese. We used a storybook-telling task to elicit semi-spontaneous ADS and IDS. The storybook contained target words that were familiar or unfamiliar to children. For each language, we asked: (1) whether IDS was slower than ADS; (2) whether mothers slowed down to highlight unfamiliar words; (3) whether the speaking rate of IDS changed between 18 and 24 months; and (4) whether mothers preferred placing unfamiliar words in isolation or utterance-final position in IDS. Results suggest that Dutch IDS, but not Mandarin Chinese IDS, was slower than ADS.Also, only Dutch mothers slowed down specifically when introducing unfamiliar words in IDS. In both languages, mothers placed target words in isolation (but not in utterance-final position) more frequently in IDS. These results suggest that the temporal modifications in IDS may vary across languages. Thus, language-specificity of IDS and its implications for language acquisition should be considered in future research.Teaching and Teacher Learning (ICLON

Language specificity of infant-directed speech: speaking rate and word position in word-learning contexts

Previous research indicates that infant-directed speech (IDS) is usually slower than adult-directed speech (ADS) and mothers prefer placing a focused word in isolation or utterance-final position in (English) IDS, which may benefit word learning. This study investigated the speaking rate and word position of IDS in two typologically-distinct languages: Dutch and Mandarin Chinese. We used a storybook-telling task to elicit semi-spontaneous ADS and IDS. The storybook contained target words that were familiar or unfamiliar to children. For each language, we asked: (1) whether IDS was slower than ADS; (2) whether mothers slowed down to highlight unfamiliar words; (3) whether the speaking rate of IDS changed between 18 and 24 months; and (4) whether mothers preferred placing unfamiliar words in isolation or utterance-final position in IDS. Results suggest that Dutch IDS, but not Mandarin Chinese IDS, was slower than ADS. Also, only Dutch mothers slowed down specifically when introducing unfamiliar words in IDS. In both languages, mothers placed target words in isolation (but not in utterance-final position) more frequently in IDS. These results suggest that the temporal modifications in IDS may vary across languages. Thus, language-specificity of IDS and its implications for language acquisition should be considered in future research.Theoretical and Experimental Linguistic

Prosodic input and children’s word learning in infant- and adult-directed speech

Theoretical and Experimental Linguistic

Pitch properties of infant-directed speech specific to word-learning contexts: a cross-linguistic investigation of Mandarin Chinese and Dutch

This study investigates the pitch properties of infant-directed speech (IDS) specific to word-learning contexts in which mothers introduce unfamiliar words to children. Using a semi-spontaneous story-book telling task, we examined (1) whether mothers made distinctions between unfamiliar and familiar words with pitch in IDS compared to adult-directed speech (ADS); (2) whether pitch properties change when mothers address children from 18 to 24 months; and (3) how Mandarin Chinese and Dutch IDS differ in their pitch properties in word-learning contexts. Results show that the mean pitch of Mandarin Chinese IDS was already ADS-like when children were 24 months, but Dutch IDS remained exaggerated in pitch at the same age. Crucially, Mandarin Chinese mothers used a higher pitch and a larger pitch range in IDS when introducing unfamiliar words, while Dutch mothers used a higher pitch specifically for familiar words. These findings contribute to the language-specificity of prosodic input in early lexical development.Theoretical and Experimental Linguistic

Two-Dimensional Critical Percolation: The Full Scaling Limit

We use SLE(6) paths to construct a process of continuum nonsimple loops in the plane and prove that this process coincides with the full continuum scaling limit of 2D critical site percolation on the triangular lattice -- that is, the scaling limit of the set of all interfaces between different clusters. Some properties of the loop process, including conformal invariance, are also proved.Comment: 45 pages, 12 figures. This is a revised version of math.PR/0504036 without the appendice