Broadcast dimension of graphs

In this paper we initiate the study of broadcast dimension, a variant of metric dimension. Let G be a graph with vertex set V (G), and let d(u, w) denote the length of a u − w geodesic in G. For k ≥ 1, let dk (x, y) = min{d(x, y), k +1}. A function f: V (G) → Z+ ∪{0} is called a resolving broadcast of G if, for any distinct x, y ∈ V (G), there exists a vertex [Formula Presented]. The broadcast dimension, bdim(G), of G is the minimum of [Formula Presented] over all resolving broadcasts of G, where bcf (G) can be viewed as the total cost of the transmitters (of various strength) used in resolving the entire network described by the graph G. Note that bdim(G) reduces to adim(G) (the adjacency dimension of G, introduced by Jannesari and Omoomi in 2012) if the codomain of resolving broadcasts is restricted to {0, 1}. We determine its value for cycles, paths, and other families of graphs. We prove that bdim(G) = Ω(log n) for all graphs G of order n, and that the result is sharp up to a constant factor. We show that [Formula Presented] and can both be arbitrarily large, where dim(G) denotes the metric dimension of G. We also examine the effect of vertex deletion on both the adjacency dimension and the broadcast dimension of graphs

The Use of Lexical and Referential Cues in Children’s Online Interpretation of Adjectives

Recent research on moment-to-moment language comprehension has revealed striking differences between adults and preschool children. Adults rapidly use the referential principle to resolve syntactic ambiguity, assuming that modification is more likely when there are 2 possible referents for a definite noun phrase. Young children do not. We examine the scope of this phenomenon by exploring whether children use the referential principle to resolve another form of ambiguity. Scalar adjectives (big, small) are typically used to refer to an object when contrasting members of the same category are present in the scene (big and small coins). In the present experiment, 5-year-olds and adults heard instructions like “Point to the big (small) coin” while their eye-movements were measured to displays containing 1 or 2 coins. Both groups rapidly recruited the meaning of the adjective to distinguish between referents of different sizes. Critically, like adults, children were quicker to look to the correct item in trials containing 2 possible referents compared with 1. Nevertheless, children's sensitivity to the referential principle was substantially delayed compared to adults', suggesting possible differences in the recruitment of this top- down cue. The implications of current and previous findings are discussed with respect to the development of the architecture of language comprehension.LinguisticsPsycholog

Cascading Activation Across Levels of Representation in Children's Lexical Processing

Recent work in adult psycholinguistics has demonstrated that activation of semantic representations begins long before phonological processing is complete. This incremental propagation of information across multiple levels of analysis is a hallmark of adult language processing but how does this ability develop? In two experiments, we elicit measures of incremental activation of semantic representations during word recognition in children. Five-year-olds were instructed to select a target (logs) while their eye-movements were measured to a competitor (key) that was semantically related to an absent phonological associate (lock). We found that like adults, children made increased looks to competitors relative to unrelated control items. However unlike adults, children continued to look at the competitor even after the target word was uniquely identified and were more likely to incorrectly select this item. Altogether, these results suggest that early lexical processing involves cascading activation but less efficient resolution of competing entries.Psycholog

Logic and Conversation Revisited: Evidence For a Division Between Semantic and Pragmatic Content in Real Time Language Comprehension

The distinction between semantics (linguistically encoded meaning) and pragmatics (inferences about communicative intentions) can often be unclear and counterintuitive. For example, linguistic theories argue that the meaning of some encompasses the meaning of all while the intuition that some implies not all results from an inference. We explored how online interpretation of some evolves using an eye-tracking while listening paradigm. Early eye-movements indicated that while some was initially interpreted as compatible with all, participants began excluding referents compatible with all approximately 800 ms later. These results contrast with recent evidence of immediate inferencing and highlight the presence of bottom-up semantic–pragmatic interactions which necessarily rely on initial access to lexical meanings to trigger inferences.Psycholog

Semantic Meaning and Pragmatic Interpretation in 5-Year-Olds: Evidence from Real-Time Spoken Language Comprehension

Recent research on children's inferencing has found that although adults typically adopt the pragmatic interpretation of some (implying not all), 5- to 9-year-olds often prefer the semantic interpretation of the quantifier (meaning possibly all). Do these failures reflect a breakdown of pragmatic competence or the metalinguistic demands of prior tasks? In 3 experiments, the authors used the visual-world eye-tracking paradigm to elicit an implicit measure of adults' and children's abilities to generate scalar implicatures. Although adults' eye-movements indicated that adults had interpreted some with the pragmatic inference, children's looks suggested that children persistently interpreted some as compatible with all (Experiment 1). Nevertheless, both adults and children were able to quickly reject competitors that were inconsistent with the semantics of some; this confirmed the sensitivity of the paradigm (Experiment 2). Finally, adults, but not children, successfully distinguished between situations that violated the scalar implicature and those that did not (Experiment 3). These data demonstrate that children interpret quantifiers on the basis of their semantic content and fail to generate scalar implicatures during online language comprehension.Psycholog

When is Four Far More Than Three? Children’s Generalization of Newly-Acquired Number Words

What is the relationship between children’s first number words and number concepts? We used training tasks to explore children’s interpretation of number words as they acquired their meanings. Children who had mastered the meanings of only the first two or three number words were systematically provided with varied input on the next word-to-quantity mapping, and their extension of the newly-trained word was assessed across a variety of test items. Children who had mastered number words to three generalized training on four to new objects and nouns, with approximate accuracy. In contrast, children who had mastered only one and two learned to apply three reliably within a single count noun context (three dogs) but not to new objects labeled with different nouns (three cows). Both findings suggest that children fail to map newly-learned words in their counting routine to fully abstract concepts of natural number.Psycholog

The Relevance of Polarity for the Online Interpretation of Scalar Terms

The interpretation of scalar terms (like, e.g., some vs. all; the numerals) has been at the center of much theoretical debate. Recently, this debate has focused on whether Scalar Implicature (SI) computation is grammatically or post grammatically driven (cf., e.g., Russell, 2006 vs. Chierchia, Fox and Spector, 2008 and references therein). In the present work, we address these issues through experimental means arguing, specifically, for two theses: Thesis 1: The interpretation of both numerals and determiners like some/all are systematically affected by the polarity (Downward monotone or DE vs. Upward monotone or UE) of the local context in which they are embedded. Thesis 2: Numerals and Determiners differ in how the ‘exact’ interpretation comes about: for numerals such interpretation is much faster. Thesis 1, if true, provides evidence against the thesis that scalar items are lexically ambiguous (for no lexical ambiguity is polarity sensitive in such a way) and in favor of the view that the ‘exact’ vs. the ‘at least’ interpretation of both types of scalar items is an implicature. Thesis 2, if true, shows that the way in which the ‘exact’ interpretation comes about for numerals vs. determiners is partly similar and partly different. This can be construed as an argument against the thesis that these elements are ‘underspecified’ in similar ways (cf., e.g., Musolino, 2003).LinguisticsPhilosophyPsycholog

Ripple Effects: How Teacher Action Research on Culturally Relevant Education Can Promote Systemic Change

Teacher action research has been shown to both promote professional growth in teachers as well as produce gains for students. However, to date, little research has examined how action research might contribute to systemic changes in schools and school districts. This qualitative study of six teachers from various districts, subject areas, and grade levels, illustrates how action research can have simultaneous impacts on teachers, their students, and their schools and districts. The teacher action research projects all focused on culturally relevant education and the pursuit of equity. Impacts included teachers’ deepened understandings of equity and inclusivity; students’ diversity awareness, positive self-identities, and access to wider opportunities; and schools’ adoption of equity-focused strategies. The findings suggest that action research on culturally relevant education serves not only as a powerful form of professional development but also as a means to potentially transform schools