A census of critical sets in the Latin squares of order at most six

A critical set in a Latin square of order n is a set of entries from the square which can be embedded in precisely one Latin square of order n, Such that if any element of the critical set. is deleted, the remaining set can be embedded, in more than one Latin square of order n.. In this paper we find all the critical sets of different sizes in the Latin squares of order at most six. We count the number of main and isotopy classes of these critical sets and classify critical sets from the main classes into various strengths. Some observations are made about the relationship between the numbers of classes, particularly in the 6 x 6 case. Finally some examples are given of each type of critical set.

An investigation of 2-critical sets in latin squares

In this paper we focus on the existence of 2-critical sets in the latin square corresponding to the elementary abelian 2-group of order 2(n). It has been shown by Stinson and van Rees that this latin square contains a 2-critical set of volume 4(n) - 3(n). We provide constructions for 2-critical sets containing 4(n) - 3(n) + 1 - (2(k-1) + 2(m-1) + 2(n-(k+m+1))) entries, where 1 less than or equal to k less than or equal to n and 1 less than or equal to m less than or equal to n - k. That is, we construct 2-critical sets for certain values less than 4(n) - 3(n) + 1 - 3 (.) 2([n /3]-1). The results raise the interesting question of whether, for the given latin square, it is possible to construct 2-critical sets of volume m, where 4(n) - 3(n) + 1 - 3 (.) 2([n/3]-1) < m < 4(n) - 3(n).

Toddler subtraction with large sets: further evidence for an analog-magnitude representation of number

Two experiments were conducted to test the hypothesis that toddlers have access to an analog-magnitude number representation that supports numerical reasoning about relatively large numbers. Three-year-olds were presented with subtraction problems in which initial set size and proportions subtracted were systematically varied. Two sets of cookies were presented and then covered The experimenter visibly subtracted cookies from the hidden sets, and the children were asked to choose which of the resulting sets had more. In Experiment 1, performance was above chance when high proportions of objects (3 versus 6) were subtracted from large sets (of 9) and for the subset of older participants (older than 3 years, 5 months; n = 15), performance was also above chance when high proportions (10 versus 20) were subtracted from the very large sets (of 30). In Experiment 2, which was conducted exclusively with older 3-year-olds and incorporated an important methodological control, the pattern of results for the subtraction tasks was replicated In both experiments, success on the tasks was not related to counting ability. The results of these experiments support the hypothesis that young children have access to an analog-magnitude system for representing large approximate quantities, as performance on these subtraction tasks showed a Webers Law signature, and was independent of conventional number knowledge.

The discourse of biology lectures : aspects of its mode and text structure

The present thesis investigates mode related aspects in biology lecture discourse and attempts to identify the position of this variety along the spontaneous spoken versus planned written language continuum. Nine lectures (of 43,000 words) consisting of three sets of three lectures each, given by the three lecturers at Aston University, make up the corpus. The indeterminacy of the results obtained from the investigation of grammatical complexity as measured in subordination motivates the need to take the analysis beyond sentence level to the study of mode related aspects in the use of sentence-initial connectives, sub-topic shifting and paraphrase. It is found that biology lecture discourse combines features typical of speech and writing at sentence as well as discourse level: thus, subordination is more used than co-ordination, but one degree complexity sentence is favoured; some sentence initial connectives are only found in uses typical of spoken language but sub-topic shift signalling (generally introduced by a connective) typical of planned written language is a major feature of the lectures; syntactic and lexical revision and repetition, interrupted structures are found in the sub-topic shift signalling utterance and paraphrase, but the text is also amenable to analysis into sentence like units. On the other hand, it is also found that: (1) while there are some differences in the use of a given feature, inter-speaker variation is on the whole not significant; (2) mode related aspects are often motivated by the didactic function of the variety; and (3) the structuring of the text follows a sequencing whose boundaries are marked by sub-topic shifting and the summary paraphrase. This study enables us to draw four theoretical conclusions: (1) mode related aspects cannot be approached as a simple dichotomy since a combination of aspects of both speech and writing are found in a given feature. It is necessary to go to the level of textual features to identify mode related aspects; (2) homogeneity is dominant in this sample of lectures which suggests that there is a high level of standardization in this variety; (3) the didactic function of the variety is manifested in some mode related aspects; (4) the features studied play a role in the structuring of the text.

The verbal transformation effect:an exploration of the perceptual organization of speech

Six experiments investigated the influence of several grouping cues within the framework of the Verbal Transformation Effect (VTE, Experiments 1 to 4) and Phonemic Transformation Effect (PTE, Experiments 5 and 6), where listening to a repeated word (VTE) or sequence of vowels (PTE) produces verbal transformations (VTs). In Experiment 1, the influence of F0 frequency and lateralization cues (ITDs) was investigated in terms of the pattern of VTs. As the lateralization difference increased between two repeating sequences, the number of forms was significantly reduced with the fewest forms reported in the dichotic condition. Experiment 2 explored whether or not propensity to report more VTs on high pitch was due to the task demands of monitoring two sequences at once. The number of VTs reported was higher when listeners were asked to attend to one sequence only, suggesting smaller attentional constraints on the task requirements. In Experiment 3, consonant-vowel transitions were edited out from two sets of six stimuli words with ‘strong’ and ‘weak’ formant transitions, respectively. Listeners reported more forms in the spliced-out than in the unedited case for the strong-transition words, but not for those with weak transitions. A similar trend was observed for the F0 contour manipulation used in Experiment 4 where listeners reported more VTs and forms for words following a discontinuous F0 contour. In Experiments 5 and 6, the role of F0 frequency and ITD cues was investigated further using a related phenomenon – the PTE. Although these manipulations had relatively little effect on the number of VTs and forms reported, they did influence the particular forms heard. In summary, the current experiments confirmed that it is possible to successfully investigate auditory grouping cues within the VTE framework and that, in agreement with recent studies, the results can be attributed to the perceptual re-grouping of speech sounds.

What drives the prediction of early reading? An analysis of stimulus and response-type

Purpose: Phonological accounts of reading implicate three aspects of phonological awareness tasks that underlie the relationship with reading; a) the language-based nature of the stimuli (words or nonwords), b) the verbal nature of the response, and c) the complexity of the stimuli (words can be segmented into units of speech). Yet, it is uncertain which task characteristics are most important as they are typically confounded. By systematically varying response-type and stimulus complexity across speech and non-speech stimuli, the current study seeks to isolate the characteristics of phonological awareness tasks that drive the prediction of early reading. Method: Four sets of tasks were created; tone stimuli (simple non-speech) requiring a non-verbal response, phonemes (simple speech) requiring a non-verbal response, phonemes requiring a verbal response, and nonwords (complex speech) requiring a verbal response. Tasks were administered to 570 2nd grade children along with standardized tests of reading and non-verbal IQ. Results: Three structural equation models comparing matched sets of tasks were built. Each model consisted of two 'task' factors with a direct link to a reading factor. The following factors predicted unique variance in reading: a) simple speech and non-speech stimuli, b) simple speech requiring a verbal response but not simple speech requiring a non-verbal-response, and c) complex and simple speech stimuli. Conclusions: Results suggest that the prediction of reading by phonological tasks is driven by the verbal nature of the response and not the complexity or 'speechness' of the stimuli. Findings highlight the importance of phonological output processes to early reading.

Semantic patterns for sentiment analysis of Twitter

Most existing approaches to Twitter sentiment analysis assume that sentiment is explicitly expressed through affective words. Nevertheless, sentiment is often implicitly expressed via latent semantic relations, patterns and dependencies among words in tweets. In this paper, we propose a novel approach that automatically captures patterns of words of similar contextual semantics and sentiment in tweets. Unlike previous work on sentiment pattern extraction, our proposed approach does not rely on external and fixed sets of syntactical templates/patterns, nor requires deep analyses of the syntactic structure of sentences in tweets. We evaluate our approach with tweet- and entity-level sentiment analysis tasks by using the extracted semantic patterns as classification features in both tasks. We use 9 Twitter datasets in our evaluation and compare the performance of our patterns against 6 state-of-the-art baselines. Results show that our patterns consistently outperform all other baselines on all datasets by 2.19% at the tweet-level and 7.5% at the entity-level in average F-measure.

Evaluating the Effectiveness of Discrete Trial Procedures for Teaching Receptive Discrimination to Children with Autism Spectrum Disorders

Research has found that children with autism spectrum disorders (ASD) show significant deficits in receptive language skills (Wiesmer, Lord, & Esler, 2010). One of the primary goals of applied behavior analytic intervention is to improve the communication skills of children with autism by teaching receptive discriminations. Both receptive discriminations and receptive language entail matching spoken words with corresponding objects, symbols (e.g., pictures or words), actions, people, and so on (Green, 2001). In order to develop receptive language skills, children with autism often undergo discrimination training within the context of discrete trial training. This training entails teaching the learner how to respond differentially to different stimuli (Green, 2001). It is through discrimination training that individuals with autism learn and develop language (Lovaas, 2003). The present study compares three procedures for teaching receptive discriminations: (1) simple/conditional (Procedure A), (2) conditional only (Procedure B), and (3) conditional discrimination of two target cards (Procedure C). Six children, ranging in age from 2-years-old to 5-years-old, with an autism diagnosis were taught how to receptively discriminate nine sets of stimuli. Results suggest that the extra training steps included in the simple/conditional and conditional only procedures may not be necessary to teach children with autism how to receptively discriminate. For all participants, Procedure C appeared to be the most efficient and effective procedure for teaching young children with autism receptive discriminations. Response maintenance and generalization probes conducted one-month following the end of training indicate that even though Procedure C resulted in less training sessions overall, no one procedure resulted in better maintenance and generalization than the others. In other words, more training sessions, as evident with the simple/conditional and conditional only procedures, did not facilitate participants’ ability to accurately respond or generalize one-month following training. The present study contributes to the literature on what is the most efficient and effective way to teach receptive discrimination during discrete trial training to children with ASD. These findings are critical as research shows that receptive language skills are predictive of better outcomes and adaptive behaviors in the future.

At 6-9 months, human infants know the meanings of many common nouns.

It is widely accepted that infants begin learning their native language not by learning words, but by discovering features of the speech signal: consonants, vowels, and combinations of these sounds. Learning to understand words, as opposed to just perceiving their sounds, is said to come later, between 9 and 15 mo of age, when infants develop a capacity for interpreting others' goals and intentions. Here, we demonstrate that this consensus about the developmental sequence of human language learning is flawed: in fact, infants already know the meanings of several common words from the age of 6 mo onward. We presented 6- to 9-mo-old infants with sets of pictures to view while their parent named a picture in each set. Over this entire age range, infants directed their gaze to the named pictures, indicating their understanding of spoken words. Because the words were not trained in the laboratory, the results show that even young infants learn ordinary words through daily experience with language. This surprising accomplishment indicates that, contrary to prevailing beliefs, either infants can already grasp the referential intentions of adults at 6 mo or infants can learn words before this ability emerges. The precocious discovery of word meanings suggests a perspective in which learning vocabulary and learning the sound structure of spoken language go hand in hand as language acquisition begins.

The acquisition of abstract words by young infants.

Young infants' learning of words for abstract concepts like 'all gone' and 'eat,' in contrast to their learning of more concrete words like 'apple' and 'shoe,' may follow a relatively protracted developmental course. We examined whether infants know such abstract words. Parents named one of two events shown in side-by-side videos while their 6-16-month-old infants (n=98) watched. On average, infants successfully looked at the named video by 10 months, but not earlier, and infants' looking at the named referent increased robustly at around 14 months. Six-month-olds already understand concrete words in this task (Bergelson & Swingley, 2012). A video-corpus analysis of unscripted mother-infant interaction showed that mothers used the tested abstract words less often in the presence of their referent events than they used concrete words in the presence of their referent objects. We suggest that referential uncertainty in abstract words' teaching conditions may explain the later acquisition of abstract than concrete words, and we discuss the possible role of changes in social-cognitive abilities over the 6-14 month period.

Formal and philological inquiries into the nature of interrogatives, indefinites, disjunction, and focus in Sinhala and other languages

In this thesis I examine a variety of linguistic elements which involve ``alternative'' semantic values---a class arguably including focus, interrogatives, indefinites, and disjunctions---and the connections between these elements. This study focusses on the analysis of such elements in Sinhala, with comparison to Malayalam, Tlingit, and Japanese. The central part of the study concerns the proper syntactic and semantic analysis of Q[uestion]-particles (including Sinhala "da", Malayalam "-oo", Japanese "ka"), which, in many languages, appear not only in interrogatives, but also in the formation of indefinites, disjunctions, and relative clauses. This set of contexts is syntactically-heterogeneous, and so syntax does not offer an explanation for the appearance of Q-particles in this particular set of environments. I propose that these contexts can be united in terms of semantics, as all involving some element which denotes a set of ``alternatives''. Both wh-words and disjunctions can be analysed as creating Hamblin-type sets of ``alternatives''. Q-particles can be treated as uniformly denoting variables over choice functions which apply to the aforementioned Hamblin-type sets, thus ``restoring'' the derivation to normal Montagovian semantics. The treatment of Q-particles as uniformly denoting variables over choice functions provides an explanation for why these particles appear in just this set of contexts: they all include an element with Hamblin-type semantics. However, we also find variation in the use of Q-particles; including, in some languages, the appearance of multiple morphologically-distinct Q-particles in different syntactic contexts. Such variation can be handled largely by positing that Q-particles may vary in their formal syntactic feature specifications, determining which syntactic contexts they are licensed in. The unified analysis of Q-particles as denoting variables over choice functions also raises various questions about the proper analysis of interrogatives, indefinites, and disjunctions, including issues concerning the nature of the semantics of wh-words and the syntactic structure of disjunction. As well, I observe that indefinites involving Q-particles have a crosslinguistic tendency to be epistemic indefinites, i.e. indefinites which explicitly signal ignorance of details regarding who or what satisfies the existential claim. I provide an account of such indefinites which draws on the analysis of Q-particles as variables over choice functions. These pragmatic ``signals of ignorance'' (which I argue to be presuppositions) also have a further role to play in determining the distribution of Q-particles in disjunctions. The final section of this study investigates the historical development of focus constructions and Q-particles in Sinhala. This diachronic study allows us not only to observe the origin and development of such elements, but also serves to delimit the range of possible synchronic analyses, thus providing us with further insights into the formal syntactic and semantic properties of Q-particles. This study highlights both the importance of considering various components of the grammar (e.g. syntax, semantics, pragmatics, morphology) and the use of philology in developing plausible formal analyses of complex linguistic phenomena such as the crosslinguistic distribution of Q-particles.

Almost Disjoint Families of Representing Sets

The thesis is concerned with a number of problems in Combinatorial Set Theory. The Generalized Continuum Hypothesis is assumed. Suppose X and K are non-zero cardinals. By successively identifying K with airwise disjoint sets of power K, a function/: X-*•K can be viewed as a transversal of a pairwise disjoint (X, K)family A . Questions about families of functions in K can thus bethought of as referring to families of transversals of A. We wish to consider generalizations of such questions to almost disjoint families; in particular we are interested in extensions of the following two problems: (i) What is the 'maximum' cardinality of an almost disjoint family of functions each mapping X into K? (ii) Describe the cardinalities of maximal almost disjoint families of functions each mapping X into K. Article in Bulletin of the Australian Mathematical Society 27(03):477 - 479 · June 1983  

Evaluating the effectiveness of discrete trial procedures for teaching receptive discrimination to children with autism spectrum disorders

Research has found that children with autism spectrum disorders (ASD) show significant deficits in receptive language skills (Wiesmer, Lord, & Esler, 2010). One of the primary goals of applied behavior analytic intervention is to improve the communication skills of children with autism by teaching receptive discriminations. Both receptive discriminations and receptive language entail matching spoken words with corresponding objects, symbols (e.g., pictures or words), actions, people, and so on (Green, 2001). In order to develop receptive language skills, children with autism often undergo discrimination training within the context of discrete trial training. This training entails teaching the learner how to respond differentially to different stimuli (Green, 2001). It is through discrimination training that individuals with autism learn and develop language (Lovaas, 2003). The present study compares three procedures for teaching receptive discriminations: (1) simple/conditional (Procedure A), (2) conditional only (Procedure B), and (3) conditional discrimination of two target cards (Procedure C). Six children, ranging in age from 2-years-old to 5-years-old, with an autism diagnosis were taught how to receptively discriminate nine sets of stimuli. Results suggest that the extra training steps included in the simple/conditional and conditional only procedures may not be necessary to teach children with autism how to receptively discriminate. For all participants, Procedure C appeared to be the most efficient and effective procedure for teaching young children with autism receptive discriminations. Response maintenance and generalization probes conducted one-month following the end of training indicate that even though Procedure C resulted in less training sessions overall, no one procedure resulted in better maintenance and generalization than the others. In other words, more training sessions, as evident with the simple/conditional and conditional only procedures, did not facilitate participants’ ability to accurately respond or generalize one-month following training. The present study contributes to the literature on what is the most efficient and effective way to teach receptive discrimination during discrete trial training to children with ASD. These findings are critical as research shows that receptive language skills are predictive of better outcomes and adaptive behaviors in the future. ^

Pretest of images associated with the expertise dimension

In this paper, we present norms concerning the perceived association that two sets of stimuli (photos of people and photos of objects) establish with the concept of expertise. Participants were presented with a set of words associated with the expertise dimension and subsequently asked to judge each stimulus on how much it related with the learned (expertise) dimension on a 7-point scale (1 – Not at all related; 7 – Very related). The interpretation of means’ confidence intervals allowed us to distinguish between images highly related with the expertise dimension and images highly unrelated with this dimension. Summarized results are presented and photos made available to support future research requiring stimuli associated with the expertise dimension.

On Ordinal VC-Dimension and Some Notions of Complexity

We generalize the classical notion of Vapnik–Chernovenkis (VC) dimension to ordinal VC-dimension, in the context of logical learning paradigms. Logical learning paradigms encompass the numerical learning paradigms commonly studied in Inductive Inference. A logical learning paradigm is defined as a set W of structures over some vocabulary, and a set D of first-order formulas that represent data. The sets of models of ϕ in W, where ϕ varies over D, generate a natural topology W over W. We show that if D is closed under boolean operators, then the notion of ordinal VC-dimension offers a perfect characterization for the problem of predicting the truth of the members of D in a member of W, with an ordinal bound on the number of mistakes. This shows that the notion of VC-dimension has a natural interpretation in Inductive Inference, when cast into a logical setting. We also study the relationships between predictive complexity, selective complexity—a variation on predictive complexity—and mind change complexity. The assumptions that D is closed under boolean operators and that W is compact often play a crucial role to establish connections between these concepts. We then consider a computable setting with effective versions of the complexity measures, and show that the equivalence between ordinal VC-dimension and predictive complexity fails. More precisely, we prove that the effective ordinal VC-dimension of a paradigm can be defined when all other effective notions of complexity are undefined. On a better note, when W is compact, all effective notions of complexity are defined, though they are not related as in the noncomputable version of the framework.