Properties of and Algorithms for Fitting Three-Way Component Models with Offset Terms

Prior to a three-way component analysis of a three-way data set, it is customary to preprocess the data by centering and/or rescaling them. Harshman and Lundy (1984) considered that three-way data actually consist of a three-way model part, which in fact pertains to ratio scale measurements, as well as additive “offset” terms that turn the ratio scale measurements into interval scale measurements. They mentioned that such offset terms might be estimated by incorporating additional components in the model, but discarded this idea in favor of an approach to remove such terms from the model by means of centering. Then estimates for the three-way component model parameters are obtained by analyzing the centered data. In the present paper, the possibility of actually estimating the offset terms is taken up again. First, it is mentioned in which cases such offset terms can be estimated uniquely. Next, procedures are offered for estimating model parameters and offset parameters simultaneously, as well as successively (i.e., providing offset term estimates after the three-way model parameters have been estimated in the traditional way on the basis of the centered data). These procedures are provided for both the CANDECOMP/PARAFAC model and the Tucker3 model extended with offset terms. The successive and the simultaneous approaches for estimating model and offset parameters have been compared on the basis of simulated data. It was found that both procedures perform well when the fitted model captures at least all offset terms actually underlying the data. The simultaneous procedures performed slightly better than the successive procedures. If fewer offset terms are fitted than there are underlying the model, the results are considerably poorer, but in these cases the successive procedures performed better than the simultaneous ones. All in all, it can be concluded that the traditional approach for estimating model parameters can hardly be improved upon, and that offset terms can sufficiently well be estimated by the proposed successive approach, which is a simple extension of the traditional approach. The author is obliged to Jos M.F. ten Berge and Marieke Timmerman for helpful comments on an earlier version of this paper. The author is obliged to Iven van Mechelen for making available the data set used in Section 6.     

Phonological complexity in school-aged children who stutter and exhibit a language disorder

PurposeThe Index of Phonological Complexity and the Word Complexity Measure are two measures of the phonological complexity of a word. Other phonological measures such as phonological neighborhood density have been used to compare stuttered versus fluent words. It appears that in preschoolers who stutter, the length and complexity of the utterance is more influential than the phonetic features of the stuttered word. The present hypothesis was that in school-age children who stutter, stuttered words would be more phonologically complex than fluent words, when the length and complexity of the utterance containing them is comparable. School-age speakers who stutter were hypothesized to differ from those with a concomitant language disorder.MethodsSixteen speakers, six females and ten males (M age = 12;3; Range = 7;7 to 19;5) available from an online database, were divided into eight who had a concomitant language disorder (S + LD) and eight age- and sex-matched speakers who did not (S-Only).ResultsWhen all stuttered content words were identified, S + LD speakers produced more repetitions, and S-Only speakers produced more inaudible sound prolongations. When stuttered content words were matched to fluent content words and when talker groups were combined, stuttered words were significantly (p ≤ 0.01) higher in both the Index of Phonological Complexity and the Word Complexity Measure and lower in density (“sparser”) than fluent words.ConclusionsResults corroborate those of previous researchers. Future research directions are suggested, such as cross-sectional designs to evaluate developmental patterns of phonological complexity and stuttering plus language disordered connections.Educational objectives: The reader will be able to: (a) Define and describe phonological complexity; (b) Define phonological neighborhood density and summarize the literature on the topic; (c) Describe the Index of Phonological Complexity (IPC) for a given word; (d) Describe the Word Complexity Measure (WCM) for a given word; (e) Summarize two findings from the current study and describe how each relates to studies of phonological complexity and fluency disorders.     

Denoting and Disquoting

Fregeans hold that predicates denote things, albeit things different in kind from what singular terms denote. This leads to a familiar problem: it seems impossible to say what any given predicate denotes. One strategy for avoiding this problem reduces the Fregean position to form of nominalism. I develop an alternative strategy that lets the Fregean hold on to the view that predicate denote things by reconceiving the nature of singular denotation and of Fregean objects.     

Finite basis problems and results for quasivarieties

Let be a finite collection of finite algebras of finite signature such that SP( ) has meet semi-distributive congruence lattices. We prove that there exists a finite collection ₁ of finite algebras of the same signature, , such that SP( ₁) is finitely axiomatizable.We show also that if , then SP( ₁) is finitely axiomatizable. We offer new proofs of two important finite basis theorems of D. Pigozzi and R. Willard. Our actual results are somewhat more general than this abstract indicates.While working on this paper, the first author was partially supported by the Hungarian National Foundation for Scientific Research (OTKA) grant no. T37877 and the second author was supported by the US National Science Foundation grant no. DMS-0245622.Special issue of Studia Logica: Algebraic Theory of Quasivarieties Presented by M. E. Adams, K. V. Adaricheva, W. Dziobiak, and A. V. Kravchenko     

Learning in context: linguistic and attentional constraints on children's color term learning

Three experiments investigated whether linguistic and/or attentional constraints might account for preschoolers' difficulties when learning color terms. Task structure and demands were equated across experiments, and both speed and degree of learning were compared. In Experiment 1, 3-year-olds who were matched on vocabulary score were taught new secondary color terms by corrective, semantic, or referential linguistic contrast. Corrective contrast produced more rapid and more extensive learning than did either semantic or referential contrast, supporting the hypothesis that targeted linguistic feedback facilitates learning. Experiment 2 replicated and extended the first experiment with Italian children and found cross-cultural differences in the amount learned about colors named differently in the two languages. In Experiment 3, some of the children were introduced to the new terms within a context of enhanced perceptual salience. These children learned as fast and performed as accurately as those given corrective linguistic feedback in Experiment 1.     

Pedagogical cliff‐jumping

This article chronicles how Introduction to the Study of Religion has become my favorite course to teach. In it, I narrate my process of pedagogical reinvention and syllabus redesign. Framed by professional and personal backstories, I share my pedagogical desires, list some pedagogical cues I took, and articulate pedagogical decisions and associated wagers. (Along the way, I draw on a range of disciplinary, interdisciplinary, and pedagogical materials as guides.) Then I tell how my Intro course realized these elements in its design and its execution. By doing so, I make a case for taking pedagogical risks and for reinventing Intro courses as performative responses to the practical and disciplinary question “how might we study religion?”     

"以生言性"的传统与孟子性善论

This article analyses the tradition of “articulating xing in terms of sheng” and related other expressions, and also examines the debate between Mencius and Gaozi concerning “xing is known by sheng.” It claims that while Mencius’ “human nature is good” discourse is influenced by the interpretive tradition of “articulating xing in terms of sheng”, Mencius also transcends and develops this tradition. Therefore it is only when Mencius’ views about the goodness of human nature are understood in the context of this interpretive tradition that his ideas can be fully understood. Utilizing this framework, the Confucian understanding of rights is then explored. Translated by Andrew Lambert from Zhexue yanjiu 哲学研究 (Philosophical Researches), 2007, (7): 36–42     

语言和文化对空间认知的影响 ——汉族和纳西族大学生空间词相似性分类的比较研究

以纳西族和汉族大学生为被试,对Yi-Fu Tuan归纳的17对空间词进行了相似性分类,并用多维标度法和分层聚类法进行了分析。结果表明,汉族大学生的空间认知围绕着4个主题：⑴三维方位;⑵边界;⑶空间饱和程度;⑷视觉距离。汉族大学生空间词的概念结构有两个维度：⑴方位/状态;⑵以观察者为参照/以物为参照。纳西族大学生的空间认知围绕着5个主题：⑴垂直方位;⑵水平方位;⑶边界;⑷空间饱和度;⑸视觉距离。纳西族大学生空间词的概念结构也有两个维度：⑴水平/垂直;⑵状态/方位。汉族大学生和纳西族大学生空间认知的差异主要表现在“水平/垂直”维度上,这与汉族和纳西族的语言和文化差异相一致。整个研究表明,语言和文化对空间认知主题和空间概念结构有着重要的影响     

Catachrestic Plural Forms. Gregory of Nyssa and Theodore Abū Qurrah on Naming and Counting Essences

The fourth-century thinker and theologian Gregory of Nyssa was a convinced realist about universals. According to him, there is just one substance man for all the individuals of the species man and this universal substance is completely instantiated by each individual. In two of his treatises – the Ad Ablabium and the Ad Graecos – he draws linguistic consequences from this realist position. This enquiry results in the thesis according to which it is incorrect to use natural kind terms (such as names of species) in the plural form, because that would involve stating a plurality of substances, when in fact there is just one substance for all the individuals of a given kind. In consequence, since the substance of all individual human beings is the same, the word ‘man’ can only be used adequately in the singular form. In this contribution, Gregory's reasoning is reconstructed. In the second part of the paper, the posterity of his theory and its endorsement by Theodore Abū Qurrah at the turn of the eighth and ninth centuries are examined.     

Curry-Howard Terms for Linear Logic

In this paper we 1. provide a natural deduction system for full first-order linear logic, 2. introduce Curry-Howard-style terms for this version of linear logic, 3. extend the notion of substitution of Curry-Howard terms for term variables, 4. define the reduction rules for the Curry-Howard terms and 5. outline a proof of the strong normalization for the full system of linear logic using a development of Girard's candidates for reducibility, thereby providing an alternative to Girard's proof using proof-nets.