Strictly positive definite functions on compact abelian groups

We study the Fourier characterisation of strictly positive definite functions on compact abelian groups. Our main result settles the case $G = F \times \mathbb{T}^r$, with $r \in \mathbb{N}$ and $F$ finite. The characterisation obtained for these groups does not extend to arbitrary compact abelian groups; it fails in particular for all torsion-free groups.Comment: 9 pages; submitted to Proc. AM

How much should we Distribute Morphology?

Studies of morphology, as carried out in practice, focus on a proper subset of bound morphemes which satisfy two properties: their inherent "meanings" are those of general grammatical categories, and they don\u27t receive stress like members of compounds. A question then arises, are there any morphology-specific principles, those of a "Morphological Component," that apply only to such forms? A number of candidates are examined in turn: "Non-maximality," Head Placement, Merger, Alternative Realization, and two Phonological Boundary Conditions. It is argued that the only principles specific to morphology are the last ones, i.e. that properly formulated principles of boundary erasure permit morphology to be completely "distributed" to the syntactic and phonological components

Q : the only Functional Head above N and A

Current versions of Chomskyan syntax take for granted that maximal or "extended" projections of the fundamental lexical categories N, A, V and P contain elaborate systems of functional heads and projections, which also differ in nature for each of these systems. This paper begins an argument, to be continued elsewhere, that this approach is currently more than "taken to extremes"; rather it is fundamentally misguided. All functional modifiers truly independent of a lexical category are types of quantifying or counting. Several unexplained properties then fall into place, among other those of subject phrases and measure phrases, and many differences between English and Japanese, both in counting and regarding subject NPs

θ-Role Assignment in Derived Nominals

Chomsky and Stowell attribute an asymmetry in noun and verb complement systems to how these categories assign Case. Here, Case assignment is dependent on structural configurations that θ-role theory determines; it is the latter which explains asymmetries in the noun and verb complement systems.Several predicate attribute and Vk (clausal) complement types are examined, and all confirm the θ-role theory in which V can assign θ-roles directly to sisters of any phrasal type, while N and A can assign θ-roles only "indirectly," to Ymax appearing in PP structures. This predicts the new patterns examined here, as well as the asymmetry in how objects of verbs and derived nominals are syntactically realized.Chomsky et Stowell attribuent l’asymétrie entre les compléments des noms et ceux des verbes aux propriétés respectives d’assignation de Cas de ces deux catégories. Ici, l’assignation du Cas dépend des configurations structurales déterminées par la théorie des rôles thématiques; c’est cette dernière qui explique les asymétries entre le système de complémentation du nom et celui du verbe.Plusieurs types d’attributs prédicatifs et de compléments Vk (phrastiques) sont examinés, et tous confirment la théorie Thêta selon laquelle V peut assigner des rôles thématiques directement aux soeurs de n’importe quel noeud phrastique, alors que N et A ne peuvent assigner qu’indirectement des rôles thématiques aux Ymax apparaissant dans des structures de PP. Ceci prédit les nouveaux patrons examinés ici, ainsi que l’asymétrie relative à la réalisation des objets des verbes et des nominaux dérivés

The single morpheme -ed/-en of the English past/passive

All English regular verbs and about half its irregular verbs have the same form for the finite past tense and the past participle. The finite past tense is different from the participle only for a closed class of about 100 irregular verbs. These latter can be analyzed by a lexical device of wide-ranging applicability called Alternative Realization. All other Past forms of Vs, finite and non-finite, can then be derived from a single morpheme -ed which appears in two contexts: one when V is finite and one when it is selected by a semantically empty stative verb, have or be. There is also a third use of -ed to form passive participles, in both verbal and adjectival passives.The paper presents a formalized system of selection features for lexical items including but going beyond classical subcategorization. This system permits formulating a single full lexical entry for the suffix -ed that covers all its uses. The final version of this entry exemplifies how to specify Alternative Realization, uninterpretability of categories and disjunctive contexts, and independently justifies each of these notations

Colony size predicts division of labour in Attine ants

Division of labour is central to the ecological success of eusocial insects, yet the evolutionary factors driving increases in complexity in division of labour are little known. The size–complexity hypothesis proposes that, as larger colonies evolve, both non-reproductive and reproductive division of labour become more complex as workers and queens act to maximize inclusive fitness. Using a statistically robust phylogenetic comparative analysis of social and environmental traits of species within the ant tribe Attini, we show that colony size is positively related to both non-reproductive (worker size variation) and reproductive (queen–worker dimorphism) division of labour. The results also suggested that colony size acts on non-reproductive and reproductive division of labour in different ways. Environmental factors, including measures of variation in temperature and precipitation, had no significant effects on any division of labour measure or colony size. Overall, these results support the size–complexity hypothesis for the evolution of social complexity and division of labour in eusocial insects. Determining the evolutionary drivers of colony size may help contribute to our understanding of the evolution of social complexity

Assembling the Tree of Life in Europe (AToLE)

A network of scientists under the umbrella of 'Assembling the Tree of Life in Europe (AToLE)' seeks funding under the FP7-Theme: Cooperation - Environment (including Climate Change and Biodiversity Conservation) programme of the European Commission.
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