Cohomological characterizations of projective spaces and hyperquadrics

We confirm Beauville's conjecture that claims that if the p-th exterior power of the tangent bundle of a smooth projective variety contains the p-th power of an ample line bundle, then the variety is either the projective space or the p-dimensional quadric hypersurface.Comment: Added Lemma 2.8 and slightly changed proof of Lemma 6.2 to make them apply for torsion-free sheaves and not only to vector bundle

Orthographic facilitation in oral vocabulary acquisition

An experiment investigated whether exposure to orthography facilitates oral vocabulary learning. A total of 58 typically developing children aged 8-9 years were taught 12 nonwords. Children were trained to associate novel phonological forms with pictures of novel objects. Pictures were used as referents to represent novel word meanings. For half of the nonwords children were additionally exposed to orthography, although they were not alerted to its presence, nor were they instructed to use it. After this training phase a nonword-picture matching posttest was used to assess learning of nonword meaning, and a spelling posttest was used to assess learning of nonword orthography. Children showed robust learning for novel spelling patterns after incidental exposure to orthography. Further, we observed stronger learning for nonword-referent pairings trained with orthography. The degree of orthographic facilitation observed in posttests was related to children's reading levels, with more advanced readers showing more benefit from the presence of orthography

Differential Forms on Log Canonical Spaces

The present paper is concerned with differential forms on log canonical varieties. It is shown that any p-form defined on the smooth locus of a variety with canonical or klt singularities extends regularly to any resolution of singularities. In fact, a much more general theorem for log canonical pairs is established. The proof relies on vanishing theorems for log canonical varieties and on methods of the minimal model program. In addition, a theory of differential forms on dlt pairs is developed. It is shown that many of the fundamental theorems and techniques known for sheaves of logarithmic differentials on smooth varieties also hold in the dlt setting. Immediate applications include the existence of a pull-back map for reflexive differentials, generalisations of Bogomolov-Sommese type vanishing results, and a positive answer to the Lipman-Zariski conjecture for klt spaces.Comment: 72 pages, 6 figures. A shortened version of this paper has appeared in Publications math\'ematiques de l'IH\'ES. The final publication is available at http://www.springerlink.co

On the Generation of Positivstellensatz Witnesses in Degenerate Cases

One can reduce the problem of proving that a polynomial is nonnegative, or more generally of proving that a system of polynomial inequalities has no solutions, to finding polynomials that are sums of squares of polynomials and satisfy some linear equality (Positivstellensatz). This produces a witness for the desired property, from which it is reasonably easy to obtain a formal proof of the property suitable for a proof assistant such as Coq. The problem of finding a witness reduces to a feasibility problem in semidefinite programming, for which there exist numerical solvers. Unfortunately, this problem is in general not strictly feasible, meaning the solution can be a convex set with empty interior, in which case the numerical optimization method fails. Previously published methods thus assumed strict feasibility; we propose a workaround for this difficulty. We implemented our method and illustrate its use with examples, including extractions of proofs to Coq.Comment: To appear in ITP 201

The British Lexicon Project: Lexical decision data for 28,730 monosyllabic and disyllabic English words

We present a new database of lexical decision times for English words and nonwords, for which two groups of British participants each responded to 14,365 monosyllabic and disyllabic words and the same number of nonwords for a total duration of 16 h (divided over multiple sessions). This database, called the British Lexicon Project (BLP), fills an important gap between the Dutch Lexicon Project (DLP; Keuleers, Diependaele, & Brysbaert, Frontiers in Language Sciences. Psychology, 1, 174, 2010) and the English Lexicon Project (ELP; Balota et al., 2007), because it applies the repeated measures design of the DLP to the English language. The high correlation between the BLP and ELP data indicates that a high percentage of variance in lexical decision data sets is systematic variance, rather than noise, and that the results of megastudies are rather robust with respect to the selection and presentation of the stimuli. Because of its design, the BLP makes the same analyses possible as the DLP, offering researchers with a new interesting data set of word-processing times for mixed effects analyses and mathematical modeling. The BLP data are available at http://crr.ugent.be/blp and as Electronic Supplementary Materials

Genome-wide association study identifies the SERPINB gene cluster as a susceptibility locus for food allergy

Genetic factors and mechanisms underlying food allergy are largely unknown. Due to heterogeneity of symptoms a reliable diagnosis is often difficult to make. Here, we report a genome-wide association study on food allergy diagnosed by oral food challenge in 497 cases and 2387 controls. We identify five loci at genome-wide significance, the clade B serpin (SERPINB) gene cluster at 18q21.3, the cytokine gene cluster at 5q31.1, the filaggrin gene, the C11orf30/LRRC32 locus, and the human leukocyte antigen (HLA) region. Stratifying the results for the causative food demonstrates that association of the HLA locus is peanut allergy-specific whereas the other four loci increase the risk for any food allergy. Variants in the SERPINB gene cluster are associated with SERPINB10 expression in leukocytes. Moreover, SERPINB genes are highly expressed in the esophagus. All identified loci are involved in immunological regulation or epithelial barrier function, emphasizing the role of both mechanisms in food allergy

Connecting Biology and Mathematics: First Prepare the Teachers

Developing the connection between biology and mathematics is one of the most important ways to shift the paradigms of both established science disciplines. However, adding some mathematic content to biology or biology content to mathematics is not enough but must be accompanied by development of suitable pedagogical models. I propose a model of pedagogical mathematical biological content knowledge as a feasible starting point for connecting biology and mathematics in schools and universities. The process of connecting these disciplines should start as early as possible in the educational process, in order to produce prepared minds that will be able to combine both disciplines at graduate and postgraduate levels of study. Because teachers are a crucial factor in introducing innovations in education, the first step toward such a goal should be the education of prospective and practicing elementary and secondary school teachers

Spelling-to-sound correspondences affect acronym recognition processes

A large body of research has examined the factors which affect the speed with which words are recognised in lexical decision tasks. Nothing has yet been reported concerning the important factors in differentiating acronyms (e.g. BBC, HIV, NASA) from non-words. It appears that this task poses little problem for skilled readers, in spite of the fact that acronyms have uncommon, even illegal, spellings in English. We used regression techniques to examine the role of a number of lexical and non-lexical variables known to be important in word processing in relation to lexical decision for acronym targets. Findings indicated that acronym recognition is affected by age of acquisition and imageability. In a departure from findings in word recognition,acronym recognition was not affected by frequency. Lexical decision responses for acronyms were also affected by the relationship between spelling and sound - a pattern not usually observed in word recognition. We argue that the complexity of acronym recognition means that the process draws phonological information in addition to semantics