Noncommutative resolutions of ADE fibered Calabi-Yau threefolds

In this paper we construct noncommutative resolutions of a certain class of Calabi-Yau threefolds studied by F. Cachazo, S. Katz and C. Vafa. The threefolds under consideration are fibered over a complex plane with the fibers being deformed Kleinian singularities. The construction is in terms of a noncommutative algebra introduced by V. Ginzburg, which we call the "N=1 ADE quiver algebra"

Sheaves on fibered threefolds and quiver sheaves

This paper classifies a class of holomorphic D-branes, closely related to framed torsion-free sheaves, on threefolds fibered in resolved ADE surfaces over a general curve C, in terms of representations with relations of a twisted Kronheimer--Nakajima-type quiver in the category Coh(C) of coherent sheaves on C. For the local Calabi--Yau case C\cong\A^1 and special choice of framing, one recovers the N=1 ADE quiver studied by Cachazo--Katz--Vafa.Comment: 13 pages, 2 figures, minor change

Diffeomorphisms and families of Fourier-Mukai transforms in mirror symmetry

Assuming the standard framework of mirror symmetry, a conjecture is formulated describing how the diffeomorphism group of a Calabi-Yau manifold Y should act by families of Fourier-Mukai transforms over the complex moduli space of the mirror X. The conjecture generalizes a proposal of Kontsevich relating monodromy transformations and self-equivalences. Supporting evidence is given in the case of elliptic curves, lattice-polarized K3 surfaces and Calabi-Yau threefolds. A relation to the global Torelli problem is discussed.Comment: Approx. 20 pages LaTeX. One reference adde

Acquisition of prosodic focus marking by English, French, and German three-, four-, five- and six-year-olds

Previous research on young children's knowledge of prosodic focus marking has revealed an apparent paradox, with comprehension appearing to lag behind production. Comprehension of prosodic focus is difficult to study experimentally due to its subtle and ambiguous contribution to pragmatic meaning. We designed a novel comprehension task, which revealed that three- to six-year-old children show adult-like comprehension of the prosodic marking of subject and object focus. Our findings thus support the view that production does not precede comprehension in the acquisition of focus. We tested participants speaking English, German, and French. All three languages allow prosodic subject and object focus marking, but use additional syntactic marking to varying degrees (English: dispreferred; German: possible; French preferred). French participants produced fewer subject marked responses than English participants. We found no other cross-linguistic differences. Participants interpreted prosodic focus marking similarly and in an adult-like fashion in all three languages

Bosniak category III cysts are more likely to be malignant than we expected in the era of multidetector computed tomography technology

Background: Complex indeterminate Bosniak category III renal cystic masses are traditionally considered to be malignant in 50%. Our aim was to retrospectively evaluate the attenuation characteristics in multiphase computed tomography (CT) and to determinate the incidence of malignancy based on histological findings on all Bosniak category III renal cystic masses investigated in our department between April 3, 2007 and November 21, 2013. Materials and Methods: Quadriphasic multidetector CT images of nineteen patients (mean age: 56.5 +/- 16.5 years) with radiologically detected Bosniak category III lesions were reviewed retrospectively. All lesions were surgically removed, and the incidence of malignancy, based on pathological results was determined. Results: Calcification was present in four lesions (21%). The mean largest diameter was 48.7 +/- 28.8 mm. All lesions were multilobulated and septated. Of the 19 removed lesions, 16 (84%) were malignant, and 3 (16%) were benign (one inflammatory cyst including a nephrolith, one cystic nephroma and one atypical angiomyolipoma). CT and histological findings of 19 Bosniak III cysts were correlated. Conclusion: Our study demonstrated much higher prevalence of malignancy (84%) in radiologically detected Bosniak category III cysts than it has been described before. It may due to the era of modern multidetector CT technology and multiphase protocol

Wall Crossing of BPS States on the Conifold from Seiberg Duality and Pyramid Partitions

In this paper we study the relation between pyramid partitions with a general empty room configuration (ERC) and the BPS states of D-branes on the resolved conifold. We find that the generating function for pyramid partitions with a length n ERC is exactly the same as the D6/D2/D0 BPS partition function on the resolved conifold in particular Kaehler chambers. We define a new type of pyramid partition with a finite ERC that counts the BPS degeneracies in certain other chambers. The D6/D2/D0 partition functions in different chambers were obtained by applying the wall crossing formula. On the other hand, the pyramid partitions describe T^3 fixed points of the moduli space of a quiver quantum mechanics. This quiver arises after we apply Seiberg dualities to the D6/D2/D0 system on the conifold and choose a particular set of FI parameters. The arrow structure of the dual quiver is confirmed by computation of the Ext group between the sheaves. We show that the superpotential and the stability condition of the dual quiver with this choice of the FI parameters give rise to the rules specifying pyramid partitions with length n ERC.Comment: 23 pages, 8 figures. CMP versio

Structure of a large social network

We study a social network consisting of over $10^4$ individuals, with a degree distribution exhibiting two power scaling regimes separated by a critical degree $k_{\rm crit}$, and a power law relation between degree and local clustering. We introduce a growing random model based on a local interaction mechanism that reproduces all of the observed scaling features and their exponents. Our results lend strong support to the idea that several very different networks are simultenously present in the human social network, and these need to be taken into account for successful modeling.Comment: 5 pages, 5 figure

Non-commutative desingularization of determinantal varieties, I

We show that determinantal varieties defined by maximal minors of a generic matrix have a non-commutative desingularization, in that we construct a maximal Cohen-Macaulay module over such a variety whose endomorphism ring is Cohen-Macaulay and has finite global dimension. In the case of the determinant of a square matrix, this gives a non-commutative crepant resolution.Comment: 52 pages, 3 figures, all comments welcom

Contrastive focus and emphasis

The paper puts forward a discourse-semantic account of the notoriously evasive phenomena of contrastivity and emphasis. Based on new evidence from Chadic, it is argued that occurrences of focus that are treated in terms of ‘contrastive focus’, ‘kontrast’ (Vallduví-Vilkuna 1998) or ‘identificational focus’ (É. Kiss 1998) in the literature should not be analyzed in familiar semantic terms as involving the introduction and subsequent exclusion of alternatives. Rather, an adequate analysis must take into account discourse-semantic notions like ‘hearer expectation’ or ‘discourse expectability’ of the focused content in a given discourse situation. The less expected the focus content is judged to be for the hearer, relative to the Common Ground, the more likely a speaker is to mark the focus constituent by means of special grammatical devices, thus giving rise to emphasis