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

Paradigmaváltás a csontmetasztázisok sebészetében. I. Végtagi és medencelokalizációjú áttétek

According to the statistical data of tumor registries the incidence of cancer has increased in the last decade, however the mortality shows only a slight change due to the new and effective multimodal treatments. The aim of our overview article is to present the changes in the survival of the metastatic patients, and to demonstrate which factors influence their prognosis. The improvement of survival resulted in a more active surgical role both in metastases of the bone of the extremities and the pelvis. We present a diagnostic flow chart and current options for the reconstruction of the different regions of the bone and skeleton, and we will discuss their potential advantages, disadvantages and complications. It is evident that apart from the impending and pathological fracture surgery it is not the first choice of treatment but rather a palliative measure. The aim of surgery is to alleviate pain, to regain mobility and improve quality of life. If possible minimal invasive techniques are performed, as they are less demanding and allow fast rehabilitation for the patient, and they are solutions that last for a lifetime. In optimal conditions radical curative surgery can be performed in about 10 to 15 per cent of the cases, and better survival is encouraging. Orv Hetil. 2017; 158(40): 1563-1569

A Ewing-sarcomás betegek tünetmentes túlélési esélyeinek értékelése a Gyermekonkológiai Szekció eredményei alapján

Correlation between different prognostic factors and the overall survival of Ewing's sarcoma patients has been investigted. In this study data have been selected from the databank of Hungarian Pediatric Oncologist Section (1988-1999) (n=65). Whenever it was possible statistical analysis has been performed. Results: In our patients time interval from the primary symptoms to the diagnosis was 2-16 months. The average event-free survival in patients suffering from Ewing's sarcoma without metastasis is 0.39. Meanwhile, this value in patients with pulmonary or other metatasis is 0.24 (Kaplan-Meier analysis). Conclusion: Our results show a moderate difference between the Hungarian and the international event-free survival. Late detection is one of the answers of this discrepancy

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

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

Curve counting via stable pairs in the derived category

For a nonsingular projective 3-fold $X$, we define integer invariants virtually enumerating pairs $(C,D)$ where $C\subset X$ is an embedded curve and $D\subset C$ is a divisor. A virtual class is constructed on the associated moduli space by viewing a pair as an object in the derived category of $X$. The resulting invariants are conjecturally equivalent, after universal transformations, to both the Gromov-Witten and DT theories of $X$. For Calabi-Yau 3-folds, the latter equivalence should be viewed as a wall-crossing formula in the derived category. Several calculations of the new invariants are carried out. In the Fano case, the local contributions of nonsingular embedded curves are found. In the local toric Calabi-Yau case, a completely new form of the topological vertex is described. The virtual enumeration of pairs is closely related to the geometry underlying the BPS state counts of Gopakumar and Vafa. We prove that our integrality predictions for Gromov-Witten invariants agree with the BPS integrality. Conversely, the BPS geometry imposes strong conditions on the enumeration of pairs.Comment: Corrected typos and duality error in Proposition 4.6. 47 page

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