Derived categories of Burniat surfaces and exceptional collections

We construct an exceptional collection $\Upsilon$ of maximal possible length 6 on any of the Burniat surfaces with $K_X^2=6$, a 4-dimensional family of surfaces of general type with $p_g=q=0$. We also calculate the DG algebra of endomorphisms of this collection and show that the subcategory generated by this collection is the same for all Burniat surfaces. The semiorthogonal complement $\mathcal A$ of $\Upsilon$ is an "almost phantom" category: it has trivial Hochschild homology, and K_0(\mathcal A)=\bZ_2^6.Comment: 15 pages, 1 figure; further remarks expande

K3-fibered Calabi-Yau threefolds I, the twist map

A construction of Calabi-Yaus as quotients of products of lower-dimensional spaces in the context of weighted hypersurfaces is discussed, including desingularisation. The construction leads to Calabi-Yaus which have a fiber structure, in particular one case has K3 surfaces as fibers. These Calabi-Yaus are of some interest in connection with Type II -heterotic string dualities in dimension 4. A section at the end of the paper summarises this for the non-expert mathematician.Comment: 31 pages LaTeX, 11pt, 2 figures. To appear in International Journal of Mathematics. On the web at http://personal-homepages.mis.mpg.de/bhunt/preprints.html , #

Numerical Ricci-flat metrics on K3

We develop numerical algorithms for solving the Einstein equation on Calabi-Yau manifolds at arbitrary values of their complex structure and Kahler parameters. We show that Kahler geometry can be exploited for significant gains in computational efficiency. As a proof of principle, we apply our methods to a one-parameter family of K3 surfaces constructed as blow-ups of the T^4/Z_2 orbifold with many discrete symmetries. High-resolution metrics may be obtained on a time scale of days using a desktop computer. We compute various geometric and spectral quantities from our numerical metrics. Using similar resources we expect our methods to practically extend to Calabi-Yau three-folds with a high degree of discrete symmetry, although we expect the general three-fold to remain a challenge due to memory requirements.Comment: 38 pages, 10 figures; program code and animations of figures downloadable from http://schwinger.harvard.edu/~wiseman/K3/ ; v2 minor corrections, references adde

Geometric Phantom Categories

In this paper we give a construction of phantom categories, i.e. admissible triangulated subcategories in bounded derived categories of coherent sheaves on smooth projective varieties that have trivial Hochschild homology and trivial Grothendieck group. We also prove that these phantom categories are phantoms in a stronger sense, namely, they have trivial K-motives and, hence, all their higher K-groups are trivial too.Comment: LaTeX, 18 page

Quantization and Compressive Sensing

Quantization is an essential step in digitizing signals, and, therefore, an indispensable component of any modern acquisition system. This book chapter explores the interaction of quantization and compressive sensing and examines practical quantization strategies for compressive acquisition systems. Specifically, we first provide a brief overview of quantization and examine fundamental performance bounds applicable to any quantization approach. Next, we consider several forms of scalar quantizers, namely uniform, non-uniform, and 1-bit. We provide performance bounds and fundamental analysis, as well as practical quantizer designs and reconstruction algorithms that account for quantization. Furthermore, we provide an overview of Sigma-Delta ($\Sigma\Delta$) quantization in the compressed sensing context, and also discuss implementation issues, recovery algorithms and performance bounds. As we demonstrate, proper accounting for quantization and careful quantizer design has significant impact in the performance of a compressive acquisition system.Comment: 35 pages, 20 figures, to appear in Springer book "Compressed Sensing and Its Applications", 201

Matrix factorisations and D-branes on K3

D-branes on K3 are analysed from three different points of view. For deformations of hypersurfaces in weighted projected space we use geometrical methods as well as matrix factorisation techniques. Furthermore, we study the D-branes on the T^4/\Z_4 orbifold line in conformal field theory. The behaviour of the D-branes under deformations of the bulk theory are studied in detail, and good agreement between the different descriptions is found.Comment: 35 pages, no figure

Expression of carbonic anhydrase 9, a potential intrinsic marker of hypoxia, is associated with poor prognosis in oesophageal squamous cell carcinoma

Carbonic anhydrase 9 (CA9) is a protein to be upregulated under exposure to hypoxic conditions. Hypoxic conditions are known to be associated with resistance to chemotherapy and radiotherapy, and with poor cancer prognosis. We examined CA9 expression in surgical specimens from oesophageal squamous cell carcinoma (ESCC) patients (n=127) using immunohistochemistry and real-time RT–PCR. We also examined CA9 expression and cell proliferation in ESCC cell lines (TE-2, TE-8 and TE-15) and an immortalised human oesophageal cell line (CHEK-1) using real-time RT–PCR, Western blotting, ELISA and MTT assay. Immunohistochemistry, high expression of CA9 was found in 63 of the 127 primary tumour specimens and was correlated with poor outcome (P=0.0003) and more aggressive/less favourable clinicopathological parameters (tumour size (P=0.0235), tumour depth (P<0.0001), regional lymph node metastasis (P=0.0031), distant lymph node metastasis (P=0.0077), stage (P<0.0001) and blood vessel invasion (P=0.006)). In vitro, CA9 expression in cultured cells and culture medium was also induced by hypoxia (P<0.01). CA9 is correlated with poor prognosis and malignant phenotype in patients with ESCC, and was upregulated by hypoxia. It is suggested that control of CA9 expression might improve the effectiveness of chemotherapy and radiotherapy in ESCC

AAV-mediated intramuscular delivery of myotubularin corrects the myotubular myopathy phenotype in targeted murine muscle and suggests a function in plasma membrane homeostasis

Myotubular myopathy (XLMTM, OMIM 310400) is a severe congenital muscular disease due to mutations in the myotubularin gene (MTM1) and characterized by the presence of small myofibers with frequent occurrence of central nuclei. Myotubularin is a ubiquitously expressed phosphoinositide phosphatase with a muscle-specific role in man and mouse that is poorly understood. No specific treatment exists to date for patients with myotubular myopathy. We have constructed an adeno-associated virus (AAV) vector expressing myotubularin in order to test its therapeutic potential in a XLMTM mouse model. We show that a single intramuscular injection of this vector in symptomatic Mtm1-deficient mice ameliorates the pathological phenotype in the targeted muscle. Myotubularin replacement in mice largely corrects nuclei and mitochondria positioning in myofibers and leads to a strong increase in muscle volume and recovery of the contractile force. In addition, we used this AAV vector to overexpress myotubularin in wild-type skeletal muscle and get insight into its localization and function. We show that a substantial proportion of myotubularin associates with the sarcolemma and I band, including triads. Myotubularin overexpression in muscle induces the accumulation of packed membrane saccules and presence of vacuoles that contain markers of sarcolemma and T-tubules, suggesting that myotubularin is involved in plasma membrane homeostasis of myofibers. This study provides a proof-of-principle that local delivery of an AAV vector expressing myotubularin can improve the motor capacities of XLMTM muscle and represents a novel approach to study myotubularin function in skeletal muscle

Expression of miRNAs miR-133b and miR-206 in the Il17a/f Locus Is Co-Regulated with IL-17 Production in αβ and γδ T Cells

Differentiation of T helper 17 cells (Th17) is a multistep process that involves the cytokines IL-6, TGF-β, and IL-23 as well as IL-1β, IL-21, and TNF-α. Thereby, robust induction of the capacity to produce IL-17 involves epigenetic modifications of the syntenic Il17a/f locus. Using inbred mouse strains, we identified co-regulation of gene transcription at the Il17a/f locus with the nearby microRNAs miR-133b and miR-206 that are clustered approximately 45 kb upstream of Il17a/f. Expression of these microRNAs was specific for Th17 as compared to other CD4+ T cell subsets and this was equally valid for in vitro polarized and ex vivo derived cells. From all factors analyzed, IL-23 was the most important cytokine for the in vitro induction of miR-133b and miR-206 in naive CD4+ T cells of wild type mice. However, analysis of IL-23R deficient mice revealed that IL-23R signaling was not essential for the induction of miR-133b and miR-206. Importantly, we found a similar co-regulation in CCR6+ and other γδ T cell subsets that are predisposed to production of IL-17. Taken together, we discovered a novel feature of T cell differentiation towards an IL-17-producing phenotype that is shared between αβ and γδ T cells. Notably, the specific co-regulation of miR-133b and miR-206 with the Il17a/f locus also extended to human Th17 cells. This qualifies expression of miR-133b and miR-206 in T cells as novel biomarkers for Th17-type immune reactions