138 research outputs found
Derived categories of Burniat surfaces and exceptional collections
We construct an exceptional collection of maximal possible length
6 on any of the Burniat surfaces with , a 4-dimensional family of
surfaces of general type with . 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 of 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 , #
Doping Dependence on Two Sizes of Superconducting Gaps on Tl1223 by Tunneling Spectroscopy at 4.2K
AbstractWe present tunneling results on tri-layered cuprate superconductors TlBa2Ca2Cu3O8.5+δ (Tl1223) with two different hole concentration, which are an over-doped Tl1223 with TC ∼ 112K (OD-112K) and a slightly over-doped Tl1223 with TC ∼ 126K (SOD-126K). The tunneling conductances on both samples exhibited two sizes of gaps originated from outer (OP) and inner (IP) CuO2 planes. The superconducting gap at each planes, Δ(OP)/e ≈ Vp(OP) and Δ(IP)/e ≈ Vp(IP) on OD-112K are observed that Vp(OP) is 22 ± 2mV and Vp(IP) is 37 ± 4mV. Similarly, Vp(OP) is 26 ± 2mV and Vp(IP) is 39 ± 3mV on SOD-126K. Although both Vp(OP) and Vp(IP) decrease with increasing oxygen contents, ΔVp(OP) = Vp(OP)(SOD-126K) - Vp(OP)(OD-112K) is larger than ΔVp(IP) for IP. Moreover, ΔVp(plane) Vp(IP) - Vp(OP) increases with overdoping. These results as a function of doping implies the OP might control the variation of TC dominantly
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
() 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
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
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
Ordered Patterns of Cell Shape and Orientational Correlation during Spontaneous Cell Migration
BACKGROUND: In the absence of stimuli, most motile eukaryotic cells move by spontaneously coordinating cell deformation with cell movement in the absence of stimuli. Yet little is known about how cells change their own shape and how cells coordinate the deformation and movement. Here, we investigated the mechanism of spontaneous cell migration by using computational analyses. METHODOLOGY: We observed spontaneously migrating Dictyostelium cells in both a vegetative state (round cell shape and slow motion) and starved one (elongated cell shape and fast motion). We then extracted regular patterns of morphological dynamics and the pattern-dependent systematic coordination with filamentous actin (F-actin) and cell movement by statistical dynamic analyses. CONCLUSIONS/SIGNIFICANCE: We found that Dictyostelium cells in both vegetative and starved states commonly organize their own shape into three ordered patterns, elongation, rotation, and oscillation, in the absence of external stimuli. Further, cells inactivated for PI3-kinase (PI3K) and/or PTEN did not show ordered patterns due to the lack of spatial control in pseudopodial formation in both the vegetative and starved states. We also found that spontaneous polarization was achieved in starved cells by asymmetric localization of PTEN and F-actin. This breaking of the symmetry of protein localization maintained the leading edge and considerably enhanced the persistence of directed migration, and overall random exploration was ensured by switching among the different ordered patterns. Our findings suggest that Dictyostelium cells spontaneously create the ordered patterns of cell shape mediated by PI3K/PTEN/F-actin and control the direction of cell movement by coordination with these patterns even in the absence of external stimuli
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
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
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