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

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

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

MiR-133a in Human Circulating Monocytes: A Potential Biomarker Associated with Postmenopausal Osteoporosis

Background: Osteoporosis mainly occurs in postmenopausal women, which is characterized by low bone mineral density (BMD) due to unbalanced bone resorption by osteoclasts and formation by osteoblasts. Circulating monocytes play important roles in osteoclastogenesis by acting as osteoclast precursors and secreting osteoclastogenic factors, such as IL-1, IL-6 and TNF-a. MicroRNAs (miRNAs) have been implicated as important biomarkers in various diseases. The present study aimed to find significant miRNA biomarkers in human circulating monocytes underlying postmenopausal osteoporosis. Methodology/Principal Findings: We used ABI TaqManH miRNA array followed by qRT-PCR validation in circulating monocytes to identify miRNA biomarkers in 10 high and 10 low BMD postmenopausal Caucasian women. MiR-133a was upregulated (P = 0.007) in the low compared with the high BMD groups in the array analyses, which was also validated by qRT-PCR (P = 0.044). We performed bioinformatic target gene analysis and found three potential osteoclast-related target genes, CXCL11, CXCR3 and SLC39A1. In addition, we performed Pearson correlation analyses between the expression levels of miR-133a and the three potential target genes in the 20 postmenopausal women. We did find negative correlations between miR-133a and all the three genes though not significant. Conclusions/Significance: This is the first in vivo miRNA expression analysis in human circulating monocytes to identif

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