Some higher order isoperimetric inequalities via the method of optimal transport

In this paper, we establish some sharp inequalities between the volume and the integral of the $k$-th mean curvature for $k+1$-convex domains in the Euclidean space. The results generalize the classical Alexandrov-Fenchel inequalities for convex domains. Our proof utilizes the method of optimal transportation.Comment: 21 page

Some Progress in Conformal Geometry

This is a survey paper of our current research on the theory of partial differential equations in conformal geometry. Our intention is to describe some of our current works in a rather brief and expository fashion. We are not giving a comprehensive survey on the subject and references cited here are not intended to be complete. We introduce a bubble tree structure to study the degeneration of a class of Yamabe metrics on Bach flat manifolds satisfying some global conformal bounds on compact manifolds of dimension 4. As applications, we establish a gap theorem, a finiteness theorem for diffeomorphism type for this class, and diameter bound of the $\sigma_2$-metrics in a class of conformal 4-manifolds. For conformally compact Einstein metrics we introduce an eigenfunction compactification. As a consequence we obtain some topological constraints in terms of renormalized volumes.Comment: This is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

A conformally invariant sphere theorem in four dimensions

In this paper we provide a sharp characterization of the smooth four-dimensional sphere. The assumptions of the theorem are conformally invariant, and can be reduced to an L^2 inequality of the Weyl tensor and positivity of the Yamabe invariant.Comment: 39 pages, 0 figure

Some Progress in Conformal Geometry

This is a survey paper of our current research on the theory of partial differential equations in conformal geometry. Our intention is to describe some of our current works in a rather brief and expository fashion. We are not giving a comprehensive survey on the subject and references cited here are not intended to be complete. We introduce a bubble tree structure to study the degeneration of a class of Yamabe metrics on Bach flat manifolds satisfying some global conformal bounds on compact manifolds of dimension 4. As applications, we establish a gap theorem, a finiteness theorem for diffeomorphism type for this class, and diameter bound of the σ2-metrics in a class of conformal 4-manifolds. For conformally compact Einstein metrics we introduce an eigenfunction compactification. As a consequence we obtain some topological constraints in terms of renormalized volumes

Clinicopathologic characteristics and treatment outcomes of hepatoid adenocarcinoma of the stomach, a rare but unique subtype of gastric cancer

<p>Abstract</p> <p>Background</p> <p>Gastric hepatoid adenocarcinoma (HAC) is a special type of gastric cancer that morphologically mimics hepatocellular carcinoma. In this study, we performed an evaluation of clinicopathologic characteristics, treatment outcome, and prognosis in patients with gastric HAC.</p> <p>Methods</p> <p>We consecutively enrolled patients with pathologically proven gastric HAC at Seoul National University Hospital between January 1996 and December 2008 and conducted a retrospective review. Among 15,253 patients with gastric cancer, 26 patients (0.17%) were diagnosed as gastric HAC.</p> <p>Results</p> <p>Among 26 patients, 22 were male and the median age was 63. Stage at diagnosis was stage IB in 3 patients, stage II in 6 patients, stage III in 7 patients, and stage IV in 10 patients. Eight patients out of 18 patients with stage IB, II, III, and IV relapsed after curative surgery. Relapse-free survival for these patients was 16.67 months. The most common metastatic site was intraabdominal lymph nodes (n = 9), followed by the liver (n = 8). Thirteen patients received palliative chemotherapy. The most commonly used regimen was a combination of fluoropyrimidine and platinum. Partial response was observed in one patient and stable disease in 5 patients. Median overall survival and progression free survival of these patients were 8.03 (95% CI: 6.59-9.47) and 3.47 months (95% CI: 0.65-6.29), respectively.</p> <p>Conclusions</p> <p>Gastric HAC is a very rare but unique type of stomach cancer. Early detection of this type of cancer is of critical importance to patient prognosis. Additional studies to reveal the biology of this tumor are warranted.</p

Calcium-sensing receptor antagonists abrogate airway hyperresponsiveness and inflammation in allergic asthma

Airway hyperresponsiveness and inflammation are fundamental hallmarks of allergic asthma that are accompanied by increases in certain polycations, such as eosinophil cationic protein. Levels of these cations in body fluids correlate with asthma severity. We show that polycations and elevated extracellular calcium activate the human recombinant and native calcium-sensing receptor (CaSR), leading to intracellular calcium mobilization, cyclic adenosine monophosphate breakdown, and p38 mitogen-activated protein kinase phosphorylation in airway smooth muscle (ASM) cells. These effects can be prevented by CaSR antagonists, termed calcilytics. Moreover, asthmatic patients and allergen-sensitized mice expressed more CaSR in ASMs than did their healthy counterparts. Indeed, polycations induced hyperreactivity in mouse bronchi, and this effect was prevented by calcilytics and absent in mice with CaSR ablation from ASM. Calcilytics also reduced airway hyperresponsiveness and inflammation in allergen-sensitized mice in vivo. These data show that a functional CaSR is up-regulated in asthmatic ASM and targeted by locally produced polycations to induce hyperresponsiveness and inflammation. Thus, calcilytics may represent effective asthma therapeutics

Landscape of somatic single nucleotide variants and indels in colorectal cancer and impact on survival

Colorectal cancer (CRC) is a biologically heterogeneous disease. To characterize its mutational profile, we conduct targeted sequencing of 205 genes for 2,105 CRC cases with survival data. Our data shows several findings in addition to enhancing the existing knowledge of CRC. We identify PRKCI, SPZ1, MUTYH, MAP2K4, FETUB, and TGFBR2 as additional genes significantly mutated in CRC. We find that among hypermutated tumors, an increased mutation burden is associated with improved CRC-specific survival (HR=0.42, 95% CI: 0.21-0.82). Mutations in TP53 are associated with poorer CRC-specific survival, which is most pronounced in cases carrying TP53 mutations with predicted 0% transcriptional activity (HR=1.53, 95% CI: 1.21-1.94). Furthermore, we observe differences in mutational frequency of several genes and pathways by tumor location, stage, and sex. Overall, this large study provides deep insights into somatic mutations in CRC, and their potential relationships with survival and tumor features. Large scale sequencing study is of paramount importance to unravel the heterogeneity of colorectal cancer. Here, the authors sequenced 205 cancer genes in more than 2000 tumours and identified additional mutated driver genes, determined that mutational burden and specific mutations in TP53 are associated with survival odds