Isoparametric foliation and Yau conjecture on the first eigenvalue

A well known conjecture of Yau states that the first eigenvalue of every closed minimal hypersurface $M^n$ in the unit sphere $S^{n+1}(1)$ is just its dimension $n$. The present paper shows that Yau conjecture is true for minimal isoparametric hypersurfaces. Moreover, the more fascinating result of this paper is that the first eigenvalues of the focal submanifolds are equal to their dimensions in the non-stable range.Comment: to appear in J.Diff.Geo

Isoparametric functions and exotic spheres

The first part of the paper is to improve the fundamental theory of isoparametric functions on general Riemannian manifolds. Next we focus our attention on exotic spheres, especially on "exotic" 4-spheres (if exist) and the Gromoll-Meyer sphere. In particular, as one of main results we prove: there exists no properly transnormal function on any exotic 4-sphere if it exists. Furthermore, by projecting an $S^3$-invariant isoparametric function on $Sp(2)$, we construct a properly transnormal but not an isoparametric function on the Gromoll-Meyer sphere with two points as the focal varieties.Comment: 21 pages, to appear in Journal f\"ur die reine und angewandte Mathematik (Crelles Journal

Topology of Blow-ups and Enumerative Geometry

Let M be the blow--up of a manifold M along a submanifold X. In this paper we present closed formulae for the integral cohomology and the total Chern class of M. As applications we compute the cohomology of the varieties of complete conics and complete quadrices in 3--space, and justify two enumerative results due to Schubert.Comment: 30 page

Using molecular imaging to assess the delivery and infection of protease activated virus in animal model of myocardial infarction

Cardiovascular diseases remain the greatest cause of death in the US and gene therapy has the potential to be an effective therapy. In this study, we demonstrated MMP-9 based protease-activatable virus (PAV) for selective infection of myocardial infarct (MI) that is associated with active MMP-9 expression. To test the specificity of PAV, we used expression of a far-red fluorescence protein (iRFP) delivered by the PAV together with a dual PET/NIRF imaging agent specific for active MMP-9 activity at the site of MI in a murine model. Calibrated fluorescence imaging employed a highly-sensitive intensified camera, laser diode excitation sources, and filtration schemes based upon the spectra of iRFP and the NIRF agent. One to two days after ligation of the left anterior descending artery, the PAV or WT AAV9 virus encoding for iRFP (5x1010 genomic particles) and radiolabeled MMP-9 imaging agent (3 nmol) were injected intravenously (i.v.). PET imaging showed MMP activity was associated with adverse tissue remodeling at the site of the MI. One week after, animals were again injected i.v. with the MMP-9 agent (3 nmol) and 18-24 h later, the animals were euthanized and the hearts were harvested, sliced, and imaged for congruent iRFP transgene expression and NIRF signals associated with MMP-9 tissue activity. The fluorescent margins of iRFP and NIRF contrasted tissues were quantified in terms Standard International units of mW/cm2/sr. The sensitivity, specificity, and accuracy of PAV and WT targeting to sites of MI was determined from these calibrated fluorescence measurements. The PAV demonstrated significantly higher delivery performance than that of the WT AAV9 virus

Neutrophil to albumin ratio: a biomarker in non-alcoholic fatty liver disease and with liver fibrosis

ObjectiveGiven the high prevalence of non-alcoholic fatty liver disease (NAFLD) and its potential to progress to liver fibrosis, it is crucial to identify the presence of NAFLD in patients to guide their subsequent management. However, the current availability of non-invasive biomarkers for NAFLD remains limited. Therefore, further investigation is needed to identify and develop non-invasive biomarkers for NAFLD.MethodsA retrospective analysis was conducted on 11,883 patients admitted to the Healthcare Center, Union Hospital, Tongji Medical College, Huazhong University of Science and Technology, from January 2016 to December 2019 and divided into NAFLD and non-NAFLD groups. Anthropometric and laboratory examination data were collected. The correlations between variables and NAFLD were evaluated using the student’s t-test or Mann–Whitney U test and binary logistic regression analysis. The predictive ability of these variables for NAFLD was assessed using the areas under the curves (AUCs) of receiver operating characteristics.ResultsAmong the included patients, 3,872 (32.58%) were diagnosed with NAFLD, with 386 (9.97%) individuals having liver fibrosis. Patients with NAFLD exhibited a higher proportion of males, elevated body mass index (BMI), and increased likelihood of hypertension, diabetes mellitus, and atherosclerosis. Logistic regression analysis identified the neutrophil to albumin ratio (NAR) as the most promising novel inflammation biomarkers, with the highest AUC value of 0.701, a cut-off value of 0.797, sensitivity of 69.40%, and specificity of 66.00% in identifying the risk of NAFLD. Moreover, NAR demonstrated superior predictive value in identifying NAFLD patients at risk of liver fibrosis, with an AUC value of 0.795, sensitivity of 71.30%, and specificity of 73.60% when NAR reached 1.285.ConclusionThese findings highlight that the novel inflammatory biomarker, NAR, is a convenient and easily accessible non-invasive predictor for NAFLD and NAFLD with liver fibrosis

Expert Consensus on Microtransplant for Acute Myeloid Leukemia in Elderly Patients -Report From the International Microtransplant Interest Group

Recent studies have shown that microtransplant (MST) could improve outcome of patients with elderly acute myeloid leukemia (EAML). To further standardize the MST therapy and improve outcomes in EAML patients, based on analysis of the literature on MST, especially MST with EAML from January 1st, 2011 to November 30th, 2022, the International Microtransplant Interest Group provides recommendations and considerations for MST in the treatment of EAML. Four major issues related to MST for treating EAML were addressed: therapeutic principle of MST (1), candidates for MST (2), induction chemotherapy regimens (3), and post-remission therapy based on MST (4). Others included donor screening, infusion of donor cells, laboratory examinations, and complications of treatment

Generalizations of RSA Public Key Cryptosystem

In this paper, for given N = pq with p and q different odd primes, and m = 1, 2, , we give a public key cryptosystem. When m = 1 the system is just the famous RSA system. And when m 2, the system is usually more secure than the one with m = 1