A CLASSIFICATION OF SOME ALMOST α-PARA-KENMOTSU MANIFOLDS

In this paper, we mainly study local structures and curvatures of the almost α-para-Kenmotsu manifolds. In particular, locally symmetric almost α-para-Kenmotsu manifolds satisfying certain nullity conditions are classified

Secoond order parallel tensors on some paracontact manifolds

The object of the present paper is to study the symmetric and skewsymmetric properties of a second order parallel tensor on paracontact metric (k;μ)- spaces and almost β-para-Kenmotsu (k;μ)-spaces. In this paper, we prove that if there exists a second order symmetric parallel tensor on a paracontact metric (k;μ)- space M, then either M is locally isometric to a product of a at n + 1-dimensional manifold and an n-dimensional manifold of constant sectional curvature -4, or the second order parallel tensor is a constant multiple of the associated metric tensor g of M2n+1. If there is a second order parallel tensor on an almost -para-Kenmotsu (k;μ)-space with k≠ 0, then it is a constant multiple of the associated metric tensor g of M2n+1.Mathematics Subject Classication (2010): 53C15, 53C25, 53D10, 53D15.Key words: Second order parallel tensor, paracontact metric (k;μ)-space, almost -para-Kenmotsu (k;μ)-space

THREE-DIMENSIONAL ALMOST α\alpha-PARA-KENMOTSU MANIFOLDS SATISFYING CERTAIN NULLITY CONDITIONS

In this paper, we study 3-dimensional  almost $\alpha$-para-Kenmotsu manifolds satisfying special types of nullity conditions depending on smooth functions $\tilde{\kappa},\tilde{\mu}$ and $\tilde{\nu}$=constant, also we present a local description of the structure of a 3-dimensional almost $\alpha$-para-Kenmotsu $(\tilde{\kappa},\tilde{\mu},\tilde{\nu}=const.)$-manifold $(M,\tilde{\varphi},\xi,\eta,\tilde{g})$ with $\tilde{\kappa}+\alpha^{2}\neq0$ such that $d\tilde{\kappa}\wedge\eta=0$

DataSheet_1_Association of CT-Based Delta Radiomics Biomarker With Progression-Free Survival in Patients With Colorectal Liver Metastases Undergo Chemotherapy.docx

Predicting the prognosis of patients in advance is conducive to providing personalized treatment for patients. Our aim was to predict the therapeutic efficacy and progression free survival (PFS) of patients with liver metastasis of colorectal cancer according to the changes of computed tomography (CT) radiomics before and after chemotherapy.MethodsThis retrospective study included 139 patients (397 lesions) with colorectal liver metastases who underwent neoadjuvant chemotherapy from April 2015 to April 2020. We divided the lesions into training cohort and testing cohort with a ratio of 7:3. Two - dimensional region of interest (ROI) was obtained by manually delineating the largest layers of each metastasis lesion. The expanded ROI (3 mm and 5 mm) were also included in the study to characterize microenvironment around tumor. For each of the ROI, 1,316 radiomics features were extracted from delineated plain scan, arterial, and venous phase CT images before and after neoadjuvant chemotherapy. Delta radiomics features were constructed by subtracting the radiomics features after treatment from the radiomics features before treatment. Univariate Cox regression and the Least Absolute Shrinkage and Selection Operator (LASSO) Cox regression were applied in the training cohort to select the valuable features. Based on clinical characteristics and radiomics features, 7 Cox proportional-hazards model were constructed to predict the PFS of patients. C-index value and Kaplan Meier (KM) analysis were used to evaluate the efficacy of predicting PFS of these models. Moreover, the prediction performance of one-year PFS was also evaluated by area under the curve (AUC).ResultsCompared with the PreRad (Radiomics form pre-treatment CT images; C-index [95% confidence interval (CI)] in testing cohort: 0.614(0.552-0.675) and PostRad models (Radiomics form post-treatment CT images; 0.642(0.578-0.707), the delta model has better PFS prediction performance (Delta radiomics; 0.688(0.627-0.749). By incorporating clinical characteristics, CombDeltaRad obtains the best performance in both training cohort [C-index (95% CI): 0.802(0.772-0.832)] and the testing cohort (0.744(0.686-0.803). For 1-year PFS prediction, CombDeltaRad model obtained the best performance with AUC (95% CI) of 0.871(0.828-0.914) and 0.745 (0.651-0.838) in training cohort and testing cohort, respectively.ConclusionCT radiomics features have the potential to predict PFS in patients with colorectal cancer and liver metastasis who undergo neoadjuvant chemotherapy. By combining pre-treatment radiomics features, post-treatment radiomics features, and clinical characteristics better prediction results can be achieved.</p

Association of random plasma glucose levels with the risk for cardiovascular disease among Chinese adults without known diabetes

IMPORTANCE Diabetes is a known risk factor for cardiovascular disease (CVD). Substantial uncertainty remains, however, about the relevance to CVD risk for blood glucose levels below the diabetes threshold. OBJECTIVE To examine the association of random plasma glucose (RPG) levels with the risk for major CVD in Chinese adults without known diabetes. DESIGN, SETTING, AND PARTICIPANTS This prospective cohort study included 467 508 men and women aged 30 to 79 years with no history of diabetes, ischemic heart disease (IHD), stroke, or transient ischemic attack. Participants were recruited from 5 urban and 5 rural diverse locations across China from June 25, 2004, to July 15, 2008, and followed up to January 1, 2014. EXPOSURES Baseline and usual (longer-term average) RPG level. MAIN OUTCOMES AND MEASURES Cardiovascular deaths, major coronary events (MCE) (including fatal I HD and nonfatal myocardial infarction), ischemic stroke (IS), major occlusive vascular disease (MOVD) (including MCE or IS), and intracerebral hemorrhage. Preliminary validation of stroke and IHD events demonstrated positive predictive values of approximately 90% and 85%, respectively. Cox regression yielded adjusted hazard ratios (aHRs) for CVD associated with RPG levels. RESULTS Among the 467 508 participants (41.0% men; 59.0% women; mean [SD] age, 51 [11] years), a significant positive association of baseline RPG levels with CVD risks continued to 4.0 mmol/L (72 mg/dL). After adjusting for regression dilution bias, each 1-mmol/L (18-mg/dL) higher usual RPG level above 5.9 mmol/L (106 mg/dL) was associated with an 11% higher risk for cardiovascular death (6645 deaths; aHR, 1.11; 95% Cl, 1.10-1.13). Similarly strong positive associations were seen for MCE (3270 events; aHR, 1.10; 95% Cl, 1.08-1.13), IS (19153 events; aHR, 1.08; 95% Cl, 1.07-1.09), and MOVD (22 023 events; aHR, 1.08; 95% Cl, 1.07-1.09). For intracerebral hemorrhage, the association was weaker, but also significant (4326 events; aHR, 1.05; 95% Cl, 1.02-1.07). These associations persisted after excluding participants who developed diabetes during follow-up. CONCLUSIONS AND RELEVANCE Among adult Chinese without diabetes, lower RPG levels are associated with lower risks for major CVDs, even within a normal range of blood glucose levels.Kadoorie Charitable Foundation, Hong Kong; UK Wellcome Trust [088158/Z/09/Z, 104085/Z/14/Z]; Chinese Ministry of Science and Technology [2011BAIO9BO1]; Chinese National Natural Science Foundation [81390541]; The British Heart Foundation; UK Medical Research Council; Cancer Research UK; British Heart Foundation Centre of Research Excellence, OxfordSCI(E)PubMedARTICLE7813-823