Isoperimetric inequality and area growth of surfaces with bounded mean curvature

In this thesis, we give a lower bound on the areas of small geodesic balls in an immersed hypersurface M contained in a Riemannian manifold N. This lower bound depends only on an upper bound for the absolute mean curvature function of M, an upper bound of the absolute sectional curvature of N and a lower bound for the injectivity radius of N. As a consequence, we prove that if M is a noncompact complete surface of bounded absolute mean curvature in Riemannian manifold N with positive injectivity radius and bounded absolute sectional curvature, then the area of geodesic balls of M must grow at least linearly in terms of their radius. In particular, this result implies the classical result of Yau that a complete minimal hypersurface in Rn must have infinite area. We also attain partial results on the conjecture: If M is a compact immersed surface in hyperbolic 3-space H3, and the absolute mean curvature function of M is bounded from above by 1, then Area(M)\u3c=1/4*(Length(boundary M))2

Selecting Genes by Test Statistics

Gene selection is an important issue in analyzing multiclass microarray data. Among many proposed selection methods, the traditional ANOVA F test statistic has been employed to identify informative genes for both class prediction (classification) and discovery problems. However, the F test statistic assumes an equal variance. This assumption may not be realistic for gene expression data. This paper explores other alternative test statistics which can handle heterogeneity of the variances. We study five such test statistics, which include Brown-Forsythe test statistic and Welch test statistic. Their performance is evaluated and compared with that of F statistic over different classification methods applied to publicly available microarray datasets

A Bayesian Approach to Multistage Fitting of the Variation of the Skeletal Age Features

Accurate assessment of skeletal maturity is important clinically. Skeletal age assessment is usually based on features encoded in ossification centers. Therefore, it is critical to design a mechanism to capture as much as possible characteristics of features. We have observed that given a feature, there exist stages of the skeletal age such that the variation pattern of the feature differs in these stages. Based on this observation, we propose a Bayesian cut fitting to describe features in response to the skeletal age. With our approach, appropriate positions for stage separation are determined automatically by a Bayesian approach, and a model is used to fit the variation of a feature within each stage. Our experimental results show that the proposed method surpasses the traditional fitting using only one line or one curve not only in the efficiency and accuracy of fitting but also in global and local feature characterization

Clinical review: Critical care medicine in mainland China

Critical care medicine began in mainland China in the early 1980s. After almost 30 years of effort, it has been recognized as a specialty very recently. However, limited data suggest that critical care resources, especially ICU beds, are inadequate compared with those of developed countries. National critical care societies work together to set up good practice standards, and to improve academic levels with scientific meetings, education programs, and training courses. Critical care research in mainland China is beginning to evolve, with great potential for improvement

An Improved Prediction Model for Zinc-Binding Sites in Proteins Based on Bayesian Method

The zinc ion is the second richest metal ion in organisms. The proteins binding to zinc ions have important biological functions. However, few scholars have integrated the existing tools to predict the zinc-binding sites in proteins. To make up for this gap, this paper combines three well-known prediction tools into an improved model called IBayes_Zinc to predict the zinc-binding sites, and utilizes the advantages of the Bayesian method in handling incomplete or partial missing data. Specifically, the prediction scores of three existing sequence-based prediction tools were adopted, and the missing values were padded, forming an integrated classification tool. Then, the probabilities of positive and negative samples were computed and categorized as the class with higher probabilities. Experiments were conducted on a non-redundant training dataset and an independent testing dataset. The results show that our method surpassed the other three methods by nearly 5–13% in Matthew correlation coefficient (MCC) and outperformed the latter in recall and precision. The research findings promote the detection of zinc-binding sites in protein sequence and the identification of metalloprotein functions

Developing Prognostic Systems of Cancer Patients by Ensemble Clustering

Accurate prediction of survival rates of cancer patients is often key to stratify patients for prognosis and treatment. Survival prediction is often accomplished by the TNM system that involves only three factors: tumor extent, lymph node involvement, and metastasis. This prediction from the TNM has been limited, because other potential prognostic factors are not used in the system. Based on availability of large cancer datasets, it is possible to establish powerful prediction systems by using machine learning procedures and statistical methods. In this paper, we present an ensemble clustering-based approach to develop prognostic systems of cancer patients. Our method starts with grouping combinations that are formed using levels of factors recorded in the data. The dissimilarity measure between combinations is obtained through a sequence of data partitions produced by multiple use of PAM algorithm. This dissimilarity measure is then used with a hierarchical clustering method in order to find clusters of combinations. Prediction of survival is made simply by using the survival function derived from each cluster. Our approach admits multiple factors and provides a practical and useful tool in outcome prediction of cancer patients. A demonstration of use of the proposed method is given for lung cancer patients