As a combination of the hesitant fuzzy set (HFS) and the single valued neutrosophic set (SVNS), the single valued neutrosophic hesitant fuzzy set (SVNHFS) is an important concept to handle uncertain and vague information existing in real-life, which consists of three membership functions including hesitancy, as the truth-hesitancy membership function, the indeterminacy-hesitancy membership func...

Recommender systems have been a hot research area recently. One of the most widely used methods is Collaborative Filtering(CF), which selects items for an individual user from other similar users. However, CF may not fully reflect the procedure of how people choose an item in real life, for users are more likely to ask friends for opinions instead of asking strangers with similar interests. Rec...

This dissertation contains two projects that are related to varying coefficient models. The traditional least squares based kernel estimates of the varying coefficient model will lose some efficiency when the error distribution is not normal. In the first project, we propose a novel adaptive estimation method that can adapt to different error distributions and provide an efficient EM algorithm ...

Inspired by Pythagoras’s belief that numbers represent the reality, we study the topological properties of networks of composite numbers, in which the vertices represent the numbers and two vertices are connected if and only if there exists a divisibility relation between them. The network has a fairly large clustering coefficient C 0:34, which is insensitive to the size of the network. The ave...

An important and ongoing topic of research is the study of infectious diseases and the speed at which these diseases spread. Modeling the spread and growth of such diseases leads to a more precise understanding of the phenomenon and accurate predictions of spread in real life. We consider a long-range infection model on an infinite regular binary tree. Given a spreading coefficient α > 1, the t...

Water body management is essential to provide quality water to the requirement of drinking, agriculture and industries. Estimation of water quality in dams, lakes, rivers is paramount activity in quality control. As phytoplankton concentration is based on the physical and chemical state of the water, it is a good indicator and its concentration represents water quality. As Chlorophyll -a(Chl-a)...

High-Occupancy/Toll (HOT) lanes have become an increasingly prevalent form of congestion management pricing in the U.S. over the past few decades. The success of a HOT facility is dependent on the pricing scheme implemented, which determines the utilization of the HOT lane, and the corresponding congestion relief on the parallel general-purpose (GP) lanes. An additional complexity in determinin...

In this paper, we study the problem of variable selection for varying coefficient transformation models with censored data. We fit the varying coefficient transformation models by maximizing the marginal likelihood subject to a shrinkage-type penalty, which encourages sparse solutions and hence facilitates the process of variable selection. We further provide an efficient computation algorithm ...

In this article, we develop a statistical inference technique for the unknown coefficient functions in the varying coefficient model with random effect. A residual-adjusted block empirical likelihood (RABEL) method is suggested to investigate the model by taking the within-subject correlation into account. Due to the residual adjustment, the proposed RABEL is asymptotically chi-squared distribu...