On Nonlinear Filtering Problems: Structure Theorem and A New Suboptimal Filter

In this thesis, we introduce two methods to solve the nonlinear filtering problem. In chapter 2, we extend Yau and his coauthors' work of Mitter conjecture for low dimensional algebras in nonlinear filtering problem. We prove the Mitter conjecture when the dimension $n=6$. Using this result, we give the structure theorem of six-dimensional estimation algebra. We shall show the structure of six-dimensional estimation algebra is not unique while when $n\leqslant 5$, the structure of estimation algebra is unique. It is hard to solve nonlinear filtering problem when we want to find the optimal filter. In Chapter 3, we first introduce several widely used suboptimal filters, Extended Kalman filter, Unscented Kalman filter, Ensemble Kalman filter, Particle filter, and splitting up method. Then, we introduce a new suboptimal filter for polynomial filtering problems. With our special assumption, we can construct a closed form for conditional mean and conditional moments for the state process. Numerical results show that our new suboptimal filter works perfectly

Raw Data of Chinese Dialect Distance for Publication "Promoting or preventing labor migration? Revisiting the role of language" (China Economics Review, 2020)

This dataset includes the calculation of dialect distance for 278 Chinese prefecture cities used in the paper "Promoting or preventing labor migration? Revisiting the role of language" (https://doi.org/10.1016/j.chieco.2020.101407

Assembly of Polymer-Grafted Magnetic Nanoparticles in Polymer Melts

Hydrophobic iron oxide nanoparticles grafted with hydrophobic polymer chains of varying molecular weights and graft densities are synthesized to underpin the role of brush entanglement and dipolar forces on creating nanostructures. Grafting density on magnetic nanoparticles is controlled in grafting-to method by changing the concentration of functionalized polymer in solution. The grafting density and brush length have varied systemically to observe the changes in nanostructures. Bridging between grafted chains and dipolar forces become effective only at low grafting density and result in long chains of particles. We demonstrate experimentally that structural transition of magnetic nanoparticles is controlled with the balance between grafted chain entanglements and dipolar forces

Funnel plots of the meta-analysis for the association of MTHFR C677T polymorphism and OSCC risk under allele, dominant, recessive models.

(a) T vs C; (b) CC+CT vs TT; (c) TT+CT vs CC.</p

Characteristic of 13 included studies in the present study.

Characteristic of 13 included studies in the present study.</p

Additional file 1 of Targeting PPARα in low ambient temperature exposure-induced cardiac dysfunction and remodeling

Additional file 1: Fig. S1. Role of PPARα in LT-related cardiac injury. Table S1. Primer sequence for RT-PCR. Table S2. General biometric and echocardiographic properties of WT and Ppara−/− mice upon 8-week room temperature or low ambient exposure. Table S3. General biometric and echocardiographic properties of C57BL/6J mice received vehicle or fenofibrate treatment upon 8-wk room temperature or low ambient temperature exposure

Fluorescence micrograph of a breast tumor stained to visualize carcinoma cells (phospho-p53, green) surrounded by macrophages (CD11b, red) (a).

<p>Nuclei appear blue (DAPI). Image courtesy of Michael Graham Espey, PhD, National Cancer Institute, NIH (private communication). (b) Representative pictures of dormant and fast-growing tumors and their vascular structure. Reprinted from Cancer Letters, 294, Almog N, Molecular mechanisms underlying tumor dormancy, 139–146, Copyright (2010), with permission from Elsevier.</p

The flowchart showing articles identification, inclusion and exclusion.

13 eligible studies were included.</p

Funnel plots of the meta-analysis for the association of MTHFR C677T polymorphism and OSCC risk under additive models.

(a) CC vs TC; (b) TT vs Ct; (c) TT vs CC.</p

Forest plots for the association between MTHFR C677T polymorphism and OSCC risk in overall population.

(a) T vs C; (b) TT vs CC.</p