Functional CLT for sample covariance matrices

Using Bernstein polynomial approximations, we prove the central limit theorem for linear spectral statistics of sample covariance matrices, indexed by a set of functions with continuous fourth order derivatives on an open interval including $[(1-\sqrt{y})^2,(1+\sqrt{y})^2]$, the support of the Mar\u{c}enko--Pastur law. We also derive the explicit expressions for asymptotic mean and covariance functions.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ250 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Microbial and epigenetic factors in the pathogenesis of nasopharyngeal carcinoma

While uncommon in most of the world, nasopharyngeal carcinoma (NPC) shows an unusual geographic and ethnic distribution, being highly prevalent in Southern China and Southeast Asia. Genetic susceptibility, Epstein-Barr virus (EBV) infection and additional environmental exposures are well established risk factors for NPC in endemic areas. However, the detailed molecular mechanisms of NPC pathogenesis remain largely unknown. In this thesis, several novel pathogenic mechanisms of NPC development and progression are presented. The interaction of EBV encoded latent membrane protein 2A (LMP2A) with cellular proteins promoting invasiveness of NPC cells is described in paper I. Spleen tyrosine kinase (Syk) interacts with integrin β4 subunit (ITGβ4) in epithelial cells through an ITAM-like motif, and concurrent LMP2A expression interferes with this interaction by competitive binding to Syk. Both Syk and LMP2A affect cell surface expression of ITGβ4. Particularly, ITGβ4 concentrates at cellular protrusions in LMP2A expressing cells, which may contribute to the migration property of NPC-cells. Paper II and paper III focus on the epigenetic alteration of candidate tumor suppressor genes (TSGs) and their possible role in NPC tumorigenesis. Cadherin 4 (CDH4) and ubiquitin-conjugating enzyme 2L6 (UBE2L6) are downregulated due to promoter hypermehtylation in NPC. Both genes suppress the proliferation and colony formation of NPC-cells. CDH4 impedes cell migration and elicits cell communication; UBE2L6 induce apoptosis of NPC cells and counteracts degradation of adipocyte triglyceride lipase (ATGL) through ISG15-conjugation of valosin-containing protein (VCP). CDH4 and UBE2L6 could be involved in both initiation and progression of NPC. Suppression of UBE2L6 encoded protein UbcH8 correlated with poor outcome in NPC patients. In paper IV, we compared the response of NPC and normal nasopharyngeal epithelial (NNE) cell lines to bacteria and bacterial cell wall components. Strong nuclear translocation of NF-κB and significant induction of proinflammatory factors IL6, IL8, IL1α and CXCL2 were observed in NNE cells, but not in NPC cells upon exposure to Gram-positive bacteria streptococci and peptidoglycan (PGN). We identified three different mechanisms by which the activation of NF-κB in NPC cells could be hampered. It could be trapped by an enhanced accumulation of cytoplasmic lipids. I-κB degradation could be impaired due to downregulation of UBE2L6. We also showed that overexpression of lysine-specific demethylase-1 (LSD1) blocked the transcriptional activation of proinflammatory genes. Together these mechanisms might contribute to decreased immune reactivity in NPC and thus affect tumor progression

Adaptive Finite Element Approximations for Kohn-Sham Models

The Kohn-Sham equation is a powerful, widely used approach for computation of ground state electronic energies and densities in chemistry, materials science, biology, and nanosciences. In this paper, we study the adaptive finite element approximations for the Kohn-Sham model. Based on the residual type a posteriori error estimators proposed in this paper, we introduce an adaptive finite element algorithm with a quite general marking strategy and prove the convergence of the adaptive finite element approximations. Using D{\" o}rfler's marking strategy, we then get the convergence rate and quasi-optimal complexity. We also carry out several typical numerical experiments that not only support our theory,but also show the robustness and efficiency of the adaptive finite element computations in electronic structure calculations.Comment: 38pages, 7figure

Methods Used to Eliminate the Students’ Chintonglish Sentences in Their Writing

In this paper the authors discuss four types of English in Chinese students’ English writing. They are Pure English, China English, Sinicized English and Chinese Tone English (Chintonglish). As the Chintonglish (Chinese Tone English) sentences appear frequently in students writing, the authors will discuss this type of “English” from the psychological and cultural point of view, which may serve as a guide for the Chinese students’ writing of good English. In the authors’ opinion the methods used for the elimination of such Chintonglish sentences in the students’ English writing are to point out the cause of such Chintonglish mistakes to the students clearly, create an English communicative environment and choose some typical pieces of passages for the students to read and imitate