Two-loop perturbative corrections to the constrained effective potential in thermal QCD

In this paper, we compute the constrained QCD effective potential up to two-loop order with finite quark mass and chemical potential. We present the explicit calculations by using the double line notation and analytical expressions for massless quarks are obtained in terms of the Bernoulli polynomials or Polyakov loops. Our results explicitly show that the constrained QCD effective potential is independent on the gauge fixing parameter. In addition, as compared to the massless case, the constrained QCD effective potential with massive quarks develops a completely new term which is only absent when the background field vanishes. Furthermore, we discuss the relation between the one- and two-loop constrained effective potential. The surprisingly simple proportionality that exists in the pure gauge theories, however, is in general no longer true when fermions are taken into account. On the other hand, for high baryon density $\mu_B$ and low temperature $T$, in the massless limit, we do also find a similar proportionality between the one- and two-loop fermionic contributions in the constrained effective potential up to ${\cal O}(T/\mu_B)$.Comment: 36 pages, 5 figs, final version in JHE

On the Griffiths numbers for higher dimensional singularities

We show that Yau's conjecture on the inequalities for (n-1)-th Griffiths number and (n-1)-th Hironaka number does not hold for isolated rigid Gorenstein singularities of dimension greater than 2. But his conjecture on the inequality for (n-1)-th Griffiths number is true for irregular singularities.Comment: to appear in Annales de l'Institut Fourie

Counting Humps in Motzkin paths

In this paper we study the number of humps (peaks) in Dyck, Motzkin and Schr\"{o}der paths. Recently A. Regev noticed that the number of peaks in all Dyck paths of order $n$ is one half of the number of super Dyck paths of order $n$. He also computed the number of humps in Motzkin paths and found a similar relation, and asked for bijective proofs. We give a bijection and prove these results. Using this bijection we also give a new proof that the number of Dyck paths of order $n$ with $k$ peaks is the Narayana number. By double counting super Schr\"{o}der paths, we also get an identity involving products of binomial coefficients.Comment: 8 pages, 2 Figure

Prognosis of nasopharyngeal carcinoma : body mass index, plasma Epstein-Barr virus DNA and oral microbiome

Nasopharyngeal carcinoma (NPC) has a geographically skewed distribution worldwide, with high incidence rates in East and Southeast Asia. Although hospital-based studies suggest that the development of new radiotherapy techniques has contributed to improved NPC prognosis, populationbased research on NPC patient survival is lacking. In addition, potential environmental prognostic factors for NPC, including body mass index (BMI) and body shape, pretreatment plasma Epstein-Barr virus (EBV) DNA, and oral microbiome, are not yet well understood. Therefore, this thesis aims to characterize population-based NPC survival patterns and identify prognostic factors for NPC in a population-based context in southern China. In Paper I, we aimed to estimate population-based NPC survival in an unbiased manner by implementing a tracing strategy to ensure a high follow-up rate in a representative cohort of NPC patients. We also aimed to compare this estimate with survival results from other studies in endemic areas, and to calculate the number of avoidable deaths from earlier detection or more widespread access to advanced medical care. Based on patients with incident NPC enrolled in the populationbased NPC Genes, Environment, and EBV (NPCGEE) project, we developed a passive-active-passive circle follow-up strategy that achieved a high rate (98.3%) of complete follow-up for vital status through 2018. We estimated that 5-year overall survival for NPC diagnosed at stages I, II, III, IVa, IVb, and IVc was 91.1%, 88.1%, 79.8%, 63.8%, 57.7%, and 34.4%, respectively. In general, we found that population-based NPC survival lags by approximately 10 years behind survival reported in large hospital-based cohorts. We estimated that 174 NPC deaths per 1000 patients could be avoided within five years of diagnosis if all advanced-stage cases were instead diagnosed at early stages. In Paper II, we examined whether pretreatment BMI and body shape were associated with the prognosis of NPC, using the NPC patient cohort from the NPCGEE project. We found that being overweight at diagnosis, was associated with a 25% lower all-cause mortality rate whereas those with a thinner body shape had a higher all-cause mortality rate, than those with a normal weight/body shape. When we examined associations with BMI and body shape 10 years before diagnosis, similar but weaker associations existed, but for BMI and body shape at age 20 years, the associations with NPC prognosis disappeared. The lack of effect modification by stage at diagnosis, along with the detection of similar associations with BMI and body shape 10 years before diagnosis, suggests that the results were not primarily due to reverse causation. In Paper III, we assessed the relationship between pretreatment plasma EBV DNA and NPC survival, using the NPC patient cohort from the NPCGEE project. We found that higher pretreatment plasma EBV DNA load was associated with increased risks of all-cause and NPC-specific mortalities, particularly in the first five years after diagnosis; cases with detectable plasma EBV DNA (compared with undetectable) had more than double the risk of all-cause and NPC-specific death. Higher pretreatment EBV DNA levels may reflect a greater tumor burden, and may signal a need for more intensive chemotherapy and/or heightened clinical surveillance. In Paper IV, we estimated associations of oral microbiome with NPC prognosis, using a subcohort of patients with saliva specimens from the NPCGEE project. We showed that lower within-community diversity was associated with higher all-cause and NPC-specific mortalities, and some (albeit not all) measures of between-community diversity were also associated with all-cause and NPC-specific mortalities. None of candidate bacteria were found to be significant prognostic biomarkers, suggesting that the observed associations resulted from global patterns rather than specific microbiota. These results indicate that microbiota may affect host immune function or contribute to the development of adverse treatment effects that in turn influence NPC prognosis. In conclusion, using a population-based patient cohort of NPCGEE project in southern China, we estimated generalizable 5-year survival rates and investigated potential environmental prognostic factors. We found that population-based NPC survival lags behind large-hospital-based survival; overweight at diagnosis indicated a favorable long-term prognosis, whereas a thinner body shape at diagnosis is associated with worse prognosis; pretreatment plasma EBV DNA is a strong prognostic factor for NPC; and decreased within-community diversity in oral microbiome is related to increased mortality. Taken together, these findings constitute some of the first population-based evidence on NPC prognosis in southern China, and point to potential routes to improving NPC management and long-term outcomes in this NPC-endemic region

Kinetics and Mechanisms of Phosphorus Adsorption in Soils from Diverse Ecological Zones in the Source Area of a Drinking-Water Reservoir.

On-site soils are increasingly used in the treatment and restoration of ecosystems to harmonize with the local landscape and minimize costs. Eight natural soils from diverse ecological zones in the source area of a drinking-water reservoir in central China are used as adsorbents for the uptake of phosphorus from aqueous solutions. The X-ray fluorescence (XRF) spectrometric and BET (Brunauer-Emmett-Teller) tests and the Scanning Electron Microscopy (SEM) and Fourier Transform Infrared (FTIR) spectral analyses are carried out to investigate the soils' chemical properties and their potential changes with adsorbed phosphorous from aqueous solutions. The intra-particle diffusion, pseudo-first-order, and pseudo-second-order kinetic models describe the adsorption kinetic processes. Our results indicate that the adsorption processes of phosphorus in soils occurred in three stages and that the rate-controlling steps are not solely dependent on intra-particle diffusion. A quantitative comparison of two kinetics models based on their linear and non-linear representations, and using the chi-square (χ2) test and the coefficient of determination (r2), indicates that the adsorptive properties of the soils are best described by the non-linear pseudo-second-order kinetic model. The adsorption characteristics of aqueous phosphorous are determined along with the essential kinetic parameters