Open Gromov-Witten invariants in dimension six

Let $L$ be a closed orientable Lagrangian submanifold of a closed symplectic six-manifold $(X, \omega)$. We assume that the first homology group $H_1 (L ; A)$ with coefficients in a commutative ring $A$ injects into the group $H_1 (X ; A)$ and that $X$ contains no Maslov zero pseudo-holomorphic disc with boundary on $L$. Then, we prove that for every generic choice of a tame almost-complex structure $J$ on $X$, every relative homology class $d \in H_2 (X, L ; \Z)$ and adequate number of incidence conditions in $L$ or $X$, the weighted number of $J$-holomorphic discs with boundary on $L$, homologous to $d$, and either irreducible or reducible disconnected, which satisfy the conditions, does not depend on the generic choice of $J$, provided that at least one incidence condition lies in $L$. These numbers thus define open Gromov-Witten invariants in dimension six, taking values in the ring $A$.Comment: 19 pages, 1 figur

Enumerative aspects of the Gross-Siebert program

We present enumerative aspects of the Gross-Siebert program in this introductory survey. After sketching the program's main themes and goals, we review the basic definitions and results of logarithmic and tropical geometry. We give examples and a proof for counting algebraic curves via tropical curves. To illustrate an application of tropical geometry and the Gross-Siebert program to mirror symmetry, we discuss the mirror symmetry of the projective plane.Comment: A version of these notes will appear as a chapter in an upcoming Fields Institute volume. 81 page

Precore Mutation of Hepatitis B Virus May Contribute to Hepatocellular Carcinoma Risk: Evidence from an Updated Meta-Analysis

BACKGROUND: Studies focused on the correlation of mutations in the genome of Hepatitis B Virus (HBV) like Pre-S mutation, Basal Core promoter (BCP), Enhancer II (EnhII), especially Precore mutation, with the risk of hepatocellular carcinoma (HCC) have triggered stiff controversies. With an increasing number of studies in this field recently, we conducted this meta-analysis to appraise the correlations. METHODS: We searched the commonly used databases both in English and Chinese till February 1(st), 2012. Meta-analysis was performed in fixed/random-effects models using STATA 10.0. Publication bias was examined through Egger's test and Begg's funnel plot. RESULTS: In total, 85 case-control studies were included involving 16745 HBV-infected patients, of whom 5781 had HCC. Statistically significant correlations were observed in Precore mutation G1896A (OR = 1.46, 95% confidence interval [CI] = 1.15-1.85, P(OR) = 0.002), G1899A (OR = 3.13, 95%CI = 2.38-4.13, P(OR)<0.001) and Pre-S mutation especially Pre-S1 deletion (OR = 2.94, 95%CI = 2.22 to 3.89) and Pre-S2 deletion (OR = 3.02, 95%CI = 2.03 to 4.50). Similar correlation existed between BCP double mutation A1762T/G1764A, T1753V, C1653T and HCC. In subgroup analysis, the Asians, genotype C or HBeAg positive patients with certain above mutations may be more susceptible to HCC. Besides, the mutations like G1896A and BCP double mutation may be associated with the progression of the liver diseases. CONCLUSIONS: Precore mutation G1896A, G1899A, deletions in Pre-S region as well as the other commonly seen mutations correlated with the increased risk of HCC, especially in Asians and may predict the progression of the liver disease

Identification of T-cell epitopes associated with immunity within the surface protein of duck hepatitis B virus

Duck hepatitis is a convenient model of hepatitis B virus (HBV) infection, but the lack of immunological reagents hampers investigation of pathogenesis and vaccine development. The aim of this study was to define T-cell epitopes in the surface peptide recognized by vaccinated immune birds. Blastogenesis assays were used to test the proliferative response of spleen mononuclear cells to synthetic peptides spanning the pre-S/S region in 22 naïve and 13 immunized and challenged immune ducks. Roughly ≥50% of the immune ducks responded to five immunodominant peptides eliciting a statistically greater proliferative response than in naïve birds. Fewer ducks responded to an additional six peptides. No statistically significant difference could be shown for the response to 11 peptides between the immune ducks and the naïve ducks. There was no clustering of the immunodominant peptides which were located throughout the surface antigen at sites of major swings in hydrophobicity. A number of peptides which induce lymphoblastogenesis in vaccinated immune ducks have been identified. Their role in spontaneous recovery from duck hepatitis B infection merits investigation.11 page(s

The Effect of surgical immunomodulation on liver inflammation and clearance of DHBV infection

The key to developing a therapeutic vaccine for chronic hepadnavirus infection lies in the characteristics of the host-immune response which leads to clearance of acute infection. Groups of 28-day-old ducks which had been surgically bursectomized (n = 10) or thymectomized (n =  13) on the day of hatch or were untreated (n = 21) were inoculated with 10⁹ viral genome equivalents (vge) DHBV, then bled twice a week, and euthanased 40 days later. Serum and liver were tested for DHBV DNA and total leukocytes and peripheral blood mononuclear cells (PBMCs) counted. Liver and spleen sections were either stained with hematoxylin and eosin, and graded for inflammation or stained with peroxidase-labeled anti-human CD3 antibody and examined for T lymphocyte distribution. PBMC counts were similar in all groups. DHBV infection combined with bursectomy increased significantly, while thymectomy decreased significantly the total leukocyte count. The spleen and liver bursectomy increased T lymphocyte number while B cells were decreased. Converse changes were observed in thymectomized ducks. Histological evidence of hepatitis was present in infected control and bursectomized ducks but not in the uninfected control or infected thymectomized ducks. In control animals, DHBV challenge caused viremia in 17 and persistent infection in 11 (56%). Fewer thymectomized ducks (3/13, 23%) and significantly more (100%) bursectomized ducks remained persistently infected (P < 0.001). Unexpectedly, bursectomy led to persistence of infection while clearance of infection occurred normally in thymectomized ducks despite decreased T lymphocyte numbers. This suggests that clearance requires T and B lymphocyte collaboration.7 page(s

Pencils of cubics as tools to solve an interpolation problem

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