Stopping Set Distributions of Some Linear Codes

Stopping sets and stopping set distribution of an low-density parity-check code are used to determine the performance of this code under iterative decoding over a binary erasure channel (BEC). Let $C$ be a binary $[n,k]$ linear code with parity-check matrix $H$, where the rows of $H$ may be dependent. A stopping set $S$ of $C$ with parity-check matrix $H$ is a subset of column indices of $H$ such that the restriction of $H$ to $S$ does not contain a row of weight one. The stopping set distribution $\{T_i(H)\}_{i=0}^n$ enumerates the number of stopping sets with size $i$ of $C$ with parity-check matrix $H$. Note that stopping sets and stopping set distribution are related to the parity-check matrix $H$ of $C$. Let $H^{*}$ be the parity-check matrix of $C$ which is formed by all the non-zero codewords of its dual code $C^{\perp}$. A parity-check matrix $H$ is called BEC-optimal if $T_i(H)=T_i(H^*), i=0,1,..., n$ and $H$ has the smallest number of rows. On the BEC, iterative decoder of $C$ with BEC-optimal parity-check matrix is an optimal decoder with much lower decoding complexity than the exhaustive decoder. In this paper, we study stopping sets, stopping set distributions and BEC-optimal parity-check matrices of binary linear codes. Using finite geometry in combinatorics, we obtain BEC-optimal parity-check matrices and then determine the stopping set distributions for the Simplex codes, the Hamming codes, the first order Reed-Muller codes and the extended Hamming codes.Comment: 33 pages, submitted to IEEE Trans. Inform. Theory, Feb. 201

Locate QCD Critical End Point in a Continuum Model Study

With a modified chemical potential dependent effective model for the gluon propagator, we try to locate the critical end point (CEP) of strongly interacting matter in the framework of Dyson-Schwinger equations (DSE). Beyond the chiral limit, we find that Nambu solution and Wigner solution could coexist in some area. Using the CornwallJackiw-Tomboulis (CJT) effective action, we show that these two phases are connected by a first order phase transition. We then locate CEP as the end point of the first order phase transition line. Meanwhile, based on CJT effective action, we give a direct calculation for the chiral susceptibility and thereby study the crossover.Comment: 9 pages, 7 figures; Version published in JHE

Dynamic comparison between Daan real-time PCR and Cobas TaqMan for quantification of HBV DNA levels in patients with CHB

BACKGROUND: Hepatitis B virus (HBV) DNA levels are crucial for managing chronic hepatitis B (CHB). It was unclear whether Daan real-time polymerase chain reaction test (Daan test) or COBAS TaqMan HBV DNA Test (Cobas TaqMan) was superior in measuring different HBV DNA levels in clinical specimens. METHODS: We enrolled 67 treatment-naïve, HBV surface antigen-positive CHB patients (high baseline viral levels) who received either lamivudine/adefovir or entecavir. Serum samples were tested at baseline and treatment week 24 using the Daan test and Cobas TaqMan. RESULTS: In the 67-baseline samples, the HBV DNA levels with the Cobas TaqMan (7.90 ± 0.73 log(10) IU/mL) were significantly greater than those of the Daan test (7.11 ± 0.44 log(10) IU/mL; P < 0.001). Of the 67 24-week samples (low viral levels), the Cobas TaqMan detected 59 (88.1%; 8 undetected); the Daan test detected 33 (49.3%; 34 undetected; P < 0.001). The Cobas TaqMan detected HBV DNA in 26 of 34 samples undetectable by the Daan test (range, 1.4–3.7 log(10) IU/mL) or 38% of samples (26/67). The reductions in viral load after 24 weeks of oral antiviral treatment in the 33 samples that were positive for both the Daan test and the Cobas TaqMan test were significantly different (3.59 ± 1.11 log(10) IU/mL versus 4.87 ± 1.58 log(10) IU/mL, respectively; P = 0.001). Spearman correlation analysis showed positive correlation between results from two tests (r(p) = 0.602,P<0.001). The HBV genotypes and the anti-viral treatment did not affect the measurements of the HBV DNA by the Daan assay and the Cobas Taqman assay. CONCLUSION: The Cobas Taqman was more sensitive at low viral loads than the Daan test and the change from complete to partial virological response could affect clinical decisions. The Cobas Taqman may be more appropriate for detection of HBV DNA levels

Supplementation of iron alone and combined with vitamins improves haematological status, erythrocyte membrane fluidity and oxidative stress in anaemic pregnant women

Pregnancy is a condition exhibiting increased susceptibility to oxidative stress, and Fe plays a central role in generating harmful oxygen species. The objective of the present study is to investigate the changes in haematological status, oxidative stress and erythrocyte membrane fluidity in anaemic pregnant women after Fe supplementation with and without combined vitamins. The study was a 2 months double-blind, randomised trial. Pregnant women (n 164) were allocated to four groups: group C was the placebo control group; group I was supplemented daily with 60 mg Fe (ferrous sulphate) daily; group IF was supplemented daily with Fe plus 400 µg folic acid; group IM was supplemented daily with Fe plus 2 mg retinol and 1 mg riboflavin, respectively. After the 2-month trial, Hb significantly increased by 15·8, 17·3 and 21·8 g/l, and ferritin by 2·8, 3·6 and 11·0 µg/l, in the I, IF and IM groups compared with placebo. Polarisation (¿) and microviscosity (¿) decreased significantly in other groups compared with placebo, indicating an increase in membrane fluidity. Significant decreases of ¿ and ¿ values compared with group C were 0·033 and 0·959 for group I, 0·037 and 1·074 for group IF and 0·064 and 1·865 for group IM, respectively. In addition, significant increases of glutathione peroxidase activities and decreases of malondialdehyde were shown in all treated groups, as well as increases of plasma retinol and urine riboflavin in group IM. The findings show that supplementation with Fe and particularly in combination with vitamins could improve the haematological status as well as oxidative stress and erythrocyte membrane fluidit

Tumor mutation burden associated with miRNA-gene interaction outcome mediates the survival of patients with liver hepatocellular carcinoma

Tumor mutation burden (TMB) is associated with immunogenic responses and the survival of cancer patients. This study demonstrates how TMB levels impact the immune-related cells, genes, and miRNAs, and how miRNA/gene interactions respond to variations in the survival rate of patients with liver hepatocellular carcinoma (LIHC). LIHC patients were divided into two groups, either a low TMB (< median) or a high TMB (≥ median) group. We found that high TMB plays a positive role in immune-mediated infiltration, generating more CD4 T-cells and memory B cells. Among the 21 immune genes that altered significantly, only C9orf24 and CYP1A1 were expected to up-regulate in LIHC patients with high TMB. A total of 19 miRNAs, which regulate various functional pathways, were significantly altered in patients with LIHC. One of the miRNA/gene pair, hsa-miR-33a/ALDH1A3 was significantly associated with the survival rate of LIHC patients. Our results suggest that LIHC patients with high TMB can be treated more effectively with immunotherapy