The performance in terms of minimal Bayes’ error probability for detection of a high-dimensional random tensor is a fundamental under-studied difficult problem. In this work, we consider two Signal to Noise Ratio (SNR)-based detection problems of interest. Under the alternative hypothesis, i.e., for a non-zero SNR, the observed signals are either a noisy rank-R tensor admitting a Q-order Canonical Polyadic Decomposition (CPD) with large factors of size Nq  R, i.e, for 1  q  Q, where R, Nq ! ¥ with R1/q/Nq converge towards a finite constant or a noisy tensor admitting TucKer Decomposition (TKD) of multilinear (M1, . . . ,MQ)-rank with large factors of size Nq  Mq, i.e, for 1  q  Q, where Nq,Mq ! ¥ with Mq/Nq converge towards a finite constant. The detection of the random entries (coefficients) of the core tensor in the CPD/TKD is hard to study since the exact derivation of the error probability is mathematically intractable. To circumvent this technical difficulty, the Chernoff Upper Bound (CUB) for larger SNR and the Fisher information at low SNR are derived and studied, based on information geometry theory. The tightest CUB is reached for the value minimizing the error exponent, denoted by s?. In general, due to the asymmetry of the s-divergence, the Bhattacharyya Upper Bound (BUB) (that is, the Chernoff Information calculated at s? = 1/2) can not solve this problem effectively. As a consequence, we rely on a costly numerical optimization strategy to find s?. However, thanks to powerful random matrix theory tools, a simple analytical expression of s? is provided with respect to the Signal to Noise Ratio (SNR) in the two schemes considered. A main conclusion of this work is that the BUB is the tightest bound at low SNRs. This property is, however, no longer true for higher SNRs.

High rates of phosphorus (P) currently being applied to soils for the production of vegetables in the Mekong Delta, Vietnam has led to the concern of its negative effect on the economics and the environment. This research presents a comprehensive study on the determination of P supplying capacity in this region of Vietnam to examine the possibility of reducing P fertilizer input. One hundred twenty (120) soil samples were collected to evaluate total P and Bray 1 available P in the soils. Phosphorus maximum sorption, degree of P saturation, P release, and the effect of P fertilizer on corn (Zea mays L.) yield in greenhouse and fields were also determined. Total P concentrations of 56.7% soil samples evaluated yielded high P concentrations (>560 mg P/kg), while 74.2% of the samples had high Bray 1 available P concentrations (>20 mg P/kg soil). Maximum P sorption ranged from 149 to 555 mg P/kg soil, respectively and has negative correlation to available P (r = - 0.63*), degrees of P saturation ranged from 0.63 to 5.46% correlated to available P (r = 0.98**) and maximum P release ranged from 1.2 to 61.9 mg P/kg soil, respectively correlated to available P (r = 0.96**). Corn grown in soils with available P concentrations >15 mg P/kg did not respond to P fertilizer in greenhouse or field experiments. We conclude that many farmers in this region can reduce P fertilizer input, thus increasing their profits and reducing negative environmental impacts associated with excess soil P for sustainable agriculture.

Rice is an important cereal crop worldwide, the growth of which is affected by rice blast disease, caused by the fungal pathogen Magnaporthe oryzae. As climate change increases the diversity of pathogens, the disease-resistance genes (R genes) in plants must be identified. The major blast-resistance genes have been identified in indica rice varieties; therefore, japonica rice varieties with R genes now need to be identified. Because leucine-rich repeat (LRR) domain proteins possess R-gene properties, we used bioinformatics analysis to identify the rice candidate LRR domain receptor-like proteins (OsLRR-RLPs). OsLRR-RLP2, which contains six LRR domains, showed differences in the DNA sequence, containing 43 single-nucleotide polymorphisms (SNPs) in indica and japonica subpopulations. The results of M. oryzae inoculation analysis indicated that indica varieties with partial deletion of OsLRR-RLP2 showed susceptibility, whereas japonica varieties with intact OsLRR-RLP2 showed resistance. oslrr-rlp2 mutant generated using clustered regularly interspaced palindromic repeats (CRISPR)/CRISPR-associated protein 9 (Cas9) showed increased pathogen susceptibility, whereas plants overexpressing this gene showed pathogen resistance. These results indicate that OsLRR-RLP2 confers resistance to rice, and OsLRR-RLP2 may be useful for breeding resistant cultivars.

BACKGROUND&AIMS: Hepatitis B virus (HBV) infection remains a major public health problem. The interaction between HBV and the host inflammatory response is an important factor contributing to liver damage and disease development. We compared the correlation between the subclinical index and PBMCs concentration in two groups of pregnant women (HBsAg positive), which are different in HBV DNA concentration in Vietnam. METHODS: The Hierarchical cluster analysis (HCA) was run with 20 different clustering methods on data collected from 80 Vietnamese pregnant women and their babies (60/80 cord blood). RESULTS: In the high viral load group (HBV DNA ≥ 5x10^7 copies/ml), a strong correlation between CBMCs with serum maternal Haemoglobin concentration and maternal platelet and maternal ALT. Their R values are: -0.88, 0.82, and 0.84 with p=8.97E-03, 2.41E-02 and 1.75E-01, respectively. CONCLUSIONS: We found a significant correlation shift of subclinical index between the two groups, which may be important in diagnosing pregnant women with chronic hepatitis B virus infection.