On singular value distribution of large dimensional auto-covariance matrices

Let $(\varepsilon_j)_{j\geq 0}$ be a sequence of independent $p-$dimensional random vectors and $\tau\geq1$ a given integer. From a sample $\varepsilon_1,\cdots,\varepsilon_{T+\tau-1},\varepsilon_{T+\tau}$ of the sequence, the so-called lag $-\tau$ auto-covariance matrix is $C_{\tau}=T^{-1}\sum_{j=1}^T\varepsilon_{\tau+j}\varepsilon_{j}^t$. When the dimension $p$ is large compared to the sample size $T$, this paper establishes the limit of the singular value distribution of $C_\tau$ assuming that $p$ and $T$ grow to infinity proportionally and the sequence satisfies a Lindeberg condition on fourth order moments. Compared to existing asymptotic results on sample covariance matrices developed in random matrix theory, the case of an auto-covariance matrix is much more involved due to the fact that the summands are dependent and the matrix $C_\tau$ is not symmetric. Several new techniques are introduced for the derivation of the main theorem

On the Performance of Spectrum Sensing Algorithms using Multiple Antennas

In recent years, some spectrum sensing algorithms using multiple antennas, such as the eigenvalue based detection (EBD), have attracted a lot of attention. In this paper, we are interested in deriving the asymptotic distributions of the test statistics of the EBD algorithms. Two EBD algorithms using sample covariance matrices are considered: maximum eigenvalue detection (MED) and condition number detection (CND). The earlier studies usually assume that the number of antennas (K) and the number of samples (N) are both large, thus random matrix theory (RMT) can be used to derive the asymptotic distributions of the maximum and minimum eigenvalues of the sample covariance matrices. While assuming the number of antennas being large simplifies the derivations, in practice, the number of antennas equipped at a single secondary user is usually small, say 2 or 3, and once designed, this antenna number is fixed. Thus in this paper, our objective is to derive the asymptotic distributions of the eigenvalues and condition numbers of the sample covariance matrices for any fixed K but large N, from which the probability of detection and probability of false alarm can be obtained. The proposed methodology can also be used to analyze the performance of other EBD algorithms. Finally, computer simulations are presented to validate the accuracy of the derived results.Comment: IEEE GlobeCom 201

Nisin and ε-polylysine combined treatment enhances quality of fresh-cut jackfruit at refrigerated storage

This study investigated the effects of nisin combined with ε-polylysine on microorganisms and the refrigerated quality of fresh-cut jackfruit. After being treated with distilled water (control), nisin (0.5 g/L), ε-polylysine (0.5 g/L), and the combination of nisin (0.1 g/L) and ε-polylysine (0.4 g/L), microporous modified atmosphere packaging (MMAP) was carried out and stored at 10 ± 1°C for 8 days. The microorganisms and physicochemical indexes were measured every 2 days during storage. The results indicated that combined treatment (0.1 g/L nisin, 0.4 g/L ε-polylysine) had the best preservation on fresh-cut jackfruit. Compared with the control, combined treatment inhibited microbial growth (total bacterial count, mold and yeast), reduced the weight loss rate, respiratory intensity, polyphenol oxidase and peroxidase activities, and maintained higher sugar acid content, firmness, and color. Furthermore, it preserved higher levels of antioxidant compounds, reduced the accumulation of malondialdehyde and hydrogen peroxide, thereby reducing oxidative damage and maintaining high nutritional and sensory qualities. As a safe application of natural preservatives, nisin combined with ε-polylysine treatment has great application potential in the fresh-cut jackfruit industry

Effect of polyhydroxyalkanoates on dark fermentative hydrogen production from waste activated sludge

Polyhydroxyalkanoates (PHA), an intracellular energy and carbon storage polymer, can be accumulated in activated sludge in substantial quantities under wastewater dynamic treatment (i.e., substrate feast-famine) conditions. However, its influence on hydrogen production has never been investigated before. This study therefore evaluated the influences of PHA level and composition in waste activated sludge (WAS) on hydrogen production. The results showed that with the increase of sludge PHA content from 25 to 178mg per gram volatile suspended solids (VSS) hydrogen production from WAS alkaline anaerobic fermentation increased from 26.5 to 58.7mL/g VSS. The composition of PHA was also found to affect hydrogen production. When the dominant composition shifted from polyhydroxybutyrate (PHB) to polyhydroxyvalerate (PHV), the amount of generated hydrogen decreased from 51.2 to 41.1mL/g VSS even under the same PHA level (around 130mg/g VSS). The mechanism studies exhibited that the increased PHA content accelerated both the cell solubilization and the hydrolysis process of solubilized substrates. Compared with the PHB-dominant sludge, the increased PHV fraction not only slowed the hydrolysis process but also caused more propionic acid production, with less theoretical hydrogen generation in this fermentation type. It was also found that the increased PHA content enhanced the soluble protein conversion of non-PHA biomass. Further investigations with enzyme analyses showed that both the key hydrolytic enzyme activities and hydrogen-forming enzyme activities were in the sequence of the PHB-dominant sludge>the PHV-dominant sludge>the low PHA sludge, which was in accord with the observed order of hydrogen yield

An efficient process for wastewater treatment to mitigate free nitrous acid generation and its inhibition on biological phosphorus removal

Free nitrous acid (FNA), which is the protonated form of nitrite and inevitably produced during biological nitrogen removal, has been demonstrated to strongly inhibit the activity of polyphosphate accumulating organisms (PAOs). Herein we reported an efficient process for wastewater treatment, i.e., the oxic/anoxic/oxic/extended-idle process to mitigate the generation of FNA and its inhibition on PAOs. The results showed that this new process enriched more PAOs which thereby achieved higher phosphorus removal efficiency than the conventional four-step (i.e., anaerobic/oxic/anoxic/oxic) biological nutrient removal process (41 ± 7% versus 30 ± 5% in abundance of PAOs and 97 ± 0.73% versus 82 ± 1.2% in efficiency of phosphorus removal). It was found that this new process increased pH value but decreased nitrite accumulation, resulting in the decreased FNA generation. Further experiments showed that the new process could alleviate the inhibition of FNA on the metabolisms of PAOs even under the same FNA concentration

Compound microsatellites in complete Escherichia coli genomes

AbstractCompound microsatellites consisting of two or more repeats in close proximity have been found in eukaryotic genomes. So far such compound microsatellites have not been investigated in any prokaryotic genomes. We have therefore examined compound microsatellites in 22 complete genomes of Escherichia coli, which is one of the ideal model organisms to analyze the nature and evolution of prokaryotic compound microsatellites. Our results indicated that about 1.75–2.85% of all microsatellites could be accounted as compound microsatellites with very low complexity, and most compound microsatellites were composed of very different motifs. Compound microsatellites were significantly overrepresented in all surveyed genomes. These results were dramatically different from those in eukaryotes. We discussed the possible reasons for the observed divergence

Biochar to improve soil fertility. A review

International audienceAbstractSoil mineral depletion is a major issue due mainly to soil erosion and nutrient leaching. The addition of biochar is a solution because biochar has been shown to improve soil fertility, to promote plant growth, to increase crop yield, and to reduce contaminations. We review here biochar potential to improve soil fertility. The main properties of biochar are the following: high surface area with many functional groups, high nutrient content, and slow-release fertilizer. We discuss the influence of feedstock, pyrolysis temperature, pH, application rates, and soil types. We review the mechanisms ruling the adsorption of nutrients by biochar

Effect of alkaline microwaving pretreatment on anaerobic digestion and biogas production of swine manure

Microwave assisted with alkaline (MW-A) condition was applied in the pretreatment of swine manure, and the effect of the pretreatment on anaerobic treatment and biogas production was evaluated in this study. The two main microwaving (MW) parameters, microwaving power and reaction time, were optimized for the pretreatment. Response surface methodology (RSM) was used to investigate the effect of alkaline microwaving process for manure pretreatment at various values of pH and energy input. Results showed that the manure disintegration degree was maximized of 63.91% at energy input of 54 J/g and pH of 12.0, and variance analysis indicated that pH value played a more important role in the pretreatment than in energy input. Anaerobic digestion results demonstrated that MW-A pretreatment not only significantly increased cumulative biogas production, but also shortened the duration for a stable biogas production rate. Therefore, the alkaline microwaving pretreatment could become an alternative process for effective treatment of swine manure