Deep Residual Learning via Large Sample Mean-Field Stochastic Optimization

We study a class of stochastic optimization problems of the mean-field type arising in the optimal training of a deep residual neural network. We consider the sampling problem arising from a continuous layer idealization, and establish the existence of optimal relaxed controls when the training set has finite size. The core of our paper is to prove the Gamma-convergence of the sequence of sampled objective functionals, i.e., show that as the size of the training set grows large, the minimizer of the sampled relaxed problem converges to that of the limiting optimization problem. We connect the limit of the large sampled objective functional to the unique solution, in the trajectory sense, of a nonlinear Fokker-Planck-Kolmogorov (FPK) equation in a random environment. We construct an example to show that, under mild assumptions, the optimal network weights can be numerically computed by solving a second-order differential equation with Neumann boundary conditions in the sense of distributions

Metal contamination of soils and crops affected by the Chenzhou lead/zinc mine spill (Hunan, China)

In 1985, the collapse of the tailing dam in Chenzhou lead/zinc mine (Hunan, southern China) led to the spread of mining waste spills on the farmland along the Dong River. After the accident, an urgent soil cleaning up was carried out in some places. Seventeen years later, cereal (rice, maize, and sorghum), pulses (soybean, Adzuki bean, mung bean and peanut), vegetables (ipomoea, capsicum, taro and string bean) and the rooted soils were sampled at four sites: (1) the mining area (SZY), (2) the area still covered with the mining tailing spills (GYB), (3) the cleaned area from mining tailing spills (JTC), and (4) a background site (REF). Metal concentrations in the crops and soils were analyzed to evaluate the long-term effects of the spilled waste on the soil and the potential human exposure through food chains. The results showed that the physical–chemical properties of the soils obviously changed due to the different farming styles used by each individual farmer. Leaching effects and plant extraction of metals from some soils were quite weak. Certain soils were still heavily polluted with As, Cd, Zn, Pb and Cu. The contamination levels were in the order of GYB>SZY>JTC showing that the clean-up treatment was effective. The maximum allowable concentration (MAC) levels for Chinese agricultural soils were still highly exceeded, particularly for As and Cd (followed by Zn, Pb and Cu), with mean concentrations of 709 and 7.6 mg kg−1, respectively. These concentrations exceed the MAC levels by 24 times for As and 13 times for Cd at GYB. Generally, the edible leaves or stems of crops were more heavily contaminated than seeds or fruits. Ipomoea was the most severely contaminated crop. The concentrations of Cd and Pb were 3.30 and 76.9 mg kg−1 in ipomoea leaves at GYB, which exceeded the maximum permit levels (0.5 mg kg−1 for Cd and 9 mg kg−1 for Pb) by 6.6 and 8.5 times, respectively. Taro (+skin) could accumulate high concentrations of Zn and Cd in the edible stem, and rice and capsicum had high Cd concentration in the edible parts. However, the toxic element concentrations in maize, sorghum, Adzuki bean, soybean and mung bean remained lower than the threshold levels. The bio-accumulation factors (BAFs) of crops were in the order: Cd>Zn>Cu>Pb>As. BAF was typically lower in the edible seeds or fruits than in stems and leaves. The accumulation effect strongly depends on the crop's physiological properties, the mobility, of the metals, and the availability of metals in soils but not entirely on the total element concentrations in the soils. Even so, the estimated daily intake amount of Cu, Zn, Cd, and Pb from the crops grown in the affected three sites and arsenic at SZY and GYB exceeded the RDA (Recommended dietary allowance) levels. Subsequently, the crops grown in Chenzhou Pb/Zn mine waste affected area might have a hazardous effect on the consumer's health. This area still needs effective measures to cure the As, Cd, Pb, Zn and Cu contamination

Use of genetically modified saccharomyces cerevisiae to convert soluble starch directly to bioethanol

Ethanol can be used as a complete fuel or as an octane enhancer, and has the advantages of being renewable and environmentally friendly. Ethanol produced by a fermentation process, generally referred to as bioethanol, is considered to be a partial solution to the worldwide energy crisis. Traditionally, industrial bioethanol fermentation involves two major steps: starch hydrolysis and fermentation. Since the key microorganism, Saccharomyces cerevisiae, lacks amylolytic activity and is unable to directly utilize starch for proliferation and fermentation, it requires intensive amount of energy and pure starch hydrolyzing enzymes to gelatinize, liquefy and dextrinize the raw starch before fermentation. It has been suggested that genetically engineered yeast which expresses amylolytic enzymes could potentially perform simultaneous starch hydrolysis and fermentation. This improvement could greatly reduce the capital and energy costs in current bioethanol producing plants and make bioethanol production more economical. In this project, a novel yeast strain of Saccharomyces cerevisiae was genetically engineered in such a way that barley alpha-amylase was constitutively expressed and immobilized on the yeast cell surface. This particular alpha-amylase was selected based on its superior kinetic properties and its pH optimum which is compatible with the pH of yeast culture media. The cDNA encoding barley Ą-amylase, with a secretion signal sequence, was fused to the cDNA encoding the C-terminal half of a cell wall anchoring protein, alpha-agglutinin. The fusion gene was cloned downstream of a constitutive promoter ADH1 in a yeast episomal plasmid pAMY. The pAMY harbouring yeast showed detectable amylolytic activity in a starch plate assay. In addition, alpha-amylase activity was detected only in the cell pellet fraction and not in the culture supernatant. In batch fermentation studies using soluble wheat starch as sole carbon source, even though pAMY harbouring yeast was able to hydrolyse soluble starch under fermentation conditions, no ethanol was produced. This was probably due to insufficient alpha-amylase activity which resulted from the enzyme being anchored on the cell wall by alpha-agglutinin. Further research using alternative cell surface anchoring system might be able to produce yeast with industrial applications

Interactions between cadmium and lead with acidic soils: Experimental evidence of similar adsorption patterns for a wide range of metal concentrations and the implications of metal migration

The importance of high- and low-affinity surface sites for cadmium and lead adsorption in typical European and Asian soils was investigated. Adsorption experiments on surface and deep horizons of acidic brown (Vosges, France) and red loess soils (Hunan, China) were performed at 25 ◦C as a function of the pH (3.5–8) and a large range of metal concentrations in solution (10−9–10−4 mol l−1). We studied the adsorption kinetics using a Cd2+-selective electrode and desorption experiments as a function of the solid/solution ratio and pH. At a constant solution pH, all samples exhibited similar maximal adsorption capacities (4.0 ± 0.5 µmol/g Cd and 20 ± 2 µmol/g Pb). A constant slope of adsorbed–dissolved concentration dependence was valid over 5 orders of magnitude of metal concentrations. Universal Langmuir and Freundlich equations and the SCM formalism described the adsorption isotherms and the pH-dependent adsorption edge over very broad ranges of metal concentrations, indicating no high- or low-affinity sites for metal binding at the soil surface under these experimental conditions. At pH 5, Cd and Pb did not compete, in accordance with the SCM. The metal adsorption ability exceeded the value for soil protection by two orders of magnitude, but only critical load guarantees soil protection since metal toxicity depends on metal availability

Soil heavy metal contamination and acid deposition: experimental approach on two forest soils in Hunan, Southern China

In 1985, a tailing dam collapsed in Hunan province (southern China) leading to soil contamination by heavy metals from the tailings waste. Moreover, acid deposition becomes more and more serious in this area. In this context, two forest soils (a red soil and a yellow red soil, typically and commonly found in southern China) were collected from Hunan. The objectives are (i) to determine releases and changes in speciation fractions of heavy metals (especially Cd, Cu, and Zn) when the soils are contaminated with heavy metals and affected by simulated acid deposition, and (ii) to study effects of soil heavy metals and acid deposition on releases of soil Ca2+, Mg2+, and Al3+. The soil samples were soaked in the solutions of CdCl2, CuCl2, and ZnCl2 for 15 days to make contaminated soils containing 200 mg kg1 of Cd, Cu, and Zn. Then the contaminated soils and the original soils were extracted with five simulated acid deposition solutions (pH ranged from 5.6 to 3.0 and total dissolved salts increased). The experimental results indicate that acid deposition leads to great releases of soil heavy metals due to complicated soil chemical processes, mostly cation exchange and partly dissolution of minerals at pH lower than 4.2. These released heavy metals come mainly from soil exchangeable pools and other labile fractions. Releases of heavy metals are closely controlled by pH values or, in some cases, total cation contents in acid deposition; meanwhile, concentrations of heavy metals are negatively related to the relevant pH values in soil equilibrium solutions when pH values are in a range of 4.2–5.1. From the point of view of heavy metal releases, Zn is the most sensitive to acid deposition, followed by Cd and Cu. Compared with the original soils, the contaminated soils could probably release more base cations Ca2+ and Mg2+ and less Al3+. Greater amounts of Cd, Cu, Zn, and Al released from Soil B show that this soil is more sensitive to acid deposition, and we could expect serious environmental contamination in Soil B area if mining activities and acid deposition are not under control in the future

Ab initio study of electron-phonon interaction in phosphorene

The monolayer of black phosphorous, or phosphorene, has recently emerged as a new 2D semiconductor with intriguing highly anisotropic transport properties. Existing calculations of its intrinsic phonon-limited electronic transport properties so far rely on the deformation potential approximation, which is in general not directly applicable to anisotropic materials since the deformation along one specific direction can scatter electrons traveling in all directions. We perform a first-principles calculation of the electron-phonon interaction in phosphorene based on density functional perturbation theory and Wannier interpolation. Our calculation reveals that 1) the high anisotropy provides extra phase space for electron-phonon scattering, and 2) optical phonons have appreciable contributions. Both effects cannot be captured by the deformation potential calculations.Comment: 25 pages, 15 figure