Nonnegative Tensor Factorization, Completely Positive Tensors and an Hierarchical Elimination Algorithm

Nonnegative tensor factorization has applications in statistics, computer vision, exploratory multiway data analysis and blind source separation. A symmetric nonnegative tensor, which has a symmetric nonnegative factorization, is called a completely positive (CP) tensor. The H-eigenvalues of a CP tensor are always nonnegative. When the order is even, the Z-eigenvalue of a CP tensor are all nonnegative. When the order is odd, a Z-eigenvector associated with a positive (negative) Z-eigenvalue of a CP tensor is always nonnegative (nonpositive). The entries of a CP tensor obey some dominance properties. The CP tensor cone and the copositive tensor cone of the same order are dual to each other. We introduce strongly symmetric tensors and show that a symmetric tensor has a symmetric binary decomposition if and only if it is strongly symmetric. Then we show that a strongly symmetric, hierarchically dominated nonnegative tensor is a CP tensor, and present a hierarchical elimination algorithm for checking this. Numerical examples are also given

SLSSNN: High energy efficiency spike-train level spiking neural networks with spatio-temporal conversion

Brain-inspired spiking neuron networks (SNNs) have attracted widespread research interest due to their low power features, high biological plausibility, and strong spatiotemporal information processing capability. Although adopting a surrogate gradient (SG) makes the non-differentiability SNN trainable, achieving comparable accuracy for ANNs and keeping low-power features simultaneously is still tricky. In this paper, we proposed an energy-efficient spike-train level spiking neural network (SLSSNN) with low computational cost and high accuracy. In the SLSSNN, spatio-temporal conversion blocks (STCBs) are applied to replace the convolutional and ReLU layers to keep the low power features of SNNs and improve accuracy. However, SLSSNN cannot adopt backpropagation algorithms directly due to the non-differentiability nature of spike trains. We proposed a suitable learning rule for SLSSNNs by deducing the equivalent gradient of STCB. We evaluate the proposed SLSSNN on static and neuromorphic datasets, including Fashion-Mnist, Cifar10, Cifar100, TinyImageNet, and DVS-Cifar10. The experiment results show that our proposed SLSSNN outperforms the state-of-the-art accuracy on nearly all datasets, using fewer time steps and being highly energy-efficient

Comparative study on appropriate drought and flood index selection in a tropical farming island in China

The traditional drought and flood analysis method had not fully considered the proportion analysis of different drought and flood grades in the historical years of each rainfall station. This made results unconvincing and made it difficult to deeply understand the characteristics and applicability of various methods. Based on the daily rainfall data of 88 stations in Hainan Island from 1970 to 2019, the China-Z index and the Standardized Precipitation Index (SPI) were used to compare and analyze the spatial and temporal distribution characteristics of droughts and floods from three different time scales (flood season, non-flood season and the whole year). The results showed that both SPI and China-Z index can well reflect the actual drought and flood situations in Hainan Island. The analysis of the proportions of different drought and flood grades in the historical years of each rainfall station and regional historical drought and flood statistics suggested that the China-Z index had a better indication effect than SPI on the extreme drought and flood grades. The alternation of drought and flood between different eras were obvious. Hainan Island generally presented an east-west reverse drought-flood variation trend, as well as a north-south reverse drought-flood variation trend. The drought and flood in the central mountainous area of Hainan Island had been relatively stable. The distribution pattern of drought and flood had a good spatial consistency in the three periods. On the whole, Hainan Island had shown a trend of flood in the east and drought in the west in the past 50 years

Molecular simulation of adsorption behaviors of methane and carbon dioxide on typical clay minerals

Knowledge of the interaction mechanisms between shale and CH4/CO2 is crucial for the implementation of CO2 sequestration with enhanced CH4 recovery (CS-EGR) in shale reservoir. As one of the main constituents of shale, clay minerals can profoundly affect the storage capacity of gases in nanopores. In this paper, the adsorption behaviors of both CO2 and CH4 on montmorillonite, illite as well as kaolinite under dry condition are investigated by Grand Canonical Monte Carlo (GCMC) simulation. The results exhibit that the maximum adsorption capacity of single-component CH4 and CO2 is associated with the types of clay crystals. Specifically, the montmorillonite has the strongest adsorption capacity for CO2, followed by illite and kaolinite, while the sequence in maximum adsorption capacity of CH4 is predicted in the order of kaolinite > montmorillonite > illite. These discrepancies are closely related to the characteristics of adsorbate molecules as well as the different structures of clay crystals. Meanwhile, the maximum adsorption capacity of CH4 in studied clay minerals gradually decreases as pore size increases, while nanopores with 2-nm basal spacing demonstrate the highest adsorption capacity for CO2. In addition, it is observed that the studied clay minerals tend to preferentially adsorb CO2 rather than CH4 during binary gas mixtures simulation. The selectivity of CH4/CO2 mixtures in montmorillonite and kaolinite exhibits various performances as the adsorption pressure increases, with the selectivity in montmorillonite being the largest, especially at low pressure. The cation exchange significantly enhances the electrostatic interaction with CO2 molecules, leading to a higher loading of CO2 as well as larger value of selectivity. These findings can provide basis and guidance for the CS-EGR project in shale reservoirs

Effect of Polyvinyl Acetate Stabilization on the Swelling-Shrinkage Properties of Expansive Soil

Polyvinyl acetate constitutes a class of polymers that can entirely dissolve in water to form a solution. In this study, polyvinyl acetate as a nontraditional chemical stabilizer was used in soil improvement. Laboratory tests were carried out to evaluate the effect of polyvinyl acetate on swelling-shrinkage properties of expansive soil. A series of shrink/swell tests were performed with adding polyvinyl acetate as amendment at a concentration 3 g/cm3 to four aggregate sizes in the range of 0–0.5 mm, 0.5–1 mm, 1-2 mm, and 2–5 mm and five concentrations 1.5 g/cm3, 3 g/cm3, 4.5 g/cm3, 6 g/cm3, and 9 g/cm3 to soils with aggregate size in the range of 0.5–1 mm for comparison of results with those of untreated soils. The results show that all the linear swelling ratio (LSWR) and linear shrinkage ratio (LSHR) values of the treated specimens decrease. SEM images and the test results indicate the achieved reduction in volume change of the soil tested using soil pore filling and particle encapsulation