A Characterization of Chover-Type Law of Iterated Logarithm

Let $0 < \alpha \leq 2$ and $- \infty < \beta < \infty$. Let $\{X_{n}; n \geq 1 \}$ be a sequence of independent copies of a real-valued random variable $X$ and set $S_{n} = X_{1} + \cdots + X_{n}, ~n \geq 1$. We say $X$ satisfies the $(\alpha, \beta)$-Chover-type law of the iterated logarithm (and write $X \in CTLIL(\alpha, \beta)$) if $\limsup_{n \rightarrow \infty} \left| \frac{S_{n}}{n^{1/\alpha}} \right|^{(\log \log n)^{-1}} = e^{\beta}$ almost surely. This paper is devoted to a characterization of $X \in CTLIL(\alpha, \beta)$. We obtain sets of necessary and sufficient conditions for $X \in CTLIL(\alpha, \beta)$ for the five cases: $\alpha = 2$ and $0 < \beta < \infty$, $\alpha = 2$ and $\beta = 0$, $1 < \alpha < 2$ and $-\infty < \beta < \infty$, $\alpha = 1$ and $- \infty < \beta < \infty$, and $0 < \alpha < 1$ and $-\infty < \beta < \infty$. As for the case where $\alpha = 2$ and $-\infty < \beta < 0$, it is shown that $X \notin CTLIL(2, \beta)$ for any real-valued random variable $X$. As a special case of our results, a simple and precise characterization of the classical Chover law of the iterated logarithm (i.e., $X \in CTLIL(\alpha, 1/\alpha)$) is given; that is, $X \in CTLIL(\alpha, 1/\alpha)$ if and only if $\inf \left \{b:~ \mathbb{E} \left(\frac{|X|^{\alpha}}{(\log (e \vee |X|))^{b\alpha}} \right) < \infty \right\} = 1/\alpha$ where $\mathbb{E}X = 0$ whenever $1 < \alpha \leq 2$.Comment: 11 page

Drilling Performance Optimization Based on Mechanical Specific Energy Technologies

Mechanical specific energy (MSE) has been widely used to quantify drilling efficiency and maximize rate of penetration (ROP) in oil and gas wells drilling. In this chapter, MSE models respectively for directional or horizontal drilling and rotating drilling with positive displacement motor (PDM) are established based on the evaluation of virtues and defects of available MSE models. Meanwhile methods for drilling performance prediction and optimization based on MSE technologies are presented. Field data presented in this chapter indicates that the developed MSE models estimate MSE values with a reasonable approximation in the absence of reliable torque measurements, the method for optimizing drilling parameters can estimate optimum WOB values with different RPM to drill a specific formation interval with PDM. It also show that the optimum WOB is low for rotating drilling with PDM compared with the conventional drilling without PDM, increasing WOB does not always increase ROP but is more likely to decrease ROP. The drilling performance prediction and optimization methods based on MSE technologies could be effectively used to maximize ROP and allow operators to drill longer and avoid unnecessary trips, and is worthy to be applied and promoted with highly diagnostic accuracy, effective optimizing and simple operation

Application of the Denitrification-Decomposition Model to Predict Carbon Dioxide Emissions under Alternative Straw Retention Methods

Straw retention has been shown to reduce carbon dioxide (CO2) emission from agricultural soils. But it remains a big challenge for models to effectively predict CO2 emission fluxes under different straw retention methods. We used maize season data in the Griffith region, Australia, to test whether the denitrification-decomposition (DNDC) model could simulate annual CO2 emission. We also identified driving factors of CO2 emission by correlation analysis and path analysis. We show that the DNDC model was able to simulate CO2 emission under alternative straw retention scenarios. The correlation coefficients between simulated and observed daily values for treatments of straw burn and straw incorporation were 0.74 and 0.82, respectively, in the straw retention period and 0.72 and 0.83, respectively, in the crop growth period. The results also show that simulated values of annual CO2 emission for straw burn and straw incorporation were 3.45 t C ha−1 y−1 and 2.13 t C ha−1 y−1, respectively. In addition the DNDC model was found to be more suitable in simulating CO2 mission fluxes under straw incorporation. Finally the standard multiple regression describing the relationship between CO2 emissions and factors found that soil mean temperature (SMT), daily mean temperature (Tmean), and water-filled pore space (WFPS) were significant

Impact of spatially variable soil salinity on crop physiological properties, soil water content and yield of wheat in a semi arid environment

In the Birchip region of the Victorian southern Mallee, Australia, subsoil salinity is an important factor determining crop growth and yield. Crop simulation models have performed poorly in this region, presumably due to their inability to account for subsoil constraints, mainly salinity. The objective of this work was to study the impact of subsoil salinity on crop physiological properties, growth, water use and yield of a wheat crop. From a calibrated electromagnetic survey (EM 38) over an area 7 m wide by 100 m long, three sites of low, medium and high salinity levels were identified. For each site, soil electrical conductivity was measured and the values averaged for the depth 0-70 cm were 0.25, 1.14 and 1.63 dS/m at the sites with low, medium and high salinity, respectively. Further, at different stages of crop growth, radiation interception by the canopy as well as soil water content were measured while plant samples were collected to estimate crop physiological properties. Grain yield at each salinity site was also measured. All the physiological properties and yield were negatively affected by increasing salinity levels due to less water use and radiation interception. Compared to the low salinity level, medium and high salinity levels reduced the above-ground dry weight of the crop at harvest by 40% and 41%, accumulated intercepted radiation by 23% and 37%, radiation use efficiency by 25% and 52%, water use by 18% and 35% and grain yield by 41% and 48%, respectively

Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological View

Graph Neural Networks (GNNs) have achieved promising performance on a wide range of graph-based tasks. Despite their success, one severe limitation of GNNs is the over-smoothing issue (indistinguishable representations of nodes in different classes). In this work, we present a systematic and quantitative study on the over-smoothing issue of GNNs. First, we introduce two quantitative metrics, MAD and MADGap, to measure the smoothness and over-smoothness of the graph nodes representations, respectively. Then, we verify that smoothing is the nature of GNNs and the critical factor leading to over-smoothness is the low information-to-noise ratio of the message received by the nodes, which is partially determined by the graph topology. Finally, we propose two methods to alleviate the over-smoothing issue from the topological view: (1) MADReg which adds a MADGap-based regularizer to the training objective;(2) AdaGraph which optimizes the graph topology based on the model predictions. Extensive experiments on 7 widely-used graph datasets with 10 typical GNN models show that the two proposed methods are effective for relieving the over-smoothing issue, thus improving the performance of various GNN models.Comment: Accepted by AAAI 2020. This complete version contains the appendi