On the capacity of the state‐dependent interference relay channel

This paper considers the state‐dependent interference relay channel (SIRC) in which one of the two users may operate as a secondary user and the relay has a noncausal access to the signals from both users. For discrete memoryless SIRC, we first establish the achievable rate region by carefully merging Han‐Kobayashi rate splitting encoding technique, superposition encoding, and Gelfand‐Pinsker encoding technique. Then, based on the achievable rate region that we derive, the capacity of the SIRC is established in many different scenarios including (a) the weak interference regime, (b) the strong interference regime, and (c) the very strong interference regime. This means that our capacity results contain all available known results in the literature. Next, the achievable rate region and the associated capacity results are also evaluated in the case of additive Gaussian noise. Additionally, many numerical examples are investigated to show the value of our theoretical derivations.     

The generalized discrete ‐centroid problem

The ‐centroid problem or leader–follower problem is generalized considering different customer choice rules where a customer may use facilities belonging to different firms, if the difference in travel distance (or time) is small enough. Assuming essential goods, some particular customer choice rules are analyzed. Linear programming formulations for the generalized ‐medianoid and ‐centroid problems are presented and an exact solution approach is applied. Some computational examples are included.     

Assessing students' conceptual understanding using an online three‐tier diagnostic test

When solving a mathematical problem, students who do not have sufficient conceptual understanding may perform poorly and exhibit misconceptions. This study was aimed to examine students' conceptual understanding and significant misconceptions when solving number sense‐related problems. An online three‐tier diagnostic test was administered to 125 fifth‐grade students with varied socio‐economic backgrounds in Hong Kong. Only 14.40% of the students exhibited high performance with high confidence, indicating that these students had a profound conceptual understanding of number sense. In addition, the majority of the students (66.40%) did not demonstrate number sense; these students exhibited several significant misconceptions and could solve the questions only by using a rule‐based method or guessing. Accordingly, most students performed unsatisfactorily on number sense‐related problems. This study is imperative in identifying early predictors and provides information for further compatible interventions in the teaching and learning of number sense in Hong Kong in particular and worldwide in general.     

Evolution of Local Structural Ordering and Chemical Distribution upon Delithiation of a Rock Salt–Structured Li1.3Ta0.3Mn0.4O2 Cathode

Lithium‐rich disordered rock‐salt oxides have attracted great interest owing to their promising performance as Li‐ion battery cathodes. While experimental and theoretical efforts are critical in advancing this class of materials, a fundamental understanding of key property changes upon Li extraction is largely missing. In the present study, single‐crystal synthesis of a new disordered rock‐salt cathode material, Li_1.3Ta_0.3Mn_0.4O₂ (LTMO), and its use as a model compound to investigate Li concentration–driven evolution of local cationic ordering, charge compensation, and chemical distribution are reported. Through the combined use of 2D and 3D X‐ray nanotomography, it is shown that Li removal accompanied by oxygen oxidation is correlated with the development of morphological defects such as particle cracking. Chemical heterogeneity, quantified by subparticle level distribution of Mn valence state, is minimal during Mn redox, which drastically increases upon the formation of cracks during oxygen redox. Density functional theory and bond valence sum mismatch calculations reveal the presence of local short‐range ordering in the pristine oxide, which gradually disappears along with the extraction of Li. The study suggests that with cycling the transformation into true cation–disordered state can be expected, which likely impacts the voltage profile and obtainable energy density of the oxide cathodes.     

Fair‐Weather Friends: Evidence of Lipoxin Dysregulation in Neurodegeneration

Lipoxins (LXs) are autacoids, specialized proresolving lipid mediators (SPMs) acting locally in a paracrine or autocrine fashion. They belong to a complex superfamily of dietary small polyunsaturated fatty acid (PUFA)–metabolites, which direct potent cellular responses to resolve inflammation and restore tissue homeostasis. Together, these SPM activities have been intensely studied in systemic inflammation and acute injury or infection, but less is known about LX signaling and activities in the central nervous system. LXs are derived from arachidonic acid, an omega‐6 PUFA. In addition to well‐established roles in systemic inflammation resolution, they have increasingly become implicated in regulating neuroinflammatory and neurodegenerative processes. In particular, chronic inflammation plays a central role in Alzheimer's disease (AD) etiology, and dysregulated LX production and activities have been reported in a variety of AD rodent models and clinical tissue samples, yet with complex and sometimes conflicting results. In addition, reduced LX production following retinal injury has been reported recently by the authors, and an intriguing direct neuronal activity promoting survival and homeostasis in retinal and cortical neurons is demonstrated. Here, the authors review and clarify this growing literature and suggest new research directions to further elaborate the role of lipoxins in neurodegeneration.     

The biological mechanisms of butanol tolerance and the application of solvent-tolerant bacteria for environmental protection

Toxicity caused by the accumulation of butanol in fermentation media is an important factor limiting the concentration of butanol. There is currently no systematic research in place investigating the butanol tolerance mechanism of bacteria such as Clostridium acetobutylicum, which adapts to butanol stress and regulates its growth and metabolism. Here, research results related to the butanol tolerance of C. acetobutylicum are reviewed to understand the molecular basis of changes in butanol-tolerant strains. Organic solvent-tolerant bacteria play an important role in the fields of biofuel production, enzyme preparation and bioremediation. An analysis of limitations of the application of organic solvent-tolerant bacteria has revealed that future research should focus on combining the microbial tolerance phenotype with specific utilization to achieve an optimal balance between organic solvent tolerance and production. This review serves as a reference for the improvement and engineering of strains that tolerate organic solvents. © 2019 Society of Chemical Industry     

X射线干涉光刻光束线关键光学元件热-结构耦合分析

为了保证上海光源X射线干涉光刻光束线的稳定性,减小热变形对实验结果的影响,对X射线干涉光刻光束线的3个关键光学元件——偏转镜、聚焦镜和精密四刀狭缝进行热-结构耦合分析。首先,计算偏转镜、聚焦镜和精密四刀狭缝所承载的功率密度;然后,建立其有限元模型;最后,获得光学元件的温度场和热变形的结果。结果表明,偏转镜和聚焦镜采用间接水冷方式可有效抑制热变形,冷却后的最大面形误差分别为7.2μrad和9.2μrad。精密四刀狭缝未冷却时,刀片组件温度介于271.56~273.27℃,刀口热变形为0.19 mm,直线导轨热变形为0.08 mm;经过铜辫子冷却后,刀片组件温度降至22.24~23.94℃,刀口热变形降至0.2μm,直线导轨热变形降至0.1μm;采用影像法和接触探头法测试后,刀口直线度、平行度和重复精度均满足技术要求。偏转镜、聚焦镜和精密四刀狭缝的热变形通过间接水冷和铜辫子的冷却方式可以得到很大程度的抑制,进而保证光斑质量。