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.     

Nonhydrolyzable Heptose Bis- and Monophosphate Analogues Modulate Pro-inflammatory TIFA-NF-κB Signaling

d -Glycero-d -manno-heptose-1β,7-bisphosphate (HBP) and d -glycero-d -manno-heptose-1β-phosphate (H1P) are bacterial metabolites that were recently shown to stimulate inflammatory responses in host cells through the activation of the TIFA-dependent NF-κB pathway. To better understand structure-based activity in relation to this process, a family of nonhydrolyzable phosphonate analogues of HBP and H1P was synthesized. The inflammation modulation by which these molecules induce the TIFA-NF-κB signal axis was evaluated in vivo at a low-nanomolar concentration (6 nM) and compared to that of the natural metabolites. Our data showed that three phosphonate analogues had similar stimulatory activity to HBP, whereas two phosphonates antagonized HBP-induced TIFA-NF-κB signaling. These results open new horizons for the design of pro-inflammatory and innate immune modulators that could be used as vaccine adjuvant.     

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.     

Reducing the complexity of distance measurement methods for circular turbo codes that use structured interleavers

The knowledge of turbo code's minimum Hamming distance (d_min) and its corresponding codeword multiplicity (A_min) is of a great importance because the error correction capability of a code is strongly tied to the values of d_min and A_min. Unfortunately, the computational complexity associated with the search for d_min and A_min can be very high, especially for a turbo code that has high d_min value. This paper introduces some useful properties of turbo codes that use structured interleavers together with circular encoding. These properties allow for a significant reduction of search space and thus reduce significantly the computational complexity associated with the determination of d_min and A_min values. © 2014 The Authors. International Journal of Communication Systems published by John Wiley & Sons, Ltd.     

Ga-doped IZO films obtained by magnetron sputtering as transparent conductors for visible and solar applications

C-axis textured thin films of gallium-doped indium zinc oxide (GIZO) with a 2% ratio of Ga/Zn, were obtained via RF-magnetron sputtering with high transparency and electrical conductivity. A Box-Behnken response surface design was used to evaluate the effects of the deposition parameters (In₂O₃ target power, deposition time, and substrate temperature) on the chemical composition, optical, electrical, and structural properties of the GIZO films. The optical constants and the electrical properties were obtained using optical models. The GIZO stoichiometry, and therefore the In/Zn atomic ratio, affected the crystallinity, crystalline parameters, band gap, and charge carrier mobility of the GIZO films. The charge carrier density was related to the change in the crystalline parameters of the hexagonal structure and the In/Zn atomic ratio. The best electrical conductivity values (1.75?×?10³ Ω^?1 cm^?1) were obtained for GIZO films with In/Zn ratio ≥?1. Several figures of merit (FOM) defined for the visible and solar regions were comparatively used to select the optimal In/Zn atomic ratio that provided the best balance between the conductivity and the transparency. The optimal In/Zn ratio was in a range of 0.85–0.90 for the GIZO films.