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.     

Quantitative UPLC‐MS/MS analysis of chlorogenic acid derivatives in antioxidant fractionates from dandelion (Taraxacum officinale) root

While qualitative studies have identified chlorogenic acids in antioxidant extracts, particularly ethyl acetate‐derived extracts, of Taraxacum officinale, quantitative analysis of these phenolic compounds remains largely unreported for this species. In this study, bioactivity‐guided fractionation of an antioxidant crude ethyl acetate extract (DPPH = 295.481 ± 0.955 mg TE g^?1 extract) from T. officinale root resulted in a number of reverse‐phase fractions that demonstrated high antioxidant activity (DPPH = 1058.733–1312.136 mg TE g^?1 extract), stronger than that of the synthetic antioxidant Trolox^®. UPLC‐MS/MS screening of these fractions for the presence of selected mono‐ and di‐caffeoylquinic acids revealed large quantities of 1,5‐dicaffeoylquinic acid present in several fractions (853.052–907.324 μg mg^?1), respectively. Due to the antioxidant potency and high levels of 1,5‐dicaffeoylquinic acid observed in these fractions, it was concluded that specifically this chlorogenic acid derivative is a major contributor to the antioxidant efficacy of dandelion root.     

Magnetic Nanoparticle Arrays Self-Assembled on Perpendicular Magnetic Recording Media

We study magnetic-field directed self-assembly of magnetic nanoparticles onto templates recorded on perpendicular magnetic recording media, and quantify feature width and height as a function of assembly time. Feature widths are determined from Scanning Electron Microscope (SEM) images, while heights are obtained with Atomic Force Microscopy (AFM). For short assembly times, widths were ~150 nm, while heights were ~14 nm, a single nanoparticle on average with a 10:1 aspect ratio. For long assembly times, widths approach 550 nm, while the average height grows to 3 nanoparticles, ~35 nm; a 16:1 aspect ratio. We perform magnetometry on these self-assembled structures and observe the slope of the magnetic moment vs. field curve increases with time. This increase suggests magnetic nanoparticle interactions evolve from nanoparticle–nanoparticle interactions to cluster–cluster interactions as opposed to feature–feature interactions. We suggest the aspect ratio increase occurs because the magnetic field gradients are strongest near the transitions between recorded regions in perpendicular media. If these gradients can be optimized for assembly, strong potential exists for using perpendicular recording templates to assemble complex heterogeneous materials.     

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.