Survey of the qualitative properties of fractional difference operators: monotonicity, convexity, and asymptotic behavior of solutions

In this article we discuss some of the qualitative properties of fractional difference operators. We especially focus on the connections between the fractional difference operator and the monotonicity and convexity of functions. In the integer-order setting, these connections are elementary and well known. However, in the fractional-order setting the connections are very complicated and muddled. We survey some of the known results and suggest avenues for future research. In addition, we discuss the asymptotic behavior of solutions to fractional difference equations and how the nonlocal structure of the fractional difference can be used to deduce these asymptotic properties

Integrative multi‐omics analyses of date palm (Phoenix dactylifera) roots and leaves reveal how the halophyte land plant copes with sea water

Date palm (Phoenix dactylifera L.) is able to grow and complete its life cycle while being rooted in highly saline soils. Which of the many well-known salt-tolerance strategies are combined to fine-tune this remarkable resilience is unknown. The precise location, whether in the shoot or the root, where these strategies are employed remains uncertain, leaving us unaware of how the various known salt-tolerance mechanisms are integrated to fine-tune this remarkable resilience. To address this shortcoming, we exposed date palm to a salt stress dose equivalent to seawater for up to 4 weeks and applied integrative multi-omics analyses followed by targeted metabolomics, hormone, and ion analyses. Integration of proteomic into transcriptomic data allowed a view beyond simple correlation, revealing a remarkably high degree of convergence between gene expression and protein abundance. This sheds a clear light on the acclimatization mechanisms employed, which depend on reprogramming of protein biosynthesis. For growth in highly saline habitats, date palm effectively combines various salt-tolerance mechanisms found in both halophytes and glycophytes: “avoidance” by efficient sodium and chloride exclusion at the roots, and “acclimation” by osmotic adjustment, reactive oxygen species scavenging in leaves, and remodeling of the ribosome-associated proteome in salt-exposed root cells. Combined efficiently as in P. dactylifera L., these sets of mechanisms seem to explain the palm's excellent salt stress tolerance

Robust and improved channel estimation for OFDM systems in frequency selective fading channels

In this paper, we present an improved and robust channel estimation method for OFDM mobile communication systems based on the use of pilot sub-carriers. Specifically, we present an inter-path interference cancellation (IPIC) method to estimate the channel multipath time delays. With the multipath time delays information, a minimum mean square error (MMSE) estimator is then derived to estimate the channel multipath gains. It is demonstrated that the proposed channel estimation scheme can significantly improve the performance of OFDM systems and that it is also quite robust to the variations in the channel statistics