Properties of Noncommutative Renyi and Augustin Information

The scaled R\'enyi information plays a significant role in evaluating the performance of information processing tasks by virtue of its connection to the error exponent analysis. In quantum information theory, there are three generalizations of the classical R\'enyi divergence---the Petz's, sandwiched, and log-Euclidean versions, that possess meaningful operational interpretation. However, these scaled noncommutative R\'enyi informations are much less explored compared with their classical counterpart, and lacking crucial properties hinders applications of these quantities to refined performance analysis. The goal of this paper is thus to analyze fundamental properties of scaled R\'enyi information from a noncommutative measure-theoretic perspective. Firstly, we prove the uniform equicontinuity for all three quantum versions of R\'enyi information, hence it yields the joint continuity of these quantities in the orders and priors. Secondly, we establish the concavity in the region of $s\in(-1,0)$ for both Petz's and the sandwiched versions. This completes the open questions raised by Holevo [\href{https://ieeexplore.ieee.org/document/868501/}{\textit{IEEE Trans.~Inf.~Theory}, \textbf{46}(6):2256--2261, 2000}], Mosonyi and Ogawa [\href{https://doi.org/10.1007/s00220-017-2928-4/}{\textit{Commun.~Math.~Phys}, \textbf{355}(1):373--426, 2017}]. For the applications, we show that the strong converse exponent in classical-quantum channel coding satisfies a minimax identity. The established concavity is further employed to prove an entropic duality between classical data compression with quantum side information and classical-quantum channel coding, and a Fenchel duality in joint source-channel coding with quantum side information in the forthcoming papers

Application and Conversion of Soybean Hulls

Soybean is one of the most cultivated crops in the world, with a global production of approximately 240 million tons, generating about 18–20 million tons of hulls, the major by-product of soy industry. The chemical composition of soybean hulls depends on the efficiency of the dehulling process, and so, the soybean hulls may contain variable amounts of cellulose (29–51%), hemicelluloses (10–25%), lignin (1–4%), pectins (4–8%), proteins (11–15%), and minor extractives. This chapter provides a review on the composition and structure of soybean hulls, especially in regard to the application and conversion of the compositions. Current applications of soybean hulls are utilizations to animal feed, treatment of wastewater, dietary fiber, and herbal medicine. The conversion of soybean hulls is concerned with ethanol production, bio-oil, polysaccharides, microfibrils, peroxidase, and oligopeptides. On the basis of the relevant findings, we recommend the use of soybean hulls as important source on environment, energy, animal breeding, materials, chemicals, medicine, and food

Predicted Optimal Bifunctional Electrocatalysts for the Hydrogen Evolution Reaction and the Oxygen Evolution Reaction Using Chalcogenide Heterostructures Based on Machine Learning Analysis of in Silico Quantum Mechanics Based High Throughput Screening

Two-dimensional van der Waals heterostructure materials, particularly transition metal dichalcogenides (TMDC), have proved to be excellent photoabsorbers for solar radiation, but performance for such electrocatalysis processes as water splitting to form H₂ and O₂ is not adequate. We propose that dramatically improved performance may be achieved by combining two independent TMDC while optimizing such descriptors as rotational angle, bond length, distance between layers, and the ratio of the bandgaps of two component materials. In this paper we apply the least absolute shrinkage and selection operator (LASSO) process of artificial intelligence incorporating these descriptors together with quantum mechanics (density functional theory) to predict novel structures with predicted superior performance. Our predicted best system is MoTe₂/WTe₂ with a rotation of 300°, which is predicted to have an overpotential of 0.03 V for HER and 0.17 V for OER, dramatically improved over current electrocatalysts for water splitting

Approximation algorithms for kk-submodular maximization subject to a knapsack constraint

In this paper, we study the problem of maximizing $k$-submodular functions subject to a knapsack constraint. For monotone objective functions, we present a $\frac{1}{2}(1-e^{-2})\approx 0.432$ greedy approximation algorithm. For the non-monotone case, we are the first to consider the knapsack problem and provide a greedy-type combinatorial algorithm with approximation ratio $\frac{1}{3}(1-e^{-3})\approx 0.317$