Quasi-Bell inequalities from symmetrized products of noncommuting qubit observables

Noncommuting observables cannot be simultaneously measured, however, under local hidden variable models, they must simultaneously hold premeasurement values, implying the existence of a joint probability distribution. We study the joint distributions of noncommuting observables on qubits, with possible criteria of positivity and the Fr\'echet bounds limiting the joint probabilities, concluding that the latter may be negative. We use symmetrization, justified heuristically and then more carefully via the Moyal characteristic function, to find the quantum operator corresponding to the product of noncommuting observables. This is then used to construct Quasi-Bell inequalities, Bell inequalities containing products of noncommuting observables, on two qubits. These inequalities place limits on local hidden variable models that define joint probabilities for noncommuting observables. We find Quasi-Bell inequalities have a quantum to classical violation as high as $\frac{3}{2}$, higher than conventional Bell inequalities. The result demonstrates the theoretical importance of noncommutativity in the nonlocality of quantum mechanics, and provides an insightful generalization of Bell inequalities.Comment: 17 page

Unconventional machine learning of genome-wide human cancer data

Recent advances in high-throughput genomic technologies coupled with exponential increases in computer processing and memory have allowed us to interrogate the complex aberrant molecular underpinnings of human disease from a genome-wide perspective. While the deluge of genomic information is expected to increase, a bottleneck in conventional high-performance computing is rapidly approaching. Inspired in part by recent advances in physical quantum processors, we evaluated several unconventional machine learning (ML) strategies on actual human tumor data. Here we show for the first time the efficacy of multiple annealing-based ML algorithms for classification of high-dimensional, multi-omics human cancer data from the Cancer Genome Atlas. To assess algorithm performance, we compared these classifiers to a variety of standard ML methods. Our results indicate the feasibility of using annealing-based ML to provide competitive classification of human cancer types and associated molecular subtypes and superior performance with smaller training datasets, thus providing compelling empirical evidence for the potential future application of unconventional computing architectures in the biomedical sciences

Role of Biotransformation of <i>Acacia nilotica</i> Metabolites by <i>Aspergillus subolivaceus</i> in Boosting <i>Lupinus termis</i> Yield: A Promising Approach to Sustainable Agriculture

Biotransformation plays a significant role in sustainable agriculture. This process involves utilizing microorganisms, such as bacteria and fungi, to transform organic compounds and metabolites into bioactive compounds which have beneficial effects on plant growth, yield, and soil characters. Accordingly, the present study aims to explore the role of biotransformation of Acacia nilotica metabolites by Aspergillus subolivaceus in boosting L. termis yield, as an important strategy in agricultural sustainability. A pilot experiment was performed on five fungal strains (Fusarium oxysporium A. aculeatus, Aspergillus. subolivaceus, Rhizopus oryzae and Trichoderma viride) which were grown on different parts of plants (A. nilotica leaves; green tea leaves, green pepper fruits and pomegranate fruits), and the results indicated that the most active metabolite for the growth of L. termis seeds was the fungal metabolite of A. subolivaceus growing on A. nilotica. More specifically, we assess how metabolites produced by Aspergillus subolivaceus using A. nilotica leaves affect the biochemical properties and chemical composition of L. termis seeds. A. subolivaceus was grown on leaves from A. nilotica to obtain metabolites and fractionated into four extracts. Two concentrations of each extract were examined by pretreating the seeds of L. termis. The study found that all four extracts contributed to an increase in yield and some biochemical properties of the yielded seeds. The best results were obtained by treating the L. termis seeds with an extract obtained from diethyl ether, which led to a significant increase in total nitrogen, amino nitrogen, glucose and protein contents of the seeds. According to 1H NMR guided GC/MS analysis, our results showed an increase in phytochemicals such as terpenes, fatty materials, and flavonoids including 3′,4′,7-trimethoxyquercetin and 4-methyl-p-menth-8-en-3-one, which have not been stated before from A. nilotica suggesting that biotransformation may have occurred due to the presence of A. subolivaceus