Gene Selection in a Single Cell Gene Space Based on D-S Evidence Theory.

If the samples, features and information values in a real-valued information system are cells, genes and gene expression values, respectively, then for convenience, this system is said to be a single cell gene space. In the era of big data, people are faced with high dimensional gene expression data with redundancy and noise causing its strong uncertainty. D-S evidence theory excels at tackling the problem of uncertainty, and its conditions to be met are weaker than Bayesian probability theory. Therefore, this paper studies the gene selection in a single cell gene space to remove noise and redundancy with D-S evidence theory. The distance between two cells in each gene is first defined. Then, the tolerance relation is established according to the defined distance. In addition, the belief and plausibility functions to grasp the uncertainty of a single cell gene space are introduced on the basis of the tolerance classes. Statistical analysis shows that they can effectively measure the uncertainty of a single cell gene space. Furthermore, several gene selection algorithms in a single cell gene space are presented using the proposed belief and plausibility. Finally, the performance of the proposed algorithm is compared to other algorithms on some published single-cell data sets. Experimental results and statistical tests show that the classification and clustering performance of the presented algorithm not only exceeds the other three state-of-the-art algorithms, but also its gene reduction rate is very high.

The modified proximal point algorithm in Hadamard spaces.

The purpose of this paper is to propose a modified proximal point algorithm for solving minimization problems in Hadamard spaces. We then prove that the sequence generated by the algorithm converges strongly (convergence in metric) to a minimizer of convex objective functions. The results extend several results in Hilbert spaces, Hadamard manifolds and non-positive curvature metric spaces.

A modified viscosity implicit-type proximal point algorithm for monotone inclusions and asymptotically nonexpansive mappings in Hadamard spaces.

The purpose of this article is to propose a modified viscosity implicit-type proximal point algorithm for approximating a common solution of a monotone inclusion problem and a fixed point problem for an asymptotically nonexpansive mapping in Hadamard spaces. Under suitable conditions, some strong convergence theorems of the proposed algorithms to such a common solution are proved. Our results extend and complement some recent results in this direction.

Implicit and explicit iterative algorithms for hierarchical variational inequality in uniformly smooth Banach spaces.

The purpose of this paper is to solve the hierarchical variational inequality with the constraint of a general system of variational inequalities in a uniformly convex and 2-uniformly smooth Banach space. We introduce implicit and explicit iterative algorithms which converge strongly to a unique solution of the hierarchical variational inequality problem. Our results improve and extend the corresponding results announced by some authors.

Leuconostoc mesenteroides growth in food products: prediction and sensitivity analysis by adaptive-network-based fuzzy inference systems.

BACKGROUND: An adaptive-network-based fuzzy inference system (ANFIS) was compared with an artificial neural network (ANN) in terms of accuracy in predicting the combined effects of temperature (10.5 to 24.5°C), pH level (5.5 to 7.5), sodium chloride level (0.25% to 6.25%) and sodium nitrite level (0 to 200 ppm) on the growth rate of Leuconostoc mesenteroides under aerobic and anaerobic conditions. METHODS: THE ANFIS AND ANN MODELS WERE COMPARED IN TERMS OF SIX STATISTICAL INDICES CALCULATED BY COMPARING THEIR PREDICTION RESULTS WITH ACTUAL DATA: mean absolute percentage error (MAPE), root mean square error (RMSE), standard error of prediction percentage (SEP), bias factor (Bf), accuracy factor (Af), and absolute fraction of variance (R (2)). Graphical plots were also used for model comparison. CONCLUSIONS: The learning-based systems obtained encouraging prediction results. Sensitivity analyses of the four environmental factors showed that temperature and, to a lesser extent, NaCl had the most influence on accuracy in predicting the growth rate of Leuconostoc mesenteroides under aerobic and anaerobic conditions. The observed effectiveness of ANFIS for modeling microbial kinetic parameters confirms its potential use as a supplemental tool in predictive mycology. Comparisons between growth rates predicted by ANFIS and actual experimental data also confirmed the high accuracy of the Gaussian membership function in ANFIS. Comparisons of the six statistical indices under both aerobic and anaerobic conditions also showed that the ANFIS model was better than all ANN models in predicting the four kinetic parameters. Therefore, the ANFIS model is a valuable tool for quickly predicting the growth rate of Leuconostoc mesenteroides under aerobic and anaerobic conditions.