Optimal Recovery of Functions on the Sphere on a Sobolev Spaces with a Gaussian Measure in the Average Case Setting

In this paper, we study optimal recovery （reconstruction） of functions on the sphere in the average case setting. We obtain the asymptotic orders of average sampling numbers of a Sobolev space on the sphere with a Gaussian measure in the Lq （S^d-1） metric for 1 ≤ q ≤ ∞, and show that some worst-case asymptotically optimal algorithms are also asymptotically optimal in the average case setting in the Lq （S^d-1） metric for 1 ≤ q ≤ ∞.

L_2-Optimal Recovery on the Riesz Potential Spaces

The problems of best reconstruction of multivariate functions of the Riesz potential spaces from their values on a given mesh are considered, and the exact results of some classes of L_2(R^n) (and L_2(Q^n)) defined by the Riesz potential are obtained.

Optimal Recovery on the Classes of Functions with Bounded Mixed Derivative

Temlyakov considered the optimal recovery on the classes of functions with bounded mixed derivative in the Lp metrics and gave the upper estimates of the optimal recovery errors. In this paper, we determine the asymptotic orders of the optimal recovery in Sobolev spaces by standard information, i.e., function values, and give the nearly optimal algorithms which attain the asymptotic orders of the optimal recovery.

Investigation of different coal types effect on the overall plant recovery

Coal washing plants are usually fed from various sources. Coals include different combinations which should be considered for increasing the plant proficiency. Thus different methods have been used to enrich various coal types. In this study, Alborz-Sharghi coal washing plant was investigated which is fed from five coalmines. The optimum recovery was achieved for all coal types individually through experimental design. The controllable operation parameters in the experiments were collector dosage,frother dosage, solid percent content and particle size. The other parameters such as impeller speed,pH, conditioning time and flotation time were kept constant for all experiments. The optimum combination of coals was also specified. The results show that the optimum recovery for coal blends is 91.2%which shows much improvement relative to the plant conditions.

Improved nonconvex optimization model for low-rank matrix recovery

Low-rank matrix recovery is an important problem extensively studied in machine learning, data mining and computer vision communities. A novel method is proposed for low-rank matrix recovery, targeting at higher recovery accuracy and stronger theoretical guarantee. Specifically, the proposed method is based on a nonconvex optimization model, by solving the low-rank matrix which can be recovered from the noisy observation. To solve the model, an effective algorithm is derived by minimizing over the variables alternately. It is proved theoretically that this algorithm has stronger theoretical guarantee than the existing work. In natural image denoising experiments, the proposed method achieves lower recovery error than the two compared methods. The proposed low-rank matrix recovery method is also applied to solve two real-world problems, i.e., removing noise from verification code and removing watermark from images, in which the images recovered by the proposed method are less noisy than those of the two compared methods.

The Partition of Unity Method for High-Order Finite Volume Schemes Using Radial Basis Functions Reconstruction

This paper introduces the use of partition of unity method for the development of a high order finite volume discretization scheme on unstructured grids for solving diffusion models based on partial differential equations.The unknown function and its gradient can be accurately reconstructed using high order optimal recovery based on radial basis functions.The methodology proposed is applied to the noise removal problem in functional surfaces and images.Numerical results demonstrate the effectiveness of the new numerical approach and provide experimental order of convergence.

Solving Airlines Disruption by Considering Aircraft and Crew Recovery Simultaneously

When disruptions occur, the airlines have to recover from the disrupted schedule. The recovery usually consists of aircraft recovery, crew recovery and passengers' recovery. This paper focuses on the integrated recovery, which means above-mentioned two or more recoveries are considered as a whole. Taking the minimization of the total cost of assignment, cancellation and delay as an objective, we present a more practical model, in which the maintenance and the union regulations are considered. Then we present a so-called iterative tree growing with node combination method. By aggregating nodes, the possibility of routings is greatly simplified, and the computation time is greatly decreased. By adjusting the consolidating range, the computation time can be controlled in a reasonable time. Finally, we use data from a main Chinese airline to test the algorithm. The experimental results show that this method could be used in the integrated recovery problem.