不确定需求下再制造系统回收、生产与定价策略研究

以单一制造商为研究对象,在需求不确定且回收量依赖于需求量的环境下,构建基于期望利润最大化的数学模型,给出最优的回收率、新品和再制造品生产量及销售价格,并通过解析和数值仿真分析了市场规模、单位节约成本、回收成本的规模参数和需求不确定性对最优策略的影响.结果表明:市场规模增大,销售价格、回收率、生产量和再制造量都随之增大,而新品生产量先增大后减小;单位节约成本越大,回收成本的规模参数越小时,进行再制造就越有利;需求不确定性增加时,进行再制造更有利,可以降低由需求不确定性所造成的损失.     

Stochastic H2 / H∞ Control for Poisson Jump-Diffusion Systems

This paper is concerned with stochastic H_2/H_∞ control problem for Poisson jump-diffusion systems with(x, u, v)-dependent noise, which are driven by Brownian motion and Poisson random jumps. A stochastic bounded real lemma(SBRL for short) for Poisson jump-diffusion systems is firstly established, which stands out on its own as a very interesting theoretical problem. Further, sufficient and necessary conditions for the existence of a state feedback H_2/H_∞ control are given based on four coupled matrix Riccati equations. Finally, a discrete approximation algorithm and an example are presented.     

Deformation in holomorphic Poisson manifolds

In this paper, we consider deforming a coisotropic submanifold Y in a holomorphic Poisson manifold $(X,\pi )$. Under the assumption that Y has a holomorphic tubular neighborhood, we associate Y with an $L_{\infty }$-algebra that controls the deformations of Y. This $L_{\infty }$-algebra can also be extended to control the simultaneous deformations of the holomorphic Poisson structure π and the coisotropic submanifold Y.     

过度离散型数据的统计模拟与分析

针对车险索赔次数数据经常出现的过度离散问题,采用数值模拟的方法,分别使用泊松模型(Poisson)、负二项回归模型(NB)以及广义泊松模型(GP)对不同程度的过度离散车险索赔次数数据进行拟合,并用均方误差、偏差以及AIC和BIC准则对Poisson、NB、GP三种模型的优良性进行比较分析,得到了不同条件下三种模型的优良性,并针对不同的条件给出了模型选择的建议.     

Copy number variants calling for single cell sequencing data by multi-constrained optimization

Variations in DNA copy number carry important information on genome evolution and regulation of DNA replication in cancer cells. The rapid development of single-cell sequencing technology allows one to explore gene expression heterogeneity among single-cells, thus providing important cancer cell evolution information. Single-cell DNA/RNA sequencing data usually have low genome coverage, which requires an extra step of amplification to accumulate enough samples. However, such amplification will introduce large bias and makes bioinformatics analysis challenging. Accurately modeling the distribution of sequencing data and effectively suppressing the bias influence is the key to success variations analysis.Recent advances demonstrate the technical noises by amplification are more likely to follow negative binomial distribution, a special case of Poisson distribution. Thus, we tackle the problem CNV detection by formulating it into a quadratic optimization problem involving two constraints, in which the underling signals are corrupted by Poisson distributed noises. By imposing the constraints of sparsity and smoothness, the reconstructed read depth signals from single-cell sequencing data are anticipated to fit the CNVs patterns more accurately. An efficient numerical solution based on the classical alternating direction minimization method (ADMM) is tailored to solve the proposed model. We demonstrate the advantages of the proposed method using both synthetic and empirical single-cell sequencing data. Our experimental results demonstrate that the proposed method achieves excellent performance and high promise of success with single-cell sequencing data.     

Computational alanine scanning mutagenesis--an improved methodological approach

Alanine scanning mutagenesis of protein-protein interfacial residues can be applied to a wide variety of protein complexes to understand the structural and energetic characteristics of the hot-spots. Binding free energies have been estimated with reasonable accuracy with empirical methods, such as Molecular Mechanics/Poisson-Boltzmann surface area (MM-PBSA), and with more rigorous computational approaches like Free Energy Perturbation (FEP) and Thermodynamic Integration (TI). The main objective of this work is the development of an improved methodological approach, with less computational cost, that predicts accurately differences in binding free energies between the wild-type and alanine mutated complexes (DeltaDeltaG(binding)). The method was applied to three complexes, and a mean unsigned error of 0.80 kcal/mol was obtained in a set of 46 mutations. The computational method presented here achieved an overall success rate of 80% and an 82% success rate in residues for which alanine mutation causes an increase in the binding free energy > 2.0 kcal/mol (warm- and hot-spots). This fully atomistic computational methodological approach consists in a computational Molecular Dynamics simulation protocol performed in a continuum medium using the Generalized Born model. A set of three different internal dielectric constants, to mimic the different degree of relaxation of the interface when different types of amino acids are mutated for alanine, have to be used for the proteins, depending on the type of amino acid that is mutated. This method permits a systematic scanning mutagenesis of protein-protein interfaces and it is capable of anticipating the experimental results of mutagenesis, thus guiding new experimental investigations.     

How Machine Learning Accelerates the Development of Quantum Dots?†

With the rapid developments in the field of information technology, the material research society is looking for an alternate scientific route to the traditional methods of trial and error in material research and process development. Machine learning emerges as a new research paradigm to accelerate the application‐oriented material discovery. Quantum dots are expanded as functional nanomaterials to enhance cutting‐edge photonic technology. However, they suffer from uncertainty in industrial fabrication and application. Here, we discuss how machine learning accelerates the development of quantum dots. The basic principles and operation procedures of machine learning are described with a few representative examples of quantum dots. We emphasize how machine learning contributes to the optimization of synthesis and the analysis of material characterizations. To conclude, we give a short perspective discussing the problems of combining machine learning and quantum dots.     

Ground state solutions for asymptotically periodic fractional Schrödinger–Poisson problems with asymptotically cubic or super‐cubic nonlinearities

In this paper, we consider the following fractional Schrödinger–Poisson problem: where s,t∈(0,1],4s+2t>3,V(x),K(x), and f(x,u) are periodic or asymptotically periodic in x. We use the non‐Nehari manifold approach to establish the existence of the Nehari‐type ground state solutions in two cases: the periodic one and the asymptotically periodic case, by introducing weaker conditions uniformly in with and with constant θ₀∈(0,1), instead of uniformly in and the usual Nehari‐type monotonic condition on f(x,τ)/|τ|³. Our results unify both asymptotically cubic or super‐cubic nonlinearities, which are new even for s=t=1. Copyright © 2017 John Wiley & Sons, Ltd.     

Error analysis of mixed finite element method for Poisson‐Nernst‐Planck system

To improve the convergence rate in L² norm from suboptimal to optimal for both electrostatic potential and ionic concentrations in Poisson‐Nernst‐Planck (PNP) system, we propose the mixed finite element method in this article to discretize the electrostatic potential equation, and still use the standard finite element method to discretize the time‐dependent ionic concentrations equations. Optimal error estimates in norm for the electrostatic potential, and in and norms for the ionic concentrations are attained. As a by‐product, the electric field can also achieve a higher approximation order in contrast with the standard finite element method for PNP system. Numerical experiments are performed to validate the theoretical results.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1924–1948, 2017     

Singular mean-field control games

This article studies singular mean field control problems and singular mean field two-players stochastic differential games. Both sufficient and necessary conditions for the optimal controls and for the Nash equilibrium are obtained. Under some assumptions the optimality conditions for singular mean-field control are reduced to a reflected Skorohod problem, whose solution is proved to exist uniquely. Motivations are given as optimal harvesting of stochastic mean-field systems, optimal irreversible investments under uncertainty and mean-field singular investment games. In particular, a simple singular mean-field investment game is studied, where the Nash equilibrium exists but is not unique.