Machine Learning Approaches for Metalloproteins

Metalloproteins are a family of proteins characterized by metal ion binding, whereby the presence of these ions confers key catalytic and ligand-binding properties. Due to their ubiquity among biological systems, researchers have made immense efforts to predict the structural and functional roles of metalloproteins. Ultimately, having a comprehensive understanding of metalloproteins will lead to tangible applications, such as designing potent inhibitors in drug discovery. Recently, there has been an acceleration in the number of studies applying machine learning to predict metalloprotein properties, primarily driven by the advent of more sophisticated machine learning algorithms. This review covers how machine learning tools have consolidated and expanded our comprehension of various aspects of metalloproteins (structure, function, stability, ligand-binding interactions, and inhibitors). Future avenues of exploration are also discussed.     

Stochastic Theory of Discrete Binary Fragmentation—Kinetics and Thermodynamics

We formulate binary fragmentation as a discrete stochastic process in which an integer mass k splits into two integer fragments j, k−j, with rate proportional to the fragmentation kernel Fj,k−j. We construct the ensemble of all distributions that can form in fixed number of steps from initial mass M and obtain their probabilities in terms of the fragmentation kernel. We obtain its partition function, the mean distribution and its evolution in time, and determine its stability using standard thermodynamic tools. We show that shattering is a phase transition that takes place when the stability conditions of the partition function are violated. We further discuss the close analogy between shattering and gelation, and between fragmentation and aggregation in general.     

遗传算法求解约束非线性规划及Matlab实现

对于约束非线性规划问题,传统的方法:可行方向法、惩罚函数法计算烦琐且精度不高.用新兴的遗传算法来解决约束非线性规划,核心是惩罚函数的构造.以前的惩罚函数遗传算法有的精度较低,有的过于复杂.本文在两个定义的基础上构造了新的惩罚函数,并在新的惩罚函数的基础上,提出了一种解决约束非线性最优化问题的方法.通过两个例子应用Matlab说明了这个算法的可行性.     

从诺贝尔经济学奖看数学对经济学的作用

本文在分析2003年诺贝尔经济学奖学术贡献的基础上，阐述了数学思维方式和数学方法对经济问题的解决、经济理论的发展等方面的作用．     

突发事件下应急物资多目标优化调度模型与算法研究：以新冠肺炎疫情为例

突发事件下应急物资调度具有高度不确定性与动态性,应急物资跨区域调度计划能否科学合理制定对应急救援的有效开展具有重要影响。以武汉市新冠肺炎疫情为例,考虑应急物资跨区域调配的时效差异、地域分散以及资金消耗等要素,建立多周期下包含软硬需求时间窗约束的多物资品种、运输方式的跨区域三级动态物资调度网络模型,并设计一种带变异操作的动态变惯性权重自适应粒子群算法(VDCWPSO),利用疫情算例验证该算法的有效性和可行性。研究结果表明,在保障应急物资供应时效性、公平性、经济性原则下,物资跨区域调度可以缓解资源严重短缺状况、提高医用物资利用率,研究可为突发事件下应急物资调度计划的制定与动态调整提供决策支持。     

Boundary behavior of harmonic functions on metric measure spaces with non-negative Ricci curvature

Let (X, d, μ) be a metric measure space with non-negative Ricci curvature. This paper is concerned with the boundary behavior of harmonic function on the (open) upper half-space X\times {\text{ℝ}}_{+}. We derive that a function f of bounded mean oscillation (BMO) is the trace of harmonic function u(x,t) on X\times {\text{ℝ}}_{+},u(x,0)=f\left(x\right), whenever u satisfies the following Carleson measure condition where \nabla =({\nabla }_x,{\partial }_t) denotes the total gradient and B(x_B,r_B) denotes the (open) ball centered at x_B with radius r_B. Conversely, the above condition characterizes all the harmonic functions whose traces are in BMO space.     

资源受限下森林火灾应急救援多目标调度优化

许多森林火灾由于救援资源受限而不能在第一时间扑灭,导致火灾扩大蔓延,进而造成更大的森林资源损失。因此,在救援资源受限情形下,如何对消防救援车辆进行合理的调度安排以快速和低成本地扑灭火灾已成为亟待解决的现实问题。本文研究了一类资源受限下森林火灾应急救援多目标调度优化问题,为该问题构建了多目标混合整数非线性规划模型,优化目标为同时最小化总灭火救援时间和救援车辆总行驶距离。为有效求解该问题,首先将上述非线性模型等价转化为线性模型。然后提出ε-约束法和模糊逻辑相结合的算法对问题进行求解。最后,以大兴安岭山发生的火灾案例和随机生成仿真算例对模型和算法有效性进行验证,结果表明所提出的模型和算法能够有效解决资源受限下森林火灾应急救援问题,并为决策者提供最优的消防调度方案。     

求一类多元多峰函数全局极小的区间斜率方法

Based on the interval analysis, an interval slope method is proposed for finding all global minimizers of a several peaks function f on domain X^0包含于R^n, which is given by interval slope discard tests and interval extension of objective function.Numerical results of representative test functions show that this method is practical and effective.