The card game 24 and its application to math education

The card game 24 is a mathematical game that traditionally engages elementary students to practice their mental computational skills. In this paper, we use probability to formulate and explore the game. We create score of difficulty level for solvable card combination set under various setup of game rules. Based on our findings, we create new playing rules and provide suggestions for different levels of players. Our results may serve as guidelines on introducing the game 24 into the practice of math education.     

Case Influence Analysis in Bayesian Inference

Abstract

We demonstrate how case influence analysis, commonly used in regression, can be applied to Bayesian hierarchical models. Draws from the joint posterior distribution of parameters are importance weighted to reflect the effect of deleting each observation in turn; the ensuing changes in the posterior distribution of each parameter are displayed graphically. The procedure is particularly useful when drawing a sample from the posterior distribution requires extensive calculations (as with a Markov Chain Monte Carlo sampler). The structure of hierarchical models, and other models with local dependence, makes the importance weights inexpensive to calculate with little additional programming. Some new alternative weighting schemes are described that extend the range of problems in which reweighting can be used to assess influence. Applications to a growth curve model and a complex hierarchical model for opinion data are described. Our focus on case influence on parameters is complementary to other work that measures influence by distances between posterior or predictive distributions.     

组合评价模型在河南省主要城市综合经济实力评价中的应用

组合评价模型通过组合多个单一评价模型的评价结果,有效弥补单一方法的不足,提高评价的全面性和科学性.首先利用河南省2010年的相关数据,分别采用综合指数法、加权平均法、主成分分析法和因子分析法,对河南省的18个主要地区的综合经济实力进行了评价和排序;其次,建立基于模糊Borda法的组合评价模型,应用该模型对河南省的18个主要地区的综合经济实力进行了重新评价和排序,得到了更为可行的评价结果.     

Evolution of co-operation among mobile agents with different influence

Co-operation is a key factor in understanding the evolution of our society. Inspired by this issue, the individual mobility in game theory has been proved to be a very useful scenario. However, it is not realistic, as described in previous studies, that each agent has the same influence on its neighbour’s movement trait. In this work, we mainly focus on the weighted influence on the mobility of agents in the prisoner’s dilemma game. Here the weight is proportional to its degree with power exponent of λ$\lambda$, where λ$\lambda$ is the adjustable parameter to control the level of heterogeneity among individuals in the network. Through numerous simulations we find that co-operation level is promoted when the heterogeneous influence factor is considered. In particular, there is an intermediate value _λopt≈10${\lambda }_{opt}\approx 10$ to guarantee the optimal evolution of co-operation. Moreover, we also prove that the effect of influence weight on the enhancement of co-operation is only valid when the agent’s interaction radius is within a threshold value. We thus present a viable method of understanding the ubiquitous co-operative behaviour in nature and hope that it will inspire further studies to resolve social dilemmas.     

Generalized quadraticity of linear combination of two generalized quadratic matrices

It is investigated the necessary and sufficient conditions for the generalized quadraticity of a linear combination of any two generalized quadratic matrices. The main result obtained is, in a sense, a generalization of the main results given in [Uç M, Özdemir H, Özban AY. On the quadraticity of linear combinations of quadratic matrices. Linear Multilinear Algebra. 2015;63:1125–1137.] which contains many of the results in the literature related to idempotency or involutivity of the linear combinations of idempotent and/or involutive matrices, to the generalized quadratic matrices.     

Nonsingularity and group invertibility of linear combinations of two k-potent matrices

An n × n complex matrix A is said to be k-potent if A ^k = A. Let T ₁ and T ₂ be k-potent and c ₁ and c ₂ be two nonzero complex numbers. We study the range space, null space, nonsingularity and group invertibility of linear combinations T = c ₁ T ₁ + c ₂ T ₂ of two k-potent matrices T ₁ and T ₂.     

The group inverse of the combinations of two idempotent matrices

In this article, we discuss the group inverse of aP + bQ + cPQ + dQP + ePQP + fQPQ + gPQPQ of idempotent matrices P and Q, where a, b, c, d, e, f, g ∈ ? and a ≠ 0, b ≠ 0, put forward its explicit expressions, and some necessary and sufficient conditions for the existence of the group inverse of aP + bQ + cPQ.     

A hybrid metaheuristic method for the Maximum Diversity Problem

The Maximum Diversity Problem (MDP) consists in selecting a subset of m$m$ elements from a given set of n$n$ elements (n>m$n>m$) in such a way that the sum of the pairwise distances between the m$m$ chosen elements is maximized. We present a hybrid metaheuristic algorithm (denoted by MAMDP) for MDP. The algorithm uses a dedicated crossover operator to generate new solutions and a constrained neighborhood tabu search procedure for local optimization. MAMDP applies also a distance-and-quality based replacement strategy to maintain population diversity. Extensive evaluations on a large set of 120 benchmark instances show that the proposed approach competes very favorably with the current state-of-art methods for MDP. In particular, it consistently and easily attains all the best known lower bounds and yields improved lower bounds for 6 large MDP instances. The key components of MAMDP are analyzed to shed light on their influence on the performance of the algorithm.     

凹凸棒石负载Cu-Fe-Co基催化剂组合体系用于CO加氢制备低碳醇

采用浸渍法(IM)和浸渍燃烧法(IMSC)制备了凹凸棒石(ATP)及凹凸棒石-多孔硅胶微球混合物(ATPS)负载CuFe-Co基改性费托催化剂,通过N_2吸附-脱附、X射线衍射(XRD)、X射线光电子能谱(XPS)、扫描电镜(SEM)、透射电镜(TEM)、H_2-程序升温还原(H_2-TPR)和CO_2-程序升温脱附(CO_2-TPD)等手段对催化剂进行了表征,并将它们应用于CO加氢制备低碳醇反应。结果表明,IMSC较IM制备催化剂更有利于CuO的负载、分散和还原,促进H_2和CO与Cu活性位的接触,但两者的最佳低碳醇合成温度均为280℃。通过对ATP和ATPS负载Cu-Fe-Co基催化剂(CFCK/ATP、CFCK/ATPS)与Cu/ZnO/Al_2O_3(CZA)甲醇催化剂的组合体系的优化,获得较理想的低碳醇合成催化剂组合体系CZA║CFCK/ATPS-IMSC。利用它们之间的"产物转化耦合效应",实现CO转化率为46.3%,低碳醇选择性为39.6%,C_(2+)醇含量为22.7%。     

基于二维MOFs构建MicroRNA荧光传感器的综合分析化学实验及"赛学结合、三位一体评价"的教学模式设计

本综合性实验将二维金属有机框架(2D MOFs)和MicroRNA (miRNA)分析等前沿研究领域引入化学(材料)本科和研究生实验教学中。主要包括2DMOFs材料的合成及表征、基于2DMOFs的荧光核酸探针构建以及将探针用于miRNA荧光分析等,共10个学时。所需掌握的实验技能包含溶剂热法、离心分散和外标法等基本材料合成和分析化学操作以及荧光、红外、X射线粉末衍射等材料表征和分析方法。我们在实验中实施了一种新型的"赛学结合、三位一体评价"教学模式。在该模式中,学生分组开展团队作业、实验和汇报,不仅要记录实验现象和结果,还需对实验过程录像并总结做成PPT。各组间通过"PPT答辩、实验报告和录像"等进行比赛,三位一体决出成绩。学生在实验中不仅学习了大量实验技能,提高了动手能力,拓展了学术视野;而且通过比赛和教学相结合,激发了你追我赶的学习热情,培养了团队合作精神,调动了学习的主观能动性。该实验和教学模式也适合推广至其他综合化学实验教学中。