We study a generalization of the vertex cover problem. For a given graph with weights on the vertices and an integer k, we aim to find a subset of the vertices with minimum total weight, so that at least k edges in th...We study a generalization of the vertex cover problem. For a given graph with weights on the vertices and an integer k, we aim to find a subset of the vertices with minimum total weight, so that at least k edges in the graph are covered. The problem is called the k-partial vertex cover problem. There are some 2-approximation algorithms for the problem. In the paper we do not improve on the approximation ratios of the previous algorithms, but we derive an iterative rounding algorithm. We present our technique in two algorithms. The first is an iterative rounding algorithm and gives a （2 ＋ Q/OPT ）-approximation for the k-partial vertex cover problem where Q is the largest finite weight in the problem definition and OPT is the optimal value for the instance. The second algorithm uses the first as a subroutine and achieves an approximation ratio of 2.展开更多
牦牛奶粉的掺假检测和产地识别有助于保障食品安全、维护消费者权益,是促进乳制品市场健康发展的重要举措。传统的DNA检测方法和稳定同位素分析技术的检测周期长,难以满足快速、低成本现场分析的需求。针对以上问题,本研究建立了一种基...牦牛奶粉的掺假检测和产地识别有助于保障食品安全、维护消费者权益,是促进乳制品市场健康发展的重要举措。传统的DNA检测方法和稳定同位素分析技术的检测周期长,难以满足快速、低成本现场分析的需求。针对以上问题,本研究建立了一种基于近红外光谱技术(Near-infrared Spectroscopy,NIRS)快速辨别牦牛奶粉掺假及产地的方法。收集了来自四川、甘肃、云南及青海的9个品牌的牦牛奶粉。在制备掺假样品之前,采用聚合酶链式反应(Polymerase Chain Reaction,PCR)技术和DNA凝胶电泳验证所收集的牦牛奶粉中是否掺杂了牛奶粉。完成验证后,进行掺假样品的制备以及近红外光谱数据的采集。采用K最邻近法(K-Nearest Neighbors,KNN)建立分类模型,偏最小二乘回归(Partial Least Squares Regression,PLSR)建立定量预测模型。通过优化光谱预处理方法和变量筛选方法进一步提升定量预测模型的预测能力。结果表明,KNN对牦牛奶粉掺假检测(纯牛奶粉、纯牦牛奶粉、掺杂着牛奶粉的牦牛奶粉)及产地识别(四川、甘肃、云南、青海)实现了100%的正确分类。掺假定量预测模型的校正集相关系数(R_(c))为0.9975,预测集相关系数(R_(p))为0.9913,预测集均方根误差(Root Mean Square Error of Prediction,RMSEP)为1.9823%,性能偏差比(Ratio of Performance to Deviation,RPD)为7.2522。本方法可快速、准确地预测牦牛奶粉中牛奶粉的掺杂以及牦牛奶粉产地的辨别,为牦牛奶粉的质量控制提供技术支持。展开更多
通过总结2004/2005～2006/2007年3个年度在长江流域冬油菜主产区10个省（市）的72个田间试验数据,以产量、增产率、偏生产力、农学效率、生理利用率及表观利用率等指标分析了长江流域施钾增产效果及钾肥利用率,以期为油菜进一步增产提...通过总结2004/2005～2006/2007年3个年度在长江流域冬油菜主产区10个省（市）的72个田间试验数据,以产量、增产率、偏生产力、农学效率、生理利用率及表观利用率等指标分析了长江流域施钾增产效果及钾肥利用率,以期为油菜进一步增产提供依据.分析结果表明,长江流域冬油菜施钾效果显著,与对照不施钾处理相比,施用钾肥油菜籽平均增产量为349 kg hm-2,平均增产率为19.8％,其中增产率小于5％的试验数占总数的20.8％,另外,油菜籽增产率随着土壤速效钾含量的升高而明显下降;施钾处理油菜地上部钾素积累量比不施钾处理显著增加38.1％;钾肥的平均偏生产力、农学效率、生理利用率和表观利用率分别为21.1、2.9、8.5 kg·kg-1和46.7％.综合结果表明,在施用氮、磷及硼肥基础上增施钾肥能够明显提高油菜地上部的生物量及钾素的累积,从而增加油菜籽产量,且根据基础地力及油菜对钾的需求规律而合理施肥极为重要.展开更多
基金Supported by the National Natural Science Foundation of China(No.11201021)
文摘We study a generalization of the vertex cover problem. For a given graph with weights on the vertices and an integer k, we aim to find a subset of the vertices with minimum total weight, so that at least k edges in the graph are covered. The problem is called the k-partial vertex cover problem. There are some 2-approximation algorithms for the problem. In the paper we do not improve on the approximation ratios of the previous algorithms, but we derive an iterative rounding algorithm. We present our technique in two algorithms. The first is an iterative rounding algorithm and gives a （2 ＋ Q/OPT ）-approximation for the k-partial vertex cover problem where Q is the largest finite weight in the problem definition and OPT is the optimal value for the instance. The second algorithm uses the first as a subroutine and achieves an approximation ratio of 2.
文摘牦牛奶粉的掺假检测和产地识别有助于保障食品安全、维护消费者权益,是促进乳制品市场健康发展的重要举措。传统的DNA检测方法和稳定同位素分析技术的检测周期长,难以满足快速、低成本现场分析的需求。针对以上问题,本研究建立了一种基于近红外光谱技术(Near-infrared Spectroscopy,NIRS)快速辨别牦牛奶粉掺假及产地的方法。收集了来自四川、甘肃、云南及青海的9个品牌的牦牛奶粉。在制备掺假样品之前,采用聚合酶链式反应(Polymerase Chain Reaction,PCR)技术和DNA凝胶电泳验证所收集的牦牛奶粉中是否掺杂了牛奶粉。完成验证后,进行掺假样品的制备以及近红外光谱数据的采集。采用K最邻近法(K-Nearest Neighbors,KNN)建立分类模型,偏最小二乘回归(Partial Least Squares Regression,PLSR)建立定量预测模型。通过优化光谱预处理方法和变量筛选方法进一步提升定量预测模型的预测能力。结果表明,KNN对牦牛奶粉掺假检测(纯牛奶粉、纯牦牛奶粉、掺杂着牛奶粉的牦牛奶粉)及产地识别(四川、甘肃、云南、青海)实现了100%的正确分类。掺假定量预测模型的校正集相关系数(R_(c))为0.9975,预测集相关系数(R_(p))为0.9913,预测集均方根误差(Root Mean Square Error of Prediction,RMSEP)为1.9823%,性能偏差比(Ratio of Performance to Deviation,RPD)为7.2522。本方法可快速、准确地预测牦牛奶粉中牛奶粉的掺杂以及牦牛奶粉产地的辨别,为牦牛奶粉的质量控制提供技术支持。
文摘通过总结2004/2005～2006/2007年3个年度在长江流域冬油菜主产区10个省（市）的72个田间试验数据,以产量、增产率、偏生产力、农学效率、生理利用率及表观利用率等指标分析了长江流域施钾增产效果及钾肥利用率,以期为油菜进一步增产提供依据.分析结果表明,长江流域冬油菜施钾效果显著,与对照不施钾处理相比,施用钾肥油菜籽平均增产量为349 kg hm-2,平均增产率为19.8％,其中增产率小于5％的试验数占总数的20.8％,另外,油菜籽增产率随着土壤速效钾含量的升高而明显下降;施钾处理油菜地上部钾素积累量比不施钾处理显著增加38.1％;钾肥的平均偏生产力、农学效率、生理利用率和表观利用率分别为21.1、2.9、8.5 kg·kg-1和46.7％.综合结果表明,在施用氮、磷及硼肥基础上增施钾肥能够明显提高油菜地上部的生物量及钾素的累积,从而增加油菜籽产量,且根据基础地力及油菜对钾的需求规律而合理施肥极为重要.
