association scheme

简明释义

结合方案

英英释义

例句

1.The association scheme proposed by the team was instrumental in improving community health outcomes.

团队提出的关联方案对改善社区健康结果起到了重要作用。

2.Implementing an association scheme in data mining can reveal hidden patterns in large datasets.

在数据挖掘中实施关联方案可以揭示大数据集中隐藏的模式。

3.In marketing, an association scheme can help identify customer preferences and behaviors.

在市场营销中，关联方案可以帮助识别客户的偏好和行为。

4.The association scheme used in this study allows for a better understanding of social networks.

本研究中使用的关联方案有助于更好地理解社交网络。

5.The researchers developed an association scheme to analyze the relationships between different species in the ecosystem.

研究人员开发了一种关联方案来分析生态系统中不同物种之间的关系。

作文

In the realm of combinatorial design and graph theory, the concept of an association scheme plays a pivotal role. An association scheme is essentially a structured way of organizing a set of objects, typically referred to as points, into classes that define how these points relate to one another. This mathematical framework allows researchers to study relationships between points in a systematic manner, providing insights that are applicable in various fields such as statistics, coding theory, and even social network analysis.To understand the significance of an association scheme, let us delve into its components. An association scheme consists of a finite set of points and a relation defined among them. This relation is characterized by a set of pairs of points, where each pair is classified into different types based on certain criteria. The most common types of relations include adjacency, which indicates that two points are directly connected, and non-adjacency, which signifies that they are not connected. By categorizing these relationships, an association scheme provides a comprehensive overview of how points interact with one another.One of the remarkable features of an association scheme is its ability to generalize various types of structures. For instance, it can be used to describe graphs, where points represent vertices, and the relations correspond to edges. Additionally, association schemes can model more complex structures such as symmetric designs and block designs, which are essential in experimental design and statistical analysis. This versatility makes association schemes a powerful tool for mathematicians and statisticians alike.Moreover, the study of association schemes is not merely an abstract exercise; it has practical applications in real-world scenarios. For example, in coding theory, association schemes can be utilized to construct error-correcting codes, which are crucial for reliable data transmission. By understanding the relationships defined in an association scheme, engineers can design codes that minimize errors during communication over noisy channels.In the context of social networks, association schemes can help analyze connections between individuals, revealing patterns of interaction and influence. By applying the principles of association schemes, researchers can identify key players in a network, understand the dynamics of information flow, and even predict the spread of trends or behaviors within a community.In conclusion, the concept of an association scheme is a fundamental aspect of combinatorial mathematics that facilitates the study of relationships among points. Its structured approach allows for the exploration of various mathematical and real-world phenomena, making it an invaluable tool across multiple disciplines. As we continue to uncover the complexities of relationships in both theoretical and practical contexts, the importance of association schemes will only grow, paving the way for new discoveries and innovations in our understanding of interconnected systems.

在组合设计和图论领域，关联方案的概念发挥着关键作用。关联方案本质上是一种组织一组对象（通常称为点）的方法，这些对象被分为不同的类，以定义这些点之间的关系。这种数学框架使研究人员能够以系统的方式研究点之间的关系，从而提供在统计学、编码理论甚至社交网络分析等多个领域中适用的见解。要理解关联方案的重要性，我们需要深入了解其组成部分。关联方案由一个有限的点集和定义在其上的关系组成。该关系通过一组点对来表征，其中每对根据某些标准被分类为不同的类型。最常见的关系类型包括邻接，表示两个点直接相连，以及非邻接，表示它们不相连。通过对这些关系进行分类，关联方案提供了关于点如何相互作用的全面概述。关联方案的一个显著特点是它能够对各种类型的结构进行概括。例如，它可以用于描述图，其中点代表顶点，而关系对应于边。此外，关联方案还可以建模更复杂的结构，如对称设计和区组设计，这在实验设计和统计分析中至关重要。这种多功能性使得关联方案成为数学家和统计学家强大的工具。此外，关联方案的研究不仅仅是一个抽象的练习；它在现实世界场景中具有实际应用。例如，在编码理论中，关联方案可以用于构造纠错码，这对于可靠的数据传输至关重要。通过理解在关联方案中定义的关系，工程师可以设计出最小化通信过程中错误的编码，以应对嘈杂信道。在社交网络的背景下，关联方案可以帮助分析个体之间的连接，揭示互动和影响的模式。通过应用关联方案的原则，研究人员可以识别网络中的关键参与者，理解信息流动的动态，甚至预测趋势或行为在社区中的传播。总之，关联方案的概念是组合数学的一个基本方面，促进了对点之间关系的研究。其结构化的方法允许探索各种数学和现实世界现象，使其成为多个学科中不可或缺的工具。随着我们继续揭示理论和实际背景中关系的复杂性，关联方案的重要性只会增加，为我们对互联系统的理解铺平道路，促进新的发现和创新。