absorbing state; absorption state

简明释义

吸收状态

英英释义

例句

1.In a Markov chain, when the system enters an absorbing state, it cannot leave, indicating that it has reached a final condition.

在马尔可夫链中，当系统进入一个吸收状态时，它无法离开，这表明它已达到最终条件。

2.In physics, certain systems can evolve into an absorbing state where no further changes occur.

在物理学中，某些系统可以演变为一个吸收状态，在该状态下不会发生进一步的变化。

3.The simulation model included several absorbing states to represent scenarios where outcomes are permanent.

模拟模型包括几个吸收状态，以表示结果是永久性的场景。

4.The game ends when a player reaches an absorbing state, which means they have completed all objectives.

当玩家达到一个吸收状态时，游戏结束，这意味着他们已完成所有目标。

5.In ecology, a population may reach an absorbing state where it cannot grow further due to limited resources.

在生态学中，种群可能会达到一个吸收状态，由于资源有限，它无法进一步增长。

作文

In the realm of mathematics and probability theory, the concept of an absorbing state or absorption state plays a crucial role in understanding Markov chains. An absorbing state is a special type of state that, once entered, cannot be left. This means that if a system transitions into an absorbing state, it remains there indefinitely. For example, consider a simple game where a player can either win or lose. If the player wins, they enter an absorbing state of victory, and if they lose, they may continue playing until they either win or lose again. The significance of absorbing states lies in their ability to simplify the analysis of complex systems by providing clear endpoints or outcomes.Understanding absorbing states is particularly important in various fields such as economics, biology, and computer science. In economics, for instance, certain market conditions can lead to absorbing states where businesses either thrive or fail, with no possibility of returning to a previous state. Similarly, in biological systems, a population may reach an absorbing state when it becomes extinct or reaches a stable equilibrium. In computer science, algorithms often utilize absorbing states to determine the end conditions of processes, such as in search algorithms or decision-making processes.The mathematical representation of absorbing states involves transition matrices, where probabilities of moving from one state to another are calculated. An absorbing state is characterized by having a probability of 1 for remaining in that state and a probability of 0 for transitioning to any other state. This property allows researchers and practitioners to model and predict the long-term behavior of systems more effectively.Moreover, the study of absorbing states extends beyond theoretical applications. In real-world scenarios, recognizing potential absorbing states can aid in strategic planning and risk management. For instance, businesses can identify points of no return in their operations, enabling them to make informed decisions about investments, resource allocation, and contingency planning. By understanding the dynamics of absorbing states, organizations can better navigate uncertainties and enhance their resilience in the face of challenges.In conclusion, the concept of absorbing states or absorption states is fundamental to various disciplines, offering insights into the behavior of complex systems. Whether in mathematics, economics, biology, or computer science, these states provide valuable frameworks for analysis and decision-making. As we continue to explore the intricacies of systems around us, the importance of absorbing states will undoubtedly persist, guiding us toward a deeper understanding of stability and change in our world.

在数学和概率理论领域，吸收状态或吸收态的概念在理解马尔可夫链中扮演着至关重要的角色。吸收状态是一种特殊类型的状态，一旦进入，就无法离开。这意味着如果一个系统过渡到吸收状态，它将无限期地停留在那里。例如，考虑一个简单的游戏，玩家可以赢或输。如果玩家赢了，他们进入胜利的吸收状态；如果他们输了，他们可能会继续玩，直到再次赢或输。吸收状态的重要性在于它们能够通过提供明确的终点或结果来简化复杂系统的分析。理解吸收状态在经济学、生物学和计算机科学等多个领域尤为重要。例如，在经济学中，某些市场条件可能导致吸收状态，企业要么繁荣，要么失败，无法返回到先前的状态。同样，在生物系统中，当一个种群灭绝或达到稳定平衡时，它可能会达到吸收状态。在计算机科学中，算法通常利用吸收状态来确定过程的结束条件，例如在搜索算法或决策过程中。吸收状态的数学表示涉及转移矩阵，其中计算从一个状态到另一个状态的转移概率。吸收状态的特征是留在该状态的概率为1，而转移到任何其他状态的概率为0。这一特性使研究人员和从业者能够更有效地建模和预测系统的长期行为。此外，吸收状态的研究超越了理论应用。在现实场景中，识别潜在的吸收状态可以帮助战略规划和风险管理。例如，企业可以识别其运营中的不可逆点，使他们能够就投资、资源分配和应急规划做出明智的决策。通过理解吸收状态的动态，组织可以更好地应对不确定性，提高面对挑战的韧性。总之，吸收状态或吸收态的概念在各个学科中都是基础，为复杂系统的行为提供了洞察力。无论是在数学、经济学、生物学还是计算机科学中，这些状态都为分析和决策提供了宝贵的框架。随着我们继续探索周围系统的复杂性，吸收状态的重要性无疑将持续存在，引导我们深入理解我们世界中的稳定与变化。