🔬 #连续门控首次通过过程：该模型描述了粒子在目标处发生事件（如结合）的条件性，需要同时满足到达目标和目标处于正确状态两个条件。

🎯 #条件性事件：事件的发生不仅依赖于粒子到达特定目标，还依赖于目标在粒子到达时是否处于允许事件发生的“反应态”，而非简单的到达。

📈 #广泛应用：此类过程在多个领域至关重要，包括生物化学中的酶-底物结合、金融领域的期权交易、气候科学中的阈值 crossing 等。

🧮 #更新理论应用：新研究利用概率论中的更新理论，将复杂的门控首次通过过程分解为更简单的重复性部分，从而进行分析和求解。

🔍 #揭示普适模式：该方法不仅解决了先前未解决的问题，还揭示了不同系统中文过程持续时间的普适模式，并解释了之前难以理解的现象。

Imagine a molecule moving randomly through a cell. Its goal is to bind to an enzyme, a process essential for many chemical reactions in the body.

However, the enzyme isn’t always ready to bind. It switches between two states: a reactive state, where it can bind the molecule, and a non-reactive state, where it cannot.

Even if the molecule reaches the enzyme, binding will only take place if the enzyme happens to be in its reactive state at that exact moment. Simply arriving at the enzyme isn’t enough -the gate must also be open.

This scenario is an example of a gated first-passage process. The term refers to situations where an event (like binding) only happens if two conditions are met: the particle must reach a specific target, and the target must be in the right state to allow the event to occur.

These processes are important in a wide range of fields including chemistry, biophysics, finance, and climate science.

Existing models have offered valuable insights in simple cases, such as point targets, but even those have left some questions unresolved — and the challenges only deepen in more realistic scenarios involving extended targets or thresholds.

In order to address this problem, a team of researchers from India and Israel set about developing a new mathematical framework to analyse these type of processes.

The new approach uses a concept called renewal theory to break down complex processes into simpler, repeatable parts. Renewal theory is a branch of probability that deals with events that happen repeatedly over time, with random intervals between them.

The team showed that their method can solve previously unsolved problems and reveals universal patterns in how long these processes take. They were even able to explain surprising effects that previously posed a major challenge.

Crucially, their method can be applied to many real-world systems, from chemical reactions to intermittent data monitoring.

The post Enzymes, stock prices and temperature alerts appeared first on Physics World.