发表机构
California Institute of Technology; Imperial College; Harvard Medical School; Brandeis University（加州理工学院; 帝国理工学院; 哈佛医学院; 布兰迪斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出用几何分布和带重置随机游走等框架统一生物探索动力学，强调终端条件主导，揭示搜索加速及变异选择的新视角。
AI 中文摘要
生物过程，从分子扩散到其调控目的地，到鲸鱼追逐食物或配偶，广泛具有探索性。当无论初始条件如何，都能达到某种可验证的功能状态或结果时，这类行为是有效的。在这些情况下，系统反复经历不同且中止的轨迹；过程仅在系统找到“正确”结果时结束。终端条件的主导性（以及对初始状态的不敏感性）引发了一种与传统“动力系统”框架截然不同的视角，而后者几个世纪以来一直是定量科学的核心。我们假设，许多这类问题并不遵循初始条件驱动或景观梯度，而这些在从力学到电动力学、化学动力学、质量与热传输等问题中非常有用。我们考察了多个数学框架，这些框架捕捉并统一了探索动力学的关键方面。一种强有力的思考方式是几何分布，其中重复的失败被一次成功的轨迹所打断。我们发展了对带重置的随机游走如何加速搜索过程的直觉。我们强调了在漂移、线索和检查点下搜索的新颖且令人惊讶的行为。最后，理解以满足宏观最终结果为条件的轨迹概率，揭示了一种语言，用于描述由选择塑造的变异在最广泛形式下的效力。这可能造成未来在当下显现的虚假表象，但我们认为这在概念上类似于非惯性参考系中“虚拟力”的出现方式。这些方法强调了统一性、开放性问题以及在一系列生物现象中的应用。
英文摘要
Biological processes, from molecules diffusing to their regulatory destinations to whales pursuing food or mates, are widely exploratory. Such behaviors are effective when some verifiable functional state or outcome can be reached regardless of initial conditions. In these cases, systems repeatedly undergo distinct and abortive trajectories; the process only ends when the system finds ``right'' outcomes. This dominance of the terminal condition (and indifference to the initial state) provokes a very different perspective than the conventional ``dynamical systems'' framework that has been a centerpiece of the quantitative sciences for centuries. We hypothesize that many of these problems defy the initial-condition driven or gradients on landscapes so useful in problems ranging from mechanics to electrodynamics to chemical kinetics to mass and heat transport. We examine several mathematical frameworks that capture and unify key aspects of exploratory dynamics. One powerful way of thinking of such processes is the geometric distribution, where repeated failures are punctuated by a successful trajectory. We develop intuitions for how random walks with resets accelerate search processes. We highlight fresh and surprising behaviors of search under drift, cues, and checkpoints. Last, appreciating the probability of trajectories conditioned on satisfying macroscopic final outcomes reveals a language for the potency of variation sculpted by selection in their broadest forms. This can give the fictitious appearance of the future making itself known in the present, but we view this as conceptually similar to the way ``fictitious forces'' arise in non-inertial reference frames. These approaches stress unity, open questions, and applications across a range of biological phenomena.
