论文标题
永生的花
Flowers of immortality
论文作者
论文摘要
最近对导致衰老的原因引起了人们的兴趣。科技公司对该领域的前所未有的研究投资与此相匹配。但是，尽管大量的研究人员付出了巨大的努力，但我们没有严格的编程衰老数学理论。为了解决这个问题，我们最近得出了一个死亡方程，该方程控制着具有给定最大年龄的不断发展的人群的过渡矩阵。在这里，我们表征了该方程解的特征值的光谱。特征值分为两个类。我们称之为花朵的复杂和负的真实特征值始终包含在复杂平面的单位圆中。他们在控制老龄化人口的动态方面发挥了可忽略的作用。我们称为茎的正真实特征值是唯一可以超过单位圆的特征值。他们控制动力学的最重要属性。特别是，光谱半径随着最大允许年龄的增长而增加。这表明编程的衰老在恒定的环境中没有任何优势。但是，控制融合速率与平衡的频谱差距随着最大允许年龄的增长而降低。这为不断变化的环境中的进化优势打开了大门。
There has been a recent surge of interest in what causes aging. This has been matched by unprecedented research investment in the field from tech companies. But, despite considerable effort from a broad range of researchers, we do not have a rigorous mathematical theory of programmed aging. To address this, we recently derived a mortality equation that governs the transition matrix of an evolving population with a given maximum age. Here, we characterize the spectrum of eigenvalues of the solution to this equation. The eigenvalues fall into two classes. The complex and negative real eigenvalues, which we call the flower, are always contained in the unit circle in the complex plane. They play a negligible role in controlling the dynamics of an aging population. The positive real eigenvalues, which we call the stem, are the only eigenvalues which can exceed the unit circle. They control the most important properties of the dynamics. In particular, the spectral radius increases with the maximum allowed age. This suggests that programmed aging confers no advantage in a constant environment. However, the spectral gap, which governs the rate of convergence to equilibrium, decreases with the maximum allowed age. This opens the door to an evolutionary advantage in a changing environment.
