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On Minimizing the Maximal Characteristic Frequency of a Linear Chain

机译：关于最小化线性链的最大特征频率

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We consider a linear chain of masses, each coupled to its two nearest neighbors by elastic springs. The maximal characteristic frequency of this dynamical system is a strictly convex function of certain parameters that depend on the masses and spring elasticities. Minimizing the maximal characteristic frequency under an affine constraint on these parameters is thus a convex optimization problem. For a homogeneous affine constraint, we prove that the mass and elasticity values that minimize the maximal characteristic frequency have a special structure: They are symmetric with respect to the middle of the chain and the optimal masses [spring elasticities] increase [decrease] toward the center of the chain. Intuitively speaking, this means that in order to minimize the maximal characteristic frequency we need to “fix” the center of the chain, by increasing [decreasing] the masses [spring elasticities] there. We further show that minimizing the maximal characteristic frequency of the linear chain is equivalent to maximizing the steady-state protein production rate in an important model from systems biology called the ribosome flow model.
机译：我们考虑质量的线性链，每个质量链都通过弹性弹簧耦合到其两个最近的邻居。该动力学系统的最大特征频率是某些参数的严格凸函数，这些参数取决于质量和弹簧弹性。因此，在对这些参数的仿射约束下使最大特征频率最小化是一个凸优化问题。对于均质仿射约束，我们证明使最大特征频率最小的质量和弹性值具有特殊的结构：它们相对于链的中部对称，并且最佳质量[弹簧弹性]朝向[链]增大[减小]。链的中心。从直觉上来说，这意味着为了最小化最大特征频率，我们需要通过增加（减少）质量[弹簧弹性]来“固定”链条的中心。我们进一步表明，最小化线性链的最大特征频率等同于最大化稳态蛋白质生产速率，这是来自称为核糖体流动模型的系统生物学的重要模型。

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