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→Sloppiness与Sloppy理论
Sloppiness在生物学领域最为普遍，但在其它领域也并不缺席。从昆虫飞行模型，到原子间势，再到加速器设计，许多目前常用的模型都是sloppy的。例如，量子蒙特卡洛是求解原子和小分子的能量和量子行为的最精确的工具；然而，赛勒斯·乌姆里加（Cyrus Umrigar）在这种方法基础上建立的非常精确的变分波函数却是极度sloppy（b列）。
Sloppiness在生物学领域最为普遍，但在其它领域也并不缺席。从昆虫飞行模型，到原子间势，再到加速器设计，许多目前常用的模型都是sloppy的。例如，量子蒙特卡洛是求解原子和小分子的能量和量子行为的最精确的工具；然而，赛勒斯·乌姆里加（Cyrus Umrigar）在这种方法基础上建立的非常精确的变分波函数却是极度sloppy（b列）。
即便参数值与真实值相差很大，有sloppy特性的模型也可以做出精确的预测。在数学中有一个经典的拟合难题<ref>Formulation, application to fitting algorithms: [https://arxiv.org/abs/0909.3884 "Why are nonlinear fits to data so challenging?"], Mark K. Transtrum, Benjamin B. Machta, and James P. Sethna, [https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.104.060201 Phys. Rev. Lett.] '''104''', 060201 (2010).</ref><ref>Expanded formulation, geometry of model manifold:[http://arxiv.org/abs/1010.1449 "Geometry of nonlinear least squares with applications to sloppy models and optimization"], Mark K. Transtrum, Benjamin B. Machta, and James P. Sethna [http://link.aps.org/doi/10.1103/PhysRevE.83.036701 Phys. Rev. E '''83''', 036701 (2011)]; </ref>：用指数衰变和去拟合放射性模型（c列和d列）得到的衰变常数与真实衰变常数截然不同，但短期内模型预测值与真实值却相差不大 。最后，用多项式系数模型<math>\sum_i a_it^i</math>拟合数据是sloppy的（h列）。但用正交多项式基<math>\sum_ib_iH_i</math>(<math>H_i</math>是一组正交多项式基）去拟合时得到的模型却往往是非sloppy的，这是因为从<math>t^i</math>到<math>H_i</math>的变换是高度非正交的<ref>Expanded formulation, geometry of model manifold: [[Expanded formulation, geometry of model manifold: "Geometry of nonlinear least squares with applications to sloppy models and optimization", Mark K. Transtrum, Benjamin B. Machta, and James P. Sethna Phys. Rev. E 83, 036701 (2011); |"Geometry of nonlinear least squares with applications to sloppy models and optimization"]], Mark K. Transtrum, Benjamin B. Machta, and James P. Sethna [https://journals.aps.org/pre/abstract/10.1103/PhysRevE.83.036701 Phys. Rev. E '''83''', 036701 (2011)]; </ref>。
即便参数值与真实值相差很大，有sloppy特性的模型也可以做出精确的预测。在数学中有一个经典的拟合难题<ref>Formulation, application to fitting algorithms: [https://arxiv.org/abs/0909.3884 "Why are nonlinear fits to data so challenging?"], Mark K. Transtrum, Benjamin B. Machta, and James P. Sethna, [https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.104.060201 Phys. Rev. Lett.] '''104''', 060201 (2010).</ref><ref name = "Mark">Expanded formulation, geometry of model manifold: [[Expanded formulation, geometry of model manifold: "Geometry of nonlinear least squares with applications to sloppy models and optimization", Mark K. Transtrum, Benjamin B. Machta, and James P. Sethna Phys. Rev. E 83, 036701 (2011); |"Geometry of nonlinear least squares with applications to sloppy models and optimization"]], Mark K. Transtrum, Benjamin B. Machta, and James P. Sethna [https://journals.aps.org/pre/abstract/10.1103/PhysRevE.83.036701 Phys. Rev. E '''83''', 036701 (2011)]; </ref>：用指数衰变和去拟合放射性模型（c列和d列）得到的衰变常数与真实衰变常数截然不同，但短期内模型预测值与真实值却相差不大 。最后，用多项式系数模型<math>\sum_i a_it^i</math>拟合数据是sloppy的（h列）。但用正交多项式基<math>\sum_ib_iH_i</math>(<math>H_i</math>是一组正交多项式基）去拟合时得到的模型却往往是非sloppy的，这是因为从<math>t^i</math>到<math>H_i</math>的变换是高度非正交的<ref name="Mark"/>。
Sloppy模型有着多种形式，每个模型的sloppniess的原因并不完全相同，部分系统的sloppiness的原因可以从数学上进行分析。但是不同系统的sloppiniess具体原因仍然极具复杂性<ref>10. [https://sethna.lassp.cornell.edu/pubPDF/Vandermonde.pdf "Sloppy model universality class and the Vandermonde matrix"], Joshua J. Waterfall, Fergal P. Casey, Ryan N. Gutenkunst, Kevin S. Brown, Christopher R. Myers, Piet W. Brouwer, Veit Elser, and James P. Sethna, Phys. Rev. Letters '''97''', 150601 (2006), also selected for Virtual Journal of Biological Physics Research '''12 (8, Miscellaneous)''', (2006). </ref>。
Sloppy模型有着多种形式，每个模型的sloppniess的原因并不完全相同，部分系统的sloppiness的原因可以从数学上进行分析。但是不同系统的sloppiniess具体原因仍然极具复杂性<ref>10. [https://sethna.lassp.cornell.edu/pubPDF/Vandermonde.pdf "Sloppy model universality class and the Vandermonde matrix"], Joshua J. Waterfall, Fergal P. Casey, Ryan N. Gutenkunst, Kevin S. Brown, Christopher R. Myers, Piet W. Brouwer, Veit Elser, and James P. Sethna, Phys. Rev. Letters '''97''', 150601 (2006), also selected for Virtual Journal of Biological Physics Research '''12 (8, Miscellaneous)''', (2006). </ref>。