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Sloppy 理论与物理学

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 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 name = “Waterfall et.al, 2006”>[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><ref name="Transtrum et.al, 2014">” Model reduction by manifold boundaries", Mark K. Transtrum, P. Qiu [https://doi.org/10.1103/PhysRevLett.113.098701 Phys. Rev. Lett. '''113''', 098701 (2014)]; pdf. </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="Transtrum et.al, 2014"/>。
+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 name = “Waterfall et.al, 2006”>[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><ref name="Transtrum et.al, 2014">” Model reduction by manifold boundaries", Mark K. Transtrum, P. Qiu [https://doi.org/10.1103/PhysRevLett.113.098701 Phys. Rev. Lett. '''113''', 098701 (2014)]; pdf. </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="Transtrum et.al, 2014"/>。
 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> [https://arxiv.org/abs/1605.08705 Bridging Mechanistic and Phenomenological Models of Complex Biological Systems], Mark K. Transtrum and Peng Qiu, PLoS Comput Biol 12(5): e1004915. https://doi.org/10.1371/journal.pcbi.1004915</ref>。
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 事实上，理论物理学就像一棵树（下图）。高能物理学家研究树的枝条，寻找更接近树干的更统一的理论。在凝聚态物理学中则向外构建，寻找“涌现的”树枝和树叶——描述声音、半导体和超流体的有效理论。但两者有许多相似之处：扩散方程描述了在静止空气中香水如何从皮肤扩散到鼻子。这个方程通常写成连续极限的形式，使用的方法类似于描述凝聚态物理学中许多其他现象——声音、磁铁和超导体——的方法。而磁性的伊辛模型分形过程，通常使用类似于高能物理学中使用的重整化群进行分析。物理学家有一套系统的方法判断哪些参数是stiff（“僵硬”）的，哪些参数是sloppy（“欠定”）的，但是在其它领域中并没有相应的方法，使用sloppy理论的概念可以更准确有效地分析系统<ref>[http://arxiv.org/abs/1710.05787 Information geometry and the renormalization group], Archishman Raju, Benjamin B. Machta, James P. Sethna (submitted). </ref><ref>[http://arxiv.org/abs/1303.6738 Parameter Space Compression Underlies Emergent Theories and Predictive Models,] Benjamin B. Machta, Ricky Chachra, Mark K. Transtrum, James P. Sethna, [http://www.sciencemag.org/content/342/6158/604 Science'''342''' 604-607 (2013)].</ref><ref>[http://arxiv.org/pdf/1409.6203v2.pdf Information topology identifies emergent model classes], Transtrum M.K., Hart G., Qiu P. </ref><ref>[https://sethna.lassp.cornell.edu/pubPDF/vanderPol.pdf Structural susceptibility and separation of time scales in the van der Pol Oscillator], Ricky Chachra, Mark K. Transtrum, and James P. Sethna, [http://link.aps.org/doi/10.1103/PhysRevE.86.026712 Phys. Rev. E '''86''', 026712 (2012)]. </ref>
-,甚至物理学领域也在逐渐应用sloppy理论<ref name = “Quinn”>Model manifolds for probabilistic models: [http://arxiv.org/abs/1709.02000 Visualizing theory space: Isometric embedding of probabilistic predictions, from the Ising model to the cosmic microwave background], Katherine N. Quinn, Francesco De Bernardis, Michael D. Niemack, James P. Sethna (submitted). </ref><ref>[https://sethna.lassp.cornell.edu/pubPDF/SloppyEverywhere.pdf ”Universally Sloppy Parameter Sensitivities in Systems Biology"], Ryan N. Gutenkunst, Joshua J. Waterfall, Fergal P. Casey, Kevin S. Brown, Christopher R. Myers, James P. Sethna, PLoS Comput Biol3(10) e189 (2007). ([http://compbiol.plosjournals.org/perlserv/?request=get-document&doi=10.1371/journal.pcbi.0030189 PLoS], [http://dx.doi.org/10.1371/journal.pcbi.0030189 doi:10.1371/journal.pcbi.0030189]). [Reviewed in [http://biomedicalcomputationreview.org/4/1/4.pdf NewsBytes] of [http://biomedicalcomputationreview.org/ Biomedical Computation Review] (Winter 07/08); rated "Exceptional" on Faculty of 1000]. </ref><ref name = “Casey et.al, 2007”>[http://arxiv.org/abs/q-bio.MN/0610024 "Optimal experimental design in an EGFR signaling and down-regulation model"], Fergal P. Casey, Dan Baird, Qiyu Feng, Ryan N. Gutenkunst, Joshua J. Waterfall, Christopher R. Myers, Kevin S. Brown, Richard A. Cerione, and James P. Sethna, IET Systems Biology 1, 190-202 (2007)</ref>。
+,甚至物理学领域也在逐渐应用sloppy理论<ref name = “Quinn”>Model manifolds for probabilistic models: [http://arxiv.org/abs/1709.02000 Visualizing theory space: Isometric embedding of probabilistic predictions, from the Ising model to the cosmic microwave background], Katherine N. Quinn, Francesco De Bernardis, Michael D. Niemack, James P. Sethna (submitted). </ref><ref>[https://sethna.lassp.cornell.edu/pubPDF/SloppyEverywhere.pdf "Universally Sloppy Parameter Sensitivities in Systems Biology"], Ryan N. Gutenkunst, Joshua J. Waterfall, Fergal P. Casey, Kevin S. Brown, Christopher R. Myers, James P. Sethna, PLoS Comput Biol3(10) e189 (2007). ([http://compbiol.plosjournals.org/perlserv/?request=get-document&doi=10.1371/journal.pcbi.0030189 PLoS], [http://dx.doi.org/10.1371/journal.pcbi.0030189 doi:10.1371/journal.pcbi.0030189]). [Reviewed in [http://biomedicalcomputationreview.org/4/1/4.pdf NewsBytes] of [http://biomedicalcomputationreview.org/ Biomedical Computation Review] (Winter 07/08); rated "Exceptional" on Faculty of 1000]. </ref><ref name = “Casey et.al, 2007”>[http://arxiv.org/abs/q-bio.MN/0610024 "Optimal experimental design in an EGFR signaling and down-regulation model"], Fergal P. Casey, Dan Baird, Qiyu Feng, Ryan N. Gutenkunst, Joshua J. Waterfall, Christopher R. Myers, Kevin S. Brown, Richard A. Cerione, and James P. Sethna, IET Systems Biology 1, 190-202 (2007)</ref>。
 ===Sloppy理论对实验的启示及应用===

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 == Sloppiness与Sloppy理论 ==
-sloppiness是多参数系统的中常见的一种特性。具有这种特性的模型的参数往往有很多个，但是模型的行为仅取决于少数几个参数或参数的线性组合，其它参数或参数 的线性组合对模型的影响微乎其微。sloppiness特性在系统生物学<ref name = “Gutenkunst et.al, 2007”>Sloppy models and parameter indeterminacy in systems biology: [http://arxiv.org/abs/q-bio/0701039 "Universally Sloppy Parameter Sensitivities in Systems Biology"], Ryan N. Gutenkunst, Joshua J. Waterfall, Fergal P. Casey, Kevin S. Brown, Christopher R. Myers, James P. Sethna, PLoS Comput Biol3(10) e189 (2007). ([http://compbiol.plosjournals.org/perlserv/?request=get-document&doi=10.1371/journal.pcbi.0030189 PLoS], [http://dx.doi.org/10.1371/journal.pcbi.0030189 doi:10.1371/journal.pcbi.0030189]), [https://sethna.lassp.cornell.edu/pubPDF/SloppyEverywhere.pdf pdf]). [Reviewed in [http://biomedicalcomputationreview.org/4/1/4.pdf NewsBytes] of [http://biomedicalcomputationreview.org/ Biomedical Computation Review] (Winter 07/08); rated "Exceptional" on Faculty of 1000]. </ref>
+sloppiness是多参数系统的中常见的一种特性。具有这种特性的模型的参数往往有很多个，但是模型的行为仅取决于少数几个参数或参数的线性组合，其它参数或参数 的线性组合对模型的影响微乎其微。sloppiness特性在系统生物学<ref name = "Gutenkunst et.al, 2007”>Sloppy models and parameter indeterminacy in systems biology: [http://arxiv.org/abs/q-bio/0701039 "Universally Sloppy Parameter Sensitivities in Systems Biology"], Ryan N. Gutenkunst, Joshua J. Waterfall, Fergal P. Casey, Kevin S. Brown, Christopher R. Myers, James P. Sethna, PLoS Comput Biol3(10) e189 (2007). ([http://compbiol.plosjournals.org/perlserv/?request=get-document&doi=10.1371/journal.pcbi.0030189 PLoS], [http://dx.doi.org/10.1371/journal.pcbi.0030189 doi:10.1371/journal.pcbi.0030189]), [https://sethna.lassp.cornell.edu/pubPDF/SloppyEverywhere.pdf pdf]). [Reviewed in [http://biomedicalcomputationreview.org/4/1/4.pdf NewsBytes] of [http://biomedicalcomputationreview.org/ Biomedical Computation Review] (Winter 07/08); rated "Exceptional" on Faculty of 1000]. </ref>
 <ref name = “Transtrum et.al, 2015”>Sloppiness, information geometry, and model reduction: [http://arxiv.org/abs/1501.07668 Perspective: Sloppiness and Emergent Theories in Physics, Biology, and Beyond], Mark K. Transtrum, Benjamin B. Machta, Kevin S. Brown, Bryan C. Daniels, Christopher R. Myers, and James P. Sethna, [http://scitation.aip.org/content/aip/journal/jcp/143/1/10.1063/1.4923066 J. Chem. Phys. '''143''', 010901 (2015)], </ref><ref name = “Manatee et.al, 2016”>[http://gutengroup.mcb.arizona.edu/wp-content/uploads/Mannakee2016.pdf Sloppiness and the Geometry of Parameter Space.] In: Geris, L., Gomez-Cabrero, D. (eds) Mannakee, B.K., Ragsdale, A.P., Transtrum, M.K., Gutenkunst, R.N. (2016).[http://dx.doi.org/10.1007/978-3-319-21296-8_11 Uncertainty in Biology. Studies in Mechanobiology, Tissue Engineering and Biomaterials], vol 17. Springer, Cham. https://doi.org/10.1007/978-3-319-21296-8_11 </ref>、物理学<ref>[https://sethna.lassp.cornell.edu/pubPDF/PC12.pdf "The Statistical Mechanics of Complex Signaling Networks: Nerve Growth Factor Signaling"], Kevin S. Brown, Colin C. Hill, Guillermo A. Calero, Christopher R. Myers, Kelvin H. Lee, James P. Sethna, and Richard A. Cerione, Physical Biology '''1''', 184-195 (2004), with [https://sethna.lassp.cornell.edu/pubPDF/PC12Supporting.pdf supplemental material]. </ref>和数学<ref name = “Brown & Sethna, 2003”> [https://sethna.lassp.cornell.edu/pubPDF/SloppyModelPRE.pdf “Statistical Mechanics Approaches to Models with Many Poorly Known Parameters"], Kevin S. Brown and James P. Sethna, Phys. Rev. E '''68''', 021904 (2003). </ref>系统中无处不在。

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 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 name = “Waterfall et.al, 2006”>[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><ref name="Transtrum et.al, 2014">” Model reduction by manifold boundaries", Mark K. Transtrum, P. Qiu [https://doi.org/10.1103/PhysRevLett.113.098701 Phys. Rev. Lett. '''113''', 098701 (2014)]; pdf. </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="Transtrum et.al, 2014"/>。
+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 name = “Waterfall et.al, 2006”>[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><ref name="Transtrum et.al, 2014">” Model reduction by manifold boundaries", Mark K. Transtrum, P. Qiu [https://doi.org/10.1103/PhysRevLett.113.098701 Phys. Rev. Lett. '''113''', 098701 (2014)]; pdf. </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="Transtrum et.al, 2014"/>。
 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> [https://arxiv.org/abs/1605.08705 Bridging Mechanistic and Phenomenological Models of Complex Biological Systems], Mark K. Transtrum and Peng Qiu, PLoS Comput Biol 12(5): e1004915. https://doi.org/10.1371/journal.pcbi.1004915</ref>。

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 == Sloppiness与Sloppy理论 ==
 sloppiness是多参数系统的中常见的一种特性。具有这种特性的模型的参数往往有很多个，但是模型的行为仅取决于少数几个参数或参数的线性组合，其它参数或参数 的线性组合对模型的影响微乎其微。sloppiness特性在系统生物学<ref name = “Gutenkunst et.al, 2007”>Sloppy models and parameter indeterminacy in systems biology: [http://arxiv.org/abs/q-bio/0701039 "Universally Sloppy Parameter Sensitivities in Systems Biology"], Ryan N. Gutenkunst, Joshua J. Waterfall, Fergal P. Casey, Kevin S. Brown, Christopher R. Myers, James P. Sethna, PLoS Comput Biol3(10) e189 (2007). ([http://compbiol.plosjournals.org/perlserv/?request=get-document&doi=10.1371/journal.pcbi.0030189 PLoS], [http://dx.doi.org/10.1371/journal.pcbi.0030189 doi:10.1371/journal.pcbi.0030189]), [https://sethna.lassp.cornell.edu/pubPDF/SloppyEverywhere.pdf pdf]). [Reviewed in [http://biomedicalcomputationreview.org/4/1/4.pdf NewsBytes] of [http://biomedicalcomputationreview.org/ Biomedical Computation Review] (Winter 07/08); rated "Exceptional" on Faculty of 1000]. </ref>
-<ref name = “Transtrum et.al, 2015”>Sloppiness, information geometry, and model reduction: [http://arxiv.org/abs/1501.07668 Perspective: Sloppiness and Emergent Theories in Physics, Biology, and Beyond], Mark K. Transtrum, Benjamin B. Machta, Kevin S. Brown, Bryan C. Daniels, Christopher R. Myers, and James P. Sethna, [http://scitation.aip.org/content/aip/journal/jcp/143/1/10.1063/1.4923066 J. Chem. Phys. '''143''', 010901 (2015)], </ref><ref name = “Manatee et.al, 2016”>[http://gutengroup.mcb.arizona.edu/wp-content/uploads/Mannakee2016.pdf Sloppiness and the Geometry of Parameter Space.] In: Geris, L., Gomez-Cabrero, D. (eds) Mannakee, B.K., Ragsdale, A.P., Transtrum, M.K., Gutenkunst, R.N. (2016).[http://dx.doi.org/10.1007/978-3-319-21296-8_11 Uncertainty in Biology. Studies in Mechanobiology, Tissue Engineering and Biomaterials], vol 17. Springer, Cham. https://doi.org/10.1007/978-3-319-21296-8_11 </ref>、物理学<ref>[https://sethna.lassp.cornell.edu/pubPDF/PC12.pdf ”The Statistical Mechanics of Complex Signaling Networks: Nerve Growth Factor Signaling"], Kevin S. Brown, Colin C. Hill, Guillermo A. Calero, Christopher R. Myers, Kelvin H. Lee, James P. Sethna, and Richard A. Cerione, Physical Biology '''1''', 184-195 (2004), with [https://sethna.lassp.cornell.edu/pubPDF/PC12Supporting.pdf supplemental material]. </ref>和数学<ref name = “Brown & Sethna, 2003”> [https://sethna.lassp.cornell.edu/pubPDF/SloppyModelPRE.pdf “Statistical Mechanics Approaches to Models with Many Poorly Known Parameters"], Kevin S. Brown and James P. Sethna, Phys. Rev. E '''68''', 021904 (2003). </ref>系统中无处不在。
+<ref name = “Transtrum et.al, 2015”>Sloppiness, information geometry, and model reduction: [http://arxiv.org/abs/1501.07668 Perspective: Sloppiness and Emergent Theories in Physics, Biology, and Beyond], Mark K. Transtrum, Benjamin B. Machta, Kevin S. Brown, Bryan C. Daniels, Christopher R. Myers, and James P. Sethna, [http://scitation.aip.org/content/aip/journal/jcp/143/1/10.1063/1.4923066 J. Chem. Phys. '''143''', 010901 (2015)], </ref><ref name = “Manatee et.al, 2016”>[http://gutengroup.mcb.arizona.edu/wp-content/uploads/Mannakee2016.pdf Sloppiness and the Geometry of Parameter Space.] In: Geris, L., Gomez-Cabrero, D. (eds) Mannakee, B.K., Ragsdale, A.P., Transtrum, M.K., Gutenkunst, R.N. (2016).[http://dx.doi.org/10.1007/978-3-319-21296-8_11 Uncertainty in Biology. Studies in Mechanobiology, Tissue Engineering and Biomaterials], vol 17. Springer, Cham. https://doi.org/10.1007/978-3-319-21296-8_11 </ref>、物理学<ref>[https://sethna.lassp.cornell.edu/pubPDF/PC12.pdf "The Statistical Mechanics of Complex Signaling Networks: Nerve Growth Factor Signaling"], Kevin S. Brown, Colin C. Hill, Guillermo A. Calero, Christopher R. Myers, Kelvin H. Lee, James P. Sethna, and Richard A. Cerione, Physical Biology '''1''', 184-195 (2004), with [https://sethna.lassp.cornell.edu/pubPDF/PC12Supporting.pdf supplemental material]. </ref>和数学<ref name = “Brown & Sethna, 2003”> [https://sethna.lassp.cornell.edu/pubPDF/SloppyModelPRE.pdf “Statistical Mechanics Approaches to Models with Many Poorly Known Parameters"], Kevin S. Brown and James P. Sethna, Phys. Rev. E '''68''', 021904 (2003). </ref>系统中无处不在。

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 事实上，理论物理学就像一棵树（下图）。高能物理学家研究树的枝条，寻找更接近树干的更统一的理论。在凝聚态物理学中则向外构建，寻找“涌现的”树枝和树叶——描述声音、半导体和超流体的有效理论。但两者有许多相似之处：扩散方程描述了在静止空气中香水如何从皮肤扩散到鼻子。这个方程通常写成连续极限的形式，使用的方法类似于描述凝聚态物理学中许多其他现象——声音、磁铁和超导体——的方法。而磁性的伊辛模型分形过程，通常使用类似于高能物理学中使用的重整化群进行分析。物理学家有一套系统的方法判断哪些参数是stiff（“僵硬”）的，哪些参数是sloppy（“欠定”）的，但是在其它领域中并没有相应的方法，使用sloppy理论的概念可以更准确有效地分析系统<ref>[http://arxiv.org/abs/1710.05787 Information geometry and the renormalization group], Archishman Raju, Benjamin B. Machta, James P. Sethna (submitted). </ref><ref>[http://arxiv.org/abs/1303.6738 Parameter Space Compression Underlies Emergent Theories and Predictive Models,] Benjamin B. Machta, Ricky Chachra, Mark K. Transtrum, James P. Sethna, [http://www.sciencemag.org/content/342/6158/604 Science'''342''' 604-607 (2013)].</ref><ref>[http://arxiv.org/pdf/1409.6203v2.pdf Information topology identifies emergent model classes], Transtrum M.K., Hart G., Qiu P. </ref><ref>[https://sethna.lassp.cornell.edu/pubPDF/vanderPol.pdf Structural susceptibility and separation of time scales in the van der Pol Oscillator], Ricky Chachra, Mark K. Transtrum, and James P. Sethna, [http://link.aps.org/doi/10.1103/PhysRevE.86.026712 Phys. Rev. E '''86''', 026712 (2012)]. </ref>
-,甚至物理学领域也在逐渐应用sloppy理论<ref name = “Quinn”>Model manifolds for probabilistic models: [http://arxiv.org/abs/1709.02000 Visualizing theory space: Isometric embedding of probabilistic predictions, from the Ising model to the cosmic microwave background], Katherine N. Quinn, Francesco De Bernardis, Michael D. Niemack, James P. Sethna (submitted). </ref><ref>[https://sethna.lassp.cornell.edu/pubPDF/SloppyEverywhere.pdf ”Universally Sloppy Parameter Sensitivities in Systems Biology"], Ryan N. Gutenkunst, Joshua J. Waterfall, Fergal P. Casey, Kevin S. Brown, Christopher R. Myers, James P. Sethna, PLoS Comput Biol3(10) e189 (2007). ([http://compbiol.plosjournals.org/perlserv/?request=get-document&doi=10.1371/journal.pcbi.0030189 PLoS], doi:10.1371/journal.pcbi.0030189). [Reviewed in [http://biomedicalcomputationreview.org/4/1/4.pdf NewsBytes] of [http://biomedicalcomputationreview.org/ Biomedical Computation Review] (Winter 07/08); rated "Exceptional" on Faculty of 1000]. </ref><ref name = “Casey et.al, 2007”>[http://arxiv.org/abs/q-bio.MN/0610024 "Optimal experimental design in an EGFR signaling and down-regulation model"], Fergal P. Casey, Dan Baird, Qiyu Feng, Ryan N. Gutenkunst, Joshua J. Waterfall, Christopher R. Myers, Kevin S. Brown, Richard A. Cerione, and James P. Sethna, IET Systems Biology 1, 190-202 (2007)</ref>。
+,甚至物理学领域也在逐渐应用sloppy理论<ref name = “Quinn”>Model manifolds for probabilistic models: [http://arxiv.org/abs/1709.02000 Visualizing theory space: Isometric embedding of probabilistic predictions, from the Ising model to the cosmic microwave background], Katherine N. Quinn, Francesco De Bernardis, Michael D. Niemack, James P. Sethna (submitted). </ref><ref>[https://sethna.lassp.cornell.edu/pubPDF/SloppyEverywhere.pdf ”Universally Sloppy Parameter Sensitivities in Systems Biology"], Ryan N. Gutenkunst, Joshua J. Waterfall, Fergal P. Casey, Kevin S. Brown, Christopher R. Myers, James P. Sethna, PLoS Comput Biol3(10) e189 (2007). ([http://compbiol.plosjournals.org/perlserv/?request=get-document&doi=10.1371/journal.pcbi.0030189 PLoS], [http://dx.doi.org/10.1371/journal.pcbi.0030189 doi:10.1371/journal.pcbi.0030189]). [Reviewed in [http://biomedicalcomputationreview.org/4/1/4.pdf NewsBytes] of [http://biomedicalcomputationreview.org/ Biomedical Computation Review] (Winter 07/08); rated "Exceptional" on Faculty of 1000]. </ref><ref name = “Casey et.al, 2007”>[http://arxiv.org/abs/q-bio.MN/0610024 "Optimal experimental design in an EGFR signaling and down-regulation model"], Fergal P. Casey, Dan Baird, Qiyu Feng, Ryan N. Gutenkunst, Joshua J. Waterfall, Christopher R. Myers, Kevin S. Brown, Richard A. Cerione, and James P. Sethna, IET Systems Biology 1, 190-202 (2007)</ref>。
 ===Sloppy理论对实验的启示及应用===
@@ 第66行： / 第66行： @@
 以上内容翻译自参考资料：
-Sloopy Model: <nowiki>https://www.lassp.cornell.edu/sethna/Sloppy/，感兴趣的朋友可以前往了解详情。</nowiki>
+Sloppy Model: <nowiki>https://www.lassp.cornell.edu/sethna/Sloppy/，感兴趣的朋友可以前往了解详情。</nowiki>
 ==参考资料==
 {{Reflist}}

@@ 第1行： / 第1行： @@
 == Sloppiness与Sloppy理论 ==
-sloppiness是多参数系统的中常见的一种特性。具有这种特性的模型的参数往往有很多个，但是模型的行为仅取决于少数几个参数或参数的线性组合，其它参数或参数 的线性组合对模型的影响微乎其微。sloppiness特性在系统生物学<ref name = “Gutenkunst et.al, 2007”>Sloppy models and parameter indeterminacy in systems biology: "Universally Sloppy Parameter Sensitivities in Systems Biology", Ryan N. Gutenkunst, Joshua J. Waterfall, Fergal P. Casey, Kevin S. Brown, Christopher R. Myers, James P. Sethna, PLoS Comput Biol3(10) e189 (2007). (PLoS, doi:10.1371/journal.pcbi.0030189), pdf). [Reviewed in NewsBytes of Biomedical Computation Review (Winter 07/08); rated "Exceptional" on Faculty of 1000]. </ref>
+sloppiness是多参数系统的中常见的一种特性。具有这种特性的模型的参数往往有很多个，但是模型的行为仅取决于少数几个参数或参数的线性组合，其它参数或参数 的线性组合对模型的影响微乎其微。sloppiness特性在系统生物学<ref name = “Gutenkunst et.al, 2007”>Sloppy models and parameter indeterminacy in systems biology: [http://arxiv.org/abs/q-bio/0701039 "Universally Sloppy Parameter Sensitivities in Systems Biology"], Ryan N. Gutenkunst, Joshua J. Waterfall, Fergal P. Casey, Kevin S. Brown, Christopher R. Myers, James P. Sethna, PLoS Comput Biol3(10) e189 (2007). ([http://compbiol.plosjournals.org/perlserv/?request=get-document&doi=10.1371/journal.pcbi.0030189 PLoS], [http://dx.doi.org/10.1371/journal.pcbi.0030189 doi:10.1371/journal.pcbi.0030189]), [https://sethna.lassp.cornell.edu/pubPDF/SloppyEverywhere.pdf pdf]). [Reviewed in [http://biomedicalcomputationreview.org/4/1/4.pdf NewsBytes] of [http://biomedicalcomputationreview.org/ Biomedical Computation Review] (Winter 07/08); rated "Exceptional" on Faculty of 1000]. </ref>
-<ref name = “Transtrum et.al, 2015”>Sloppiness, information geometry, and model reduction: Perspective: Sloppiness and Emergent Theories in Physics, Biology, and Beyond, Mark K. Transtrum, Benjamin B. Machta, Kevin S. Brown, Bryan C. Daniels, Christopher R. Myers, and James P. Sethna, J. Chem. Phys. 143, 010901 (2015), </ref><ref name = “Manatee et.al, 2016”>Mannakee, B.K., Ragsdale, A.P., Transtrum, M.K., Gutenkunst, R.N. (2016). Sloppiness and the Geometry of Parameter Space. In: Geris, L., Gomez-Cabrero, D. (eds) Uncertainty in Biology. Studies in Mechanobiology, Tissue Engineering and Biomaterials, vol 17. Springer, Cham. https://doi.org/10.1007/978-3-319-21296-8_11 </ref>、物理学<ref>”The Statistical Mechanics of Complex Signaling Networks: Nerve Growth Factor Signaling", Kevin S. Brown, Colin C. Hill, Guillermo A. Calero, Christopher R. Myers, Kelvin H. Lee, James P. Sethna, and Richard A. Cerione, Physical Biology 1, 184-195 (2004), with supplemental material. </ref>和数学<ref name = “Brown & Sethna, 2003”> “Statistical Mechanics Approaches to Models with Many Poorly Known Parameters", Kevin S. Brown and James P. Sethna, Phys. Rev. E 68, 021904 (2003). </ref>系统中无处不在。
+<ref name = “Transtrum et.al, 2015”>Sloppiness, information geometry, and model reduction: [http://arxiv.org/abs/1501.07668 Perspective: Sloppiness and Emergent Theories in Physics, Biology, and Beyond], Mark K. Transtrum, Benjamin B. Machta, Kevin S. Brown, Bryan C. Daniels, Christopher R. Myers, and James P. Sethna, [http://scitation.aip.org/content/aip/journal/jcp/143/1/10.1063/1.4923066 J. Chem. Phys. '''143''', 010901 (2015)], </ref><ref name = “Manatee et.al, 2016”>Mannakee, B.K., Ragsdale, A.P., Transtrum, M.K., Gutenkunst, R.N. (2016). [http://gutengroup.mcb.arizona.edu/wp-content/uploads/Mannakee2016.pdf Sloppiness and the Geometry of Parameter Space.] In: Geris, L., Gomez-Cabrero, D. (eds) [http://dx.doi.org/10.1007/978-3-319-21296-8_11 Uncertainty in Biology. Studies in Mechanobiology, Tissue Engineering and Biomaterials], vol 17. Springer, Cham. https://doi.org/10.1007/978-3-319-21296-8_11 </ref>、物理学<ref>[https://sethna.lassp.cornell.edu/pubPDF/PC12.pdf ”The Statistical Mechanics of Complex Signaling Networks: Nerve Growth Factor Signaling"], Kevin S. Brown, Colin C. Hill, Guillermo A. Calero, Christopher R. Myers, Kelvin H. Lee, James P. Sethna, and Richard A. Cerione, Physical Biology '''1''', 184-195 (2004), with [https://sethna.lassp.cornell.edu/pubPDF/PC12Supporting.pdf supplemental material]. </ref>和数学<ref name = “Brown & Sethna, 2003”> [https://sethna.lassp.cornell.edu/pubPDF/SloppyModelPRE.pdf “Statistical Mechanics Approaches to Models with Many Poorly Known Parameters"], Kevin S. Brown and James P. Sethna, Phys. Rev. E '''68''', 021904 (2003). </ref>系统中无处不在。
-几年前，在研究细胞内外信号传递过程中蛋白质相互作用机制<ref>Formulation, application to fitting algorithms: "Why are nonlinear fits to data so challenging?", Mark K. Transtrum, Benjamin B. Machta, and James P. Sethna, Phys. Rev. Lett. 104, 060201 (2010).</ref><ref>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); </ref>时，几名物理和生物领域的科学家建立了一个有48个参数的模型，模型中参数之间难以独立分离，且参数变化范围都超过50倍。在面对一个参数不确定性如此之大的复杂模型时，一位生物学家却指出：根据研究经验，模型的实验结果甚至不用电脑就可以估算出来。因为系统的行为与大多数参数不确定性之间的关系并不紧密。
+几年前，在研究细胞内外信号传递过程中蛋白质相互作用机制<ref>Formulation, application to fitting algorithms: [http://arxiv.org/abs/0909.3884 "Why are nonlinear fits to data so challenging?"], Mark K. Transtrum, Benjamin B. Machta, and James P. Sethna, [http://link.aps.org/doi/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 Phys. Rev. E '''83''', 036701 (2011); </ref>时，几名物理和生物领域的科学家建立了一个有48个参数的模型，模型中参数之间难以独立分离，且参数变化范围都超过50倍。在面对一个参数不确定性如此之大的复杂模型时，一位生物学家却指出：根据研究经验，模型的实验结果甚至不用电脑就可以估算出来。因为系统的行为与大多数参数不确定性之间的关系并不紧密。
 大量的生物模型都存在类似的现象，例如生物钟的模型。该模型有36个参数，参数空间中符合模型行为特征的参数点构成了一个线性空间，把参数空间向某一平面投影，如图所示。在图上可以看出有实验点分布的方向是sloppy（“欠定”)的（即沿着这个方向变化参数，模型的行为不会发生明显改变），而垂直实验点分布方向是stiff（“僵硬”）的（即在这个方向上改变模型参数，模型的行为会发生显著变化），而在垂直于这个平面的参数空间中，大部分方向都是sloppy（“欠定”）的。
@@ 第21行： / 第21行： @@
 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 name = “Waterfall et.al, 2006”>”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><ref name="Transtrum et.al, 2014">” Model reduction by manifold boundaries", Mark K. Transtrum, P. Qiu Phys. Rev. Lett. 113, 098701 (2014); pdf. </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="Transtrum et.al, 2014"/>。
+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 name = “Waterfall et.al, 2006”>[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><ref name="Transtrum et.al, 2014">” Model reduction by manifold boundaries", Mark K. Transtrum, P. Qiu [https://doi.org/10.1103/PhysRevLett.113.098701 Phys. Rev. Lett. '''113''', 098701 (2014)]; pdf. </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="Transtrum et.al, 2014"/>。
-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> Bridging Mechanistic and Phenomenological Models of Complex Biological Systems, Mark K. Transtrum and Peng Qiu, PLoS Comput Biol 12(5): e1004915. https://doi.org/10.1371/journal.pcbi.1004915</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> [https://arxiv.org/abs/1605.08705 Bridging Mechanistic and Phenomenological Models of Complex Biological Systems], Mark K. Transtrum and Peng Qiu, PLoS Comput Biol 12(5): e1004915. https://doi.org/10.1371/journal.pcbi.1004915</ref>。
 ==Sloppy 理论与物理学==
 事实上，科学能够向前发展与sloppy模型的普适性相连，任何一个系统都是由大量参数决定的，而人们能够发现系统的规律是因为系统的规律由少数stiff（“僵硬”）参数决定，而与大量的sloppy（“欠定”）参数无关。以声音传播的现象为例，声音传播与分子的大小、分子的速度等众多参数相关，但是要准确预测声音传播的速度只需要知道宏观的密度与压缩比。同样，高能物理学家不需要求解弦理论来预测希格斯玻色子或描述夸克的行为。
-事实上，理论物理学就像一棵树（下图）。高能物理学家研究树的枝条，寻找更接近树干的更统一的理论。在凝聚态物理学中则向外构建，寻找“涌现的”树枝和树叶——描述声音、半导体和超流体的有效理论。但两者有许多相似之处：扩散方程描述了在静止空气中香水如何从皮肤扩散到鼻子。这个方程通常写成连续极限的形式，使用的方法类似于描述凝聚态物理学中许多其他现象——声音、磁铁和超导体——的方法。而磁性的伊辛模型分形过程，通常使用类似于高能物理学中使用的重整化群进行分析。物理学家有一套系统的方法判断哪些参数是stiff（“僵硬”）的，哪些参数是sloppy（“欠定”）的，但是在其它领域中并没有相应的方法，使用sloppy理论的概念可以更准确有效地分析系统<ref>Information geometry and the renormalization group, Archishman Raju, Benjamin B. Machta, James P. Sethna (submitted). </ref><ref>Parameter Space Compression Underlies Emergent Theories and Predictive Models, Benjamin B. Machta, Ricky Chachra, Mark K. Transtrum, James P. Sethna, Science342 604-607 (2013).</ref><ref>Information topology identifies emergent model classes, Transtrum M.K., Hart G., Qiu P. </ref><ref>Structural susceptibility and separation of time scales in the van der Pol Oscillator, Ricky Chachra, Mark K. Transtrum, and James P. Sethna, Phys. Rev. E 86, 026712 (2012). </ref>
+事实上，理论物理学就像一棵树（下图）。高能物理学家研究树的枝条，寻找更接近树干的更统一的理论。在凝聚态物理学中则向外构建，寻找“涌现的”树枝和树叶——描述声音、半导体和超流体的有效理论。但两者有许多相似之处：扩散方程描述了在静止空气中香水如何从皮肤扩散到鼻子。这个方程通常写成连续极限的形式，使用的方法类似于描述凝聚态物理学中许多其他现象——声音、磁铁和超导体——的方法。而磁性的伊辛模型分形过程，通常使用类似于高能物理学中使用的重整化群进行分析。物理学家有一套系统的方法判断哪些参数是stiff（“僵硬”）的，哪些参数是sloppy（“欠定”）的，但是在其它领域中并没有相应的方法，使用sloppy理论的概念可以更准确有效地分析系统<ref>[http://arxiv.org/abs/1710.05787 Information geometry and the renormalization group], Archishman Raju, Benjamin B. Machta, James P. Sethna (submitted). </ref><ref>[http://arxiv.org/abs/1303.6738 Parameter Space Compression Underlies Emergent Theories and Predictive Models,] Benjamin B. Machta, Ricky Chachra, Mark K. Transtrum, James P. Sethna, [http://www.sciencemag.org/content/342/6158/604 Science'''342''' 604-607 (2013)].</ref><ref>[http://arxiv.org/pdf/1409.6203v2.pdf Information topology identifies emergent model classes], Transtrum M.K., Hart G., Qiu P. </ref><ref>[https://sethna.lassp.cornell.edu/pubPDF/vanderPol.pdf Structural susceptibility and separation of time scales in the van der Pol Oscillator], Ricky Chachra, Mark K. Transtrum, and James P. Sethna, [http://link.aps.org/doi/10.1103/PhysRevE.86.026712 Phys. Rev. E '''86''', 026712 (2012)]. </ref>
-,甚至物理学领域也在逐渐应用sloppy理论<ref name = “Quinn”>Model manifolds for probabilistic models: Visualizing theory space: Isometric embedding of probabilistic predictions, from the Ising model to the cosmic microwave background, Katherine N. Quinn, Francesco De Bernardis, Michael D. Niemack, James P. Sethna (submitted). </ref><ref>”Universally Sloppy Parameter Sensitivities in Systems Biology", Ryan N. Gutenkunst, Joshua J. Waterfall, Fergal P. Casey, Kevin S. Brown, Christopher R. Myers, James P. Sethna, PLoS Comput Biol3(10) e189 (2007). (PLoS, doi:10.1371/journal.pcbi.0030189). [Reviewed in NewsBytes of Biomedical Computation Review (Winter 07/08); rated "Exceptional" on Faculty of 1000]. </ref><ref name = “Casey et.al, 2007”>"Optimal experimental design in an EGFR signaling and down-regulation model", Fergal P. Casey, Dan Baird, Qiyu Feng, Ryan N. Gutenkunst, Joshua J. Waterfall, Christopher R. Myers, Kevin S. Brown, Richard A. Cerione, and James P. Sethna, IET Systems Biology 1, 190-202 (2007)</ref>。
+,甚至物理学领域也在逐渐应用sloppy理论<ref name = “Quinn”>Model manifolds for probabilistic models: [http://arxiv.org/abs/1709.02000 Visualizing theory space: Isometric embedding of probabilistic predictions, from the Ising model to the cosmic microwave background], Katherine N. Quinn, Francesco De Bernardis, Michael D. Niemack, James P. Sethna (submitted). </ref><ref>[https://sethna.lassp.cornell.edu/pubPDF/SloppyEverywhere.pdf ”Universally Sloppy Parameter Sensitivities in Systems Biology"], Ryan N. Gutenkunst, Joshua J. Waterfall, Fergal P. Casey, Kevin S. Brown, Christopher R. Myers, James P. Sethna, PLoS Comput Biol3(10) e189 (2007). ([http://compbiol.plosjournals.org/perlserv/?request=get-document&doi=10.1371/journal.pcbi.0030189 PLoS], doi:10.1371/journal.pcbi.0030189). [Reviewed in [http://biomedicalcomputationreview.org/4/1/4.pdf NewsBytes] of [http://biomedicalcomputationreview.org/ Biomedical Computation Review] (Winter 07/08); rated "Exceptional" on Faculty of 1000]. </ref><ref name = “Casey et.al, 2007”>[http://arxiv.org/abs/q-bio.MN/0610024 "Optimal experimental design in an EGFR signaling and down-regulation model"], Fergal P. Casey, Dan Baird, Qiyu Feng, Ryan N. Gutenkunst, Joshua J. Waterfall, Christopher R. Myers, Kevin S. Brown, Richard A. Cerione, and James P. Sethna, IET Systems Biology 1, 190-202 (2007)</ref>。
 ===Sloppy理论对实验的启示及应用===

@@ 第29行： / 第29行： @@
 事实上，理论物理学就像一棵树（下图）。高能物理学家研究树的枝条，寻找更接近树干的更统一的理论。在凝聚态物理学中则向外构建，寻找“涌现的”树枝和树叶——描述声音、半导体和超流体的有效理论。但两者有许多相似之处：扩散方程描述了在静止空气中香水如何从皮肤扩散到鼻子。这个方程通常写成连续极限的形式，使用的方法类似于描述凝聚态物理学中许多其他现象——声音、磁铁和超导体——的方法。而磁性的伊辛模型分形过程，通常使用类似于高能物理学中使用的重整化群进行分析。物理学家有一套系统的方法判断哪些参数是stiff（“僵硬”）的，哪些参数是sloppy（“欠定”）的，但是在其它领域中并没有相应的方法，使用sloppy理论的概念可以更准确有效地分析系统<ref>Information geometry and the renormalization group, Archishman Raju, Benjamin B. Machta, James P. Sethna (submitted). </ref><ref>Parameter Space Compression Underlies Emergent Theories and Predictive Models, Benjamin B. Machta, Ricky Chachra, Mark K. Transtrum, James P. Sethna, Science342 604-607 (2013).</ref><ref>Information topology identifies emergent model classes, Transtrum M.K., Hart G., Qiu P. </ref><ref>Structural susceptibility and separation of time scales in the van der Pol Oscillator, Ricky Chachra, Mark K. Transtrum, and James P. Sethna, Phys. Rev. E 86, 026712 (2012). </ref>
-,甚至物理学领域也在逐渐应用sloppy理论<ref name = “Quinn et.al, 2017”>Model manifolds for probabilistic models: Visualizing theory space: Isometric embedding of probabilistic predictions, from the Ising model to the cosmic microwave background, Katherine N. Quinn, Francesco De Bernardis, Michael D. Niemack, James P. Sethna (submitted). </ref><ref>”Universally Sloppy Parameter Sensitivities in Systems Biology", Ryan N. Gutenkunst, Joshua J. Waterfall, Fergal P. Casey, Kevin S. Brown, Christopher R. Myers, James P. Sethna, PLoS Comput Biol3(10) e189 (2007). (PLoS, doi:10.1371/journal.pcbi.0030189). [Reviewed in NewsBytes of Biomedical Computation Review (Winter 07/08); rated "Exceptional" on Faculty of 1000]. </ref><ref name = “Casey et.al, 2007”>"Optimal experimental design in an EGFR signaling and down-regulation model", Fergal P. Casey, Dan Baird, Qiyu Feng, Ryan N. Gutenkunst, Joshua J. Waterfall, Christopher R. Myers, Kevin S. Brown, Richard A. Cerione, and James P. Sethna, IET Systems Biology 1, 190-202 (2007)</ref>。
+,甚至物理学领域也在逐渐应用sloppy理论<ref name = “Quinn”>Model manifolds for probabilistic models: Visualizing theory space: Isometric embedding of probabilistic predictions, from the Ising model to the cosmic microwave background, Katherine N. Quinn, Francesco De Bernardis, Michael D. Niemack, James P. Sethna (submitted). </ref><ref>”Universally Sloppy Parameter Sensitivities in Systems Biology", Ryan N. Gutenkunst, Joshua J. Waterfall, Fergal P. Casey, Kevin S. Brown, Christopher R. Myers, James P. Sethna, PLoS Comput Biol3(10) e189 (2007). (PLoS, doi:10.1371/journal.pcbi.0030189). [Reviewed in NewsBytes of Biomedical Computation Review (Winter 07/08); rated "Exceptional" on Faculty of 1000]. </ref><ref name = “Casey et.al, 2007”>"Optimal experimental design in an EGFR signaling and down-regulation model", Fergal P. Casey, Dan Baird, Qiyu Feng, Ryan N. Gutenkunst, Joshua J. Waterfall, Christopher R. Myers, Kevin S. Brown, Richard A. Cerione, and James P. Sethna, IET Systems Biology 1, 190-202 (2007)</ref>。
 ===Sloppy理论对实验的启示及应用===
@@ 第38行： / 第38行： @@
 但这并不是说可以忽略一些参数，哪怕忽略一个stiff（“僵硬”）方向有投影的参数，模型的行为也会完全不可控。这也给实验造成了困扰，有时忽略了一半以上的参数模型的行为不会有太大改变，但即使忽略了在stiff（“僵硬”）方向有投影的一个参数，要准确预测模型的行为也会变得完全不可能。
 {| class="wikitable"
-| colspan="1" rowspan="1" |还是以上述48参数的模型为例<ref name="Quinn et.al, 2017"/>，研究其在另一种工作模式下的行为：特定细胞在特定生长激素 （EGF作用下）的活性 Erk 与时间的关系。如果 Erk 在 10 分钟后下降，细胞就会增殖；如果它保持下去，细胞就会分化（像神经元一样生长分支）。药物LY，红色X）会关闭两种蛋白质（图中左侧灰色的两个蛋白）。实验想确定给细胞提供更多的LY会发生什么。下面使用四种类型的预测。
+| colspan="1" rowspan="1" |还是以上述48参数的模型为例<ref name = “Quinn”/>，研究其在另一种工作模式下的行为：特定细胞在特定生长激素 （EGF作用下）的活性 Erk 与时间的关系。如果 Erk 在 10 分钟后下降，细胞就会增殖；如果它保持下去，细胞就会分化（像神经元一样生长分支）。药物LY，红色X）会关闭两种蛋白质（图中左侧灰色的两个蛋白）。实验想确定给细胞提供更多的LY会发生什么。下面使用四种类型的预测。
 #经验：一名生物学家认为图中左侧的回路在十分钟后会阻止Erk流失。因此，在添加药物LY后，他预测Erk将保持活跃。