| 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 | | 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>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>"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><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. [http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1004915 https://doi.org/10.1371/journal.pcbi.1004915]</ref><ref>[http://arxiv.org/pdf/1409.6203v2.pdf Information topology identifies emergent model classes], Transtrum M.K., Hart G., Qiu P.</ref>,甚至物理学领域也在逐渐应用sloppy理论<ref> | + | <ref>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>"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><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. [http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1004915 https://doi.org/10.1371/journal.pcbi.1004915]</ref><ref>[http://arxiv.org/pdf/1409.6203v2.pdf Information topology identifies emergent model classes], Transtrum M.K., Hart G., Qiu P.</ref>,甚至物理学领域也在逐渐应用sloppy理论<ref name ="Transtrum"> |
| [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><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> | | [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><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/abs/1710.05787 Information geometry and the renormalization group], Archishman Raju, Benjamin B. Machta, James P. Sethna (submitted).</ref>。 | | [http://arxiv.org/abs/1710.05787 Information geometry and the renormalization group], Archishman Raju, Benjamin B. Machta, James P. Sethna (submitted).</ref>。 |