arXiv physics/06030352006-03-06physics.bio-phphysics.comp-ph

统计物理学和生物学中的模拟：一些应用

Simulations in statistical physics and biology: some applications

Maria del Pilar Monsivais-Alonso

备注：: 82 pages, 33 figures, 4 tables, somewhat reduced version of the M.Sc. thesis defended in Jan. 2006 at IPICyT, San Luis Potosi, Mx. (Supervisers: Drs. R. Lopez-Sandoval and H.C. Rosu). Last sections 3.3 and 3.4 can be found at http://lanl.arxiv.org/abs/physics/0411088

摘要：

在过去的几十年里，物理学最活跃的领域之一是临界现象，而蒙特卡罗模拟作为验证和预测接近临界点的系统性质的指南发挥了重要作用。对于Betts晶格（从三角形晶格中去除1/7的位置而构建的晶格）发生的相变的种类已经在之前用Potts模型针对值q=3、铁磁和反铁磁区域进行了研究。在这里，我们把q=4和5的铁磁情况加到这个研究线上。在第一种情况下，临界指数估计的二阶过渡，而对于后一种情况下的直方图方法适用于发生的一阶过渡。此外，还回顾了Domany的基于蒙特卡罗的聚类技术，主要用于对表达水平相似的基因进行分组。最后，一个控制理论的工具-自适应观测器-被施加到估计的指数参数中所涉及的著名的Gompertz曲线。通过处理所有这些主题，我们的目的是强调不同学科之间合作的重要性，以解决生物学中出现的复杂问题。内容：第1章-统计学中的蒙特卡罗模拟。物理学;第2章：生物学中的MC模拟;第3章：Gompertz方程

英文摘要：

One of the most active areas of physics in the last decades has been that of critical phenomena, and Monte Carlo simulations have played an important role as a guide for the validation and prediction of system properties close to the critical points. The kind of phase transitions occurring for the Betts lattice (lattice constructed removing 1/7 of the sites from the triangular lattice) have been studied before with the Potts model for the values q=3, ferromagnetic and antiferromagnetic regime. Here, we add up to this research line the ferromagnetic case for q=4 and 5. In the first case, the critical exponents are estimated for the second order transition, whereas for the latter case the histogram method is applied for the occurring first order transition. Additionally, Domany's Monte Carlo based clustering technique mainly used to group genes similar in their expression levels is reviewed. Finally, a control theory tool --an adaptive observer-- is applied to estimate the exponent parameter involved in the well-known Gompertz curve. By treating all these subjects our aim is to stress the importance of cooperation between distinct disciplines in addressing the complex problems arising in biology. Contents: Chapter 1 - Monte Carlo simulations in stat. physics; Chapter 2: MC simulations in biology; Chapter 3: Gompertz equation

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