图 书 馆
图论Graph Theory |
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| 课程网址: | http://videolectures.net/netadis2013_monasson_graph_theory/ |
| 主讲教师: | Rémi Monasson |
| 开课单位: | 国家科学研究中心 |
| 开课时间: | 2013-11-21 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | Random graphs are of central importance in probability theory, combinatorics, and statistical physics. The purpose of these lectures is to review, in a non-rigorous manner, the typical properties of random graphs, with a strong emphasis on the Erdos-Renyi ensemble. We will illustrate those properties, and in particular the percolation transition, on the special case of random systems of Boolean equations. Statistical mechanics techniques will be introduced to study rare properties, that is, large deviations from the typical case. In the second lecture we will focus on dynamical processes modifying random graph structures, and analyze their evolution. Furthermore the replica method for 'dilute' systems will be presented. Finally, in the third lecture, random spatial maps will be considered, in relationship with the modeling of recent experiments in neurobiology. Lecture 1: Typical and Rare Properties of Random Graphs Lecture 2: Dynamical Processes on Random Graphs Lecture 3: Storage of spatial maps in Hopfield-like models. For details about the statistical mechanics derivation of the phase diagram of the model, see this paper. Suggestions for further readings: B. Bollobas, Random Graphs, Cambridge University Press (2001) N.C. Wormald, The differential equation method for random graph processes and greedy algorithms, in Lectures on Approximation and Randomized Algorithms (M. Karonski and H.J. Proemel, eds), pp. 73-155. PWN, Warsaw (1999) D.J. Amit, Modeling Brain Function: The World of Attractor Neural Networks, Cambridge University Press (1992) for more on statistical mechanics and random Boolean systems, see R. Monasson, Introduction to Phase Transitions in Random Optimization Problems, Lecture Notes of Les Houches Summer School, Elsevier (2006) and references therein. |
| 关 键 词: | 随机图论; 布尔方程; 随机系统; 渗透迁跃 |
| 课程来源: | 视频讲座网 |
| 数据采集: | 2023-04-22：chenxin01 |
| 最后编审: | 2023-05-18：chenxin01 |
| 阅读次数: | 23 |