最佳化網路成長模型的理論研究｜國立中央大學博碩士論文系統

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研究生：	鄭安良 An-Liang Cheng
論文名稱：	最佳化網路成長模型的理論研究 Theoretical Studies on Some Optimized Growing Network Models
指導教授：	黎璧賢 Pik-Yin Lai
口試委員:
學位類別：	碩士 Master
系所名稱：	理學院 - 物理學系 Department of Physics
畢業學年度：	94
語文別：	英文
論文頁數：	79
中文關鍵詞：	網路、資訊理論、最佳化、小世界、相互資訊、相變、成長
外文關鍵詞：	network, information theory, optimized, small world, mutual information, phase transition, grow
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網路研究是一門非常重要的領域。網路可以描述我們世界中許多不同的系統，例如社會、生物、及科技網路等。如何找出最佳化的網路成長的模型是我們研究的目的。我們建構了許多不同的能量及限制條件的二維成長網路模型，運用 Metropolis 方法及 Simulated Annealing（模擬降火法）來執行模擬的工作。我們的目標是得到一個網路具有最小材料的消耗（例如網路的長度及能量）而同時間能夠得到最大的訊息內容。在這篇論文中，我們藉由不同的的能量及限制條件得到了許多不同特徵的網路，且在某些網路中觀察到了類似小世界網路及訊息內容的相變現象。我們對模擬出來的網路模型分析了許多網路性質，且進一步和一些真實的網路做比較。最後我們得到一些系統相圖，且發現到了一些和真實網路比較的有趣現象。

Network research is important because complex networks can describe a wide variety of systems in our world. How to find a optimized growing networks is the purpose of this research. We construct models with different Hamiltonians and constraints for the growth of some two dimensional networks, and employ the Metropolis algorithm and Simulated Annealing to perform simulation. Our proposed model aimed at minimizing the material cost while at the same time maximizing the information content. In this thesis, we obtain different kinds of networks display small world characteristics. We also observe a possible phase transition phenomenon in the information content. We analyze many network properties of our results and go further to compare our model networks with some realistic networks. Finally, several "phase diagrams" for our model system are presented and it appears some interesting phenomena can also be found in realistic networks.

Introduction 1
Theoretical Backgrounds 3
1 Review of Some network theories . . . . . . . . . . . . . . . . . . . . 3
1.1 Basic network properties . . . . . . . . . . . . . . . . . . . . . 4
1.2 The Erdos-Renyi Random graph . . . . . . . . . . . . . . . . . 5
1.3 Small world networks . . . . . . . . . . . . . . . . . . . . . . . 5
2 Information theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1 Basic concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Information transfer in complex networks . . . . . . . . . . . . 13
2.3 Correlation function . . . . . . . . . . . . . . . . . . . . . . . 16
2.4 Degree entropy . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3 Comparison with real networks . . . . . . . . . . . . . . . . . . . . . 17
3.1 Random electric circuit networks . . . . . . . . . . . . . . . . 17
3.2 Growing neuronal networks . . . . . . . . . . . . . . . . . . . 18
Simulation Methods 20
1 Monte Carlo Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 20
1.1 Metropolis method . . . . . . . . . . . . . . . . . . . . . . . . 21
1.2 Simulated Annealing . . . . . . . . . . . . . . . . . . . . . . . 23
2 Model and Simulation details . . . . . . . . . . . . . . . . . . . . . . 24
2.1 The Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2 The Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Results and discussion 28
1 γ= 0 Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.1 Simple case: No added constraint . . . . . . . . . . . . . . . . 29
1.2 No bond crossing network . . . . . . . . . . . . . . . . . . . . 32
1.3 Network grown with special searching characteristics . . . . . 39
2 λ= 0 Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.1 Simple case: No added constraint . . . . . . . . . . . . . . . . 48
2.2 No bond crossing network . . . . . . . . . . . . . . . . . . . . 54
3 λ≠0, γ≠0 Case . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.1 No bond crossing network . . . . . . . . . . . . . . . . . . . . 59
4 Comparison with some realistic networks . . . . . . . . . . . . . . . . 71
Conclusion 76

                                

[1] D. J. Watts and S. H. Strogatz, Nature (London) 393, 440 (1998).
[2] R. Albert, A. L. Barabasi, Rev. Mod. Phys. 74, 57 (2002).
[3] S. Milgram, Psychology Today, 2, 60-67 (1967).
[4] A.L. Barabasi, and R. Albert, Science 286, 509 (1999).
[5] A.L. Barabasi, Z.N. Oltvai, and S.Wuchty, Characteristics of Biological Networks, Lect. Notes Phys 650, 446 (2004).
[6] C. E. Shannon. Bell Sys. Tech. J. 27: 379, 623 (1948).
[7] E.T.Jaynes, Phys. Rev. 106, 620 (1957).
[8] A. H. Carter, Classical and Statistical Thermodynamics. 376, (New Jersey, Pretice Hall, 2001).
[9] This figure takes from David J.C. MacKay, Information Theory, Inference, and Learning Algorithms, Chapter 8. (Cambridge University Press, 2003).
[10] R. V. Sole and S. Valverde, Information Theory of Complex Networks: On Evolution and Architecural Constraints, Lecture Notes in Physics, Springer-Verlag, 189-207 (2004).
[11] M. E. J. Newman, Physical Review E 67, 026126 (2003).
[12] K. I. Goh, E. Oh, B. Kahng, and D. Kim, Physical Review E 67, 017101 (2003).
[13] R. Ferrer, R. V. Sole, Lecture Notes in Physics, Springer (Berlin), 114-125 (2003).
[14] The detail about action potential, Heinrish Reichert, neurobiologie 2e, Chapter 1 (2004).
[15] K. Macleod, A. Backer, G. Laurent , Nature 395, 693-698 (1998).
[16] L. F. Lago-Fernandez, R. Huerta, F. Corbacho, J. A. Siguenza1, Physical Review Letters 84, 2758-2761 (2000).
[17] L.A.N. Amaral, A. Scala, M. Barthelemy, H.E. Stanley, Proc. Nat. Ac. Sci. USA 97, 11149-11152 (2000).
[18] N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller, J. Chem. Phys., 21(6):1087-1092, June (1953).
[19] H. Gould and J. Tobochnik, An Introduction to Computer Simulation Methods, Applications to Physical Systems, (Addison-Wesley, 1996).
[20] S. E. Koonin, Computational Physics: Fortran Version, (Addison Wesley, 1998).
[21] M. E. J. Newman, Siam Review, Vol.45, No.2, pp. 167-256 (2003).

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