CONTENTS -- Preface -- International Symposium on Topological Aspects of Critical Systems and Networks -- Group Photo -- I. General Properties of Networks -- Physics of Network Security Y.-C. Lai, X. Wand and C. H. Lai -- 1. Introduction -- 2. Model of cascades in complex networks -- 3. Formula for phase-transition point c -- 4. Determination of s: criterion for designing cascade-free networks -- 5. Discussions -- References -- Multi-State Interacting Particle Systems on Scale-Free Networks N. Masuda and N. Konno -- 1. Introduction -- 2. SIS model -- 3. SIRS-type Models -- 4. Multi-state Epidemic Dynamics -- References -- Homotopy Reduction of Complex Networks Y. Hiraoka and T. Ichinomiya -- References -- Analysis of the Susceptible-Infected-Susceptible Model on Complex Network T. Ichinomiya -- References -- II. Complexity in Social Science -- Innovation and Development in a Random Lattice J. Lahtinen -- 1. Introduction -- 2. Model -- 3. Simulations -- 4. Conclusions -- Acknowledgments -- References -- Long-Tailed Distributions in Biological Systems: Revisit to Lognormals N. Kobayashi, K. Kohyama, O. Moriyama, Y. Sasaki, M. Matsushita and S. Matsushita -- 1. Introduction -- 2. Long-tailed Distribution of Duration of Disability for Aged People -- 3. Food Fragmentation by Human Mastication -- 4. Conclusion -- References -- Two-Class Structure of Income Distribution in the USA: Exponential Bulk and Power-Law Tail V. M. Yakovenko and A. Christian Silva -- References -- Power Law Distributions in Two Community Currencies N. Kichiji and M. Nishibe -- 1. Introduction -- 2. Two Community Currencies -- 3. Zipf 's Law -- 4. Summary -- Acknowledgments -- References -- III. Patterns in Biological Objects.

Stoichiometric Network Analysis of Nonlinear Phenomena in a Reaction Mechanism for TWC Converters M. Marek, O. Hadac, I. Schreiber, M. Schejbal and M. Kubicek -- 1. Introduction -- 2. Mathematical Model -- 3. Stoichiometric Network Analysis and Classification of Oscillatory Dynamics -- 4. Conclusions -- Acknowledgements -- References -- Collective Movement and Morphogenesis of Epithelial Cells H. Haga and K. Kawabata -- 1. Collective Cell Movement -- 2. Cellular Wave -- 3. Lumen Formation of Epithelial Cells -- Acknowledgments -- References -- Indecisive Behavior of Amoeba Crossing an Environmental Barrier S. Takagi, Y. Nishiura, T. Nakagaki, T. Ueda and K.-I. Ueda -- 1. Introduction -- 2. Experiment -- 2.1. Materials and methods -- 2.2. Experimental result -- 2.3. Experiment on the frontal tip activity of locomotion -- 3. Mathematical Model -- 4. Discussion -- References -- Effects of Amount of Food on Path Selection in the Transport Network of an Amoeboid Organism T. Nakagaki, T. Saigusa, A. Tero and R. Kobayashi -- 1. Introduction -- 2. Accumulation of mass of organism to FS in relation to the amount of nutrient at the FS -- 3. Fate of the connections between two FSs in relation to the amount of food present -- 4. Order of tube collapse among five connections of different lengths between two FSs -- 5. Mathematical modeling of tube selection between two FSs -- 6. Possible physiological significance of tube selection involving three FSs -- References -- Light Scattering Study in Double Network Gels M. Fukunaga, M. Takesada, A. Onodera, R. Kuwadara, J. P. Gong, Y. Osada and T. Yagi -- 1. Introduction -- 2. Experiment -- 3. Result -- 4. Discussion -- 5. Conclusion -- Acknowledgments -- References -- Blood Flow Velocity in the Choroid in Punctate Inner Choroidopathy and Vogt-Koyanagi-Harada Disease.

and Multifractal Analysis of Choroidal Blood Flow in Age-Related Macular Degeneration K. Yoshida, W. Saito, H. Fujii and K. Yakubo -- 1. OCULAR BLOOD FLOW -- 2. LASER SPECKLE FLOWGRAPHY -- 3. PUNCTATE INNER CHOROIDOPATHY -- 4. VOGT-KOYANAGI-HARADA DISEASE -- 5. MULTIFRACTAL ANALYSIS OF CHOROIDAL BLOOD FLOW -- References -- Topological Analysis of Placental Arteries: Correlation with Neonatal Growth H. Yamada and K. Yakubo -- 1. Introduction -- 2. Materials and methods -- 2.1. Patients characteristics -- 2.2. Network indices as topological determinants -- 3. Results -- 4. Discussion -- References -- IV. Criticality in Pure and Applied Physics -- Droplets in Disordered Metallic Quantum Critical Systems A. H. Castro Neto and B. A. Jones -- 1. Introduction -- 2. The model -- 3. Replica symmetry breaking -- 4. Droplet tunneling -- 5. Conclusion -- Acknowledgments -- References -- Importance of Static Disorder and Inhomogeneous Cooperative Dynamics in Heavy-Fermion Metals O. O. Bernal -- 1. Correlated, Heavy, Non-Fermi-Liquid Electron Systems -- 2. Spectroscopic Techniques: NMR and µSR -- 3. NMR/ SR and UCu5-xPdx -- 4. NMR/ SR in Other NFL Systems -- Acknowledgments -- References -- Competition between Spin Glass and Antiferromagnetic Phases in Heavy Fermion Materials S. Sullow -- 1. Introduction -- 2. Experimental review -- 3. Discussion -- Acknowledgments -- References -- Emergent Phases via Fermi Surface Reconstruction near the Metamagnetic Quantum Critical Point in U(Ru1-xRhx)2Si2 K. H. Kim, Y. S. Oh, N. Harrison, P. A. Sharma, M. Jaime, H. Amitsuka and J. A. Mydosh -- 1. Introduction -- 2. Experimentals -- 3. Results and discussion -- 3.1. Construction of phase diagram -- 3.2. Evidences of quantum criticality -- 3.3. Nexus between phase formation and quantum critical point via avoiding quasiparticle instability.

3.4. Discontinuous Hall coefficient changes -- 4. Summary -- References -- Continuous Evolution of the Fermi Surface of CeRu2Si2 Across the Metamagnetic Transition R. Daou, C. Bergemann and S. R. Julian -- 1. Introduction -- 2. Experiment -- 3. Interpretation -- 4. Consequences of the model -- 5. The electronic topological transition -- 6. Summary -- References -- Phase Transition between the Itinerant and the Localized f-electron States in Heavy Fermion Antiferromagnet Ce(Ru0.9Rh0.1)2(Si1-yGey)2 Y. Tabata, C. Kanadani, R. Yamaki, T. Taniguchi and S. Kawarazaki -- References -- Relation between Magnetism and Metal-Insulator Transition in Mn-Doped SrRuO3 M. Yokoyama, C. Satoh, K. Fujita, Y. Nishihara, H. Kawanaka and H. Bando -- References -- Magnetization Study of Pairing and Vortex States in Sr2RuO4 K. Tenya, R. Yamahana, A. Ishii, H. Amitsuka, M. Yokoyama, K. Deguchi and Y. Maeno -- 1. Introduction -- 2. Experimental Procedure -- 3. Results and Discussions -- 4. Summary -- Acknowledgments -- References -- Single-Site Effects of Pr Ions Doped in ThRu2Si2 A. Morishita, Y. Saito, K. Matsuda, T. Wakabayashi, I. Kawasaki, K. Tenya and H. Amitsuka -- 1. Introduction -- 2. Experimental -- 3. Results and Discussions -- 4. Summary -- Acknowledgments -- References -- 51V-NMR Studies of Heisenberg Triangular System V15 Cluster Y. Furukawa, Y. Nishisaka, K. Kumagai and P. Kogerler -- 1. Introduction -- 2. Experimental -- 3. Results and discussion -- Acknowledgments -- References -- Menger Sponge-like Fractal Body Created with a Designed Template Method H. Mayama and K. Tsujii -- 1. Introduction -- 2. Experiment -- 2.1. Experimental strategy -- 2.2. Experimental procedures -- 3. Results and discussion -- Nonlinear Lattice Relaxation Mechanism for Photoexcited Dimetal-Hallide Chain Compounds J. Ohara and S. Yamamoto -- 1. Introduction.

2. Calculational Procedure -- 3. Photogeneration of Solitons and Polarons -- 4. Summary -- Acknowledgments -- References -- Real Space Renormalization Group Analysis with the Replica Method for the Two-Dimensional Ising Spin Glass T. Hasegawa and K. Nemoto -- 1. Introduction -- 2. Model -- 3. Method -- 4. Results -- 5. Summary -- Acknowledgment -- References -- Quantum Network Models and Their Symmetry Properties T. Ohtsuki and K. M. Slevin -- 1. Introduction -- 2. Symmetry Properties -- 2.1. S matrix -- 2.2. Transfer matrix -- 3. Summary -- References -- Fractality of Critical Percolation Networks M. Mitobe and K. Yakubo -- 1. Introduction -- 2. Distribution of fractal dimensions -- 3. Non-fractal critical clusters -- 4. Conclusions -- References -- Ising Phase Transition on Curved Surfaces Y. Sakaniwa, I. Hasegawa and H. Shima -- 1. Introduction -- 2. Poincare disk model -- 3. Model and methods -- 4. Results -- Acknowledgment -- References -- Quantum Confinement in Deformed Cylindrical Surfaces H. Taira and H. Shima -- 1. Introduction -- 2. Schrodinger's equation in curved surfaces -- 3. Model and methods -- 4. Results and discussions -- References -- Topological Spin Currents due to Nonadiabatic Quantum Pumping K. Yakubo and M. Morikawa -- 1. Introduction -- 2. Systems and Formalism -- 3. Charge and Spin Pumping Currents -- 4. Conclusions -- Acknowledgments -- References -- Charge Density Wave State in Topological Crystal T. Nogawa and K. Nemoto -- References -- Spatiotemporal Mapping of Symmetrical Surface Acoustic Fields on Crystals and Periodic Microstructures T. Tachizaki, O. B. Wright, O. Matsuda and Y. Sugawara -- 1. Introduction : Surface acoustic waves and its imaging -- 2. Experiments -- 3. Conclusion -- Acknowledgements -- References -- Clean Optical Vortex Beam Generation for Large Topological Charge J. Hamazaki, Y. Mineta and R. Morita.

1. Introduction.