Lixin Tian Vice President of Nanjing Normal University, Professor

Transcription

1 Lixin Tian Vice President of Nanjing Normal University, Professor Lixin Tian, Doctor of Science, Professor, and Doctoral Supervisor, is currently a Vice President of Nanjing Normal University. Professor Tian graduated from the Department of Mathematics, East China Normal University, in 1983, with a Bachelor of Science degree. In 1998, he graduated from the Department of Mathematics, Suzhou University, with a Doctor of Science degree. Professor Tian has been engaged in the theoretical analysis and application of nonlinear system, dynamic large-scale system modeling and control, and the energy-economic system. He has led 12 research projects funded by National Natural Science Foundation, 9 of which have already been completed, including four listed as Major Projects funded by the National Natural Science Foundation. He has also led and completed two research projects, including one Major Project funded by the National Social Science Foundation. He has presided over more than 30 provincialand ministerial-level research projects. He has published more than 240 research papers in Chinese and international journals, including over 180 SCI papers. He is also the author of five monographs. As Chief Contributor, he has won Jiangsu Province's Science and Technology Progress Award on three occasions, including one First Prize (2001), one Second Prize (2014), one Third Prize (2009). He also won 2 Second Prizes of Shanghai Science and Technology Progress Award (ranked the third contributor in 2001 and 2007). As Chief Contributor, he has won Jiangsu Province Philosophy and Social Sciences Award on four occasions, including 1 First Prize (2014), 1Second Prize (2005), and 2Third Prize (2001, 2007). As Chief Contributor, he has won 1 First Prize of the Ministry of Education Outstanding Scientific Achievement (Humanities and Social Sciences) at Higher Education Institutes (2015). Professor Tian is also working as Council Member of the Chinese Mathematical Association, Supervisor of the Society for Industrial and Applied Mathematics of Jiangsu Province, Vice Chairman of Jiangsu Province Institute of Systems Science, Vice Chairman of the Committee of Chinese Scholars of International Association for Energy Economics, Vice Chairman of the Professional Committee of Energy Systems Engineering of China Energy Society, Vice Chairman of the Professional Committee of Complex Systems of China Law Society, and Executive Vice Editor-in-chief of Inter.J.Nonli.Sci.

2 NSFC-FRQSC Workshop on Big Data Management and Decision-making, 2018, Nanjing Resilience of networks with community structure Lixin Tian (Nanjing Normal University) Gaogao Dong (Jiangsu University)

3 Outline Background External field on complex network Real data analysis Conclusion Current research

4 "It's just data. Data volume and velocity is exponentially increasing, but has always been too big to easily store and process One thing that has changed in the last few years is the recognition from decision makers not just analysts that data is a valuable resource." Tom Smith Big Data refers to the use of a massive amount and diverse forms of data to conduct analysis so that the pattern and relationship of the data can be used for classification, clustering, anomaly detection, prediction, and other decision making needs. The Big Data Network will shape our knowledge of society and help us prepare and evaluate better government policies in the future and consists of a range of strategic complementary investments.

5 As big data become more available about real-world systems, network science has opened new perspectives in the study of management decision about real system.

6 Networks or modules within one network in nature do not act in isolation, but instead exchange information and depend on one another to function properly. Community structure Different kinds of critical infrastructure are also coupled together, such as systems of water and food supply, communications, fuel, financial transactions and power generation and transmission. Liu, X., Stanley, H. E., & Gao, J. (2016). Breakdown of interdependent directed networks. Proceedings of the National Academy of Sciences, 113(5), Newman M E J. Modularity and community structure in networks[j]. PNAS, 2006, 103(23):

7 Fundamental definitions Degree : The degree of a node in a network (sometimes referred to incorrectly as the connectivity) is the number of connections or edges the node has to other nodes. Degree Distribution : The degree distribution P(k) of a network is then defined to be the fraction of nodes in the network with degree k. Thus if there are N nodes in total in a network and K of them have degree k, we have P(k) = K/N. Giant Component : In network theory, a giant component is a connected component of a given random graph that contains a finite fraction of the entire graph's vertices.

8 Scale-free Network (1) GROWTH : At every time-step add a new node with m edges (connected to the nodes already present in the system). (2) PREFERENTIAL ATTACHMENT : The probability that a new node will be connected to node i depends on the connectivity ki of that node ( k ) i ki k j j P(k) ~k -3 Real-World Networks Communication networks: telephone, internet, www Transportation networks: airports, highways, rail, electric power Biological networks: genetic,protein-protein interaction, metabolic Social networks: friendship networks, collaboration networks Barabási A L, Albert R. Emergence of scaling in random networks[j]. science, 1999, 286(5439):

9 What is the Resilience? Studies on resilience are popular in multiple disciplines, such as ecology, environmental science, computer science, engineering, management science, economics, and physiology. They investigate resilience of a broad variety of complex systems involving individuals, teams, ecosystems, organizations, communities, supply chains, financial networks, computer networks, and building infrastructures. Common property of many complex systems is resilience, that is, the ability of the system to react to perturbations, internal failures, and environmental events by absorbing the disturbance and/or rebuild to maintain its functions. Nowadays, understanding how complex systems demonstrate resilience is critical in many different fields, because examples of collapses and crises caused by low resilience are more and more spreading all over the world including transportation, financial, energy, communication, and ecological systems. Against risks, Designing more security real systems, Optimizing network transportation/ informal spreading, Suggesting to make new standard. Gao, J., Barzel, B., & Barabási, A.-L. (2016). Universal resilience patterns in complex networks. Nature, 530(7590),

10 The study of resilient in complex networks is important for many fields. In economics, network resilience principles can help understanding of the stability and risks of banking systems. In ecology, resilience is an important attribute of ecosystems, and can give insight into the reaction to disturbances such as the extinction of species. For biologists, network resilience can help the study of diseases and mutations, and how to recover from some mutations. And in engineering, network resilience can help to evaluate the resilience of infrastructure networks such as the Internet or power grids Approaching zero at the percolation threshold pc. In the first-order case, the giant component approaches zero discontinuously. In the second-order case, the giant component is continuously Gao, J., Buldyrev, S. V, Stanley, H. E., & Havlin, S. (2011). Networks formed from interdependent networks. Nature Physics, 8(1),

11 Interdependent networks Modern systems are coupled together. They developed a framework for understanding the robustness of interacting networks. The results show that a broader degree distribution increases the vulnerability of interdependent networks to random failure, which is opposite to how a single network behaves. Buldyrev S. V., Parshani R., Paul G., Stanley H. E., & Havlin, S., Catastrophic cascade of failures in interdependent networks[j]. Nature, 2010, 464(7291): 1025.

12 Partially Interdependent networks Analogous to critical point in liquid-gas transition Black links: connectivity links Red links: dependency links Parshani R., Buldyrev S. V., Havlin, S., Stanley H. E. Interdependent networks: Reducing the coupling strength leads to a change from a first to second order percolation transition. PRL, 2010, 105(4),

13 Dong G, Tian L*, Zhou D, et al. Robustness of n interdependent networks with partial support-dependence relationship[j]. EPL,2013, 102(6): Shao J, Buldyrev S V, Havlin S, et al. Cascade of failures in coupled network systems with multiple supportdependence relations[j]. Physical Review E, 2011, 83(3): Multiple support-dependence networks Two types of nodes: Autonomous nodes (no dependent nodes in the other network) Non-autonomous nodes (have dependent nodes in the other network) A functional node in network is: (i) have at least one functional support node in network B (ii) must belong to the giant component of functional nodes in network A. Only average degree is very large, behavior of the mutually supported giant components can be described by the second-order phase transition, while in all other cases (in the absence of autonomous nodes) it is described by a first-order transition.

14 Inspired by above two expressive works, a kind of fully interacting network model was introduced. Nodes within different networks are fully interacted together, Random attack Belonging to giant component. Black links: intra-connectivity links Black dash links: inter-connectivity links Leicht, E. A., & D'Souza, R. M. (2009). Percolation on interacting networks. arxiv preprint arxiv:

15 Model Globe real airline network (2018) nodes: airports within different continents Blue links: airlines Partial faction of nodes are international airports Demonstration of two interconnected modules from the co-author collaboration network (dblp). Green links: inter-connectivity links Transparent nodes: interconnecting nodes(authors) Based on the modular structure in real-world networks, where a number of well connected groups of nodes (modules or networks) have only some nodes with connectivity links to other modules. (spatial networks) Red nodes have interand intra-connectivity links. Blue nodes only have Intra-connectivity links. Non-duplicate links Dong G., Fan J., Shekhtman, L. M., Shai S., Du R., Tian L., Chen S., Stanley H. E, Havlin, S., (2018 ), PNAS, 115 (27) Fan, J., Dong, G., Shekhtman, L. M., Zhou, D., Meng, J., Chen, X., Havlin, S, (2018). NJP, Accepted.

16 External field on Ising model Schematic of a ferromagnetic phase transition on lattice Temperature T >>Tc, the spontaneous magnetization m vanishes. For T << Tc, the material has a nonzero m. Tc separates the ferro-magnetic (FM) and paramagnetic (PM) phases.

17 External field on complex networks ER network with average degree k=4. r = 0 (red), r = (blue), r = (purple) r = (magenta). r is fraction of interconnected nodes. S is fraction of giant component. k is average degree of intra network. K is average degree of between networks Dong G., Fan J., Shekhtman, L. M., Shai S., Du R., Tian L., Chen S., Stanley H. E, Havlin, S., (2018 ), PNAS, 115 (27)

18 Analogous to critical point in liquid-gas transition Partially Interdependent Networks (PRL,2010,105(4), ) Analogous to ferromagnetic phase transition???? Our Model Parshani R., Buldyrev S. V., Havlin, S., Stanley H. E., PRL, 2010, 105(4), Dong G., Fan J., Shekhtman, L. M., Shai S., Du R., Tian L., Chen S., Stanley H. E, Havlin, S., (2018 ), PNAS, 115 (27)

19 With S(r, p), p and r, serving as the analogues of magnetization, temperature, and external field respectively, we investigated the scaling relations and critical exponents of our model. To quantify how the external field affects the percolation phase transition, we define the critical exponent δ and γ, which describes the susceptibility near criticality in the presence of external field r. Random network For single ER network, β=1 where for ER networks. Critical exponents β, δ and γ, following universal Widom identity, δ-1= γ/ β Cohen, R., Ben-Avraham, D., & Havlin, S. (2002). Percolation critical exponents in scale-free networks. Physical Review E, 66(3), Dong G., Fan J., Shekhtman, L. M., Shai S., Du R., Tian L., Chen S., Stanley H. E, Havlin, S., (2018 ), PNAS, 115 (27)

20 SF networks For SF networks, β=1, for λ>4, β=1/(λ-3), for 3<λ<4, β=1/(3- λ), for 2<λ<3. Critical exponents β, δ and γ, following Widom identity, δ-1= γ/ β for SF networks. Cohen, R., Ben-Avraham, D., & Havlin, S. (2002). Percolation critical exponents in scale-free networks. Physical Review E, 66(3), Dong G., Fan J., Shekhtman, L. M., Shai S., Du R., Tian L., Chen S., Stanley H. E, Havlin, S., (2018 ), PNAS, 115 (27)

21 The dependence of S(r, pc) on r under different cases of Minter are shown on left panel. From the right figures, we observe that for small r=0.0001, γ remains unchanged even for small Minter. (a) ER networks, (b) SF networks with λ=4.5, (c) SF networks with λ=3.35, (d) SF networks with λ=2.8. Dong G., Fan J., Shekhtman, L. M., Shai S., Du R., Tian L., Chen S., Stanley H. E, Havlin, S., (2018 ), PNAS, 115 (27)

22 Real Data Analysis i) Co-author dblp collaboration network. ii) Co-authorship collaboration MathSciNet We find that, the values of critical exponents δ and γ for the real networks are also consistent with theoretical results. Dong G., Fan J., Shekhtman, L. M., Shai S., Du R., Tian L., Chen S., Stanley H. E, Havlin, S., (2018 ), PNAS, 115 (27)

23 Analogous to critical point in liquid-gas transition Partially Interdependent Networks (PRL,2010,105(4), ) Analogous to ferromagnetic phase transition. Our Model Parshani R., Buldyrev S. V., Havlin, S., Stanley H. E., PRL, 2010, 105(4), Dong G., Fan J., Shekhtman, L. M., Shai S., Du R., Tian L., Chen S., Stanley H. E, Havlin, S., (2018 ), PNAS, 115 (27)

24 Conclusion: Big data networking can describe the different module relationship can be help for designing more security and stable real networks and decision-making. A framework of partially interacting-modules (or networks) model were present. A universal scaling relations of complex network near a phase transition was found. (The fraction of nodes with interconnections is analogous to an external field in a physical phase transition.) In particular, defining critical exponents based on S, p, and r the scaling relations governing the external field are analogous to macroscopic magnetization, temperature, and the external field, respectively, near criticality. And, these critical exponents obey universal scaling relations of physical systems near a phase transition. We also find similar results for real social networks. Video demonstration

25 Current research (looking forward to collaboration): Based on 18 years data of Global mergers and acquisitions(m&a), about companies and connection links during 2000 and 2017, the M&A interacting network is already built. To study dynamic of Investing behaviors, and design more globalization finance relationships against the impact of the international financial crisis. The generalized interacting network model and analytical framework are almost completed. If you think it s interesting, could I make an appointment with you or talk to you later. Maybe, we can find a more interesting story and better decision-making suggestions. Thank you very much!!!

26 Members of Energy Dependence Behavior and Strategy Research Center of Nanjing Normal University Dr. Minggang Wang ( 王明刚 ) is an associate Professor of Nanjing Normal University. He has served as a visiting scholar at Boston University. Currently, his research focuses on big data, complex network theory and application and energy finance. He has published more than 20 research papers in SCI journals such as Applied Energy, Energy Economics, Phycical Review E etc. magic821204@sina.com Dr. Ruijin Du ( 杜瑞瑾 ) is an associate Professor of Center for Strategic Studies of energy development and environmental protection of Jiangsu University. She received her PH.D. degree in systems engineering from Jiangsu University in She was a Research Associate in Boston University (USA) during , a visiting scholar in Malardalen University (Sweden) during , and a visiting scholar in Boston University (USA) during Her research focuses on modeling and analysis of complex system, data mining and big data analysis, robustness of complex networks etc. She has published more than 20 academic papers in PNAS, Applied Energy, Physical Review E, Chaos etc. dudo999@126.com Dr. Min Fu ( 傅敏 ) is an associate Professor of Center for Strategic Studies of energy development and environmental protection of Jiangsu University. From July to September 2015, she received financial support from Jiangsu Provincial Student Fund Committee and made an academic visit to Texas-pan American University in the United States. She is mainly engaged in the research of energy economy and carbon cycle theory. She has published 25 papers in domestic and international journals. In the doctoral stage, she has achieved certain results in the analysis and application of regional urban carbon cycle systems. fumin@ujs.edu.cn

27