1. Dynamical Processes on Large Networks B. Aditya Prakash http://www.cs.cmu.edu/~badityap Carnegie Mellon University UMD-College Park, April 26, 2012

2. Networks are everywhere! Human Disease Network [Barabasi 2007] Gene Regulatory Network [Decourty 2008] Facebook Network [2010] The Internet [2005]

3. 3 Dynamical Processes over networks are also everywhere!

4. Why do we care? Online Information Diffusion Viral Marketing Epidemiology and Public Health Cyber Security Human mobility Games and Virtual Worlds Ecology........ 4

5. Why do we care? (1: Epidemiology) Dynamical Processes over networks [AJPH 2007] CDC data: Visualization of the first 35 tuberculosis (TB) patients and their 1039 contacts Diseases over contact networks 5

6. Why do we care? (1: Epidemiology) Dynamical Processes over networks Each circle is a hospital ~3000 hospitals More than 30,000 patients transferred [US-MEDICARE NETWORK 2005] 6 Problem: Given k units of disinfectant, whom to immunize?

7. Why do we care? (1: Epidemiology) CURRENT PRACTICEOUR METHOD ~6x fewer! [US-MEDICARE NETWORK 2005] 7 Hospital-acquired inf. took 99K+ lives, cost $5B+ (all per year)

8. Why do we care? (2: Online Diffusion) 8 > 800m users, ~$1B revenue [WSJ 2010] ~100m active users > 50m users

9. Why do we care? (2: Online Diffusion) Dynamical Processes over networks Celebrity Buy Versace™! Followers 9 Social Media Marketing

10. Why do we care? (3: To change the world?) Dynamical Processes over networks Social networks and Collaborative Action 10

11. High Impact – Multiple Settings Q. How to squash rumors faster? Q. How do opinions spread? Q. How to market better? 11 epidemic out-breaks products/viruses transmit s/w patches

12. Research Theme DATA Large real-world networks & processes 12 ANALYSIS Understanding POLICY/ ACTION Managing

13. Research Theme – Public Health DATA Modeling # patient transfers ANALYSIS Will an epidemic happen? POLICY/ ACTION How to control out-breaks?

14. Research Theme – Social Media DATA Modeling Tweets spreading POLICY/ ACTION How to market better? ANALYSIS # cascades in future?

15. In this talk 15 ANALYSIS Understanding Given propagation models: Q1: Will an epidemic happen?

16. In this talk 16 Q2: How to immunize and control out-breaks better? POLICY/ ACTION Managing

17. In this talk 17 DATA Large real-world networks & processes Q3: How do #hashtags spread?

18. Outline Motivation Epidemics: what happens? (Theory) Action: Who to immunize? (Algorithms) Learning Models: Twitter (Empirical Studies) Other 18

19. A fundamental question Strong Virus Epidemic? 19

20. example (static graph) Weak Virus Epidemic? 20

21. Problem Statement Find, a condition under which – virus will die out exponentially quickly – regardless of initial infection condition above (epidemic) below (extinction) # Infected time 21 Separate the regimes?

22. Threshold (static version) Problem Statement Given: – Graph G, and – Virus specs (attack prob. etc.) Find: – A condition for virus extinction/invasion 22

23. Threshold: Why important? Accelerating simulations Forecasting (‘What-if’ scenarios) Design of contagion and/or topology A great handle to manipulate the spreading – Immunization – Maximize collaboration ….. 23

24. Outline Motivation Epidemics: what happens? (Theory) – Background – Result and Intuition (Static Graphs) – Proof Ideas (Static Graphs) – Bonus 1: Dynamic Graphs – Bonus 2: Competing Viruses Action: Who to immunize? (Algorithms) Learning Models: Twitter (Empirical Studies) Other 24

25. “SIR” model: life immunity (mumps) Each node in the graph is in one of three states – Susceptible (i.e. healthy) – Infected – Removed (i.e. can’t get infected again) 25 Prob. β Prob. δ t = 1t = 2t = 3

26. Terminology: continued Other virus propagation models (“VPM”) – SIS : susceptible-infected-susceptible, flu-like – SIRS : temporary immunity, like pertussis – SEIR : mumps-like, with virus incubation (E = Exposed) ….…………. Underlying contact-network – ‘who-can-infect- whom’ 26

27. Related Work  R. M. Anderson and R. M. May. Infectious Diseases of Humans. Oxford University Press, 1991.  A. Barrat, M. Barthélemy, and A. Vespignani. Dynamical Processes on Complex Networks. Cambridge University Press, 2010.  F. M. Bass. A new product growth for model consumer durables. Management Science, 15(5):215–227, 1969.  D. Chakrabarti, Y. Wang, C. Wang, J. Leskovec, and C. Faloutsos. Epidemic thresholds in real networks. ACM TISSEC, 10(4), 2008.  D. Easley and J. Kleinberg. Networks, Crowds, and Markets: Reasoning About a Highly Connected World. Cambridge University Press, 2010.  A. Ganesh, L. Massoulie, and D. Towsley. The effect of network topology in spread of epidemics. IEEE INFOCOM, 2005.  Y. Hayashi, M. Minoura, and J. Matsukubo. Recoverable prevalence in growing scale-free networks and the effective immunization. arXiv:cond-at/0305549 v2, Aug. 6 2003.  H. W. Hethcote. The mathematics of infectious diseases. SIAM Review, 42, 2000.  H. W. Hethcote and J. A. Yorke. Gonorrhea transmission dynamics and control. Springer Lecture Notes in Biomathematics, 46, 1984.  J. O. Kephart and S. R. White. Directed-graph epidemiological models of computer viruses. IEEE Computer Society Symposium on Research in Security and Privacy, 1991.  J. O. Kephart and S. R. White. Measuring and modeling computer virus prevalence. IEEE Computer Society Symposium on Research in Security and Privacy, 1993.  R. Pastor-Santorras and A. Vespignani. Epidemic spreading in scale-free networks. Physical Review Letters 86, 14, 2001.  ……… All are about either: Structured topologies (cliques, block-diagonals, hierarchies, random) Specific virus propagation models Static graphs All are about either: Structured topologies (cliques, block-diagonals, hierarchies, random) Specific virus propagation models Static graphs 27

28. Outline Motivation Epidemics: what happens? (Theory) – Background – Result and Intuition (Static Graphs) – Proof Ideas (Static Graphs) – Bonus 1: Dynamic Graphs – Bonus 2: Competing Viruses Action: Who to immunize? (Algorithms) Learning Models: Twitter (Empirical Studies) Other 28

29. How should the answer look like? Answer should depend on: – Graph – Virus Propagation Model (VPM) But how?? – Graph – average degree? max. degree? diameter? – VPM – which parameters? – How to combine – linear? quadratic? exponential? 29 …..

30. Static Graphs: Our Main Result Informally, 30 For,  any arbitrary topology (adjacency matrix A)  any virus propagation model (VPM) in standard literature the epidemic threshold depends only 1.on the λ, first eigenvalue of A, and 2.some constant, determined by the virus propagation model λ λ No epidemic if λ * < 1 In Prakash+ ICDM 2011 (Selected among best papers).

31. Our thresholds for some models s = effective strength s < 1 : below threshold Models Effective Strength (s) Threshold (tipping point) SIS, SIR, SIRS, SEIR s = λ. s = 1 SIV, SEIV s = λ. ( H.I.V. ) s = λ. 31

32. Our result: Intuition for λ “Official” definition: Let A be the adjacency matrix. Then λ is the root with the largest magnitude of the characteristic polynomial of A [det(A – xI)]. Doesn’t give much intuition! “Un-official” Intuition λ ~ # paths in the graph 32 u u ≈. (i, j) = # of paths i  j of length k

33. better connectivity higher λ Largest Eigenvalue (λ) 33

34. N nodes Largest Eigenvalue (λ) λ ≈ 2λ = Nλ = N-1 34 N = 1000 λ ≈ 2λ= 31.67λ= 999 better connectivity higher λ

35. Examples: Simulations – SIR (mumps) (a) Infection profile (b) “Take-off” plot PORTLAND graph 31 million links, 6 million nodes Fraction of Infections Footprint Effective Strength Time ticks 35

36. Examples: Simulations – SIRS (pertusis) Fraction of Infections Footprint Effective StrengthTime ticks (a) Infection profile (b) “Take-off” plot PORTLAND graph 31 million links, 6 million nodes 36

37. Outline Motivation Epidemics: what happens? (Theory) – Background – Result and Intuition (Static Graphs) – Proof Ideas (Static Graphs) – Bonus 1: Dynamic Graphs – Bonus 2: Competing Viruses Action: Who to immunize? (Algorithms) Learning Models: Twitter (Empirical Studies) Other 37

38. λ * < 1 Graph-based Model-based 38 Proof Sketch General VPM structure Topology and stability

39. Models and more models ModelUsed for SIRMumps SISFlu SIRSPertussis SEIRChicken-pox …….. SICRTuberculosis MSIRMeasles SIVSensor Stability H.I.V. ………. 39

40. Ingredient 1: Our generalized model 40 Endogenous Transitions SusceptibleInfected Vigilant Exogenous Transitions Endogenous Transitions SusceptibleInfected Vigilant

41. Special case SusceptibleInfected Vigilant 41

42. Special case: H.I.V. Multiple Infectious, Vigilant states 42 “Terminal” “Non-terminal”

43. Ingredient 2: NLDS+Stability View as a NLDS – discrete time – non-linear dynamical system (NLDS) Probability vector Specifies the state of the system at time t 43 size mN x 1.......... size N (number of nodes in the graph)...... S S I I V V

44. Ingredient 2: NLDS + Stability View as a NLDS – discrete time – non-linear dynamical system (NLDS) Non-linear function Explicitly gives the evolution of system 44 size mN x 1................

45. Ingredient 2: NLDS + Stability View as a NLDS – discrete time – non-linear dynamical system (NLDS) Threshold  Stability of NLDS 45

46. = probability that node i is not attacked by any of its infectious neighbors Special case: SIR size 3N x 1 I I R R S S NLDS I I R R S S 46

47. Fixed Point 11.11. 11.11. 00.00. 00.00. 00.00. 00.00. State when no node is infected Q: Is it stable? 47

48. Stability for SIR Stable under threshold Unstable above threshold 48

49. λ * < 1 Graph-based Model-based 49 General VPM structure Topology and stability See paper for full proof

50. Outline Motivation Epidemics: what happens? (Theory) – Background – Result and Intuition (Static Graphs) – Proof Ideas (Static Graphs) – Bonus 1: Dynamic Graphs – Bonus 2: Competing Viruses Action: Who to immunize? (Algorithms) Learning Models: Twitter (Empirical Studies) Other 50

51. Dynamic Graphs: Epidemic? adjacency matrix 8 8 Alternating behaviors DAY (e.g., work) 51

52. adjacency matrix 8 8 Dynamic Graphs: Epidemic? Alternating behaviors NIGHT (e.g., home) 52

53. SIS model – recovery rate δ – infection rate β Set of T arbitrary graphs Model Description day N N night N N, weekend….. Infected Healthy XN1 N3 N2 Prob. β Prob. δ 53

54. Informally, NO epidemic if eig (S) = < 1 Our result: Dynamic Graphs Threshold Single number! Largest eigenvalue of The system matrix S In Prakash+, ECML-PKDD 2010 54 S =

55. Synthetic MIT Reality Mining log(fraction infected) Time BELOW AT ABOVE AT BELOW Infection-profile 55

56. “Take-off” plots Footprint (# infected @ “steady state”) Our threshold (log scale) NO EPIDEMIC EPIDEMIC NO EPIDEMIC SyntheticMIT Reality 56

57. Outline Motivation Epidemics: what happens? (Theory) – Background – Result and Intuition (Static Graphs) – Proof Ideas (Static Graphs) – Bonus 1: Dynamic Graphs – Bonus 2: Competing Viruses Action: Who to immunize? (Algorithms) Learning Models: Twitter (Empirical Studies) Other 57

58. Competing Contagions 58 iPhone v AndroidBlu-ray v HD-DVD Biological common flu/avian flu, pneumococcal inf etc

59. A simple model Modified flu-like Mutual Immunity (“pick one of the two”) Susceptible-Infected1-Infected2-Susceptible 59 Virus 1 Virus 2

60. Question: What happens in the end? 60 green: virus 1 red: virus 2 Footprint @ Steady State = ? Number of Infections ASSUME: Virus 1 is stronger than Virus 2

61. Question: What happens in the end? 61 green: virus 1 red: virus 2 Number of Infections ASSUME: Virus 1 is stronger than Virus 2 Strength ?? = Strength 2 Footprint @ Steady State

62. Answer: Winner-Takes-All 62 green: virus 1 red: virus 2 ASSUME: Virus 1 is stronger than Virus 2 Number of Infections

63. Our Result: Winner-Takes-All 63 In Prakash+ WWW 2012 Given our model, and any graph, the weaker virus always dies-out completely 1.The stronger survives only if it is above threshold 2.Virus 1 is stronger than Virus 2, if: strength(Virus 1) > strength(Virus 2) 3.Strength(Virus) = λ β / δ  same as before!

64. Real Examples 64 Reddit v DiggBlu-Ray v HD-DVD [Google Search Trends data]

65. Outline Motivation Epidemics: what happens? (Theory) Action: Who to immunize? (Algorithms) Learning Models: Twitter (Empirical Studies) Other 65

66. ? ? Given: a graph A, virus prop. model and budget k; Find: k ‘best’ nodes for immunization (removal). k = 2 ? ? Full Static Immunization 66

67. Outline Motivation Epidemics: what happens? (Theory) Action: Who to immunize? (Algorithms) – Full Immunization (Static Graphs) – Fractional Immunization Learning Models: Twitter (Empirical Studies) Other 67

68. Challenges Given a graph A, budget k, Q1 (Metric) How to measure the ‘shield- value’ for a set of nodes (S)? Q2 (Algorithm) How to find a set of k nodes with highest ‘shield-value’? 68

69. Proposed vulnerability measure λ Increasing λ Increasing vulnerability λ is the epidemic threshold “Safe”“Vulnerable”“Deadly” 69

70. 1 9 10 3 4 5 7 8 6 2 9 1 11 10 3 4 5 6 7 8 2 9 Original Graph Without {2, 6} Eigen-Drop(S) Δ λ = λ - λ s Eigen-Drop(S) Δ λ = λ - λ s Δ A1: “Eigen-Drop”: an ideal shield value 70

71. (Q2) - Direct Algorithm too expensive! Immunize k nodes which maximize Δ λ S = argmax Δ λ Combinatorial! Complexity: – Example: 1,000 nodes, with 10,000 edges It takes 0.01 seconds to compute λ It takes 2,615 years to find 5-best nodes ! 71

72. A2: Our Solution Part 1: Shield Value – Carefully approximate Eigen-drop (Δ λ) – Matrix perturbation theory Part 2: Algorithm – Greedily pick best node at each step – Near-optimal due to submodularity NetShield (linear complexity) – O(nk 2 +m) n = # nodes; m = # edges 72 In Tong, Prakash+ ICDM 2010

73. Experiment: Immunization quality Log(fraction of infected nodes) NetShield Degree PageRank Eigs (=HITS) Acquaintance Betweeness (shortest path) Lower is better Time 73

74. Outline Motivation Epidemics: what happens? (Theory) Action: Who to immunize? (Algorithms) – Full Immunization (Static Graphs) – Fractional Immunization Learning Models: Twitter (Empirical Studies) Other 74

75. 75 Fractional Immunization of Networks B. Aditya Prakash, Lada Adamic, Theodore Iwashyna (M.D.), Hanghang Tong, Christos Faloutsos Submitted to PNAS

76. Fractional Asymmetric Immunization Hospital Another Hospital 76 Drug-resistant Bacteria (like XDR-TB)

77. Fractional Asymmetric Immunization Hospital Another Hospital Drug-resistant Bacteria (like XDR-TB) 77 = f

78. Fractional Asymmetric Immunization Hospital Another Hospital 78 Problem: Given k units of disinfectant, how to distribute them to maximize hospitals saved?

79. Our Algorithm “SMART-ALLOC” CURRENT PRACTICESMART-ALLOC [US-MEDICARE NETWORK 2005] 79 Each circle is a hospital, ~3000 hospitals More than 30,000 patients transferred ~6x fewer!

80. Running Time 80 ≈ SimulationsSMART-ALLOC > 1 week 14 secs > 30,000x speed-up! Wall-Clock Time Lower is better

81. Experiments 81 K = 200K = 2000 PENN-NETWORK SECOND-LIFE ~5 x ~2.5 x Lower is better

82. Outline Motivation Epidemics: what happens? (Theory) Action: Who to immunize? (Algorithms) Learning Models: Twitter (Empirical Studies) Other 82

83. Tweets Diffusion: Problem Definition Given: – Action log of people tweeting a #hashtag – A network of users Find: – How external influence varies with #hashtags? ?? ? ? ?? 83

84. Tweet Diffusion: Data Yahoo! Twitter firehose More than 750 million tweets (> 10 Tera-bytes) Test-bed of > 6000 machines – Hadoop+PIG system ver 0.20.204.0 Took top 500 hashtags (by volume) in Feb 2011 Network of users: – connecting user X to user Y if X directed at least 3 @-messages to Y (or RT-ed a tweet) 84

85. Tweet Diffusion Propagation = Influence + External Developed a model – takes the previous observations into account – with parameters representing external influence Learn from previous data – EM-style alternating minimizing algorithm Group tags according to learnt params 85

86. Results: External Influence vs Time time “External Effects” #nowwatching, #nowplaying, #epictweets #purpleglasses, #brits, #famouslies #oscar, #25jan #openfollow, #ihatequotes, #tweetmyjobs Can also use for Forecasting, Anomaly Detection! Bursty, external events “Word-of-mouth” Not trending Long-running tags “Word-of-mouth” 86

87. Outline Motivation Epidemics: what happens? (Theory) Action: Who to immunize? (Algorithms) Learning Models: Twitter (Empirical Studies) Other – Chipping communities – Time-series analysis 87

88. Mobile Call Graphs 88 200K users Millions of calls 200K users Millions of calls In Prakash+ PAKDD 2010

89. How do these graphs look like? Chain? Collection of Stars? Cliques+Stars? 89

90. How do these graphs look like? Use Singular(eigen)-vectors? – Intuition: Encode connectivity patterns 0 0 1 1 0 1 0 0 0 0 0 1 1 1 0 0 …… ≈. 0 0 0 1 1 1 0 0 90 From To Adjacency Matrix V ΣV^T Dimensionality Reduction

91. EigenPlots Plot Eigenvectors side-by-side (EE-plot) 91 V1 First Principal Component (Score) V2 Second Principal Component (Score) V1 Score Smith Johnson Smith Johnson V Matrix V2 Score

92. Mock Quiz: EE-plots in our real graph? Plot Eigenvectors side-by-side (EE-plots) 92 Spokes!

93. EigenSpokes: they are everywhere Mobile call graphs – multiple regions and different months And in diverse graphs – Patents citation – Internet – Dictionary 93

94. EigenSpokes: Reason Loosely connected – Near Cliques – Near Bi-partite cores 94 Core “Communities” (near) cliques (near) bi-cores

95. EigenSpokes: Usefulness? Help with community-detection! * – extract nodes with high scores – similar connectivity 95 Spy Plots of Top 20 nodes * http://www.cs.cmu.edu/~ badityap/code/spoken.tar

96. “SpokEn” in action! 96 magnified bipartite community patents from same inventor(s)‏ cut-and-paste bibliography! Patent Graph All patents on photosensitive pigments for color printers

97. Outline Motivation Epidemics: what happens? (Theory) Action: Who to immunize? (Algorithms) Learning Models: Twitter (Empirical Studies) Other – Chipping communities – Time-series analysis 97

98. BGP router updates Datapository.net Abilene Network 18 million updates over two years! 98 Find patterns and anomalies

99. BGP-lens at Work Event 1: – Prefix and Origin-AS pointed to Alabama Supercomputing Net. – Sysadmin : “the route for 207.157.115.0/24 was appearing and disappearing in [the] IGP routing table... [which] may have caused BGP to flap.” – Anomaly went undetected and unresolved for 30 days! 99 In Prakash+ SIGKDD 2009

100. 100 Primary and middle Schools in Guangzhou, China. May 12 – 8 hr spike Results from real data – Prolonged Spikes

101. 101 Low High High energy Low energy ‘Tornado’ doesn’t touch down time -> E2 Frequency Analysis – Wavelet Scalogram Fake Real

102. Answering Similarity Queries 102 SELECT * FROM db WHERE TimeSeries LIKE “ db In Li and Prakash ICML 2011 BGP Health-care Datacenter Monitoring Motion-capture ……..

103. Answering Similarity Queries 103 Euclidean? DTW? ……

104. Our Method Complex Linear Dynamical Systems (Kalman Filters) 104 Properties Learns joint dynamics Interpretable Features Time Shifts Frequency Proximity Scalable Includes PCA, DFT, AR as special cases

105. Times Series Analysis 105 BGP data: PLiF + hierarchical clustering

106. Outline Motivation Epidemics: what happens? (Theory) Action: Who to immunize? (Algorithms) Learning Models: Twitter (Empirical Studies) Other 106

107. ML & Stats. Comp. Systems Theory & Algo. Biology Econ. Social Science Physics 107 Dynamical Processes on Networks

108. Publications 1. Winner-takes-all: Competing Viruses or Ideas on fair-play networks (B. Aditya Prakash, Alex Beutel, Roni Rosenfeld, Christos Faloutsos) – In WWW 2012, Lyon 2. Threshold Conditions for Arbitrary Cascade Models on Arbitrary Networks (B. Aditya Prakash, Deepayan Chakrabarti, Michalis Faloutsos, Nicholas Valler, Christos Faloutsos) - In IEEE ICDM 2011, Vancouver (Invited to KAIS Journal Best Papers of ICDM.) 3. Times Series Clustering: Complex is Simpler! (Lei Li, B. Aditya Prakash) - In ICML 2011, Bellevue 4. Epidemic Spreading on Mobile Ad Hoc Networks: Determining the Tipping Point (Nicholas Valler, B. Aditya Prakash, Hanghang Tong, Michalis Faloutsos and Christos Faloutsos) – In IEEE NETWORKING 2011, Valencia, Spain 5. Formalizing the BGP stability problem: patterns and a chaotic model (B. Aditya Prakash, Michalis Faloutsos and Christos Faloutsos) – In IEEE INFOCOM NetSciCom Workshop, 2011. 6. On the Vulnerability of Large Graphs (Hanghang Tong, B. Aditya Prakash, Tina Eliassi-Rad and Christos Faloutsos) – In IEEE ICDM 2010, Sydney, Australia 7. Virus Propagation on Time-Varying Networks: Theory and Immunization Algorithms (B. Aditya Prakash, Hanghang Tong, Nicholas Valler, Michalis Faloutsos and Christos Faloutsos) – In ECML-PKDD 2010, Barcelona, Spain 8. MetricForensics: A Multi-Level Approach for Mining Volatile Graphs (Keith Henderson, Tina Eliassi-Rad, Christos Faloutsos, Leman Akoglu, Lei Li, Koji Maruhashi, B. Aditya Prakash and Hanghang Tong) - In SIGKDD 2010, Washington D.C. 9. Parsimonious Linear Fingerprinting for Time Series (Lei Li, B. Aditya Prakash and Christos Faloutsos) - In VLDB 2010, Singapore 10. EigenSpokes: Surprising Patterns and Scalable Community Chipping in Large Graphs (B. Aditya Prakash, Ashwin Sridharan, Mukund Seshadri, Sridhar Machiraju and Christos Faloutsos) – In PAKDD 2010, Hyderabad, India 11. BGP-lens: Patterns and Anomalies in Internet-Routing Updates (B. Aditya Prakash, Nicholas Valler, David Andersen, Michalis Faloutsos and Christos Faloutsos) – In ACM SIGKDD 2009, Paris, France. 12. Surprising Patterns and Scalable Community Detection in Large Graphs (B. Aditya Prakash, Ashwin Sridharan, Mukund Seshadri, Sridhar Machiraju and Christos Faloutsos) – In IEEE ICDM Large Data Workshop 2009, Miami 13. FRAPP: A Framework for high-Accuracy Privacy-Preserving Mining (Shipra Agarwal, Jayant R. Haritsa and B. Aditya Prakash) – In Intl. Journal on Data Mining and Knowledge Discovery (DKMD), Springer, vol. 18, no. 1, February 2009, Ed: Johannes Gehrke. 14. Complex Group-By Queries For XML (C. Gokhale, N. Gupta, P. Kumar, L. V. S. Lakshmanan, R. Ng and B. Aditya Prakash) – In IEEE ICDE 2007, Istanbul, Turkey. * ** * * * * *

109. Submitted 1. Fractional Immunization of Networks (B. Aditya Prakash, Lada Adamic, Theodore Iwashyna, Hanghang Tong, Christos Faloutsos) 2. How much of Twitter is Influence? (B. Aditya Prakash, Deepayan Chakrabarti, Kunal Punera) 3. Who is to blame? Finding Culprits in Epidemics (B. Aditya Prakash, Jilles Vreeken, Christos Faloutsos) 4. Competing Viruses on Composite Networks: Who wins? (Xuetao Wei, Nicholas Valler, B. Aditya Prakash, Iulian Neamtiu, Michalis Faloutsos and Christos Faloutsos) 5. Gelling, and Melting, Large Graphs through Edge Manipulation (Hanghang Tong, B. Aditya Prakash, Tina Eliassi-Rad, Michalis Faloutsos, Christos Faloutsos) 6. Worst-case Footprints in the SIS model (B. Aditya Prakash, Varun Gupta and Christos Faloutsos) Patents 1. Determining User Communities in Communication Networks (Ashwin Sridharan, Mukund Seshadri, James Schneider, B. Aditya Prakash, Christos Faloutsos) Sprint Inc., filed March 2010 2. Analysis of Computer Network Activity by Successively Removing Accepted Types of Access Events (B. Aditya Prakash, Alice Zheng, Jack Stokes, Eric Fitzgerald, Theodore Hardy) Microsoft Research, filed April 2010 109 * *

110. Acknowledgements Collaborators Christos Faloutsos Roni Rosenfeld, Michalis Faloutsos, Lada Adamic, Theodore Iwashyna (M.D.), Dave Andersen, Tina Eliassi-Rad, Iulian Neamtiu, Varun Gupta, Jilles Vreeken, Deepayan Chakrabarti, Hanghang Tong, Kunal Punera, Ashwin Sridharan, Sridhar Machiraju, Mukund Seshadri, Alice Zheng, Lei Li, Polo Chau, Nicholas Valler, Alex Beutel, Xuetao Wei 110

111. Acknowledgements Funding 111

112. Analysis Policy/Action Data Dynamical Processes on Large Networks B. Aditya Prakash http://www.cs.cmu.edu/~badityap 112