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An exploration of complex network theory and its potential uses for futures. A presentation to the Association of Professional Futurists.

An exploration of complex network theory and its potential uses for futures. A presentation to the Association of Professional Futurists.

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  • I am not a cog in the machine but a node in many different networks!!!!!!!!!!!!
  • The Seven Bridges of Königsberg is a problem inspired by an actual place and situation. The city of Königsberg, Prussia (now Kaliningrad, Russia ) is set on the river Pregel , and included two large islands which were connected to each other and the mainland by seven bridges. The question is whether it is possible to walk with a route that crosses each bridge exactly once, and return to the starting point. In 1736 , Leonhard Euler proved that it was not possible. In proving the result, Euler formulated the problem in terms of graph theory , by abstracting the case of Königsberg -- first, by eliminating all features except the landmasses and the bridges connecting them; second, by replacing each landmass with a dot, called a vertex or node , and each bridge with a line, called an edge or link . Note that graph theory is a branch of topology . The shape of a graph may be distorted in any way, so long as the links between nodes are unchanged. It does not matter whether the links are straight or curved, or whether one node is to the left of another. Euler showed that a circuit of the desired form is possible if and only if there are no nodes (dots in the picture of the graph) that have an odd number of edges touching them. Such a walk is called an Eulerian circuit or an Euler tour . Since the graph corresponding to Königsberg has four such nodes, the path is impossible. If the starting point does not need to coincide with the end point there can be either zero or two nodes that have an odd number of edges touching them. Such a walk is called an Eulerian trail or Euler walk . So this too was impossible for the seven bridges of Königsberg.
  • Paul Erdős (also Pál Erdős , March 26 , 1913 – September 20 , 1996 ) was an immensely prolific and famously eccentric mathematician who, with hundreds of collaborators, worked on problems in combinatorics , graph theory , number theory , classical analysis , approximation theory , set theory and probability theory . He wrote around 1,500 mathematical articles in his lifetime, mostly with co-authors, all of them nontrivial. He had about 500 collaborators, and made mathematical collaboration a social activity in a way that changed the way many mathematicians worked.
  • A Nobel prizewinner and Henry Ford
  • The “switch” numbers identified in the following sample graphs are a measure of the average number of nodes reachable from each node in n hops (including the originating node). So, in the above example, there are on average seven nodes reachable by taking 3 hops or switches. The numbers can be used as a measure of diffusion, how quickly things could proliferate throughout the network.
  • Assortative mixing – property of social networks that has nodes with many links more often connected to other nodes with many links (popular people know other popular people)
  • Clustering is one way to measure cohesion in a network. Generically, if node A is connected to node B and node B is connected to node C, then there is a higher probability that node A will be connected to node C (friends of my friends are usually my friends). In other words, the clustering coefficient is the mean probability that two nodes that are neighbors in the network of the same other node will themselves be neighbors. Triangles are used because it is a measurement of the relationship between three nodes. Newman states that the clustering coefficient measures the fraction of triples that have their third edge filled to complete a triangle. The three is in the numerator of the equation because each triangle in the network in composed of three connected triples and it keep C between zero and one. If a network has a high clustering coefficient then there is tight cohesion in the network (lots of triangles). Source: Newman, M. E. J., The structure and function of complex networks
  • Below are references detailing numerical proofs showing that the removal of nodes with the highest degree causes network breakdown: Albert, R., Jeong, H. and Barabasi, A.-L., 2000. Attack and error tolerance of complex networks. Nature 406 , 378-382. Broder, A., Kumar, R., Maghoul, F., Raghavan, P., Rajagopalan, S., Stata, R., Tomkins, A. and Wiener, J., 2000. Graph structure in the web. Computer Networks 33 , 309-320. Callaway, D. S., Newman, M. E. J., Strogatz, S. H. and Watts, D. J., 2000. Network robustness and fragility: Percolation on random graphs. Phys. Rev. Lett. 85 , 5468-5471. Cohen, R., Erez, K., ben-Avraham, D. and Havlin, S., 2001. Breakdown of the Internet under intentional attack. Phys. Rev. Lett. 86 , 3682-3685. For a complete description of the derivation of the equation in the above slide see the paper: Random graphs as models of networks, M. E. J. Newman, in Handbook of Graphs and Networks , S. Bornholdt and H. G. Schuster (eds.), Wiley-VCH, Berlin (2003). LINK: http://aps.arxiv.org/abs/cond-mat/0202208/
  • Degree correlation ( r ) is a way of measuring if high degree nodes in a network associate preferentially with other high degree nodes. If the number is positive, the network is assortative (meaning that high degree nodes associate with other high degree nodes). If the number is negative, the network is disassortative (high degree nodes attach to low degree nodes). Being disasstorative increases your networks resiliency since the hubs within the network would not be directly connected. To think of it another way, in a degree distribution histogram, it is the relationship between the bars on that histogram that is also an important network property.

Possibility Networks Possibility Networks Presentation Transcript

  • “Possibility Networks”An Exploration of Complex Network Theory and Its Potential Uses for FuturesFor the Association of Professional Futurists Professional Development Seminar Chicago, Illinois July 29th, 2005 By: David A. Jarvis
  • An Opening Thought… “The greatest challenge today, not just in cellbiology and ecology but in all of science, is the accurate and complete description of complex systems. Scientists have broken down manykinds of systems. They think they know most of the elements and forces. The next task is to reassemble them, at least in mathematical models that capture the key properties of the entire ensembles.” - E.O. Wilson, Consilience: The Unity of Knowledge 2
  • Why Complex Networks and Futures?• It has been expressed by members of the APF that the futures field needs new tools, techniques and methodologies – The field’s last major development was scenario planning, which evolved from military planning during World War II and was adopted by the corporate world in the 1960’s – In a recent APF professional development survey, members said they wanted more information on simulation and games, chaos and agent-based models• Complex systems can significantly augment the spectrum of tools that futurists can offer clients and organizations• Those trained in studying the future have explored systems thinking, chaos and complex systems, but tools and applications have not widely moved beyond the metaphorical level• Where do complex systems and the systemic study of the future intersect? Can new tools be created for futurists extracted from the research done in complex systems? 3
  • What to Expect• Gain a basic understanding of the science and math behind network theory - what it is and what it isn’t• Learn about the major players in network theory and the foundational books and papers for the field• Understand the theoretical basis behind such concepts as “diffusion of innovations” and “idea contagions”• Learn how social networks can be used as a futures tool• Participate in an exercise demonstrating the usefulness and power of social networks• This is a BROAD and SHALLOW view of network theory – its purpose is to stimulate thinking and help form questions 4
  • IntroductionI. History and BackgroundII. Scientific BasicsIII. Examples and ApplicationsIV. Demonstration 5
  • Definition of a Complex Network• A society tends to view itself through a lens of the technologies it creates• Networks are EVERYWHERE! – Power grids – Computer networks – Ecological systems (e.g. food webs) – Social interaction patterns – Romantic and sexual networks – The Internet and World Wide Web – Transportation (roads, airlines, rail, etc.) – Communication networks (phones, post, etc.) – Protein interactions and cellular networks – Biological systems (the brain, circulatory system, etc.) 6
  • Definition of a Complex Network• Complex system - a collection of interacting elements arranged for purpose that exhibits high-dimensionality, non-linearity, sensitive dependence of initial conditions, and possibly emergent behavior• Complex network - a representation of a complex system, comprised of nodes and links 7
  • I. History and Background 8
  • The Seven Bridges of Königsberg• Question: Is it possible to cross all seven bridges only once and return to your starting point?• In 1736, Leonhard Euler proved that it was not possible through one of the first formal mathematical discussions using graph theory Node Link 9
  • Paul Erdős• Hungarian mathematician and prolific scientific author• With Alfréd Rényi did fundamental research into how networks form• Discovered random network theory – simplest method of creating a network, God plays dice• Emergence of a giant component• Erdős number – small world phenomenon 10
  • Buttons and Strings 11
  • The Strength of Weak Ties• Mathematical sociologist Mark Granovetter (article in American Journal of Sociology, 1973)• “…the degree of overlap of two individuals’ friendship networks varies directly with the strength of their tie to one another.”• Weak ties can serve as bridges between different social groups, allow you to reach more people more quickly• Strong ties lead to fragmentation, weak ties lead to integration• Example: finding a job 12
  • Six Degrees of Separation• Hungarian author Karinthy’s short story entitled “Chains” (1929)• Milgram’s experiment (1967) – Find the “distance” between any two people in the U.S. – Sent a letter to a few hundred randomly selected people from Boston and Omaha with instructions to send to a Massachusetts stockbroker, the recipient could only send the letter to someone they knew on a first name basis – Common sense says it should take hundreds of steps, it only took six on average, it’s a small world after all! – Idealized vs. real social networks 13
  • Small Worlds & Scale Free• Small world networks – Duncan Watts and Steven Strogatz (1998) – Each node can reach every other node in a small number of steps – Characterized by high clustering, short characteristic path lengths• Scale-free networks – Albert-László Barabási (professor of physics at Notre Dame) & Réka Albert (currently at Penn State) – Examined networks that exhibited a power-law distribution in their degree (Internet and WWW) • Large number of poorly connected nodes and a small number of well-connected hubs 14
  • Scale-Free Networks • Poisson distributions vs. power-law distributions – Power law example: distribution of wealth Number of nodes with k links Number of nodes with k links Most nodes have the same Large number number of links of nodes have few links Small number of nodes (hubs) have many links Number of links (k) Number of links (k) Normal (Poisson) Distribution Power-Law DistributionAdapted from: Linked, Barabási , pg. 71 15
  • Related Topics• Fads• Memes• Chaos Theory• Social Networking• Diffusion of Innovations• Contagion• Agent-Based Modeling• Collective Robotics and Distributed Systems• Emergence 16
  • Fads• Definition – Ideas or things in a culture that become extremely popular very quickly, and just as quickly become unpopular; linked to herd mentality – Bandwagon effect – a benefit that a person enjoys as a result of others’ doing the same thing that they do• Relation – accelerated s-curve behavior• Examples – Irrational exuberance in the stock market – Flash mobs – Christmas toys – Fashion – Music & dance crazes 17
  • Memes• Definition – concept created by Richard Dawkins in his book The Selfish Gene (1976); a piece of information that can be transmitted between two minds; parallels to evolution• Relation – Alternate explanation for how ideas propagate through a society 18
  • Chaos Theory• Definition – “The irregular, unpredictable behavior of deterministic, nonlinear dynamical systems.”, Roderick V. Jensen, Yale University• Relation – descriptive of natural systems, sensitivity to initial conditions, patterns• Examples – Double pendulums – Multi-body gravitational problems – Turbulent fluids (e.g. the atmosphere) – Work of Lorenz, Mandelbrot 19
  • Diffusion of Innovations• Definition – – The theories of diffusion can trace their roots back to the French sociologist Gabriel Tarde who identified the innovation adoption S- curve, group mind, laws of imitation – Progressed through the agricultural research of Ryan and Gross in the 1940’s, lead to the notion of adopter categories (innovators, early adopters, early majority, late majority, laggards) – Rogers seminal work Diffusion of Innovation (1962) formalized these theories• Relation – there are many researches who study the diffusion of innovations in complex networks • Information Flow in Social Groups • A generalized model of social and biological contagion • Modeling diffusion of innovations in a social network • The Power of a Good Idea: Quantitative Modeling of the Spread of Ideas from Epidemiological Models 20
  • Contagion VIDEO“Contact Networks in Predicting and Controlling Emerging Infectious Diseases” Lauren Ancel Meyers SFI External Faculty, University of Texas at Austin 7:00 - 15:30 – Background 30:00 - 36:00 – Contact Network Epidemiology 21
  • Agent-Based Modeling• Definition – ABM is a simulation tool that is characterized by large numbers of simple agents interacting through well defined rule sets• Relation – ABM is widely used as a tool for modeling complex adaptive systems• Examples – Crowd dynamics – Traffic patterns – Economic markets – Insect behavior – Genetic algorithms Bonabeau, Eric (2002) Proc. Natl. Acad. Sci. USA 99, 7280-7287 22
  • Emergence• Definition – surprising or unexpected global results that can occur when the parts of any system interact locally via simple rules; the whole is greater than the sum of its parts• Relation – Emergent behavior arises in complex systems; self-organization• Examples – Human consciousness – Traffic patterns – Galaxy formation – Ant colonies, flocking behavior – Urban evolution – Life 23
  • Emergence “I begin to think that this matter of ‘late emergent properties’ that the physicists talk about when theydiscuss complexity and cascading sensitivities is an important concept for historians. Justice may be anlate emergent property. And maybe we can glimpse the beginnings of it emerging; or maybe it emerged long ago, among the primates and proto-humans,and is only now gaining leverage in the world, aided by the material possibility of postscarcity.” - The Years of Rice and Salt, Kim Stanley Robinson 24
  • Social Networking• Definition – business and social networking services• Relation – uses complex network principles like “small worlds” and “six degrees of separation”• Examples – Friendster – LinkedIn – Orkut – Yahoo 360 – MySpace – Ryze 25
  • Collective Robotics• Definition – large numbers of coordinated simple robots designed to perform a complex task, inspired by social insects• Relation – still a very immature technology, collective robotics uses agent-based modeling and principles of emergence• Examples – Swarms of unmanned military vehicles (air, land, sea) – Mobile sensors networks for ocean research, search and rescue, etc. Image taken from iRobot website 26
  • Complex Network Literature• Multi-disciplinary• Most works are fairly recent• Still no definitive academic textbook on complex networks• Three levels – Metaphor – Popular Scientific – Technical 27
  • Metaphor• The Tipping Point: How Little Things Can Make a Big Difference by Malcolm Gladwell (2000)• The Rise of the Creative Class: And How Its Transforming Work, Leisure, Community and Everyday Life by Richard Florida (2002)• The Wisdom of Crowds: Why the Many Are Smarter Than the Few and How Collective Wisdom Shapes Business, Economies, Societies and Nations by James Surowiecki (2004)• Smart Mobs: The Next Social Revolution by Howard Rheingold (2003) 28
  • Popular Scientific• Linked: How Everything Is Connected to Everything Else and What It Means by Albert-Laszlo Barabasi (2002)• Small Worlds: The Dynamics of Networks between Order and Randomness by Duncan Watts (1999)• Critical Mass: How One Thing Leads to Another by Philip Ball (2004)• Harnessing Complexity: Organizational Implications of a Scientific Frontier by Robert Axelrod, Michael D. Cohen (2000) 29
  • Technical• Adaptation in Natural and Artificial Systems : An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence by John H. Holland (1992)• Theories of Communication Networks by Peter R. Monge, Noshir S. Contractor (2003)• Social Network Analysis : Methods and Applications by Stanley Wasserman, Katherine Faust (1995)• Technical Papers 30
  • VIDEO“Social Theories of Human Communication Networks” Peter Monge Professor, Annenberg School for Communication, University of Southern California 8:20 - 14:10 – Role that networks play in society 31
  • Institutions and Organizations• Santa Fe Institute• Center for Complex Network Research, University of Notre Dame• Collective Dynamics Group, Department of Sociology, Columbia University• Center for the Study of Complex Systems, University of Michigan• Networks and Social Dynamics at Cornell University• Northwestern Institute on Complex Systems, Northwestern University• New England Complex Systems Institute (NECSI)• International Network for Social Network Analysis 32
  • Companies• Marketing – Visible Path • How to leverage “relationship capital” – Spoke • Identifying business prospects – Books • The Anatomy of Buzz, by Emanuel Rosen • Seth Godin’s books (Purple Cow, Unleashing the Ideavirus) • Buzzmarketing, by Mark Hughes• Icosystems (Cambridge, MA) – Eric Bonabeau• NuTech Solutions (Charlotte, NC) – Used to be Biosgroup• Redfish Group (Santa Fe, NM) – Visualization, modeling, simulation and adaptive systems design 33
  • II. Scientific Basics 34
  • Network Theory Basics• Types of networks• Classes of networks – Technological – Social – Biological (Ecological) – Information• Examples• Important network properties• Software applications 35
  • Types of Networks• Minimally connected – Network has one less link than the number of nodes, a chain• Maximally connected – Each node is connected to every other node in the network• Random – Links are assigned randomly between nodes• Regular – Each node in the network has an identical degree, a grid• Small world – A regular network with shortcuts• Scale-free w/preferential attachment – Degree distribution follows a power-law, as the network grows new links are more likely to attach to hubs (rich get richer) 36
  • Types of NetworksMinimally connected Maximally connected 37
  • Types of NetworksErdös random network Random network w/growth 38
  • Types of NetworksRegular network (lattice) Small world network 39
  • Types of Networks “Scale Free,” Power Law121086420 1 2 3 4 5 6 7 8 Scale-free network w/preferential attachment 40
  • Classes of Networks • Technological – Man-made networks created for the distribution of some resource or commodity – Electric power grid, airlines, roads, railways, pedestrian traffic, Internet, telephone, post • Social – Group of people connected by a pattern of interactions – Friendships, business relationships, intermarriages, email, collaboration – Problems include inaccuracy, subjectivity and small sample size • Biological – Metabolic pathways, protein interactions, genetic regulatory networks, food webs, neural networks, blood vessels • Information – Citation networks (patents, papers), World Wide WebSource: Newman, M. E. J., The structure and function of complex networks 41
  • Technological Networks THE INTERNETSource: Hal Burch and Bill Cheswick, Lumeta Corp 42
  • Technological Networks AIRLINE ROUTE MAPSource: Continental Airlines 43
  • Social Networks ENRON EMAIL DATA 44
  • Social Networks HIGH SCHOOL DATINGSource: Image by Mark Newman, data drawn from Peter S. Bearman, James Moody, and Katherine Stovel, Chains of affection:The structure of adolescent romantic and sexual networks, American Journal of Sociology 110, 44-91 (2004). 45
  • Biological Networks FOOD WEBSource: Freshwater food web: Neo Martinez and Richard Williams 46
  • Information Networks2004 Election “Blogosphere” Source: HP Labs 47
  • Important Network Properties• Network Considerations – Structure: The definition of links, nodes and their possible connections – Dynamics: Feed-back or feed-forward links that create network effects – Evolution: Long-term statistics as the network fulfills its purpose 48
  • Important Network Properties• Number of nodes and links• Link/node ratio – helpful in comparing the structural similarity of networks with different sizes• Degree distribution – a representation of the connection pattern of a network; how many nodes have a specific degree• Characteristic path length (CPL) – the median of the average distance from each node to every other node in the network – useful in measuring diffusion rates in the network• Clustering – a measure of local cohesion in a network – measures the extent to which nodes that are connected to a particular node are also connected to each other• Susceptibility/Resilience/Robustness – the extent a network can avoid catastrophic failure as links or nodes are removed and how other properties are affected by node/link removal• Betweenness – measure of a node’s importance to dynamic behaviors in a complex network – measures the extent to which a node serves as an intermediary between other nodes – number of shortest paths that pass through a node 49
  • Important Network Properties C D 1 2 Degree 4 E3 B Nodes Links A F 2 4Link/node ratio = 1.33 (8 links, 6 nodes) Characteristic path length (CPL)Degree distribution (histogram) A B C D E F Avg 3 A 0 1 2 2 2 1 1.6 B 1 0 1 2 1 1 1.2 # of nodes 2 C 2 1 0 3 2 2 2.0 D 2 2 3 0 1 1 1.8 1 E 2 1 2 1 0 1 1.4 F 1 1 2 1 1 0 1.2 0 1 2 3 4 5 6 7 8 CPL = 1.5 (median of the averages) # of connections per node 50
  • Important Network Properties C D B E A F Betweenness - Can be used as a measure ofClustering coefficient network resilience 3 x # of triangles C B ( ni ) = ∑ g jk ( ni )C= g jk Number of connected triples of nodes j<k C B ( ni ) = Betweenness centrality for node i g jk = # of shortest paths (geodesics) linking the two actors j and kC = 3 x 3 / 34 = ~0.26 g jk ( ni ) = # of shortest paths (geodesics) linking actors j and k that contain i 51
  • Important Network Properties Robustness - What fraction of nodes need to be removed to destroy the giant component in a power-law graph? You can destroy the giant component of a power-law graph by removing less than 3% of high-degree nodes The most robust graphs have an α of around 2.2 H k(α ) fc = 1 − c ζ (α )Source: Newman, M. E. J., Random graphs as models of networks 52
  • Selected Scale-Free Networks Network Type n l z d α C(1) C(2) r Social Directed 59,912 86,300 1.44 4.95 1.5/ 0.16 E-mail messages 2.0 Social Directed 449,913 25,516,482 113.43 3.48 2.3 0.20 0.78 0.208 Film actors Information Directed 269,504 1,497,135 5.55 11.27 2.1/ 0.11 0.29 -0.067 WWW nd.edu 2.4 Biological Undirected 2,115 2,240 2.12 6.80 2.4 0.072 0.071 -0.156 Protein interactions Biological Undirected 765 3,686 9.64 2.56 2.2 0.090 0.67 -0.240 Metabolic network Technological Undirected 24,097 53,248 4.34 11.05 3.0 0.010 0.030 -0.154 Electronic circuits Technological Undirected 10,697 31,992 5.98 3.31 2.5 0.035 0.39 -0.189 Internet Technological Undirected 880 1,296 1.47 4.28 2.1 0.012 0.011 -0.366 Peer-to-peer network n = number of nodes α = exponent of degree distribution if distribution follows a power-law l = number of links C = clustering coefficient z = mean degree r = degree correlation coefficient d = mean node-node distanceSource: Newman, M. E. J., The structure and function of complex networks 53
  • Software Applications• Pajek• UCINET/NetDraw – Analytic Technologies (Cambridge, MA)• InFlow – Valdis Krebs, orgnet.com• NetMiner• GUESS/Zoomgraph – HP Labs• NetLogo and RePast (ABM)• INSNA List – http://www.insna.org/INSNA/soft_inf.html 54
  • III. Examples and Applications 55
  • Symantec Example• Computer Worm Simulator 56
  • Terrorist Network Example • Complex network analysis has been used to look at terrorist, criminal, and drug cartel networks • News articles on the technique: – Clan, Family Ties Called Key To Armys Capture of Hussein; Link Diagrams Showed Everyone Related by Blood or Tribe (Washington Post, December 16, 2003) – Six Degrees of Mohamed Atta, byThomas A. Stewart, (Business 2.0, December 01, 2001)Courtesy Valid Krebs – orgnet.com 57
  • Mark Lombardi Example • Known for his “conspiracy art” • Looked at the Iran- Contra Affair and links between global finance and international terrorism 58
  • HP Email Example Week by week evolution of an email networkBernardo A. HubermanHP Senior Fellow and Director of the Information Dynamics Labhttp://www.hpl.hp.com/research/idl/ 59
  • Military Email Analysis Example• Problem / Issue: Warfighters are faced with increasingly complex command and control (C2) networks – Increasing number of IP networks, communication networks, and applications all creating a complex information environment – Warfighter’s capability and effectiveness of new applications and networks are difficult to analyze – Traditional C2 analyses limited to IT performance and human interface• Possible Solution – New complex network analysis techniques can now be applied to define the structure, dynamics and evolution of collaboration in command and control network – Techniques enable the analysis of how warfighters actually use networks, as opposed to how engineers tell us how to build them – Metrics can be used in defining and measuring new information architectures 60 ©2005 Alidade Incorporated. All Rights Reserved
  • Military Email Analysis Example• Introduction of analysis method within CJTFEX 04-2 (a 12-day joint US/UK naval exercise)• Analysis Focus - Email – The analysis is applicable to a wide range of networks, email used as a stepping stone – Email is the primary method of asynchronous electronic communication in the Information Age – Indicates structures of collaboration and command and control 61 ©2005 Alidade Incorporated. All Rights Reserved
  • Questions for Analysis1. Does the email cross domain solution change previously established operating procedures?2. Who are the key nodes for email traffic flow?3. How robust is the email network in light of the removal of nodes and/or links?4. How does the structure of the email network evolve over the course of the experiment?5. What are the internal dynamics of select sub-networks and how to the sub-networks interact with each other? 62 ©2005 Alidade Incorporated. All Rights Reserved
  • Question #1 Does the email cross domain solution (CDS) change previously established operating procedures?• We found: – CDS increased integration between US and UK networks – Additional baseline information required to fully define cross domain email need and use• Method supports: – Defining role for individual liaison officers 63 ©2005 Alidade Incorporated. All Rights Reserved
  • Question #1 Aggregate Network of UK Interactions = UK = US 64 ©2005 Alidade Incorporated. All Rights Reserved
  • Question #2 Who are the key nodes for email traffic flow?• Based on multiple metrics, we found: – J2 ACOS – Information Operations – Asst. JOC Watch• Method supports: – Developing network defense for most important nodes – Providing input to plans for graceful degradation of capability – Examining use of method to exploit adversary networks and C2 structure 65 ©2005 Alidade Incorporated. All Rights Reserved
  • Question #2 Collaboration Measures tors s ster 10 0 00 d ca ra r oa abo B r s 0 ive 0 0 0 10 10 Rec e Coll ) ut ko 0 0 e e( 10 10 gr t- De ) k in Ou ( ee r g De n- 10 Timeframe Receive 0Only Xmit Only Xmit & I 1 Receive Day 6 1200- 684 (56%) 91 (7%) 441 (36%) 1800 1 1 66 Day 8 1200- 894 (58%) 146 (10%) 504 (33%) 1800 ©2005 Alidade Incorporated. All Rights Reserved
  • Question #3 How robust is the email network in light of the removal of nodes and/or links?• We found: – Resilient to random node removal – Vulnerable to targeted node removal – Network structure makes rapid recovery possible• Method supports: – Critical node placement in distribution of staff – Development of alternate C2 paths – Improving node counter-targeting 67 ©2005 Alidade Incorporated. All Rights Reserved
  • Question #3 Robustness Measurement Robustness Measurements Detailed Timeframe – Day 8 1200-1800 (6/15 1200-1800) 1600 1550 1500 1450 Size of Giant Component 1400 1350 Degradation 1300 is not linear 1250 1200 1150 1100 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Number of Nodes Deleted Targeted Random 68 ©2005 Alidade Incorporated. All Rights Reserved
  • Question #4How does the structure of the email network evolve over the course of the experiment?• We found: – Network structure follows staff daily battle rhythm, significant events did not alter the network structure – Distance to get information from one person to another remained roughly constant• Method supports: – Re-engineering networks based on user behaviors to assist in meeting warfighter requirements 69 ©2005 Alidade Incorporated. All Rights Reserved
  • Network Progression (DayQuestion #4 5) = US & UK 70 ©2005 Alidade Incorporated. All Rights Reserved
  • Question #5 What are the internal dynamics of select sub-networks and how to the sub-networks interact with each other?• We found: – Structures of the sub-networks were very different from entire CJTFEX email network, the CJTFEX was scale-free, the staff sub- networks were not – Identifiable nucleus of communications in each staff – The two nuclei of Staff #1 and Staff #2 were well-connected – Using different link definitions (reciprocal, threshold) can provide additional information about the network• Method supports: – Development of techniques to split staffs between assets 71 ©2005 Alidade Incorporated. All Rights Reserved
  • Question #5 Network Diagram Staff #2 Sub-Network Interactions – Entire Exp. (Reciprocal Link Definition) = nucleus node 72 ©2005 Alidade Incorporated. All Rights Reserved
  • Potential Futures Implications• William Gibson famously said that “the future is already here; it’s just unevenly distributed”• Futurists try to identify where critical distribution points in society are and monitor them for change – Futurists study emerging trends and new ideas in societies and how they spread – Futurists pride themselves on being able to identify early adopters at the beginning of the innovation “S-curve”• Many tried and true techniques to perform these identifications – Environmental scanning, interviewing experts and trend-setters, etc.• Techniques missing from the futurist toolbox are mathematical methods and models to determine how fast an idea, concept, or innovation will spread through a fixed network – Are there new rules, laws that we should know and codify? 73
  • Potential Futures Implications• In Duncan Watts’ book Six Degrees, he outlines a network theory- based explanation of how innovations are adopted by social networks• Not only the predilection one has to change that determines success of an innovation, but also how many “neighbors” an individual has that have potential to exert influence• Discovered that a determination of how likely innovations spread through a society can be made by examining a network for a large connected group of early adopters• It is not the resilience of the individual, but network connectivity that is the primary obstacle to the diffusion of an innovation throughout society• Success of innovations really has little to do with the actual innovation or innovator and more to do with the structure of the network that it is introduced in 74
  • Potential Futures Implications• Possible philosophical shift in futures thinking?• A move away from discrete forecasting and scenario planning?• “Instead of long-term planning, the aim should be to create the conditions most conducive to a process of continuous change.” – Chaos, Management And Economics: The Implications of Non-Linear Thinking, David Parker and Ralph Stacey, 1994 75
  • Potential Futures Applications• Complex network principles are ones that all futurists should be familiar with• Should we concentrate less on the “what” of the future and more on the “how” and “why”?• Structure and process – Possibility Networks – Are we walking in the neighborhood of Hari Seldon?• Discussion – What can we do with complex network theory? – Modifications of old tools, development of new tools – Role of APF in next steps 76
  • IV. Demonstration 77
  • Questions? 78