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An exploration of complex network theory and its potential uses for futures. A presentation to the Association of Professional Futurists.
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“Possibility Networks”An Exploration of Complex Network Theory and
Its Potential Uses for Futures
For the Association of Professional Futurists Professional Development Seminar
Chicago, IllinoisJuly 29th, 2005
By: David A. Jarvis
2
An Opening Thought…
“The greatest challenge today, not just in cell biology and ecology but in all of science, is the accurate and complete description of complex systems. Scientists have broken down many
kinds 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
3
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?
4
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
5
Introduction
I. History and Background
II. Scientific Basics
III. Examples and Applications
IV. Demonstration
6
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.)
7
• 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
Definition of a Complex Network
8
I. History and Background
9
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
10
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
11
Buttons and Strings
12
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
13
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
14
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
15
Scale-Free Networks
• Poisson distributions vs. power-law distributions– Power law example: distribution of wealth
Normal (Poisson) Distribution Power-Law Distribution
Number of links (k) Number of links (k)
Nu
mb
er
of
no
de
s w
ith k
lin
ks
Nu
mb
er
of
no
de
s w
ith k
lin
ks Most nodes have the same number of links
Large number of nodes have few links
Small number of nodes (hubs) have many links
Adapted from: Linked, Barabási , pg. 71
16
Related Topics
• Fads• Memes • Chaos Theory• Social Networking• Diffusion of Innovations• Contagion• Agent-Based Modeling• Collective Robotics and Distributed Systems• Emergence
17
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
18
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
19
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
20
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
21
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 – Background30:00 - 36:00 – Contact Network Epidemiology
22
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
23
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
24
Emergence
“I begin to think that this matter of ‘late emergent properties’ that the physicists talk about when they discuss complexity and cascading sensitivities is an important concept for historians. Justice may be an late 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
25
Social Networking• Definition – business
and social networking services
• Relation – uses complex network principles like “small worlds” and “six degrees of separation”
• Examples– Friendster
– Orkut
– Yahoo 360
– MySpace
– Ryze
26
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
27
Complex Network Literature
• Multi-disciplinary
• Most works are fairly recent
• Still no definitive academic textbook on complex networks
• Three levels– Metaphor– Popular Scientific– Technical
28
Metaphor
• The Tipping Point: How Little Things Can Make a Big Difference by Malcolm Gladwell (2000)
• The Rise of the Creative Class: And How It's 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)
29
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)
30
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
31
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
32
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
33
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
34
II. Scientific Basics
35
Network Theory Basics
• Types of networks• Classes of networks
– Technological– Social– Biological (Ecological)– Information
• Examples• Important network properties• Software applications
36
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)
37
Types of Networks
Minimally connected Maximally connected
38
Types of Networks
Erdös random network Random network w/growth
39
Types of Networks
Regular network (lattice) Small world network
40
Types of Networks
0
2
4
6
8
10
12
1 2 3 4 5 6 7 8
“Scale Free,”Power Law
Scale-free network w/preferential attachment
41
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 Web
Source: Newman, M. E. J., The structure and function of complex networks
42
THE INTERNET
Technological Networks
Source: Hal Burch and Bill Cheswick, Lumeta Corp
43
Technological Networks
AIRLINE ROUTE MAP
Source: Continental Airlines
44
ENRON EMAIL DATA
Social Networks
45
Social Networks
HIGH SCHOOL DATING
Source: 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).
46
Biological Networks
FOOD WEBSource: Freshwater food web: Neo Martinez and Richard Williams
47
Information Networks
2004 Election “Blogosphere” Source: HP Labs
48
• 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
Important Network Properties
49
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
50
Characteristic path length (CPL)
CPL = 1.5 (median of the averages)
0
1
1
2
1
1
F
1.2
1.4
1.8
2.0
1.2
1.6
Avg
11211F
01212E
10322D
23012C
12101B
22210A
EDCBA
D
Link/node ratio = 1.33 (8 links, 6 nodes)
Important Network Properties
Degree distribution (histogram)
0
1
2
3
1 2 3 4 5 6 7 8
# of connections per node
# o
f n
od
es
Nodes
LinksA
B
C
E
F
2
3
42
4
1Degree
51
A
B
C D
E
F
Clustering coefficient
C = 3 x 3 / 34 = ~0.26
nodes of triplesconnected ofNumber
trianglesof #x 3C
Betweenness - Can be used as a measure of network resilience
ikjng
kjg
inC
g
ngnC
ijk
jk
iB
kj jk
ijkiB
contain that and actors linking )(geodesics pathsshortest of # )(
and actors two thelinking )(geodesics pathsshortest of #
nodefor centrality ss Betweenne)(
)()(
Important Network Properties
52
Source: Newman, M. E. J., Random graphs as models of networks
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
Robustness - What fraction of nodes need to be removed to destroy the giant component in a power-law graph?
)(1
)(
ck
c
Hf
Important Network Properties
53
Selected Scale-Free Networks
Source: Newman, M. E. J., The structure and function of complex networks
Network Type n l z d α C(1) C(2) r
SocialE-mail messages
Directed 59,912 86,300 1.44 4.95 1.5/2.0
0.16
SocialFilm actors
Directed 449,913 25,516,482 113.43 3.48 2.3 0.20 0.78 0.208
InformationWWW nd.edu
Directed 269,504 1,497,135 5.55 11.27 2.1/2.4
0.11 0.29 -0.067
BiologicalProtein interactions
Undirected 2,115 2,240 2.12 6.80 2.4 0.072 0.071 -0.156
BiologicalMetabolic network
Undirected 765 3,686 9.64 2.56 2.2 0.090 0.67 -0.240
TechnologicalElectronic circuits
Undirected 24,097 53,248 4.34 11.05 3.0 0.010 0.030 -0.154
TechnologicalInternet
Undirected 10,697 31,992 5.98 3.31 2.5 0.035 0.39 -0.189
Technological Peer-to-peer network
Undirected 880 1,296 1.47 4.28 2.1 0.012 0.011 -0.366
n = number of nodesl = number of linksz = mean degreed = mean node-node distance
α = exponent of degree distribution if distribution follows a power-lawC = clustering coefficient r = degree correlation coefficient
54
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
55
III. Examples and Applications
56
Symantec Example• Computer Worm Simulator
57
Terrorist Network Example
Courtesy Valid Krebs – orgnet.com
• 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 Army's 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)
58
Mark Lombardi Example
• Known for his “conspiracy art”
• Looked at the Iran-Contra Affair and links between global finance and international terrorism
59
HP Email Example
Bernardo A. HubermanHP Senior Fellow and Director of the Information Dynamics Labhttp://www.hpl.hp.com/research/idl/
Week by week evolution of an email network
60
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
©2005 Alidade Incorporated. All Rights Reserved
61
• 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
Military Email Analysis Example
©2005 Alidade Incorporated. All Rights Reserved
62
Questions for Analysis
1. 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?
©2005 Alidade Incorporated. All Rights Reserved
63
• 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
Question #1Does the email cross domain solution (CDS) change previously
established operating procedures?
©2005 Alidade Incorporated. All Rights Reserved
64
Aggregate Network of UK Interactions= UK= US
Question #1
©2005 Alidade Incorporated. All Rights Reserved
65
• 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
Question #2Who are the key nodes for email traffic flow?
©2005 Alidade Incorporated. All Rights Reserved
66
Collaboration Measures
1
10
100
1000
1 10 100 1000 10000
Out-Degree (kout)
In-D
egre
e (k
in)
Broadcasters
Receivers
Collaborators
Timeframe Receive Only
Xmit Only
Xmit & Receive
Day 6 1200-1800
684 (56%) 91 (7%) 441 (36%)
Day 8 1200-1800
894 (58%) 146 (10%) 504 (33%)
Question #2
©2005 Alidade Incorporated. All Rights Reserved
67
• 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
Question #3How robust is the email network in light of the removal of nodes
and/or links?
©2005 Alidade Incorporated. All Rights Reserved
68
Robustness MeasurementDetailed Timeframe – Day 8 1200-1800
1100
1150
1200
1250
1300
1350
1400
1450
1500
1550
1600
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
Siz
e o
f G
ian
t C
om
po
nen
t
Targeted Random
Degradation is not linear
Question #3
©2005 Alidade Incorporated. All Rights Reserved
69
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
©2005 Alidade Incorporated. All Rights Reserved
70
Network Progression (Day 5)Question #4
= US & UK
©2005 Alidade Incorporated. All Rights Reserved
71
• 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
Question #5What are the internal dynamics of select sub-networks and
how to the sub-networks interact with each other?
©2005 Alidade Incorporated. All Rights Reserved
72
Network DiagramStaff #2 Sub-Network Interactions – Entire Exp.
(Reciprocal Link Definition)
= nucleus node
Question #5
©2005 Alidade Incorporated. All Rights Reserved
73
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?
74
• 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
Potential Futures Implications
75
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
76
• 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
Potential Futures Applications
77
IV. Demonstration
78
Questions?