Adaptive Systems Lecture 3: Natural Systems part 2

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Adaptive SystemsLecture 3 Natural Systems
(part 2)

• Dr Giovanna Di Marzo Serugendo
• Department of Computer Science
• and Information Systems
• Birkbeck College, University of London
• Email dimarzo_at_dcs.bbk.ac.uk
• Web Page http//www.dcs.bbk.ac.uk/dimarzo

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Lecture 2 Review

• Non-living systems
• Pattern formation
• Living systems
• Pattern formation
• Animals
• Plants
• Collective behaviour
• Micro-organisms (cells)
• Animals Social Behaviour
• Swarms

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Lecture 3 Overview

• Living Systems
• Human Social Behaviour
• Human Social Networks
• Small-Worlds
• Scale-Free Networks
• Trust and Reputation
• Gossip
• Markets

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Human Social Networks

• Social network (Defined by J. A. Barnes, 1954)
• Social structure between individuals or
  organisations
• Indicates the ways in which individuals or
  organisations are connected
• Casual acquaintances
• Family links
• Different levels families, friends, nations
• Play a role in
• resolution of problems, organisations,
  individuals success

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Human Social Networks

• Online social networks
• Internet applications
• connect friends, business partners, or other
  individuals together using a variety of tools.
• https//www.linkedin.com (links of trust
  contacts)
• http//360.yahoo.com, http//www.myspace.com/
  (shared spaces, emails, blogs, etc.)
• http//www.facebook.com

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Social Networks

• Social Network
• Nodes Individuals
• Links ties among individuals
• Network map of ties among the different
  considered individuals
• Tight networks
• Open networks (with weak ties)
• Better for reaching other communities

Adaptive Systems - Giovanna Di Marzo Serugendo
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Complex Networks

• Analysis of the network structure
• Study of the complexity in the network structure
• Network is a graph
• G P, E
• P set of nodes
• E set of links
• Topologies
• Regular graphs
• Random graphs
• Small-world graphs
• Scale-free graphs

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Complex Networks

• Regular Graphs

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Complex Networks

• Random Graphs
• n nodes, m links inserted at random
• If m gt n/2
• Single giant components
• No hubs
• Short paths

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Complex Networks

• Small-World Network
• Start from a regular network
• Rewire some original links with a probability in
  0,1
• Transform into small-world network
• Short paths between two nodes
• High clustering coefficient
• Heavily linked clusters

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Complex Networks

• Scale-free networks
• New nodes attached at random to existing nodes
• Probability of attachment
• Proportional to degree of node
• The more a node is linked the more it is
  attractive
• Formation of hubs

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Small-Worlds

• Small-world phenomenon (or effect)
• Hypothesis
• Everyone in the world can be reached through a
  short chain of social acquaintances.
• Initial experiment
• Stanley Milgram, social psychologist, 1967
• 60 people have to send a letter to a specific
  person
• Means available pass the letters (by hand) to
  personal acquaintances who could reach the target
  (directly or via a friend)
• 1 letter reached target within 4 days
• Two random US citizens are connected by an
  average of a chain of six acquaintances
• Funneling effect small number of nodes with high
  connectivity
• Six degrees of separation

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Small-Worlds

• 6 degrees of separation
• Not formally proved for whole world
• Several small worlds inside whole world
• Erdos number (among mathematicians)
• Number of published papers
• Erdos 1500 papers, most co-authored
• Erdos number 1 if co-authored with Erdos
• Erdos number 2 if co-authored with Erdos
  co-author, etc
• http//www.oakland.edu/enp/
• Kevin Bacon number (among actors)
• Number of movies were actors appear together with
  Bacon
• http//en.wikipedia.org/wiki/Bacon_number

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Small-Worlds Networks

• Networks
• Watts, Strogatz, 1998
• First network model on the small-world phenomenon
  
• Natural networks, man-made networks (neural
  networks, computer networks, grids) show
  small-world property
• addition of a small number of random links
  reduces the networks diameter

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Small-Worlds Networks

• Small-World network
• Complex Network (non-trivial topological
  structure)
• Generalisation of the small-world phenomenon
• Characteristics
• Connectivity is not confined to a certain scale
• Every node can be reached from every other by a
  small number of hops or steps.

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Small-Worlds Networks

• A graph is small-world if
• High clustering coefficient
• One node
• Clustering coefficient of whole system
• Average on each node
• Measures connectivity
• Mean-shortest path length
• Small average length of the shortest path

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Small-Worlds Networks

• Properties
• High clustering
• High number of sub-networks
• All nodes in sub-networks connected directly
• Mean-shortest length path
• Almost any two nodes in two sub-networks are
  connected by a short path

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Small-World Networks
http//fred.bioinf.uni-sb.de4711/homepages/schaef
er/images/4_protein_network_large.jpg

• Examples
• Natural World
• Proteins networks
• Man-made world
• Road maps
• Food chains
• Electric power grids
• Telephone graphs

http//www.tburg.k12.ny.us/mcdonald/web.jpg
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Scale-Free Networks

• Scale-Free Networks
• Small-World Networks
• High number of Hubs
• Nodes with high connectivity
• Self-similarity
• Parts are similar to the whole
• Fractals

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Scale-Free Networks

• Scale-free networks
• Networks' structure is independent of the number
  of nodes the system has.
• Same properties, independently of number of nodes
• Probability that a node connects with k other
  nodes
• P(k) k-? - power law (independent of scale)?

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Scale-Free Networks

• Examples
• Flights pass through hubs
• Few connections for each trip
• Internet
• Web pages links are scale-free
• New site will have links to well-known existing
  sites
• Geographic connectivity of Internet nodes is
  scale-free
• Web interests group connected is scale-free way
• E-mails propagation is scale-free
• Robust against random perturbations
• Removal of peripheral node (not hub) does not
  affect mean-shortest path length
• Weak against hub attacks

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Reputation

• Reputation
• General opinion of the public toward a person, a
  group of people, or an organisation
• Transmitted belief about properties related to X
• Meta-belief belief about belief
• Anonymous
• From individual belief to social propagation
  (meta-beliefs)
• Propagation of reputation
• Through recommendations / gossip
• Act as distributed, spontaneous social control

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Reputation

• Recommendation (not anonymous)
• Precise or vague (gossip)
• 3 categories
• A declares that it believes the potential partner
  B is (is not) good for property p
• A declares that it believes that another agent C
  believes that the potential partner B is (is not)
  good for property p
• A declares that it believes that in an undefined
  set of agents, there is a belief that the
  potential partner B is (is not) good for property
  p
• Additional characteristics
• Different levels of truth wrong, lie, etc.

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Reputation

• Dynamic phenomenon
• Subject to change
• Adaptation of reputation/recommendation based on
  experiences, errors, etc.
• Emerges as an effect of a multi-level
  bidirectional process (from society to individual
  and vice-versa)
• Examples
• Credit cards (trusted third party)
• E-Commerce (in general)
• Social software / online communities
• Tools for people to connect and form online
  communities
• Mailing lists, chats, blogs, virtual worlds,
  massively multi-players online games
• Based on trust and reputation

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Reputation

• Reputation Management
• Recording of
• Agent's actions
• Opinions of others about those actions
• Records are published / made known
• to allow other agents to make informed decisions
• Ranking and Rewarding Systems
• eBay
• users can record positive or negative feedback
  about buyers or sellers

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Gossip

• Definitions
• Light informal conversation for social occasions
  WorldReference.com dictionary
• Rumour or talk of a personal, sensational, or
  intimate nature Merriam-Webster online
  dictionary
• Mechanism
• Periodic exchange and update of information among
  members of a group
• Allows aggregation of global information inside
  a population, social learning
• Parameters neighbourhood, level of precision of
  information
• Metaphor
• Information spreading, knowledge exchange, group
  organisation
• Applications
• P2P systems protocols, sensor networks protocols

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Trust

• Human notion of trust
• Uncertainty and partial knowledge
• Human beings make choices, take decisions, learn
  by experience, adapt their behavior
• Decisions implicitly rely on trust
• Peers
• Legal institutions
• Business companies

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Trust

• Trust Measures
• Level of confidence of agent A towards agent B
  about property P
• Value
• Built on
• Reputation management
• Recommendations / Gossip propagation
• Direct interactions / Experiences

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Markets
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Markets

• Market (Economics)
• Theoretical model in which buyers and sellers
  interact to optimize certain variables such as
  utility or profit.
• Utility
• Measure of the satisfaction gained consuming good
  and services
• Economic behaviour explained in terms of rational
  attempts to increase one's utility

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Markets

• Utility function (microeconomics)
• Describes the preferences of consumers wrt goods
  
• u X ? R
• X set of Goods, R Real numbers
• u(x) gt u(y) user prefers x to y

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Financial Markets

• Financial market
• Mechanism allowing people to trade
• theory of supply and demand
• price mechanism
• bid and ask process
• Supply and Demand
• Supply (S curve) availability of good at price p
• Demand (D curve) request for good at price p
• Price equilibrium point
• If demand increases, then price will increase too

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Financial Markets

• Financial market
• Bid and ask
• Bid offer to pay a fixed amount that is held
  open for a period of time
• Ask offer to sell for a fixed amount that is
  held open for a period of time
• Matching pair Bid-Ask
• Transaction

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Financial Markets

• Types of financial markets
• Stock markets, bonds markets, money markets,
  commodities markets, insurances markets

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Business Theories

• Feedbacks
• Positive feedback
• Amplification of phenomenon
• Example
• Rumours turn to be true
• More income causes more spending which causes
  more income
• Expectations e.g. consumer confidence
• Prosperous economy ? optimism ? increase
  prosperity
• Bad economy performance ? pessimism ? decrease
  economy performance
• Dampening feedback
• Towards stabilisation of economy
• Stops increasing loops
• Macroeconomic policies should lead economy
  towards stabilisation

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Game Theory

• Game Theory
• To analyse economic phenomena
• Voting systems, coalition formation, auctions,
  social networks
• To provide a theory of economic and strategic
  behavior when people interact directly
• Based on sets of strategies known as equilibria
  in games
• Historically
• Introduced by John Von Neumann for military
  strategy

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Game Theory

• Game Theory
• Playing a game
• Choices/Strategies of individuals depend
• on his own choices
• choices/strategies of the other members of the
  group
• Predictions about
• Choices of rational game players
• Consequences for the whole group
• Best rational choice for individuals may lead to
  worst outcome for all.

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Game Theory

• Set of players i 1, ..., n
• Each player has a set of m actions or strategies
• Let ai be the action chosen by i
• Let a (a1, ..., an)?
• Payoff (reward) of player i given by Mi(a)?
• Goal of players maximise their own payoff

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Game Theory

• Equilibrium
• No player can improve its current strategy
• Different types of equilibrium
• Nash equilibrium no communication among players
• Correlate equilibrium communication via
  correlation
• Cooperative equilibrium communication and
  coalition

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Game Theory

• Nash Equilibrium
• A set of strategies is a Nash equilibrium if
  each strategy represents a best response to the
  other strategies
• Players are in equilibrium if a change in
  strategies by any one of them would lead that
  player to earn less than if she remained with her
  current strategy
• Collective best choice
• Not necessarily individual best solution

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Prisoners Dilemma

• Classical Prisoners Dilemma
• Two suspects, A and B, are arrested by the
  police. The police have insufficient evidence for
  a conviction, and having separated both
  prisoners, visit each of them and offer the same
  deal
• If one testifies for the prosecution against the
  other and the other remains silent, the silent
  accomplice receives the full 10-year sentence and
  the betrayer goes free.
• If both stay silent, the police can only give
  both prisoners 6 months for a minor charge.
• If both betray each other, they receive a 2-year
  sentence each.
• Each prisoner must make a choice - to betray the
  other, or to remain silent. However, neither
  prisoner knows for sure what choice the other
  prisoner will make.

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Prisoners Dilemma

• Dilemma occurs if
• Each prisoner is self-interested
• Each prisoner wants to maximise his own advantage
• Wants to minimise his jail period
• No one can trust the other
• No one knows the other choice

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Prisoners Dilemma

• Nash Equilibrium (collective strategy)
• Reached when both players choose betrays
• If A plays another strategy (and not B), then A
  receives 10 years jail
• If B plays another strategy (and not A), then B
  receives 10 years jail
• However
• total payoff obtained by both player is greater
  if both cooperate

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Prisoners Dilemma
If A changes strategy
Nash Equilibrium
If B changes strategy
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Tragedy of the Commons

• Agents selfishly act so as to increase their own
  rewards, global (long term) result is disastrous
  for all
• Pollution
• Energy usage
• Advertising
• Mortgage crisis
• http//www.steverrobbins.com/articles/tragedyofthe
  commons.htm

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Readings

• http//en.wikipedia.org/wiki
• Castelfranchi 01 C. Castelfranchi. The theory
  of social functions challenges for computational
  social science and multi-agent learning. Journal
  of Cognitive Systems Research, 2(1)5--38, 2001.
• Stewart, 01 Stewart, M. (2001). The Coevolving
  Organization. Rutland, UK, Decomplexity
  Associates LtD.