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The power of Openness.
Irreversible Non - Hermitian Extensions of Quantum
                     Mechanics
  Open Data and Open Knowledge
                       I. Antoniou
                   Ioannis E. Antoniou
        CHAOS AND INNOVATION Research Unit
               Mathematics Department
               Mathematics Department
          Aristotle University of Thessaloniki
                   Aristotle University ,
                           54124
             54124 Thessaloniki, Greece
                 iantonio@math.auth.gr
                iantonio@math.auth.gr
                 iantonio@math.auth.gr


         3rd International Workshop on
                    2012-04-06
Pseudo-Hermitian Hamiltonians in Quantum Physics
• What is a Complex System?
Physico-Chemical Organization
Life
Brain-Mind
Socio-economic structures
Communication Networks
WWW
Complexity emerges in Open Systems Far From Equilibrium ?

Poincare, De Donder, Schroedinger
indicated the need
to extend thermodynamics
to Open Systems Far From Equilibrium.
Open Systems may receive Information
communicating with their Εnvironment.
Entropy S becomes the sum of
Internal Entropy SI and Entropy “Flow” SF
S = SI + SF
ΔS = ΔSI + ΔSF
ΔSI ≥ 0 the Internal Entropy (2nd Law)

Complex networks
Social networks
Web of Knowledge
What are the qualifying Features of Complex Systems?
1)   Far From Thermodynamic Equilibrium Structures [Ilya Prigogine]
     Complex Structures Self-Organize Dissipating Energy and/or Information!

2)   Innovation
     Complex Processes ⇔ Emergence-Creation of New Information
                           at each Stage Internal Time-Age Operator
     Complex Processes are not boring !

3)   Robustness
     Complex Processes ⇔ Structurally Stable Processes
     Why Complex Processes emerged in Nature !

4)   High Interdependence of the Constituent Units
     There is no constructive Way to represent the system
     in terms of disentangled fragmented independent components
     You cannot divide and conquer !

5) Distributed Non Local Processing
How to describe
Interdependence?

Graphs and Networks

The Structure of Complex Systems

Distributed Processing
Network
                                   Links

                   2


Nodes       1.2              0.5



                       0.2            3
        1



             2.1

                       4
The weight distribution defines
           Network Function




How many nodes are linked with k nodes
Crystals: The simplest netwotks
Telephone Networks are not Regular
         Renyi, Erdos 1960
PSTN
(Public Switched Telephone Network)
Random Networks
The Networks of Life
Are neither Regular nor Random!

Prigogine 1980
From Being to Becoming

Life operates between
The perfect predictable Crystals
and
The meaningless structuress Randomness

Study concrete Life Networks to identify
their qualifying features
The Networks of Life
!
2 new Networks were discovered!

 -Small Worlds
            Social Nets
            Εpilepsy
            Synchronization of Fireflies
                                  [Strogats, Watts 1998]

  -Self-Similar,Scale-Free Networks
            WWW
                             [Barabasi,Albert 1999]
Small Worlds

Small Communication Pathways
Six Degrees of Separation                                                          Kentaro
                                                                                   Toyama
Milgram (1967)                  Allan               Robert
                                                                     Mike
                               Wagner ?            Sternberg
                                                                     Tarr




                                 John Guare wrote the play
                                 Six Degrees of
                                   Separation,
                                 based on this concept.


“Everybody on this planet is separated by only six other people. Six degrees of
separation. Between us and everybody else on this planet. The president of the United
States. A gondolier in Venice… It’s not just the big names. It’s anyone. A native in a rain
forest. A Tierra del Fuegan. An Eskimo. I am bound to everyone on this planet by a trail
of six people…”
Small Worlds Distribution
Self-Similar Networks
Αναξαγοπαρ:
“αρχας των οντων ομοιομεπειαρ απεφηνατο” [Αετιος, DK 59A46]

Emelard tablet Alchemy:
«As above so below»




P(k) ~ k−γ Power Law
World-Wide Web power law
P(k) ~ k−γ
as Fractals
Real self-simlar networks
Friendships                Sexual             Terrorists
(Moody J., 2001)
                      Potterat et al (2002)




        Web)
                         Airlines
Brain-Web analogy
Brain as distributed Complex system (Web)
Web of Documents
• Analogy :
a global file system

• Primary objects :
documents

• Links between:
documents (or sub-parts of)

• Degree of structure in objects:
fairly low

• Semantics of content and links:
implicit

• Designed for:
human consumption
Web 2.0



•   Wikis
•   Blogs
•   Flickr
•   YouTube
•   MySpace
•   Facebook
Web 2.0
Web 2.0



DRAWBACKS :

• No data integration.

• Impossible to run queries in multiple data sources .

e.g. which diseases are related to the heart AND have a prevalence
>2% AND in 2010 there where >100 publications about them.
What is the Problem?
Consider a typical web page:
                               Markup consists of:
                                   rendering
                                   information (e.g.,
                                   font size and
                                   colour)
                                   Hyper-links to
                                   related content
                               Semantic content is
                               accessible to humans
                               but not (easily) to
                               computers…

                                                     25
Openness
Inter- operability
Semantic Processing
the Engineering solution of Nature for
managing Complexity

Open Knowledge Transfer
The unified open knowledge

The Vision of Encyclopaedists

Αristotle 384-322 BC
Denis Diderot
1713-1784




Jean-Baptiste
le Rond d'Alembert
1717 –1783
Mikhail Lomonosov 1711 –1765
Open Knowledge
Libetation of Intuition

Bringing people together
for max mutual benefit

Help us give meaning to our Life

OKFN the universal catalyst
in the Planetary Transmutation
Psycho-Cybernetics

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Antoniou: complex systems and web

  • 1. The power of Openness. Irreversible Non - Hermitian Extensions of Quantum Mechanics Open Data and Open Knowledge I. Antoniou Ioannis E. Antoniou CHAOS AND INNOVATION Research Unit Mathematics Department Mathematics Department Aristotle University of Thessaloniki Aristotle University , 54124 54124 Thessaloniki, Greece iantonio@math.auth.gr iantonio@math.auth.gr iantonio@math.auth.gr 3rd International Workshop on 2012-04-06 Pseudo-Hermitian Hamiltonians in Quantum Physics
  • 2. • What is a Complex System? Physico-Chemical Organization Life Brain-Mind Socio-economic structures Communication Networks WWW
  • 3. Complexity emerges in Open Systems Far From Equilibrium ? Poincare, De Donder, Schroedinger indicated the need to extend thermodynamics to Open Systems Far From Equilibrium. Open Systems may receive Information communicating with their Εnvironment. Entropy S becomes the sum of Internal Entropy SI and Entropy “Flow” SF S = SI + SF ΔS = ΔSI + ΔSF ΔSI ≥ 0 the Internal Entropy (2nd Law) Complex networks Social networks Web of Knowledge
  • 4. What are the qualifying Features of Complex Systems? 1) Far From Thermodynamic Equilibrium Structures [Ilya Prigogine] Complex Structures Self-Organize Dissipating Energy and/or Information! 2) Innovation Complex Processes ⇔ Emergence-Creation of New Information at each Stage Internal Time-Age Operator Complex Processes are not boring ! 3) Robustness Complex Processes ⇔ Structurally Stable Processes Why Complex Processes emerged in Nature ! 4) High Interdependence of the Constituent Units There is no constructive Way to represent the system in terms of disentangled fragmented independent components You cannot divide and conquer ! 5) Distributed Non Local Processing
  • 5. How to describe Interdependence? Graphs and Networks The Structure of Complex Systems Distributed Processing
  • 6. Network Links 2 Nodes 1.2 0.5 0.2 3 1 2.1 4
  • 7. The weight distribution defines Network Function How many nodes are linked with k nodes
  • 9. Telephone Networks are not Regular Renyi, Erdos 1960 PSTN (Public Switched Telephone Network) Random Networks
  • 10. The Networks of Life Are neither Regular nor Random! Prigogine 1980 From Being to Becoming Life operates between The perfect predictable Crystals and The meaningless structuress Randomness Study concrete Life Networks to identify their qualifying features
  • 11. The Networks of Life ! 2 new Networks were discovered! -Small Worlds Social Nets Εpilepsy Synchronization of Fireflies [Strogats, Watts 1998] -Self-Similar,Scale-Free Networks WWW [Barabasi,Albert 1999]
  • 13. Six Degrees of Separation Kentaro Toyama Milgram (1967) Allan Robert Mike Wagner ? Sternberg Tarr John Guare wrote the play Six Degrees of Separation, based on this concept. “Everybody on this planet is separated by only six other people. Six degrees of separation. Between us and everybody else on this planet. The president of the United States. A gondolier in Venice… It’s not just the big names. It’s anyone. A native in a rain forest. A Tierra del Fuegan. An Eskimo. I am bound to everyone on this planet by a trail of six people…”
  • 15. Self-Similar Networks Αναξαγοπαρ: “αρχας των οντων ομοιομεπειαρ απεφηνατο” [Αετιος, DK 59A46] Emelard tablet Alchemy: «As above so below» P(k) ~ k−γ Power Law
  • 17. P(k) ~ k−γ as Fractals
  • 18. Real self-simlar networks Friendships Sexual Terrorists (Moody J., 2001) Potterat et al (2002) Web) Airlines
  • 19. Brain-Web analogy Brain as distributed Complex system (Web)
  • 20. Web of Documents • Analogy : a global file system • Primary objects : documents • Links between: documents (or sub-parts of) • Degree of structure in objects: fairly low • Semantics of content and links: implicit • Designed for: human consumption
  • 21.
  • 22. Web 2.0 • Wikis • Blogs • Flickr • YouTube • MySpace • Facebook
  • 24. Web 2.0 DRAWBACKS : • No data integration. • Impossible to run queries in multiple data sources . e.g. which diseases are related to the heart AND have a prevalence >2% AND in 2010 there where >100 publications about them.
  • 25. What is the Problem? Consider a typical web page: Markup consists of: rendering information (e.g., font size and colour) Hyper-links to related content Semantic content is accessible to humans but not (easily) to computers… 25
  • 27. Semantic Processing the Engineering solution of Nature for managing Complexity Open Knowledge Transfer
  • 28. The unified open knowledge The Vision of Encyclopaedists Αristotle 384-322 BC
  • 31. Open Knowledge Libetation of Intuition Bringing people together for max mutual benefit Help us give meaning to our Life OKFN the universal catalyst in the Planetary Transmutation