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  • INTER-FACULTY MASTER PROGRAM on

    COMPLEX SYSTEMS and NETWORKS SCHOOL of MATHEMATICS

    SCHOOL of BIOLOGY SCHOOL of GEOLOGY

    SCHOOL of ECONOMICS ARISTOTLE UNIVERSITY of THESSALONIKI

    Net Awareness 1: History

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    05-12-2014

  • Networks History

    600 X

  • Networks History 500 , : , [. 41]. , , , [. 10].

  • Networks History Parts-Whole Analysis-Synthesis, Modular Decomposition 390 : , , , . [ 265,] First, the taking in of scattered particulars under one Idea, so that by precise definition, everyone understands what is being talked about ...Second, the analysis of the Idea into parts, by dividing it at the joints, naturally, not breaking any part as a bad carver might." [Plato, Phaedrus, 265d,e]

  • Networks History System 390 : , , , , [ 991] for it is necessary to explain it thus far: every diagram, and system of number, and every combination of harmony, and the agreement of the revolution of the stars must be made manifest as one through all to him who learns in the proper way, and will be made manifest if, as we say, a man learns aright by keeping his gaze on unity

    [Plato Epanomis 991e]

    Nearness Affinity Eros E- [ . 191], [ . 195],

  • Networks History 330 ' , , . ' . , ' , , , , 1045 9-19. , . . . , the whole is more than the sum of its parts.

  • Networks History -agasena ~120 X Nagasena: just as the King's chariot is neither its wheels nor its framework nor its axle nor its pole, nor its ropes, neither is man his matter, form, impressions, ideas, instincts or consciousness, nor the combination of these parts, nor does man exists outside them. . .

    King Milinda of Bactriana: It is all these things, the wheels and the framework and the axle and the pole and the ropes,

    in their interdependence that give the denomination chariot"

    The Questions of King Milinda (Milinda Panha) The Chariot Story is quoted by BORGES J. L. 1962 Translations: Rhys T.W. 1890 and Horner I.B. 1969 in Labyrinths, New Directions, New York

    Hutchinson 1934 Story of the Nations,

    Hutchinson and Co., London. ~130

    http://www.coinarchives.com/a/lotviewer.php?LotID=84652&AucID=90&Lot=1029

  • Networks History 60 [ 12: 25]

  • Networks History 180 , : , , . , , , [ , (7,9)].

  • Networks History 1272 A visually spare, elegant record of English history from Alfred the Great (87199) to Henry III (121672), includes 23 roundel portraits of English kings Rosenberg D. and Grafton A. 2010,

    Cartographies of Time Princeton Architectural Press, New York.

  • Networks History 1585 Lorenz Faust Anatomia statuae Danielis Rosenberg D. and Grafton A. 2010,

    Cartographies of Time

    Princeton Architectural Press,

    New York.

  • Networks History Isaac Newton 1700 To Newton I Newton Trinity College, Cambridge,

    32TUhttp://cudl.lib.cam.ac.uk/view/MS-ADD-03996/5U32T

    http://cudl.lib.cam.ac.uk/view/MS-ADD-03996/5http://cudl.lib.cam.ac.uk/view/MS-ADD-03996/5http://cudl.lib.cam.ac.uk/view/MS-ADD-03996/5http://cudl.lib.cam.ac.uk/view/MS-ADD-03996/5http://cudl.lib.cam.ac.uk/view/MS-ADD-03996/5http://cudl.lib.cam.ac.uk/view/MS-ADD-03996/5

  • Euler L. 1736, The 7 Bridges of Konigsberg Is there a path crossing all 7 bridges of Konigsberg exactly once each? Leonard Euler used graph theory to prove that there is no such path. Solutio problematic ad Geometriam situs pertinentis, Comm. Academiae Petropolitanae, 8, 128-140.

    Paths in GRAPHS Graph Theory and Network Theory The mathematical language for describing Interdependence.

  • Paths in GRAPHS (Strokes) o 9 , 4

  • Paths in GRAPHS (Strokes) o 9 , 4 Graph Embedding ()

  • Euler L. 1752 Polyhedral Formula

    , V , F E: + = 2 he foundation of graph theory

  • - Chemical Affinity Networks Alchemy Newton Cayley A. 1875 Trees Sylvester 1878 Graphs

  • 1845 Kirchhoff G. Circuit Laws (current and voltage laws) Kirchhoff G. 1845, Ueber den durchgang eines elektrischen stromes durch eine ebene, insbesondere durch eine kreisformige. Poggendroffs Ann. Physik Chemie 64(1), 497514. generalized circuit theory information networks Watanabe H. 1993, A basic theory of information network,

    IEICE Transactions on Fundamentals; E76-A(3), 265276.

    Kirchhoff G. 1847, Ann Physik Chemie, 72:497508.

    English translation, IRE Trans Circuit Theory, CT5 (1958)4-7

  • 1895 Henri Poincar Topology Algebraic Topology. Topology Algebra Graphs Poincar, Henri, "Analysis situs", Journal de l'cole Polytechnique ser 2, 1 (1895) pp. 1123

    1900 Poincare Incidence Matrix H. Poincare 1900, Second complement de l'Analysis Situs, Proc. London Math. Soc. 32, 277-308.

    Extension of Kirchhoff Circuit Laws Graphs as Abstract Geometry Biggs N., Lloyd E. and Wilson R. 1977, Graph Theory 1736-1936, Clarendon Press, Oxford

  • 1899 Henri Poincar Dynamical Systems Topological Dynamics Non-Integrability Chaos Differential Equations as Dynamical Systems Solvay 2011 The value of the unknown variable as a function of the initial condition Previously the unknown variable was considered as a function of the the independent variable (time) Orbits, Phase Portrait, Stability, Periodicity, Recurrence Statistical Analysis of Dynamical Systems Analytic Non-Integrability of the 3-Body Problem (Chaos)

  • Moreno Jacob 1934 Freud 1912 Freud asked him what he was doing Well, Dr. Freud, I start where you leave off. You meet people in the artificial setting of your office. I meet them on the street and in their homes, in their natural surroundings. You analyze their dreams. I give them the courage to dream again. You analyze and tear them apart. I let them act out their conflicting roles and help them to put the parts back together again. Mathematics, philosophy, medicine interpersonal relations Psychodrama group psychotherapy Sociometry Social Networks Analysis quantitative evaluation of the role of an individual in a group or community by analysis of the network of connections between them and others. 1934 Who Shall Survive? earliest graphical depictions of social networks

  • Moreno Jacob 1934 Sociometry Social Networks Analysis role of individuals in a group or community by analysis of the network of connections between them and others. Communities in a Network earliest social networks 1934 Who Shall Survive?

  • Moreno Jacob 1934 Sociometry Social Networks Analysis Roles and Communities From Relations

  • The Role of Nodes in a Network as a consequence of the Link Topology is assessed by the Centrality Indices Camille Jordan (1838-1922) for Trees Jordan C. 1869, Sur les assemblages des lignes, J. Reine Angew. Math. 70, 185190 Permutations Jordan Form of Matrices Jordan Curve in the Complex Plane Jordan Measure

  • Herbert Spencer 1880 Interdependence as Evolutionary Integration 1) Universality of natural law. The laws of nature applied without exception, to the organic realm as much as to the inorganic, and to the human mind as much as to society. 2) Evolution of Complexity. All structures in the universe develop from a simple, undifferentiated, homogeneity to a complex, differentiated, heterogeneity, a process of greater integration of the differentiated parts. A universal law, applying to the stars and the galaxies as much as to biological organisms, and to human social organization as much as to the human mind. 3) Individual and Social Evolution Increase of social aggregates accompanied by increase of the complexity of structures and Interdependence Creation of specialized social roles and institutions Spencer H. 1855-1880, A System of Synthetic Philosophy 10 volumes, Williams and Norgate, London

    1902 Spencer was nominated for the Nobel Prize for literature.

  • Pareto 1897 Power Law Distribution Pareto collected data and Observed that 80% of Italy's land was owned by 20% of the population

    x =

    +1,

    0 , <

    Pareto Principle (8020 rule) 80% of the Effects come from 20% of the Causes () () Pareto V. 1897, Cours dEconomie Politique, Lausanne Pareto V. 1906, Manuale di Economia Politica, Milano, Societa Editrice Libraria. English translation: Manual of political economy, by A.M. Kelley, 1971, ISBN 978-0-678-00881-2

  • Pareto 1906 Collective Utility Interdependence Society as System Pareto Improvement of an Allocation of Goods among a set of agents is a change to a different allocation that improves at