Introduction to Physics of Complexity. Statistical physics of complex networks 1100-WFZ-OG

The evolving complex networks are the most significant global socio-economical structures that wind our planet playing a decisive role in our everyday life. This role is particularly well seen, for instance, during the blackout caused by failure in energetic network (e.g. as a result of a fatal error which unexpectedly appeared in the controling of this network by the computer software) or during the cascade of banks' bancruptcies caused by markets' crashes. Obviously, we see the fundamental role in our everyday life of the trading, telecommunication, and transportation networks. In particular, the internet introduced into our life a new quality being a source of true eruption of new ideas/innovations, knowledge and technologies. All these things based on modern social networks changed our life in sudden and critical ways.

Obviously, besides networks existing outside of us, there are strongly ramified bionetworks present inside of us, that have multiobject, multilevel and multiscale characters.

All these things (presented above) create new research methodologies and methods which are clearly and systematically presented during my lectures. They can be considered as an introduction to the complexity - a modern quickly developing brench of knowledge.

It should be emphasized that my lectures have inter-, multi,- and crossdisciplinary characters which are quite unique for the University of Warsaw.

Frame schedule of my lectures

I. Operational definition of complexity - a holistic approach
I. 1. The origin of complexity
I. 2. Complexity as a new paradigm
I. 3. Singnature of complexity
I. 4. The universal Turing machine and complexity
I. 5. Emergence of complexity and the arrow of time
I. 6. The role of computer simulations
I. 7. Synergy, coherence, complexity, emergence

II. Basic elements of graph theory (necessary for analysis of real
networks)
II. 1. Distriburion of vertices' degrees
II. 2. Clustring coefficient
II. 3. Small world networks
II. 4. Measures of centralities
II. 5. Correlations, scaling, and modularity in complex networks

III. Power laws
III. 1. Power-law distributions
III. 2. Phase transitions, critical phenomena, renormalization,
elements of catastrophe theory, fractals and fractal
networks, multifractality, percolation on complex networks
III. 3. Hamilton formalism of thermodynamcs for complex networks

IV. Canonical models of complex networks

V. Classification of complex networks
- static networks
- evolving networks
- deterministic networks
- random networks

VI. Examples of real complex networks
VI. 1. Structure, topology, and dynamics of social networks
VI. 2. Damages of complex networks (e.g. by terrorist attacks)
VI. 3. Spreading of epidemies in complex networks
VI. 4. Biological networks

Main fields of studies for MISMaP

physics

Type of course

general courses

Prerequisites (description)

The main goal of these inter-, intra-, and multidisciplinary lectures is to present and discuss a modern idea of complexity and its consequences. In the recent decade, the complexity of a real world forced emergent approches and viepoints. They are, to some extend,quite universal ones, particularly, in the case of complex evolving networks. They are the main subject of these lectures.

Course coordinators

Ryszard Kutner

Mode

Remote learning

Learning outcomes

It is asssumed that participants of lectures will acquire the basic knowledge concerning quickly developing branch of science that is, the science of complex systems. Particularly significant is in this context the statistical physics of complex evolving networks. Statements presented during the lectures will be illustrated by several very instructive examples containing (among others) komputer simulations. The audience will be introduced with so significant terms as the emergence, synergy, coherency, synchronisation, herd and flock effects, correlations (in particular, in the vicinity of a critical point), dependence, universality, renormalisation, scale free and power-law phenomena, hierarchy, percolation, feedback and several others as well so significant collective phenomenon and processes as phase transitions (the first and the second orders, static and dynamic ones).
We wish to inspire by these lectures the audience to a more personal reserach activity by preparing themselves, for example, bachelor, master, and even doctoral theses.

Assessment criteria

Three equivalent ways were proposed to pass an examination (the necessary condition is also to pass exercises if they will be offerred in a given academic year). The first one is a traditional way, that is a spoken examination. The second one (in the form of a seminar) is a chosen lecture presentation before the audience. The third way concerns the realization and public presentation of some project earlier accepted by myself.

Practical placement

Absent

Bibliography

[1] G. Nicolis, K. Nicolis: Foundations of Complex
Systems, World Scientific, 2012
[2] N. Johnson: Simply Complexity: A Clear Giude to
Complexity Theory, World Scientific, 2012.
[3] J. Spałek: Emergentność w Prawach Przyrody i
Hierarchiczna Struktura Nauki, Postępy Fizyki, tom 63,
zeszyt 1, 8-18, 2012.
[4] W. Weidlich, G. Haag: Concepts and Models of a
Quantitative Sociology. The Dynamics of Interacting
Populations, Springer-Verlag, New York 1983.
[5] S. N. Dorogovtsev, A. V. Goltsev, J. F. F. Mendes:
Critical phenomena in networks, Rev. Modern Phys.
80, 1275-1335, 2008.
[6] S. N. Dorogovtsev: Lectures on Complex Networks,
Clarendon Press, Oxford 2010.
[7] F. Schweizer, G. Fagiolo, D. Sornette, F. Vega-Redondo, D.
R. White: Economic Networks: What Do We Know and
What Do We Need to Know?, Adv. Complex Syst. 12
(4&5), 407- 422 (2009).
[8] A. Fronczak, P. Fronczak: Świat sieci złożonych. Od fizyki
do internetu, Wydawnictwo Naukowe PWN, Warszawa
2009
[9] N. F. Johnson, P. Jefferies, P. M. Hui: Financial Market
Complexity, Oxford University Press, Oxford 2007.
[10] R. Badii, A. Politi: Complexity. Hierarchical structures
and scaling in physics, Cambridge University Press,
Cambridge 1997.
[11] Wybrane artykuły i hasła z Encyclopedia of Complexity
and System Science, ed. R. A. Meyers, Springer, Berlin
2009.

Additional information

Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:

Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system:

Description of 1100-WFZ-OG in USOSweb