Workshop Networks, Complexity & CompetitionA B S T R A C T S |
| SPEAKER | TITLE | A b s t r a c t |
| Simone Alfarano | A statistical equilibrium model of competitive firms | We argue that the complex interactions of competitive heterogeneous firms lead to a statistical equilibrium distribution of firms' profit rates. The statistical equilibrium distribution turns out to be an exponential power (or Subbotin) distribution. In order to gain insights into the dynamical evolution of profit rates, we consider a diffusion process with constant diffusion function that have the Subbotin distribution as its stationary density. This leads to a phenomenologically inspired economic interpretation of variations in the shape parameter of the statistical equilibrium distribution of profit rates.
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| Vladimir Batagelj | Multiplication of networks | A product of two compatible networks is defined on the basis of
the product of their matrices. In the case of large sparse
networks their product need not to be sparse itself. We present
some conditions that guarantee the sparsity of product and
a fast algorithm to compute the product.
Multiplication of networks has many applications in network
analysis. We present some examples: analysis of European
projects on simulation, analysis of networks from Web of Science,
and computing derived kinship relations in genealogies. |
| Ulrich Behn | Randomly evolving idiotypic networks | B-Lymphocytes express on their surface
receptors (antibodies) of a given
specifity (idiotype). Crosslinking these receptors by complementary
structures, antigens or antibodies, stimulates the lymphocyte; unstimulated
lymphocytes die. In this way a large functional network of interacting
lymphocytes, the idiotypic network, emerges. The idiotypic network paradigm,
developed by Niels Jerne 30 years ago, experiences these days a renewed
interest, e.g. in the context of autoimmune diseases. In a minimalistic model
we investigate the random evolution of the network towards a highly organized
functional architecture which is driven by the influx of new idiotypes,
randomly generated in the bone marrow. The nodes can be classified into
different groups, which are clearly distinguished by their statistical
characteristics. They include densely connected core groups and peripheral
groups of isolated nodes, resembling central and peripheral part of the
biological network. We found the building principles of the architecture
which allows to calculate analytically size and linking of the groups. In a
mean field approach, mean occupation of the groups and mean life time of
occupied nodes are determined in good agreement with simulations. (Joint work
with Holger Schmidtchen). |
| Ginestra Bianconi | Dynamics of condensation in growing networks |
A condensation transition, mapping to a Bose-Einstein condensation, was predicted for technological
and social growing
networks evolving by preferential attachment and competing quality
of their nodes.
Earlier studies based on steady degree distribution of
the fitness model where able to characterize the critical point.
Here we characterize the dynamics of condensation and we present evidence that below the condensation temperature
there is a
slow down of the dynamics and that a single node (not necessarily the
best node in the network) emerges as the winner for very long times.
The characteristic time t* at which this phenomenon occurs diverges
both at the critical point and at T-> 0 when only the
fitness drives the dynamics of attachment of new links. |
| Zdzislaw Burda | Zero range process on networks | We shall discuss zero-range process (ZRP) on networks. ZRP is a simple stochastic process describing a gas
of indistinguishable particles hopping between neighboring
nodes of the network. ZRP process undergoes a phase transition
to a condensed phase in which one of the nodes is
occupied by an extensive number of particles. The ZRP is a probably
the simplest non-trivial example of a non-equilibrium system which
in some specific cases can be solved analytically. |
| Anuska Ferligoj | Generalized Blockmodeling | The goal of blockmodeling is to reduce a large, potentially incoherent
network to a smaller comprehensible structure that can be interpreted more
readily. Blockmodeling, as an empirical procedure, is based on the idea that units in a network can be clustered according to the extent to which they are equivalent, under some meaningful definition of equivalence. In the talk an optimizational approach to blockmodeling will be discussed. Methods where a set of observed relations are fitted to a pre-specified blockmodel will be presented (Doreian, Batagelj, and Ferligoj 2005). All presented blockmodeling methods are implemented in the program Pajek, developed by Batagelj and Mrvar (de Nooy, Mrvar, and Batagelj 2005). Some new developments will be also discussed: blockmodeling of three-way networks (Batagelj, Ferligoj, Doreian 2007) and blockmodeling of valued networks (Ziberna 2007, 2008).
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| Albert Diaz-Guilera | Synchronization in complex networks | I will present some recent results on
synchronization in complex networks. I will focus mainly on the applications of the subject to
computer science, engineering, social sciences and economy.
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| Igor Grabec | Modelling Traffic Flow on Roads Network | Road traffic is a consequence of population activity caused by numerous agents. Consequently, practically random character of tr
affic flow could be expected. In opposition to this expectation, records of traffic flow exhibit rather regular properties. The
regularity is a consequence of highly synchronized population activity. The synchronization mainly stems from regularly changing
illumination of the Earth that is described by a clock and calendar. Beside this, an additional synchronization is generated in
herently in the population by a consensus about working days and holidays. In agreement with this, we consider the road traffic
flow as a non-autonomous dynamic phenomenon that is influenced by variables representing hour and character of days. Its dynamic
s is modelled non-parametrically based upon recorded traffic flow time series. We further demonstrate how this model could be ap
plied for rather accurate forecasting of traffic flow rate on roads networks of various countries. |
| Jelena Grujic | Bipartite E-social Networks | E-social networks represent social interaction over the Internet. In contrast to
the direct communication, such as e-mail network, we can also investigate socia
l structures where users communicate through common interests, like books, music
s, movies, etc. We investigate the customers recommendation
networks based on the large data set from the Internet Movie Data
base. Networks were based on two types of inputs: first (monopartite) generated
directly from the recommendation lists on the website, and second (bipartite) ge
nerated through the users habits. We introduced a control parameter and tested u
niversality of our conclusions in function of the control parameter.COAUTHOR: B. Tadic (POSTER) |
| Rudolf Hanel | From limit theorems to generalized-generalized entropies |
In recent years the importance of non exponential distributions, for
instance fat-tailed distributions (presence of power laws), has been
established in the field of complex systems. It is known that for variables
following a power law the associated maximum entropy principle can be
formulated in terms of generalized entropies replacing the usual logarithm
of the Boltzmann entropy with the so called q-logarithm. However, frequently
distributions may be observed in diverse fields of complex system research
which do not fit into the setting of the established class of generalized
entropies. We will show how limit theorems for correlated random variables
pave a road that leads to generalized-generalized entropy functionals.
Although the level of generalization of the entropy notion that is required
to incorporate all possible distributions resulting from such limit theorems
is considerable this new class of functional entropies is still fully
compatible with the two fundamental thermodynamic requirements, i.e. the
first and the second law of thermodynamics. |
| Stephen Hardiman | A random walk through the 'Bebo' network | We examine the characteristics of a real world social network by taking a random walk through the pages of an online social
networking website (Bebo, a website popular in Ireland, similar to its more international counterpart, facebook). By examini
ng the statistics of degree and first passage time of walks which return to the initial vertex, we can estimate characterist
ics of the network such as degree distribution, degree correlations and clustering as well as estimate the overall size of t
he social network. Our estimate compares well with figures published in the technical press and media.(POSTER)
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| Janusz Holyst | Competition of complex networks | We investigate the behavior of the Ising model on two connected Barbasi-Albert scale-free networks that correspond to competing social groups dynamics. We extend previous analysis and show that a first order temperature-driven phase transition occurs in such system. The transition between antiparalelly ordered networks to paralelly ordered networks is shown to be discontinuous. We calculate the critical temperature. We confirm the calculations with numeric simulations using Monte-Carlo methods. COAUTHOR: Krzysztof Suchecki |
| Kimo Kaski | Emergence of Communities in Weighted Social Networks | In complex social networks with variable interactions strengths or weights between nodes, the topology and the weights are closely related, which is reflected in the modular structure of the network. Here we present a simple network model where the weights are generated dynamically and they shape the developing network topology. By tuning a model parameter governing the importance of weights, the resulting networks undergo a gradual structural transition from a module free topology to one with communities. The model also reproduces many features of large social networks, including the weak links property.
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| Janos Kertesz | Hierarchy of overlapping communities in weighted networks | We present a new local method of community detection [1], which is suitable to identify overlapping modules and their hierarchies. The method is based on a node fitness function which can be defined with respect to a community and it naturally accounts for nodes belonging to more than one modules, i.e., for overlaps. Using a continuously tunable parameter the resolution of the method can be changed and hierarchical structures can be uncovered. A natural generalization to weighted graphs enables to apply the method to important examples, including association network, cooperation networks [2].
[1] A. Lancichinetti, S. Fortunato, J. Kertesz:
Detecting the overlapping and hierarchical community structure of complex networks http://arxiv.org/abs/0802.1218
[2] G. Tibely, S. Fortunato, J. Kertesz:
Hierarchies of in weighted overlapping networks (in preparation) |
| Renaud Lambiotte | Dynamics of non-conservative Voters | We study a family of opinion formation models in one dimension where the propensity for a voter to align with its local environment depends non-linearly on the fraction of disagreeing neighbors. Depending on this non-linearity in the voting rule, the population may exhibit a bias toward zero magnetization or toward consensus and the average magnetization is generally not conserved. We use a decoupling approximation to truncate the equation hierarchy for multi-point spin correlations and thereby derive the probability to reach a final state of +1 consensus as a function of the initial magnetization. The case when voters are influenced by more distant voters is also considered by focusing in detail on the Sznajd model.
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| Zoran Levnajic | Coupled 2D Maps with Time-delay on Modular Networks | We study the collective dynamics of Standard maps coupled with a time-delay on a modular tree grown by adding clique-motifs to a scalefree tree. The results are compared to the known scalefree tree results [2],[3]. Analogies are found in the statistical properties of the emergent motion along with the differences in the dynamics regularization process.
[2] Z. Levnajic and B. Tadic Self-organization in Trees and Motifs of Two-Dimensional Chaotic Maps with Time Delay, J.Stat.Mech. P03003, 2008.
[3] Z. Levnajic and B. Tadic Dynamical Patterns in Scalefree Trees of Coupled 2D Chaotic Maps, Springer-Verlag LNCS 4488 p.633-640, 2007 (POSTER)
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| Rosario Mantegna | Specialization and herding behavior of trading firms in a financial market | Agent based models of financial markets
are usually making assumptions about agent\\\'s preferred stylized strategies. Empirical
validations of these assumptions have not been performed so far on a full market scale.
Here we present a comprehensive study of the resulting strategies followed by the firms
which are members of the Spanish Stock Exchange. We are able to show that they can be
characterized by a resulting strategy and classified in three well-defined groups of firms.
Firms of the first group have a change of inventory of the traded stock which is positively
correlated with the synchronous stock return whereas firms of the second group show a negative
correlation. Firms of the third group have an inventory variation uncorrelated with stock return.
Firms tend to stay in the same group over the years indicating a long term specialization in
the strategies controlling their inventory variation. We detect a clear asymmetry in the
Granger causality between inventory variation of firms and stock return. We also detect
herding in the buying and selling activity of firms. The herding properties of the two groups
are markedly different and consistently observed over a four-year period of trading. Firms of
the second group herd much more frequently than the ones of the first group. Our results can be
used as an empirical basis for agent based models of financial markets.
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| Marija MItrovic | Multiscale networks: modeling and spectral analysis | Complex networks represent abstract of our knowledge about complex dynamical systems. These networks appear to have modular (or community ) structure which is strongly connected with respective dynamical processes. Better understanding of evolution and
dynamics of complex networks requires development of efficient methods for search of subgraphs in complex networks. Here we
represnet a model of multiscale networks with well defined modular structure and demonstrate how maximum likelihood method works on these networks. Comparing spectra of scale free and multiscale networks, we show that spectra of normalized adjacency matrix can be used as diagnostic tool for network structure. Information deduced form spectra can be used to improve maximum likelihood method. COAUTHORS: B. Tadic (POSTER)
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| Jorge M. Pacheco | Evolutionary games on self-organizing networks | I will discuss the evolutionary dynamics of populations in which individuals engage in games associated with popular social
dilemmas.
The dynamical structure of their social ties co-evolves with individual strategies, such that individuals differ in the rate
at which they seek new interactions. Moreover, once a link between two individuals has formed, the productivity of this lin
k is evaluated. Links can be broken off at different rates. Whenever the active dynamics of links is sufficiently fast, popu
lation structure leads to a transformation of the payoff matrix of the original game. We explore the evolutionary dynamics o
f one shot games, deriving analytical conditions for evolutionary stability. |
| Milan Rajkovic | Dynamic updating of topological features of graphs and simplicial complexes | The network (nodes and links) is encoded into a simplicial
complex and in the first part of the exposition we present static properties
of these complexes as reflected in topological invariants and their statistical features.
In the second part of the exposition, the construction of simplicial
complexes from graphs is extended to include dynamical changes the network
(simplicial complex) may experience. We present new topological methods and
a branch of topology called persistence topology which enables updating
(instead of complete calculation) of various invariant measures due
dynamical changes of the network. Applications to gene-regulatory networks are presented. |
| Peter Richmond | Wither COST? | COST P10 comes to an end in June this year. The Chair will - rather like Charles Dickens' Scrooge - look into the past an
d the present and, depending on the outcome of a recent submission for a new action, speculate on possible future activity.
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| Geoff Rodgers | Self-Organisation in Health Care Systems | Abstract... We present an analysis of one years' worth of empirical data on
the arrival and discharge times at a UK Accident and Emergency
(A&E) department. We find that discharges rates vary slightly
with the workload and that the distribution of the length of stay
has a fat tail. A sand pile model is considered to show that the
A&E department is a self-organised system, where the department
stuff manage their work time to cope with the department's
occupancy. We use in our model a variable input space to mimic the
queuing discipline related to different cases of accidents found
in the department. The input space is defined by two parameters;
its size sxs and the distance m from two nearest edges.
We show for the length of stay distribution the transition from
power law to Poissonian like curve while s or m are increased
from s=1 and m=0.COAUTHORS: Alexander Hellervik,
Bernard Kujawski, Terry Young |
| J. Philip Schmidt | Human brain functional networks | In this project the functional structure and long-term changes in cognitive functions will be investigated. Goal of the project i
s to model the functional connectivity of the brain as a network and to give a structural characterization of the functional conn
ectivity in the ageing brain. Under functional connectivity we understand the correlation in neural activity in the brain, measur
ed indirectly by functional magnetic tomography data(fMRI). The nodes of the network represent brain voxels and edges are strong
correlations between pairs of voxels (measured by fMRI data). The structure of the network will then be analyzed using statistica
l parameters such as clustering coefficient, assortativity, robustness and techniques such as spectral graph analysis.(POSTER) |
| Peter Schuster | Networks from replicating molecules | Abstract..(to be added). |
| Dejan Stokic | Dynamics of Genes & Gene Networks | We study a set of linearized catalytic reactions to model gene to gene interactions.
The model is based on experimentally motivated interaction network topologies
and is designed to capture some key properties of gene expression statistics.
We impose a non-linearity to the system by enforcing a boundary condition which guarantees non-negative concentrations of chemical substances. System stability is quantified by maximum Lyapunov exponents. We use this model to reverse engineering a gene regulatory network.
The functional relationships between genes are being retrieved by inferring the gene network with a set of single gene overexpression experiments.
COAUTHORS: S. Thurner |
| Milovan Suvakov | Networks of Aggregated Colloids with Bio-Recognition Binding | We present a numerical model of two- and three-dimensional self-assembly
of binary colloidal nanoparticles with biorecognition cross-linking between
particles of the different kind. We consider a Lennard-Jones interaction
between particles of different kinds and short-range repulsion between
particles of the same kind. Our approach is based on molecular dynamics
simulations with Langevin stochastic term in the equation of motion.
We study topology of emergent structures which depend on model parameters
by considering the structure as a graph and using standard graph theory
methods.COAUTHORS: B. Tadic. (POSTER)
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| Piotr Swiatek | News from the COST Office | ...(State-ot-the-art information) |
| Bosiljka Tadic | Networks' Fine Structure---Dynamics View | In functional networks the structure can be seen as a support of dynamic processes on networks. Identifying the relevant subgraphs for each type of processes is then of key importance for the control and improvement of the network function.
We present a model network which consists of subnetworks (modules) of a controlled structure and show how the topological modularity affects the transport processes and Laplacian spectra. |
| Stefan Thurner | Towards a dynamics of the adjacent-possible | Abstract... |
| Gregor Trefalt | Distribution of Ions in Disordered Porous Media | Abstract... COAUTHORS: B. Hribar |
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