
THE
FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES 
June
1719, 2015 at the Fields Institute, Stewart Library
2015
Summer Solstice
7th International Conference on Discrete Models of Complex Systems



Conference Overview
Complex systems are pervasive in many fields of science and we encounter
them everyday and everywhere in our life. Their examples include financial
markets, highway transportation networks, telecommunication networks, human
economies, social networks, immunological systems, ant colonies, ect. The
key feature of a complex system is that it is composed of large number of
interconnected and interacting entities exhibiting much richer dynamical
properties on global scale than they could be inferred from the properties
and behaviours of its individual entities.
Complex systems are studied in many areas of natural sciences, social sciences,
engineering and mathematical sciences. The integral part of these interdisciplinary
studies forms discrete modeling in terms of cellular automata, lattice gas
cellular automata, multiagent based models, or networks. These models can
be seen as the simplest digital laboratories to study phenomena exhibited
by complex systems like selforganization processes, pattern formation,
cooperation, adaptation, competition, attractors, or multiscale phenomena.
The aim of this conference is to bring together researchers from around
the world working on discrete modeling of complex systems and analysis of
their dynamics. The objective of this conference is to provide a forum for
exchange of ideas, presentation of results of current research and to discuss
potential future directions and developments in the field of discrete modeling
of complex systems and analysis of their dynamics from methodological and
phenomenological point of view. The conference will cover both theoretical
and applied research. It will focus on discrete modeling methodologies and
their applications to analysis across different scales of dynamics of complex
systems.
The 2015 Summer Solstice Conference topics include, but are not limited
to, the following:
•
Challenges, benefits and theory
of modeling and simulation of complex systems using cellular automata,
lattice gas cellular automata, multiagent based models, complex networks
•
Discrete models in biology
and medicine
•
Discrete models in economy
and social sciences
•
Discrete models of man made
complex systems from nanotechnology to information networks
•
Tools of analysis of dynamics
and multiscale phenomena of discrete models of complex systems
There will be sessions of contributed presentations. The organizers reserve
the right to assign contributed presentation as oral or poster. The Post
Conference Proceedings are planned and all conference presenters will be
invited to submit a paper for publication in the Proceedings. All submissions
will be peerreviewed.
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Previous Editions Of Summer
Solstice
•
2009 Gdansk, Poland 
http://www.iftia.univ.gda.pl/solstice/
• 2010
Nancy, France  http://solstice.loria.fr/CFP.html
• 2011
Turku, Finland  http://iftia.univ.gda.pl/solstice/
• 2012
Arcidosso, Italy 
http://summersolstice2012.complexworld.net/home
•
2013 Warsaw, Poland  http://summersolstice2013.if.pw.edu.pl/index.html
•
2014 Ljubljana, Slovenia  http://wwwf1.ijs.si/~tadic/Workshops/Solstice14/?page=home
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Call For Abstract
Submission
Researchers and scientists working in the area of discrete modeling of
complex systems are invited to submit abstracts on their research to be
presented at the conference. Of particular interest are approaches: cellular
automata, lattice gas cellular automata, multiagent based simulation models,
individually based simulation models, networks. Both theoretical and applied
research is of interest. Accepted abstracts will be scheduled as talks or
posters.
Please, submit your abstract of maximum one page (i.e. of maximum of 500
words), before June 2, 2015. The abstract should include title, authors,
affiliation, description of research, some key results, and if applicable
acknowledgments and references. To submit the abstract follow the link:
http://at.yorku.ca/cgibin/abstract/submit/cbky01.
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Scientific Program Committee
•
Giovanni Acampora, Nottingham Trent University, UK
•
Franco Bagnoli, University of Florence, Italy
•
Marian Boguna, University of Barcelona, Spain
•
Monica Cojocaru, University of Guelph, Canada
•
Bruno Di Stefano, Nuptek Systems Ltd, Canada
•
Nazim Fates, INRIA Lorraine  Loria, France
•
Henryk Fuks, Brock University, Canada
•
Eric Antonio Goles, Adolfo Ibanez University, Santiago, Chile
•
Andrzej Krawiecki, Warsaw University of Technology, Poland
•
Anna T Lawniczak, University of Guelph, Canada
•
Danuta Makowiec, University of Gdansk, Poland
•
Jose Mendes, University of Aveiro, Portugal
•
Pedro de Oliveira, Universidade Presbiteriana Mackenzie, Brazil
•
Andrea Rapisarda, University of Catania, Italy
•
Raul Rechtman, UNAM,Ciudad de México, Mexico
•
M. Angeles Serrano, University of Barcelona, Spain
•
Bosiljka Tadic, Jozef Stefan Institute, Slovenia
•
Burton Voorhees, Athabasca University, Canada
•
Gabriel A. Wainer, Carlton University, Canada
•
Jian Yuan, Tsinghua University, Beijing, China
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List of Invited Speakers
•
Daniel Ashlock, University of Guelph, Canada
•
Jan Baetens, Ghent University, Belgium
Talk Title: Behavioral analysis and identification of discrete models
•
Franco Bagnoli, University of Florence, Italy
Talk Title: Topological phase transitions in a parallel Ising model
•
Andreas Deutsch, Technical University of Dresden, Germany
•
Stanislaw Drozdz, Polish Academy of Sciences, Cracow, Poland
•
Babak Farzad, Brock University, Canada
Talk Title: Strategic models for network formation
•
Paola Flocchini, University of Ottawa, Canada
•
Rolf Hoffmann, Technical University of Darmstadt, Germany
•
Pietro Lio, University of Cambridge, UK
•
Jose Mendes, University of Aveiro, Portugal
•
Raul J Mondragon, Queen Mary University of London, UK
•
Dawn Cassandra Parker, U Waterloo, Canada
•
Andrea Rapisarda, University of Catania, Italy
•
Henry Thille, University of Guelph, Canada
•
Edward
Thommes, GlaxoSmithKline Inc., Canada
•
Bosiljka Tadic, Jozef Stefan Institute, Slovenia
•
Jaroslaw Was, AGH University of Science and Technology, Poland
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Important Dates
•
Abstract
Submission
June 2, 2015  abstract submission deadline
June 4, 2015  notification if contributed presentation is accepted and
if it is oral or poster
•
Financial
Support Of Graduate Students And Postdoctoral Fellows
May 17, 2015  application deadline for financial support
May 26, 2015  notifications about receiving the financial support
•
October
5 , 2015  Post Conference Proceedings manuscript submission for referring
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Registration information
Online registration has now closed, but participants may register onsite
at the Fields Insitute during the conference.
Registration fees:
•
Before June 5: $280 regular rate, $210 graduate students
and postdoctoral fellows
•
After June 5: $330 regular rate, $260 graduate students
and postdoctoral fellows
The registration fee of regular conference participant covers: coffee breaks,
lunch, reception, and PostConference Proceedings.
The student and Postdoctoral Fellows registration fee covers: coffee breaks,
lunch and reception.
Tickets for the banquet on Thursday the 18th can be bought for participants
and guests for $72 / ticket.
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Post Conference Proceedings Information
Each presenter is invited to submit an article for publication in Post
Conference Proceedings. All articles will be referred and only accepted
articles will be published in the Post Conference Proceedings.
The deadline of submission of the article for publication in the Post Conference
Proceedings is October 5, 2015. The details about where to upload
your paper for refereeing will be provided at the Conference.
The Proceedings are planned for publication with Acta Physica Polonica
B Proc. Suppl., which is open access http://www.actaphys.uj.edu.pl/_cur/pl/home_page/
The Post Conference Proceedings of the previous Summer Solstice Conferences
can be found here:
•
2009 Summer Solstice, Gdansk, Poland: Acta Physica Polonica
B Proc. Suppl., 3(2) 251494 (2010), http://www.actaphys.uj.edu.pl/_old/sup3/t2.htm
•
2010 Summer Solstice, Nancy, France: Acta Physica Polonica
B Proc. Suppl., 4(2) 115265 (2011), http://www.actaphys.uj.edu.pl/_old/sup4/t2.htm
•
2011 Summer Solstice, Turku, Finland, Acta Physica Polonica
B Proc. Suppl., 5(1) 1190 (2012), http://www.actaphys.uj.edu.pl/_old/sup5/t1.htm
•
2013 Summer Solstice, Warsaw, Poland, Acta Physica Polonica
B Proc. Suppl., 7(2) 233408 (2014), http://www.actaphys.uj.edu.pl/_cur/pl/acta_physica_polonica_b_proceedings_suplement/?show_all=S
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Financial Support Of Graduate
Students And Postdoctoral Fellows
Limited financial support is available for graduate students and postdoctoral
fellows to partially cover conference participation. Application deadline:
May 17, 2015. Notifications about the financial support: May 26,
2015.
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Invited Speaker Abstracts
Evolving Transparently Scalable Level Maps with Cellular Automata
Daniel Ashlock
University of Guelph, Canada
Cellular automata can be used to rapidly generate complex images. This
presentation introduces fashionbased cellular automata that can be evolved
to generate cavernlike level maps. Fashionbased automata are defined
by a competition matrix that specifies the benefit to a given cell state
of having a neighbor of each possible cell state. Rules for these automata
are selected with an evolutionary algorithm to produce cavernlike maps.
The fact that cellular automata act on local neighborhoods has the pleasant
side effect that, once a rule is located, it can be used to generate a
diverse set of level maps of any size without added evolution or processing.
Behavioral analysis and identification of discrete models
Jan Baetens
KERMIT, Department of Mathematical Modelling, Statistics and Bioinformatics,
Coupure links 653, 9000 Gent, Belgium
Coauthors: Bernard De Baets
Catalyzed by the emergence of modern computers, cellular automata (CAs)
became a fullfledged research domain in the eighties of the previous
century. The relevant literature is of a dichotomous nature in the sense
that studies either focus on the spatiotemporal dynamics that is evolved
by CAs, while others merely use the CA paradigm to build a model for a
given biological, natural or physical process. It goes without saying
that a profound understanding of CA dynamics is a prerequisite for building
realistic, identifiable CAbased models, though this is not straightforward
due the fact that a CA is discrete in all its senses (state, time, space).
In an attempt to quantify CA behavior in a meaningful and reproducible
way, several socalled behavioral measures have been proposed during the
last two decades.
Here, we will show how Lyapunov exponents and Boolean derivatives can
be used to get a complete picture of CA dynamics in the sense that they
not only make it possible to unravel the nature of a given CA, but also
allow for assessing the effect of changing model design parameters on
the CA behavior, an understanding that is a prerequisite for CAbased
models to become appreciated as a fullfledged modeling paradigm. Besides,
it will be demonstrated that the scope of these measures is not limited
to twostate CAs.
Phase transitions in parallel Ising model
Franco Bagnoli
Department of Physics and Astronomy and CSDC, University of Florence (Italy)
Coauthors: Raul Rechtman, Tommaso Matteuzzi
We present simulations about the parallel version of the Ising model,
focussing on phase transitions. We show the effect of "diluting"
the parallel update, thus exploring the transition between the parallel
and the usual sequential version of the model, and the effects of a nonlinear
Hamiltonian. In this case the meanfield approximation is a chaotic map,
a behaviour that can be recovered also in microscopic simulations by changing
the topology of the network, i.e., exploiting the smallworld effect.
Cellular automaton models for collective cell behavior
Andreas Deutsch
Centre for Information Services and High Performance Computing, Technische
Universität Dresden, Germany
Collective dynamics of interacting cell populations drives key processes
in biological tissue formation and maintenance under normal and diseased
conditions. Latticegas cellular automata have proven successful to model
and analyze collective migration and pattern formation emerging from specific
cell interactions. Here, we introduce latticegas cellular automaton models
for collective cell migration, clustering, growth and invasion and demonstrate
how analysis of the models allows for predicting emerging properties at
the individual cell and the cell population level. Finally, we discuss
applications of the growth and invasion models to glioma tumours.
References: Deutsch, S. Dormann: Cellular Automaton Modeling of
Biological Pattern Formation: Characterization, Applications, and Analysis,
Birkhauser, Boston, 2005
Complexity characteristics of world literature
Stanislaw Drozdz
Polish Academy of Sciences and Cracow University of Technology, Poland
Coauthors: Andrzej Kulig, Jaroslaw Kwapien, Pawel Oswiecimka
This study, based on a large corpus of world famous literary works and
using concepts of multiscaling and of complex networks quantifies character
of the longrange, both linear and nonlinear correlations in narrative
texts and reveals their origin. The leading factor of such correlations
appears to be encoded in the sentence length variability or equivalently
in the recurrence patterns of the full stops and to a much lesser degree
in the recurrence patterns of the most frequent words. A distinct character
of the 'stream of consciousness' narrative involving cascadelike nonlinear
correlations is also identified.
Strategic models for network formation
Babak Farzad
Brock University, Canada
The emergence of largescale smallworld networks has been mostly explained
within stochastic frameworks. We study the dynamics of gametheoretic
network formation models that yield such networks. In these models, links
are formed due to strategic behaviors of individuals rather than based
on probabilities. In this talk, we focus on a gridbased model inspired
by Kleinberg's smallworld random graphs, and also on a hierarchical or
treebased network formation model. This was a joint project with Omid
Atabati.
TimeVarying Graphs and Dynamic Networks
Paola Flocchini
University of Ottawa, Canada
Highly dynamic networks are networks where connectivity changes in time
and connection patterns display possibly complex dynamics. Such networks
are more and more pervasive in everyday life and the study of their properties
is the object of extensive investigation in a wide range of very different
contexts. This is the case, for example, of wireless adhoc networks, vehicular
networks, satellites, military and robotic networks, the nervous system,
epidemiological networks, and various forms of social networks.
In spite of being quite different in many aspects, these domains display
several common features. In particular, they all have a fundamental temporal
nature, with timedependent interactions between the entities.
TimeVarying Graphs (TVGs) represent a model that formalizes highly dynamic
networks encompassing the above contexts into a unique framework and emphasizing
their temporal component.
In this talk I will introduce the TVG model, showing examples of its use
in various applications.
Cellular automata agents can form a pattern more effectively by using
signs
Rolf Hoffmann
Technical University of Darmstadt, Germany
Considered is a 2D cellular automaton with moving agents. Each cell contains
a particle with a value = (color, sign), which can be changed by an agent.
Initially the agents and values are randomly distributed. The agent's
task is to form a specific target pattern belonging to a predefined pattern
class. The target patterns (path patterns) shall consist of preferably
long narrow paths with the same color, they are called "path patterns".
The quality of the path patterns is measured by the degree of order that
is computed by counting matching 3 x 3 patterns (templates). The signs
act as artificial pheromones that improve the solution's quality (effectiveness)
and the efficiency of the task. The agents' behavior is controlled by
a finite state machine (FSM). The used agents can perform 32 actions,
combinations of moving, turning and value setting. They react on the own
particle's value, the value in front, and blocking situations. The number
of FSM states was restricted to 6. For given n x n fields (n = 4, 8, 16),
near optimal FSMs were separately evolved by a genetic algorithm. The
evolved agents are capable to form path patterns with a very high degree
of order. The whole multiagent system was modeled by cellular automata.
The CAw model (cellular automata with write access) [1] was used for
the implementation of the system in order to reduce the implementation
effort and to speed up the simulation. Application areas could be the
alignment of particles [2], fibers [3] or spins.
[1] Hoffmann, R.: Rotorrouting algorithms described by CAw. Acta Phys.
Polonica B Proc. Suppl. 5(1) (2012) pp. 5368
[2] Hoffmann, R.: How Agents Can Form a Specific Pattern, Cellular Automata,
LNCS Volume 8751 (2014) pp. 660669
[3] Shi, D., He, P., Lian, J., Chaud, X. et al.: Magnetic alignment of
carbon nanofibers in polymer composites and anisotropy of mechanical properties.
Journal of Applied Physics 97, 064312 (2005)
Cancer cell dynamics and liquid biopsies
Pietro Lio'
Computer LAboratory, University of Cambridge, UK
Coauthors: Gianluca Ascolani and Annalisa Occhipinti
Ductal carcinoma is one of the most common cancers among women, and the
main cause of death is the formation of metastases. The development of
metastases is caused by cancer cells that migrate from the primary tumour
site (the mammary duct) through the blood vessels and extravasating they
initiate metastasis. Here, we propose a multicompartment model which
mimics the dynamics of tumoural cells in the mammary duct, in the circulatory
system and in the bone. Through a branching process model, we describe
the relation between the survival times and the four markers mainly involved
in metastatic breast cancer (EPCAM, CD47, CD44 and MET). In particular,
the model takes into account the gene expression profile of circulating
tumour cells to predict personalised survival probability. We also include
the administration of drugs as bisphosphonates, which reduce the formation
of circulating tumour cells and their survival in the blood vessels, in
order to analyse the dynamic changes induced by the therapy.
Structural properties of complex networks
José Fernando Ferreira Mendes
University of Aveiro, Portugal
In this talk I will revisit a number of wellstudied problems concerning
structural properties of complex networks. Some concepts like percolation,
kcore organization, bootstrap percolation and avalanche collapse of the
giant viable component in multiplex networks are well wellknown to the
audience but I will present them in a different perspective showing the
recent analytical advances from a network theory point of view. Recent
studies of damage to multiplex and interdependent networks have revealed
a variety of complex critical phenomena, including a dramatic discontinuous
collapse of the system. Here we propose an activation process on multiplex
networks, which exhibits a similar discontinuous hybrid transition. Our
multiplex bootstrap model constitutes the simplest example of a contagion
process on a multiplex network and has potential applications in critical
infrastructure recovery and information security. We further introduce
a new pruning process, which is the dual of this activation process. We
collectively refer to these two models as "weak" percolation,
to distinguish them from the somewhat classical concept of ordinary ("strong")
percolation. While the two models coincide in simplex networks, we show
that they decouple when considering multiplexes, giving rise to a wealth
of critical phenomena. Moreover, we show that our pruning percolation
model may provide a way to diagnose missing layers in a multiplex network.
Network ensembles based on the Maximal Entropy and the RichClub
Raul J Mondragon
Queen Mary University of London, UK
In Complex Networks, ensembles of networks are used as null models to
discriminate network structures. We present some results about how to
construct network ensembles based on the maximal entropy method with the
constraints that the degree and richclub coefficient are conserved. The
method can generate correlated and uncorrelated nullmodels of real networks,
which in turn, the nullmodels can be used to define the partition of
a network into soft communities.
Integration of agentbased modeling, network science, analytical models,
and inductive metamodelling for applied analysis of complex systems phenomena
Dawn Cassandra Parker
University of Waterloo, School of Planning and WICI, Canada
This talk draws on examples of discrete models of complex systems that
have been presented through the Waterloo Institute for Complexity and
Innovation's seminar series over the last five years to illustrate the
potential integration of agentbased modeling, network analysis, analytical
modeling, and estimation of metamodels. Agentbased discrete event computational
simulation models are often used to simulate entities that act autonomously,
but in response to environmental triggers, in social and natural systems.
Often these agents interact within networks. Tools from network science
are used to represent and analyze social and natural network structures.
Analytical mathematical models are often used in a complementary role
with both methods, as a startingoff point from which to increase model
complexity, or as a point of docking and verification. Inductive methods
are increasingly applied in order to understand the behaviour of aggregate
outputs from simulation models, ideally in the form of a fitted model
of the aggregate dynamical behaviour of the system. WICIhosted talks
over the last five years provide many examples of each of these four approaches,
applied individually and in combination. In addition to highlighting key
findings of the various research talks, the talk will discuss alternative
modeling approaches, identify complementarities, and present open methodological
challenges.
This talk will draw on and synthetize material from previous WICI talks
on models of global governance (Hofmann, 2009), electricity markets (Tesfatsion,
2010), technological progress and innovation (Farmer, 2009; Arthur, 2011),
urban growth and change (Batty, 2011; Parker, 2013; Tolmie and Parker,
2015), critical transitions (Scheffer, 2011; Zeeman, 2014), landuse change
(Lambin, Deadman, Cabrera, and Le Page, 2011; Anand, 2012; Heckbert, 2014;
Robinson, 2015), coordination, communication, and disruption in social
networks (Onnela, 2010; Sundaram, 2011, 2012; Grabowicz, 2013; McLevey,
2014; De Sterck, 2015), consumer behaviour (Cojocaru, 2011; Schröder,
2013), and epidemiology (Bauch, 2013; De Sterck, 2015). (Full citation
information and links to talk video are available at http://wici.ca/new/events/.)
Selective altruism in collective games
Andrea Rapisarda
Dipartimento di Fisica e Astronomia and Infn  Università di Catania,
Italy
Coauthors: Dario Zappalà and Alessandro Pluchino
We study the emergence of altruistic behaviour in collective games. In
particular, we take into account Toral's version of collective Parrondo's
paradoxical games, in which the redistribution of capital between agents,
who can play different strategies, creates a positive trend of increasing
capital. In this framework, we insert two categories of players, altruistic
and selfish ones, and see how they interact and how their capital evolves.
More in detail, we analyse the positive effects of altruistic behaviour,
but we also point out how selfish players take advantage of that situation.
The general result is that altruistic behaviour is discouraged, because
selfish players get richer while altruistic ones get poorer. We also consider
a smarter way of being altruistic, based on reputation, called ''selective
altruism'', which prevents selfish players from taking advantage of altruistic
ones. In this new situation it is altruism, and not selfishness, to be
encouraged and stabilized. Finally, we introduce a mechanism of imitation
between players and study how it influences the composition of the population
of both altruistic and selfish players as a function of time for different
initial conditions and network topologies adopted.
Modeling The Dynamics of Knowledge Creation in Online Communities
Bosiljka Tadic
Department of Theoretical Physics, Jozef Stefan Institute, Ljubljana, Slovenia
Coauthors: Marija Mitrovic Dankulov, Scientific Computing Laboratory,
Institute of Physics Belgrade, Serbia
Exchange of knowledge contents supported by online communication systems
can lead to the emergent behavior, where interacting communities share
an accumulated knowledge. In this process, both the knowledge of individual
actors as well as the patterns of their conduct over time play an important
role. In Ref. [1], we have analyzed the emergence of collective knowledge
in a modern Questions & Answers (Q& A) system Mathematics, where
cognitive elements of each artifact are marked by several tags within
the standard mathematical classification scheme. Here, we present a microscopicmodel
of knowledge sharing, which correctly accounts for the detailed description
of the process from the elementary to the global scale. Based on our experience
in modeling online social communications [2, 3, 4], the knowledgebased
interactions in this model are closely related to the dynamics observed
in the empirical system [1]. Specifically, the interaction rules match
the studied Q& A system, and the profiles of the actors in the model
are statistically similar to the profiles of users in Mathematics. In
addition, we assume that at least minimal matching occurs between the
cognitive contents of the answered question and the actor's expertise,
which can be expressed by a combination of tags.
Following the sequence of events in the simulations, we observe the growth
of a bipartite graph of actors and their artifacts, and the appearance
of network communities. The structure of communities reveals the principal
actors and the involved cognitive elements. We sample time series related
to the integral activity in the network as well as the activity that is
strictly involving a particular cognitive element or specified combinations
of such elements. By analysis of these time series, we determine various
indicators of the collective behavior and the related knowledge contents.
Furthermore, we investigate how these indicators depend on the actors'
profiles and the range of their expertise.
This work was supported by the program P10044 of the Research Agency
of the Republic of Slovenia and the European Community's COST action TD1210
Analyzing the dynamics of information and knowledge landscapesKNOWeSCAPE.
References
[1] M. Mitrovic Dankulov, R.Melnik, B. Tadic, Dynamics of meaningful social
interactions and emergence of collective knowledge, under review.
[2] M. Mitrovic, B. Tadic, Dynamics of bloggers' communities: Bipartite
networks from empirical data and agentbased modeling, Physica A 391,
52645278 (2012).
[3] B. Tadic and M. Šuvakov, Can HumanLike Bots Control Collective
Mood: AgentBased Simulations of Online Chats J. Stat. Mech. Theory and
Experiment, P10014 (2013).
[4] B. Tadic, Modeling behavior of Web users as agents with reason and
sentiment, in "Advances in Computational Modeling Research: Theory,
Developments and Applications", edited by A.B. Kora, Novapublishing,
N.Y., 2013, ISBN: 9781626180659
Speculative Constraints on Oligopoly
Henry Thille
University of Guelph, Department of Economics & Finance, Canada
Coauthors: Sebastien Mitraille
The activity of speculators in markets for storable commodities is viewed
with suspicion by many people, however this activity plays a relatively
benign role in most economic models that allow for it. Most of the research
on the economics of speculation employs a perfectly competitive assumption
that we show is crucial to generate the generally positive view of speculation
prevalent in the economic literature. By allowing for imperfectly competitive
production, as would be appropriate for many mineral and energy commodities,
we show that speculation can result in outcomes that are more ambiguous
in their implications for welfare.
Our approach is to analyze an infinitehorizon game in which producers'
output can be purchased by speculators for resale in a future period.
The existence of speculators serves to constrain the feasible set of prices
that can result from producers' output game in each period. In the absence
of speculation, producers play a repeated Cournot game with random demand.
With speculative inventories possible, the game becomes a dynamic one
in which speculative stocks are a state variable which firms can control
via their influence on price. We employ collocation methods to find the
unknown expected price and value functions required for computation of
equilibrium quantities. We demonstrate that strategic considerations result
in an incentive to sell to speculators that is nonmonotonic in the number
of producers: speculation has the largest effect on equilibrium prices
and welfare for market structures intermediate between monopoly and perfect
competition. Using a computed example, we demonstrate that the effect
of speculative storage on the average price level can be substantial,
even though the effects on social welfare can be ambiguous.
A stochastic compartmental model of herd immunity within semiclosed
environments
Edward W. Thommes
Department of Mathematics & Statistics, University of Guelph, Canada
We numerically investigate local herd immunity, that is, the herd effect
which arises when vaccination occurs in an environment, community etc.
within which members spend some but not all of their time. Examples are
vaccination programs in workplaces, schools or nursing homes. Since such
environments typically contain only small populations, an ODEbased continuum
model is not the best approach to realistically characterize the transmission
dynamics. On the other end of the spectrum, the level of detail of an
individualbased model is not needed for a simple analysis. Instead, we
start out with an intermediate approach, and use a stochastic compartmental
model. We report model results using influenza as an example.
Agentbased approach and Cellular Automata: a promising perspective
in crowd dynamics modeling?
Jaroslaw Was
AGH University of Science and Technology, Poland
Coauthors: Robert Lubas, Jakub Porzycki, Marcin Mycek
In recent years, one can observe a sharp increase of interest in crowd
behavior modeling. Depending on the applications different simulations
have been created. In many fields fast and reliable simulations of crowd
dynamics are required. Efficiency of Cellular Automata combined with complexity
of Agentbased approach seem to be an interesting solution. A few interesting
crowd modeling case studies from international projects will be analyzed
and the current challenges will be discussed.
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Contributed Abstracts
Concurrent Behaviourally Motivated NonPharmaceutical Intervention and
Vaccination Decisions in an Agent Based Model of Seasonal Influenza
Michael Andrews
University of Guelph, Guelph, ON, Canada
Coauthors: Chris Bauch
Human behaviour can have a large impact on the spread of infectious diseases.
For example, people have been observed to change their regular social
routines in response to the presence of a disease, in order to reduce
their risk of becoming infected. To accomplish this, there are two primary
selfprotective intervention strategies individuals can utilize. These
are pharmaceutical interventions, such as vaccination, and nonpharmaceutical
interventions (NPIs), such as social distancing, strict respiratory etiquette,
and increased hand washing. The usage of these intervention strategies
are largely voluntary, and so individual decision making plays an important
role in how often they are utilized.
Theoretical models of disease spread have incorporated how individuals
make decisions concerning these interventions in the face of disease risks
and intervention costs. However, previous models have generally considered
these two intervention strategies separately from one another. Here, we
utilize an agentbased simulation model on a contact network to simultaneously
incorporate decisionmaking processes for both of these intervention strategies
with respect to seasonal influenza.
The choices of whether or not to vaccinate and practice NPIs in our model
are driven by concepts from decision field theory. This method allows
us to capture the decisionmaking processes of individuals in an uncertain
environment. These decisions are based on previous experience with the
disease, the current state of infection amongst one's contacts, and the
personal and social impacts of the choices they make.
We find that when considering these two major disease interventions as
behaviorallydriven decisions, measures taken to increase the uptake of
one intervention can alter transmission patterns, thus reshaping perceived
risks which in turn reduce the uptake of the other intervention. The effectiveness
of the interventions also play an important role in the level of interference
each receives from the other. As a result, measures that support expansion
of only vaccination (such as reducing vaccine cost), or measures that
simultaneously support vaccination and NPIs (such as emphasizing harms
of influenza infection, or satisfaction from preventing infection in others
through both interventions) can significantly reduce influenza incidence,
whereas measures that only support expansion of NPI practice (such as
making hand sanitizers more available) have little net impact on influenza
incidence. (However, measures that improve NPI efficacy may fare better.)
We conclude that the impact of interference on programs relying on multiple
interventions should be carefully studied, for both influenza and other
infectious diseases.
MeanField Teams
Jalal Arabneydi
McGill University, Montreal, QC, Canada
Coauthors: Aditya Mahajan
We introduce a model of decentralized control systems that consists of
a finite population of heterogeneous agents. Each agent has a local state
(that evolves with time) and a type (that does not change with time).
The meanfield denotes the empirical distribution of agents of each type.
The dynamics of the state of each agent depends on the local control action
and the (global) meanfield. The objective is to minimize the expected
cost over a finite or infinite horizon, where the perstep cost is an
arbitrary function of the states and actions of all agents.
The above model, which we call meanfield teams, arises in many engineered
systems including smart grids and communication networks. The salient
features of the model are the following. First, information is decentralized.
Each agent only observes its local state and the meanfield; there is
no agent that observes the complete state of the system . Second, all
agents operate as a team and have a common objective. Third, the system
is dynamic and the agents can signal partial information about their local
states to other agents through the meanfield. Finally, the objective
is to identify teamoptimal decision rules (rather than personbyperson
optimal rules).
We use the common information approach and spatial symmetry to identify
a dynamic program that determines the optimal decision strategies for
all agents. The solution complexity of the dynamic program is polynomial
in the number of agents and exponential in the number of types. The theory
is illustrated on examples motivated by demand response in smart grids.
Identifying Continuous Cellular Automata in partial observation setting
using differential evolution
Witold Bolt
Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland
Coauthors: Jan M. Baetens, Bernard De Baets (KERMIT, Department of
Mathematical Modelling, Statistics and Bioinformatics, Ghent University,
Ghent, Belgium)
We consider the identification problem of Continuous Cellular Automata
(CCAs) [2], defined as convex combinations of Boolean Cellular Automata
(CAs), generalized to the unit interval. The identification problem is
defined and solved in the context of partial observations with time gaps
of unknown length [1], i.e. prerecorded, partial configurations of the
system at certain, unknown time steps. This partial context allows for
modeling situations with malfunctioning measuring equipment or timescale
synchronization issues between the model and observations.
A solution of the identification problem, which is proposed here is based
on one of the variants of Differential Evolution (DE) algorithm, namely
adaptive DE [4] with a radiuslimited selection [3]. The initial results
of the experiments shows that for many CCAs, full identification is possible,
even when the amount of missing observations is relatively high (for example
more than 70% of cells missing in each of the captured time frames). Yet,
further experiments indicate that the performance of the algorithm and
the identifiability of a given CCA depend on dynamical characteristics
of the identified system.
Up until now, the identification problem in the setting proposed here,
which is based on partial observations has not yet been discussed in the
literature in the context of CCAs. The presented results justify further
research on the topic of identification based on partial information.
Moreover, the DE algorithm has not yet been widely used in the CA domain.
The results of experiments conducted in this study are very promising,
and potential for further applications of this algorithm in the CCA context
are very broad.
References:
[1] Bolt, W.; Baetens, J.M.; De Baets, B., "An evolutionary approach
to the identification of Cellular Automata based on partial observations",
Evolutionary Computation (CEC), 2015 IEEE Congress on [this was presented
few weeks ago in Sendai, Japan, and will be published shortly]
[2] Bolt, W.; Baetens, J.M.; De Baets, B., "On the decomposition
of stochastic cellular automata", arXiv:1503.03318
[3] Spector, L., and J. Klein. 2005. Trivial Geography in Genetic Programming.
In Genetic Programming Theory and Practice III, edited by T. Yu, R.L.
Riolo, and B. Worzel, pp. 109124. Boston, MA: Kluwer Academic Publishers.
[4] Brest, J.; Greiner, S.; Boskovic, B.; Mernik, M.; Zumer, V., "SelfAdapting
Control Parameters in Differential Evolution: A Comparative Study on Numerical
Benchmark Problems," Evolutionary Computation, IEEE Transactions
on , vol.10, no.6, pp.646,657, Dec. 2006
Answering Simple Questions About Spatially Spreading Systems
Mark Crowley
Electrical and Computer Engineering, University of Waterloo, ON, Canada
An important subclass of complex dynamic systems are ones that contain
some form of spatially spreading process such as fire, infectious disease,
urban sprawl, etc. In some of these domains machine learning approaches
have been applied to try to learn compact predictive models or to find
optimal policies for intervening[1][2]. One challenge in these domains
is that practitioners in the field rarely directly use them to make decisions.
Rather, the algorithm provides a small input into a larger human making
decision process, so the full model or optimized policy is not used.
I will discuss some ideas for a different, minimalist approach, to learn
just enough to answer some core questions about the current policy: 'Should
we do something different?' or 'Should an expert look at this more closely
to make a decision?'.
Another way to look at this is to ask: "Do the data, historical records
and simulations indicate that the current approach will likely lead to
a catastrophic event (huge wildfire, onset of disease, large outbreak
of pest or invasive plant) in the near or not so near future?"
These questions are simpler than detailed prediction or performing a full
policy optimization but they can still be used with machine learning techniques
if we have the right data. I'll talk about what the right data is in this
case and how it could be used to provide tools which answer these questions
for a range of systems containing spatially spreading processes.
One idea I will demonstrate is using dense visualizations of trajectories
to implicitly encode causal relationships and human knowledge but designing
these visualizations as input data for training classifiers and simple
predictive models rather than solely for human use.
References
[1] Crowley, M. Using Equilibrium Policy Gradients for Spatiotemporal
Planning in Forest Ecosystem Management. IEEE Transactions on Computers.
2013
[2] Dietterich, T., Taleghan, M., Crowley, M. PAC Optimal Planning for
Invasive Species Management : Improved Exploration for Reinforcement Learning
from SimulatorDefined MDPs. AAAI2013. Bellevue, WA, USA. 2013
Fractional Dynamic in Oligopoly Model
Sipang Dirakkhunakon
Sripatum University, University in Bangkok, Thailand
The nonlinear dynamics in economics have been intensively studied since
the discovery of chaotic property in weather model by Lorenz. The studies
of discrete chaotic model are proliferating since the study of the discrete
logistic function by May. Oligopoly market is the market structure in
which a trade is dominant by a few firms; the mathematical model described
the interaction among the firms in this market type was proposed by French
Mathematician Cournot in 1838. The original model was explained by the
interaction between two firms that produce the same product type with
linear equation and assumed that each firms adjust their quantity of product
to the market, as there are no reaction from the rivals. The recent nonlinear
studies of economics show that the nonlinear behaviors of this market
structure are complex. Rand has shown the existence of chaotic dynamics
in Cournot duopoly model by assuming two unimodal reaction functions.
Kopel has proved that the cost functions yield unimodal reaction curve
by assuming that the inverse demand curve is unchanged and linear. Puu
has shown that in a discrete model of Cournot duopoly dynamics, if there
is an isoelastic market demand curve with price, simply the reciprocal
of the sum of the two firms' outputs and the firms faced constant marginal
cost, periodic and chaotic dynamics could easily exhibit. Bischi and Kopel
have proposed the duopoly model where reaction function is described by
logistic equation. They have proved the longrun behavior characterized
by multistability where coexisting stable are Nash equilibriums where
players have adaptive expectations. They have shown that the reaction
functions of the two players are assumed to be nonlinear and nonmonotonic.
In this paper, we have study the discrete Cournot duopoly model proposed
by Bischi and Kopel further with fractional calculus. Our approach is
to understand how the behaviors of the model changes upon slight changes
in reaction functions. The numerical results of fractionalorder are presented
in graphical form of phase space where the limit cycle, Nash equilibrium
and chaotic exists in different regime.
References
1. Cournot A. (1838), Researches into the principles of the theory of
wealth, Engl. transl., Chapter VII, 1963, Irwin Paperpack Classic in Economics,.
2. Lorenz E.N. : Deterministic Nonperiodic Flow, Journal of the Atmospheric
Sciences 20: 130141 (1963).
3. May R.M. : Simple mathematical models with complicated dynamics, Nature,
261, pp.459467 (1976)
4. Kopel, M.: Periodic and chaotic behavior of a simple R&D model.
Ricerche Economiche 50, 235265 (1996a).
5. Kopel, M.: Simple and complex adjustment dynamics in Cournot Duopoly
Models. Chaos, Solitons, and Fractals 7, 20312048 (1996b)
6. Bischi, G.I., Kopel, M.: Equilibrium selection in a nonlinear duopoly
game with adaptive expectations. Journal of Economic Behavior & Organization
46(1), pp.73100 (2001)
7. Bischi G.I., Mammana C., Gardini L. : Multistability and cyclic attractors
in duopoly games, Chaos, Solitons and Fractals 11, pp.543564 (2000)
8. Podlubny I.: Fractional Differential Equations, vol. 198, Academic
Press, San Diego, Calif, USA (1999)
9. Puu T.: Chaos in duopoly pricing, Chaos, Solitons & Fractals 1
, pp. 573581 (1991)
10. Puu T.: Complex dynamics with three oligopolists, Chaos, Solitons
& Fractals 7 , pp.20752081 (1996)
Slides. Note: This presentation
was received from a registered participant but not delivered at the conference
due to lastminute cancellation.
Microscopic rules of multispecies interaction lead to a class of macroscopic
crossdiffusion problems
Hermann J Eberl
University of Guelph, Guelph, ON, Canada
Coauthors: Kazi A Rahman
Starting with a discreteinspace, continuousintime master equation
we formulate a framework of local rules for spatial interactions between
species, where the local movement of individuals depends both on the densities
of species in the current (departure) and target (arrival) site. We show
that a continuous refinement of the underlying discrete space leads to
a class of nonlinear partial differential equations with crossdiffusion
effects, which has applications in various areas of mathematical biology.
We can furthermore show that this construction preserves positivity, which
is not a trivial property of crossdiffusion problems in general. We apply
the framework to simulate dualspecies biofilms systems.
Hyperbolic and degenerate hyperbolic behaviour in cellular automata
Henryk Fuks
Brock University, St. Catharines, ON, Canada
Cellular automata are infinitelydimensional dynamical systems, yet a
behaviour similar to hyperbolicity in finitedimensional systems has been
observed in many of them. In particular, in some binary cellular automata
in one dimension, known as asymptotic emulators of identity, if the initial
configuration is drawn from a Bernoulli distribution, the expected proportion
of ones (or zeros) tends to its stationary value exponentially fast. We
show that if one allows more than two states, or considers probabilistic
cellular automata, degenerate hyperbolicity can be observed, similar to
degenerate hyperbolicity in finitelydimensional systems. In such cases,
the convergence to stationary value is linearexponential. For selected
cellular automata rules exhibiting degenerate hyperbolicity, we demonstrate
how to construct explicit expressions for probabilities of occurrences
of symbols of the alphabet as a function of time.
On the shortcut network within protein residue networks
Susan Khor
Memorial University of Newfoundland, St John's NL
A Protein Residue Network (PRN) is a network of interacting amino acids
within a protein. The smallworld network (SWN) [1] within protein molecules
has held a special interest for protein scientists who use its properties
to identify functional (e.g. binding and nucleation) sites, and to map
the communication pathways within proteins [2, 3]. However, modeling the
formation of the SWN within proteins is still a challenge for those seeking
an algorithmic understanding of protein folding logic. We propose that
a sparser but more volatile subnetwork of a PRN called the shortcut
network (SCN) is a suitable object of study for modeling the evolution
of navigable SWNs in proteins. A SCN comprises a subset of PRN edges that
function as shortcuts in the course of a local greedy search. A PRN with
N nodes has about 2N shortcut edges [4]. The shortcut edges are enriched
with shortrange contacts and have high betweenness [4]. Here, we describe
the dynamical aspects of SCNs as observed in two Molecular Dynamics (MD)
simulations. We find that a (wellformed) SCN grows as a protein folds
to span almost all the nodes of its PRN. SCN wellformness correlates
strongly with the presence of secondary structures. SCNs from "unsuccessful"
MD trajectories were less wellformed than those from "successful"
MD trajectories. The set of links that make up an SCN undergo significantly
more changes (additions and deletions) during protein folding than other
PRN links. Nonetheless, we observed that deleted shortcuts can be predicted
from a given set of shortcuts, and there is a nonrandom relationship
between deleted and added shortcuts. With respect to a spanning tree,
the majority of added shortcuts are found in the edge cutset of at least
one deleted shortcut, and the majority of deleted shortcuts contain
at least one added shortcut in their edge cutsets. This high edge replacement
rate helps to maintain connectivity, and coupled with strong SCN transitivity
[5], fosters the growth of the largest connected component of a SCN.
Acknowledgements
This work was made possible by the facilities of the Shared Hierarchical
Academic Research Computing Network (SHARCNET:www.sharcnet.ca) and Compute/Calcul
Canada. Funding was provided in part through a postdoctoral research
position at Memorial University.
References
[1] Watts DJ and Strogatz SH (1998) Collective dynamics of 'smallworld'
networks. Nature 393, 440442.
[2] Vendruscolo M, Dokholyan NV, Paci E and Karplus M (2002) Smallworld
view of the amino acids that play a key role in protein folding. Physical
Review E 65 0619101.
[3] Atilgan AR, Akan P and Baysal C (2004) Smallworld communication of
residues and significance for protein dynamics. Biophysical Journal 86:8591.
[4] Khor S (2015) Protein residue networks from a local search perspective.
Journal of Complex Networks. In press. doi:10.1093/comnet/cnv014.
[5] Serrano MA and Boguna M (2006) Clustering in complex networks. II.
Percolation properties. Phys. Rev. E 74, 056115.
[6] A preprint of this work is available at arXiv:1412.2155v4 (section
4).
Performance Of Simple Cognitive Agents Using Observational Learning
Anna T. Lawniczak
University of Guelph, Guelph, ON, Canada
We present a model of simple cognitive agents, called "creatures"
learning to cross a highway. The creatures use a type of "social
observational learning", that is each creature learns from the behaviour
of other creatures. The creatures may experience fear and/or desire and
they a capable of evaluating if a strategy of crossing a highway has been
applied successfully or not, and they are able of applying this strategy
again to similar but new situations. We study performance of various populations
of the creatures, characterized by fear and desire, when they are learning
to safely cross various types of highway. We present selected simulation
results and their analysis.
Acknowledgement: The author acknowledges joint work and discussions with
Bruno Di Stefano, Jason Ernst, Leslie Ly and Shengkun Xie
Networkdriven ranking in complex systems
Hao Liao
Department of Physics, University of Fribourg, Switzerland
The complex systems research domain continues to attract attention of
scholars worldwide and produces new models, concepts, and applications
in various disciplines of science. Complex network theory in particular
has been applied to understand human behavioral patterns and the formation
of social structures, and filter the abundant information. At most online
services and website such as YouTube and Facebok, the complexity arises
from the large number of users and their activities as well as from their
interactions. In order to unveil the useful information in a complex system,
two strategies are investigated. We present an improved iterative refinement
based algorithm, which determines the reputation of users by comparing
their ratings with the aggregate ratings provided by the whole rating
system. We improve the original iterative refinement algorithm by two
methods: reputationredistribution process and rating projection data
pretreatment. The results show that these methods effectively enhance
the weight of the highly reputed users and reduce the weight of the users
with low reputation in estimating the quality of objects, which significantly
improve the algorithm's robustness against malicious spamming behaviors.
Supporting the facility design process in terms of optimal pedestrian
flow
Robert Lubas, Jakub Porzycki
Department of Applied Computer Science, AGH University of Science and Technology
in Kraków, Poland
Coauthors: Jaroslaw Was
Safety and comfort in public use facilities like stadiums, theatres,
and shopping centres depends strongly on their ability to handle high
crowd loads, both during the typical use and in case of evacuation scenarios.
This paper describes the methodology of supporting of the facility design
process in order to increase that facility's safety and comfort of use.
The main issue of facility design support is to define how particular
architecture solutions (e.g. the placement and width of exits and corridors,
arrangement of barriers and columns) influence the pedestrian flow. Another
important aspect discussed in this paper is the development and application
of simulation tools that allow for quick and reliable testing of architectural
solutions in terms of crowd dynamic characteristics.
Currently there is a long list of regulations that public use facility
architectural plans should meet. However, it should be highlighted that
even with these regulations one can design a building with low pedestrian
flow characteristics. The illustrative case studies of facility designs
in terms of optimization of pedestrian flow are presented.
Analytical approach to calculating shortest path lengths on networks
Sergey Melnik
MACSI, Department of Mathematics & Statistics, University of Limerick,
Ireland
Coauthors: James P. Gleeson
The length of the shortest path between two nodes, also known as the
intervertex distance or geodesic distance, is an important metric characterizing
the network topology and how efficiently one can traverse the network.
The calculation of shortest path lengths is necessary for a wide range
of applications: from assessing the resilience of communication networks
to attacks and failures [1] to estimating the accuracy of analytical approximations
for dynamics on networks [2].
Significant effort has been devoted to the development of efficient numerical
algorithms for the exact or approximate calculation of intervertex distances
on a given network (see, for example, Ref. [3] and references therein),
but there is still a need for improved analytical results for ensembles
of random networks [48].
We present an analytical approach to calculating the distribution of lengths
of shortest paths between two randomly chosen nodes (i.e., the probability
that a randomlychosen pair of nodes is a certain distance apart) in unweighted
undirected random networks.
Our analytical approach compares favorably with several other analytical
methods in terms of its simplicity and accuracy. We obtain accurate results
for random configuration model networks (specified by their degree distribution
p(k)) and for degreecorrelated random networks (specified by their joint
degreedegree distribution P(k.k')). We also find good agreement with
numerical calculations of intervertex distances for several realworld
networks. Another advantage of our approach is that it is readily applicable
to networks consisting of several modules [9] or networks with high clustering
coefficient [10].
[1] R. Albert, H. Jeong, and A. L. Barabási, Nature (London) 406,
378 (2000).
[2] S. Melnik, A. Hackett, M. A. Porter, P. J. Mucha, and J. P. Gleeson,
Phys. Rev. E 83, 036112 (2011).
[3] U. Zwick, in Proc. of 9th ESA (Springer, 2001), pp. 3348.
[4] M. E. J. Newman, S. H. Strogatz, and D. J. Watts, Phys. Rev. E 64,
026118 (2001).
[5] A. Fronczak, P. Fronczak, and J. A. Holyst, Phys. Rev. E 70, 056110
(2004).
[6] S. N. Dorogovtsev, J. F. F. Mendes, and A. N. Samukhin, Nucl. Phys.
B 653, 307 (2003).
[7] S. N. Dorogovtsev, J. F. F. Mendes, and J. G. Oliveira, Phys. Rev.
E 73, 056122 (2006).
[8] A. Fronczak, P. Fronczak, and J. A. Holyst, AIP Conf. Proc. 776, 52
(2005).
[9] S. Melnik, M. A. Porter, P. J. Mucha, and J. P. Gleeson, Chaos 24,
023106 (2014); J. P. Gleeson, Phys. Rev. E 77, 046117 (2008).
[10] J. P. Gleeson, Phys. Rev. E 80, 036107 (2009); J. P. Gleeson and
S. Melnik, Phys. Rev. E 80, 046121 (2009).
Wide motifs: a new tool for when cycles matter
PierreAndre Noel
University of California, Davis, CA, USA (Postdoctoral Researcher)
From epidemiology to power engineering, modern society faces numerous
problems that can be understood as dynamical processes taking place on
complex networks. Random graph ensembles help us understand how these
processes' outcomes are affected by different network properties, and
how to leverage this knowledge to control the issue. However, the existing
analytical apparatus mainly deals with treelike random graphs [16],
thus seriously restricting the spectrum of complex networks and dynamical
processes that can be investigated through them. I will present how to
remove this requirement for treelike graphs, instead allowing for cycles
of any length sharing intricate overlaps. These advancements greatly improve
our analytical capabilities and should enable exciting new research. Although
the original motivation concerns the study of cascading failures on power
grids, the method should prove useful in a plethora of different applications
for which cycles play a fundamental role.
The crux of the new approach is the introduction of "wide motifs",
a concept generalizing both ideas of network motifs [37] and tree decomposition
[8]. Standard network motifs can be thought of as "meta vertices"
containing a subgraph of "real vertices", and wide motifs inherit
this property. However, different wide motifs may be joined by "meta
edges" containing a certain number of "real edges". Hence,
where the standard approach defines treelike random graphs by assembling
trees of network motifs, the new approach can assemble trees of wide motifs
to define non treelike random graphs containing cycles of any length
with intricate overlaps. Given a specific dynamical process, a transfer
tensor (generalizing transfer matrices) can be associated to each wide
motif: these tensors are contracted in the same way that the motifs are
assembled. This procedure results in a probability generating function
specifying the distribution of different outcomes for this dynamical process
on the random graph ensemble.
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arbitrary degree distributions and their applications. Physical Review
E 64, 026118 (2001). http://dx.doi.org/10.1103/PhysRevE.64.026118
[2] A. Allard, P.A. Noel, L. J. Dubé and B. Pourbohloul. Heterogeneous
bond percolation on multitype networks with an application to epidemic
dynamics. Physical Review E 79, 036113 (2009). http://dx.doi.org/10.1103/PhysRevE.79.036113
[3] M. E. J. Newman. Random Graphs with Clustering. Physical Review Letters
103, 058701 (2009). http://dx.doi.org/10.1103/PhysRevLett.103.058701
[4] J. C. Miller. Percolation and epidemics in random clustered networks.
Physical Review E 80, 020901(R) (2009). http://dx.doi.org/10.1103/PhysRevE.80.020901
[5] B. Karrer and M. E. J. Newman. Random graphs containing arbitrary
distributions of subgraphs. Physical Review E 82, 066118 (2010). http://dx.doi.org/10.1103/PhysRevE.82.066118
[6] A. Allard, L. HébertDufresne, P.A. Noël, V. Marceau
and L. J. Dubé. Bond percolation on a class of correlated and clustered
random graphs. Journal of Physics A: Mathematical and Theoretical 45,
405005 (2012). http://dx.doi.org/10.1088/17518113/45/40/405005
[7] R. Milo, S. ShenOrr, S. Itzkovitz, N. Kashtan, D. Chklovskii and
U. Alon. Network Motifs: Simple Building Blocks of Complex Networks. Science
298, 824 (2002). http://dx.doi.org/10.1126/science.298.5594.824
[8] H. L. Bodlaender. Treewidth: Characterizations, Applications, and
Computations. In GraphTheoretic Concepts in Computer Science (LNCS 4271),
Springer (2006). http://dx.doi.org/10.1007/11917496_1
Modeling Complex Networks by (Dynamic) Markov Random Fields
Dimitri Papadimitriou
Bell Labs, Antwerpen, Belgium
Probabilistic graphical models allows for succinct representation of
highdimensional distributions, where each node in the graph represents
a random variable and the graph encodes the conditional independence relations
among the random variable. A Markov random field (MRF) defines an undirected
graphical model representation where the absence of an edge between two
nodes implies that the corresponding random variables are independent,
conditioned on all the other random variables in the network. Undirected
graphical models are useful in modeling a variety of phenomena where one
cannot naturally ascribe a directionality to the interaction between random
variables. Furthermore, undirected models offer a different and often
simpler perspective on directed models, both in terms of the independence
structure and the inference task.
The goal of MRF structure learning is to discover regions of high probability
in the instance space, form features to represent them, and learn the
corresponding weights. More specifically, learning the underlying graph
structure of a Markov random field refers to the problem of determining
if there is an edge between each pair of nodes, given independent and
identically distributed samples drawn from the joint distribution of the
vector of random variables X. The conventional techniques for learning
MRF structure correspond to two different interpretations of a graphical
model. On the one hand, to learn the underlying graph, the parameter estimation
techniques exploit the conditional independence interpretation of a graphical
model which lead to a factorization of the joint probability function
according to the cliques of the graph. These techniques are tailored for
a specific parametric form of the probability distribution by assuming
a certain form of the potential function; thereby they relate the structurelearning
problem to one of finding a sparse maximum likelihood estimator of a distribution
from its samples. When a parametric family is known, the (log) likelihood
of the data is written as a function (often convex) of the parameters
of the distribution; this likelihood is then maximized with added regularizes
to find these parameters. On the other hand, methods based on learning
conditional independence relations between the variables rely on the notion
that a node's Markov blanket, i.e. its neighborhood in the graphical model,
makes a node conditionally independent of other nodes. These methods are
potential agnostic, i.e., to learn the graph structure they do not rely
on the knowledge of the underlying parameterization or make assumptions
on the parameterization of the distribution. Instead, they involve an
exhaustive search over all potential neighborhoods of a node which results
in a high computational complexity for the algorithms which need some
assumption on the properties of the underlying distribution and graph
structure (such as the maximum node degree) in order to succeed. Hence,
search strategies are often based on heuristics including greedy search
strategies, e.g., greedy hillclimbing, greedily adding nodes that give
the highest reduction in conditional entropy.
The general idea behind the exploitation of the MRF model in the context
of complex systems and networks is to enable drawing largescale maps
when each entity can take one of multiple (in particular, two) basic stands
on a network state taking into account their interactions and external
field or influence. In the most general formulation of this model, one
would allow interactions of various strength or intensity between entities.
This kind of model enables also to determine the influence of external
field (e.g., influence) and neighbordriven "alignment" from
interactions. This already constitutes an interesting research question
as of whether combination of pairwise potential (a.k.a. edge potentials)
would be sufficient or higherorder potential functions should be used
instead to model multipartite interactions. Another fundamental question
relates to the parameter estimation and tuning in settings where the spatiotemporal
dynamics of the phenomena influences the model. In turn, extending MRF
capability would enable modeling complex networks phenomena such as dynamic
network formation (selforganization), opinion formation/prediction but
also information diffusion processes.
Dynamic data driven simulation as a basis of crowd management supporting
system
Jakub Porzycki; Robert Lubas
AGH University of Science and Technology in Kraków, Department of
Applied Computer Science
Coauthors: Jaroslaw Was
Nowadays, one can notice growing demands for tools that which can support
police forces/LEA (Law Enforcement Agency) during mass gatherings in order
to increase the comfort and the safety of event attendees. In this paper
we present a concept of the system that uses dynamic data driven simulation
to support decision processes for crowd management.
The proposed system consist of three layers: the first is dedicated to
extraction of pedestrian movement parameters (such as speed, size and
mass), the second is the crowd simulation layer (CAbased model applied)
that acquires information about pedestrians from the first layer, the
third layer is responsible for the analysis or simulation output. A crucial
part of this system is a proper crowd dynamic model  efficient enough
to simulate different scenarios faster than real time and reliable in
terms of application for crowd safety. Therefore we decided to use the
Social Distances Model designed for mass evacuation. This is a cellular
automaton, agent based model of crowd dynamics, which takes into account
proxemics relations between pedestrians and dynamic route choice.
In the paper, we show a sample dynamic data driven simulator that uses
pedestrian movement parameters obtained from a depth sensor. We provide
technical aspect of this prototype including data processing and a description
of system components and their connections.
An illustrative example of possible application of crowd management supporting
system is provided. We take into account, as an example, the relatively
complicated geometry of a public facility building with a capacity for
thousands of people. Simulation results of the base scenario, without
crowd management, show some clogging and high egress time. However, by
simulation of different scenarios and its result's analysis we can chose
which action should be performed in order to minimalize potential risk
and optimize the crowd transportation parameters.
We believe that an approach applying sensor data as input to reliable
and quick, discrete crowd simulation with a result analysis can be a step
towards the crowd management supporting system. This paper proposes a
possible system architecture, discusses selection criteria for crowd models
and shows details of its most critical parts.
Anomalous diffusion of deterministic walks on a square lattice
Raúl Rechtman
Instituto de Energías Renovables, Universidad Nacional Autónoma
de México
A walker moves on a two dimensional square lattice, the landscape. At
every site of the lattice there is an obstacle which is in one of two
possible states, say 1 and 1, that force the walker to turn either left
or right. After the walker passes the state of the obstacle changes. In
this way, the walker modifies the landscape during his walk. If p is the
initial fraction of randomly placed obstacles in state 1 when the walk
starts and we consider an ensemble of initial landscapes, we find anomalous
diffusion for some values of p. Two types of landscape are studied, obstacles
that act as rotors and obstacles that act as mirrors.
Biomimicry Based Decision Of Computationally Minimal Cognitive Agents
Bruno Di Stefano
Nuptek Systems Ltd., Toronto, ON, Canada
Coauthors: Anna T. Lawniczak
Imitation is a type of social observational learning allowing the transfer
of knowledge between individuals and from generation to generation without
the need for genetic inheritance. Babies imitate individuals they come
in contact with, be they other babies, children, or grownups. It is conceivable
that through this type of learning, both animal and human knowledge and
behavior may include a concatenation of: "observation", "evaluation",
"imitation", "evaluation", and "learning".
Once the results of certain behavior have been shown to be good or bad,
this information becomes part of what has been learned. Once a sufficient
number of lessons have been learned, all these lessons become part of
the animal or human toolbox to navigate through life.
Biomimicry, the imitation of living biological entities to solve problems,
allows developing cognitive agents based on this social observational
learning, agents that have partially been improved by their own evolution.
These agents can be instantiated as software programs of hardware robots
or a combination of hardware and software.
Chaos in semiconductor laser optical injection at fractionalorder
Yoothana Suansook
Defence Technology Institute (Public Organisation) Bangkok, Thailand
Nonlinear dynamical system is fascinating subject to study. This subject
feasibly describes wide range of physical system from large scale to small
scale. The study of nonlinear dynamical system gained substantially since
the discovery of instabilities in atmospheric convection model by Lorenz.
The equations that described the dynamical system are differential equations
which yield different types of solutions such as limit cycle, periodic,
periodic doubling, nonperiodic and chaotic. Theory of PoincareBendixson
states that chaos exists in system with a least three independent variables.
Recently, the studies in this field have applied the theory of fractional
calculus to study the dynamical systems where the derivative can be fractionalorder.
In this paper, we have analyze the fractional dynamics of semiconductor
laser with monochromatic optical injection proposed by S.Wieczorek et
al., The model is described by threedimensional rate equations that consists
of the complex electric field and the normalized population inversion.
The numerical calculation of fractional order is obtained by modified
trapezoidal rule for fractional integral. Fractional order dynamics presented
by means of bifurcation diagrams and time series. We have numerically
investigated the chaotic behavior of the semiconductor laser rate equation
at different parameters. Numerical results confirm that fractionalorder
chaos does exist in this semiconductor laser model.
Slides.
Note: This presentation was received from a registered participant but
not delivered at the conference due to lastminute cancellation
Cellular Automat(ic) Design and Finite Nature: Theorizing HumanComputer
Interaction Using Discreet Mathematical Models
Stephen Trothen
University of Waterloo, Waterloo, ON, Canada
The use of discreet mathematical models as organizational techniques
for artistic practice has a long and varied history. From musical works
such as Iannis Xenakis' Horos in which the artist used cellular automata
to determine chord changes across progressions, to the use of fractals
in architecture, complex systems have traditionally provided numerous
techniques for artistic design and decision making. These techniques are
often materialized as a hybrid of mind and system in which the machine
becomes an entangled part of the artist's cognitive process and subsequent
output.
As N. Katherine Hayles notes, the automation that results from this hybridity
also extends to the way in which intelligence is handled in discussions
of feedback between the human and the technical, such that the "analogs
between intelligent machines and humans construct the human in terms of
the machine" (64). Drawing on the historical use of cellular automata
in design practice, my paper attempts to discuss the implications of automation,
and how this signals an increased blurring between conceptions of further
binaries such as: pattern/noise, body/environment, human/machine, art/algorithm.
This consideration will be anchored in a reading of the current resurgence
of neurofeedback and biofeedback in hardware and software from both a
technical, theoretical, and design perspective.
Further, in the way that approaches to generative design through the utilisation
of discreet models draws much inspiration from natural and biological
processes, my research seeks to explore the place of cognition within
the blurring of these various binaries. Of particular interest is Edward
Fredkin's Finite Nature Hypothesis in which he contended that the "digital
mechanics of the universe is much like a cellular automata, deterministic
in nature but computed with unknowable determinism". Fredkin's conception
will allow for a theoretical discussion of how his claim that all properties
can be "expressed by numbers because all properties are discrete
and stepwise" echoes the increased blurring of human and machine
and how this might be used as a method to understand the increasing interest
in designing for the mind and quantifying the self in interface design.
A General Framework for Sparse Random Graphs
Victor Veitch
Department of Statistical Sciences, University of Toronto, Toronto, ON,
Canada
Coauthors: Daniel M. Roy, Department of Statistical Sciences, University
of Toronto
It is a consequence of the wellknown AldousHoover theorem that any
random graph model that is both projective and satisfies a simple probabilistic
symmetry, exchangeability, must be either empty or dense. This means that
the majority of random graph models currently in use are inappropriate
for modeling realworld random network phenomena that result in sparse
structures. A recent paper of Caron and Fox circumvents this problem by
exploiting a connection between certain discrete random measures and random
graphs, giving rise to a family of sparse, projective random graph models.
In this work we extend this insight by establishing a relationship between
exchangeable random measures on the plane and random graphs. We give a
simple representation theorem for random graphs of this type and derive
a number of their basic properties, including the expected number of nodes,
expected number of edges, the asymptotic degree structure and the asymptotic
connectivity structure. This results in a general statistical framework
suitable for the analysis of real world networks; with both powerlaw
degree distributions and small world behaviour arising naturally in particular
examples.
Modelling awareness and adoption: aggregate behaviour versus agentbased
interactions with network effects
Erin Wild
University of Guelph, Guelph, ON, Canada
Coauthors: Monica Cojocaru
We construct and examine a model of adoption of a product or policy using,
firstly, a system of differential equations and then secondly, through
simulation, an agent based model. Awareness must come before adoption,
and we model this as a simple epidemic type model, where information is
spread through advertising and contact with other agents in the population.
Adoption is then conditional on awareness and occurs only if the agent
finds the perceived cost acceptable. After simulating the system using
an agentbased model, we introduce heterogeneity through the model parameters,
which are then considered individual attributes and include influence
rates, effectiveness of advertising, price sensitivity, and speed of adoption.
We also examine the effects of various network topologies by organizing
individuals into lattice and preferential attachment networks. From there,
we add two extra components to the adoption mechanism by introducing a
social influence factor by which an agent can be influenced by the adoption
patterns of their neighbourhood, as well as a green factor, which assumes
an environmental product or policy being adopted and is the likelihood
that an individual will adopt based on environmental reasons alone. We
found that advertising had the most effect on the length of time it took
for the model to reach its equilibrium. Influence rates and the speed
of adoption rate had a small effect on how fast awareness and adoption
took place within the first 100 time steps. The price sensitivity was
the only parameter to affect the resulting equilibrium point. Finally,
we found that various networks had less of an influence than expected
on the resulting equilibrium, and overall the results from the agentbased
simulations were very close to those obtained through differential equations.
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Program
Wednesday: June 17, 2015
8:459:15 Registration, Breakfast
Session Chair of Invited Talks: Bosiljka Tadic
9:159:30 Opening Remarks
9:3010:00  Paola Flocchini
University of Ottawa, Ottawa, ON, Canada
TimeVarying Graphs and Dynamic Networks
10:0010:30  Babak Farzad
Brock University, St. Catharines, ON Canada
Strategic models for network formation
10:3011:00 Break
Session Chair of Invited Talks: Paola Flocchini
11:0011:30  Raul J Mondragon
Queen Mary University of London, UK
Network ensembles based on the Maximal Entropy and the RichClub
11:3012:00  Bosiljka Tadic
Dept. of Theoretical Physics, Jozef Stefan Institute, Ljubljana, Slovenia
Modeling The Dynamics of Knowledge Creation in Online Communities
12:001:30 Lunch
Session Chair of Contributed Talks: Raul J Mondragon
1:301:50  Monica Cojocaru
University of Guelph, Guelph, ON, Canada
Modelling awareness and adoption: aggregate behaviour versus agentbased
interactions with network effects
1:502:10  Sergey Melnik
MACSI, Dept. of Math. & Stat., University of Limerick, Ireland
Analytical approach to calculating shortest path lengths on networks
2:102:30  PierreAndre Noel
University of California, Davis, CA, USA
Wide motifs: a new tool for when cycles matter
2:302:50  Victor Veitch
Dept. of Statistical Sciences, University of Toronto, Toronto, ON, Canada
A General Framework for Sparse Random Graphs
2:503:30 Break
Session Chair of Invited Talks: Pietro Lio'
3:304:00  Stanislaw Drozdz
Polish Academy of Sciences and Cracow University of Technology, Poland
Complexity characteristics of world literature
4:004:30  José Fernando Ferreira Mendes
University of Aveiro, Portugal
Structural properties of complex networks
4:306:00 Reception
Thursday: June 18, 2015
8:459:00 Breakfast
Session Chair of Invited Talks: Andrea Rapisarda
9:009:30  Dawn Cassandra Parker
University of Waterloo, School of Planning and WICI, Waterloo, ON, Canada
Integration of agentbased modeling, network science, analytical
models, and inductive metamodelling for applied analysis of complex
systems phenomena
9:3010:00  Jaroslaw Was
AGH University of Science and Technology, Cracow, Poland
Agentbased approach and Cellular Automata: a promising perspective
in crowd dynamics modeling?
10:0010:30 Break
Session Chair of Contributed Talks: Rolf Hoffmann
10:3010:50  Jakub Porzycki, Robert Lubas
AGH University of Science and Technology in Kraków, Poland
Dynamic data driven simulation as a basis of crowd management supporting
system
10:5011:10  Robert Lubas, Jakub Porzycki
AGH University of Science and Technology in Kraków, Poland
Supporting the facility design process in terms of optimal pedestrian
flow
11:1011:30  Jalal Arabneydi
McGill University, Montreal, QC, Canada
MeanField Teams
11:3011:50  Bruno Di Stefano
Nuptek Systems Ltd., Toronto, ON, Canada
Biomimicry Based Decision Of Computationally Minimal Cognitive Agents
11:5012:10  Anna T. Lawniczak
University of Guelph, Guelph, ON, Canada
Performance Of Simple Cognitive Agents Using Observational Learning
12:101:30 Lunch
Session Chair of Invited Talks: Franco Bagnoli
1:302:00  Andreas Deutsch
Centre for Information Services and High Performance Computing, Technische
Universität Dresden, Germany
Cellular automaton models for collective cell behaviour
2:002:30  Pietro Lio'
Computer Laboratory, University of Cambridge, UK
Cancer cell dynamics and liquid biopsies
2:303:00  Edward W. Thommes
Dept. of Mathematics & Statistics, University of Guelph, Canada
A stochastic compartmental model of herd immunity within semiclosed
environments
3:003:30 Break
Session Chair of Contributed Talks: Andreas Deutsch
3:303:50  Mark Crowley
Electrical and Computer Engineering, University of Waterloo, ON, Canada
Answering Simple Questions About Spatially Spreading Systems
3:504:10  Susan Khor
Memorial University of Newfoundland, St John's NL, Canada
On the shortcut network within protein residue networks
4:104:30  Hermann J Eberl
University of Guelph, Guelph, ON, Canada
Microscopic rules of multispecies interaction lead to a class of
macroscopic crossdiffusion problems
4:304:50  Michael Andrews
University of Guelph, Guelph, ON, Canada
Concurrent Behaviourally Motivated NonPharmaceutical Intervention
and Vaccination Decisions in an Agent Based Model of Seasonal Influenza
6:30 Banquet Dinner at Il Posto, 148 Yorkville Ave, Toronto,
ON M5R 1C2 Website: http://www.ilposto.ca/
Directions: http://www.ilposto.ca/Contact/Location/tabid/106091/Default.aspx
Friday: June 19, 2015
8:459:00 Breakfast
Session Chair of Contributed Talks: Daniel Ashlock
9:009:30  Franco Bagnoli
Dept. of Physics and Astronomy and CSDC, University of Florence, Italy
Phase transitions in parallel Ising model
9:309:50  Witold Bolt
Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland
Identifying Continuous Cellular Automata in partial observation setting
using differential evolution
9:5010:10  Raúl Rechtman
Instituto de Energías Renovables, Universidad Nacional Autónoma
de México
Anomalous diffusion of deterministic walks on a square lattice
11:0010:30 Break
Session Chair of Invited Talks: Monica Cojocaru
10:3011:00  Andrea Rapisarda
Dipartimento di Fisica e Astronomia and Infn  Università di
Catania, Italy
Selective altruism in collective games
11:0011:30  Henry Thille
University of Guelph, Department of Economics & Finance, Canada
Speculative Constraints on Oligopoly
11:3012:00  Jan Baetens
KERMIT, Dept. of Math. Modelling, Stat. & Bioinformatics, Gent,
Belgium
Behavioral analysis and identification of discrete models
12:00  1:30 Lunch
Session Chair of Invited Talks: Jan Baetens
1:302:00  Rolf Hoffmann
Technical University of Darmstadt, Germany
Cellular automata agents can form a pattern more effectively by using
signs
2:002:30  Daniel Ashlock
University of Guelph, Guelph, ON, Canada
Evolving Transparently Scalable Level Maps with Cellular Automata
9:009:20  Henryk Fuks
Brock University, St. Catharines, ON, Canada
Hyperbolic and degenerate hyperbolic behaviour in cellular automata
3:003:30 Break
Session Chair of Contributed Talks: Henryk Fuks
3:303:50 Dimitri Papadimitriou
Bell Labs, Antwerpen, Belgium
Modeling Complex Networks by (Dynamic) Markov Random Fields
3:504:10  Stephen Trothen
University of Waterloo, Waterloo, ON, Canada
Cellular Automat(ic) Design and Finite Nature: Theorizing HumanComputer
Interaction Using Discreet Mathematical Models
4:104:30 Closing Remarks
4:30 End of the Conference
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Information For Presenters
Information
for presenters can be found here.
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Contributed Slides
The following presentations were received from registered participants
but not delivered at the conference due to lastminute cancellations:
Conference Venue & Directions
The Conference will take place at the Fields Institute (222
College St., Toronto), in the Stewart Library.
For information on travelling to the Institute, please visit this page:
www.fields.utoronto.ca/aboutus/directions.html
Other resources for Fields visitors can be found here: www.fields.utoronto.ca/resources/members.html
The Banquet Dinner will take place at at Il Posto, 148
Yorkville Ave, Toronto, ON M5R 1C2 (6:30 p.m. on Thursday the 18th).
http://www.ilposto.ca/
http://www.ilposto.ca/Contact/Location/tabid/106091/Default.aspx
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Hotels & Visitors Information
All participants make their own accommodation arrangements. The following
links provide the information about accommodation and other useful information:
Resources
on hotels and housing can be found here.
Information
about Toronto for visitors to the city can be found here.
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