August 29, 2016
THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES

June 17-19, 2015 at the Fields Institute, Stewart Library

2015 Summer Solstice
7th International Conference on Discrete Models of Complex Systems

Conference Chair

Prof. Anna T. Lawniczak, University of Guelph, Canada

 

Conference Organizing Committee

Monica Cojocaru, University of Guelph, Canada
Bruno N. Di Stefano, Nuptek Systems Ltd, Canada
Henryk Fuks, Brock University, Canada
Danuta Makowiec, Gdansk University, Poland

 

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, multi-agent based models, or networks. These models can be seen as the simplest digital laboratories to study phenomena exhibited by complex systems like self-organization processes, pattern formation, cooperation, adaptation, competition, attractors, or multi-scale 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, multi-agent 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 peer-reviewed.

 

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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://www-f1.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, multi-agent 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/cgi-bin/abstract/submit/cbky-01.

 

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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 Post-Conference 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) 251-494 (2010), http://www.actaphys.uj.edu.pl/_old/sup3/t2.htm
2010 Summer Solstice, Nancy, France: Acta Physica Polonica B Proc. Suppl., 4(2) 115-265 (2011), http://www.actaphys.uj.edu.pl/_old/sup4/t2.htm
2011 Summer Solstice, Turku, Finland, Acta Physica Polonica B Proc. Suppl., 5(1) 1-190 (2012), http://www.actaphys.uj.edu.pl/_old/sup5/t1.htm
2013 Summer Solstice, Warsaw, Poland, Acta Physica Polonica B Proc. Suppl., 7(2) 233-408 (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 fashion-based cellular automata that can be evolved to generate cavern-like level maps. Fashion-based 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 cavern-like 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 full-fledged 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 spatio-temporal 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 CA-based 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 so-called 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 CA-based models to become appreciated as a full-fledged modeling paradigm. Besides, it will be demonstrated that the scope of these measures is not limited to two-state 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 mean-field 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 small-world 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. Lattice-gas cellular automata have proven successful to model and analyze collective migration and pattern formation emerging from specific cell interactions. Here, we introduce lattice-gas 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 long-range, 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 cascade-like nonlinear correlations is also identified.

Strategic models for network formation
Babak Farzad
Brock University, Canada

The emergence of large-scale small-world networks has been mostly explained within stochastic frameworks. We study the dynamics of game-theoretic 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 grid-based model inspired by Kleinberg's small-world random graphs, and also on a hierarchical or tree-based network formation model. This was a joint project with Omid Atabati.


Time-Varying 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 time-dependent interactions between the entities.
Time-Varying 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 multi-agent system was modeled by cellular automata. The CA-w 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.: Rotor-routing algorithms described by CA-w. Acta Phys. Polonica B Proc. Suppl. 5(1) (2012) pp. 53-68
[2] Hoffmann, R.: How Agents Can Form a Specific Pattern, Cellular Automata, LNCS Volume 8751 (2014) pp. 660-669
[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 multi-compartment 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 well-studied problems concerning structural properties of complex networks. Some concepts like percolation, k-core organization, bootstrap percolation and avalanche collapse of the giant viable component in multiplex networks are well well-known 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 Rich-Club
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 rich-club coefficient are conserved. The method can generate correlated and uncorrelated null-models of real networks, which in turn, the null-models can be used to define the partition of a network into soft communities.


Integration of agent-based modeling, network science, analytical models, and inductive meta-modelling 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 agent-based modeling, network analysis, analytical modeling, and estimation of meta-models. Agent-based 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 starting-off 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. WICI-hosted 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), land-use 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 knowledge-based 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 P1-0044 of the Research Agency of the Republic of Slovenia and the European Community's COST action TD1210 Analyzing the dynamics of information and knowledge landscapes-KNOWeSCAPE.
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 agent-based modeling, Physica A 391, 5264-5278 (2012).
[3] B. Tadic and M. Šuvakov, Can Human-Like Bots Control Collective Mood: Agent-Based 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: 978-1-62618-065-9

 

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 infinite-horizon 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 non-monotonic 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 semi-closed 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 ODE-based 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 individual-based 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.

Agent-based 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 Agent-based 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 Non-Pharmaceutical 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 self-protective intervention strategies individuals can utilize. These are pharmaceutical interventions, such as vaccination, and non-pharmaceutical 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 agent-based simulation model on a contact network to simultaneously incorporate decision-making 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 decision-making 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 behaviorally-driven 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.

 

Mean-Field 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 mean-field 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) mean-field. The objective is to minimize the expected cost over a finite or infinite horizon, where the per-step cost is an arbitrary function of the states and actions of all agents.
The above model, which we call mean-field 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 mean-field; 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 mean-field. Finally, the objective is to identify team-optimal decision rules (rather than person-by-person 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. pre-recorded, partial configurations of the system at certain, unknown time steps. This partial context allows for modeling situations with malfunctioning measuring equipment or time-scale 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 radius-limited 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. 109-124. Boston, MA: Kluwer Academic Publishers.
[4] Brest, J.; Greiner, S.; Boskovic, B.; Mernik, M.; Zumer, V., "Self-Adapting 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 Simulator-Defined 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 long-run 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 non-monotonic.
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 fractional-order 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: 130-141 (1963).
3. May R.M. : Simple mathematical models with complicated dynamics, Nature, 261, pp.459--467 (1976)
4. Kopel, M.: Periodic and chaotic behavior of a simple R&D model. Ricerche Economiche 50, 235-265 (1996a).
5. Kopel, M.: Simple and complex adjustment dynamics in Cournot Duopoly Models. Chaos, Solitons, and Fractals 7, 2031-2048 (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.73--100 (2001)
7. Bischi G.I., Mammana C., Gardini L. : Multistability and cyclic attractors in duopoly games, Chaos, Solitons and Fractals 11, pp.543-564 (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. 573--581 (1991)
10. Puu T.: Complex dynamics with three oligopolists, Chaos, Solitons & Fractals 7 , pp.2075--2081 (1996)

Slides. Note: This presentation was received from a registered participant but not delivered at the conference due to last-minute cancellation.

 

Microscopic rules of multi-species interaction lead to a class of macroscopic cross-diffusion problems
Hermann J Eberl
University of Guelph, Guelph, ON, Canada
Coauthors: Kazi A Rahman

Starting with a discrete-in-space, continuous-in-time 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 cross-diffusion 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 cross-diffusion problems in general. We apply the framework to simulate dual-species biofilms systems.

 

Hyperbolic and degenerate hyperbolic behaviour in cellular automata
Henryk Fuks
Brock University, St. Catharines, ON, Canada

Cellular automata are infinitely-dimensional dynamical systems, yet a behaviour similar to hyperbolicity in finite-dimensional 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 finitely-dimensional systems. In such cases, the convergence to stationary value is linear-exponential. 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 short-cut 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 small-world 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 sub-network of a PRN called the short-cut 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 short-cuts in the course of a local greedy search. A PRN with N nodes has about 2N short-cut edges [4]. The short-cut edges are enriched with short-range 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 (well-formed) SCN grows as a protein folds to span almost all the nodes of its PRN. SCN well-formness correlates strongly with the presence of secondary structures. SCNs from "unsuccessful" MD trajectories were less well-formed 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 short-cuts can be predicted from a given set of short-cuts, and there is a non-random relationship between deleted and added short-cuts. With respect to a spanning tree, the majority of added short-cuts are found in the edge cut-set of at least one deleted short-cut, and the majority of deleted short-cuts contain at least one added short-cut in their edge cut-sets. 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 post-doctoral research position at Memorial University.
References
[1] Watts DJ and Strogatz SH (1998) Collective dynamics of 'small-world' networks. Nature 393, 440-442.
[2] Vendruscolo M, Dokholyan NV, Paci E and Karplus M (2002) Small-world view of the amino acids that play a key role in protein folding. Physical Review E 65 061910-1.
[3] Atilgan AR, Akan P and Baysal C (2004) Small-world communication of residues and significance for protein dynamics. Biophysical Journal 86:85-91.
[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

 

Network-driven ranking in complex systems
Hao Liao
Department of Physics, University of Fribourg, Switzerland

The complex systems research domain continues to attract attention of scholars world-wide 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: reputation-redistribution process and rating projection data pre-treatment. 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 [4-8].
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 randomly-chosen 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 degree-correlated random networks (specified by their joint degree-degree distribution P(k.k')). We also find good agreement with numerical calculations of intervertex distances for several real-world 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. 33-48.
[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
Pierre-Andre 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 tree-like random graphs [1-6], 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 tree-like 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 [3-7] 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 tree-like random graphs by assembling trees of network motifs, the new approach can assemble trees of wide motifs to define non tree-like 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.
[1] M. E. J. Newman, S. H. Strogatz and D. J. Watts. Random graphs with 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. Hébert-Dufresne, 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/10.1088/1751-8113/45/40/405005
[7] R. Milo, S. Shen-Orr, 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 Graph-Theoretic 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 high-dimensional 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 structure-learning 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 hill-climbing, 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 large-scale 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 neighbor-driven "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 higher-order potential functions should be used instead to model multi-partite interactions. Another fundamental question relates to the parameter estimation and tuning in settings where the spatio-temporal dynamics of the phenomena influences the model. In turn, extending MRF capability would enable modeling complex networks phenomena such as dynamic network formation (self-organization), 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 (CA-based 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 fractional-order
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, non-periodic and chaotic. Theory of Poincare-Bendixson 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 fractional-order. 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 three-dimensional 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 fractional-order 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 last-minute cancellation

 

Cellular Automat(ic) Design and Finite Nature: Theorizing Human-Computer 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 step-wise" 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 well-known Aldous-Hoover 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 real-world 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 power-law degree distributions and small world behaviour arising naturally in particular examples.

 

Modelling awareness and adoption: aggregate behaviour versus agent-based 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 agent-based 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 agent-based simulations were very close to those obtained through differential equations.

 

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Program

Wednesday: June 17, 2015

8:45-9:15 Registration, Breakfast

Session Chair of Invited Talks: Bosiljka Tadic

9:15-9:30 Opening Remarks

9:30-10:00 - Paola Flocchini
University of Ottawa, Ottawa, ON, Canada
Time-Varying Graphs and Dynamic Networks

10:00-10:30 - Babak Farzad
Brock University, St. Catharines, ON Canada
Strategic models for network formation

10:30-11:00 Break

Session Chair of Invited Talks: Paola Flocchini

11:00-11:30 - Raul J Mondragon
Queen Mary University of London, UK
Network ensembles based on the Maximal Entropy and the Rich-Club

11:30-12:00 - Bosiljka Tadic
Dept. of Theoretical Physics, Jozef Stefan Institute, Ljubljana, Slovenia
Modeling The Dynamics of Knowledge Creation in Online Communities

12:00-1:30 Lunch

Session Chair of Contributed Talks: Raul J Mondragon

1:30-1:50 - Monica Cojocaru
University of Guelph, Guelph, ON, Canada
Modelling awareness and adoption: aggregate behaviour versus agent-based interactions with network effects

1:50-2:10 - Sergey Melnik
MACSI, Dept. of Math. & Stat., University of Limerick, Ireland
Analytical approach to calculating shortest path lengths on networks

2:10-2:30 - Pierre-Andre Noel
University of California, Davis, CA, USA
Wide motifs: a new tool for when cycles matter

2:30-2:50 - Victor Veitch
Dept. of Statistical Sciences, University of Toronto, Toronto, ON, Canada
A General Framework for Sparse Random Graphs

2:50-3:30 Break

Session Chair of Invited Talks: Pietro Lio'

3:30-4:00 - Stanislaw Drozdz
Polish Academy of Sciences and Cracow University of Technology, Poland
Complexity characteristics of world literature

4:00-4:30 - José Fernando Ferreira Mendes
University of Aveiro, Portugal
Structural properties of complex networks

4:30-6:00 Reception

 

Thursday: June 18, 2015

8:45-9:00 Breakfast

Session Chair of Invited Talks: Andrea Rapisarda

9:00-9:30 - Dawn Cassandra Parker
University of Waterloo, School of Planning and WICI, Waterloo, ON, Canada
Integration of agent-based modeling, network science, analytical models, and inductive meta-modelling for applied analysis of complex systems phenomena

9:30-10:00 - Jaroslaw Was
AGH University of Science and Technology, Cracow, Poland
Agent-based approach and Cellular Automata: a promising perspective in crowd dynamics modeling?

10:00-10:30 Break

Session Chair of Contributed Talks: Rolf Hoffmann

10:30-10:50 - 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

10:50-11:10 - Robert Lubas, Jakub Porzycki
AGH University of Science and Technology in Kraków, Poland
Supporting the facility design process in terms of optimal pedestrian flow

11:10-11:30 - Jalal Arabneydi
McGill University, Montreal, QC, Canada
Mean-Field Teams

11:30-11:50 - Bruno Di Stefano
Nuptek Systems Ltd., Toronto, ON, Canada
Biomimicry Based Decision Of Computationally Minimal Cognitive Agents

11:50-12:10 - Anna T. Lawniczak
University of Guelph, Guelph, ON, Canada
Performance Of Simple Cognitive Agents Using Observational Learning

12:10-1:30 Lunch

Session Chair of Invited Talks: Franco Bagnoli

1:30-2:00 - Andreas Deutsch
Centre for Information Services and High Performance Computing, Technische Universität Dresden, Germany
Cellular automaton models for collective cell behaviour

2:00-2:30 - Pietro Lio'
Computer Laboratory, University of Cambridge, UK
Cancer cell dynamics and liquid biopsies

2:30-3:00 - Edward W. Thommes
Dept. of Mathematics & Statistics, University of Guelph, Canada
A stochastic compartmental model of herd immunity within semi-closed environments

3:00-3:30 Break

Session Chair of Contributed Talks: Andreas Deutsch

3:30-3:50 - Mark Crowley
Electrical and Computer Engineering, University of Waterloo, ON, Canada
Answering Simple Questions About Spatially Spreading Systems

3:50-4:10 - Susan Khor
Memorial University of Newfoundland, St John's NL, Canada
On the short-cut network within protein residue networks

4:10-4:30 - Hermann J Eberl
University of Guelph, Guelph, ON, Canada
Microscopic rules of multi-species interaction lead to a class of macroscopic cross-diffusion problems

4:30-4:50 - Michael Andrews
University of Guelph, Guelph, ON, Canada
Concurrent Behaviourally Motivated Non-Pharmaceutical 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

8:45-9:00 Breakfast

Session Chair of Contributed Talks: Daniel Ashlock

9:00-9:30 - Franco Bagnoli
Dept. of Physics and Astronomy and CSDC, University of Florence, Italy
Phase transitions in parallel Ising model

9:30-9:50 - Witold Bolt
Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland
Identifying Continuous Cellular Automata in partial observation setting using differential evolution

9:50-10:10 - Raúl Rechtman
Instituto de Energías Renovables, Universidad Nacional Autónoma de México
Anomalous diffusion of deterministic walks on a square lattice

11:00-10:30 Break

Session Chair of Invited Talks: Monica Cojocaru

10:30-11:00 - Andrea Rapisarda
Dipartimento di Fisica e Astronomia and Infn - Università di Catania, Italy
Selective altruism in collective games

11:00-11:30 - Henry Thille
University of Guelph, Department of Economics & Finance, Canada
Speculative Constraints on Oligopoly

11:30-12:00 - 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

1:30-2:00 - Rolf Hoffmann
Technical University of Darmstadt, Germany
Cellular automata agents can form a pattern more effectively by using signs

2:00-2:30 - Daniel Ashlock
University of Guelph, Guelph, ON, Canada
Evolving Transparently Scalable Level Maps with Cellular Automata

9:00-9:20 - Henryk Fuks
Brock University, St. Catharines, ON, Canada
Hyperbolic and degenerate hyperbolic behaviour in cellular automata

3:00-3:30 Break

Session Chair of Contributed Talks: Henryk Fuks

3:30-3:50- Dimitri Papadimitriou
Bell Labs, Antwerpen, Belgium
Modeling Complex Networks by (Dynamic) Markov Random Fields

3:50-4:10 - Stephen Trothen
University of Waterloo, Waterloo, ON, Canada
Cellular Automat(ic) Design and Finite Nature: Theorizing Human-Computer Interaction Using Discreet Mathematical Models

4:10-4:30 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 last-minute 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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