Namur Institute For Complex Systems

Jérôme Kunegis (NaXys)
2017-06-27 13:00 - 14:00 (Europe/Paris) | Seminar room, Rempart de la Vierge 8, Namur, 1170
Title: The New KONECT Project at the University of Namur
Abstract: In this talk I give an overview of the KONECT project, and highlight some of its applications. The KONECT Project is a project to collect, analyse and disseminate network datasets as used in various fields of research such as network science, web science, etc. The name “KONECT” stands for “Koblenz Network Collection” as the project was initiated at the University of Koblenz-Landau (Germany), but is now maintained at the University of Namur in parallel with my move to this university. This talk will give a motivation for the need of such a project, highlighting the benefits of performing research on large sets of network datasets, and why the motto of KONECT is “Everything is a Network”. I will also briefly present recent papers by myself and colleagues that have made use of the KONECT corpus. Finally, I will give a brief introduction to the Stu build automation tool that I wrote in order to manage the highly parallel and structurally complex computations in KONECT.

Marco Sansottera (University of Milan)
2017-06-30 13:00 - 14:00 | Seminar room, Rempart de la Vierge 8, Namur, 1170
Title: Quasi-convexity of the Hamiltonian for non Harmonic or non Keplerian
central potentials.
Abstract:
We consider the planar central motion with a real analytic potential. We
prove that the corresponding Hamiltonian, when written in action angle
variables, is almost everywhere quasiconvex, the only exceptions being
the Keplerian and the Harmonic potentials. We deduce persistence of most
KAM tori for the perturbed planar system. We also deduce a Nekhoroshev
type stability result for the perturbed spatial central motion. Such a
latter result covers also the case where the central system is put in
interaction with a slow system.

Alex Matzkin (CNRS/Université de Cergy-Pontoise)
2017-07-06 11:00 - 12:00 | CH12
Title: Can the properties of a quantum system vanish?
Abstract:
The Weak Measurements approach is a framework based on implementing non-destructive, non-perturbing measurements on a quantum system as the system evolves from an initially prepared state to a final state obtained by performing a standard measurement. The result of a weak measurement is called the “weak value” of the weakly measured observable. Weak values have peculiar features. In particular, a vanishing weak value means that the corresponding system property cannot be found at the location where the observable was weakly measured. This may have striking consequences, like not being able to detect a particle inside an interferometer although it went in and out, or observing a spatial separation between a particle and one of its properties. I will describe situations in which quantum properties appear to “vanish” and I will put forward an explanation based on the analysis of null weak values.

VBIH (Virtual Belgium in Health) - Presentation of the results
2017-10-30 09:00 - 12:00 | E11

Duccio Fanelli (University of Florence, Italy)
2017-11-02 13:00 - 14:00 | E25
Title: Noise-driven neuromorphic tuned amplifier
Abstract: Living systems execute an extraordinary plethora of complex functions, that result from the intertwined interactions among key microscopic actors. Positive and negative feedbacks appear to orchestrate the necessary degree of macroscopic coordination, by propagating information to distant sites while supporting the processing steps that underly categorization and decision making. Excitatory and inhibitory circuits play, in this respect, a role of paramount importance. As an example, networks of excitatory and inhibitory neurons constitute the primary computational units in the brain cortex and can adjust to different computational modalities, as triggered by distinct external stimuli. The genetic regulation also relies on sophisticated inhibitory and excitatory loops. Working in this context, we shall here discuss a minimal model for a discrete collection of agents in mutual interaction via excitatory and inhibitory loops, bearing universality traits in light of its inherent simplicity. Endogenous-noise stemming from finite size corrections induces quasi-cyclic dynamics that display unusual long-range correlations, persisting over arbitrary large network structures. When the excitatory and inhibitory species are distributed on a directed network, the internal noise seeds giant quasi-cycles, with tunable frequency and amplitude. The system spontaneously behaves as an effective, stochastic driven pacemaker, a non-trivial self-organized dynamics that hold general interest, for its fundamental to applied implications. The phenomenon is characterized analytically. The theoretical prediction is corroborated by direct stochastic simulations.

naXys Board meeting
2017-11-09 12:10 - 13:30, 2018-06-05 14:00 - 16:00 | E25

Olivier Deparis (UNamur)
2017-11-10 13:00 - 14:00 | E22
Title: Alternative expression of the Bloch wave group velocity using the Sturm-Liouville formalism applied to electromagnetic wave propagation in periodic dielectric media

Astero Provata (National Center for Scientific Research Demokritos, Athens)
2017-11-16 13:00 - 14:00 | E25
Title: The influence of the network connectivity in the spatial patterns of chimera states
Abstract: Chimera states emerge in systems of nonlocally coupled identical oscillators and are characterized by the coexistence of alternating coherent and incoherent domains. These hybrid states appear unexpectedly since all elementary oscillators in the network are identical and are identically coupled. A characteristic feature of chimera states is their mean frequency profile: In the coherent regions, all elements have equal, constant mean phase velocity, while in the incoherent ones the frequency profiles take arc shapes. Here we present synchronization properties leading to chimera states in networks of coupled neuronal oscillators. To understand the influence of connectivity in the chimera form we investigate the Leaky Integrate and Fire (LIF) model under different connectivity architectures. In the case of nonlocal connectivity, we show evidence of a coexistence state where multileveled chimera patterns are formed and they coexist with domains consisting of near-threshold elements. The oscillating elements form complex mean phase velocity profiles while the potentials of the near-threshold elements present small fluctuations and never drop to the resting state. We study different synchronization patterns in the parameter space of the LIF system when the oscillators are nonlocally coupled in 1, 2 and 3 spatial dimensions. We also investigate the effects of different connectivity schemes: nonlocal connectivity, reflecting coupling, diagonal or hierarchical (fractal) connectivity.
– Tsigkri-DeSmedt, N.D., Hizanidis, J., Schöll, E., Hövel, P., Provata, A.
Chimeras in leaky integrate-and-fire neural networks: effects of reflecting connectivities,
European Physical Journal B 90(7),139 (2017).
– Tsigkri-DeSmedt, N.D., Hizanidis, J., Hövel, P., Provata, A.
Multi-chimera states and transitions in the Leaky Integrate-and-Fire model with nonlocal and hierarchical connectivity,
European Physical Journal: Special Topics 225(6-7), pp. 1149-1164 (2016).
– Schmidt, A., Kasimatis, T., Hizanidis, J., Provata, A., Hövel, P.
Chimera patterns in two-dimensional networks of coupled neurons
Physical Review E 95(3),032224 (2017).

Yérali Gandica (UNamur)
2017-11-23 13:00 - 14:00 | E25
Title: Language as a signature of collective identity: Wikipedia editing across twelve languages

Marco Sansottera (University of Milan)
2017-11-30 13:00 - 14:00 | E25
Title: On the continuation of degenerate periodic orbits via normal form: full dimensional resonant tori
Abstract: We reconsider the classical problem of the continuation of degenerate periodic orbits in Hamiltonian systems. In particular we focus on periodic orbits that arise from the breaking of a completely resonant maximal torus. We here propose a suitable normal form construction that allows to identify and approximate the periodic orbits which survive to the breaking of the resonant torus. Our algorithm allows to treat the continuation of approximate orbits which are at leading order degenerate, hence not covered by classical averaging methods. We discuss possible future extensions and applications to localized periodic orbits in chains of weakly coupled oscillators.

Henri Vanhomwegen (UNamur)
2017-12-07 13:00 - 14:00 | E25
Title: Mutual funds styles distinctiveness and financial performance insights from Europe
Asbtract: Do mutual funds following a same style adopt similar investment strategies? Are these potential differences more salient over certain periods? What drives a mutual fund to be distinct from its peers? Does it pay? Those are central questions for both academics and market practitioners that we aim to address in this paper. More generally, we propose to study the degree of commonality among European equity mutual funds over time, and its impact on financial performance. To this end, we use several market-based measures of commonality among 4957 European equity mutual fund returns over the 1999-2016 period. We pay a particular attention to the computation of adequate metrics, the so-called « strategy distinctiveness index » applying up-to-date techniques from statistics and machine learning to generate clusters of mutual funds associated to “styles”, from which we can gauge how similar or distinct a mutual fund is from its peers (i.e. the mutual funds belonging to the same cluster or style). Our results show marked changes in the level of commonality over time, distinctiveness among European mutual funds decreasing sharply before the crisis before going up and eventually reaching a new low in the recent months. We find strong evidence regarding the contribution of fund-level as well as cluster characteristics to strategy distinctiveness. Turning to financial performance, our results show a strong and robust, positive impact of strategy distinctiveness on financial performance.

Sébastien Clesse (UCL - UNamur)
2017-12-14 13:00 - 14:00 | E22
Title: Is Dark Matter made of Primordial Black Holes?
Abstract: The detection of gravitational waves by Advanced-LIGO/VIRGO has opened a wide new field of astronomy. Strangely, the merging rate of massive black holes was found to be compatible with the rate expected if they constitute the Dark Matter. This has revived the interest for Primordial Black Holes (PBH) formed in the early Universe constituting a fraction or even the totality of Dark Matter . This scenario is however well constrained by other astrophysical observations. I will review the pros and cons of this scenario, in the view of the most recent results and observations, and I will emphasize how PBH Dark Matter could resolve some long-standing cosmological and astrophysical puzzles. The presentation will be understandable by a broad audience of mathematicians, physicists and students.

Anthony Hendrickx
2017-12-21 13:00 - 14:00 | E25
Title: Algorithme génétique et Rotifères Bdelloïdes: les mathématiques au service de la biologie
Résumé: Existant depuis 1962, les algorithmes génétiques se sont toujours basés sur un mode de reproduction sexuée, la reproduction asexuée entraînant une accumulation de mutations délétères, censée provoquer l’extinction de l’espèce. Cependant, l’espèce du Bdelloïde, malgré son mode de reproduction asexuée, survit depuis des dizaines de millions d’années dans des milieux extrêmes et variés. Cette incroyable faculté semble être expliquée par l’observation, chez cette espèce, de phénomènes connus sous les noms de conversion génique et transfert horizontal. L’objectif de ce mémoire était de modéliser, sous forme d’algorithmes génétiques, l’évolution asexuée du Rotifère Bdelloïde, afin d’étudier l’importance et l’influence de ces deux phénomènes. Des relations mathématiques connues en génétique, liant taux de mutation, longueur d’ADN et taux de conversion génique, sont retrouvées numériquement, permettant de valider et de simplifier notre modélisation. L’utilité du phénomène de conversion génique, permettant de rendre nos algorithmes plus stables, robustes et précis qu’un algorithme génétique classique, est ensuite démontrée. Enfin, l’importance du mécanisme de transfert horizontal, améliorant l’efficacité du modèle asexué, est mise en évidence, permettant d’envisager un algorithme plus efficace que les modèles classiques.

Justin Buhendwa Nyenyezi (UNamur)
2018-01-25 13:00 - 14:00
Title: Polynomial preconditioners versus matrix-splitting preconditioners for linear systems arising in 3D medical image registration
Abstract: Many methods exist to solve large sparse linear systems. However, a given method may perform well for a particular problem while it may not work as well for another [2]. For designing ecient system solvers, one may analyze structures of general operators or matrices used by the algorithms. In non-rigid medical image registration, matrices are derived from physical principles, modelled as Partial Dierential Equations (PDEs). Although these systems are often sparse and structured, they are very large and ill-conditioned. Thus, their solvers are time consuming and their complexity in operation counts is polynomial. As a consequence, fast and superfast direct methods reveal numerical instabilities and thus lead to breakdowns or inaccurate solutions. The most used alternative are iterative system solvers that enable a reduction of the number of expensive operations such as matrix-vector products and thus a speed up of the registration process. Although iterative solvers provide only an approximation of the solution, they are well suited for very large systems when cheap and well suited preconditioners are available. Preconditioners may be stationary (Jacobi, Gauss-Seidel or SOR) and non-stationary (e.g, polynonmial or low-rank inverse approximation).
In this study, we are especially interested in benchmarking [3, 4] iterative system solvers on a large set of 3D medical images. These system solvers are based on the Conjugate Gradient method but dierent from the preconditioning techniques [6, 5] . The ongoing results conrm [4] that there is no single system solver that is the best for all the problems. However, the results indicate which solver has the highest probability of being the best within a factor f ∈ [1, ∞[ and considering a limited computional budget in terms of time and storage require-
ments.
References
[1] Oseledets, Ivan and Tyrtyshnikov, Eugene and Zamarashkin, Nickolai. Evaluation of optimization methods for nonrigid medical image registration using mutual information and B-splines. Image Processing, IEEE Transactions on, 16:12,28792890, 2007.
[2] Barrett, Richard and & all. Templates for the solution of linear systems: building blocks for iterative methods. SIAM , 1994.
[3] Moré, Jorge J and Wild, Stefan M. Benchmarking derivative-free optimization algorithms. SIAM Journal on Optimization , 20:1,172191, 2009.
[4] Gould, Nicholas and Scott, Jennifer. The State-of-the-Art of Preconditioners for Sparse Linear Least-Squares Problems. ACM Transactions on Mathematical Software (TOMS) , 43:4,36, 2017.
[5] Nocedal, Jorge and Wright, Stephen J. Numerical optimization. Springer New York , 2, 2006.
[6] SAAD,Yousef Iterative methods for sparse linear systems. Society for Industrial and Applied Mathematics , 2003.

Eve-Aline Dubois (UNamur)
2018-02-15 13:00 - 14:00 | E25
Titre: The early times of stationary cosmologies
Abstract: The Steady-state model of Bondi and Gold, on the one hand, and Hoyle’s model on the other hand are the most famous examples of stationary cosmologies. However, they are actually quite different in terms of motivations and content and were not the only stationary models. In this talk, we will look back at the very beginning of relativistic cosmology and the first stationary cosmological models. They were lead by various motivations and suggest a surprising phenomenon: creation of matter. From Einstein to Hoyle, we will follow the different stationary cosmologies, their development and their interplay.

François Lamoline (UNamur)
2018-02-20 13:00 - 14:00 | E25
Title: Well-Posedness of Boundary Controlled and Observed Stochastic Port-Hamiltonian systems
Abstract: On finite-dimensional spaces, the well-posedness is not a concern and is usually not even mentioned. However, on infinite-dimensional spaces, establishing the well-posedness is of paramount importance and paves the way for dealing with control/estimation, transfer function, etc. In this talk, stochastic port-Hamiltonian systems on infinite-dimensional spaces governed by Ito stochastic differential equations and with boundary control and observation operators are introduced and some properties of this new class of systems are studied. They are an extension of stochastic port-Hamiltonian systems defined on a finite-dimensional state space. The concept of well-posedness in the sense of Weiss and Salamon is generalized to the stochastic context. Under this extended definition, stochastic port-Hamiltonian systems are shown to be well-posed. The theory is illustrated on an example of a vibrating string subject to a Hilbert-space valued Gaussian white noise process.

naXys extended Board meeting
2018-02-22 13:00 - 14:00 | E25

Alexandre Bovet (UNamur - UCL)
2018-03-01 13:00 - 14:00 | E25
Title: Opinion dynamics and fake versus traditional news influence in Twitter
Abstract: We investigate the opinion of Twitter users during the 2016 US elections using a large scale dataset of more than 170 millions tweets. We develop a method to infer the opinion of Twitter users regarding the candidates by using a combination of natural language processing of the tweet contents, machine learning classification and analysis of the hashtags co-occurrence network. We study the temporal social networks formed by the interactions among millions of Twitter users and infer the support of each user to the presidential candidates. The resulting Twitter opinion trend follows the New York Times National Polling Average, which represents an aggregate of hundreds of independent traditional polls, with remarkable accuracy.
Going beyond the daily opinion analysis and analyzing the level of activity, the repartition of the supporters between the strongly connected giant component and the rest of the network and the daily fluctuations in the number of users reveal a clear dichotomy between the behavior of supporters of each candidate. Although Clinton supporters are the majority in Twitter, Trump supporters are generally more active and more constant in their support, while Clinton supporters are less active and show their support only occasionally.
To understand the role of information diffusion on Twitter opinion dynamics, we consider tweets containing URLs directing to news outlet websites. In particular, we compare websites known to diffuse fake news compared to traditional, fact-based, news outlets. We find that 29% of the tweets linking to news outlets points to websites containing fake or extremely biased news. Analyzing the information diffusion networks, we find that user diffusing fake news form more connected and less heterogeneous networks than users in traditional news diffusion networks. While influencers of traditional news outlets are journalists and public figures with verified Twitter accounts, most influencers of fake news and extremely biased websites are unknown users or users with deleted Twitter accounts. Finally, an analysis of the activity dynamics of influencers reveals that influencers of tradition news are driving the most part of Twitter while fake news influencers are, in fact, mostly driven by the activity of Trump supporters.

Alexey Medvedev (UNamur)
2018-03-08 13:00 - 14:00 | E25
Title: Modelling structure and predicting dynamics of discussion threads in online boards using Hawkes processesAbstract: Online social platforms provide a fruitful source of information about social interaction. Depending on the platform, various tree-like cascading patterns emerge as a consequence of such interaction. For example, on Twitter or on Facebook people interact via resharing messages, which turns into cascade trees of reshares, in email networks people forward messages to their peers resulting in trees of email forwards, in online boards like Digg or Reddit people interact via discussing particular posts, which leaves a trace of discussion trees. The two main questions arise: what is the shape of these cascades and how to predict the dynamics of their evolution? The question of evolution of discussion threads is now gradually being understood. By now researchers studied only the structural evolution of discussion trees and the dynamical properties are left out of consideration. Nevertheless, there was proposed a sort of a mean-field model for dynamics and structure, however by the design the model has limited utility in practice. We consider cascades given by discussion trees of posts in online board Reddit. The dataset of Reddit discussion threads consists of all posts and comments submitted to Reddit from Jan, 2008 till Jan, 2015. The dataset in total contains more than 150 million posts and around 1.4 billion comments. We propose a model of discussion trees generation based on the self-exciting Hawkes processes, which represents both the tree structure and temporal information. We use the dataset of Reddit discussion threads to show that structurally trees resemble Galton-Watson trees with a special root offspring distribution, and distinct the cases when the dynamics of comments attraction can be well predicted using Hawkes processes.

Jean Teyssandier (Cornell University, USA)
2018-03-29 13:00 - 14:00 | E25
Title: Orbital evolution during planet-⁠disc interactions
Abstract: The origin and wide distribution of eccentricities and inclinations in planetary systems remains to be explained, in particular in the context of planet-disc interactions. In this talk I will present a study of the evolution of eccentricity in discs and planets that combines methods from celestial mechanics and hydrodynamics, and takes the form of a linear secular theory. I will compare the predictions of this linear theory against direct hydrodynamical simulations and show how eccentricity can grow. I will discuss what these results imply for the orbital structure of protoplanetary discs and young planetary systems. I will also discuss how moderate inclinations can be generated via similar mechanisms.

Julien Petit (Ecole Royale Militaire - UNamur)
2018-04-10 13:00 - 14:00 | E22
Title : Peculiarities of reaction and diffusion on temporal networks
Abstract: A common assumption in the ever-increasing literature on network-defined dynamical systems is to view the underlying graph as a static entity. In many cases however, the temporal properties of the network – its fluctuating links and appearing and vanishing nodes – prove critical.
This presentation is firstly meant as an overview of linear (diffusion) processes on temporal networks. After a survey of recent methods and results, we subsequently focus on a random walk model with lasting node-to-node interactions. Relying on analytics and numerics, we discuss how the Markov property of the process is lost even when using memoryless probability distributions for the model-driven edges dynamics, and the independent nodes processes.
If time permits and in an attempt to highlight other results about systems evolving on top of temporal networks, and which stem from the intrinsic network dynamics, we finally consider a generic nonlinear model. In particular, this setting allows us to discuss pattern formation and oscillations death in reaction-diffusion systems through the Turing mechanism, under the assumption of a fast-varying periodic topology.

Aivar Sootla (University of Oxford)
2018-04-19 13:00 - 14:00 | E25
Title: Applications of Monotone Systems Theory to Synthetic Biology
Abstract: In this talk, we will discuss some mathematical problems arising in the fast developing field of synthetic biology. Synthetic biology is concerned with creating genetically modified bacteria for the production of useful chemical compounds (e.g., drugs, bio-degradable plastic, fuels etc), for detecting viruses, toxins or prohibited substances (e.g. in a biological sample, water supply), and even for new methods of drug delivery. Due to complexity and variability of bacterial systems modelling presents a serious challenge. Furthermore, quantitative data analysis is impeded by technological and physical constraints, therefore scientists often rely on qualitative analysis of their designs. From the modelling perspective, qualitative analysis is not always straightforward unless models have specific properties. We will argue that a class of models called monotone can offer effective tools for qualitative analysis of biological processes. Monotone systems often appear in biological modelling and possess a powerful property: a partial order in their trajectories. Partial order enables a number of stability results, which are crucial for simplified analysis and control of nonlinear systems. Equipped with the Koopman operator framework, we present methods for analysis and control of monotone systems, which are computationally efficient and can provide answers for a range of parameters.

APRES-MIDI de la RECHERCHE à l'UNamur
2018-05-03 08:00 - 17:00

10th CECI Scientific Day @UNamur
2018-05-04 13:30 - 17:30

Nikos Kouvaris (UNamur)
2018-05-15 13:00 - 14:00 | E25
Title: Feedback induced stationary and oscillatory patterns in complex bistable networks
Abstract: In this talk we will present theoretical and experimental findings on pattern formation in bistable chemical networks. Effects of feedbacks on self-organization phenomena will also be discussed. For regular trees, an approximate analytical theory for localized stationary patterns under application of global feedbacks is constructed. Using it, properties of such patterns in different parts of the parameter space are discussed. We will also show that localized oscillatory patterns can be formed in these networks if the global feedback is applied with certain time delay. Linear stability analysis has revealed a critical time delay for which the system undergoes a Hopf bifurcation and exhibits limit cycles of small amplitudes. Furthermore, we will present results from numerical investigations for large random Erdös-Rényi and scale-free networks. In both kinds of systems localized active patterns consist of a subnetwork, whose size decreases as the feedback intensity increases. In the later random networks local feedbacks affecting only the hubs or the peripheral nodes are also considered.

Pietro Coletti (University of Hasselt)
2018-05-23 13:00 - 14:00 | E25
Title: Regular school closure & influenza epidemics: a data-driven spatial transmission model for Belgium

Abstract: School closure is often considered as an option to mitigate influenza epidemics because of its potential to reduce transmission in children and then in the community. The policy is still however highly debated because of controversial evidence. Moreover, the specific mechanisms leading to mitigation are not clearly identified. We introduced a stochastic spatial age-specific metapopulation model to assess the role of holiday-associated behavioral changes and how they affect seasonal influenza dynamics. The model is applied to Belgium, parameterized with country-specific data on social mixing and travel, and calibrated to the 2008/2009 influenza season. It includes behavioral changes occurring during weekend vs. week, and holiday vs. school-term. Several experimental scenarios are explored to identify the relevant social and behavioral mechanisms.
Stochastic numerical simulations show that holidays considerably delay the peak of the season and mitigate its impact. Changes in mixing patterns are responsible for the observed effects, whereas changes in travel behavior do not alter the epidemic. Weekends are important in slowing down the season by periodically dampening transmission. Christmas holidays have the largest impact on the epidemic, however later school breaks may help in reducing the epidemic size, stressing the importance of considering the full calendar.
Changes in the way individuals establish contacts during holidays are the key ingredient explaining the mitigating effect of regular school closure. Our findings highlight the need to quantify these changes in different demographic and epidemic contexts in order to provide accurate and reliable evaluations of closure effectiveness. They also suggest strategic policies in the distribution of holiday periods to minimize the epidemic impact.

Ludovic Renson (University of Bristol, UK)
2018-06-07 13:00 - 14:00 | E25
Title: Exploring the dynamics of nonlinear experiments using control-based continuation
Abstract: With the constant drive for better performance and efficiency, technological boundaries are being pushed to their limits. In mechanics, this often means that the dynamic behaviour of structures becomes increasingly nonlinear. Nonlinearity can arise, for instance, from the large displacements and rotations of flexible components (such as blades in wind turbines).
While a significant effort has been, and is, devoted to the mathematical modelling and numerical analysis of such systems, relatively little research addresses the issue of rigourous experimental testing. In fact, until now, there has been no general, systematic method that can directly measure and characterise nonlinear dynamic behaviour during laboratory tests. Nonlinear systems are still tested as linear ones. Time series are collected for a whole range of excitation parameters and one relies on post-processing tools to understand the behaviour of the system. So far, this sort of approach has not allowed quantitative comparisons between experiments and mathematical models; hence it is extremely challenging to incorporate nonlinear features into model development and validation processes.
In this talk, I will present a method, control-based continuation (CBC), which uses sensors and actuators to intelligently probe a physical system. Combining feedback control with numerical continuation algorithms, CBC modifies, on-line, the excitation applied to the system in order to isolate the nonlinear behaviour of interest. In this way, CBC offers the best conditions to analyse these dynamic features in detail, to follow them as inputs and controllable parameters are changed, and to detect and track boundaries between qualitatively different types of behaviour.

Takaaki Aoki (Kagawa University, Japan)
2018-06-19 13:00 - 14:00 | E25
Title: Cities and roads as pattern formation of their co-evolving dynamics on real-world landscape

Abstract: Cities and their inter-connected transport networks form part of the fundamental infrastructure developed by human societies. Their organisation reflects a complex interplay between many natural and social factors, including inter alia natural resources, landscape, and climate on the one hand, combined with business, commerce, politics, diplomacy and culture on the other. Nevertheless, despite this complexity, there has been some success in capturing key aspects of city growth and network formation in relatively simple models that include non-linear positive feedback loops. However, these models are typically embedded in an idealised, homogeneous space, leading to regularly-spaced, lattice-like distributions arising from Turing-type pattern formation. Here we argue that the geographical landscape plays a much more dominant, but neglected role in pattern formation. To examine this hypothesis, we evaluate the weighted distance between locations based on a least cost path across the natural terrain, determined from high-resolution digital topographic databases for the Hokkaido region of Japan. These weights are included in a co-evolving, dynamical model of both population aggregation in cities, and movement via an evolving transport network. We compare the results from the stationary state of the system with current population distributions from census data, and show a reasonable fit, both qualitatively and quantitatively, compared with models in homogeneous space. Thus we infer that that addition of weighted topography from the natural landscape to these models is both necessary and almost sufficient to reproduce the majority of the real-world spatial pattern of city sizes and locations in this example.

Eleonora Andreotti (Università di Torino, Italy)
2018-06-21 13:00 - 14:00 | E25
Title: Statistical properties of non linear random walks on networks
Abstract: Random walks simulate various interacting entities (the nodes) which exchange ’particles’ according to the topological structure defined by the links and they are considered to introduce a dynamics on networks. These stochastic dynamical systems can be applied to model complex systems like transportation networks, ecological systems, neural networks, economic systems etc.. In the linear case the statistical properties are defined by single particles dynamics and the equilibrium distribution depends on the network structure. We introduce non linear effects by assuming a finite transportation capacity of the links or a finite capacity in the nodes. As a consequence the transition probabilities depend on the dynamical state of the network and one cannot derive statistical properties of the system from single particle dynamics. We show that non-linear effects can be described by introducing an entropic force among the node states which allows to derive a master equation for the evolution of the probability distribution of the node population. This entropic force has a relevant effect on stationary distribution and the relaxation time scale depends on the numerosity of the population so that the thermodynamics limit is non trivial and the lifetime of the transient state is very long. Using numerical simulation we derive an analytical form of the entropic force and we study the dependence of the stationary distribution on the network topology.
