# Determinants of creativity and innovation in science, art and technology  (DCIS) Session 2

## Chair: Vittorio Loreto

 15006 How creative, participatory and innovation strategies can improve the quality of scientific research? [abstract] Abstract: We will explain and discuss several experiences where artistic and creative practices can drive ambitious scientific research. We will focuss on topics and actions directly related to complex systems science to exemplify all their potentialities. We will describe how participatory strategies, public engagement, community processes and wide multidisciplinary teams are able to transform an ordinary research activity into a complete experience where impact and outputs are multiple, diverse and long-lasting. The list of actors involved should necessary include artists, designers, public agencies or administrations, and then must also take place in uncommon places such as museums, cultural spaces and public spaces. Working with many actors and building tailored-made research collectives have the capacity to raise shared concerns, to address societal challenges in a novel and innovative way, and to enhance the value of the results by publicly discussing and sharing the whole research cycle. Close Josep Perello 15007 From Innovation to Diversification: A Simple Competitive Model [abstract] Abstract: Few attempts have been proposed in order to describe the statistical features and historical evolution of the export bipartite matrix countries/products. An important standpoint is the introduction of a products network, namely a hierarchical forest of products that models the formation and the evolution of commodities. In the present article, we propose a simple dynamical model where countries compete with each other to acquire the ability to produce and export new products. Countries will have two possibilities to expand their export: innovating, i.e. introducing new goods, namely new nodes in the product networks, or copying the productive process of others, i.e. occupying a node already present in the same network. In this way, the topology of the products network and the country-product matrix evolve simultaneously, driven by the countries push toward innovation. Close Riccardo Di Clemente 15008 Identifying the Features of Popular and Significant Artworks in Popular Music Production [abstract] Abstract: In the world of artistic production there is a constant struggle to achieve fame and popularity. This fierce competition between artistic creations results in the emergence of highly popular elements that are usually well remembered throughout the years, while many other works that did not achieve that status are long-forgotten. However, there is another level of importance that must be considered in order to have a more complete picture of the system. In fact many works that have influenced the production itself, both due to their aesthetic and cultural value, might have not been or might not be popular anymore. Due to their relevance for the whole artistic production, it is important to identify them and save their memory for obvious cultural reasons. In this paper we focus on the duality between popularity and significance in the context of popular music, trying to understand the features of music albums belonging to one or both of these classes. Close Bernardo Monechi 15009 Social networks evolution with old and and new ties: how our social horizon grows [abstract] Abstract: By means of user-generated data gathered on Last.fm, an on-line catalog of music albums, we define a growing conceptual space in the form of a network of tags representing the evolution of music production during the years. We use this network in order to define a set of general metrics, characterizing the features of the albums and their impact on the global music production. We then use these metrics to implement an automated prediction method of both the commercial success of a creation and its belonging to expert-made lists of particularly significant and important works. We show that our metrics are not only useful to asses such predictions, but can also highlight important differences between culturally relevant and simply popular products. Finally, our method can be easily extended to other areas of artworks creation. Close Raffaella Burioni

# Non-stationarity and ergodicity in Economic and Financial Systems  (NCEF) Session 1

## Chair: Francesco Caravelli

 47000 When is equilibrium a reasonable assumption? [abstract] Abstract: Abstract: Equilibrium in economics is based on the assumption that agents? actions are consistent with their beliefs, and usually means convergence to a fixed point in the Close Doyne Farmer 47001 Complexity Economics and the Synergy of Game Theory: Higher Order Dependencies for out of Equilibrium Economics [abstract] Abstract: In an article entitled Complexity Economics: A Different Framework for Economic Thought (W.B. Arthur, 2013) Brian Arthur discusses ?Complexity Economics? and the basis of economic theory if neoclassical economics is to be replaced by a non-equilibrium, dynamic and process focused understanding of economics in which neoclassical equilibrium, if it exists at all, is a special case. The importance of finding an alternative approach comes from the difficulties classical economics has in explaining economic processes: historical contingencies, learning, innovations, and the imperfections of human perception and decision-making. In this talk I present some preliminary work on an interpretation of game theory as ?interacting logic gates? for which Nash Equilibrium is only a subset of possible outcomes. This model addresses Arthur?s point regarding the economy as a massively parallel system of concurrent and recurrent behaviour that is ?perpetually 'computing' itself?. The information theoretical measure of synergy is applied to data from a behavioural economics experiment to practically demonstrate how the whole can be different from the sum of the parts in applied economics. Close Mike Harré 47002 Emergence of Cooperative Long-Term Market Loyalty in Double Auction Markets [abstract] Abstract: Loyal buyer-seller relationships can arise by design, e.g. when a seller tailors a product to a specific market niche to accomplish the best possible returns, and buyers respond to the dedicated efforts the seller makes to meet their needs. We ask whether it is possible, instead, for loyalty to arise spontaneously, and in particular as a consequence of repeated interaction and co-adaptation among the agents in a market. We devise a stylized model of double auction markets and adaptive traders that incorporates these features. Traders choose where to trade (which market) and how to trade (to buy or to sell) based on their previous experience. We find that when the typical scale of market returns (or, at fixed scale of returns, the intensity of choice) become higher than some threshold, the preferred state of the system is segregated: both buyers and sellers are segmented into subgroups that are persistently loyal to one market over another. We characterize the segregated state analytically in the limit of large markets: it is stabilized by some agents acting cooperatively to enable trade, and provides higher rewards than its unsegregated counterpart both for individual traders and the population as a whole. Close Aleksandra Aloric, Peter Sollich, Peter McBurney, Tobias Galla 47003 Economics without assuming ergodicity [abstract] Abstract: The mathematics of randomness began in the 1650s, with imagined parallel worlds where all possible events coexist. Economics immediately adopted the new concepts, especially expectation values, as its most basic foundation. The 1700s saw challenges to the nascent economic formalism but found patches, notably utility theory, to keep it alive. In the 1870s the mathematics of randomness took a leap forward with Maxwell and Boltzmann realising that an average across parallel worlds may not be reflective of an average over time. These developments made the earlier patches unnecessary, but by this time the formalism had become too established to adapt. Boltzmann coined the term ergodicity??, and questioned the meaning of expectation values. The following century saw great refinements and mathematical formalisation of the concept of ergodicity. Over the last few decades we have seen much interest in what happens when ergodicity is absent. In my talk I will ask this question in the context of economic thinking. Economics, broadly, is based on the assumption of noisy growth, which is mathematised with non-stationary non-ergodic models, most famously geometric Brownian motion. Close Ole Peters 47004 Optimal growth strategies with carrying capacity [abstract] Abstract: I will discuss the problem of determining optimal portfolios and general strategies, while taking into account their market impact, i.e. the effect of the position taken on the prices of the assets involved. I will examine the case of ordinary (multivariate) Gaussian diffusion and the one of jump diffusions, with a brief analysis of the structure of the general case. The Kelly criterion and other objectivefunctions can then be reexamined in this broader context. Close Lorenzo Sindoni 47005 Far from equilibrium: Wealth reallocation in the United States [abstract] Abstract: Studies of wealth inequality often assume that an observed wealth distribution reflects a system in equilibrium, a constraint rarely tested empirically. In this talk we introduce a simple model that allows equilibrium without assuming it. To geometric Brownian motion we add reallocation: all individuals contribute in proportion to their wealth and receive equal shares of the amount collected. We fit the reallocation rate parameter required for the model to reproduce observed wealth inequality in the United States from 1917 to 2012 and find that this rate was positive until the 1980s, after which it became negative and of increasing magnitude. With negative reallocation or even with the positive reallocation rates observed, equilibration is impossible or too slow to be practically relevant. Therefore, studies which assume equilibrium must be treated skeptically. Currently the system is best described by a negative reallocation rate. Each time we observe it, we see a snapshot of a distribution in the process of diverging. It is much like taking a photo of an explosion in space, whose finite extent tells us nothing of the eventual distance between pieces of debris. Studies that assume equilibrium are incapable of detecting the dramatic conditions one finds without this assumption. Close Yonatan Berman, Ole Peters, Alexander Adamou 47006 Financial Networks [abstract] Abstract: In this talk I will present the basics of the network approach in order to evaluate the resilience of a financial network to shocks and distresses, quantify the probability of contagion in an interbank network, individuate early-warning signals of upcoming financial crises and reconstruct missing interbank linkages (in monopartite, bipartite and multiplex networks). Close Guido Caldarelli 47007 The organization of the interbank network [abstract] Abstract: The properties of the interbank market have been discussed widely in the literature. However a proper model selection between alternative organizations of the network in a small number of blocks, for example bipartite, core-periphery, and modular, has not been performed. In this paper, by inferring a Stochastic Block Model on the e-MID interbank market in the period 2010-2014, we show that in normal conditions the network is organized either as a bipartite structure or as a three community structure, where a group of intermediaries mediates between borrowers and lenders. In exceptional conditions, such as after LTRO, one of the most important unconventional measure by ECB at the beginning of 2012, the most likely structure becomes a random one and only in 2014 the e-MID market went back to a normal bipartite organization. By investigating the strategy of individual banks, we show that the disappearance of many lending banks and the strategy switch of a very small set of banks from borrower to lender is likely at the origin of this structural change. Close Paolo Barucca, Fabrizio Lillo

# Hot Topics in the Study of Complex Systems in Asia  (HTCS) Session 1

## Chair: Siew Ann CHEONG

 29000 Modeling the activity of the entire primate brain: A meso-scale dynamical perspective [abstract] Abstract: Nonlinear dynamics of interactions between clusters of neurons via complex networks lie at the base of all brain activity. How such communication between brain regions gives rise to the rich behavioral repertoire of the organism has been a long-standing question. In this talk, we will explore this question by looking at the simulations of collective dynamics of a detailed network of cortical areas in the Macaque brain recently compiled from the CoCoMac database, as well as, a model of global coupled brain regions used as a benchamrk. To understand the large-scale dynamics of the brain, we simulate it at the mesoscopic level with each node representing a local region of cortex, comprising between 10^3-10^6 neurons. The dynamical behavior of each such region has been described using a phenomenological model consisting of a pool of excitatory neurons coupled to a pool of inhibitory neurons, which exhibits oscillations over a large range of parameter values. Coupling these regions according to the Macaque cortical network produces activation patterns strikingly similar to those observed in recordings from the brain. Our results help to connect recent experimental findings of the olfactory system and suggest that a part of the complicated activity patterns seen in the brain may be explained even without a full knowledge of its wiring diagram. Close Sitabhra Sinha (Institute of Mathematical Sciences, INDIA) 29001 A Generalized Betweenness for Studying Network Performance against Perturbations [abstract] Abstract: Betweenness is an important network property to study system performance against perturbations (such as random natural disasters and intended terrorism attacks). Traditionally, betweenness of a node/link is defined as how many times the node/link appears as intermediate node/link in all shortest paths between nodes. Traditional betweenness can help to answer how likely the 1st best paths between nodes will be cut off by perturbations. However, in reality, it is more concerned with a general situation, i.e., how likely those paths whose lengths are within a given range will be affected by perturbations. For instance, for a researcher to attend a conference, whether the 1st best path is available is not important at all, and instead, whether s/he can arrive on time is the key. Unfortunately, this general situation has barely been discussed in literature. To assess network performance in the general situation, we propose a generalized betweenness which is mathematically defined as how many times a node/link appears as intermediate node/link in all those paths whose lengths are within a given range. No existing method can effectively calculate the generalized betweenness, because it is difficult to find out, between every pair of nodes in a network, all those paths whose lengths are within a given range. By modifying a newly reported nature-inspired method, i.e., ripple-spreading algorithm (RSA), it becomes possible to calculate the generalized betweenness. Surprisingly, the proposed RSA can effectively find out all those paths whose lengths are within a given range by just a single run of ripple relay race. This work makes progress towards the general performance assessment of a network system against perturbations. Close Xiaobing Hu (Beijing Normal University, CHINA) 29002 Understanding the organization of cities from route analysis [abstract] Abstract: Urban street structure is a snapshot of the human mobility and an important medium facilitating the human interaction. Previous studies have analyzed the topology and morphology of street structure in various ways; fractal patterns, complex spatial network and so on. In practical term, it is also important to discuss how street networks are used by people. There are studies analyzing the efficiency, accessibility and road usage in the street networks too. In those studies, people usually investigate routes, either empirical routes or theoretical routes, to understand the functionality of the network. The travel route is a good proxy to understand the street structure and city attributes from user perspective. It is a selected path from the whole network by people or under the given standard, so it reveals how people use the networks. The selected route is also influenced by various factors such as spatial pattern and travel demand of city. Thus studying the empirical or theoretical optimal routes can help us understand the urban characteristics which are often hidden. For instance, fastest routes show the distribution of traffic in a city as well as the street structure. In this paper, we analyze the geometric property of routes to understand the geometry of practical street network where hierarchy and traffic is included. We use the two types of optimal routes collected from time minimizing algorithm and distance minimizing algorithm via the OpenStreetMap API. We suggest a new metric, center-philic level, to measure how much a route is bent toward the city center. We measured the center-philic level of a number of route within 30km radius from the center. By analyzing the center-philic level for different location of routes, we can understand and simplify the geometry of street network based on the center. The center-philic level patterns for two different algorithms can also reveal the effect of street hierarchy and traffic. In urban transportation, we can imagine two forces competing each other. By the agglomeration of business and people inside of city, street networks become denser around the center area to satisfy the demand. Such centralized street networks attract traffic toward inside of city. However many cities have arterial roads located outside of city to disperses the traffic concentrated on the inside of city. The arterial roads act as another force pulling traffic toward outside of the city. This tendency is well captured by our suggested metric. We firstly compare the general average center-philic level of both shortest and fastest routes to point out the fundamental difference between them. Later we analyze the center-philic level of individual cities and discuss how the metric can explain the street layout and street hierarchy. Close Minjin Lee (Sungkyunkwan University, KOREA), Hugo Serrano Barbosa (University of Rochester, USA), Gourab Ghoshal (University of Rochester, USA), Petter Holme (Sungkyunkwan University, KOREA) 29003 Integration of Network Analysis into Power-grid Analysis: sustainability and stability [abstract] Abstract: Network analysis has become a powerful tool to analyze complex systems over wide range of topics. For last two decades, researchers have made much progress particularly in the topics of disease spreading, social interaction, biological metabolism, neural network, urban mobility, etc. However, energy system has yet been plentifully covered. In this talk, we seek to apply network theory into electric power systems. Firstly, we integrate network analysis into environmental impact analysis. We introduce energy distance in order to estimate the greenhouse gas emissions of electricity transmission taking both the amount of electricity consumption and transmission distance into account. Secondly, we analyze the functional stability of power grids. The stable synchronization of power-grid nodes is the essential condition for the secure electric power systems. We investigate the transition of the synchronization stability of power-grid nodes and classify nodes based on the transition patterns. We conclude that network analysis is a good complement for energy system analysis. Close Heetae Kim (Sungkyunkwan University, KOREA), Sang Hoon Lee (KAIST, KOREA), Petter Holme (Sungkyunkwan University, KOREA) 29004 A new scientific collaboration network model [abstract] Abstract: Scientific collaboration plays an important role in the knowledge production and scientific development. The researchers have constructed several network models of scientific collaboration. In traditional collaboration network, two scientists are linked if they have coauthored one paper. However, this construction of network undervalues the role of the first author. In this paper, we propose a new collaboration network model considering the importance of the partnership between the first author and others. We make an empirical analysis based on the data of American Physical Society (APS). The?results?show?that?there?are??some? differences?of properties?between?the?new?network?and?the?traditional?one. And the node importance is studied on the new network to identify potential researchers. Close Ying Fan, Zhangang Han (Beijing Normal University, CHINA) 29005 Fusion of nations, fusion of disciplines: network evolution in nuclear fusion research [abstract] Abstract: Nuclear fusion research, which originated from atomic weapon developments by USA and USSR, attracts public attention as a promising energy source for the future. After the Cold War, Nations have collaborated in order to build research capacity in nuclear fusion. ITER (International Thermonuclear Experimental Reactor) is an example of big science' projects at the international level. Scientists from different disciplines involve in the project. The goal of our study is to investigate collaboration structure of nuclear fusion research and its evolution through an open access bibliometric database, Microsoft Academic Graph (MAG). We examine not only scientific journal citations but also the impact of IAEA Fusion Energy Conference on the research field. Dynamics of co-authorship networks reveal how nations take part and collaborate in nuclear fusion research. We expect that this study would be helpful for managing research activities and for suggesting national S&T policies. Close Hyunuk Kim, Inho Hong, and Woo-Sung Jung (POSTECH, KOREA) 29006 The robustness of spatially embedded and coupled infrastructure networks under localized attacks [abstract] Abstract: In the real world, infrastructure networks such as communication networks, power grid networks, transportation networks, solidly underlie the development of the whole society. The structure of infrastructure networks become more and more complicate and always couple together to perform intact service capacity. There commonly exist dependency among components as well as sub-networks, which make failure propagation. Currently, numerous literatures focused on the vulnerability and robustness of classical complex networks (e.g. random network, regular network, small-world network and scale-free network) under malicious attacks or random attacks. As one kind of real-world networks, besides having the topological characteristic of classical complex network, infrastructure networks are restricted by social-economic and geographical factors, so that they have short length links and some of them are planar graphs. Infrastructure network distributes in a specific spatially geographical domain, which probably exposures to real-world localized attacks (such as natural disasters). Recently, investigation on spatially embedded infrastructure networks under localized attacks is getting more and more attention. But full consideration of spatial characteristic of nodes and links in the robustness investigation of infrastructure network is still a big challenge due to involving real-world factors. In this paper, we aim to study the robustness of spatially embedded and coupled infrastructure networks under localized attacks. We first generate different kinds of spatially embedded infrastructure networks. Then a density-based index is proposed to depict the spatial characteristic of infrastructure network, dependency links among sub-networks are placed according to geographical restriction. Localized attacks are described by the circles with different radius. Finally, numerical simulation is conducted and the result illustrates that the spatial characteristic of infrastructure network and location of dependency links have significant effect on the robustness of infrastructure network under localized attack. Close Saini Yang, Fuyu Hu, Weiping Wang (Beijing Normal University, CHINA) 29007 Exploring the Collective Mobility Pattern of Intra-Urban Taxi Passengers [abstract] Abstract: The study of human mobility patterns is of both theoretical and practical values in many aspects. For long-distance travels, a few research endeavors have shown that the displacements of human travels follow the power-law distribution. However, the intra-urban travels do not simply follow the same power-law of longer-distance travels. What?s more, controversies remain in the issue of the scaling law of human mobility in intra-urban areas. In this work we focus on the mobility pattern of taxi passengers by examining five datasets of the three metropolitans of New York, Dalian and Nanjing. Through statistical analysis, we find the mixed distribution of lognormal and power-law better explain both the displacement and the duration time of taxi trips, as well as the vacant time of taxicabs, in all the examined cities. The universality of scaling law of human mobility is subsequently discussed, in accordance with the data analytics. Close Ling Zhang (Dalian University of Technology, CHINA), Shuangling Luo (Dalian Maritime University, CHINA), Haoxiang Xia (Dalian University of Technology, CHINA) 29008 The Effects of Correlation between Influential Level and Threshold in Opinion Dynamics [abstract] Abstract: We live in a society, where people interact with each other. An individual's opinion is formed with a neighbor's opinion. How do people accept a different opinion? Threshold model is the most well-known and proved theoretical model for the question. The model assumes that a person receives a different opinion when the ratio of their neighbor, whose opinion is different with one's opinion, is higher than one's threshold for an acceptance. Much research has been conducted on the opinion dynamics in the society with 'threshold model', and diverse aspects of key features in opinion dynamics have been revealed by the model. Most of the researches related with the threshold model in opinion dynamics are placed in the homogeneous threshold assumption. It means every person has the same level of threshold for an acceptance of an opinion. The usefulness of this assumption is clear in terms of statistical analysis. Howeve, we all know that heterogenuity of threshold exists. Even the threshold has a relationship with social capital like the number of neighbors, which can be represented as the characteristic of a network structure. Surprisingly, investigation on the correlation between network structure and threshold has not been conducted well. In this study, we investigate the influence of the correlation between the number of neighbors (influential level) and individual threshold on opinion dynamics. Given the scale-free network, as the representative network model of society, we change a level of correlation ($\beta$) from negative (-1) to positive (+1): 'negative' ('positive') is for the case that small (large) degree node has high threshold. The minimum of a threshold is set to 0.5 since we assume that people change their opinion when there are people more than a half of their neighbor generally. Additionally, opinion is composed with 0 and 1, and 60% of people in the network has opinion 1 as an initial condition. In this setting, we conduct the opinion dynamics while changing the correlation with degree and threshold. We found that the importance of the correlation betwen degree and threshold as to opinion dynamics. In this result, negative correlation region spreads information to entire system, but the positive correlation has a finite steady state. Additionally, there is a transition point around 0.5 regarding to correlation level. So far, we are conducting a finite size scaling analysis to figure out the characteristic of the transition, however, we were able to deduce from this result, there could be a transition of the system. To see the specific origin of this asymmetric contagion, we measured fixation time and final opinion. Fixation time is the time the node is fixed its final opinion. Moreover, the tendency of fixation time changes in positive correlation around the critical point, which is close to 0.5. This point is very close with the transition point for opinion switching. It means there is a balanced dependency between influential level and threshold so that from the point, the system can be divided with two different regimes: one is the regime for threshold dominant effect, the other is for the confused information effect. Another interesting result is: low influential nodes start to fluctuate more with high degree of dependency. Even though they have low threshold with positive correlation, they still receive a lot of influences from high degree nodes so they confused with mixed information from high degree nodes. This result suggests that the correlation between network structure and threshold of an acceptance can be important for opinion formation. Since we often experience the effect of correlation between influential level and threshold, it is worth to stress out the meaning of result. We can interpret the result as follows: positive correlation with influential level and conservative characteristic can block the unification of opinion in less influential group so that the majority opinion could not reach the whole society. Close Eun Lee, Peter Holme (Sungkyunkwan University, KOREA) 29009 Inferring the model of ants movements and aggregation in circular region [abstract] Abstract: Inferring the model of animal movements and aggregation have been a long-term challenging task. Although numerous of realistic-looking models have been proposed, model-based methods often rely on untested assumptions. Besides, many sets of microscopic hypotheses can produce the same macroscopic behaviors, it is dubious that they uncovered the real inherent mechanism. In this work, we conducted experiments with ants in two-dimensional circular surface. We try to infer behavioral rules directly from experimental data instead of traditional model-based research strategy. By defining a new metric to measure the ants aggregation extent, we study the influence of edge ?wall? and other individual on ants aggregation. Instead of studying large groups from 50 to 150, we study small number of ants from 1 to 3. By analyzing and comparing the data, we proposed a simple yet effective model, which may help to account for the micro-foundation of ants aggregation and infer how they amplify aggregation extent in large groups. Close Yikun Xu, Zhangang Han (Beijing Normal University, CHINA) 29010 Multiple individuals tracking algorithm for fish in 2D space [abstract] Abstract: As the increasing interest in the investigation of collective motion of a group of animals, it is important to tracking multiple moving animals and acquiring their position over time and space. There are several studies that have tried to solve this problem and make this data acquisition automated. However, none of these studies has solved the problem very well and automatically tracking is very difficult thanks to the individual?s various shape, complex motion and frequent occlusion. There are several published algorithms working on this problem, usually aim at one special specie, zebra fish, for instance. However, these algorithms have very high demands on the video quality, such as high frame rates, high image resolution and steady background, some of them are very time-consuming. Here we have developed an integrated approach based on artificial neural networks that enables us to automatically extract individuals? trajectories from both high quality and low quality videos. First we combine a background subtraction method and artificial neural networks to effectively detect the individuals. Then we use a linear assignment model to track the individuals. At last, we build a function to measure the confidence coefficient for each frame to help correct the possible errors. We applied our method to track different fish videos, the results showed that our method has a high efficiency and accuracy in most situations. Close Qi Zhang, Li Jiang, Zhangang Han (Beijing Normal University, CHINA) 29011 A new measure based on information theory to quantify the co-ordination of fish groups [abstract] Abstract: Collective motion of fish is an interesting research field. There is an essential question that how to quantify the how collective a group is, namely, how to recognize that fish in the group are interacting. Generally, researchers quantify the strength of interaction between fish intuitively using the correlation of velocities or spins, and measure the whole group?s polarization and rotation, etc. to determine whether it?s synergetic. It is because researchers consider the animal group motions as multi-body physical phenomena. However, it poses a problem that if an animal group does not display a visible collective structure, these physical statistics will fail to recognize the underlying mechanism. We introduce a new measure based on differential mutual information from information theory to quantify the co-ordination. Information theory is used in many fields but rarely in the field of collective animal motion. The original mutual information is a value to measure the correspondence of two signals, if there is any correspondence between these two agents? moving, mutual information will reveal it, while old statistics like polarization fail if the relationship is strange. The new statistic will be compared with classical statistics like polarization and correlation on Couzin model and Vicsek model. We will try different parameters to analyze the properties of all these statistics. And we will show that the new statistic is more efficient than old statistics when the model displays confusion and has even efficiency when the model displays order. We record the trajectories of different amounts of Glass Goldfishes swimming in a tank with a radius of 40 centimeters. The new statistic is used to measure the co-ordination of the groups. We will show that the co-ordination grows while the fish amount grows. In short, we will illustrate that the new measure can be helpful to reveal the strength of the co-ordination in a group. Close Yinong Zhao, Zhangang Han (Beijing Normal University, CHINA)

# Estimation of probability density functions in noisy complex ows  (EPD) Session 1

## Chair: Fred Wubs

 3000 Estimation of Markov processes using operator eigenpairs [abstract] Abstract: Modeling the effective macroscopic dynamics of complex systems as noise-driven motion in a potential landscape has found its use for topics ranging from protein folding to the thermohaline ocean circulation. I will discuss the estimation of such models from timeseries, focussing on a methodology that makes use of the spectral properties (leading eigenpairs) of the Fokker-Planck operator associated with the diffusion process. This methodology is well suited to infer stochastic differential equations that give effective, coarse-grained descriptions of multiscale systems. I will discuss estimation of coordinate-dependent diffusion, subsampling, nonconstant sampling intervals and inference from non-equilibrium data. Close Daan Crommelin 3001 Mixing in Noisy Nonlinear Oscillators: Application to Low-Frequency Climate Variability [abstract] Abstract: Much can be learned about systems exhibiting complex dynamics by studying the evolution of probability densities rather than single trajectories. In the stochastic case, this evolution is governed by the transfer semigroup which allows to connect the correlation functions and power spectra to the Fokker-Planck equation. Here, we propose to approximate the transfer operators of high-dimensional systems by Markov operators on a reduced space. While these Markov operators do not in general constitute a semigroup, rigorous results can be obtained regarding their spectral properties, in particular allowing to reconstruct correlation functions and quantify mixing in the reduced space. The approach is applied to the study of the variability and the stability stochastic nonlinear oscillators exhibiting resonant behavior. New analytical and numerical results are found for the mixing spectrum of the Hopf bifurcation with additive noise, bringing new insights on the phenomena of noise-induced oscillations and phase diffusion. These results allow to give new interpretations on the stochastic dynamics of high-dimensional climate models and support the applicability of the method to the study of stochastic bifurcations. Close Alexis Tantet 3002 Deterministic Methods for Stochastically Forced PDEs [abstract] Abstract: In this talk I shall illustrate an approach to study the dynamics of stochastic PDEs (or more generally stochastic dynamical systems) with respect to parameters using deterministic continuation methods. In particular, I shall focus on the case of local fluctuations for the stochastic Allen-Cahn equation and explain the practical implementation as well as applications in various scientific disciplines. Close Christian Kuehn 3003 On the numerical solution of large-scale linear matrix equations [abstract] Abstract: Linear matrix equations such as the Lyapunov and Sylvester equations play an important role in the analysis of dynamical systems, in control theory, in eigenvalue computation, and in other scientific and engineering application problems. A variety of robust numerical methods exists for the solution of small dimensional linear equations, whereas the large scale case still provides a great challenge. In this talk we review several available methods, from classical ADI to recently developed projection methods making use of `second generation'' Krylov subspaces. All methods reply on the possible low-rank form of the given data. Both algebraic and computational aspects will be considered. Close Valeria Simoncini 3004 Studying critical transitions in stochastic ocean-climate models by solving Lyapunov equations [abstract] Abstract: Techniques from numerical bifurcation analysis are very useful when studying transitions between steady states of flows and the instabilities that are involved. In this presentation we discuss how we use parameter continuation in determining probability density functions of flows governed by stochastic partial differential equations near fixed points under small noise perturbations. We first discuss the traditional way of doing this by stochastically forced time forward simulation, and then show how this can also be done by solving generalized Lyapunov equations using a novel iterative method involving low-rank approximations. One of the advantages of this method is that preconditioning techniques that are known from iterative methods for linear systems can be used. We illustrate the capabilities of the method on a phenomenon in physical oceanography: the occurrence of multiple equilibria in the Atlantic Meridional Ocean Circulation. Close Sven Baars and Fred Wubs