# Biology  (B) Session 3

## Chair: Roland Kupers

 327 A simple model for the maintenance of complex immune repertoires [abstract] Abstract: The immune system is a fascinating complex system taking decisions on how to respond to a wide variety of stimuli, varying from lethal pathogens to harmless proteins in the food. This system relies on a large repertoire of randomly generated ‘detectors’ in the form of naïve lymphocytes. We are interested in the mechanisms behind the maintenance of these detectors during ageing. Nowadays, deep sequencing methods can be used to characterize the repertoires of naïve lymphocytes. To get a deeper understanding of how an important part of the complex immune system works, we developed a model regarding naïve lymphocyte dynamics which is similar to Hubbell’s Neutral Community Model used in ecology. The simulations and analytical solution of this model give a geometric clone-size distribution, whereas it has been argued that the repertoire is power-law distributed. In addition, we show that current diversity measures tend to overestimate the effect of ageing. Indeed, Next Generation Sequencing (NGS) data shows a geometric distribution, which is in line with our neutral model. Our simple model appears to be sufficient to describe the complex maintenance of naïve detectors in the immune system. Close Peter de Greef, Theres Oakes, Bram Gerritsen, James M. Heather, Rutger Hermsen, Benny Chain and Rob de Boer 273 Chain-like organization and hierarchy in the human functional brain network [abstract] Abstract: The analysis of brain functional architecture is a paradigmatic example of complex system, since brain functionality emerges as a global property of local interactions. A complete description of multi-scale and multi-level segregation and integration of brain regions represents a challenging issue to address and unearths the complexity of its whole functional organization. Here we analysed functional magnetic resonance imaging data from forty human healthy subjects during resting condition. Network theory is able to visualize the skeleton of functional correlations (weights) between different regions (nodes) of the brain and to extract information, by selecting only the most important features out of the noise. On the resulting human functional brain network, we performed a modified version of the percolation analysis and compared the results with a null model: a not-trivial hierarchical organization in modules emerges. A zoom in the modular structure through a maximum spanning forest (MSF) approach unveiled a chain-like organization of the brain regions, never observed before. Intuitively, nodes tend to link with nodes in the same anatomical area, except for regions in the Temporal Lobe. Passing from the MSF to the maximum spanning tree, the network preserved the chain-like structure, confirming some outcomes and revealing the centrality of the Occipital Lobe and some regions from the Temporal Lobe and the Cerebellum. Furthermore, we explored the hierarchical organization of the brain function looking at network configurations when specific thresholds are introduced. Many connections within, rather than between, anatomical regions disclosed a high level of segregation of a specific area. Both the Occipital Lobe and the Cerebellum exhibit together this feature, even if an important difference emerged: while the former represents the core of the whole functional network with all the other modules connecting gradually to it, the latter is peripheral, joining the network only at the end. Close Rossana Mastrandrea, Fabrizio Piras, Andrea Gabrielli, Gianfranco Spalletta, Guido Caldarelli and Tommaso Gili 317 Characterization of influenza spread patterns in France [abstract] Abstract: Influenza activity shows a complex spatio-temporal pattern with a strong seasonal dynamic whose complete understanding is still missing. Here we study 30 years of seasonal influenza circulation in France at the regional level from influenza-like-illness (ILI) cases time series. Our aim is to characterize common patterns of synchronization across seasons and assess how they change from the start of the outbreak to the time at which influenza activity reaches its peak. To each season we associate two vectors whose elements are the epidemic onset time or the epidemic peak time in a given region of France, normalized to remove seasonal trends. We cluster seasons according to their epidemic onset time (peak time) based on the distance between their corresponding vectors. We found that the distance computed on the peak time is generally smaller than the one computed on the onset time. A stronger clustering is therefore observed at the peak time, highlighting the larger synchronization that regions reach in the period of highest incidence with respect to the beginning of the epidemic. Seasons starting with rather different geographic distribution of epidemic onset become more similar in their peak time synchronization pattern. They are also characterized by larger epidemics and show no relevant correlation to weather time series, differently from the seasons not showing this recurrent pattern. Multi-scale transportation networks are found to play an important role in the emergence of such patterns. The study identifies the relevant factors in the shaping of the spatio-temporal diffusion of influenza in France, offering important information for the understanding of seasonal behavior and for the developments of realistic models of influenza spread. Close Pietro Coletti, Chiara Poletto and Vittoria Colizza 125 Does swallowing resemble a phase transition? [abstract] Abstract: To better understand the complex relations between physical properties of foods and sensory perception, we have explored methods that are also used in the area of complex systems. We analysed temporal dominance of sensations (TDS) data [1] using methods from information theory[2]. We report that vastly different TDS curves can be mapped onto one master curve as a function of normalized time and an information theoretical measure. Furthermore the theory provides the basis for a recently proposed quantitative measure for complexity[3]. Interestingly, we find that this measure versus time maximizes at a point that is near to the moment of swallowing. This behaviour has a strong resemblance to that of a system near a phase transition[4]. Such an analogy has been put forward by Gershenson et al. for a random Boolean network[3]. New visualisation methods are investigated, like directed graphs, to research TDS profiles on an individual level for different food model systems. This showed that for most individuals the sequence of dominant sensations depended on system type, while for some it was independent of that. References [1] M. Devezeaux de Lavergne, M. van Delft, F. van de Velde, M. a. J. S. van Boekel, and M. Stieger, “Dynamic texture perception and oral processing of semi-solid food gels: Part 1: Comparison between QDA, progressive profiling and TDS,” Food Hydrocoll., vol. 43, pp. 207–217, 2015. [2] C. E. Shannon, “A Mathematical Theory of Communication,” Bell Syst. Tech. J., vol. 27, no. July, pp. 379–423, 1948. [3] C. Gershenson and N. Fernández, “Complexity and information: Measuring emergence, self-organization, and homeostasis at multiple scales,” Complexity, vol. 18, no. 2, pp. 29–44, Nov. 2012. [4] M. Prokopenko, J. T. Lizier, O. Obst, and X. R. Wang, “Relating Fisher information to order parameters,” Phys. Rev. E, vol. 84, no. 4, p. 041116, 2011. Close Leen Sturtewagen, Harald van Mil, Marine Devezeaux de Lavergne, Markus Stieger and Erik van der Linden 103 Assessing the Dynamics and Control of Droplet- and Aerosol-Transmitted Influenza Using an Indoor Positioning System [abstract] Abstract: There is increasing evidence that aerosol transmission is a major contributor to the spread of influenza. Despite this, virtually all studies assessing the dynamics and control of influenza assume that it is transmitted solely through direct contact and large droplets that require close physical proximity. Here, we use wireless sensors to measure simultaneously both the location and close proximity contacts in the population of a US high school. This dataset, highly resolved in space and time, allows us to model both droplet and aerosol transmission either in isolation or in combination. In particular, it allows us to computationally assess the effectiveness of overlooked mitigation strategies such as improved ventilation that are available in the case of aerosol transmission. While the effects of the type of transmission on disease outbreak dynamics appear to be weak, we find that good ventilation could be as effective in mitigating outbreaks as vaccinating the majority of the population. In simulations using empirical transmission levels observed in Hong Kong and Bangkok households, we find that bringing ventilation to recommended levels has the same effect as vaccinating between 50% and 60% of the population, in the combined droplet-aerosol model. Our study therefore suggests that improvements of ventilation in public spaces could be an important strategy supplementing vaccination efforts for effective control of influenza spread. Close Gianrocco Lazzari, Timo Smieszek and Marcel Salathe 481 Human Sexual cycles are driven by culture and collective moods [abstract] Abstract: It is a long-standing question whether human sexual and reproductive cycles are affected predominantly by biology, hemisphere location, or culture. Here we show that interest in sex peaks sharply online during the major cultural and religious celebrations of countries with predominantly Christian or Muslim populations, regardless of hemisphere. These peaks in sex-related searches correspond to documented human birth cycles, even after adjusting sex-search data for numerous factors such as search language, season, amount of free time due to holidays, and changes in the overall volume of online searches. We further show that public mood sentiment measured independently from the Twitter content generated by the same country populations, contains distinct collective emotions associated with those cultural celebrations, even after removing all known greetings used during cultural and religious celebrations. Additionally, the observed collective moods correlate with sex search volume outside of these holidays. Our results provide converging evidence that the cyclic sexual and reproductive behavior of human populations is driven above all else by culture, and specifically that the seasonal sex-search and corresponding birth peaks derive from emotions that are maximized during major cultural and religious celebrations, but appear in other occasions when interest in sex also tends to increase. Close Luis M. Rocha, Ian Wood, Joana Gonçalves-Sá and Johan Bollen

# Cognition  (C) Session 2

## Chair: Simon Dedeo

 9 Committed activists and the reshaping of status-quo social consensus [abstract] Abstract: The role of committed minorities in shaping public opinion has been recently addressed with the help of multi-agent models. However, previous studies focused on homogeneous populations where zealots stand out only for their stubbornness. Here, we consider the more general case in which individuals are characterized by different propensities to communicate. In particular, we correlate commitment with a higher tendency to push an opinion, acknowledging the fact that individuals with unwavering dedication to a cause are also more active in their attempts to promote their message. We show that these activists are not only more efficient in spreading their message but that their efforts require an order of magnitude fewer individuals than a randomly selected committed minority to bring the population over to a new consensus. Finally, we address the role of communities, showing that partisan divisions in the society can make it harder for committed individuals to flip the status-quo social consensus. Close Dina Mistry, Qian Zhang, Nicola Perra and Andrea Baronchelli 195 Stochastic heterogeneous mean field approximation of the utterance selection model [abstract] Abstract: The utterance selection model (USM) for language change (Baxter et al. 2006) is a stochastic agent-based model developed to simulation language change. In this model, agents are vertices of a graph and interact along its edges by stochastically producing utterances and learning from them. The dynamics of such an agent-based model is defined at the agent level and it is usually difficult to deduce the average dynamics of the complete population. In the original paper, the authors derived a continuous time limit in the form of a Fokker-Planck equation. This limit is only valid for a restricted set of parameters. In this talk, I will derive a new continuous time limit of the USM, which has no constraints on parameters and use it to derive a coarse-grained population level approximation of the dynamics. This approximation is a stochastic version of the heterogeneous mean field approximation. Using this approximation, I will characterize the dynamics of the USM at the population level. In particular, I will show that the population dynamics of the system can mainly be captured by three parameters. The analysis also reveals a finite-size effect in the dynamics. Close Jérôme Michaud 583 Detection and Analysis of Political Leaders’ Facial Emotions:The Impact on Voters' Behavior [abstract] Abstract: Facial emotions are believed to be very expressive social stimuli; hence significant amount of efforts have been made within the past two decades to detect, study and analyze these emotions in a way to reveal specific human behaviors and characteristics, in this paper we aim to decode some of the detected facial emotions on political leaders in a way to find potential correlations between their facial expressions and impacts on voter preference decisions in the United States, we study facial emotions detected on images of selected Republican and Democratic presidential candidates during their most controversial campaign speeches and debates for the 2016 United States presidential election. Our facial detection application is based on the Face API recently developed by Microsoft Cognitive Services, which is designed to recognize eight universal groups of facial emotions including sadness, neutral, contempt, disgust, anger, surprise, fear and happiness. 180 images were collected and analyzed for Donald Trump, John Kasich and Ted Cruz; Republican party nominees, also Hillary Clinton and Bernie Sanders for the Democratic party nominees, the results of the detected groups of facial emotions are scored forming an eight-dimensional vector and then re-scaled to two-dimensional vectors using Principal Component Analysis technique, the findings are discussed in the context of direct correlation between some facial expressions and voters decisions for the primary presidential election taking place since February first 2016. Close Alaa Alazzam and Hiroki Sayama 514 Method of assessment of textual emotiveness with use of psycholinguistic markers on base of morphological features for analysis of social processes in networks and blogs [abstract] Abstract: A combined approach to identify emotionally colored texts, which reflect the excited state of its authors and also make the sentiment analysis of these texts is proposed. This approach is based on one side on use of psycholinguistic markers that are calculated on the basis of the morphological characteristics of the text and on other side on use of object oriented sentiment analyser based on SVM classification. A complex indicator reflecting emotiveness of texts on the basis of the core group of markers was presented. On an example of two thematic collections it was shown that on the basis of that complex indicator the most emotional topic could be automatically detected. In this article an integrated approach is presented which combines the assessment of the text using the sentiment analysis method and context-independent psycholinguistic markers based on morphological features. The proposed approach can be a useful extension of Social Mining methods in different languages and it can be applicable in developing methods in the fields of affective and personality computing. Close Alexandr Sboev, Dmitry Gudovskikh, Ivan Moloshnikov and Roman Rybka 528 Industrialisation by Invitation: A Community Detection Approach to Mapping FDI-related Knowledge Diffusion in Ireland. [abstract] Abstract: As Ireland emerges from recession, riding a wave of growth largely driven by the presence of large profitable foreign multi-nationals, recurring questions surrounding the long-term durability of the so-called 'industrialisation by invitation' approach to modernisation persist. If Ireland is to benefit from this strategy, there needs to be significant transfer of knowledge between foreign and domestic firms, thus enabling the latter to emerge as global competitors in their own right. In order to investigate patterns of knowledge diffusion within the Irish economy, here we build a network of labour transitions (job switches) between foreign-owned multi-nationals and domestic firms using a new dataset constructed from the Irish economic census of 2014. Using network techniques for community detection, we identify a highly modular network structure, as workers tend to switch to a narrow set of similar industries that share their own skill set. We find that while some sectors such as pharmaceuticals, with a high share of foreign firms, are largely disconnected from the wider economy, other sectors such as financial services, IT and food processing are more integrated with domestic economic activities. This analysis suggests that policies focusing on increasing labour mobility between certain sectors, and hence enabling workers to move more freely throughout the economy, could result in improved knowledge and expertise transfer from foreign to domestic firms (and vice versa). Close Eoin Flaherty, Matte Hartog and Neave O'Clery

# Foundations & Economics  (FE) Session 2

## Chair: Silvia Bartolucci

 325 Systemic risk in multiplex networks with asymmetric coupling and threshold feedback [abstract] Abstract: We study cascades on a two-layer multiplex network, with asymmetric feedback that depends on the coupling strength between the layers. Based on an analytical branching process approximation, we calculate the systemic risk measured by the final fraction of failed nodes on a reference layer. The results are compared with the case of a single layer network that is an aggregated representation of the two layers. We find that systemic risk in the two-layer network is smaller than in the aggregated one only if the coupling strength between the two layers is small. Above a critical coupling strength, systemic risk is increased because of the mutual amplification of cascades in the two layers. We even observe sharp phase transitions in the cascade size that are less pronounced on the aggregated layer. Our insights can be applied to a scenario where firms decide whether they want to split their business into a less risky core business (layer A) and a more risky subsidiary business (layer B). In such setting a failure (or bankruptcy) on the core layer implies a failure on the subsidiary layer as well, as the failed firm is out of business. On the other hand, a failure on the subsidiary layer only decreases a firm's failure threshold on the core layer and, thus, increases its absolute failure probability in the core business. We show that in most cases, this kind of business diversification may lead to a drastic increase of systemic risk, which is underestimated in an aggregated approach. Close Rebekka Burkholz, Matt V. Leduc, Antonios Garas and Frank Schweitzer 215 Detecting early-signs of the 2007 crisis in the world trade [abstract] Abstract: Since 2007, several contributions have tried to identify early-warning signals of the financial crisis. However, the vast majority of analyses has focused on financial systems and little theoretical work has been done on the economic counterpart. In the present paper we fill this gap and employ the theoretical tools of network theory to shed light on the response of world trade to the financial crisis of 2007 and the economic recession of 2008-2009. We have explored the evolution of the bipartite World Trade Web (WTW) across the years 1995-2010, monitoring the behavior of the system both before and after 2007. Our analysis shows early structural changes in the WTW topology: since 2003, the WTW becomes more and more compatible with the picture of a network where correlations between countries and products are progressively lost. Moreover, the WTW structural modification can be considered as concluded in 2010, after a seemingly stationary phase of three years. We have also refined our analysis by considering specific subsets of countries and products: the most statistically significant early-warning signals are provided by the most volatile macrosectors, especially when measured on emerging economies, suggesting the latter as the most sensitive indicators of the WTW health. Close Fabio Saracco, Riccardo Di Clemente, Andrea Gabrielli and Tiziano Squartini 77 The hidden relationship between Zipf’s law and segregation [abstract] Abstract: Modern societies are often faced to segregation dictated by race, religion, social status or incomes differences. The understanding of the rise of such phenomenon has thus attracted a lot of attention from economists, politicians and sociologists. We first introduce a metapopulation version of the Schelling model showing that an hidden relationship emerges, for low tolerances, between the segregation patterns and the population variability in different urban areas. In particular, we observe that the population frequencies of each node, emerging from the model, once ordered according to the population ranking, follow a Zipf’s law. Motivated by this theoretical result we analyze the internal composition of several metropolitan areas in the US. We show that a universal Zipf’s law is present also at the urban scale and that a correlation between the population heterogeneity and the segregation patterns can be observed. Moreover we analyze the internal urban preferences for different ethnic groups, using the z-score for identifying the overestimation of a certain ethnic group in each zip. We show that density “preferences” can be observed and that the ethnic composition strongly depends on the density. Close Floriana Gargiulo and Timoteo Carletti 74 Emergence of giant strongly connected components in continuum disk-spin percolation [abstract] Abstract: We propose a continuum model of percolation in two dimensions for overlapping disks with spin. In this model the existence of bonds is determined by the distance between the centers of the disks, and by the scalar product of the (randomly) directed spin with the direction of the vector connecting the centers of neighboring disks. The direction of a single spin is controlled by a “temperature”, representing the amount of polarization of the spins in the direction of an external field. Our model is inspired by biological neuronal networks and aims to characterize their topological properties when axonal guidance plays a major role. We numerically study the phase diagram of the model observing the emergence of a giant strongly connected component, representing the portion of neurons that are causally connected. We provide strong evidence that the critical exponents depend on the temperature. Close Francesco Caravelli, Marco Bardoscia and Fabio Caccioli 97 Input-output relationship in social communication datasets characterized by neuronal spike train analysis [abstract] Abstract: As human communication datasets become increasingly rich, various approaches have been employed to improve the network modeling in order to uncover hidden aspects of human dynamics. In particular, records of communication events between individuals with high temporal resolutions have enabled us to study dynamical properties of networks rather than static ones, in the emerging field of temporal networks. We study the dynamical properties of human communication through different channels, i.e., short messages, phone calls, and emails, adopting techniques from neuronal spike train analysis in order to characterize the temporal fluctuations of successive inter-event times. We measured the so-called local variation (LV) of incoming and outgoing event sequences of users, which is originally designed to characterize temporal fluctuations in spike train data. We found that these in- and out-LV values are positively correlated for short messages, and uncorrelated for phone calls and emails. An important originality of our work is to focus on the relationship between incoming and outgoing events involving social agents and its impacts on temporal fluctuations. Similarly to neurons, receiving inputs and integrating them to send outputs, social agents are subject to incoming messages that may, or not, trigger reactions. In order to test this idea and to understand the observed LV-correlations, we analyzed the response-time distribution in empirical datasets and developed a generalized Hawkes process to model the observed dynamical properties. Numerical simulations of the model indicate that a quick response to incoming events and a refractory effect after outgoing events are key factors to reproduce the positive LV correlations. This investigation of the input-output relationship in human messaging processes may provide us important insight on how information flows in human communications. Close Takaaki Aoki, Taro Takaguchi, Ryoya Kobayashi and Renaud Lambiotte 418 Natural hazards, individual behavior and non-linearities in market flood risk assessments [abstract] Abstract: Flood risk is one of the most frequently occurring disasters worldwide, and cost-benefit analysis is widely applied to assess management strategies. The central number that influences the balance between costs and benefits here is the price of flood risk. It is usually assessed either through the analysis of market-level data using hedonic pricing or by eliciting individual willingness to pay to avoid risk through surveys. The two approaches constitute two different paradigms – micro vs macro – and often produce contrasting results in pricing flood risks. The assessment is also sensitive to the timing after the shock. At the times of natural disasters price trends in flood prone areas shift significantly and abruptly implying that there are systemic changes in property markets. On the one hand, it implies that transactions in the past may not be representative anymore when making current price assessments or projections for the future. On the other hand, it is essential to trace the link between individual risk perceptions and macro-level market outcomes as the former fuel these structural market shifts. This calls for new computation methods for assessing capital-at risk and its fluctuations as shocks occur and markets aggregate individual reactions to these natural hazards. We present an agent-based model of a housing market covering flood prone areas, in which we not only utilize the most recent sales in conducting market price predictions but also explicitly test the evolution of housing prices (and consequently the price of flood risk) emerging from interactions of heterogeneous household agents with various individual representations of risk perceptions. We compare market outcomes under three common behavioral models: expected utility, prospect theory and risk negligence Our results demonstrate non-linearity between agents’ individuals risk perceptions and aggregated price discount, which uncovers the nature of the gap between the two measurement approaches. Close Tatiana Filatova and Koen de Koning

# Cognition & ICT  (CI) Session 1

## Chair: Andrea Nanetti

 338 Mapping bilateral information interests using the activity of Wikipedia editors [abstract] Abstract: We live in a global village where electronic communication has eliminated the geographical barriers of information exchange. The road is now open to worldwide convergence of information interests, shared values and understanding. Nevertheless, interests still vary between countries around the world. This raises important questions about what today’s world map of information interests actually looks like and what factors cause the barriers of information exchange between countries. To quantitatively construct a world map of information interests, we devise a scalable statistical model that identifies countries with similar information interests and measures the countries’ bilateral similarities. From the similarities we connect countries in a global network and find that countries can be mapped into 18 clusters with similar information interests. Through regression we find that language and religion best explain the strength of the bilateral ties and formation of clusters. Our findings provide a quantitative basis for further studies to better understand the complex interplay between shared interests and conflict on a global scale. The methodology can also be extended to track changes over time and capture important trends in global information exchange. References: - Karimi, Bohlin, Samoilenko, Rosvall and Lancichinetti. Mapping bilateral information interests using the activity of Wikipedia editors, Palgrave Communications 1 (2015) - Samoilenk, Karimi, Edler, Kunegis and Strohmaier. Linguistic neighbourhoods: explaining cultural borders on Wikipedia through multilingual co-editing activity, EPJ Data Science 5 (2016) Close Fariba Karimi, Ludvig Bohlin, Anna Samoilenko, Martin Rosvall and Andrea Lancichinetti 107 Connecting tweeting behavior to voting activity in the European Parliament: A study of cohesion and coalitions. [abstract] Abstract: Social media activities often reflect phenomena that naturally occur in other complex systems. By observing the networks and the content propagated through these networks, we can describe or even predict the processes that influence the observed social media activities. In this study, we explore the connection between the voting and retweeting (endorsing) behavior of the members of the 8th European Parliament (MEPs). Utilizing roll-call vote data between October 2014 and February 2016, we investigate the processes responsible for the formation of coalitions in the European Parliament (EP). We study the formation of coalitions at different levels of granularity. First, we focus on political groups in the EP and quantify the voting agreement between their members (cohesion) and explore the inter-group voting agreement employing a distance based method. Second, we investigate which role party affiliation, origin of MEPs as well as the topic of the ballot play for the covoting behavior in the European Parliament. Using Exponential Random Models in combination with a meta-analysis technique, we show that the cohesion of political groups and strength of alliances between these groups depend to a large extent on the topic of the ballot. We study the retweet network between the MEPs, as observed in the same time period. Again, we define the intra- and inter-group measures of cohesiveness, and investigate the retweeting behavior of MEPs across topics. We compare the results with the results based on the roll-call votes and show that retweeting behavior of MEPs across several topics exhibits explanatory power for the covoting behavior of MEPs. References: Cherepnalkoski, Mozetič. A Retweet Network Analysis of the European Parliament. In Proceedings of SITIS 2015. IEEE. p.350-357. Lubbers. Group composition and network structure in school classes: a multilevel application of the p model. Social Networks. 2003, 25(4):309-332 Close Darko Cherepnalkoski, Andreas Karpf, Igor Mozetič and Miha Grčar 370 Homophily and missing links in citation networks [abstract] Abstract: Citation networks have been widely used to study the evolution of science through the lenses of the underlying patterns of knowledge flows among academic papers, authors, and research sub-fields. Here we focus on citation networks to cast light on the salience of homophily, namely the principle that similarity breeds connection, for knowledge transfer between papers. To this end, we assess the degree to which citations tend to occur between papers that are concerned with seemingly related topics or research problems. Drawing on a large data set of articles published in the journals of the American Physical Society, we propose a novel method for measuring the similarity between articles through the statistical validation of the overlap between their bibliographies. We define the probability P_{i\to j}(p*) that a citation between any two articles i and j whose similarity is validated at the threshold p* exists as the ratio between the number of pairs of articles validated at that threshold in the APS citation network and the number of existing citations between those validated pairs. Results suggest that the probability of a citation made by one article to another is an increasing function of the similarity between the two articles. Our study enables us to uncover missing citations between pairs of highly related articles, and may help identify barriers to effective knowledge flows. By quantifying the proportion of missing citations, we conduct a comparative assessment of distinct journals and research sub-fields in terms of their ability to facilitate or impede the dissemination of knowledge. Findings indicate that knowledge transfer is facilitated by journals of wide visibility, such as PRL, than by lower-impact ones. Our study has important implications for authors, editors and reviewers of scientific journals, as well as public preprint repositories, as it provides a procedure for recommending relevant yet missing references. Close Valerio Ciotti, Moreno Bonaventura, Vincenzo Nicosia, Pietro Panzarasa and Vito Latora 28 Functional Constructions in Language Networks [abstract] Abstract: The emergence of the human language is perhaps the most significant event in the course of our evolution. Unlike primitive forms of animal communication, the vastness of our lexicon and the recursive application of structural rules allows human language almost infinite creative potential in producing meaningful utterances. Despite the complexity and variety of language, the processes of generating and deciphering meaningful utterances are accomplished remarkably rapidly. This paper demonstrates that these efficiencies are not accidental – lexicon and syntax in human language are organized purposefully in networks with maximized navigational performance. Starting from a word-to-word co-occurrence network of a corpus, we adopt an unsupervised learning algorithm to identify coherent sub-sequences (motifs) of nodes (words) shared by many paths (sentences). We believe that instead of navigating the language network word by word when one generates a sentence, motifs are employed as functional shortcuts to accelerate the process i.e. from the network perspective, motifs connect words that were previously far apart. We show that these functional motifs reduce the effective path lengths between words much more efficiently than motifs created from a null model. We also establish the importance of stop words (highly frequent words with low semantic value) in motifs. A large proportion of motifs can be characterized by a relatively small set of stop word templates. Moreover, these same templates are reused recursively to embed the language network to higher levels of abstraction. Our findings are surprisingly consistent with the theory of Construction Grammar (CxG). CxG purports that constructions are irreducible components of language carrying both form and meaning within. Words, sequences of words, and even templates of phrase formation are all treated equally as constructions in this paradigm. Similarly, in our language network, we allow words, phrases, and generalizable templates to coexist and interact. Close Woon Peng Goh and Siew Ann Cheong 440 Percolation in homophilious social networks [abstract] Abstract: In network theory, homophily is a tendency to connections between nodes of similar characteristics. Social networks, such as friendship networks, tend to be homophilious, since they connect individuals of similar tastes or opinions. The effect of homophily and information diffusion in social networks are difficult to distinguish in empirical studies: an homophilious network might display a behavior similar to diffusion through word-of-mouth just because agents with similar characteristics are likely to both adopt similar things and be connected to each other. The objective of this study is to analyze the effect of homophily in diffusion by word-of-mouth and to compare it with a non-homophilious benchmark. We introduce homophily in a percolation model of word-of-mouth diffusion as a modification of the small world algorithm. This novel algorithm reorganizes the nodes according to their individual characteristics, so the resulting network is highly homophilious. A comparison between diffusion in the modified network and in the benchmark scenario allows to isolate the effect of homophily in adoption. The main result is that homophily reduces the effect of the network structure: homophilious networks with different link structures present almost identical adoption sizes. In other words, the diffusion size does not differ substantially for different values of the rewiring probability. This is equivalent to saying that the network structure of a population does not play much of a role in this context. This effect results from the extreme case of homophily considered. Nonetheless, this novel approach to introduce homophily in a social network allows for an intuitive development of the word-of-mouth diffusion process in homophilious networks. The prevalence of homophily in social networks calls for studies that introduce homophily in simulation models of diffusion such as this. Close Elena M. Tur, Paolo Zeppini and Koen Frenken 39 Assessing ICT Risk through a Monte Carlo Ecology [abstract] Abstract: Risk assessment and management of an ICT infrastructure requires a large amount of data on the joint behavior of the system and its users. Usually, data is collected over time by observing such a joint behavior after the deployment. This implies that the design step cannot assess and manage because of lack of data. As a consequence, risk can be assessed after the deployment only. Monte Carlo Ecology is a methodology to predict the behavior of a system under attacks at any step of its life. The methodology introduces an ecosystem that includes an environment that models the target system and some organisms that models the various agents that interact among themselves and with the system. Some organisms attack the environment and other ones update it to improve its resiliency. The interactions in the ecosystem determine its evolution and events of interest such as an agent that reach one of its predefined goals. An evolution is stochastic because several events of interest, such as the success of an attacks, are ruled by probability distributions. For this reason, Monte Carlo Ecology applies a Monte Carlo method that runs multiple, independent evolutions to build a statistical sample to assess the system resiliency in an ecosystem. Each evolution generates some data to assess a system. We have developed the Haruspex suite to support Monte Carlo Ecology. Some of the suite tools build the models of the target system and of the agents in an ecosystem. Other tools implement the Monte Carlo approach and return the sample to assess the system. To fully exploit this sample, we have defined the security stress, a synthetic measure of resiliency in an environment. After describing the models of the system and of the agents, the full paper will detail the proposed methodology and present a case study. Close Fabrizio Baiardi and Federico Tonelli

# Physics  (P) Session 1

## Chair: Sumit Sourabh

 333 Combination of physical and chemical factors as a source of spatiotemporal dissipative patterns in nonlinear chemical systems with the inhomogeneous temperature field [abstract] Abstract: Spatiotemporal and spatial non-equilibrium patterns in chemical systems can emerge due to the coupling of nonlinear chemical kinetics with the diffusion of reacting particles, with eventual contribution from excitable characteristics. All these phenomena are explainable in terms of the assumption of the isothermal conditions. In our searches for new mechanisms underlying the spatiotemporal instabilities in aqueous media we studied several chemical systems in which hydrogen peroxide was an oxidant for various sulfur-containing species. In one of these systems, containing hydrogen peroxide and thiocyanates as the main reactants [1], which produces sustained oscillations, we discovered the emergence of luminescent patterns. Based on experimental studies and numerical modeling of the reaction kinetics, we found that the observed patterns were essentially the phase waves, caused by the spatially inhomogenous distribution of the solution temperature which affected the local frequency of oscillations. This finding allowed us to take control over the evolution of these phase waves by externally imposed temperature gradient applied to quasi 1-dimensional thin-layer reactor [2]. The second chemical system, containing hydrogen peroxide and thiosulfates, produces only a single oscillatory peak, but in the presence of externally imposed temperature gradient became a source of color front progressing along the reactor. The mechanistic reason for the observed instability is again the dependence of the local chemical reaction kinetics on temperature, i.e. the thermokinetic coupling. Also in this case the experimental findings were successfully reproduced by numerical modeling [3]. We consider these phenomena the novel and rather unique examples of instabilities caused by thermokinetic coupling in liquid media, instead of typical isothermal reaction-diffusion coupling. References: [1] M. Orbán, J. Am. Chem. Soc., 108 (1986) 6893 [2] A. Wiśniewski, M. T. Gorzkowski, K. Pekala, M. Orlik, J. Phys. Chem. A, 117 (2013) 11155 [3] M. Jędrusiak, M. Orlik, J. Phys. Chem. B, 120 (2016) 3169 Close Marek Orlik 44 Complexity of slip avalanches in flowing granular matter [abstract] Abstract: The search for scale-bridging relations in the deformation of amorphous materials presents a current challenge with tremendous applications in material science, engineering and geology. While generic features in the flow and microscopic dynamics support the idea of a universal scaling theory of deformation, direct microscopic evidence remains poor. We study the evolution of slowly sheared granular systems deforming via discrete strain bursts (slips). The granular sample consisting of 105 hard spheres is subjected to applied shear and studied with the combination of two techniques – precise stress-strain measurements and 3D laser sheet imaging. Fluctuations in the stress-strain profile allow us to calculate the magnitude of small internal slip avalanches occurring in the sample due to the shear. 3D laser sheet imaging allows us to visualize each individual slip event, estimate its spatial distribution and connect it to fluctuation in the stress-strain curve. By combining macroscopic force fluctuation measurements with internal strain imaging, we demonstrate the existence of robust scaling relations from particle-scale to macroscopic flow [1]. The presence of the power-law distributions characterizing the spatial and temporal properties of the avalanches suggests the presence of the externally induced critical state in the system. Moreover by building the 3D-map of the critical stress distribution through the system we observe a strongly connected complex network spanning through the whole sample. At a certain critical point the external stress distributed through such network can lead to a creation of a system-wide avalanche resulting in a complete system failure/reconfiguration. These experimental results pave the way to a new universal theory of deformation allowing prediction and possibly prevention of the large avalanches and their negative effects. [1] D.V. Denisov, K.A. Lorincz, J. T. Uhl, K. A. Dahmen & P. Schall, “Universality of slip avalanches in flowing granular matter”, Nature Communications 7, 10641 (2016). Close Dmitry Denisov, Kinga Lorincz, Karin Dahmen and Peter Schall 126 Spatial network surrogates for disentangling complex system structure from spatial embedding of nodes [abstract] Abstract: Networks with nodes embedded in a metric space have gained increasing interest in recent years. The effects of spatial embedding on the networks’ structural characteristics, however, are rarely taken into account when studying their macroscopic properties. Here, we propose a hierarchy of null models to generate random surrogates from a given spatially embedded network that can preserve global and local statistics associated with the nodes’ embedding in a metric space. Comparing the original network’s and the resulting surrogates’ global characteristics allows to quantify to what extent these characteristics are already predetermined by the spatial embedding of the nodes and links. We apply our framework to various real-world spatial networks and show that the proposed models capture macroscopic properties of the networks under study much better than standard random network models that do not account for the nodes’ spatial embedding. Depending on the actual performance of the proposed null models, the networks are categorized into different classes. Since many real-world complex networks are in fact spatial networks, the proposed approach is relevant for disentangling underlying complex system structure from spatial embedding of nodes in many fields, ranging from social systems over infrastructure and neurophysiology to climatology. Close Marc Wiedermann, Jonathan F. Donges, Jürgen Kurths and Reik Donner 394 Randomization techniques for the analysis of dynamical processes on temporal networks [abstract] Abstract: Randomization techniques deal with the controlled destruction of given temporal or topological structures in complex networks. This is done by resampling certain motifs of the original (empirical) temporal network, such as the edges between nodes or the temporal order of interactions. By comparing how a given dynamical process evolves on the randomized network with how it evolves on the original network, we may identify how the different characteristics affect the dynamical process. Randomization techniques provide a powerful tool for the study of dynamical processes on temporal networks. They may be applied in very general settings as they are purely numerical and non-parametric. They may notably be applied to systems for which no realistic model exists, which is the case for most real systems. A multitude of different randomization techniques exists [Holme, EPJB (2015)], each destroying certain characteristics while preserving others. However, no general procedure exists for their application. Researchers are thus confronted with the non-trivial problem of how to choose/develop techniques and in which order to apply them to be able to identify the important characteristics for each given dynamical phenomenon and dataset under study. As a first step towards a general methodology for randomization-based inference, we propose a taxonomy of existing randomization techniques, based on their methodological nature, their effect on dynamical and topological characteristics of temporal networks, and their known effects on dynamical processes taking place on the networks. This collection should help researches wanting to apply randomization techniques to the study of a given phenomena, providing guidelines for which techniques to apply to most effectively divide the space of possibilities. It is our hope that it may serve as a starting point for the development of a principled randomization-based approach for the characterization of general dynamical networked systems. Close Laetitia Gauvin, Mathieu Génois, Márton Karsai, Taro Takaguchi, Eugenio Valdano and Christian Lyngby Vestergaard 377 The hidden universality of movement in cities [abstract] Abstract: The dynamics of how people collectively visit different places in cities determines the population’s mixing rate and ultimately drives the socio-economic development of urban areas. Despite the crucial role of the temporal dimension of movement, the laws of attraction to locations that give rise to 'pulsating' population flows with varying frequencies of visitation have remained elusive. In this paper we show the existence of a surprisingly simple scaling function that directly connects i) the number of people attracted to a location, ii) their travel distance from home and iii) their visiting frequency. By combining first principles calculations with dimensional arguments, we find that the collective influx of individuals decreases with the product of travel distance and visiting frequency in form of a power law (slope ≈ -2). This hitherto hidden regularity allows for the prediction of the frequency-distance distribution by just counting the total number of visitors to a given location. The trajectories derived from anonymized mobile phone records of millions of individuals in various countries worldwide confirm that empirical population flows obey the derived scaling function in virtually all tested areas. This suggests that the collective visitation dynamics follow the same underlying principles, regardless of the detailed cultural, socio-economic and infrastructural conditions. Finally, we show how deviations from the inverse square law allow for the identification of locations that trigger significantly more (or less) traffic than should be expected from the total visitor counts. The derived scaling function thus provides an appropriate baseline for the identification of unusual hotspots of activity or under-performing regions in need of stimulation. The revealed dynamics places an important constraint on any theory of human spatial organization, and provides a microscopic basis for traffic forecasting, urban planning and epidemiology. Close Markus Schlapfer, Michael Szell, Carlo Ratti and Geoffrey West

# Foundations & ICT & Physics  (FIP) Session 1

## Chair: Louis Dijkstra

 11 Random matrix theory and decoherence in quantum systems [abstract] Abstract: Random matrix theory (RMT) is a tool to study complex quantum systems. In this talk I will present the basic idea of RMT, and how it can be used to study open quantum systems and present some of our results concerning decoherence. In particular, we shall show how purity decay can be predicted with this tool, show that generic quantum open systems display non-markovian behaviour and how this behaviour is smeared out when the coupling between the system of interest and the environment is weak. The transition from non-Markovian to Markovian dynamics for generic environments , Phys. Rev. A 93, 012113 (2016) Random density matrices versus random evolution of open systems, J. Phys. A: Math. Theor. 48 425005 (2015) A random matrix theory of decoherence, New J. Phys. 10, 115016 (2008) Close Carlos Pineda 52 Relaxation of disordered memristive networks [abstract] Abstract: We discuss the average relaxation properties of the internal memory in models of pure memristive networks. We consider the simplest linear model of memristor unit and introduce a dynamical equation for the evolution of internal memory in terms of projection operators. We find that for the case of passive components the dynamics is described by an orthogonal projection operator and for the case of active elements by a non-orthogonal projector. We analyze the average properties of internal memory parameters for random projection operators, and find that this is well described by a slow relaxation evolution if no active components are present. We provide a simple explanation for the emerging slow relaxation as a superposition of exponential relaxations with broad time scales range. Close Francesco Caravelli, Fabio Lorenzo Traversa and Massimiliano Di Ventra 292 Activity Dynamics in Collaboration Networks [abstract] Abstract: Many online collaboration networks struggle to gain user activity and become self-sustaining due to the ramp-up problem or dwindling activity within the system. Prominent examples include online encyclopedias such as (Semantic) MediaWikis, Question and Answering portals such as StackOverflow, online ontology editors and repositories, such as WebProtégé or BioPortal, and many others. Only a small fraction of these systems manage to reach self-sustaining activity, a level of activity that prevents the system from reverting to a non-active state. In this paper, we model and analyze activity dynamics in synthetic and empirical collaboration networks. Our approach is based on two opposing and well-studied principles: (i) without incentives, users tend to lose interest to contribute and thus, systems become inactive, and (ii) people are susceptible to actions taken by their peers (social or peer influence). With the activity dynamics model that we introduce in this paper we can represent typical situations of such collaboration networks. For example, activity in a collaborative network, without external impulses or investments, will vanish over time, eventually rendering the system inactive. However, by appropriately manipulating the activity dynamics and/or the underlying collaboration networks, we can jump-start a previously inactive system and advance it towards an active state. To be able to do so, we first describe our model and its underlying mechanisms. We then provide illustrative examples of empirical datasets and characterize the barrier that has to be breached by a system before it can become self-sustaining in terms of critical mass and activity dynamics. Additionally, we expand on this empirical illustration and introduce a new metric p—the Activity Momentum—to assess the activity robustness of collaboration networks. Full paper: http://dl.acm.org/citation.cfm?id=2873060 Close Simon Walk, Denis Helic, Florian Geigl and Markus Strohmaier 526 Stochastic dynamics and predictability of big hits in online videos [abstract] Abstract: The competition for the attention of users is a central element of the Internet. Crucial issues are the origin and predictability of big hits, the few items that capture a big portion of the total attention. We address these issues analyzing 10 million time series of videos’ views from YouTube. We find that the average gain of views is linearly proportional to the number of views a video already has, in agreement with usual rich-get-richer mechanisms and Gibrat’s law, but this fails to explain the prevalence of big hits. The reason is that the fluctuations around the average views are themselves heavy tailed. Based on these empirical observations, we propose a stochastic differential equation with Lévy noise as a model of the dynamics of videos. We show how this model is substantially better in estimating the probability of an ordinary item becoming a big hit, which is considerably underestimated in the traditional proportional-growth models. Close José M. Miotto, Holger Kantz and Eduardo Altmann 444 Temporal density of complex networks and ego-community dynamics. [abstract] Abstract: At first, we say that a ego-community structure is a probability measure defined on the set of network nodes. Any subset of nodes may engender its own ego-community structure around. Many community detection algorithms can be modified to yield a result of this type, for instance, the personalized pagerank. Next, we present a continuous version of Viard-Latapy-Magnien link streams, that we call "temporal density". Classical kernel density estimation is used to move from discrete link streams to their continuous counterparts. Using matrix perturbation theory we can prove that ego-community structure changes smoothly when the network evolves smoothly. This is very important, for example, for visualization purposes. Combining the temporal density and personalized pagerank methods, we are able to visualize and study the evolution of the ego-community structures of complex networks with a large number of temporal links. We illustrate and validate our approach using "Primary school temporal network data" provided by sociopatterns.org, and we show how the temporal density can be applied to the study of very large datasets, such as a collection of tweets written by European Parliament candidates during European Parliament election in 2014. Main Topic: Foundations of Complex Systems Sub Topic: Social networks Close Sergey Kirgizov and Eric Leclercq 568 Finitely Supported Mathematics [abstract] Abstract: Many (experimental) sciences don't work or assume actual infinity. Finitely Supported Mathematics (FSM) is introduced as a mathematics dealing with a more relaxed notion of (in)finiteness. FSM has strong connections with the Fraenkel-Mostowski (FM) permutative model of Zermelo-Fraenkel set theory with atoms. However, FSM can characterize infinite algebraic structures using their finite supports. More exactly, FSM is ZF mathematics rephrased in terms of finitely supported structures by using an infinite set of atoms. In FSM, 'sets' are replaced either by invariant sets' (sets endowed with some group actions satisfying a finite support requirement) or by finitely supported sets' (finitely supported elements in the powerset of an invariant set), and developed a theory of invariant algebraic structures'. We describe FSM by using principles (rather than axioms), and the principles of constructing FSM have historical roots both in the definition of Tarski logical notions' and in the Erlangen Program of F.Klein for the classification of geometries according to invariants under suitable groups of transformations. There exist other connections between FSM, admissible sets and Gandy machines. The main principle of constructing FSM is that all the structures have to be invariant or finitely supported. As a consequence, we cannot obtain a property in FSM only by involving a ZF result without an appropriate proof reformulated according to the finite support requirement. Moreover, not every ZF result can be directly reformulated in terms of finitely supported objects because, given an invariant set, some of its subsets might be non-finitely supported (an example is given by a simultaneously infinite and coinfinite subset of the invariant set of all atoms). We have specific techniques of reformulating ZF properties of algebraic structures in FSM. More details are presented in the papers published by the authors in the last 2 years. Close Andrei Alexandru and Gabriel Ciobanu

# Cognition & Biology  (CB) Session 1

## Chair: Francesc Font Clos

 172 Context-specific protein-protein interactions in Mycobacterium Tuberculosis [abstract] Abstract: Traditional Protein-Protein Interactions Networks (PPIN), although they have proved their usefulness, fall short to describe the variability of a real system. For instance, the interactions between proteins can be strengthened or weakened under different conditions as a consequence of gene expression variation of the genes codifying the proteins. In order to capture this higher dimensionality, we combine gene expression data and a traditional PPIN of the pathogen Mycobacterium Tuberculosis to build a multilayer network where each layer corresponds to a different experimental condition and contains only those genes that are highly expressed under such environment. Specifically we will focused on a 6 layer network, corresponding to the 6 major stresses that the bacterium faces in the phagosomical environment (Hypoxia, Starvation, Cell Wall Damage, Ion Deprivation, Exposure to NO and Oxidation). The posterior analysis of this multilayer network allows us to identify hubs or modules of genes with high importance for a certain stress condition and to study if they are preserved throughout the different environments or if they appear as a specific response to a particular stimulus. For the specific case of M.Tuberculosis we identify genes of the family of ESAT-6 as network hubs under most types of stresses. These proteins, that are not hubs of the original PPIN, remarkably contain one of the main virulence markers of the pathogen: the ESAT-6 protein itself and its partner cfp-10. This method could provide useful insights to understand the behavior of the pathogen at the infection process and other stages of its cycle. It is easily generalizable to different organisms and datasets, constituting a promising approach to the observation of cellular adaptive response to different conditions at a systemic scale. Close Sergio Arregui, Fernando Cid, Joaquín Sanz and Yamir Moreno 449 Trail pheromone mediated termite royal chamber construction [abstract] Abstract: We present results from a new three dimensional agent-based model, designed to investigate the role of trail pheromone in the self-organised construction of a royal chamber in termite species Macrotermes Subhyalinus (Rambur). The royal chamber is a dome-like structure which worker termites build around a much enlarged termite queen and observations have shown that the building proceeds from the ground upwards, involving the formation of distinct pillars which become joined together laterally at a specific height. Earlier models have demonstrated how an attractive pheromone in the building material used by the termites (cement pheromone) can mediate the building process such that pillars begin to form to some extent, but have not succeeded in reproducing other observed characteristics of the construction, or quantified the dependency of the pillar formation on model parameters. A factor not included in these models, and yet known to be key to the success of royal chamber construction, is the use of trail pheromone by the termites. In order to investigate the dependency of the building process on the use of trail pheromone, our model incorporates a new hypothesis; that the termites use trail pheromone to coordinate their movement to building sites and a combination of both trail and cement pheromones to moderate their building activity. The model is able to show evidence of observed construction features not present in earlier models. In addition, hierarchical cluster analysis is used to identify forming pillars, and a measure of the shape of the pillars, together with the mean intra-pillar angular separation, is used to quantify the dependency of this aspect of the building process on the model parameters and the extent to which the new model differs from the earlier models. Close Nicholas Hill and Seth Bullock 391 Evolution of Interval Timing in an Embedded Non-Plastic Neural Network [abstract] Abstract: Interval timing (IT) is the capacity to count the passing of time. It has been shown that humans can quite accurately memorize the duration of a stimulus, and reuse that information later on. Simpler organisms also show this ability, such as the slime mold physarium polycephalum that can memorize durations despite the absence of a neural system. Our work explores how IT can be implemented using only the dynamics of a neural network, i.e. without synaptic plasticity. We evolved using a genetic algorithm (GA) a continuous time recurrent neural network (CTRNN) to control a simulated robot who must memorize the duration of an initially presented stimulus, to then move to a target location and remain there for the same duration before exiting it. For this experiment, we required the CTRNN to be able to detect and memorize durations from 1s up to 5s with 1s increments, by using the realistic parameter values of the CTRNN. The successfully evolved CTRNNs have proven that a purely dynamical solution to IT can be found, but, more surprisingly, that the evolved strategy can detect and memorize any duration between 1s and 6s. Indeed, the evolved strategy does not implement the memories as stable attractors, but rather through different trajectories within the state space of the network. Each trajectory is unique to each duration, and the memory will decay progressively after having been used. This work presents the first demonstration of an embedded dynamical system implementing IT for a continuous range of durations, differing from a discrete range generally obtained with stable attractors. This result proves that IT could have evolved in living organisms before any kind of structural plasticity appeared, and supports some observations indicating that it could still be so, i.e. purely dynamical, in the human brain for some time related tasks. Close Julien Hubert and Takashi Ikegami 138 SIS Epidemic Spreading with Heterogeneous Infection Rates [abstract] Abstract: In this work, we aim to understand the influence of the heterogeneity of infection rates on the Susceptible-Infected-Susceptible (SIS) epidemic spreading. Specifically, we keep the recovery rates the same for all nodes and study the influence of the independently identically distributed (i.i.d.) infection rates on the average fraction y of infected nodes in the meta-stable state, which indicates the severity of the overall infection. Motivated by real-world datasets, we consider the log-normal and gamma distributions for the infection rates and we design as well a symmetric distribution so that we have a systematic view of the influence of various distributions. We compare the average fraction y of infected nodes in the heterogeneous case where the infection rate of each link is an i.i.d. random variable following aforementioned distributions with that of the corresponding homogeneous case where all the links have the same infection rate that equals the average infection rate of the heterogeneous case. By continuous-time simulations on several types of networks, theoretical proofs and physical interpretations, (1) we unveil two contrary effects: the heterogeneity of infection rates could both enhance and mitigate the epidemic spread depending on the network structure and the average infection rate normalized by the recovery rate (2) we illustrate that to what extent the heterogeneous infection rates enhance or mitigate the epidemic spread depends further on their distribution. Finally, we verify our conclusions via real-world networks with their heterogeneous infection rates. Our results indicate to what extent and in which situations real-world heterogeneous viral spreading may differ from what classic homogenous SIS model predicts. Close Bo Qu and Huijuan Wang 225 Can ABM Simulation Help Legal Theory? [abstract] Abstract: The marriage between mobile communication and Internet breeds strange social creatures. Such systems -- let’s call them complexes -- tend to produce emergent behaviors. Eisenhower's notion of the USA Military-Industrial Complex is an excellent real-life example. Legal theory has been some 17 years in confrontation with the music-user community. This is a complex: its agents are diverse (consumers, artists, producers, retail, right enforcers, etc.), connected and reciprocally dependent. The complex is moreover a co-evolving bunch (considering dynamics in its environment). As legal theorists we have some questions here. The foundation of our trade is a conception of individual freedom that supports liability. Thus: pressures on individual agents' capacities to comprehend and to be responsible will disrupt the basic paradigms of our discipline. This is worth to be investigated from a legal-theory perspective, when we value informed regulation in our society. As the current issue concerns a complex, we need the complexity-theory perspective too. In our contribution, we emulate the recent history of the music-using-community in the EU and the USA, from the birth of file sharing until the “appification” via iTunes and Spotify. We construct datasets (1) with American judicial decisions involving “fair use” rule in music file sharing disputes and (2) with European landmark decisions and legislation-changes. Thus we support investigating their influences on the complex (and the other way around) through agent modeling. We use ABM of agents that operate on stochastically distributed preferences to trace the evolution of this rule. We first investigate how history can be emulated best. Subsequently we observe and discuss how differences in comprehensiveness of enforcement (a parameter in the model) turn out. Close Aernout Schmidt and Kunbei Zhang

# Economics & Socio-Ecology  (ES) Session 2

## Chair: Neil Huynh Hoai Nguyen

 445 Stock-dependent discrete-time dynamic pollution games [abstract] Abstract: In this paper we address the dynamics of strategic actions in a pollution game model where the payoff matrix of the game depends endogenously on the accumulation or depletion of an environmental stock variable described by a non-linear discrete time dynamical system. The model has the structure of a stock-dependent dynamic game, that is a game where the payoffs to the players changes with the evolution of an external state variable, which in turn depends on the action of the players. More specifically, we analyze a two-player stock-dependent dynamic game in which the stage game is a normal form game with myopic players who use Markov stationary strategy, that is they play a stage game Nash equilibrium in each period. A dynamic consequence of stock-dependent payoffs on the strategies played is that the qualitative structure of the solution of the stock-dependent stage game might change as the stock variable evolves. The method is applied to the discrete time dynamic ecological-economic interest conflicts in the lake pollution problem in which by varying the economic parameters we study the pattern of possible changes in the Nash equilibria structure of the stage game played by the farmers at each time period as a result of the change in the payoffs ranking, classify the corresponding economic outcomes and environmental impacts. The qualitative changes in the game dynamic is represented geometrically in the payoffs space utilizing the notion of the bifurcation diagram. The diagram is partitioned into twelve different regions corresponding to different types of the two-by-two games. We also vary the stiffness or responsiveness of the lake by varying and analyze its consequences on the dynamic of the game. Close Saeed Moghayer, Florian Wagener and Paolo Zeppini 201 A Dynamic Network Of Physical Contacts Derived From A Multiplex Social Network [abstract] Abstract: We present our work on a multiplex block-structured social network among a statistically sampled population, which we use to induce a time-varying network of physical contacts. We generate up to 8 Mio nodes with age, sex and place of residence etc. and allocate them into blocks on different layers/regimes like households and workplaces based on statistical and demographic data. From survey data we sample social relations among the nodes which result in physical contacts with a predefined periodicity. Sampling of social relations happens either on a per-block and -layer basis or based on additional assortative (wealth and geographic position) and clustering principles. It is clear that sampling of such "high-dimensional" structures involves a great number of heuristics and assumptions (e.g. commuting area for workplaces, ...). On the one hand, we try to assess the influence of some assumptions and identify steps and concepts in the sampling approach which are irrelevant or negligible to the resulting social network structure. Secondly we try to validate the resulting structure with other contact models by investigating classical measures as well as simple epidemic spread simulations on the secondary quasi-dynamic contact network (which also is a main application scenario). Furthermore we try to find network generation algorithms and parameters that deliver the same key characteristics as the data-driven network generation approach. Close Günter Schneckenreither and Niki Popper 337 Complex economies have a lateral escape from the poverty trap [abstract] Abstract: In the standard view of the industrialization process of countries, these have to face a barrier to escape from the poverty trap, which is a monetary threshold defined in terms of average wage (as measured, for example, by GDP per capita, GDPpc in the following) or physical capital. When such a threshold is reached, a self-feeding process quickly brings the country from one state of equilibrium (the poverty trap) to another, catching up with the fully developed countries. During this transition, the growth is mainly due to inputs, that is, to capital investments and increase in the labor force. This view, if correct, should lead to a positive relation between the growth due to inputs and GDPpc for low values of GDPpc, and a negative relation for high values of GDPpc, i.e. to an upside down parabola. Only the first relation is supported by the empirical evidence. In this work we use a non-monetary measure of the economic complexity of a country, called Fitness, and we see that complex economies start to industrialize with a lower threshold. On the contrary, if the Fitness is low, a sustainable growth can be reached only if a higher standard, monetary threshold is reached. As a consequence, we can introduce the concept of a two-dimensional poverty trap: a country will start the industrialization process if it is not complex but rich (following the neo-classical economic theories), or if it is poor but very complex (exploiting this new dimension and laterally escaping from the poverty trap), or a linear combination of the two. This naturally leads to our proposal of a Development Index that, when studied as a function of the growth due to input, shows the same shape of an upside down parabola that one was expecting from the standard economic theories. Reference: arXiv:1511.08622. Close Emanuele Pugliese, Andrea Zaccaria, Guido Chiarotti and Luciano Pietronero 360 Games of corruption in preventing the overuse of common-pool resources [abstract] Abstract: Overuse and corruption are major obstacles to managing common-pool resources. Although corruption has traditionally been studied in economics, evolutionary game theory offers certain advantages when analyzing corruption in the context of managing common-pool resources. By incorporating the selection process, evolutionary game theory explicitly accounts for the temporal dynamics of the investigated system. This inclusion of the selection process permits the coupling of evolutionary and resource dynamics to create a more general and powerful analytical framework for the management of common-pool resources. Within such a framework, it is possible to study (i) the influence of ecological parameters (e.g. the resource growth rate) on the prospects that a resource will be overused and (ii) the efficiency of decision making in situations when the resource is still in a transient state due to the slow convergence of the resource dynamics. The traits of our analytical framework are: (i) an arbitrary number of harvesters share the responsibility to sustainably exploit a specific part of an ecosystem, (ii) harvesters face three strategic choices for exploiting the resource, (iii) a delegated enforcement system is available if called upon, (iv) enforcers are either honest or corrupt, and (v) the resource abundance reflects the choice of harvesting strategies. The resulting dynamical system is bistable; depending on the initial conditions, it evolves either to cooperative or defecting equilibria. Using the domain of attraction to cooperative equilibria as an indicator of successful management, we find that the more resilient the resource (i.e. the higher the growth rate), the more likely the dominance of corruption suppressing the cooperative outcome. A qualitatively similar result arises when slow resource dynamics relative to the dynamics of decision-making mask the benefit of cooperation. We discuss the implications of these results in the context of managing common-pool resources. Close Marko Jusup, Joung-Hun Lee and Yoh Iwasa 576 Nonlinear analysis of climate data by techniques of complex networks - ClimNet [abstract] Abstract: Climate analysis is a fast growing field of study with many economic, political and social implications. In the last years many techniques of complex network analysis have found application in climate research. This big data approach consists of embedding patters found in climate variables, as pseudo-periodic changes in temperature, pressure or rainfall into the topology of complex networks by means of appropriate linear and nonlinear measures. These patterns are also found to be acting on various time scales, such as synoptic atmospheric waves in the extra-tropics or longer time scale events in the tropics. The analysis of this topology can yield insight on the actual behaviour of regional or global climate, taking advantage of the well-developed branch of network analysis. In this paper we present ClimNet, a software toolkit for the construction of complex networks’ adjacency matrices from climate time series. Apart from finding linear and nonlinear relationships, ClimNet also provides ways to fine-tune relationships to different time-scales by means of symbolic ordinal analysis. The functions available in the software and their performance on multi-core platforms are introduced in this work. Close J. Ignacio Deza and Hisham Ihshaish 500 Scaling laws in Cities - a statistical mechanics approach [abstract] Abstract: The main function and the essence of the city is to generate interactions in space and time between different individuals. Human settlements leverage interactions by spatially joining its inhabitants. Accordingly Bettencourt, the cities are organized on a network: the mere fact that individuals are spatially close increases the number of potential encounters between them. Theoretically, the probability of encounters and interaction grows as the population and produces reductions in transaction costs and communication society, and other co-location advantages. Socioeconomic related properties of a city seems to grow faster than a linear relationship with the population, called superlinear scaling. Reversely, the larger a city, the more efficient it is in the use of its infrastructure, leading to a sublinear scaling. To build a quantitative theory of cities we must take into account the city's geometry to calculate aggregate amounts that generate social and infrastructure indexes. In the present work we address a simple explanation for the scaling law in cities based on fractal properties of the cities and as well as on the behavior of individuals. We follow the statistical mechanics approach and the result was a very simple model, just to obtain the scaling of social and infrastructure indicators. For that, we introduce a measure of social potential energy which capture the influence of social interaction on the economic performance and the benefits of facilities in the case of infrastructure offered by the city. We assume that the population density depends on the fractal dimension and the individual interaction intensity decay with distance. As a result we obtain a power Law scaling for social indexes and for infrastructure. Those scaling are coherent with empirical data. An agent based model was proposed to make computational experiments and test the hypothesis. Close Fabiano Ribeiro, Joao Meirelles, Camilo Rodrigues Neto and Fernando Fagundes Ferreira

# Foundations & Socio-Ecology  (FS) Session 2

## Chair: Federico Battiston

 219 Temporal correlations in social multiplex networks [abstract] Abstract: Social interactions are composite, involve different communication layers and evolve in time. However, a rigorous analysis of the whole complexity of social networks has been hindered so far by lack of suitable data. Here we consider both the multi-layer and dynamic nature of social relations by analysing a diverse set of empirical tem- poral multiplex networks. We focus on the measurement and charac- terization of inter-layer correlations to investigate how activity in one layer affects social acts in another layer. We define observables able to detect when genuine correlations are present in empirical data, and single out spurious correlation induced by the bursty nature of human dynamics. We show that such temporal correlations do exist in social interactions, where they act to depress the tendency to con- centrate long stretches of activity on the same layer. They also imply some amount of potential predictability in the connection patterns between layers, and may affect the dynamics of spreading processes unfolding on different layers. Our work sets up a general framework to measure temporal correlations in multiplex networks, and we an- ticipate that it will be of interest to researchers in a broad array of fields. Close Michele Starnini, Andrea Baronchelli and Romualdo Pastor-Satorras 110 The Law of Complementary Variety: when does it pay off for evolution to coarse- or fine-grain in space and time? [abstract] Abstract: Biological and socio-economic populations can sometimes increase their fitness by identifying and adjusting to more details of the fitness landscape in which they evolve. When does it pay off for the population to use a more detailed classification system? This depends on the particular shape of the fitness matrix in both space and time. Sometimes the population does not need to bother looking closer. It is at least as beneficial to simply let natural selection act as a blind watchmaker. Other times, proactive resource redistribution among fine-grained distinctions pays off, such as done by a portfolio manager or genetic phenotype switches. In order to understand the difference we decompose population fitness and represent the strength of evolutionary selection with the information theoretic metric of relative entropy (Kullback-Leibler divergence). It is a multivariate metric that allows us to analyze selection pressure over multiple taxonomic levels in one single equation. It turns out that difference in relative entropy between different strategies is proportional to the potential to increase population fitness through intervention. As such, differences in relative entropy allow to quantify the potential to increase fitness. An intuitive interpretation is that it quantifies the amount of complementary variety between different population types and corresponding environmental states. The more type fitness is skewed to opposing directions in different environmental states, the proportionally larger the potential benefit of strategic intervention over natural selection. In reference to the literature of bet-hedging and portfolio theory, it is shown that the higher the degree of specialization of different population types to different environmental states, the larger the complementary variety among them, and therefore the larger the potential payoff. Complementary variety is the necessary condition to increase overall fitness through resource redistribution. This suggests developing classification systems of population types and environmental states that contain complementary variety. Close Martin Hilbert 140 Effect of environmental colored noise in population dynamics [abstract] Abstract: Variability on the external conditions, such as the temperature, humidity, available nutrients, etc., have important consequences for the dynamics and organization of communities of living systems. Furthermore, the interplay between the timescales of the environment and the intrinsic dynamics plays a fundamental role in many situations. However, most of the mathematical models neglect temporal correlations of the environment. We propose a unifying framework of some precedent available analytical and numerical tools to deal with colored noise, and provide a general scheme to answer some relevant questions concerning population dynamics: quantification of the population growth rate and population density, under which internal and internal conditions the population may become extinct, and in such a case, how much time does it take to disappear. These questions are of fundamental relevance, for instance, in the context of epidemiology, as they provide valuable information for the control and eradication of disease spreading. We test our results in a SIS model in which the infection rate fluctuates in time with environmental conditions. Close Tommaso Spanio, Jorge Hidalgo and Miguel A Muñoz 192 The effect of hierarchical order in directed networks [abstract] Abstract: Hierarchy is pervasive in both natural and man-made systems. A significant part of complex networks science is concerned with identifying hierarchical features in observed real world networks, explaining their origins via generative models with simple assembly rules and studying the interplay between features on many scales by studying appropriate random network ensembles. Recently it has been shown that a new topological feature of directed networks termed "trophic coherence" is a prominent in many real world networks ranging from ecological food-webs to gene transcription networks. Trophic coherence characterizes how "layered" a directed network is - the tendency of nodes to form well defined, hierarchically organized groups. In networks with high trophic coherence interactions via directed links start from base nodes with no incoming connections and follow up the hierarchy of nodes in a chain-of-command fashion. In networks with less trophic coherence, however, "shortcuts" may be present that distorts the hierarchy and allows interactions between groups of nodes far apart in the network. This has implications on local topological features and information spread. We present results on how trophic coherence affects the local structure of food-webs. Our findings indicate that trophic coherence reveals that the majority of known food-webs fall into one of two groups - those with relatively little omnivory and those with a lot of omnivory as defined by the presence of feed-forward loops. This result complements previous results by Johnson et al. where a network model with trophic coherence was shown to reproduce most food-web features better than the standard Niche and Cascade models. Additionally, work on studying contagion processes on trophically coherent networks has shown that the level of trophic coherence plays a large role in determining the final size of an outbreak. We briefly discuss numerical results and future work. Close Janis Klaise 91 Graph partitions and cluster synchronization in networks of oscillators [abstract] Abstract: Synchronization processes are ubiquitous in nature, from the entrainment of circadian rhythms and the synchronous firing of neurons to the flocking of birds or the shoaling of fish. The emergence of collective consensus in networked systems is thus a current focus in biology, physics, chemistry, as well as in social and technological networks. Previous studies have typically focused on total synchronization, where all agents on the network converge to the same dynamics. Here we use tools from graph theory to study the phenomenon of cluster synchronization, where groups of agents converge to several distinct behaviors. We show that cluster synchronization can emerge in networks with certain regularities, as captured via a graph partition called the external equitable partition. Indeed, when the underlying coupling network presents certain regularities, the dynamics can be coarse-grained into clusters by means of external equitable partitions and their associated quotient graphs. We derive conditions and properties of networks under which such clustered behavior emerges, and show that the ensuing dynamics is the result of a localization of the eigenvectors of the associated graph Laplacians. The framework is applied to both linear (consensus dynamics) and non-linear models (generic oscillator models, including the classic Kuramoto model), first in the standard case of networks with positive edges, before being generalized to the case of signed networks with both positive and negative interactions. Furthermore, we demonstrate how our graph-theoretical approach allows us to extend the analysis to cluster synchronization of signed networks (with positive and negative links), which are used to describe social interactions and inhibitory-excitatory interactions in biology. Close Michael Schaub, Neave O'Clery, Yazan N. Billeh, Jean-Charles Delvenne, Renaud Lambiotte and Mauricio Barahona 470 Percolation-based precursors of transitions in extended systems [abstract] Abstract: Complex systems may display strong changes in their dynamics: bifurcations, tipping points, phase transitions, etc. Some examples of special relevance are phase transitions in condensed matter systems (magnetism, superconductivity), sudden physiological alterations (strokes, epileptic seizures), economic crisis or climatic changes associated to the global warming such as potential modifications of weather and oceanic circulation patterns. The origin of these sudden changes can be traced down to the interactions between the system components. In most cases, the correlation of the components' dynamics enhances before the transition due to the cooperative phenomena that give raise to the emergence of a new global dynamical state. While understanding the ultimate causes of the change is of great importance, from a practical point of view it is absolutely crucial to count with metrics able to act as early warning signals or precursors of the dynamic transition. This may mean the difference between being able to react preemptively to the change or arriving to it unaware. In this work, we exploit the increase of microscopic correlations when the tipping point gets closer and define a set of early warning metrics using concepts imported from percolation theory on the functional network framework. We show that the functional networks encoding the system dynamics undergo a percolation transition way before the tipping point arrives. Furthermore, the number of clusters of size s peaks way before the percolation transition and, therefore, the sequence of peaks clearly mark the path to the transition. Our warning signals are general, as shown by analyzing three very different types of transitions, they precedes other early warning signals proposed in the literature and are straightforwardly applicable to many real-world complex systems, as proven by the analysis run with them on the South Pacific El Nino Oscillation. Our results have made available online at http://arxiv.org/abs/1601.01978 Close Jose J. Ramasco

# Foundations  (F) Session 3

## Chair: Mile Gu

 247 Embedding networks in Lorentzian Spacetime [abstract] Abstract: Geometric representations of data provide useful tools for visualisation, classification and prediction. In particular, geometric approaches to network analysis have grown in popularity recently as the effectiveness of simple geometric models to generate complex networks with interesting properties becomes clearer. Techniques such as Multidimensional Scaling (MDS) provide a method of embedding high dimensional data, or networks into lower-dimensional spaces. However, classical MDS forces a representation in Euclidean space, which may not necessarily be appropriate. In this talk we use ideas from the causal set approach to quantum gravity to find a general method for embedding networks in spaces with any metric signature, not just a Riemannian one (with all eigenvalues of the metric positive). We demonstrate this on the most common case found in physics, a Lorentzian manifold (with one negative eigenvalue of the metric). These manifolds represent spacetime as used in relativity. We show that for networks which naturally form Directed Acyclic Graphs (DAG), such as citation networks, spacetime embeddings are appropriate. This is because the constraint of having no cycles in a DAG corresponds to the causal structure of events in spacetime: that if A caused B to happen, it cannot also be the case that B caused A. As an illustration of these techniques we embed well known citation networks from papers on the arXiv, and from cases of the US Supreme Court in flat spacetime and see that this embedding accurately predicts edges in the networks. Close James Clough and Tim Evans 345 On the physical foundations of self-organization: energy, entropy and interaction [abstract] Abstract: Self-organization is defined as the spontaneous emergence of order arising out of local interactions in a complex system. The central to the idea of self-organization is the interaction between the agents, the particles, the elements that constitute the system. In biological systems, particle-particle interactions or particle-field interactions are often mediated by chemical trails (chemotaxis), or swarm behaviour that optimizes system efficiency. In non-biological systems, particle-field interaction plays the crucial role, as these interactions modify the surrounding field or often the topology of the energy landscape. Interactions in a system, or a system and its surroundings, are governed by energetic and entropic exchanges, either in terms of forces or in terms of statistical information. Since, energy and time, the two properties of matter and space we look into the Principle of Least Action to search for answers as it involves both time and energy into its formulation. Since, the Action Principle minimizes action and directs the system elements along least action trajectories on the energy landscape (surrounding field), it is imperative that a one to one correspondence exists between the Second Law of Thermodynamics and the Action Principle. In a system in equilibrium, the system particles can occupy all possible microstates whereas in a self-organizing, out-of-equilibrium system only certain microstates will be accessible to the system particles. In these systems, in order to organize efficiently the system particles interact locally and coordinate globally, in a way that lets swarms of agents to uniformly follow least action trajectories and simultaneously degrade their free-energies in order to maintain the organizational structure of the system at the expense of entropy export along the least action paths. The question we ask is how the symmetry breaking is mediated in a physical system? Close Atanu Chatterjee, Georgi Georgiev, Thanh Vu and Germano Iannachione 414 Complexity: From Local Hidden Symmetries to Zoo of Patterns [abstract] Abstract: We present universal framework for generation, analysis and control of non-trivial states/patterns in the complex systems like kinetic hierarchies describing general set-up for non-equilibrium dynamics and their important reductions. We start from the proper underlying functional spaces and their internal hidden symmetries which generate all dynamical effects. The key ingredients are orbits of these symmetries, their representations, and Local Nonlinear Harmonic Analysis on these orbits. All that provides the possibility to consider the maximally localized fundamental generic modes, non-linear (in case of the non-abelian underlying symmetry) and non-gaussian, which are not so smooth as gaussians and as a consequence allowing to consider fractal-like images and possible scenarios for generation chaotic/stochastic dynamics on the level of representation theory only. As a generic example we consider the modeling of fusion dynamics in plasma physics. http://math.ipme.ru/zeitlin.html, http://mp.ipme.ru/zeitlin.html Close Antonina Fedorova and Michael Zeitlin 185 The geometric nature of weights in real complex networks [abstract] Abstract: Complex networks have been conjectured to be embedded in hidden metric spaces, in which distances between nodes encode their similarity and, thus, their likelihood of being connected. This hypothesis, combined with a suitable underlying space, has offered a geometric interpretation of the complex topologies observed in real networks, including scale-free degree distributions, the small-world effect, strong clustering as a reflection of the triangle inequality, and self-similarity. It has also explained their efficient inter-node communication without a knowledge of the complete structure. Moreover, it has been shown that for networks whose degree distribution is scale-free, the natural geometry of their underlying metric space is hyperbolic. These results have led to geometric models for real growing networks that reproduce their evolution and in which preferential attachment emerges from local optimization principles. Using real networks from very different domains, we present empirical evidence that the magnitude of the connections, the weights, also have a geometric nature. To quantify the level of coupling between the topology, the weights, and the underlying metric space in real networks, we introduce the most general and versatile class of weighted networks embedded in hidden metric spaces. This framework allows us to independently regulate the coupling between the topology and the geometry and between the weights and the geometry. We show that such couplings can be significantly different in real networks, which supports the hypothesis that the formation of connections and the assignment of their magnitude is ruled by different processes. Our empirical findings, combined with our new class of models, open the path towards the uncovering of the natural geometry of real weighted complex networks. Close Antoine Allard, M. Ángeles Serrano, Guillermo García-Pérez and Marián Boguñá 167 Synchronization loss for the Ginzburg Landau equation on asymmetric lattices with long-range couplings. [abstract] Abstract: Dynamical processes on networks are currently being considered in different domains of cross-disciplinary interest. Reaction-diffusion systems hosted on directed graphs are in particular relevant for their widespread applications, from neuroscience, to computer networks and traffic systems. We shall here consider as a paradigmatic example the complex Ginzburg-Landau equation defined on a asymmetric lattice, with next-nearest-neighbors couplings. The peculiar spectrum of the discrete Laplacian operator yields an extended class of modulational instabilities which can be analytically predicted. Specifically, the synchronized regime can turn unstable to external perturbation because of the imposed degree of spatial asymmetry, and for a choice of the paramaters for which the instability cannot develop on undirected graphs. The excited modes can then stabilize in traveling wave solutions. Alternatively, the modulus of the complex quantity that obeys Ginzburg-Landau equation can display a complicated mosaic of patterned structures in the non linear regime of evolution. The bifurcation between the different regimes is predicted by the theory and ultimately relates to the long range nature of the spatial coupling imposed. The case of an heterogeneous generic directed network will be also discussed. Close Duccio Fanelli, Timoteo Carletti, Francesca Di Patti and Filippo Miele 296 Discrete vs continuous time formulation of the epidemic threshold on a time-varying network [abstract] Abstract: The interplay between network evolution and the dynamics of a spreading process impacts the conditions for large-scale propagation, by altering the epidemic threshold, i.e., the critical transmissibility value above which the disease turns epidemic. In order to study these processes many works have resorted to discrete-time approximations of both network and spreading dynamics. While this is practical from both the numerical and the theoretical point of view, it is known to bias results in some circumstances. Here we analytically derive the epidemic threshold for a generic time varying network, in both continuous and discrete time. We focus on the susceptible-infected-susceptible spreading process, within the quenched mean field framework. In discrete time, the epidemic threshold of a generic network can be computed from the spectral radius of the infection propagator, a matrix encoding a multi-layer representation of both network and spreading dynamics [Valdano et al (2015) Phys Rev X, Valdano et al (2015) Eur Phys J B]. We build a new theoretical framework that allows us to perform the continuous time limit of the infection propagator, and we find it correctly describes the linearized form of the continuous-time Markov equations of the process. This yields a solution for the epidemic threshold in continuous time that admits an explicit form in specific cases. The mathematical formalism proposed here allows addressing the effect of discretization and temporal resolution on the epidemic threshold accounting for different network properties and parameter regimes. Close Eugenio Valdano, Chiara Poletto and Vittoria Colizza

# Foundations  (F) Session 4

## Chair: Colm Connaughton

 174 The second will be first: competition on directed networks [abstract] Abstract: Multiple sinks competition is investigated for a walker diffusing on directed complex networks. The asymmetry of the imposed spatial support makes the system non transitive. As a consequence, it is always possible to identify a suitable location for the second absorbing sink that screens at most the flux of agents directed against the first trap, whose position has been preliminarily assigned. The degree of mutual competition between pairs of nodes is analytically quantified through apt indicators that build on the topological characteristics of the hosting graph. Moreover, the positioning of the second trap can be chosen so as to minimize, at the same time the probability of being in turn shaded by a thirdly added trap. Supervised placing of absorbing traps on a asymmetric disordered and complex graph is hence possible, as follows a robust optimization protocol. This latter is here discussed and successfully tested against synthetic data. Close Giulia Cencetti, Duccio Fanelli, Franco Bagnoli and Francesca Di Patti 516 Instability of Multilayer Networks Induced by Inter-Layer Coupling [abstract] Abstract: Most of the real world complex systems consist of multiple subsystems that interact with each other, which can be represented as multilayer networks. Implications of such multilayer topologies have been studied for system robustness, cascading failures, reaction-diffusion dynamics, etc., but little research has been conducted on the dynamical stability of multilayer networks. Here we study the stability of multilayer networks and its relationships with the stabilities of networks within individual layers. Specifically, we generated two random networks following the method of May's random ecological network model, and then coupled them to create a random multilayer network. Two parameters were systematically varied: the strength of within-layer connections, alpha, and the strength of inter-layer coupling, kappa. Stabilities of those networks were evaluated by calculating eigenvalues of their (supra-) adjacency matrices. Numerical analysis showed that, with alpha above a certain threshold, individual networks become unstable, as is well known from May's work. We also found, however, that the whole multilayer network can be unstable with alpha below the threshold, if the inter-layer coupling kappa is above another threshold. This form of instability was previously not known, and it indicates that a system made of individually stable layers may get destabilized because of too strong inter-layer coupling. We also investigated the effects of the network size in each layer. As the number of nodes increases, the thresholds of alpha and kappa both decrease, further manifesting the network instability induced by inter-layer coupling. Our study illustrates that the strength of inter-layer coupling has a critical role in the stability of the whole network. Close Hyobin Kim, Farnaz Zamani Esfahlani, Samuel Heiserman, Nasim Nezamoddini and Hiroki Sayama 196 Sparse subgraph counts biases graphlet correlation methods [abstract] Abstract: We would like to draw the network science community's attention to a scenario in which the graphlet correlation distance (GCD) method, introduced by Yaveroglu et al. [1], can give misleading results. The aim of the talk is to introduce attendees to the method and offer an appreciation of its subtleties. Graphlet correlation distance (GCD) has been proposed as an alignment-free method for the comparison of networks in systems biology and other domains. In particular, GCD has been shown to outperform other alignment-free methods, both in terms of accuracy and computational efficiency [1, 2]. The method correlates counts of graphlets, that is, induced subgraphs of a network that are of order 5 or less, for individual nodes of a network. A set of networks can then be clustered based upon a distance between their graphlet correlation matrices. In this talk we argue that GCD is very sensitive to low counts of graphlets; which, in turn, can bias results. Thus, when a set of networks contains negligible amounts of some graphlets, correlations between these underrepresented graphlets dominates the resulting partition. We illustrate this problem by constructing artificial networks which lack some graphlets in their makeup. We then add a statistically insignificant amount of edges to individual networks such that they now contain an instance of the missing graphlet. We conclude by proposing a modification to the method and then applying it to a dataset of street networks. [1] Yaveroğlu, Ömer Nebil, et al. "Revealing the hidden language of complex networks." Scientific reports 4 (2014). [2] Yaveroğlu, Ömer Nebil, Tijana Milenković, and Nataša Pržulj. "Proper evaluation of alignment-free network comparison methods." Bioinformatics 31.16 (2015): 2697-2704. Close Garvin Haslett, Seth Bullock and Markus Brede 210 Grand-canonical validation of bipartite networks [abstract] Abstract: Bipartite networks are currently regarded as providing a major insight into the organization of real-world systems, unveiling the mechanisms shaping the interactions occurring between separate groups of nodes. One of the major problems encountered when dealing with bipartite networks is obtaining a (monopartite) projection over the layer of interest, preserving as much as possible the information encoded into the original bipartite structure. In the present paper we propose an algorithm able to obtain statistically-validated projections of bipartite networks: our method com- pares the number of shared neighbors between two nodes on the same layer with the expectation from a recently null-models for bipartite networks, [1,2]. The output of our method is a p-value per couple of nodes, encoding the statistical significance of the observation: if the p-value is small, the observation is not explained by the null-model and it is statistically relevant. A validated projection can thus be obtained by choosing a threshold and linking the nodes passing the test. We also show an alternative approach, intended to retain all the information provided by the whole matrix of p-values: upon doing so, we are able to detect the (potentially) hierarchical relationships occurring between different subsets of elements. We test our procedure on the bipartite projection of the trade network (i.e. usual Economic Complexity framework) and on the bipartite social network of MovieLens100k between users and rated films. The resulting similarities between countries have interesting explanations in terms of the economic development of different nations; on the social side, our methods is able to cluster films respect to some non trivial features (cast, directors, sub-genres..). [1] Saracco F., et al. Randomizing bipartite networks: the case of the World Trade Web. Sci. Rep. 5(10595) [2] Saracco F., et al. Detecting the bipartite world trade web evolution across 2007: a motifs-based analysis, arXiv:1508.03533. Close Fabio Saracco, Riccardo Di Clemente, Andrea Gabrielli and Tiziano Squartini 243 Numerical simulation of 3D polydisperse bubble column [abstract] Abstract: Bubbly flows are frequently observed in nature or industrial applications. Is some cases, inception of such flows are undesirable, like boiling of coolant liquid which prevents effective heat loss. On other hand, there are processes, like bubble chemical reactors, where formation of bubbly flows are necessary but should be carried out in specific fashion. Prediction of such regimes are crucial for robust equipment design. It is not always possible to apply experimental methods for investigation of bubbly flows, thus modern numerical methods are of high importance and can be used to predict flow patterns, bubble formation and evolution for complex systems and set-ups. Numerical simulation of three-dimensional bubbly column will be presented in the scope of that work as a representative case of polydisperse bubbly flow. Numerical algorithm is based on the mathematical model which utilizes Euler-Euler approach for description of dispersed phases, supplemented by k-omega SST turbulence model for bubbly flows and extended for polydisperse flow description by multi-class approach. Main problem arises from coupling between carrier phase and multiple dispersed classes, which is overcome by specific numerical realization of the mathematical model. In-house computer code was developed on the basis of the proposed numerical algorithm. Main feature of that code is unstructured meshes, pseudo-time solution algorithm, modified phase-coupled SIMPLEC method, TVD-based interpolation schemes. Velocity and gas concentration distributions presented for bubbly flow column and compared with the existed experimental data (Sokolichin at al 1999). Column is represented as parallelepiped with gas injector (sparger) installed on the bottom surface with the offset towards one vertical wall. It was shown, that numerical simulation predicts well entire jet structure produced by buoyant bubbles, but also provides detailed information of flow near bubble inlet and close to vertical walls, with formation of thin regions with local maximum of bubble concentration. Close Alexander Chernyshev and Alexander Schmidt