# Foundations & Physics  (FP) Session 3

## Chair: Louis Dijkstra

 116 Onset of anomalous diffusion from local motion rules [abstract] Abstract: Anomalous diffusion processes, in particular superdiffusive ones, are known to be powerful strategies for searching and navigation by animals and also in human mobility. One way to create such regimes are Lévy Flights, where the walkers are allowed to perform jumps, the “flights”, that can eventually be very long as their length distribution is asymptotically power-law distributed. In our work, we present a model in which walkers are allowed to perform, on a 1D lattice, “cascades” of n unitary steps instead of a jump in the Lévy case. In analogy with the Lévy approach, the size of such cascades is distributed according to a power-law tailed PDF P(n); on the other hand, at difference with Lévy Flights, we do not require an a priori knowledge of the jump length since, in our model, the walker follows strictly local rules. We thus show that this local mechanism for the walk gives indeed rise to superdiffusion or normal diffusion according to the P(n) power law exponent. We also investigate the interplay with the possibility to be stuck on a node, introducing waiting times that are power-law distributed as well. In this case, the competition of the two processes extends the palette of the reachable diffusion regimes and, again, this switch relies on the two PDF's power-law exponents. As a perspective, our approach may engender a possible generalization of anomalous diffusion in context where distances are difficult to define, as in the case of complex networks. Close Timoteo Carletti, Sarah de Nigris and Renaud Lambiotte 485 Dynamics on multiplex networks [abstract] Abstract: We will show some of the recent result in our group concerning dynamics in multiplex networks. On the one hand we consider multiplex networks as set of nodes in different layers. At each layer the set of nodes is the same but the connections among the nodes can be different in the layers. Furthermore the connections among the layers is described by a “network of layers”. We have studied different processes across the layers (diffusion) and between the layers (reaction) [1]. In this case Turing patterns appear as an effect of different average connectivities in different layers [2]. We also show that a multiplex construction where the layers correspond to contexts in which agents make different sets of connections can make a model of opinion formation to show stationary states of coexistence that are not observed in simple layers [3]. Finally, as a particular case of multiplex network, one can also analyze networks that change in time, since in this case each layer of the multiplex corresponds to a snapshot of the interaction pattern. For this situation, we have shown that there are different mechanisms that dominate the diffusion of information in the system depending on the relative effect of mobility and diffusion among the nodes [4]. [1] Replicator dynamics with diffusion on multiplex networks. RJ Requejo, A. Diaz-Guilera. Arxiv:1601.05658 (2016) [2] Pattern formation in multiplex networks. NE Kouvaris, S Hata & A. Diaz-Guilera. Scientific Reports 5, Article number: 10840 (2015) [3] Agreement and disagreement on multiplex networks. R Amato, N E Kouvaris, M San Miguel and Albert Díaz-Guilera, in preparation. [4] Tuning Synchronization of Integrate-and-Fire Oscillators through Mobility. L. Prignano, O. Sagarra, and A. Díaz-Guilera Phys. Rev. Lett. 110, 114101 (2013) Close Albert Diaz-Guilera 284 Promiscuity of nodes in multilayer networks [abstract] Abstract: The interplay of multiple types of interactions has been of interest in the social sciences for decades. Recent advances in the complexity sciences allow the analysis of such multilayer networks in a quantitative way. The question to what extent nodes are similarly important in all layers arises naturally. We define the promiscuity of a node as a measure for the variability of its degree across layers. This builds on similar frameworks that investigate such questions in networks with modular structure while taking into account that different layers can vary in their importance themselves. Using those tools on a range of empirical networks from a variety of disciplines including transportation, economic and social interactions, and biological regulation we show that the observed promiscuity distributions are different on the networks of different origins. Transportation networks, for example, where the layers represent different modes of transportation tend to have a majority of low promiscuity nodes. A few hub nodes with high promiscuity enable the transit between different modes of transportation. The representation of global trade as a multilayer network reveals that country’s imports are often very diverse whereas the export of some countries depends extremely on a single commodity. Employing the promiscuity on transcription factor interaction in multiple cell types reveals proteins that are potential biomarkers of cell fate. Despite its simplicity, the presented framework gives novel insights into numerous types of multilayer networks and expands the available toolbox for multilayer network analysis. Close Florian Klimm, Gorka Zamora-López, Jonny Wray, Charlotte Deane, Jürgen Kurths and Mason Porter 188 Coarse analysis of collective behaviors: Bifurcation analysis of traffic jam formation [abstract] Abstract: Collective phenomena have investigated in various fields of science, such as material science, biological science and social science. Examples of such phenomena are slacking of granular media, group formation of organisms, jam formation in traffic flow and lane formation of pedestrians. Scientists usually investigate them only using the equation of motion of individuals directly. It is generally difficult to derive the macroscopic laws of collective behaviors from such microscopic models. We challenge to develop a new approach to analyze macroscopic laws of these phenomena. In this paper, we describe collective behaviors in a low-dimensional space of macroscopic states obtained by dimensionality reduction. Such a space is constructed by using Diffusion maps as one of the pattern classification techniques. We obtain a few appropriate coarse-grained variables to distinguish the macroscopic states by the similarity of patterns, and we construct the low-dimensional space. A time development of collective behavior is represented as a trajectory in the space. We apply this method to the optimal velocity model for the analysis of the macroscopic property of traffic jam formation. The phenomena is considered as the dynamical phase transition of a non-equilibrium system. The important property of the transition is bistability of jammed flow and free flow. This property has been investigated by many researchers using the model. However their analysis does not satisfactory explain. Using our method, we clearly reveal a bifurcation structure, which features the bistability. Close Yasunari Miura and Yuki Sugiyama 352 Design Principles for Self-Assembling Polyomino Tilings [abstract] Abstract: The self-assembly of simple molecular units into regular 2d (monolayer) lattice patterns continues to provide an exciting intersection between experiment, theory and computational simulation. We study a simple model of polyominoes with edge specific interactions and introduce a visualisation of the configuration space that allows us to identify all possible ground states and the interactions which stabilise them. By considering temperature induced phase transitions away from ground states, we demonstrate kinetic robustness of particular configurations with respect to local rearrangements. We also present a rigorous sampling algorithm for larger lattices where complete enumeration is computationally intractable and discuss common features of the configuration space across different polyomino shapes. Close Joel Nicholls, Gareth Alexander and David Quigley

# Cognition & Foundations  (CF) Session 2

## Chair: Massimo Stella

 561 Similarity of Symbol Frequency Distributions with Heavy Tails [abstract] Abstract: How similar are two examples of music or text from different authors or disciplines? How fast is the vocabulary of a language changing over time? How can one distinguish between coding and noncoding regions in DNA? Quantifying the similarity between symbolic sequences is a traditional problem in information theory which requires comparing the frequencies of symbols in different sequences. We will address this problem for the important case in which the frequencies of symbols show heavy-tailed distributions (e.g. the famous Zipf's law for word-frequencies), which hinder an accurate finite-size estimation of entropies, and for a family of similarity measures based on the generalized entropy of order α. We will show analytically how the systematic (bias) and statistical (fluctuations) errors in these estimations depend on the sample size N, on the exponent γ of the heavy-tailed distribution and the order alpha of the similarity measure. Our primary finding is that, for heavy-tailed distributions, (i) the error decay is often much slower than 1/N, illustrating the difficulty in obtaining accurate estimates even for large sample sizes, and (ii) there is a critical value of the order of the entropy α∗=1+1/γ≤2 for which the normal 1/N dependence is recovered. We emphasize the importance of these findings in the example of quantifying how fast the English vocabulary has changed within the last 200 years, showing that these finite-size effects have to be taken into account even for very large databases (N≳1,000,000,000 words). Associated reference: DOI:http://dx.doi.org/10.1103/PhysRevX.6.021009 Close Martin Gerlach, Francesc Font-Clos and Eduardo Altmann 145 Universal properties of culture: evidence for the multiple self'' in preference formation [abstract] Abstract: Understanding the formation of subjective human traits, such as preference and opinions, is an important, but poorly explored problem. It is essential that traits collectively evolve under the repeated action of social influence, which is the focus of many studies of cultural dynamics. In this paradigm, other mechanisms potentially relevant for trait formation are reduced to specifying the initial cultural state for the social influence models, state which usually is generated in a uniformly random way. However, recent work has shown that the outcome of social influence dynamics strongly depends on the nature of the initial state: a higher level of cultural diversity is found after long-term dynamics, for the same level of propensity towards collective behaviour in the short term, if the initial cultural state is sampled from empirical data instead of being generated in a uniformly random way. First, this study shows that this effect is remarkably robust across data sets. In a certain sense, the analysis suggests that systems from which such data is extracted function close to criticality. Second, this study presents a stochastic model for generating cultural states that retain the universal properties. One ingredient of the model, already used in previous work, assumes that every individual's set of traits is partly dictated by one of several cultural prototypes'', which are abstract entities informally postulated by several social science theories. A second, new ingredient, taken from the same theories, assumes that apart from a dominant prototype, each individual also has a certain exposure to the other prototypes. The fact that this combination of ingredients is compatible with regularities of empirical data suggests that cultural traits in the real world form under the combined influence of several cultural prototypes, thus providing indirect evidence for the class of social science theories compatible with this description. Close Alexandru-Ionut Babeanu, Leandros Talman and Diego Garlaschelli 380 Temporal Network Analysis of Small Group Discourse [abstract] Abstract: The analysis of school-age children engaged in engineering projects has proceeded by examining the conversations that take place among those children. The analysis of classroom discourse often considers a conversational turn to be the unit of analysis. In this study, small-group conversations among students engaged in a robotics project are analyzed by forming a dynamic network with the students as nodes and the utterances of each turn as edges. The data collected for this project contained more than 1000 turns for each group, with each group consisting of 4 students (and the occasional inclusion of a teacher or other interloper). The conversational turns were coded according to their content to form edges that vary qualitatively, with the content codes taken from prior literature on small group discourse during engineering design projects, resulting in approximately 10 possible codes for each edge. Analyzed as a time sequence of networks, clusters across turns were created that allow for a larger unit of analysis than is usually used. These larger units of analysis are more fruitfully connected to the stages of engineering design. Furthermore, the patterns uncovered allow for hypotheses to be made about the dynamics of transition between these stages, and also allow for these hypotheses to be compared to expert consideration of the group’s stage at various times. Although limited by noise and inter-group variation, the larger units allowed for greater insight into group processes during the engineering design cycle. Close Bernard Ricca and Michelle Jordan 403 Ranked communities and the detection of dominance and influence hierarchies [abstract] Abstract: In directed networks, edges often represent a transfer of power, social influence, or confidence. In some cases, this is explicit, as in the case of directed acts of dominance inflicted by one animal upon another. In other cases, the relationship is more implicit: when one university hires another's graduate, the hiring department is expressing confidence in the quality of the graduate's department's training. Given such a network, it is possible to rank individual vertices using a variety of methods, such as minimum violations or PageRank. However, in many real-world systems, groups of individuals are ranked, and expressions of influence or dominance by individuals, captured by network edges, simply reflect group affiliations--a type of large-scale network structure that has not been previously described. In this work, we introduce a definition of ranked communities in directed networks and propose an algorithm to efficiently identify them. The mathematical framework of our method is placed in the context of the related problem of classic modularity maximization and we introduce an important distinction between strict (dominance) and inclusive (endorsement) hierarchies. We confirm our method's ability to extract planted ranked community structure in synthetic networks before applying it to learn about real-world networks. In particular, this method allows us to quantitatively study a question posed over half a century ago regarding the relationship between social network structure and the Indian caste system. We show that our recently collected data of a social support network in two South Indian villages is structured according to a mixture of ranked caste-based communities and community-transcending individual relationships. In this system, organization by ranked community is related to known social structure, but we also apply our method to learn about other social and ecological networks in which the organizing mechanisms have yet to be identified. Close Daniel Larremore, Laurent Hebert-Dufresnse and Eleanor Power 81 The Assessment of Self-organized Criticality in Daily High School Attendance Rates [abstract] Abstract: One important aspect of studying the behavior of dynamical systems is the analysis of processes of stability and change over time. This requires an estimation of auto-correlative and cyclical patterns in sets of frequently repeated measurements of the behavior of such systems. Traditional mean and (co)variance computations typically used for cross-sectional data are not adequate to characterize these distributions, and may actually be misleading (Beran, 1994). Daily school attendance is presented as a case in point. Since 2004 and to this day, the New York City Department of Education has published daily attendance rates on its website for all of its schools. These data exhibit the degree of resolution needed to detect underlying systems dynamics that are hidden in the conventionally reported weekly, monthly or yearly average rates. Daily attendance rates in six small high schools were analyzed over a ten-year period (2005 – 2014). The analysis proceeded as follows: 1. intervention models were fitted to handle the most extreme values in the series (usually low attendance) for each school, 2. Conventional time series analyses were used to estimate short-term dependencies and cyclical patterns, 3. The goodness of fit of those models was compared with that of models including long-range estimates (fractional differencing parameter, Hurst exponent). Preliminary analyses suggest significant long-range dependencies in two of these six schools, suggesting self-organized criticality (tension-release, unpredictable cycles), and strong weekly cycles in the four others. The presentation will illustrate how the initial appearance of the data in the various diagnostic plots suggests long-range dependencies, and the parameters of the best fitting models are interpreted. Implications of the findings for the field are discussed, and a note is included about the available software options for conducting these types of analyses. References: Beran, J. (1994). Statistics for long-memory processes. Boca Raton, FL: Chapman & Hall/CRC. Close Matthijs Koopmans 59 Organisational decision making as network coupled oscillators: validation and case study [abstract] Abstract: Organisational decision making, where many individuals interact to share information, formulate decisions and perform actions, is at heart a social system oriented towards outcomes - success in a military mission or business venture. In recent years I have proposed the Kuramoto model of synchronising oscillators to represent such a system that may be developed towards predictive modelling against specific scenarios. Essentially here, the oscillator limit cycle represents what is known in cognitive psychology as a Perception-Action cycle, or in military parlance an Observe-Orient-Decide-Action loop; the network of interactions may represent the range of formal, information and technology based exchanges of information; finally, a native frequency represents the individual speed of decision-making for an agent left to themselves. To such a system may be added stochastic influences, or “noise”, to represent the human properties of intuition, indecision or degrading of communication under stress or mood shifts. In this paper, I propose the model in application to a military organisation as may be located in a deployed headquarters. I use data based on a recent study of such an organisation where participants responded to surveys and interviews probing their pattern of interactions and level of cognition (in the sense of the Perception-Action cycle) for two scenarios: routine business and an emergency response. For noise I use a combination of stable Lévy noise both in spatial and temporal dimensions, where the underlying probability distributions for this exhibit power-law heavy tails. I summarise an initial validation of the model, invoking another approach in organisation theory known as Contingency Theory. The model thus integrates ideas from quantitative and qualitative complexity theory. To illustrate the utility of the model, I study a number of interventions in the model: local network modifications and/or training in order to tighten frequency distributions. I conclude with prospects for future work. Close Alexander Kalloniatis

# Foundations & Biology  (FB) Session 1

## Chair: Samuel Johnson

 276 Structurally induced noncritical power-laws in neural avalanches [abstract] Abstract: Percolation has been used as a model for describing a wide range of different phenomena [Saberi Phys. Reports 2015; Eckmann et al, Phys. Reports 2007]. For example, the distribution of sizes of epidemics or neural avalanches has been studied using models of percolation on networks [Faqeeh et al arXiv:1508.05590, 2015]. In particular, using a model of percolation, it was shown [Friedman and Landsberg, Chaos 2013] that the hierarchical modular structure observed in brain networks can contribute to a power-law distribution of avalanche sizes and durations, and critical behavior of neural dynamics. This study shows the potential of percolation models to help understand the origin of the various power-law behaviors, observed in experimental setups [Freidman et al, PRL 2012] and computational simulations [Rubinov, Plos. Comp. Biol. 2011] of neural systems. Here, we use methods employed in percolation theories, popularity dynamics, and critical branching processes to investigate the distribution of avalanche sizes on random networks with arbitrary degree distribution. We show, using theoretical and numerical calculations, that even a simple model of neural dynamics can produce a range of distinct power-law behaviors: For scale-free networks with degree distribution exponent $3<\nu<4$, the avalanche size distribution $P(s)$, at the critical point of the neural dynamics model, has a power-law form with exponent $(2\nu-3)/(\nu-2)$. Interestingly, for such scale-free networks, in the subcritical regime, $P(s)$ is also a power-law with exponent $\nu$. This refutes the previous analysis [Cohen PRE 66, 036113, 2002] that indicated that away from the critical point, $P(s)$ should be a power-law (with exponent 5/2) with exponential cutoff. In networks with $\nu>4$ or in non-scale-free networks, at the critical point, $P(s)$ is a pure power-law with exponent 5/2; nonetheless, even away from the critical point, a power-law with exponent 5/2 which is extended for several orders of magnitude can be observed for $P(s)$. Close Ali Faqeeh and James Gleeson 383 Stochastic modeling of tumor emergence induced by cell-to-cell communication disruption in elastic epithelial tissue [abstract] Abstract: It is known that the noise during gene expression comes about in two ways. The inherent stochasticity of biochemical processes generates "intrinsic" noise. "Extrinsic" noise refers to variation in identically-regulated quantities between different cells. The small number of reactant molecules involved in gene regulation can lead to significant fluctuations in protein concentrations. To study the spatial effects of intrinsic and extrinsic noises on the gene regulation determining the emergence of tumor we have applied a multiscale chemo-mechanical model of cancer development in epithelial tissue proposed recently in [1]. The epithelium is represented by an elastic 2D array of polygonal cells with its own gene regulation dynamics. The model allows for the simulation of evolution of multiple cells interacting via the chemical signaling or mechanically induced strain. The algorithm includes the transformation of normal cells into a cancerous state triggered by a local failure of spatial synchronization of the cellular rhythms. To model the delay-induced stochastic chemical signaling we have used a generalization of the Gillespie algorithm that accounts for delay suggested in [2]. The possibility of the stochastic pattern formation produced by the joint action of time delay and noise was demonstrated in [3]. In this work, we study the effect of the stochastic oscillations responsible for cell-to-cell communications on the emergence of tumor. Both the intrinsic and extrinsic contributions to stochastic pattern formation and circadian rhythm disruption have been explored numerically. [1] Bratsun D.A., Merkuriev D.V., Zakharov A.P., Pismen L.M. Multiscale modeling of tumor growth induced by circadian rhythm disruption in epithelial tissue. J. Biol. Phys. 42, 107-132 (2016). [2] Bratsun, D., Volfson, D., Hasty, J., Tsimring, L.S. Delay-induced stochastic oscillations in gene regulation. PNAS 102, 14593-14598 (2005). [3]Bratsun D.A., Zakharov A.P. Spatial Effects of Delay-Induced Stochastic Oscillations in a Multi-scale Cellular System. Springer Proceedings in Complexity, 93-103 (2016). Close Dmitry Bratsun and Ivan Krasnyakov 173 Hyper-rarity in tropical forests: beyond species richness [abstract] Abstract: Tropical forests have long been recognised as one of the largest pools of biodiversity, and tree inventory database from closed canopy forests have recently been used to estimate their species richness. Global patterns of empirical abundance distributions for vascular plant species show that tropical forests vary in their absolute number of species, but display surprising similarities in the distribution of populations across species. In the Amazonia hyper-dominant species are only 1.4% of the total, but they account for half of all trees; on the other spectrum, hyper-rare species make up nearly 70% of the entire pool, but their total population is only 0.12% of all trees. This extreme heterogeneity in abundances across species forms the core of the Fisher’s paradox, an important open question in ecology. Here we introduce an analytical framework which allows one to provide robust and accurate estimates of species richness and abundance distributions in biodiversity-rich ecosystems. We find that previous methods have systematically overestimated the total number of species. Also, our analysis of 15 empirical forest plots highlights that ecosystems at stationarity tend to maximise their relative fluctuation of abundances. This produces a large number of rare species and only a few common species. We argue that a large number of rare species provides a buffer against declines. When biotic factors or environmental conditions change, some of the rare species may be abler than others in maintaining ecosystem’s functions, because different species respond differently to environmental changes. This further underscores the importance of rare species and their link with the insurance effect. Close Anna Tovo, Samir Suweis, Marco Formentin, Marco Favretti, Jayanth Banavar, Sandro Azaele and Amos Maritan 389 Human mobility network and persistence of rapidly mutating pathogens [abstract] Abstract: Rapidly mutating pathogens may be able to persist in the population and reach an endemic equilibrium by escaping acquired immunity of hosts. For such diseases, multiple biological, environmental and population level mechanisms determine epidemic dynamics, including pathogen’s epidemiological traits, seasonality, interaction with other circulating strains and spatial fragmentation of hosts and their mixing. We focus on the two latter factors and study the impact of the heterogeneities characterizing population distribution and mobility network on the equilibrium dynamics of the infection both with one strain and with multiple competing strains. We consider a susceptible-infected-recovered-susceptible model on a metapopulation system where individuals are distributed in subpopulations connected with a network of mobility flows. We simulate disease spreading by means of a mechanistic stochastic model and we systematically explore different levels of spatial disaggregation, probability of traveling among subpopulations and mobility network topology, reconstructing the phase space of pathogen persistence and the dynamics out of the equilibrium. Results depict a rich dynamical behaviour. The increase in the average duration of immunity reduces the chance of persistence until extinction is certain above a threshold value. Such critical parameter, however, is crucially affected by the traveling probability, being larger for intermediate levels of mobility coupling. The dynamical regimes observed are very diversified and present oscillations and metastable states. Topological heterogeneities leave their signature on the spatial dynamics, where subpopulation connectivity affects recurrence of epidemic waves, spreading velocity and chance to be infected. The present work uncovers the crucial role of hosts’ space structure on the ecological dynamics of rapidly mutating pathogens, opening the path for further studies on disease ecology in presence of a complex and heterogeneous environment. Close Alberto Aleta, Yamir Moreno, Sandro Meloni, Chiara Poletto and Vittoria Colizza 156 Applying the Epidemic Spreading Model to Explain Brain Activity [abstract] Abstract: The role of correlations in the communication process in the functional brain networks is still highly debated in neuroscience. In this study, we apply a simple SIS epidemic spreading model on the human connectome to analyze the structural topological properties that drive these correlations of activity. We first verify results from previous discrete-time studies with our continuous-time simulations. Then, we introduce a small time delay and analyze the so-called delayed correlations of one brain region to the others. We find that just above the critical threshold direct structural connections induce higher cross-correlations between two brain regions and that the larger the distance between two nodes in the structural network, the lower is their delayed correlation. We prove analytically that the delayed auto-correlation is decreasing for small time lags and show with simulations that it even seems to be exponentially decaying for very small time lags. Hubs seem to have a lower auto-correlation than other nodes, but their delayed correlation with direct neighbors seems to be much higher than with other nodes. Previous studies found that the direction of activity spreading in the human connectome seems to be mostly from the back to the front. Using the delayed correlations and the measure of transfer entropy we can confirm this dominant back-to-front pattern with our SIS model. We show that the "rich club" structure of densely connected hubs seems to be responsible for this observed spreading pattern. Close Jil Meier, Xiangyu Zhou, Cornelis Jan Stam and Piet Van Mieghem 535 On Complex Dynamics of Sparse Discrete Hopfield Networks and Its Implications [abstract] Abstract: It has been argued that complex behavior in many biological systems, including but not limited to human and animal brains, is to a great extent a consequence of high interconnectedness among the individual elements, such as neurons in brains. As a very crude approximation, brain can be viewed as an associative memory that is implemented as a large network of heavily interconnected neurons. Hopfield Networks are a popular model of associative memory. From a dynamical systems perspective, it has been posited that the complexity of possible behaviors of a Hopfield network is largely due to the aforementioned high level of interconnectedness. We show, however, that many aspects of provably complex – and, in particular, unpredictable within realistic computational resources – behavior can also be obtained in very sparsely connected Hopfield networks and related classes of Boolean Network Automata. In fact, it turns out that the most fundamental problems about the memory capacity of a Hopfield network are computationally intractable, even for restricted types of networks that are uniformly sparse, with only a handful neighbors per node. This is significant not only from a theoretical computer science standpoint, but also from connectionist science and neuroscience perspectives: animal brains viewed as networks of neurons are relatively sparse and have local structure. One implication of our work is that some of the most fundamental aspects of biological (and other) networks’ dynamics do not require high density, in order to exhibit provably complex, computationally intractable to predict behavior. Close Predrag Tosic