Session S16: Complex Networks and Human Behaviour

Live

The knowledge of the connectivity of in-vitro neuronal cultures can provide important insights for understanding brain networks. We present a method that estimates directed effective connectivity and synaptic weights of cortical neuronal cultures from the recordings of a multielectrode array. The neuronal culture is modelled as a dynamical system governed by a generic set of differential equations with noise. We have derived a mathematical result showing that the time-lagged cross-covariance of the dynamics is related to the equal-time cross-covariance of the dynamics via the connectivity matrix of the network. Using this relation, we reconstruct the directed effective connectivity matrix and the synaptic weights of the links with each electrode taken as a node of the network. The neuronal networks reconstructed have several interesting properties. In particular, the distributions of the average synaptic strength of the incoming and outgoing links are non-Gaussian and skewed with long tails. We show that the long-tailed distribution of the average synaptic strength of the incoming links is the underlying cause of the long-tailed distributions of spiking activity.   

Live

Humans communicate using systems of interconnected stimuli or concepts—from language and music to literature and science—yet it remains unclear how, if at all, the structure of these networks supports the communication of information. Although information theory provides tools to quantify the information produced by a system, traditional metrics do not account for the inefficient ways that humans process this information. Here, we develop an analytical framework to study the information generated by a system as perceived by a human observer. We demonstrate experimentally that this perceived information depends critically on a system’s network topology. Applying our framework to several real networks, we find that they communicate a large amount of information (having high entropy) and do so efficiently (maintaining low divergence from human expectations). Moreover, we show that such efficient communication arises in networks that are simultaneously heterogeneous, with high-degree hubs, and clustered, with tightly connected modules—the two defining features of hierarchical organization. Together, these results suggest that many communication networks are constrained by the pressures of information transmission, and that these pressures select for specific structural features.   

Live

Our network model of aging represents aspects of human health as nodes in a network. The nodes damage stochastically over time based on the health of their neighbours. Mortality occurs stochastically with a rate proportional to the overall damage in the network. Previous work has shown that human health and mortality data can be captured using a scale-free network and that the model is very sensitive to the choice of network structure. Does the network structure represent an organism’s robustness to damage in a meaningful way? We address this question from the bottom up using a network optimization approach. We optimize the network structure with respect to various health outcomes, such as longevity and health-related quality of life. We investigate which network motifs emerge depending on the optimization health outcome, and how these aspects of the network structure affect damage propagation. We add measures of network entropy to penalize “trivial” network structures.   

Live

Adaptation plays a pivotal role in the evolution of natural and artificial complex systems, and in the determination of their functionality. Here, we investigate the impact of adaptive inter-layer processes on intra-layer synchronization in multiplex networks. The considered adaptation mechanism is governed by a Hebbian learning rule, i.e., the link weight between a pair of interconnected nodes is enhanced if the two nodes are in phase. Such adaptive coupling induces an irreversible first-order transition route to synchronization accompanied with a hysteresis. We provide rigorous analytic predictions of the critical coupling strengths for the onset of synchronization and de-synchronization, and verify all our theoretical predictions by means of extensive numerical simulations   

Live

Understanding how people process and learn information remains an elusive goal in the study of human statistical learning. In particular, many recent studies have probed the ways in which humans process information that is organized as a network. Previous work has demonstrated that humans learn networks through building internal mental models of network structure. However, these mental models are often inaccurate due to limitations in human information processing. These limitations raise a clear question: Given a target network that one wishes for a human to learn, how should a network presented to the human be designed so as to correct for errors in human learning? To answer this question, we study the optimization of learnability in modular and lattice graphs. We find that the learnability of both networks can be enhanced by reinforcing connections within modules or small clusters. Then, we extend our analyses to networks created from generative models, and finally to real-world networks. Overall, our findings suggest that the accuracy of human network learning can be significantly enhanced through purposeful misrepresentation of presented network structures.   

Live

For millennia, humans have looked to the night sky and chosen star groups to name. But why does Centaurus comprise that specific set of stars rather than some other? We hypothesize that the perception of star groups (constellations) can be explained by a simple model of eye movements taking a random walk along a network of star-to-star transition probabilities. The walk is biased by angular distances between stars, preferred angular distances of human eye movements (also known as saccades), and stars’ apparent magnitudes. To derive predicted constellations from the random walk, we employ a free energy model of mental calculations that maximizes the accuracy of perception while minimizing computational complexity. The model transforms the true transition probability matrix among stars into a perceived matrix, in which star clusters are evident. We show that the statistics of the perceived star clusters naturally align with the boundaries between true constellations. Our findings offer a simple explanation for the identities of the 88 standard constellations. More generally, our study suggests that temporal contingencies between human observations may be an important driver of early naming practices in the sciences.   

Live

Predicting and classifying the spontaneous emergence of order is of great importance to understanding biological systems. A famous example is the behavior of a flock of birds which can spontaneously change their direction of flight in unison. We are interested in the generic conditions under which order emerges in a large collection of such active interacting agents that can influence each other’s behavior over at long distances.
We recognize that in order to extract information on existence of interactions between agents, looking at complex spatial dynamics is not strictly necessary. Instead, we use the framework of dynamic networks to directly characterize the state of agents and their mutual influence. This approach allows us to concentrate on the dynamics of the order parameters instead of the dynamics of individuals. We can solve the resulting model analytically in a mean-field approximation, which gives us a second-order phase transition. Solving the full nonlinear model, we retain the critical temperature from the phase transition, and find a full phase diagram in terms of the key parameters, the orientational noise and the network rearrangement time.   

Live

Complex networks encountered in biology, ecology, sociology and technology often contract due to node failures, infections or attacks. The ultimate failure, taking place when the network fragments into disconnected components was studied extensively using percolation theory. We show [1-2] that long before reaching fragmentation, contracting networks lose their distinctive features. In particular, we identify that a very large class of network structures, which experience a broad class of node deletion processes, exhibit a stable flow towards a universal fixed point, representing a maximum-entropy ensemble, namely the Erdös-Rényi ensemble characterized by a Poisson degree distribution. This is in sharp contrast to network expansion processes, which lead to diverse families of complex networks, whose structure is highly sensitive to details of the growth mechanism.
These results imply that contracting networks in the late stages of node failure cascades, attacks and epidemics reach a common universal structure, providing a unifying framework for their analysis.

[1] I. Tishby, O. Biham and E. Katzav, Phys. Rev. E 100, 032314 (2019).
[2] I. Tishby, O. Biham and E. Katzav, Phys. Rev. E 101, 062308 (2020).   

Live

Multiplex networks are abstract representations of those complex systems in which multiple types of relationships exist amongst components. The control properties of such networks in response to perturbations can be understood in the framework of network control theory. In control tasks where the control signals are injected into a specific `input' layer, how are the control properties of a target layer determined by its structure and its relationship with the input layer? Here, we characterize the structure of multiplex networks in terms of the eigenspectra of individual layers and the alignment between their eigenmodes, and determine the dependence of control energy on these structural parameters. We study the role of layer density, layer topology, and interlayer alignment in determining the control properties of duplex networks with the layers constructed from the networks of different topologies. Further, we investigate the role of the alignment between the eigenmodes of the `input' layer and the `target' layer in setting the control cost of specific modes of the target layer. We discuss the applications of our results in understanding the layered architecture of brain networks from the perspective of control.   

Live

Societal structures are influenced by the interpersonal
behavior of their members, which includes the prosperity
to define oneself relative to other, denoted here `envy'. We
develop a game theoretical formulation which includes choice,
competition and envy [fn] C. Gros, Royal Society
Open Science, 7:200411, 2020.[/fn]. In a correspondence to interacting
classical particle the bare utility, choice, is equivalent
to a confining potential, competition to Coulomb repulsion
and envy to a self-consistent molecular field interaction.
Envy induces low reward agents to search for alternative
strategies, which runs out of phase space when envy reaches
a critical point. The spectrum of rewards (energy, in the
phsyics analogy), splits into two disjoint bands, which
correspond to a lower and an upper class. Extensive numerical
simmulation are presented together with a self-consitent
analytic treatment of class sperated state.   

Live

The collective voting through individual buying decisions measured by music charts can lead to self-organized phenomena. This has been shown in the analysis of four album charts. The album lifetime is nowadays distributed like a power-law, a telltale sign of self-organized criticality. This has evolved since the 1980s, when the lifetime was a log-normally distributed. Using an information theoretical approach we hypothesize that this evolution is due to shortening of the universal time scale of opinion formation.

A similar distinction is observable when comparing the lifetime distribution of weekly and daily compiled album charts on Spotify. This indicates that the above mentioned time scale of opinion formation in the cultural domain of music albums is nowadays below a week but not yet shorter than a day.

Social acceleration can also be shown by the chart diversity, which for music charts increased by a factor of more than two in the last four decades. Surprisingly a similar trend can be observed in the chart diversity of the New York Times best-seller list. Additionally, the time needed for a number-one hit to reach the top of chart has decreased from more than five weeks to bellow one week. Thereby, the speed of cultural penetration has increased drastically.   

Live

Curiosity is widely recognized as a fundamental mode of cognition, driving people and animals towards novel experiences that yield new insights about the world and its underlying processes. Curiosity is therefore linked to information-seeking in novel environments and is an important part of behavior that we perceive as ``intelligent". While simple greedy actors may be optimal in simple and highly determinate environments, it is expected that curiosity is beneficial in more complex, evolving environments. We approach the question of curiosity by comparing reinforcement learning agents using different phenomenological models of curiosity in environments of controlled complexity. We find that indeed, greedy agents are inferior to curious ones in certain complex environments (where high reward strategies may be harder to find). However, when environments are too complex or noisy, curiosity imparts no benefit. These findings imply that curiosity is useful in a window of intermediate environmental complexity.   

Not Participating

Traffic jams are endemic in both biological and engineered systems when cargo needs to be transported between locations. Various strategies have been proposed to mitigate jams, to improve the efficiency of transportation. We consider jam formation on a single-lane where cars can cooperate and travel as part of a caravan at a speed set by its size, or depart from the travelling end of the caravan at maximum speed. In a periodic setting, when the rate at which cars leave the caravan is large compared to the rate of formation of caravans we observe a diffused, gaseous state. As the density of cars increases or the rate at which cars depart from the caravan decreases, cars coalesce to form a single caravan. We map the regimes in the phase-space and propose a mean-field description of the dynamics through Toner-Tu equations to capture the observed macroscopic behavior.   

Live

Patterns of avoidance, adjacency, and association in complex systems design emerge from the system's underlying logical architecture (functional relationships among components) and physical architecture (component physical properties and spatial location). Understanding the physical--logical architecture interplay that gives rise to patterns of arrangement requires a quantitative approach that bridges both descriptions. Here, we show that statistical physics reveals patterns of avoidance, adjacency, and association across sets of complex, distributed system design solutions. Using an example arrangement problem and tensor network methods, we identify several phenomena in complex systems design, including placement symmetry breaking, propagating correlation, and emergent localization. Our approach generalizes straightforwardly to a broad range of complex systems design settings where it can provide a platform for investigating basic design phenomena.