Phenomenological models of socioeconomic network dynamics

First-passage distributions of an asymmetric noisy voter model

This paper explores the first-passage times in an asymmetric noisy voter model through analytical methods. The noise in the model leads to bistable behavior, and the asymmetry arises from heterogeneous rates for spontaneous switching. We obtain exact analytical expressions for the probability distribution for two different initial conditions, first-passage times for switching transitions and first return times to a stable state for all system sizes, offering a deeper understanding of the model's dynamics. Additionally, we derive exact expressions for the mean switching time, mean return time, and their mean square variants. The findings are verified through numerical simulations. To enhance clarity regarding the model's behavior, we also provide approximate solutions, emphasizing the parameter dependence of first-passage times in the small switching parameter regime. An interesting result in this regime is that while the mean switching time in the leading order is independent of system size, the mean return time depends inversely on system size. This study not only advances our analytical understanding of the asymmetric noisy voter model but also establishes a framework for exploring similar phenomena in social and biological systems where the noisy voter model is applicable.

AI Pontryagin or how artificial neural networks learn to control dynamical systems

The efficient control of complex dynamical systems has many applications in the natural and applied sciences. In most real-world control problems, both control energy and cost constraints play a significant role. Although such optimal control problems can be formulated within the framework of variational calculus, their solution for complex systems is often analytically and computationally intractable. To overcome this outstanding challenge, we present AI Pontryagin, a versatile control framework based on neural ordinary differential equations that automatically learns control signals that steer high-dimensional dynamical systems towards a desired target state within a specified time interval. We demonstrate the ability of AI Pontryagin to learn control signals that closely resemble those found by corresponding optimal control frameworks in terms of control energy and deviation from the desired target state. Our results suggest that AI Pontryagin is capable of solving a wide range of control and optimization problems, including those that are analytically intractable.

Motion, fixation probability and the choice of an evolutionary process

Seemingly minor details of mathematical and computational models of evolution are known to change the effect of population structure on the outcome of evolutionary processes. For example, birth-death dynamics often result in amplification of selection, while death-birth processes have been associated with suppression. In many biological populations the interaction structure is not static. Instead, members of the population are in motion and can interact with different individuals at different times. In this work we study populations embedded in a flowing medium; the interaction network is then time dependent. We use computer simulations to investigate how this dynamic structure affects the success of invading mutants, and compare these effects for different coupled birth and death processes. Specifically, we show how the speed of the motion impacts the fixation probability of an invading mutant. Flows of different speeds interpolate between evolutionary dynamics on fixed heterogeneous graphs and well-stirred populations; this allows us to systematically compare against known results for static structured populations. We find that motion has an active role in amplifying or suppressing selection by fragmenting and reconnecting the interaction graph. While increasing flow speeds suppress selection for most evolutionary models, we identify characteristic responses to flow for the different update rules we test. In particular we find that selection can be maximally enhanced or suppressed at intermediate flow speeds.

Whether a mutation spreads in a population or not is one of the most important questions in biology. The evolution of cancer and antibiotic resistance, for example, are mediated by invading mutants. Recent work has shown that population structure can have important consequences for the outcome of evolution. For instance, a mutant can have a higher or a lower chance of invasion than in unstructured populations. These effects can depend on seemingly minor details of the evolutionary model, such as the order of birth and death events. Many biological populations are in motion, for example due to external stirring. Experimentally this is known to be important; the performance of mutants in E. coli populations, for example, depends on the rate of mixing. Here, we focus on simulations of populations in a flowing medium, and compare the success of a mutant for different flow speeds. We contrast different evolutionary models, and identify what features of the evolutionary model affect mutant success for different speeds of the flow. We find that the chance of mutant invasion can be at its highest (or lowest) at intermediate flow speeds, depending on the order in which birth and death events occur in the evolutionary process.

Controllability of social networks and the strategic use of random information

Background

This work is aimed at studying realistic social control strategies for social networks based on the introduction of random information into the state of selected driver agents. Deliberately exposing selected agents to random information is a technique already experimented in recommender systems or search engines, and represents one of the few options for influencing the behavior of a social context that could be accepted as ethical, could be fully disclosed to members, and does not involve the use of force or of deception.

Methods

Our research is based on a model of knowledge diffusion applied to a time-varying adaptive network and considers two well-known strategies for influencing social contexts: One is the selection of few influencers for manipulating their actions in order to drive the whole network to a certain behavior; the other, instead, drives the network behavior acting on the state of a large subset of ordinary, scarcely influencing users. The two approaches have been studied in terms of network and diffusion effects. The network effect is analyzed through the changes induced on network average degree and clustering coefficient, while the diffusion effect is based on two ad hoc metrics which are defined to measure the degree of knowledge diffusion and skill level, as well as the polarization of agent interests.

Results

The results, obtained through simulations on synthetic networks, show a rich dynamics and strong effects on the communication structure and on the distribution of knowledge and skills.

Conclusions

These findings support our hypothesis that the strategic use of random information could represent a realistic approach to social network controllability, and that with both strategies, in principle, the control effect could be remarkable.

Basin stability measure of different steady states in coupled oscillators

In this report, we investigate the stabilization of saddle fixed points in coupled oscillators where individual oscillators exhibit the saddle fixed points. The coupled oscillators may have two structurally different types of suppressed states, namely amplitude death and oscillation death. The stabilization of saddle equilibrium point refers to the amplitude death state where oscillations are ceased and all the oscillators converge to the single stable steady state via inverse pitchfork bifurcation. Due to multistability features of oscillation death states, linear stability theory fails to analyze the stability of such states analytically, so we quantify all the states by basin stability measurement which is an universal nonlocal nonlinear concept and it interplays with the volume of basins of attractions. We also observe multi-clustered oscillation death states in a random network and measure them using basin stability framework. To explore such phenomena we choose a network of coupled Duffing-Holmes and Lorenz oscillators which are interacting through mean-field coupling. We investigate how basin stability for different steady states depends on mean-field density and coupling strength. We also analytically derive stability conditions for different steady states and confirm by rigorous bifurcation analysis.

Models of life: epigenetics, diversity and cycles

This review emphasizes aspects of biology that can be understood through repeated applications of simple causal rules. The selected topics include perspectives on gene regulation, phage lambda development, epigenetics, microbial ecology, as well as model approaches to diversity and to punctuated equilibrium in evolution. Two outstanding features are repeatedly described. One is the minimal number of rules to sustain specific states of complex systems for a long time. The other is the collapse of such states and the subsequent dynamical cycle of situations that restitute the system to a potentially new metastable state.

The evolving cobweb of relations among partially rational investors

To overcome the limitations of neoclassical economics, researchers have leveraged tools of statistical physics to build novel theories. The idea was to elucidate the macroscopic features of financial markets from the interaction of its microscopic constituents, the investors. In this framework, the model of the financial agents has been kept separate from that of their interaction. Here, instead, we explore the possibility of letting the interaction topology emerge from the model of the agents’ behavior. Then, we investigate how the emerging cobweb of relationship affects the overall market dynamics. To this aim, we leverage tools from complex systems analysis and nonlinear dynamics, and model the network of mutual influence as the output of a dynamical system describing the edge evolution. In this work, the driver of the link evolution is the relative reputation between possibly coupled agents. The reputation is built differently depending on the extent of rationality of the investors. The continuous edge activation or deactivation induces the emergence of leaders and of peculiar network structures, typical of real influence networks. The subsequent impact on the market dynamics is investigated through extensive numerical simulations in selected scenarios populated by partially rational investors.

Breakdown of interdependent directed networks

Increasing evidence shows that real-world systems interact with one another via dependency connectivities. Failing connectivities are the mechanism behind the breakdown of interacting complex systems, e.g., blackouts caused by the interdependence of power grids and communication networks. Previous research analyzing the robustness of interdependent networks has been limited to undirected networks. However, most real-world networks are directed, their in-degrees and out-degrees may be correlated, and they are often coupled to one another as interdependent directed networks. To understand the breakdown and robustness of interdependent directed networks, we develop a theoretical framework based on generating functions and percolation theory. We find that for interdependent Erdős-Rényi networks the directionality within each network increases their vulnerability and exhibits hybrid phase transitions. We also find that the percolation behavior of interdependent directed scale-free networks with and without degree correlations is so complex that two criteria are needed to quantify and compare their robustness: the percolation threshold and the integrated size of the giant component during an entire attack process. Interestingly, we find that the in-degree and out-degree correlations in each network layer increase the robustness of interdependent degree heterogeneous networks that most real networks are, but decrease the robustness of interdependent networks with homogeneous degree distribution and with strong coupling strengths. Moreover, by applying our theoretical analysis to real interdependent international trade networks, we find that the robustness of these real-world systems increases with the in-degree and out-degree correlations, confirming our theoretical analysis.

Demography-based adaptive network model reproduces the spatial organization of human linguistic groups

The distribution of human linguistic groups presents a number of interesting and nontrivial patterns. The distributions of the number of speakers per language and the area each group covers follow log-normal distributions, while population and area fulfill an allometric relationship. The topology of networks of spatial contacts between different linguistic groups has been recently characterized, showing atypical properties of the degree distribution and clustering, among others. Human demography, spatial conflicts, and the construction of networks of contacts between linguistic groups are mutually dependent processes. Here we introduce an adaptive network model that takes all of them into account and successfully reproduces, using only four model parameters, not only those features of linguistic groups already described in the literature, but also correlations between demographic and topological properties uncovered in this work. Besides their relevance when modeling and understanding processes related to human biogeography, our adaptive network model admits a number of generalizations that broaden its scope and make it suitable to represent interactions between agents based on population dynamics and competition for space.

Macroscopic description of complex adaptive networks coevolving with dynamic node states

In many real-world complex systems, the time evolution of the network's structure and the dynamic state of its nodes are closely entangled. Here we study opinion formation and imitation on an adaptive complex network which is dependent on the individual dynamic state of each node and vice versa to model the coevolution of renewable resources with the dynamics of harvesting agents on a social network. The adaptive voter model is coupled to a set of identical logistic growth models and we mainly find that, in such systems, the rate of interactions between nodes as well as the adaptive rewiring probability are crucial parameters for controlling the sustainability of the system's equilibrium state. We derive a macroscopic description of the system in terms of ordinary differential equations which provides a general framework to model and quantify the influence of single node dynamics on the macroscopic state of the network. The thus obtained framework is applicable to many fields of study, such as epidemic spreading, opinion formation, or socioecological modeling.

Fishing out collective memory of migratory schools

Animals form groups for many reasons, but there are costs and benefits associated with group formation. One of the benefits is collective memory. In groups on the move, social interactions play a crucial role in the cohesion and the ability to make consensus decisions. When migrating from spawning to feeding areas, fish schools need to retain a collective memory of the destination site over thousands of kilometres, and changes in group formation or individual preference can produce sudden changes in migration pathways. We propose a modelling framework, based on stochastic adaptive networks, that can reproduce this collective behaviour. We assume that three factors control group formation and school migration behaviour: the intensity of social interaction, the relative number of informed individuals and the strength of preference that informed individuals have for a particular migration area. We treat these factors independently and relate the individuals' preferences to the experience and memory for certain migration sites. We demonstrate that removal of knowledgeable individuals or alteration of individual preference can produce rapid changes in group formation and collective behaviour. For example, intensive fishing targeting the migratory species and also their preferred prey can reduce both terms to a point at which migration to the destination sites is suddenly stopped. The conceptual approaches represented by our modelling framework may therefore be able to explain large-scale changes in fish migration and spatial distribution.

Consensus time and conformity in the adaptive voter model

The adaptive voter model is a paradigmatic model in the study of opinion formation. Here we propose an extension for this model, in which conflicts are resolved by obtaining another opinion, and analytically study the time required for consensus to emerge. Our results shed light on the rich phenomenology of both the original and extended adaptive voter models, including a dynamical phase transition in the scaling behavior of the mean time to consensus.

Multistability with a metastable mixed state

Complex dynamical systems often show multiple metastable states. In macroevolution, such behavior is suggested by punctuated equilibrium and discrete geological epochs. In molecular biology, bistability is found in epigenetics and in the many mutually exclusive states that a human cell can take. Sociopolitical systems can be single-party regimes or a pluralism of balancing political fractions. To introduce multistability, we suggest a model system of D mutually exclusive microstates that battle for dominance in a large system. Assuming one common intermediate state, we obtain D+1 metastable macrostates for the system, one of which is a self-reinforced mixture of all D+1 microstates. Robustness of this metastable mixed state increases with diversity D.

Early fragmentation in the adaptive voter model on directed networks

We consider voter dynamics on a directed adaptive network with fixed out-degree distribution. A transition between an active phase and a fragmented phase is observed. This transition is similar to the undirected case if the networks are sufficiently dense and have a narrow out-degree distribution. However, if a significant number of nodes with low out degree is present, then fragmentation can occur even far below the estimated critical point due to the formation of self-stabilizing structures that nucleate fragmentation. This process may be relevant for fragmentation in current political opinion formation processes.

Phase change in an opinion-dynamics model with separation of time scales

We define an opinion formation model of agents in a one-dimensional ring, where the opinion of an agent evolves due to its interactions with close neighbors and due to its either positive or negative attitude toward the overall mood of all the other agents. While the dynamics of the agent's opinion is described with an appropriate differential equation, from time to time pairs of agents are allowed to change their locations to improve the homogeneity of opinion (or comfort feeling) with respect to their short-range environment. In this way the timescale of transaction dynamics and that of environment update are well separated and controlled by a single parameter. By varying this parameter we discovered a phase change in the number of undecided individuals. This phenomenon arises from the fact that too frequent location exchanges among agents result in frustration in their opinion formation. Our mean field analysis supports this picture.

Coevolution of Glauber-like Ising dynamics and topology

We study the coevolution of a generalized Glauber dynamics for Ising spins with tunable threshold and of the graph topology where the dynamics takes place. This simple coevolution dynamics generates a rich phase diagram in the space of the two parameters of the model, the threshold and the rewiring probability. The diagram displays phase transitions of different types: spin ordering, percolation, and connectedness. At variance with traditional coevolution models, in which all spins of each connected component of the graph have equal value in the stationary state, we find that, for suitable choices of the parameters, the system may converge to a state in which spins of opposite sign coexist in the same component organized in compact clusters of like-signed spins. Mean field calculations enable one to estimate some features of the phase diagram.

Socioeconomic networks with long-range interactions

We study a modified version of a model previously proposed by Jackson and Wolinsky to account for communication of information and allocation of goods in socioeconomic networks. In the model, the utility function of each node is given by a weighted sum of contributions from all accessible nodes. The weights, parametrized by the variable delta , decrease with distance. We introduce a growth mechanism where new nodes attach to the existing network preferentially by utility. By increasing delta , the network structure evolves from a power-law to an exponential degree distribution, passing through a regime characterized by shorter average path length, lower degree assortativity, and higher central point dominance. In the second part of the paper we compare different network structures in terms of the average utility received by each node. We show that power-law networks provide higher average utility than Poisson random networks. This provides a possible justification for the ubiquitousness of scale-free networks in the real world.

Adaptive coevolutionary networks: a review

Adaptive networks appear in many biological applications. They combine topological evolution of the network with dynamics in the network nodes. Recently, the dynamics of adaptive networks has been investigated in a number of parallel studies from different fields, ranging from genomics to game theory. Here we review these recent developments and show that they can be viewed from a unique angle. We demonstrate that all these studies are characterized by common themes, most prominently: complex dynamics and robust topological self-organization based on simple local rules.

Generic absorbing transition in coevolution dynamics

We study a coevolution voter model on a complex network. A mean-field approximation reveals an absorbing transition from an active to a frozen phase at a critical value [see text for formula] that only depends on the average degree micro of the network. In finite-size systems, the active and frozen phases correspond to a connected and a fragmented network, respectively. The transition can be seen as the sudden change in the trajectory of an equivalent random walk at the critical point, resulting in an approach to the final frozen state whose time scale diverges as tau approximately |p(c) - p|(-)} near p(c).

Adaptive coevolutionary networks: a review

Adaptive networks appear in many biological applications. They combine topological evolution of the network with dynamics in the network nodes. Recently, the dynamics of adaptive networks has been investigated in a number of parallel studies from different fields, ranging from genomics to game theory. Here we review these recent developments and show that they can be viewed from a unique angle. We demonstrate that all these studies are characterized by common themes, most prominently: complex dynamics and robust topological self-organization based on simple local rules.

Optimal transportation network with concave cost functions: loop analysis and algorithms

Transportation networks play a vital role in modern societies. Structural optimization of a transportation system under a given set of constraints is an issue of great practical importance. For a general transportation system whose total cost C is determined by C = Sigma(i<j)C(ij)(I(ij)), with C(ij) (I(ij)) being the cost of the flow I(ij) between node i and node j, Banavar and co-workers [Phys. Rev. Lett. 84, 4745 (2000)] proved that the optimal network topology is a tree if C(ij) proportional |I(ij)|(gamma) with 0 < gamma < 1. The same conclusion also holds in the more general case where all the flow costs are strictly concave functions of the flow I(ij). To further understand the qualitative difference between systems with concave and convex cost functions, a loop analysis of transportation cost is performed in the present paper, and an alternative mathematical proof of the optimality of tree-formed networks is given. The simple intuitive picture of this proof then leads to an efficient global algorithm for the searching of optimal structures for a given transportation system with concave cost functions.