Does Spending More Always Ensure Higher Cooperation? An Analysis of Institutional Incentives on Heterogeneous Networks.

Humans have developed considerable machinery used at scale to create policies and to distribute incentives, yet we are forever seeking ways in which to improve upon these, our institutions. Especially when funding is limited, it is imperative to optimise spending without sacrificing positive outcomes, a challenge which has often been approached within several areas of social, life and engineering sciences. These studies often neglect the availability of information, cost restraints or the underlying complex network structures, which define real-world populations. Here, we have extended these models, including the aforementioned concerns, but also tested the robustness of their findings to stochastic social learning paradigms. Akin to real-world decisions on how best to distribute endowments, we study several incentive schemes, which consider information about the overall population, local neighbourhoods or the level of influence which a cooperative node has in the network, selectively rewarding cooperative behaviour if certain criteria are met. Following a transition towards a more realistic network setting and stochastic behavioural update rule, we found that carelessly promoting cooperators can often lead to their downfall in socially diverse settings. These emergent cyclic patterns not only damage cooperation, but also decimate the budgets of external investors. Our findings highlight the complexity of designing effective and cogent investment policies in socially diverse populations.

Propagation of Bankruptcy Risk over Scale-Free Economic Networks.

The propagation of bankruptcy-induced shocks across domestic and global economies is sometimes very dramatic; this phenomenon can be modelled as a dynamical process in economic networks. Economic networks are usually scale-free, and scale-free networks are known to be vulnerable with respect to targeted attacks, i.e., attacks directed towards the biggest nodes of the network. Here we address the following question: to what extent does the scale-free nature of economic networks and the vulnerability of the biggest nodes affect the propagation of economic shocks? We model the dynamics of bankruptcies as the propagation of financial contagion across the banking sector over a scale-free network of banks, and perform Monte-Carlo simulations based on synthetic networks. In addition, we analyze the public data regarding the bankruptcy of US banks from the Federal Deposit Insurance Corporation. The dynamics of the shock propagation is characterized in terms of the Bank Failures Diffusion Index, i.e., the average number of new bankruptcies triggered by the bankruptcy of a single bank, and in terms of the Shannon entropy of the whole network. The simulation results are in-line with the empirical findings, and indicate the important role of the biggest banks in the dynamics of economic shocks.

Conflict Dynamics in Scale-Free Networks with Degree Correlations and Hierarchical Structure.

We present a study of the dynamic interactions between actors located on complex networks with scale-free and hierarchical scale-free topologies with assortative mixing, that is, correlations between the degree distributions of the actors. The actor's state evolves according to a model that considers its previous state, the inertia to change, and the influence of its neighborhood. We show that the time evolution of the system depends on the percentage of cooperative or competitive interactions. For scale-free networks, we find that the dispersion between actors is higher when all interactions are either cooperative or competitive, while a balanced presence of interactions leads to a lower separation. Moreover, positive assortative mixing leads to greater divergence between the states, while negative assortative mixing reduces this dispersion. We also find that hierarchical scale-free networks have both similarities and differences when compared with scale-free networks. Hierarchical scale-free networks, like scale-free networks, show the least divergence for an equal mix of cooperative and competitive interactions between actors. On the other hand, hierarchical scale-free networks, unlike scale-free networks, show much greater divergence when dominated by cooperative rather than competitive actors, and while the formation of a rich club (adding links between hubs) with cooperative interactions leads to greater divergence, the divergence is much less when they are fully competitive. Our findings highlight the importance of the topology where the interaction dynamics take place, and the fact that a balanced presence of cooperators and competitors makes the system more cohesive, compared to the case where one strategy dominates.

Extraction of bouton-like structures from neuropil calcium imaging data.

The neuropil, the plexus of axons and dendrites, plays a critical role in operating the circuit processing of the nervous system. Revealing the spatiotemporal activity pattern within the neuropil would clarify how the information flows throughout the nervous system. However, calcium imaging to examine the circuit dynamics has mainly focused on the soma population due to their discrete distribution. The development of a methodology to analyze the calcium imaging data of a densely packed neuropil would provide us with new insights into the circuit dynamics. Here, we propose a new method to decompose calcium imaging data of the neuropil into populations of bouton-like synaptic structures with a standard desktop computer. To extract bouton-like structures from calcium imaging data, we introduced a new type of modularity, a widely used quality measure in graph theory, and optimized the clustering configuration by a simulated annealing algorithm, which is established in statistical physics. To assess this method's performance, we conducted calcium imaging of the neuropil of Drosophila larvae. Based on the obtained data, we established artificial neuropil imaging datasets. We applied the decomposition procedure to the artificial and experimental calcium imaging data and extracted individual bouton-like structures successfully. Based on the extracted spatiotemporal data, we analyzed the network structure of the central nervous system of fly larvae and found it was scale-free. These results demonstrate that neuropil calcium imaging and its decomposition could provide new insight into our understanding of neural processing.

Extinction and stationary distribution of a stochastic SIQR epidemic model with demographics and non-monotone incidence rate on scale-free networks.

By taking full consideration of contact heterogeneity of individuals, quarantine measures, demographics, information transmission and random environments, we present a stochastic SIQR epidemic model with demographics and non-monotone incidence rate on scale-free networks, which introduces stochastic perturbations to death rate. The formula of the basic reproduction number of the deterministic model is obtained by utilizing the existence of the endemic equilibrium. Next, we define a stopping time, then the existence of a unique global positive solution for the stochastic model is proved by constructing appropriate Lyapunov function to demonstrate the stopping time is infinite. In addition, we also manifest sufficient conditions for diseases extinction and the existence of ergodic stationary distribution by constructing appropriate stochastic Lyapunov functions. At last, numerical simulations illustrate the analytical results.

Agent-based evolving network modeling: a new simulation method for modeling low prevalence infectious diseases.

Agent-based network modeling (ABNM) simulates each person at the individual-level as agents of the simulation, and uses network generation algorithms to generate the network of contacts between individuals. ABNM are suitable for simulating individual-level dynamics of infectious diseases, especially for diseases such as HIV that spread through close contacts within intricate contact networks. However, as ABNM simulates a scaled-version of the full population, consisting of all infected and susceptible persons, they are computationally infeasible for studying certain questions in low prevalence diseases such as HIV. We present a new simulation technique, agent-based evolving network modeling (ABENM), which includes a new network generation algorithm, Evolving Contact Network Algorithm (ECNA), for generating scale-free networks. ABENM simulates only infected persons and their immediate contacts at the individual-level as agents of the simulation, and uses the ECNA for generating the contact structures between these individuals. All other susceptible persons are modeled using a compartmental modeling structure. Thus, ABENM has a hybrid agent-based and compartmental modeling structure. The ECNA uses concepts from graph theory for generating scale-free networks. Multiple social networks, including sexual partnership networks and needle sharing networks among injecting drug-users, are known to follow a scale-free network structure. Numerical results comparing ABENM with ABNM estimations for disease trajectories of hypothetical diseases transmitted on scale-free contact networks are promising for application to low prevalence diseases.

The effect of social distancing on the reach of an epidemic in social networks.

How does social distancing affect the reach of an epidemic in social networks? We present Monte Carlo simulation results of a susceptible-infected-removed with social distancing model. The key feature of the model is that individuals are limited in the number of acquaintances that they can interact with, thereby constraining disease transmission to an infectious subnetwork of the original social network. While increased social distancing typically reduces the spread of an infectious disease, the magnitude varies greatly depending on the topology of the network, indicating the need for policies that are network dependent. Our results also reveal the importance of coordinating policies at the 'global' level. In particular, the public health benefits from social distancing to a group (e.g. a country) may be completely undone if that group maintains connections with outside groups that are not following suit.

The Fractional Preferential Attachment Scale-Free Network Model.

Many networks generated by nature have two generic properties: they are formed in the process of preferential attachment and they are scale-free. Considering these features, by interfering with mechanism of the preferential attachment, we propose a generalisation of the Barabási-Albert model-the 'Fractional Preferential Attachment' (FPA) scale-free network model-that generates networks with time-independent degree distributions p ( k ) ∼ k - γ with degree exponent 2 < γ ≤ 3 (where γ = 3 corresponds to the typical value of the BA model). In the FPA model, the element controlling the network properties is the f parameter, where f ∈ ( 0 , 1 〉 . Depending on the different values of f parameter, we study the statistical properties of the numerically generated networks. We investigate the topological properties of FPA networks such as degree distribution, degree correlation (network assortativity), clustering coefficient, average node degree, network diameter, average shortest path length and features of fractality. We compare the obtained values with the results for various synthetic and real-world networks. It is found that, depending on f, the FPA model generates networks with parameters similar to the real-world networks. Furthermore, it is shown that f parameter has a significant impact on, among others, degree distribution and degree correlation of generated networks. Therefore, the FPA scale-free network model can be an interesting alternative to existing network models. In addition, it turns out that, regardless of the value of f, FPA networks are not fractal.

Network Rewiring in the r-K Plane.

We generate correlated scale-free networks in the configuration model through a new rewiring algorithm that allows one to tune the Newman assortativity coefficient r and the average degree of the nearest neighbors K (in the range - 1 ≤ r ≤ 1 , K ≥ 〈 k 〉 ). At each attempted rewiring step, local variations Δ r and Δ K are computed and then the step is accepted according to a standard Metropolis probability exp ( ± Δ r / T ) , where T is a variable temperature. We prove a general relation between Δ r and Δ K , thus finding a connection between two variables that have very different definitions and topological meaning. We describe rewiring trajectories in the r-K plane and explore the limits of maximally assortative and disassortative networks, including the case of small minimum degree ( k m i n ≥ 1 ), which has previously not been considered. The size of the giant component and the entropy of the network are monitored in the rewiring. The average number of second neighbors in the branching approximation z ¯ 2 , B is proven to be constant in the rewiring, and independent from the correlations for Markovian networks. As a function of the degree, however, the number of second neighbors gives useful information on the network connectivity and is also monitored.

Viral disease spreading in grouped population.

BACKGROUND AND OBJECTIVE: The currently active COVID-19 pandemic has increased, among others, public interest in the computational techniques enabling the study of disease-spreading processes. Thus far, numerous approaches have been used to study the development of epidemics, with special attention paid to the identification of crucial elements that can strengthen or weaken the dynamics of the process. The main thread of this research is associated with the use of the ordinary differential equations method. There also exist several approaches based on the analysis of flows in the Cellular Automata (CA) approach. METHODS: In this paper, we propose a new approach to disease-spread modeling. We start by creating a network that reproduces contacts between individuals in a community. This assumption makes the presented model significantly different from the ones currently dominant in the field. It also changes the approach to the act of infection. Usually, some parameters that describe the rate of new infections by taking into account those infected in the previous time slot are considered. With our model, we can individualize this process, considering each contact individually. RESULTS: The typical output from calculations of a similar type are epidemic curves. In our model, except of presenting the average curves, we show the deviations or ranges for particular results obtained in different simulation runs, which usually lead to significantly different results. This observation is the effect of the probabilistic character of the infection process, which can impact, in different runs, individuals with different significance to the community. We can also easily present the effects of different types of intervention. The effects are studied for different methods used to create the graph representing a community, which can correspond to different social bonds. CONCLUSIONS: We see the potential usefulness of the proposition in the detailed study of epidemic development for specific environments and communities. The ease of entering new parameters enables the analysis of several specific scenarios for different contagious diseases.

Vulnerability analysis of water distribution networks to accidental pipe burst.

Even the best-maintained water distribution network (WDN) might suffer pipe bursts occasionally, and the utility company must reconstruct the damaged sections of the system. The affected area must be segregated by closing the corresponding isolation valves; as a result, the required amount of drinking water might not be available. This paper explores the behaviour and topology of segments, especially their criticality from the viewpoint of the whole system. A novel, objective, dimensionless, segment-based quantity is proposed to evaluate the vulnerability of both the segments and the whole WDN against a single, incidental pipe break, computed as the product of the probability of failure within the segment and the amount of unserved consumption. 27 comprehensive real-life WDNs have been examined by means of the new metric and with the help of complex network theory, exploiting the concept of the degree distribution and topology-based structural properties (e.g. network diameter, clustering coefficient). It was found that metrics based purely on topology suggest different network behaviour as vulnerability analysis, which also includes the hydraulics. The investigation of the global network vulnerabilities has revealed several critically exposed systems, and the local distributions unveiled new properties of WDNs in the case of a random pipe break.

Training LSTM-neural networks on early warning signals of declining cooperation in simulated repeated public good games.

We present results of attempts to expand and enhance the predictive power of Early Warning Signals (EWS) for Critical Transitions (Scheffer et al. 2009) through the deployment of a Long-Short-Term-Memory (LSTM) Neural Network on agent-based simulations of a Repeated Public Good Game, which due to positive feedbacks on experience and social entrainment transits abruptly from majority cooperation to majority defection and back. Our method extension is inspired by several known deficiencies of EWS and by lacking possibilities to consider micro-level interaction in the so far primarily used simulation methods. We find that•The method is applicable to agent-based simulations (as an extension of equation-based methods).•The LSTM yields signals of imminent transitions that can complement statistical indicators of EWS.•The less tensely connected part of an agent population could take a larger role in causing a tipping than the well-connected part.

Adaptive Foraging in Dynamic Environments Using Scale-Free Interaction Networks.

Group interactions are widely observed in nature to optimize a set of critical collective behaviors, most notably sensing and decision making in uncertain environments. Nevertheless, these interactions are commonly modeled using local (proximity) networks, in which individuals interact within a certain spatial range. Recently, other interaction topologies have been revealed to support the emergence of higher levels of scalability and rapid information exchange. One prominent example is scale-free networks. In this study, we aim to examine the impact of scale-free communication when implemented for a swarm foraging task in dynamic environments. We model dynamic (uncertain) environments in terms of changes in food density and analyze the collective response of a simulated swarm with communication topology given by either proximity or scale-free networks. Our results suggest that scale-free networks accelerate the process of building up a rapid collective response to cope with the environment changes. However, this comes at the cost of lower coherence of the collective decision. Moreover, our findings suggest that the use of scale-free networks can improve swarm performance due to two side-effects introduced by using long-range interactions and frequent network regeneration. The former is a topological consequence, while the latter is a necessity due to robot motion. These two effects lead to reduced spatial correlations of a robot's behavior with its neighborhood and to an enhanced opinion mixing, i.e., more diversified information sampling. These insights were obtained by comparing the swarm performance in presence of scale-free networks to scenarios with alternative network topologies, and proximity networks with and without packet loss.

Simple epidemic network model for highly heterogeneous populations.

Network models for disease transmission and dynamics are popular because they are among the simplest agent-based models. Highly heterogeneous populations (in the number of contacts) may be modeled by networks with long-tailed degree distributions for which the variance is much greater than the mean degree. An example is given by scale-free networks where the degree distribution follows a power law. In these type of networks there is not a typical degree. Some nodes may have low representation in the population but are key to drive disease transmission. Coarse graining may be used to simplify these complex networks. In this work we present a simple model consisting in of a network where nodes have only two possible degrees, a low degree close to the mean degree and a high degree about ten times the mean degree. We show that in spite of this extreme simplification, main features of disease dynamics in scale-free networks are well captured by our model.

Analysis of the SAITS alcoholism model on scale-free networks with demographic and nonlinear infectivity.

A more realistic alcoholism model on scale-free networks with demographic and nonlinear infectivity is introduced in this paper. The basic reproduction number [Formula: see text] is derived from the next-generation method. Global stability of the alcohol-free equilibrium is obtained. The persistence of our model is also derived. Furthermore, the SAITS model with nonlinear infectivity is also investigated. Stability of all the equilibria and persistence are also obtained. Some numerical simulations are also presented to verify and extend our theoretical results.

Synaptic Failure Differentially Affects Pattern Formation in Heterogenous Networks.

The communication of neurons is primarily maintained by synapses, which play a crucial role in the functioning of the nervous system. Therefore, synaptic failure may critically impair information processing in the brain and may underlie many neurodegenerative diseases. A number of studies have suggested that synaptic failure may preferentially target neurons with high connectivity (i.e., network hubs). As a result, the activity of these highly connected neurons can be significantly affected. It has been speculated that anesthetics regulate conscious state by affecting synaptic transmission at these network hubs and subsequently reducing overall coherence in the network activity. In addition, hubs in cortical networks are shown to be more vulnerable to amyloid deposition because of their higher activity within the network, causing decrease in coherence patterns and eventually Alzheimer's disease (AD). Here, we investigate how synaptic failure can affect spatio-temporal dynamics of scale free networks, having a power law scaling of number of connections per neuron - a relatively few neurons (hubs) with a lot of emanating or incoming connections and many cells with low connectivity. We studied two types of synaptic failure: activity-independent and targeted, activity-dependent synaptic failure. We defined scale-free network structures based on the dominating direction of the connections at the hub neurons: incoming and outgoing. We found that the two structures have significantly different dynamical properties. We show that synaptic failure may not only lead to the loss of coherence but unintuitively also can facilitate its emergence. We show that this is because activity-dependent synaptic failure homogenizes the activity levels in the network creating a dynamical substrate for the observed coherence increase. Obtained results may lead to better understanding of changes in large-scale pattern formation during progression of neuro-degenerative diseases targeting synaptic transmission.

Controllability, Matching Ratio and Graph Convergence.

There is an important parameter in control theory which is closely related to the directed matching ratio of the network, as shown in the paper of Liu et al. (Nature 473:167-173, 2011). We give proofs of two main statements of Liu et al.  (2011) on the directed matching ratio, which were based on numerical results and heuristics from statistical physics. First, we show that the directed matching ratio of directed random networks given by a fix sequence of degrees is concentrated around its mean. We also examine the convergence of the (directed) matching ratio of a random (directed) graph sequence that converges in the local weak sense, and generalize the result of Elek and Lippner (Proc Am Math Soc 138(8):2939-2947, 2010). We prove that the mean of the directed matching ratio converges to the properly defined matching ratio parameter of the limiting graph. We further show the almost sure convergence of the matching ratios for the most widely used families of scale-free networks, which was the main motivation of Liu et al.  (2011).

Scale-free networks in metabolomics.

Metabolomics is an expanding discipline in biology. It is the process of portraying the phenotype of a cell, tissue or species organism using a comprehensive set of metabolites. Therefore, it is of interest to understand complex systems such as metabolomics using a scale-free topology. Genetic networks and the World Wide Web (WWW) are described as networks with complex topology. Several large networks have vertex connectivity that goes beyond a scale-free power-law distribution. It is observed that (a) networks expand constantly by the addition of recent vertices, and (b) recent vertices attach preferentially to sites that are already well connected. Scalefree networks are determined with precision using vital features such as a structure, a disease and a patient. This is pertinent to the understanding of complex systems such as metabolomics. Hence, we describe the relevance of scale-free networks in the understanding of metabolomics in this article.

Resisting Influence: How the Strength of Predispositions to Resist Control Can Change Strategies for Optimal Opinion Control in the Voter Model.

In this paper, we investigate influence maximization, or optimal opinion control, in a modified version of the two-state voter dynamics in which a native state and a controlled or influenced state are accounted for. We include agent predispositions to resist influence in the form of a probability q with which agents spontaneously switch back to the native state when in the controlled state. We argue that in contrast to the original voter model, optimal control in this setting depends on q: For low strength of predispositions q, optimal control should focus on hub nodes, but for large q, optimal control can be achieved by focusing on the lowest degree nodes. We investigate this transition between hub and low-degree node control for heterogeneous undirected networks and give analytical and numerical arguments for the existence of two control regimes.

Scale invariance in natural and artificial collective systems: a review.

Self-organized collective coordinated behaviour is an impressive phenomenon, observed in a variety of natural and artificial systems, in which coherent global structures or dynamics emerge from local interactions between individual parts. If the degree of collective integration of a system does not depend on size, its level of robustness and adaptivity is typically increased and we refer to it as scale-invariant. In this review, we first identify three main types of self-organized scale-invariant systems: scale-invariant spatial structures, scale-invariant topologies and scale-invariant dynamics. We then provide examples of scale invariance from different domains in science, describe their origins and main features and discuss potential challenges and approaches for designing and engineering artificial systems with scale-invariant properties.