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Moving the epidemic tipping point through topologically targeted social distancing

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arXiv 2021年

作者： Ansari, Sara Anvari, Mehrnaz Pfeffer, Oskar Molkenthin, Nora Hellmann, Frank Heitzig, Jobst Kurths, Jürgen FutureLab on Game Theory and Networks of Interacting Agents Complexity Science Department Potsdam Institute for Climate Impact Research Leibniz Association PO Box 601203 Potsdam14412 Germany Potsdam Institute for Climate Impact Research Potsdam14473 Germany Institute of Theoretical Physics Technische Universität Berlin Hardenbergstr. 36 BerlinD-10623 Germany Institute of Physics Humboldt University Berlin12489 Germany

The epidemic threshold of a social system is the ratio of infection and recovery rate above which a disease spreading in it becomes an epidemic. In the absence of pharmaceutical interventions (i.e. vaccines), the only way to control a given disease is to move this threshold by non-pharmaceutical interventions like social distancing, past the epidemic threshold corresponding to the disease, thereby tipping the system from epidemic into a non-epidemic regime. Modeling the disease as a spreading process on a social graph, social distancing can be modeled by removing some of the graphs links. It has been conjectured that the largest eigenvalue of the adjacency matrix of the resulting graph corresponds to the systems epidemic threshold. Here we use a Markov chain Monte Carlo (MCMC) method to study those link removals that do well at reducing the largest eigenvalue of the adjacency matrix. The MCMC method generates samples from the relative canonical network ensemble with a defined expectation value of λmax. We call this the "well-controlling network ensemble" (WCNE) and compare its structure to randomly thinned networks with the same link density. We observe that networks in the WCNE tend to be more homogeneous in the degree distribution and use this insight to define two ad-hoc removal strategies, which also substantially reduce the largest eigenvalue. A targeted removal of 80% of links can be as effective as a random removal of 90%, leaving individuals with twice as many contacts. Finally, by simulating epidemic spreading via either an SIS or an SIR model on network ensembles created with different link removal strategies (random, WCNE, or degree-homogenizing), we show that tipping from an epidemic to a non-epidemic state happens at a larger critical ratio between infection rate and recovery rate for WCNE and degree-homogenized networks than for those obtained by random removals. © 2021, CC BY.

关键词： Disease control

Resilience basins of complex systems: an application to prosumer impacts on power grids

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arXiv 2021年

作者： Bien, Samuel Schultz, Paul Heitzig, Jobst Donges, Jonathan F. Institute of Environmental Science and Geography Potsdam University Potsdam14469 Germany Institute of Physics Potsdam University Potsdam14469 Germany Complexity Science Department Potsdam Institute for Climate Impact Research Potsdam14473 Germany FutureLab for Earth Resilience in the Anthropocene Earth System Analysis Department Potsdam Institute for Climate Impact Research Potsdam14473 Germany 50Hertz Transmission GmbH Berlin10557 Germany FutureLab for Game Theory and Networks of Interacting Agents Potsdam Institute for Climate Impact Research Potsdam14473 Germany Stockholm Resilience Centre Stockholm University Stockholm106 91 Sweden

Comparable to the traditional notion of stability in system dynamics, resilience is typically measured in a way that assesses the quality of a system’s response, for example the speed of its *** present a broadly applicable complementary measurement framework that quantifies resilience similarly to basin stability by estimating a resilience basin which reflects the extent of adverse influences that the system can recover from in a sufficient manner. In contrast to basin stability, the adverse influences considered here are not necessarily displacements in state space, but arbitrarily complex impacts to the system, quantified by adequate parameters. As a proof of concept, we present two applications: (i) the well-studied single-node power system as an easy-to-follow example and (ii) a stochastic model of a low-voltage DC power grid undergoing an unregulated energy transition consisting in the random appearance of prosumers. These act as decentral suppliers of photovoltaic power and alter the flow patterns while the grid topology remains unchanged. The resilience measurement framework is applied to evaluate the effect and efficiency of two response options: (i) upgrading the capacity of existing power lines and (ii) installing batteries in the prosumer households. The framework demonstrates that line upgrades can provide potentially unlimited resilience against energy decentralization, while household batteries are inherently limited (achieving ≤ 70% of the resilience of line upgrades). Further, the framework aids in optimizing budget efficiency by pointing toward threshold budget values as well as budget-dependent ideal strategies for the allocation of line upgrades and for the battery charging algorithm. Copyright © 2021, The Authors. All rights reserved.

关键词： Stochastic models

Efficient democratic decisions via nondeterministic proportional consensus

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arXiv 2020年

作者： Heitzig, Jobst Simmons, Forest W. FutureLab on Game Theory and Networks of Interacting Agents Potsdam Institute for Climate Impact Research PO Box 60 12 03 PotsdamD-14412 Germany Liberal Arts & Mathematics Division Portland Community College Cascade Campus 705 N. Killingsworth Street TH 220 PortlandOR97217 United States

Are there voting methods which (i) give everyone, including minorities, an equal share of effective power even if voters act strategically, (ii) promote consensus rather than polarization and inequality, and (iii) do not favour the status quo or rely too much on chance? We show the answer is yes by describing two nondeterministic voting methods, one based on automatic bargaining over lotteries, the other on conditional commitments to approve compromise options. Our theoretical analysis and agent-based simulation experiments suggest that with these, majorities cannot consistently suppress minorities as with deterministic methods, proponents of the status quo cannot block decisions as in consensus-based approaches, the resulting aggregate welfare is comparable to existing methods, and average randomness is lower than for other nondeterministic *** Codes 91B14, 91A80, 91B12 Copyright © 2020, The Authors. All rights reserved.

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A DYNAMIC NETWORK MODEL OF SOCIETAL COMPLEXITY AND RESILIENCE INSPIRED BY TAINTER’S theory OF COLLAPSE

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arXiv 2021年

作者： Schunck, Florian Wiedermann, Marc Heitzig, Jobst Donges, Jonathan F. Helmholtz Centre for Environmental Research GmbH—UFZ Research Group System Ecotox Permoserstraße 15 Leipzig04318 Germany Osnabrück University Institute of Mathematics Research Group System Science Barbarastraße 12 Osnabrück49076 Germany Potsdam Institute for Climate Impact Research Member of the Leibniz Association FutureLab on Game Theory and Networks of Interacting Agents P.O. Box 60 12 03 PotsdamD-14412 Germany Potsdam Institute for Climate Impact Research Member of the Leibniz Association FutureLab on Earth Resilience in the Anthropocene P.O. Box 60 12 03 PotsdamD-14412 Germany Stockholm Resilience Centre Stockholm University Kräftriket 2B Stockholm106 91 Sweden

In recent years, several global events have severely disrupted economies and social structures, undermining confidence in the resilience of modern societies. Examples include the COVID-19 pandemic, which brought unprecedented health challenges and economic disruptions, and the emergence of geopolitical tensions and conflicts that have further strained international relations and economic stability. While empirical evidence on the dynamics and drivers of past societal collapse is mounting, a process-based understanding of these dynamics is still in its infancy. Here we aim to identify and illustrate the underlying drivers of such societal instability or even collapse. The inspiration for this work is Joseph Tainter’s theory of the "collapse of complex societies", which postulates that the complexity of societies increases as they solve problems, leading to diminishing returns on complexity investments, and ultimately to collapse. In this work we have abstracted this theory into a low-dimensional and stylised model of two classes of networked agents, hereafter referred to as "laborers" and "administrators". We numerically modeled the dynamics of societal complexity, measured as the fraction of "administrators", which is assumed to affect the productivity of connected energy-producing "laborers". We show that collapse becomes increasingly likely as the complexity of the model society continuously increases in response to external stresses that emulate Tainter’s abstract notion of problems that societies must solve. We also provide an analytical approximation of the system’s dominant dynamics, which matches well with the numerical experiments, and use it to study the influence on network link density, social mobility and productivity. Our work advances the understanding of social-ecological collapse and illustrates its potentially direct link to an ever-increasing societal complexity in response to external shocks or stresses via a self-reinforcing feedback. © 2021, CC

关键词： Investments

A modeler's guide to studying the resilience of social-technical-environmental systems

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arXiv 2020年

作者： Tamberg, Lea A. Heitzig, Jobst Donges, Jonathan Friedemann Institute of Environmental Systems Research University of Osnabrück Barbarastraße 12 Osnabrück49076 Germany FutureLab Earth Resilience in the Anthropocene Earth System Analysis Potsdam Institute for Climate Impact Research Member of the Leibniz Association Telegrafenberg A31 Potsdam14473 Germany FutureLab on Game Theory and Networks of Interacting Agents Complexity Science Potsdam Institute for Climate Impact Research Member of the Leibniz Association Telegrafenberg A31 Potsdam14473 Germany Stockholm Resilience Centre Stockholm University Kräftriket 2B Stockholm114 19 Sweden

The term 'resilience' is increasingly being used in social-technical-environmental systems sciences and particularly also in the Earth system sciences. However, the diversity of resilience concepts and a certain (sometimes intended) openness of proposed definitions can lead to misunderstandings and may impede their application to complex systems modelling. We propose a guideline that aims to ease communication as well as to support systematic development of research questions and models in the context of resilience. It can be applied independently of the modelling framework or underlying theory of choice. At the heart of this guideline is a checklist consisting of four questions to be answered: (i) Resilience of what? (ii) Resilience regarding what? (iii) Resilience against what? (iv) Resilience how? We refer to the answers to these resilience questions as the "system", the "sustainant", the "adverse influence", and the "response options". The term 'sustainant' is a neologism describing the feature of the system (state, structure, function, pathway, . . .) that should be maintained (or restored quickly enough) in order to call the system resilient. The use of this proposed guideline in the field of Earth system resilience is demonstrated for the application example of a potential climate tipping element: the Amazon rainforest. The example illustrates the diversity of possible answers to the checklist's questions as well as their benefits in structuring the modelling process. The guideline supports the modeller in communicating precisely what is actually meant by 'resilience' in a specific context. This combination of freedom and precision could help to advance the resilience discourse by building a bridge between those demanding unambiguous definitions and those stressing the benefits of generality and flexibility of the resilience concept. Copyright © 2020, The Authors. All rights reserved.

关键词： Earth system models

Anticipation-induced social tipping – Can the environment be stabilised by social dynamics?

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arXiv 2020年

作者： Müller, Paul Manuel Heitzig, Jobst Kurths, Jürgen Lüdge, Kathy Wiedermann, Marc FutureLab on Game Theory and Networks of Interacting Agents Potsdam Institute for Climate Impact Research PO Box 60 12 03 Potsdam14412 Germany Institute for Theoretical Physics Technische Universität Berlin Hardenbergstraße 36 Berlin10623 Germany Department of Neurology Charité - Universitätsmedizin Berlin Charitéplatz 1 Berlin10117 Germany Centre for Analysis of Complex Systems Sechenov First Moscow State Medical University Moscow Russia

Macroscopic approximation methods for the analysis of adaptive networked agent-based models: The example of a two-sector investment model

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arXiv 2019年

作者： Kolb, Jakob J. Müller-Hansen, Finn Kurths, Jürgen Heitzig, Jobst FutureLab on Game Theory and Networks of Interacting Agents Potsdam Institute for Climate Impact Research Potsdam Germany Department of Physics Humboldt University Berlin Berlin Germany Mercator Research Institute on Global Commons and Climate Change Berlin Germany Potsdam Institute for Climate Impact Research Potsdam Germany

In this paper, we propose a statistical aggregation method for agent-based models with heterogeneous agents that interact both locally on a complex adaptive network and globally on a market. The method combines three approaches from statistical physics: (a) moment closure, (b) pair approximation of adaptive network processes, and (c) thermodynamic limit of the resulting stochastic process. As an example of use, we develop a stochastic agent-based model with heterogeneous households that invest in either a fossil-fuel or renewables-based sector while allocating labor on a competitive market. Using the adaptive voter model, the model describes agents as social learners that interact on a dynamic network. We apply the approximation methods to derive a set of ordinary differential equations that approximate the macro-dynamics of the model. A comparison of the reduced analytical model with numerical simulations shows that the approximation fits well for a wide range of parameters. The proposed method makes it possible to use analytical tools to better understand the dynamical properties of models with heterogeneous agents on adaptive networks. We showcase this with a bifurcation analysis that identifies parameter ranges with multi-stabilities. The method can thus help to explain emergent phenomena from network interactions and make them mathematically traceable. Copyright © 2019, The Authors. All rights reserved.

关键词： Computational methods

Optimization of coupling and global collapse in diffusively coupled socio-ecological resource exploitation networks

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arXiv 2020年

作者： Holstein, Tanja Wiedermann, Marc Kurths, Jürgen FutureLab on Game Theory & Networks of Interacting Agents Complexity Science Potsdam Institute for Climate Impact Research Leibniz Association P.O. Box 60 12 03 Potsdam14412 Germany Department of Physics Humboldt University Newtonstr. 15 Berlin12489 Germany Federal Institute for Materials Research and Testing Unter den Eichen 87 Berlin12205 Germany Complexity Science Potsdam Institute for Climate Impact Research Leibniz Association P.O. Box 60 12 03 Potsdam14412 Germany Lobachevsky University of Nizhny Novgorod Nizhnij Novgorod603950 Russia

Single- and multi-layer complex networks have been proven as a powerful tool to study the dynamics within social, technological, or natural systems. An often observed common goal there is to optimize these systems for specific purposes by minimizing certain costs while maximizing a desired output. Acknowledging that especially real-world systems from the coupled socio-ecological realm are highly intertwined this work exemplifies that in such systems the optimization of a certain subsystem, e.g., to increase the resilience against external pressure in an ecological network, may unexpectedly diminish the stability of the whole coupled system. For this purpose we utilize an adaptation of a previously proposed conceptual bilayer network model composed of an ecological network of diffusively coupled resources co-evolving with a social network of interacting agents that harvest these resources and learn each other’s strategies depending on individual success. We derive an optimal coupling strength that prevents a collapse in as many resources as possible if one assumes that the agents’ strategies remain constant over time. However, we then show that if agents socially learn and adapt strategies according to their neighbors’ success, this optimal coupling strength is revealed to be a critical parameter above which the probability for a global collapse in terms of irreversibly depleted resources is high – an effect that we denote the tragedy of the optimizer. We thus find that measures which stabilize the dynamics within a certain part of a larger co-evolutionary system may unexpectedly cause the emergence of novel undesired globally stable states. Our results therefore underline the importance of holistic approaches for managing socio-ecological systems because stabilizing effects which focus on single subsystems may be counter-beneficial for the system as a whole. Copyright © 2020, The Authors. All rights reserved.

关键词： Complex networks

Deep reinforcement learning in World-Earth system models to discover sustainable management strategies

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arXiv 2019年

作者： Strnad, Felix M. Barfuss, Wolfram Donges, Jonathan F. Heitzig, Jobst Potsdam Institute for Climate Impact Research FutureLab on Game Theory and Networks of Interacting Agents Research Department 4: Complexity Science Potsdam14473 Germany Department of Physics University of Göttingen Göttingen37077 Germany Potsdam Institute for Climate Impact Research FutureLab on Earth Resilience in the Anthropocene Research Department 1: Earth System Analysis Potsdam14473 Germany Max Planck Institute for Mathematics in the Sciences Leipzig04103 Germany Stockholm Resilience Center Stockholm University Stockholm104 05 Sweden

Increasingly complex, non-linear World-Earth system models are used for describing the dynamics of the biophysical Earth system and the socio-economic and socio-cultural World of human societies and their interactions. Identifying pathways towards a sustainable future in these models for informing policy makers and the wider public, e.g. pathways leading to a robust mitigation of dangerous anthropogenic climate change, is a challenging and widely investigated task in the field of climate research and broader Earth system science. This problem is particularly difficult when constraints on avoiding transgressions of planetary boundaries and social foundations need to be taken into account. In this work, we propose to combine recently developed machine learning techniques, namely deep reinforcement learning (DRL), with classical analysis of trajectories in the World-Earth system. Based on the concept of the agent-environment interface, we develop an agent that is generally able to act and learn in variable manageable environment models of the Earth system. We demonstrate the potential of our framework by applying DRL algorithms to two stylized World-Earth system models. Conceptually, we explore thereby the feasibility of finding novel global governance policies leading into a safe and just operating space constrained by certain planetary and socio-economic boundaries. The artificially intelligent agent learns that the timing of a specific mix of taxing carbon emissions and subsidies on renewables is of crucial relevance for finding World-Earth system trajectories that are sustainable on the long term. Copyright © 2019, The Authors. All rights reserved.

关键词： Earth system models