Physics

Real-world complex systems often comprise many distinct types of elements as well as many more types of networked interactions between elements. When the relative abundances of types can be measured well, we further observe heavy-tailed categorical distributions for type frequencies. For the comparison of type frequency distributions of two systems or a system with itself at different time points in time -- a facet of allotaxonometry -- a great range of probability divergences are available. Here, we introduce and explore `probability-turbulence divergence', a tunable, straightforward, and interpretable instrument for comparing normalizable categorical frequency distributions. We model probability-turbulence divergence (PTD) after rank-turbulence divergence (RTD). While probability-turbulence divergence is more limited in application than rank-turbulence divergence, it is more sensitive to changes in type frequency. We build allotaxonographs to display probability turbulence, incorporating a way to visually accommodate zero probabilities for `exclusive types' which are types that appear in only one system. We explore comparisons of example distributions taken from literature, social media, and ecology. We show how probability-turbulence divergence either explicitly or functionally generalizes many existing kinds of distances and measures, including, as special cases, L (p) norms, the Sørensen-Dice coefficient (the F 1 statistic), and the Hellinger distance. We discuss similarities with the generalized entropies of R{é}nyi and Tsallis, and the diversity indices (or Hill numbers) from ecology. We close with thoughts on open problems concerning the optimization of the tuning of rank- and probability-turbulence divergence.

Non-pharmaceutical interventions (NPIs) such as quarantine, self-isolation, social distancing, and virus-contact tracing can greatly reduce the spread of the virus during a pandemic. In the wave of the COVID-19 pandemic, many countries have implemented various NPIs for infection control and mitigation. However, the stringency of the NPIs and the resulting impact among different countries remain unclear due to the lack of quantitative factors. In this study we took a further step to incorporate the effect of the NPIs into the pandemic dynamics model using the concept of policy intensity factor (PIF). This idea enables us to characterize the transition rates as time varying quantities instead of constant values, and thus capturing the dynamical behavior of the basic reproduction number variation in the pandemic. By leveraging a great amount of data reported by the governments and the World Health Organization, we projected the dynamics of the pandemic for the major economies in the world, including the numbers of infected, susceptible, and recovered cases, as well as the pandemic durations. It is observed that the proposed variable-rate susceptible-exposed-infected-recovered (VR-SEIR) model fits and projects the pandemic dynamics very well. We further showed that the resulting PIFs correlate with the stringency of NPIs, which allows us to project the final affected numbers of people in those countries when their current NPIs have been imposed for 90, 180, 360 days. It provides a quantitative insight into the effectiveness of the implemented NPIs, and sheds a new light on minimizing both affected people from COVID-19 and the economic impact.

The evolution of complex transport networks is investigated under three strategies of link removal: random, intentional attack and "Pseudo-Darwinian" strategy. At each evolution step and regarding the selected strategy, one removes either a randomly chosen link, or the link carrying the strongest flux, or the link with the weakest flux, respectively. We study how the network structure and the total flux between randomly chosen source and drain nodes evolve. We discover a universal power-law decrease of the total flux, followed by an abrupt transport collapse. The time of collapse is shown to be determined by the average number of links per node in the initial network, highlighting the importance of this network property for ensuring safe and robust transport against random failures, intentional attacks and maintenance cost optimizations.

Typically, mathematical simulation studies on COVID-19 pandemic forecasting are based on deterministic differential equations which assume that both the number ( n ) of individuals in various epidemiological classes and the time ( t ) on which they depend are quantities that vary continuous. This picture contrasts with the discrete representation of n and t underlying the real epidemiological data reported in terms daily numbers of infection cases, for which a description based on finite difference equations would be more adequate. Adopting a logistic growth framework, in this paper we present a quantitative analysis of the errors introduced by the continuous time description. This analysis reveals that, although the height of the epidemiological curve maximum is essentially unaffected, the position T c 1/2 obtained within the continuous time representation is systematically shifted backwards in time with respect to the position T d 1/2 predicted within the discrete time representation. Rather counterintuitively, the magnitude of this temporal shift τ≡ T c 1/2 − T d 1/2 <0 is basically insensitive to changes in infection rate κ . For a broad range of κ values deduced from COVID-19 data at extreme situations (exponential growth in time and complete lockdown), we found a rather robust estimate τ≃−2.65 day −1 . Being obtained without any particular assumption, the present mathematical results apply to logistic growth in general without any limitation to a specific real system.

Public policy must confront emergencies that evolve in real time and in uncertain directions, yet little is known about the nature of policy response. Here we take the coronavirus pandemic as a global and extraordinarily consequential case, and study the global policy response by analyzing a novel dataset recording policy documents published by government agencies, think tanks, and intergovernmental organizations (IGOs) across 114 countries (37,725 policy documents from Jan 2nd through May 26th 2020). Our analyses reveal four primary findings. (1) Global policy attention to COVID-19 follows a remarkably similar trajectory as the total confirmed cases of COVID-19, yet with evolving policy focus from public health to broader social issues. (2) The COVID-19 policy frontier disproportionately draws on the latest, peer-reviewed, and high-impact scientific insights. Moreover, policy documents that cite science appear especially impactful within the policy domain. (3) The global policy frontier is primarily interconnected through IGOs, such as the WHO, which produce policy documents that are central to the COVID19 policy network and draw especially strongly on scientific literature. Removing IGOs' contributions fundamentally alters the global policy landscape, with the policy citation network among government agencies increasingly fragmented into many isolated clusters. (4) Countries exhibit highly heterogeneous policy attention to COVID-19. Most strikingly, a country's early policy attention to COVID-19 shows a surprising degree of predictability for the country's subsequent deaths. Overall, these results uncover fundamental patterns of policy interactions and, given the consequential nature of emergent threats and the paucity of quantitative approaches to understand them, open up novel dimensions for assessing and effectively coordinating global and local responses to COVID-19 and beyond.

The spatial homogeneity of an urban road network (URN) measures whether each distinct component is analogous to the whole network and can serve as a quantitative manner bridging network structure and dynamics. However, given the complexity of cities, it is challenging to quantify spatial homogeneity simply based on conventional network statistics. In this work, we use Graph Neural Networks to model the 11,790 URN samples across 30 cities worldwide and use its predictability to define the spatial homogeneity. The proposed measurement can be viewed as a non-linear integration of multiple geometric properties, such as degree, betweenness, road network type, and a strong indicator of mixed socio-economic events, such as GDP and population growth. City clusters derived from transferring spatial homogeneity can be interpreted well by continental urbanization histories. We expect this novel metric supports various subsequent tasks in transportation, urban planning, and geography.

The reputation of firms is largely channeled through their ownership structure. We use this relation to determine reputation spillovers between transnational companies and their participated companies in an ownership network core of 1318 firms. We then apply concepts of network controllability to identify minimum sets of driver nodes (MDS) of 314 firms in this network. The importance of these driver nodes is classified regarding their control contribution, their operating revenue, and their reputation. The latter two are also taken as proxies for the access costs when utilizing firms as driver nodes. Using an enrichment analysis, we find that firms with high reputation maintain the controllability of the network, but rarely become top drivers, whereas firms with medium reputation most likely become top driver nodes. We further show that MDSs with lower access costs can be used to control the reputation dynamics in the whole network.

This paper investigates the fairness of the 2018 FIFA World Cup qualification process via Monte-Carlo simulations. The qualifying probabilities are calculated for 102 nations, all teams except for African and European countries, on the basis of their Elo ratings, which is used for seeding in each qualification, too. A method is proposed to quantify the degree of unfairness. Although the qualifications within four FIFA confederations are constructed fairly, serious differences are found between the continents: for example, a South American team could have doubled its chances by playing in Asia. Choosing a fixed matchup in the inter-continental play-offs instead of the current random draw can reduce the level of unfairness. The move of Australia from the Oceanian to the Asian zone is shown to increase its probability of participating in the 2018 FIFA World Cup by about 75\%. Our results provide important insights for the administrators on how to reallocate the qualifying berths.

Traffic systems are complex systems that exhibit non-stationary characteristics. Therefore, the identification of temporary traffic states is significant. In contrast to the usual correlations of time series, here we study those of position series, revealing structures in time, i.e. the rich non-Markovian features of traffic. Considering the traffic system of the Cologne orbital motorway as a whole, we identify five quasi-stationary states by clustering reduced rank correlation matrices of flows using the k -means method. The five quasi-stationary states with nontrivial features include one holiday state, three workday states and one mixed state of holidays and workdays. In particular, the workday states and the mixed state exhibit strongly correlated time groups shown as diagonal blocks in the correlation matrices. We map the five states onto reduced-rank correlation matrices of velocities and onto traffic states where free or congested states are revealed in both space and time. Our study opens a new perspective for studying traffic systems. This contribution is meant to provide a proof of concept and a basis for further study.

Global coordination is required to solve a wide variety of challenging collective action problems from network colorings to the tragedy of the commons. Recent empirical study shows that the presence of a few noisy autonomous agents can greatly improve collective performance of humans in solving networked color coordination games. To provide further analytical insights into the role of behavioral randomness, here we study myopic artificial agents attempt to solve similar network coloring problems using decision update rules that are only based on local information but allow random choices at various stages of their heuristic reasonings. We consider that agents are distributed over a random bipartite network which is guaranteed to be solvable with two colors. Using agent-based simulations and theoretical analysis, we show that the resulting efficacy of resolving color conflicts is dependent on the specific implementation of random behavior of agents, including the fraction of noisy agents and at which decision stage noise is introduced. Moreover, behavioral randomness can be finely tuned to the specific underlying population structure such as network size and average network degree in order to produce advantageous results in finding collective coloring solutions. Our work demonstrates that distributed greedy optimization algorithms exploiting local information should be deployed in combination with occasional exploration via random choices in order to overcome local minima and achieve global coordination.