Physics

The spatial distribution of population and activities within urban areas, or urban form at the mesoscopic scale, is the outcome of multiple antagonist processes. We propose in this paper to benchmark different models of urban morphogenesis, to systematically compare the urban forms they can produce. Different types of approaches are included, such as a reaction-diffusion model, a gravity-based model, and correlated percolation. Applying a diversity search algorithm, we estimate the feasible space of each model within a space of urban form indicators, in comparison of empirical values for worldwide urban areas. We find a complementarity of the different types of processes, advocating for a plurality of urban models.

The Mean Field Approximation (MFA), or continuum method, is often used in courses on Networks to derive the degree distribution of preferential attachment networks. This method is simple and the outcome is close to the correct answer. However, this paper shows that the method is flawed in several aspects, leading to unresolvable contradictions. More importantly, the MFA is not explicitly derived from a mathematical model. An analysis of the implied model shows that it makes an approximation which is far from the truth and another one which can not be motivated in general. The success of the MFA for preferential attachment networks is therefore accidental and the method is not suitable for teaching undergraduates.

In the past twenty years several events disrupted global economies and social well-being and generally shook the confidence in the stability of western societies such as during the 2008 financial crisis and its economic aftermath. Here, we aim to identify and illustrate underlying drivers of such societal instability or even consequential collapse. For this purpose we propose a low-dimensional and stylised model of two classes of networked agents (termed "labourers" and "administrators" hereafter) that is inspired by Joseph Tainter's theory of collapse of complex societies. We numerically model the dynamics of societal complexity, measured as the share of "administrators", which is assumed to affect the productivity of energy-producing `labourers". We show that collapse becomes increasingly likely if the model society's complexity continuously increases in response to external stresses that emulate Tainter's abstract notion of problems that societies need to solve. We additionally provide an analytical approximation of the system's dominant dynamics which matches well with the numerical experiments, thus, allowing for a precise estimate of tipping points beyond which societal collapse is triggered. The administration's ability for increasing productivity of labour shows to be the most influential parameter for longer survival times which is additionally fostered by a minimum level of social connectivity. Finally, we show that agents' stochastic transitions between labour force and administration, i.e. social mobility, can increase the survival time of the modeled society even further. Our work fosters the understanding of socio-ecological collapse and illustrates its potentially direct link to an ever increasing complexity in response to external shocks or stress via a self-reinforcing feedback.

One of the central tools to control the COVID-19 pandemics is the knowledge of its spreading dynamics. Here we develop a fractal model capable of describe this dynamics, in term of daily new cases, and provide quantitative criteria for some predictions. We propose a fractal dynamical model using conformed derivative and fractal time scale. A Burr-XII shaped solution of the fractal-like equation is obtained. The model is tested using data from several countries, showing that a single function is able to describe very different shapes of the outbreak. The diverse behavior of the outbreak on those countries is presented and discussed. Moreover, a criterion to determine the existence of the pandemic peak and a expression to find the time to reach herd immunity are also obtained.

A multilayer network approach combines different network layers, which are connected by interlayer edges, to create a single mathematical object. These networks can contain a variety of information types and represent different aspects of a system. However, the process for selecting which information to include is not always straightforward. Using data on two agonistic behaviors in a captive population of monk parakeets (Myiopsitta monachus), we developed a framework for investigating how pooling or splitting behaviors at the scale of dyadic relationships (between two individuals) affects individual- and group-level social properties. We designed two reference models to test whether randomizing the number of interactions across behavior types results in similar structural patterns as the observed data. Although the behaviors were correlated, the first reference model suggests that the two behaviors convey different information about some social properties and should therefore not be pooled. However, once we controlled for data sparsity, we found that the observed measures corresponded with those from the second reference model. Hence, our initial result may have been due to the unequal frequencies of each behavior. Overall, our findings support pooling the two behaviors. Awareness of how selected measurements can be affected by data properties is warranted, but nonetheless our framework disentangles these efforts and as a result can be used for myriad types of behaviors and questions. This framework will help researchers make informed and data-driven decisions about which behaviors to pool or separate, prior to using the data in subsequent multilayer network analyses.

We provide a general analytic solution to Herbert Simon's 1955 model for time-evolving novelty functions. This has far-reaching consequences: Simon's is a pre-cursor model for Barabasi's 1999 preferential attachment model for growing social networks, and our general abstraction of it more considers attachment to be a form of link selection. We show that any system which can be modeled as instances of types---i.e., occurrence data (frequencies)---can be generatively modeled (and simulated) from a distributional perspective with an exceptionally high-degree of accuracy.

When the interactions of agents on a network are assumed to follow the Deffuant opinion dynamics model, the outcomes are known to depend on the structure of the underlying network. This behavior cannot be captured by existing mean-field approximations for the Deffuant model. In this paper, a generalised mean-field approximation is derived that accounts for the effects of network topology on Deffuant dynamics through the degree distribution or community structure of the network. The accuracy of the approximation is examined by comparison with large-scale Monte Carlo simulations on both synthetic and real-world networks.

Many spreading processes in our real-life can be considered as a complex contagion, and the linear threshold (LT) model is often applied as a very representative model for this mechanism. Despite its intensive usage, the LT model suffers several limitations in describing the time evolution of the spreading. First, the discrete-time step that captures the speed of the spreading is vaguely defined. Second, the synchronous updating rule makes the nodes infected in batches, which can not take individual differences into account. Finally, the LT model is incompatible with existing models for the simple contagion. Here we consider a generalized linear threshold (GLT) model for the continuous-time stochastic complex contagion process that can be efficiently implemented by the Gillespie algorithm. The time in this model has a clear mathematical definition and the updating order is rigidly defined. We find that the traditional LT model systematically underestimates the spreading speed and the randomness in the spreading sequence order. We also show that the GLT model works seamlessly with the susceptible-infected (SI) or susceptible-infected-recovered (SIR) model. One can easily combine them to model a hybrid spreading process in which simple contagion accumulates the critical mass for the complex contagion that leads to the global cascades. Overall, the GLT model we proposed can be a useful tool to study complex contagion, especially when studying the time evolution of the spreading.

We have developed a globally applicable diagnostic Covid-19 model by augmenting the classical SIR epidemiological model with a neural network module. Our model does not rely upon previous epidemics like SARS/MERS and all parameters are optimized via machine learning algorithms employed on publicly available Covid-19 data. The model decomposes the contributions to the infection timeseries to analyze and compare the role of quarantine control policies employed in highly affected regions of Europe, North America, South America and Asia in controlling the spread of the virus. For all continents considered, our results show a generally strong correlation between strengthening of the quarantine controls as learnt by the model and actions taken by the regions' respective governments. Finally, we have hosted our quarantine diagnosis results for the top 70 affected countries worldwide, on a public platform, which can be used for informed decision making by public health officials and researchers alike.

With the hit of new pandemic threats, scientific frameworks are needed to understand the unfolding of the epidemic. The use of mobile apps that are able to trace contacts is of utmost importance in order to control new infected cases and contain further propagation. Here we present a theoretical approach using both percolation and message--passing techniques, to the role of contact tracing, in mitigating an epidemic wave. We show how the increase of the app adoption level raises the value of the epidemic threshold, which is eventually maximized when high-degree nodes are preferentially targeted. Analytical results are compared with extensive Monte Carlo simulations showing good agreement for both homogeneous and heterogeneous networks. These results are important to quantify the level of adoption needed for contact-tracing apps to be effective in mitigating an epidemic.