Tantilla hobartsmithi

Number of Pages: 2Integrative BiologyGeological Science

Phase transition of the susceptible-infected-susceptible dynamics on time-varying configuration model networks

We present a degree-based theoretical framework to study the susceptible-infected-susceptible (SIS) dynamics on time-varying (rewired) configuration model networks. Using this framework, we provide a detailed analysis of the stationary state that covers, for a given structure, every dynamic regimes easily tuned by the rewiring rate. This analysis is suitable for the characterization of the phase transition and leads to three main contributions. (i) We obtain a self-consistent expression for the absorbing-state threshold, able to capture both collective and hub activation. (ii) We recover the predictions of a number of existing approaches as limiting cases of our analysis, providing thereby a unifying point of view for the SIS dynamics on random networks. (iii) We reinterpret the concept of hub-dominated phase transition. Within our framework, it appears as a heterogeneous critical phenomenon : observables for different degree classes have a different scaling with the infection rate. This leads to the successive activation of the degree classes beyond the epidemic threshold.Comment: 14 pages, 11 figure

Developments in the Control of Foreign Investment in France

This Article will first review the legal provisions for the control of foreign investment in France and then will analyze them in light of France\u27s position in the Common Market and its other international obligations. Finally, it will attempt to describe the developing guidelines established by the government for foreign investment and will illustrate the application of these guidelines by a survey of recent investment cases

Control of Foreign Investment in France

The principle of freedom of investment by foreigners in France has, with few statutory exceptions, long been recognized in French law. In practice, however, exchange controls, requiring French government authorization for all foreign exchange transactions within France, have supplied the legal foundation for governmental control of foreign investment. Initiated in 1939 as a wartime measure to stem the outflow of the nation\u27s currency to safer havens,1 exchange controls were continued in the postwar era to protect a weak currency and were elaborated, in piecemeal fashion, to suit diverse and changing governmental policies. The complex and pervasive regulations provided an instrument which could be used not only to protect France\u27s monetary position but also to safeguard other national interests affected by foreign investment. In fact, exchange controls were used by the government to screen all foreign investment, and to limit those deemed inconsistent with French economic planning or political interests

Deep learning of contagion dynamics on complex networks

Forecasting the evolution of contagion dynamics is still an open problem to which mechanistic models only offer a partial answer. To remain mathematically or computationally tractable, these models must rely on simplifying assumptions, thereby limiting the quantitative accuracy of their predictions and the complexity of the dynamics they can model. Here, we propose a complementary approach based on deep learning where effective local mechanisms governing a dynamic on a network are learned from time series data. Our graph neural network architecture makes very few assumptions about the dynamics, and we demonstrate its accuracy using different contagion dynamics of increasing complexity. By allowing simulations on arbitrary network structures, our approach makes it possible to explore the properties of the learned dynamics beyond the training data. Finally, we illustrate the applicability of our approach using real data of the COVID-19 outbreak in Spain. Our results demonstrate how deep learning offers a new and complementary perspective to build effective models of contagion dynamics on networks

Tantilla planiceps

Number of Pages: 2Integrative BiologyGeological Science

Deep learning of contagion dynamics on complex networks

Forecasting the evolution of contagion dynamics is still an open problem to which mechanistic models only offer a partial answer. To remain mathematically or computationally tractable, these models must rely on simplifying assumptions, thereby limiting the quantitative accuracy of their predictions and the complexity of the dynamics they can model. Here, we propose a complementary approach based on deep learning where the effective local mechanisms governing a dynamic on a network are learned from time series data. Our graph neural network architecture makes very few assumptions about the dynamics, and we demonstrate its accuracy using different contagion dynamics of increasing complexity. By allowing simulations on arbitrary network structures, our approach makes it possible to explore the properties of the learned dynamics beyond the training data. Finally, we illustrate the applicability of our approach using real data of the COVID-19 outbreak in Spain. Our results demonstrate how deep learning offers a new and complementary perspective to build effective models of contagion dynamics on networks