Since the beginning of the COVID-19 spreading, the number of studies on the epidemic models increased dramatically. It is important for policy makers to know how the disease will spread, and what are the effects of the policies and environment on the
spreading. In this paper, we propose two extensions to the standard infectious disease models: (a) We consider the prevention measures adopted based on the current severity of the infection, those measures are adaptive and change over time. (b) Multiple cities and regions are considered, with population movements between those cities/regions, while taking into account that each region may have different prevention measures. While the adaptive measures and mobility of the population were often observed during the pandemic, these effects are rarely explicitly modeled and studied in the classical epidemic models. The model we propose gives rise to a plateau phenomenon: the number of people infected by the disease stay at the same level during an extended period of time. We show what are conditions needs to be met in order for the spreading to exhibit a plateau period, and we show that this phenomenon is interdependent: when considering multiples cities, the conditions are different from a single city. We verify from the real-world data that plateau phenomenon does exists in many regions of the world in the current COVID-19 development. Finally, we provide theoretical analysis on the plateau phenomenon for the single-city model, and derive a series of results on the emergence and ending of the plateau, and on the height and length of the plateau. Our theoretical results match well with our empirical findings.
Random walks on bipartite networks have been used extensively to design personalized recommendation methods. While aging has been identified as a key component in the growth of information networks, most research has focused on the networks structura
l properties and neglected the often available time information. Time has been largely ignored both by the investigated recommendation methods as well as by the methodology used to evaluate them. We show that this time-unaware approach overestimates the methods recommendation performance. Motivated by microscopic rules of network growth, we propose a time-aware modification of an existing recommendation method and show that by combining the temporal and structural aspects, it outperforms the existing methods. The performance improvements are particularly striking in systems with fast aging.
Predicting the future evolution of complex systems is one of the main challenges in complexity science. Based on a current snapshot of a network, link prediction algorithms aim to predict its future evolution. We apply here link prediction algorithms
to data on the international trade between countries. This data can be represented as a complex network where links connect countries with the products that they export. Link prediction techniques based on heat and mass diffusion processes are employed to obtain predictions for products exported in the future. These baseline predictions are improved using a recent metric of country fitness and product similarity. The overall best results are achieved with a newly developed metric of product similarity which takes advantage of causality in the network evolution.
Evaluating the economies of countries and their relations with products in the global market is a central problem in economics, with far-reaching implications to our theoretical understanding of the international trade as well as to practical applica
tions, such as policy making and financial investment planning. The recent Economic Complexity approach aims to quantify the competitiveness of countries and the quality of the exported products based on the empirical observation that the most competitive countries have diversified exports, whereas developing countries only export few low quality products -- typically those exported by many other countries. Two different metrics, Fitness-Complexity and the Method of Reflections, have been proposed to measure country and product score in the Economic Complexity framework. We use international trade data and a recent ranking evaluation measure to quantitatively compare the ability of the two metrics to rank countries and products according to their importance in the network. The results show that the Fitness-Complexity metric outperforms the Method of Reflections in both the ranking of products and the ranking of countries. We also investigate a Generalization of the Fitness-Complexity metric and show that it can produce improved rankings provided that the input data are reliable.
The recommender system is one of the most promising ways to address the information overload problem in online systems. Based on the personal historical record, the recommender system can find interesting and relevant objects for the user within a hu
ge information space. Many physical processes such as the mass diffusion and heat conduction have been applied to design the recommendation algorithms. The hybridization of these two algorithms has been shown to provide both accurate and diverse recommendation results. In this paper, we proposed two similarity preferential diffusion processes. Extensive experimental analyses on two benchmark data sets demonstrate that both recommendation and accuracy and diversity are improved duet to the similarity preference in the diffusion. The hybridization of the similarity preferential diffusion processes is shown to significantly outperform the state-of-art recommendation algorithm. Finally, our analysis on network sparsity show that there is significant difference between dense and sparse system, indicating that all the former conclusions on recommendation in the literature should be reexamined in sparse system.
