Detection of patient-zero can give new insights to the epidemiologists about the nature of first transmissions into a population. In this paper, we study the statistical inference problem of detecting the source of epidemics from a snapshot of spreading on an arbitrary network structure. By using exact analytic calculations and Monte Carlo estimators, we demonstrate the detectability limits for the SIR model, which primarily depend on the spreading process characteristics. Finally, we demonstrate the applicability of the approach in a case of a simulated sexually transmitted infection spreading over an empirical temporal network of sexual interactions.

Finding an optimal subset of nodes in a network that is able to efficiently disrupt the functioning of a corrupt or criminal organization or contain an epidemic or the spread of misinformation is a highly relevant problem of network science. In this paper, we address the generalized network-dismantling problem, which aims at finding a set of nodes whose removal from the network results in the fragmentation of the network into subcritical network components at minimal overall cost. Compared with previous formulations, we allow the costs of node removals to take arbitrary nonnegative real values, which may depend on topological properties such as node centrality or on nontopological features such as the price or protection level of a node. Interestingly, we show that nonunit costs imply a significantly different dismantling strategy. To solve this optimization problem, we propose a method which is based on the spectral properties of a node-weighted Laplacian operator and combine it with a fine-tuning mechanism related to the weighted vertex cover problem. The proposed method is applicable to large-scale networks with millions of nodes. It outperforms current state-of-the-art methods and opens more directions for understanding the vulnerability and robustness of complex systems.

In the study of disease spreading on empirical complex networks in SIR model, initially infected nodes can be ranked according to some measure of their epidemic impact. The highest ranked nodes, also referred to as "superspreaders", are associated to dominant epidemic risks and therefore deserve special attention. In simulations on studied empirical complex networks, it is shown that the ranking depends on the dynamical regime of the disease spreading. A possible mechanism leading to this dependence is illustrated in an analytically tractable example. In systems where the allocation of resources to counter disease spreading to individual nodes is based on their ranking, the dynamical regime of disease spreading is frequently not known before the outbreak of the disease. Therefore, we introduce a quantity called epidemic centrality as an average over all relevant regimes of disease spreading as a basis of the ranking. A recently introduced concept of phase diagram of epidemic spreading is used as a framework in which several types of averaging are studied. The epidemic centrality is compared to structural properties of nodes such as node degree, k-cores and betweenness. There is a growing trend of epidemic centrality with degree and k-cores values, but the variation of epidemic centrality is much smaller than the variation of degree or k-cores value. It is found that the epidemic centrality of the structurally peripheral nodes is of the same order of magnitude as the epidemic centrality of the structurally central nodes. The implications of these findings for the distributions of resources to counter disease spreading are discussed. Author SummaryStudies of disease spreading on complex networks have provided a deep insight into the conditions of onset, dynamics and prevention of epidemics in human populations and malicious software propagation in computer networks. Identifying nodes which, when initially infected, on average infect the largest part of the network and ranking them according to their epidemic impact (the portion of the network eventually infected) is a priority for public health policies. In the study of epidemic spreading on empirical complex networks in the Susceptible-Infected-Recovered model, we find that the required ranking depends on the disease spreading regime, i.e. on how fast the disease is transmitted between nodes and how fast the infected node recovers. A measure called epidemic centrality, averaging the epidemic impact over all possible disease spreading regimes, is introduced as a basis of epidemic ranking. We find the epidemic centrality of nodes which are structurally central, to be of the same order of magnitude as the epidemic centrality of structurally peripheral nodes. These findings point to the need to study if the impact of an epidemic starting at structurally peripheral nodes might be considerably underestimated. Network periphery should gain a more prominent role in the study of the allocation of resources in future epidemic preparedness plans.

Bitcoin is one of the most prominent decentralized digital cryptocurrencies, currently having the largest market capitalization among cryptocurrencies. Ability to understand which factors drive the fluctuations of the Bitcoin price and to what extent they are predictable is interesting both from theoretical and practical perspective. In this paper, we study the problem of the Bitcoin short-term volatility forecasting by exploiting volatility history and order book data. Order book, consisting of buy and sell orders over time, reflects the intention of the market and is closely related to the evolution of volatility. We propose temporal mixture models capable of adaptively exploiting both volatility history and order book features for short-term volatility forecasting. By leveraging rolling and incremental learning and evaluation procedures, we demonstrate the prediction performance of our model as well as studying the robustness, in comparison to a variety of statistical and machine learning baselines. Meanwhile, our temporal mixture model enables to decipher time-varying effect of order book features on the volatility. It demonstrates the prospect of our temporal mixture model as an interpretable forecasting framework over heterogeneous Bitcoin data.

The robustness of complex networks under targeted attacks is deeply connected to the resilience of complex systems, which is defined as the ability to make appropriate response to the attack. In this paper, we study robustness of complex networks under a realistic assumption that the cost of removing a node is not constant but rather proportional to the degree of a node or equivalently to the number of removed links a removal action produces. We have investigated the state-of-the-art targeted node removing algorithms and demonstrate that they become very inefficient when the cost of the attack is taken into consideration. For the case when it is possible to attack or remove links, we propose a simple and efficient edge removal strategy named Hierarchical Power Iterative Normalized cut (HPI-Ncut). The results on real and artificial networks show that the HPI-Ncut algorithm outperforms all the node removal and link removal attack algorithms when the same definition of cost is taken into consideration. In addition, we show that, on sparse networks, the complexity of this hierarchical power iteration edge removal algorithm is only ( log 2+ ).