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We introduce a policy model coupled with the susceptible–infected- recovered (SIR) epidemic model to study interactions between policy-making and the dynamics of epidemics. We considered both single-region policies as well as game-theoretic models involving interactions among several regions and hierarchical interactions among policy-makers modeled as multi-layer games. We assumed that the policy functions are piece-wise constant with a minimum time interval for each policy stage, considering that policies cannot change frequently in time or be easily followed. The optimal policy was obtained by minimizing a cost function that consists of an implementation cost, an impact cost, and, in the case of multi-layer games, a non-compliance cost. We show, in a case study of COVID-19 in France, that when the cost function is reduced to the impact cost and parameterized as the final epidemic size, the solution approximates that of the optimal control in Bliman et al, (2021) for a sufficiently small minimum policy time interval. For a larger time interval, however, the optimal policy is a step down function, quite different from the step up structure typically deployed during the COVID-19 pandemic. In addition, we present a counterfactual study of how the pandemic would have evolved if herd immunity was reached during the second wave in the county of Los Angeles, California. Finally, we study a case of three interacting counties with and without a governing state. 

The water discharge and sediment load have been increasingly altered by climate change and human activities in recent decades. For the Pearl River, however, long-term variations in the sediment regime, especially in the last decade, remain poorly known. Here we updated knowledge of the temporal trends in the sediment regime of the Pearl River at annual, seasonal and monthly time scales from the 1950s to 2020. Results show that the annual sediment load and suspended sediment concentration (SSC) exhibited drastically decreased, regardless of water discharge. Compared with previous studies, we also found that sediment load and SSC reached a conspicuous peak in the 1980s, and showed a significant decline starting in the 2000s and 1990s, respectively. In the last decade, however, water discharge and sediment load showed slightly increasing trends. At the seasonal scale, the wet-season water discharge displays a decreasing trend, while the dry-season water discharge is increasing. At the monthly scale, the flood seasons in the North and East Rivers typically occur one month earlier than that in the West River due to the different precipitation regimes. Precipitation was responsible for the long-term change of discharge, while human activities (e.g. dam construction and land use change) exerted different effects on the variations in sediment load among different periods. Changes in the sediment regime have exerted substantial influences on downstream channel morphology and saltwater intrusion in the Greater Bay Area. Our study proposes a watershed-based solution, and provides scientific guidelines for the sustainable development of the Greater Bay Area. 

Deterministic compartmental models for infectious diseases give the mean behaviour of stochastic agent-based models. These models work well for counterfactual studies in which a fully mixed large-scale population is relevant. However, with finite size populations, chance variations may lead to significant departures from the mean. In real-life applications, finite size effects arise from the variance of individual realizations of an epidemic course about its fluid limit. In this article, we consider the classical stochastic Susceptible-Infected-Recovered (SIR) model, and derive a martingale formulation consisting of a deterministic and a stochastic component. The deterministic part coincides with the classical deterministic SIR model and we provide an upper bound for the stochastic part. Through analysis of the stochastic component depending on varying population size, we provide a theoretical explanation of finite size effects. Our theory is supported by quantitative and direct numerical simulations of theoretical infinitesimal variance. Case studies of coronavirus disease 2019 (COVID-19) transmission in smaller populations illustrate that the theory provides an envelope of possible outcomes that includes the field data. 

API misuses are prevalent and extremely harmful. Despite various techniques have been proposed for API-misuse detection, it is not even clear how different types of API misuses distribute and whether existing techniques have covered all major types of API misuses. Therefore, in this paper, we conduct the first large-scale empirical study on API misuses based on 528,546 historical bug-fixing commits from GitHub (from 2011 to 2018). By leveraging a state-of-the-art fine-grained AST differencing tool, GumTree, we extract more than one million bug-fixing edit operations, 51.7% of which are API misuses. We further systematically classify API misuses into nine different categories according to the edit operations and context. We also extract various frequent API-misuse patterns based on the categories and corresponding operations, which can be complementary to existing API-misuse detection tools. Our study reveals various practical guidelines regarding the importance of different types of API misuses. Furthermore, based on our dataset, we perform a user study to manually analyze the usage constraints of 10 patterns to explore whether the mined patterns can guide the design of future API-misuse detection tools. Specifically, we find that 7,541 potential misuses still exist in latest Apache projects and 149 of them have been reported to developers. To date, 57 have already been confirmed and fixed (with 15 rejected misuses correspondingly). The results indicate the importance of studying historical API misuses and the promising future of employing our mined patterns for detecting unknown API misuses. 

Automated debugging techniques, including fault localization and program repair, have been studied for over a decade. However, the only existing connection between fault localization and program repair is that fault localization computes the potential buggy elements for program repair to patch. Recently, a pioneering work, ProFL, explored the idea of unified debugging to unify fault localization and program repair in the other direction for the first time to boost both areas. More specifically, ProFL utilizes the patch execution results from one state-of-the-art repair system, PraPR, to help improve state-of-the-art fault localization. In this way, ProFL not only improves fault localization for manual repair, but also extends the application scope of automated repair to all possible bugs (not only the small ratio of bugs that can be automatically fixed). However, ProFL only considers one APR system (i.e., PraPR), and it is not clear how other existing APR systems based on different designs contribute to unified debugging. In this work, we perform an extensive study of the unified-debugging approach on 16 state-of-the-art program repair systems for the first time. Our experimental results on the widely studied Defects4J benchmark suite reveal various practical guidelines for unified debugging, such as (1) nearly all the studied 16 repair systems can positively contribute to unified debugging despite their varying repairing capabilities, (2) repair systems targeting multi-edit patches can bring extraneous noise into unified debugging, (3) repair systems with more executed/plausible patches tend to perform better for unified debugging, and (4) unified debugging effectiveness does not rely on the availability of correct patches in automated repair. Based on our results, we further propose an advanced unified debugging technique, UniDebug++, which can localize over 20% more bugs within Top-1 positions than state-of-the-art unified debugging technique, ProFL.