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In the late stages of an epidemic, infections are often sporadic and geographically distributed. Spatially structured stochastic models can capture these important features of disease dynamics, thereby allowing a broader exploration of interventions. Here we develop a stochastic model of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission among an interconnected group of population centers representing counties, municipalities, and districts (collectively, “counties”). The model is parameterized with demographic, epidemiological, testing, and travel data from Ontario, Canada. We explore the effects of different control strategies after the epidemic curve has been flattened. We compare a local strategy of reopening (and reclosing, as needed) schools and workplaces county by county, according to triggers for county-specific infection prevalence, to a global strategy of province-wide reopening and reclosing, according to triggers for province-wide infection prevalence. For trigger levels that result in the same number of COVID-19 cases between the two strategies, the local strategy causes significantly fewer person-days of closure, even under high intercounty travel scenarios. However, both cases and person-days lost to closure rise when county triggers are not coordinated and when testing rates vary among counties. Finally, we show that local strategies can also do better in the early epidemic stage, but only if testing rates are high and the trigger prevalence is low. Our results suggest that pandemic planning for the far side of the COVID-19 epidemic curve should consider local strategies for reopening and reclosing.

The novel Coronavirus (COVID-19) is spreading and has caused a large-scale infection in China since December 2019. This has led to a significant impact on the lives and economy in China and other countries. Here we develop a discrete-time stochastic epidemic model with binomial distributions to study the transmission of the disease. Model parameters are estimated on the basis of fitting to newly reported data from January 11 to February 13, 2020 in China. The estimates of the contact rate and the effective reproductive number support the efficiency of the control measures that have been implemented so far. Simulations show the newly confirmed cases will continue to decline and the total confirmed cases will reach the peak around the end of February of 2020 under the current control measures. The impact of the timing of returning to work is also evaluated on the disease transmission given different strength of protection and control measures.

Network analysis is becoming one of the most active research areas in statistics. Significant advances have been made recently on developing theories, methodologies and algorithms for analyzing networks. However, there has been little fundamental study on optimal estimation. In this paper, we establish optimal rate of convergence for graphon estimation. For the stochastic block model with k clusters, we show that the optimal rate under the mean squared error is n⁻¹ log k + k²/n². The minimax upper bound improves the existing results in literature through a technique of solving a quadratic equation. When $k\\, \\leqslant \\,\\sqrt {n\\,\\log \\,n} $, as the number of the cluster k grows, the minimax rate grows slowly with only a logarithmic order n⁻¹ log k. A key step to establish the lower bound is to construct a novel subset of the parameter space and then apply Fano's lemma, from which we see a clear distinction of the non-parametric graphon estimation problem from classical nonparametric regression, due to the lack of identifiability of the order of nodes in exchangeable random graph models. As an immediate application, we consider nonparametric graphon estimation in a Holder class with smoothness α. When the smoothness α ≥ 1, the optimal rate of convergence is n⁻¹ log n, independent of α, while for α ∈ (0, 1), the rate is n-2α/(α+1), which is, to our surprise, identical to the classical nonparametric rate.

As laser scanning technology has improved a lot in recent years, terrestrial laser scanners (TLS) have become popular devices for surveying tasks with high accuracy demands, such as deformation analyses. For this reason, finding a stochastic model for TLS measurements is very important in order to get statistically reliable results. The measurement accuracy of laser scanners—especially of their rangefinders—is strongly dependent on the scanning conditions, such as the scan configuration, the object surface geometry and the object reflectivity. This study demonstrates a way to determine the intensity-dependent range precision of 3D points for terrestrial laser scanners that measure in 3D mode by using range residuals in laser beam direction of a best plane fit. This method does not require special targets or surfaces aligned perpendicular to the scanner, which allows a much quicker and easier determination of the stochastic properties of the rangefinder. Furthermore, the different intensity types—raw and scaled—intensities are investigated since some manufacturers only provide scaled intensities. It is demonstrated that the intensity function can be derived from raw intensity values as written in literature, and likewise—in a restricted measurement volume—from scaled intensity values if the raw intensities are not available.

The greenhouse gas emissions due to the energy use in production and distribution in a supply chain are of interest to industries aiming to achieve decarbonization. The industry subjected to carbon regulations require recycling and reusing materials to promote a circular economy through a closed-loop supply chain (CLSC). In this research, we propose a two-stage stochastic model to design the CLSC under a carbon trading scheme in the multi-period planning context by considering the uncertain demands and carbon prices. We also provide a four-step solution procedure with scenario reduction that enables the proposed model to be solved using popular commercial solvers efficiently. This solution makes the proposed model distinguished from the existing models that assume the firms can purchase or sell carbon credits without quantity limitation. The application of the proposed model is demonstrated via simulation-based analysis of the aluminum industry. The results that the proposed stochastic model generates a network with capacity redundancy to cope with the varying customer demands and carbon prices, while only a slight increase in cost and emission is observed compared with the deterministic model. Furthermore, using scenario reduction, the model solved with 80% of the scenarios share the same CLSC network configuration with the model with full scenarios, while the deviation of the total costs is less than 0.53% and the computational burden can be diminished by more than 40%. This research is expected to be useful to solve optimization problems facing large-scale scenarios with known occurrence probabilities aiming for energy conservation and emissions reduction.

Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of hypergraphs. However, theoretical aspects of such methods have seldom received attention in the literature as compared to the extensive studies on the guarantees of graph partitioning. For instance, consistency results of spectral graph partitioning under the stochastic block model are well known. In this paper, we present a planted partition model for sparse random nonuniform hypergraphs that generalizes the stochastic block model. We derive an error bound for a spectral hypergraph partitioning algorithm under this model using matrix concentration inequalities. To the best of our knowledge, this is the first consistency result related to partitioning nonuniform hypergraphs.

Hydrological analyses carried out based on precipitation in the Brazilian Legal Amazon (BLA) are essential due to their importance in climate regulation and regional and global atmospheric circulation. However, data series with short periods and many gaps, especially at the daily scale, are a limitation in this region. In order to improve precipitation analysis, a non-parametric stochastic model based on Artificial Neural Networks (ANNs) was used to estimate daily precipitation in the BLA . For this purpose, 22 rain gauge stations were adopted and organized, taking into account the complete series and the seasonal periods (rainy and dry).The results obtained showed a good performance of the model, with ranges of MSE (0.0022–0.2665), MAPE (0.0083–1.5343) and RMSE (0.0017–0.0214), which characterize an acceptable estimate for the estimation daily precipitation, especially in those with a wetter climate and more frequent precipitation during the year, as is the case in those located in the Amazon Biome. However, in regions that suffer from droughts, such as the Amazon-Cerrado ecotone areas, the results were less satisfactory due to the greater recurrence of zeros in the historical series. The seasonal division into dry and rainy periods did not provide better estimates for the model, except for some rain gauge stations located at latitudes close to the equator. However, this study could support future research on the estimation of daily precipitation in the region.

Statistical node clustering in discrete time dynamic networks is an emerging field that raises many challenges. Here, we explore statistical properties and frequentist inference in a model that combines a stochastic block model for its static part with independent Markov chains for the evolution of the nodes groups through time.We model binary data as well as weighted dynamic random graphs (with discrete or continuous edges values). Our approach, motivated by the importance of controlling for label switching issues across the different time steps, focuses on detecting groups characterized by a stable within-group connectivity behaviour. We study identifiability of the model parameters and propose an inference procedure based on a variational expectation–maximization algorithm as well as a model selection criterion to select the number of groups. We carefully discuss our initialization strategy which plays an important role in the method and we compare our procedure with existing procedures on synthetic data sets.We also illustrate our approach on dynamic contact networks: one of encounters between high school students and two others on animal interactions. An implementation of the method is available as an R package called dynsbm.

State-of-the-art stochastic volatility models generate a \"volatility smirk\" that explains why out-of-the-money index puts have high prices relative to the Black-Scholes benchmark. These models also adequately explain how the volatility smirk moves up and down in response to changes in risk. However, the data indicate that the slope and the level of the smirk fluctuate largely independently. Although single-factor stochastic volatility models can capture the slope of the smirk, they cannot explain such largely independent fluctuations in its level and slope over time. We propose to model these movements using a two-factor stochastic volatility model. Because the factors have distinct correlations with market returns, and because the weights of the factors vary over time, the model generates stochastic correlation between volatility and stock returns. Besides providing more flexible modeling of the time variation in the smirk, the model also provides more flexible modeling of the volatility term structure. Our empirical results indicate that the model improves on the benchmark Heston stochastic volatility model by 24% in-sample and 23% out-of-sample. The better fit results from improvements in the modeling of the term structure dimension as well as the moneyness dimension.

Covering point process theory, random geometric graphs and coverage processes, this rigorous introduction to stochastic geometry will enable you to obtain powerful, general estimates and bounds of wireless network performance and make good design choices for future wireless architectures and protocols that efficiently manage interference effects. Practical engineering applications are integrated with mathematical theory, with an understanding of probability the only prerequisite. At the same time, stochastic geometry is connected to percolation theory and the theory of random geometric graphs and accompanied by a brief introduction to the R statistical computing language. Combining theory and hands-on analytical techniques with practical examples and exercises, this is a comprehensive guide to the spatial stochastic models essential for modelling and analysis of wireless network performance.