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Although deterministic compartmental models are useful for predicting the general trend of a disease’s spread, they are unable to describe the random daily fluctuations in the number of new infections and hospitalizations, which is crucial in determining the necessary healthcare capacity for a specified level of risk. In this paper, we propose a stochastic SEIHR (sSEIHR) model to describe such random fluctuations and provide sufficient conditions for stochastic stability of the disease-free equilibrium, based on the basic reproduction number that we estimated. Our extensive numerical results demonstrate strong threshold behavior near the estimated basic reproduction number, suggesting that the necessary conditions for stochastic stability are close to the sufficient conditions derived. Furthermore, we found that increasing the noise level slightly reduces the final proportion of infected individuals. In addition, we analyze COVID-19 data from various regions worldwide and demonstrate that by changing only a few parameter values, our sSEIHR model can accurately describe both the general trend and the random fluctuations in the number of daily new cases in each region, allowing governments and hospitals to make more accurate caseload predictions using fewer compartments and parameters than other comparable stochastic compartmental models.

We present an algorithm for performing attributed graph matching. This algorithm is derived from a generalized framework for describing functionally expanded interpolators which is based on the theory of reproducing kernel Hilbert spaces (RKHS). The algorithm incorporates a general approach to a wide class of graph matching problems based on attributed graphs, allowing the structure of the graphs to be based on multiple sets of attributes. No assumption is made about the adjacency structure of the graphs to be matched

The 2019 novel coronavirus disease (COVID-19) outbreak has become a worldwide problem. Due to globalization and the proliferation of international travel, many countries are now facing local epidemics. The existence of asymptomatic and pre-symptomatic transmissions makes it more difficult to control disease transmission by isolating infectious individuals. To accurately describe and represent the spread of COVID-19, we suggest a susceptible-exposed-infected-hospitalized-removed (SEIHR) model with human migrations, where the "exposed" (asymptomatic) individuals are contagious. From this model, we derive the basic reproduction number of the disease and its relationship with the model parameters. We find that, for highly contagious diseases like COVID-19, when the adjacent region's epidemic is not severe, a large migration rate can reduce the speed of local epidemic spreading at the price of infecting the neighboring regions. In addition, since "infected" (symptomatic) patients are isolated almost immediately, the transmission rate of the epidemic is more sensitive to that of the "exposed" (asymptomatic) individuals. Furthermore, we investigate the impact of various interventions, e.g. isolation and border control, on the speed of disease propagation and the resultant demand on medical facilities, and find that a strict intervention measure can be more effective than closing the borders. Finally, we use some real historical data of COVID-19 caseloads from different regions, including Hong Kong, to validate the modified SEIHR model, and make an accurate prediction for the third wave of the outbreak in Hong Kong.

We propose a method for estimating depth from images captured with a real aperture camera by fusing defocus and stereo cues. The idea is to use stereo-based constraints in conjunction with defocusing to obtain improved estimates of depth over those of stereo or defocus alone. The depth map as well as the original image of the scene are modeled as Markov random fields with a smoothness prior, and their estimates are obtained by minimizing a suitable energy function using simulated annealing. The main advantage of the proposed method, despite being computationally less efficient than the standard stereo or DFD method, is simultaneous recovery of depth as well as space-variant restoration of the original focused image of the scene.

Mine vehicles are a leading cause of mining fatalities. A reliable anti-collision system is needed to prevent vehicle-personnel collisions. The proposed collision detection system uses the fusion of a three-dimensional (3D) sensor and thermal infrared camera for human detection and tracking. In addition to a thermal camera, a distance sensor will provide depth information and allow the calculation of the vehicle and pedestrian velocities. The results of subsystem tests show that a simple temperature range is sufficient for segmentation and a neural network shows the best classification results in terms of speed and accuracy. Results of initial tests performed on two different 3D sensors show a significant disadvantage to the use of time of flight cameras in a mine environment.