In this paper, we introduce and analyze a discrete-time model of an epidemic spread in a heterogeneous population. As the heterogeneous population, we define a population in which we have two groups which differ in a risk of getting infected: a low-risk group and a high-risk group. We construct our model without discretization of its continuous-time counterpart, which is not a common approach. We indicate functions that reflect the probability of remaining healthy, which are based on the mass action law. Additionally, we discuss the existence and local stability of the stability states that appear in the system. Moreover, we provide conditions for their global stability. Some of the results are expressed with the use of the basic reproduction number $ \mathcal{R}_0 $. The novelty of our paper lies in assuming different values of every coefficient that describe a given process in each subpopulation. Thanks to that, we obtain the pure population's heterogeneity. Our results are in a line with expectations - the disease free stationary state is locally stable for $ \mathcal{R}_0 < 1 $ and loses its stability after crossing $ \mathcal{R}_0 = 1 $. We supplement our results with a numerical simulation that concerns the real case of a tuberculosis epidemic in Poland.

Hyperparameter optimization (HPO) has been well-developed and evolved into a well-established research topic over the decades. With the success and wide application of deep learning, HPO has garnered increased attention, particularly within the realm of machine learning model training and inference. The primary objective is to mitigate the challenges associated with manual hyperparameter tuning, which can be ad-hoc, reliant on human expertise, and consequently hinders reproducibility while inflating deployment costs. Recognizing the growing significance of HPO, this paper surveyed classical HPO methods, approaches for accelerating the optimization process, HPO in an online setting (dynamic algorithm configuration, DAC), and when there is more than one objective to optimize (multi-objective HPO). Acceleration strategies were categorized into multi-fidelity, bandit-based, and early stopping; DAC algorithms encompassed gradient-based, population-based, and reinforcement learning-based methods; multi-objective HPO can be approached via scalarization, metaheuristics, and model-based algorithms tailored for multi-objective situation. A tabulated overview of popular frameworks and tools for HPO was provided, catering to the interests of practitioners.

Competing failure models with degradation phenomena and sudden failures are becoming more and more common and important in practice. In this study, the generalized pivotal quantity method was proposed to investigate the modeling of competing failure problems involving both degradation and sudden failures. In the competing failure model, the degradation failure was modeled through a Wiener process and the sudden failure was described as a Weibull distribution. For point estimation, the maximum likelihood estimations of parameters $ \mu $ and $ \sigma^2 $ were provided and the inverse estimation of parameters $ \eta $ and $ \beta $ were derived. The exact confidence intervals for parameters $ \mu $, $ \sigma^2 $, and $ \beta $ were obtained. Furthermore, the generalized confidence interval of parameter $ \eta $ was obtained through constructing the generalized pivotal quantity. Using the substitution principle, the generalized confidence intervals for the reliability function, the $ p $th percentile of lifetime, and the mean time to failure were also obtained. Simulation technique was carried out to evaluate the performance of the proposed generalized confidence intervals. The simulation results showed that the proposed generalized confidence interval was effective in terms of coverage percentage. Finally, an example was presented to illustrate the application of the proposed method.

Cancer is a disease that arises from the uncontrolled growth of abnormal (tumor) cells in an organ and their subsequent spread into other parts of the body. If tumor cells spread to surrounding tissues or other organs, then the disease is life-threatening due to limited treatment options. This work applies an agent-based model to investigate the effect of intra-tumoral communication on tumor progression, plasticity, and invasion, with results suggesting that cell-cell and cell-extracellular matrix (ECM) interactions affect tumor cell behavior. Additionally, the model suggests that low initial healthy cell densities and ECM protein densities promote tumor progression, cell motility, and invasion. Furthermore, high ECM breakdown probabilities of tumor cells promote tumor invasion. Understanding the intra-tumoral communication under cellular stress can potentially lead to the design of successful treatment strategies for cancer.

An accurate ultra-short-term time series prediction of a power load is an important guarantee for power dispatching and the safe operation of power systems. Problems of the current ultra-short-term time series prediction algorithms include low prediction accuracy, difficulty capturing the local mutation features, poor stability, and others. From the perspective of series decomposition, a multi-scale sequence decomposition model (TFDNet) based on power spectral density and the Morlet wavelet transform is proposed that combines the multidimensional correlation feature fusion strategy in the time and frequency domains. By introducing the time-frequency energy selection module, the "prior knowledge" guidance module, and the sequence denoising decomposition module, the model not only effectively delineates the global trend and local seasonal features, completes the in-depth information mining of the smooth trend and fluctuating seasonal features, but more importantly, realizes the accurate capture of the local mutation seasonal features. Finally, on the premise of improving the forecasting accuracy, single-point load forecasting and quantile probabilistic load forecasting for ultra-short-term load forecasting are realized. Through the experiments conducted on three public datasets and one private dataset, the TFDNet model reduces the mean square error (MSE) and mean absolute error (MAE) by 19.80 and 11.20% on average, respectively, as compared with the benchmark method. These results indicate the potential applications of the TFDNet model.

Mosquito-borne diseases are threatening half of the world's population. To prevent the spread of malaria, dengue fever, or other mosquito-borne diseases, a new disease control strategy is to reduce or eradicate the wild mosquito population by releasing sterile mosquitoes. To study the effects of sterile insect technique on mosquito populations, we developed a mathematical model of constant release of sterile Aedes aegypti mosquitoes with strong and weak Allee effect and considered interspecific competition with Anopheles mosquitoes. We calculated multiple release thresholds and investigated the dynamical behavior of this model. In order to get closer to reality, an impulsive differential equation model was also introduced to study mosquito suppression dynamics under the strategy of releasing $ c $ sterile male mosquitoes at each interval time $ T $. Finally, the relationship between the releasing amount or the waiting period and the number of days required to suppress mosquitoes was illustrated by numerical simulations.

After the many failures in the control of the COVID-19 pandemic, identifying robust principles of epidemic control will be key in future preparedness. In this work, we propose an optimal control model of an age-of-infection transmission model under a two-phase control regime where social distancing is the only available control tool in the first phase, while the second phase also benefits from the arrival of vaccines. We analyzed the problem by an ad-hoc numerical algorithm under a strong hypothesis implying a high degree of prioritization to the protection of health from the epidemic attack, which we termed the "low attack rate" hypothesis. The outputs of the model were also compared with the data from the Italian COVID-19 experience to provide a crude assessment of the goodness of the enacted interventions prior to the onset of the Omicron variant.

Retinal vessel segmentation plays a vital role in the clinical diagnosis of ophthalmic diseases. Despite convolutional neural networks (CNNs) excelling in this task, challenges persist, such as restricted receptive fields and information loss from downsampling. To address these issues, we propose a new multi-fusion network with grouped attention (MAG-Net). First, we introduce a hybrid convolutional fusion module instead of the original encoding block to learn more feature information by expanding the receptive field. Additionally, the grouped attention enhancement module uses high-level features to guide low-level features and facilitates detailed information transmission through skip connections. Finally, the multi-scale feature fusion module aggregates features at different scales, effectively reducing information loss during decoder upsampling. To evaluate the performance of the MAG-Net, we conducted experiments on three widely used retinal datasets: DRIVE, CHASE and STARE. The results demonstrate remarkable segmentation accuracy, specificity and Dice coefficients. Specifically, the MAG-Net achieved segmentation accuracy values of 0.9708, 0.9773 and 0.9743, specificity values of 0.9836, 0.9875 and 0.9906 and Dice coefficients of 0.8576, 0.8069 and 0.8228, respectively. The experimental results demonstrate that our method outperforms existing segmentation methods exhibiting superior performance and segmentation outcomes.

Long non-coding RNA (lncRNA) is considered to be a crucial regulator involved in various human biological processes, including the regulation of tumor immune checkpoint proteins. It has great potential as both a cancer biomolecular biomarker and therapeutic target. Nevertheless, conventional biological experimental techniques are both resource-intensive and laborious, making it essential to develop an accurate and efficient computational method to facilitate the discovery of potential links between lncRNAs and diseases. In this study, we proposed HRGCNLDA, a computational approach utilizing hierarchical refinement of graph convolutional neural networks for forecasting lncRNA-disease potential associations. This approach effectively addresses the over-smoothing problem that arises from stacking multiple layers of graph convolutional neural networks. Specifically, HRGCNLDA enhances the layer representation during message propagation and node updates, thereby amplifying the contribution of hidden layers that resemble the ego layer while reducing discrepancies. The results of the experiments showed that HRGCNLDA achieved the highest AUC-ROC (area under the receiver operating characteristic curve, AUC for short) and AUC-PR (area under the precision versus recall curve, AUPR for short) values compared to other methods. Finally, to further demonstrate the reliability and efficacy of our approach, we performed case studies on the case of three prevalent human diseases, namely, breast cancer, lung cancer and gastric cancer.

In the present work, both direct and inverse problems are considered for a Fisher-type fractional diffusion equation, which is proposed to describe the phenomenon of cell migration. For the direct problem, a solution is given via the Fourier method and the Laplace transform. On the other hand, we solved the inverse problem from a Bayesian statistical framework using a set of data that are the result of a cell migration experiment on a wound closure assay. We estimated the parameters of the mathematical model via Markov Chain Monte Carlo methods.