To describe the transmission dynamics of maize streak virus infection, in the paper, we first formulate a stochastic maize streak virus infection model, in which the stochastic fluctuations are depicted by a logarithmic Ornstein-Uhlenbeck process. This approach is reasonable to simulate the random impacts of main parameters both from the biological significance and the mathematical perspective. Then we investigate the detailed dynamics of the stochastic system, including the existence and uniqueness of the global solution, the existence of a stationary distribution, the exponential extinction of the infected maize and infected leafhopper vector. Especially, by solving the five-dimensional algebraic equations corresponding to the stochastic system, we obtain the specific expression of the probability density function near the quasi-endemic equilibrium of the stochastic system, which provides valuable insights into the stationary distribution. Finally, the model is discretized using the Milstein higher-order numerical method to illustrate our theoretical results numerically. Our findings provide a groundwork for better methods of preventing the spread of this type of virus.

A complete framework of predicting the attributes of sea clutter under different operational conditions, specified by wind speed, wind direction, grazing angle, and polarization, is proposed for the first time. This framework is composed of empirical spectra to characterize sea-surface profiles under different wind speeds, the Monte Carlo method to generate realizations of sea-surface profiles, the physical-optics method to compute the normalized radar cross-sections (NRCSs) from individual sea-surface realizations, and regression of NRCS data (sea clutter) with an empirical probability density function (PDF) characterized by a few statistical parameters. JONSWAP and Hwang ocean-wave spectra are adopted to generate realizations of sea-surface profiles at low and high wind speeds, respectively. The probability density functions of NRCSs are regressed with K and Weibull distributions, each characterized by two parameters. The probability density functions in the outlier regions of weak and strong signals are regressed with a power-law distribution, each characterized by an index. The statistical parameters and power-law indices of the K and Weibull distributions are derived for the first time under different operational conditions. The study reveals succinct information of sea clutter that can be used to improve the radar performance in a wide variety of complicated ocean environments. The proposed framework can be used as a reference or guidelines for designing future measurement tasks to enhance the existing empirical models on ocean-wave spectra, normalized radar cross-sections, and so on.

Protein soils must be removed for both appearance and hygienic reasons. They are denatured by heat treatment or bleaching and cleaned using enzymes. Among the various types of protein soils, blood soils are the most noticeable and known to be denatured by heat and bleaching by oxidation. We verified herein that the detergency of heat and oxidatively denatured hemoglobin is greatly improved by the enzyme immersing treatment in the detergency with SDS and can be analyzed using the probability density functional method. The probability density functional method evaluates the cleaning power by assuming that the adhesion and cleaning force of soils are not uniquely determined, but instead have a distribution in intensity, with a usefulness that had recently been demonstrated. This analytical method showed that the cleaning power of the enzyme immersing treatment improved when the soil adhesive force was decreased due to denatured protein degradation, even though the cleaning power of the SDS remained unchanged, and the values were consistent with those in the cleaning test. In conclusion, the probability density functional method can be used to analyze enzymatic degradation of denatured protein soils and the resulting changes in their detergency.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a novel virus known as coronavirus 2 (SARS-CoV-2) that affects the pulmonary structure and results in the coronavirus illness 2019 (COVID-19). Tuberculosis (TB) and COVID-19 codynamics have been documented in numerous nations. Understanding the complexities of codynamics is now critically necessary as a consequence. The aim of this research is to construct a co-infection model of TB and COVID-19 in the context of fractional calculus operators, white noise and probability density functions, employing a rigorous biological investigation. By exhibiting that the system possesses non-negative and bounded global outcomes, it is shown that the approach is both mathematically and biologically practicable. The required conditions are derived, guaranteeing the eradication of the infection. Sensitivity analysis and bifurcation of the submodel are also investigated with system parameters. Furthermore, existence and uniqueness results are established, and the configuration is tested for the existence of an ergodic stationary distribution. For discovering the system\'s long-term behavior, a deterministic-probabilistic technique for modeling is designed and operated in MATLAB. By employing an extensive review, we hope that the previously mentioned approach improves and leads to mitigating the two diseases and their co-infections by examining a variety of behavioral trends, such as transitions to unpredictable procedures. In addition, the piecewise differential strategies are being outlined as having promising potential for scholars in a range of contexts because they empower them to include particular characteristics across multiple time frame phases. Such formulas can be strengthened via classical technique, power-law, exponential decay, generalized Mittag-Leffler kernels, probability density functions and random procedures. Furthermore, we get an accurate description of the probability density function encircling a quasi-equilibrium point if the effect of TB and COVID-19 minimizes the propagation of the codynamics. Consequently, scholars can obtain better outcomes when analyzing facts using random perturbations by implementing these strategies for challenging issues. Random perturbations in TB and COVID-19 co-infection are crucial in controlling the spread of an epidemic whenever the suggested circulation is steady and the amount of infection eliminated is closely correlated with the random perturbation level.

The hygroscopicity of PM2.5 particles plays an important role in PM2.5 haze in Northeast Asian countries by influencing particle growth and chemical composition. New particle formation (NPF) and atmospheric volatile organic compounds (VOCs) are factors that influence particle hygroscopicity. However, the lack of real-time hygroscopicity measurements has deterred the understanding of their effects on particle hygroscopicity. In this study, two intensive monitoring campaigns were conducted during the summer of 2021 and spring of 2022 using real-time aerosol instruments, including a humidified tandem differential mobility analyzer (HTDMA), in Seosan, Republic of Korea. The hygroscopicity parameter κ was calculated from the real-time HTDMA measurement data (κGf). The diurnal variations in κGf exhibited strong inverse linear correlations with the total concentration of VOCs (CTVOC) during the two campaigns. The higher atmospheric CTVOC in summer increased the growth rate of the particle diameter from 10 to 40 nm (6 nm/h) compared with that in spring (2.7 nm/h), resulting in a faster change in κGf for 40-nm particles in summer than in spring because of the increase in organic matter in the chemical compositions of particles. In addition, NPF events introduced additional tiny fresh particles into the atmosphere, which reduced the κGf of 40-nm particles and increased the intensity of the less hygroscopic peaks (κGf < 0.1) of κ-probability density functions (κ-PDF) in NPF days. However, 100-nm particles exhibited fewer changes in κGf than 40-nm particles, resulting in additional dominant hygroscopic peaks (κ ∼ 0.2) of κ-PDFs in both NPF and non-NPF days. When κGf values measured in Seosan were compared with those in other Northeast Asian countries in the literature, the κ values for 40-nm particles were lower than those (κ > 0.2) measured in Beijing and Guangzhou, but those for 100-nm particles were close to those measured in the two cities.

The role of medical diagnosis is essential in patient care and healthcare. Established diagnostic practices typically rely on predetermined clinical criteria and numerical thresholds. In contrast, Bayesian inference provides an advanced framework that supports diagnosis via in-depth probabilistic analysis. This study\'s aim is to introduce a software tool dedicated to the quantification of uncertainty in Bayesian diagnosis, a field that has seen minimal exploration to date. The presented tool, a freely available specialized software program, utilizes uncertainty propagation techniques to estimate the sampling, measurement, and combined uncertainty of the posterior probability for disease. It features two primary modules and fifteen submodules, all designed to facilitate the estimation and graphical representation of the standard uncertainty of the posterior probability estimates for diseased and non-diseased population samples, incorporating parameters such as the mean and standard deviation of the test measurand, the size of the samples, and the standard measurement uncertainty inherent in screening and diagnostic tests. Our study showcases the practical application of the program by examining the fasting plasma glucose data sourced from the National Health and Nutrition Examination Survey. Parametric distribution models are explored to assess the uncertainty of Bayesian posterior probability for diabetes mellitus, using the oral glucose tolerance test as the reference diagnostic method.

In this paper, we present a virus infection model that incorporates eclipse-stage and Beddington-DeAngelis function, along with perturbation in infection rate using logarithmic Ornstein-Uhlenbeck process. Rigorous analysis demonstrates that the stochastic model has a unique global solution. Through construction of appropriate Lyapunov functions and a compact set, combined with the strong law of numbers and Fatou\'s lemma, we obtain the existence of the stationary distribution under a critical condition, which indicates the long-term persistence of T-cells and virions. Moreover, a precise probability density function is derived around the quasi-equilibrium of the model, and spectral radius analysis is employed to identify critical condition for elimination of the virus. Finally, numerical simulations are presented to validate theoretical results, and the impact of some key parameters such as the speed of reversion, volatility intensity and mean infection rate are investigated.

In this paper, we present the kernel density estimation (KDE)-based parallelized ultrasound entropy imaging and apply it for hepatic steatosis characterization. A KDE technique was used to estimate the probability density function (PDF) of ultrasound backscattered signals. The estimated PDF was utilized to estimate the Shannon entropy to construct parametric images. In addition, the parallel computation technique was incorporated. Clinical experiments of hepatic steatosis were conducted to validate the feasibility of the proposed method. Seventy-two participants and 204 patients with different grades of hepatic steatosis were included. The experimental results show that the KDE-based entropy parameter correlates with log10 (hepatic fat fractions) measured by magnetic resonance spectroscopy in the 72 participants (Pearson\'s r = 0.52, p < 0.0001), and its areas under the receiver operating characteristic curves for diagnosing hepatic steatosis grades ≥ mild, ≥moderate, and ≥severe are 0.65, 0.73, and 0.80, respectively, for the 204 patients. The proposed method overcomes the drawbacks of conventional histogram-based ultrasound entropy imaging, including limited dynamic ranges and histogram settings dependence, although the diagnostic performance is slightly worse than conventional histogram-based entropy imaging. The proposed KDE-based parallelized ultrasound entropy imaging technique may be used as a new ultrasound entropy imaging method for hepatic steatosis characterization.

Medical diagnosis is the basis for treatment and management decisions in healthcare. Conventional methods for medical diagnosis commonly use established clinical criteria and fixed numerical thresholds. The limitations of such an approach may result in a failure to capture the intricate relations between diagnostic tests and the varying prevalence of diseases. To explore this further, we have developed a freely available specialized computational tool that employs Bayesian inference to calculate the posterior probability of disease diagnosis. This novel software comprises of three distinct modules, each designed to allow users to define and compare parametric and nonparametric distributions effectively. The tool is equipped to analyze datasets generated from two separate diagnostic tests, each performed on both diseased and nondiseased populations. We demonstrate the utility of this software by analyzing fasting plasma glucose, and glycated hemoglobin A1c data from the National Health and Nutrition Examination Survey. Our results are validated using the oral glucose tolerance test as a reference standard, and we explore both parametric and nonparametric distribution models for the Bayesian diagnosis of diabetes mellitus.

OBJECTIVE: To weight the prognostic value of thyroid hormones in catastrophic acute-on-chronic liver failure (ACLF).
METHODS: A retrospective cohort (n = 635) and two prospective cohorts (n = 353, and 198) were enrolled in this study. The performance of a novel developed prognostic score was assessed from aspects of reliability, discrimination, and clinical net benefit.
RESULTS: Thyroid-stimulating hormone (TSH) was identified to have the most potential as a prognostic predictor for hepatitis B virus-related ACLF among thyroid hormones. The novel score (modified chronic liver failure-organ failure score [mCLIF-OFs]) was developed with weighted TSH and other scored organs in the CLIF-OFs using the retrospective cohort (n = 635). The predicted risk and observed probabilities of death were comparable across the deciles of mCLIF-OFs (Hosmer-Lemeshow χ2  = 4.28, p = 0.83; Brier scaled = 11.9). The C-index of mCLIF-OFs (0.885 [0.883-0.887]) for 30-day mortality was significantly higher than that of the CLIF-OFs, chronic liver failure-sequential organ failure assessment score (CLIF-SOFAs), CLIF-C ACLFs, Model of End-stage Liver Disease (MELD), and Child-Pugh (all p < 0.001). The absolute improvements of prediction error rates of the mCLIF-OFs compared to the above five scores were from 19.0% to 61.1%. After the analysis of probability density function, the mCLIF-OFs showed the least overlapping coefficients (27.9%) among the above prognostic scores. Additionally, the mCLIF-OFs showed greater net benefit than the above five prognostic scores over a wide range of risk threshold of death. Similar results were validated in two prospective ACLF cohorts with HBV and non-HBV etiologies.
CONCLUSIONS: Weighted TSH portended the outcome of ACLF patients, which could be treated as a \"damaged organ\" of the hypothalamic-pituitary-thyroid axis. The novel mCLIF-OFs is a reliable prognostic score with better discrimination power and clinical net benefit than CLIF-OFs, CLIF-SOFAs, CLIF-C ACLFs, MELD, and Child-Pugh.