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PublicationA quantitative measurement method for nuclear-pleomorphism scoring in breast cancer(MDPI, 2024-09)Background/Objectives: Nuclear pleomorphism, a crucial determinant of breast cancer grading under the Nottingham Histopathology Grading (NHG) system, remains inadequately quantified in the existing literature. Motivated by this gap, our study seeks to investigate and establish correlations among morphological features across various scores of nuclear pleomorphism, as per the NHG system. We aim to quantify nuclear pleomorphism across these scores and validate our proposed measurement method against ground-truth data. Methods: Initially, we deconstruct the descriptions of nuclear pleomorphism into three core elements: size, shape, and appearance. These elements are subsequently mathematically modeled into equations, termed (Formula presented.), (Formula presented.), and (Formula presented.). These equations are then integrated into a unified model termed Harmonic Mean (HM). The HM equation yields a value approaching 1 for nuclei demonstrating characteristics of score-3 nuclear pleomorphism and near 0 for those exhibiting features of score-1 nuclear pleomorphism. Results: The proposed HM model demonstrates promising performance metrics, including Accuracy, Recall, Specificity, Precision, and F1-score, with values of 0.97, 0.96, 0.97, 0.94, and 0.95, respectively. Conclusions: In summary, this study proposes the HM equation as a novel feature for the precise quantification of nuclear pleomorphism in breast cancer.
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PublicationOptimizing quantum reflection of Bose–Einstein condensates with angle of incidence(Institute of Physics, 2024-12)We investigated the effect of the angle of incidence on the quantum reflection of Bose-Einstein condensates (BECs) from regions with rapid potential variations. The reflection process was examined for both isotropic and anisotropic 2D disk-shaped BECs. In both cases, the angle of incidence was found to play a crucial role during reflection, inducing non-uniform atom-surface interactions and thus manipulating severe disruptions on the atomic cloud in the low incident velocity regime. In this scenario, the angle of incidence minimizes or even eliminates disruptions or fragmentation of the atomic cloud, especially for incidence angles far from the normal incidence direction. Consequently, anomalous reflectivity or saturation effects, which have been challenging in previous studies, can be effectively addressed and controlled. These findings provide new insights into optimizing the quantum reflection of BECs from a solid surface, particularly regarding the enhancement of the reflection probability of BECs from a planar silicon surface, which, since their first experiments, have not been maximized due to saturation effects.
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PublicationRisk factor analysis for stunting incidence using sparse categorical principal component logistic regression(Elsevier, 2025-01)The risk factors for stunting incidence involve categorical data in both the response and predictor variables. Therefore, we developed a sparse categorical principal component logistic regression model capable of handling data with multicollinearity. The parameters of the sparse categorical principal component logistic regression model were estimated using the maximum likelihood method and the Newton-Raphson iterative approach. The analysis yielded a likelihood ratio value of 144.81 and a chi-square statistic value of 11.07, indicating that all factors included in the model are statistically significant. The results highlight that medical history, inadequate complementary feeding, formula feeding, lack of complementary feeding programs, and lack of iron supplementation for mothers are highly associated with the risk of stunting in toddlers. This emphasizes the need for attention to maternal nutrition from pregnancy through breastfeeding, as well as the nutrition of the toddler. Some important points proposed in this method are: • Stunting data consists of categorical variables containing multicollinearity. • The method applied is sparse logistic regression combined with categorical principal component analysis. • Analysis of risk factors for stunting in toddlers is based on the child's own condition, as well as parental factors, namely age, education, and intake of additional food and supplementary tablets during pregnancy.
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PublicationMalaria dynamics of transmission for individuals with multi-layered susceptibility(Lviv Polytechnic National University, 2025-03)The alarming prevalence of vector-borne diseases, such as malaria, has long been a global concern due to their ability to infect individuals across all social classes, thus leading to high morbidity and mortality rates. This study investigates the role of mosquito bites frequency in dynamics of transmission of malaria. Mainly, featuring the mathematical classification of susceptible individuals into high and low risk. The present study employs a time-dependent, social hierarchy-structured deterministic model to analyse the vulnerability of multi-layered classes to the transmission dynamics of malaria disease. This analysis takes into account the interaction between the human population and the mosquito vector population. Human infection statuses are divided into four categories: susceptible, infected, and recovered individuals, with further stratification of susceptible individuals based on their risk level. Concurrently, the total vector population is divided into susceptible and infected mosquitoes. The disease free equilibrium, basic reproduction number and endemic equilibrium were computed. The findings show that the higher the number susceptible humans subjected to high risk the higher number of infected human individuals.
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PublicationMathematical analysis of the transmission dynamics for malaria in individuals with varying levels of risk(Springer, 2025-01)Malaria continues to be a critical global health issue due to its profound impact on human development. This study explores the dynamics of malaria transmission within a population exhibiting multiple human susceptibilities, which arise from behavioral, locational, and occupational factors. We have formulated a nonlinear, time-dependent differential equation model to capture these dynamics. The model distinguishes between low- and high-risk susceptible human populations, offering a detailed analysis of malaria transmission patterns. We calculated the basic reproduction number R0, along with the disease-free equilibrium (DFE) and endemic equilibrium (EE) points. The DFE is locally asymptotically stable when R0<1, while the EE is globally asymptotically stable when R0>1. Additionally, the model exhibits a backward bifurcation. Moreover, we have graphically illustrated the impact of multiple human susceptibilities. These effects become more evident over time: as the proportion of highly susceptible individuals within the population increases, the overall transmission rate rises accordingly. Furthermore, the mosquito-human contact rate and the mosquito death rate have exhibited effects consistent with our expectations.