Reliability is very important characteristic of systems. One of the principal tasks of reliability analysis is evaluation of importance of individual system components for the system proper work. This investigation is known as importance analysis, and it can be qualitative or quantitative. The former focuses on identification of situations in which a change of component activity causes that system performance will change. Its results can be used to detect situations in which the component is critical for system failure/degradation or to propose procedures that are necessary for system repair. The main objective of quantitative analysis is to estimate and evaluate influence of a change of component activity on system performance, and its outcomes can be used to plan system maintenance or to optimize system availability. This paper focuses on importance analysis of multistate systems. It introduces new types of logic derivatives and uses them to identify different types of situations in which a system component is critical for system activity. Furthermore, these derivatives are also used to propose a complex framework for quantitative analysis of multi-state systems.

The prevalence of some chronic diseases, such as cancer or neurodegenerative disorders, differs between sexes. Animal models provide an important tool to adopt potential therapies from preclinical studies to humans. Laboratory rats are the most popular animals in toxicology, neurobehavioral, or cancer research. Our study aimed to reveal the basic differences in blood metabolome (amino acids, biogenic amines, and acylcarnitines) of the adult male (n = 10) and female (n = 10) Wistar rats. Partial least square-discrimination analysis (PLS-DA) and a variance im portance in projection (VIP) score was used to identify the key sex-specific metabolites. All groups of metabolites, as the main markers of energy metabolism, showed a significant sex-dependent pattern. The most important features calculated in PLS-DA according to VIP score were free carnitine (C0), tyrosine (Tyr), and acylcarnitine C5-OH. While aromatic amino acids, such as Tyr and phenylalanine (Phe), were significantly elevated in the blood plasma of males, tryptophan (Trp) was found in higher levels in the blood plasma of females. Besides, significant sex-related changes in urea cycle were found. Our study provides an important insight into sex-specific differences in energy metabolism in rats and indicates that further studies should consider sex as the main aspect in design and data interpretation.

Endometrial cancer (EC) is the most prevalent cancer within the female reproductive system in developed countries. Despite its high incidence, there is currently no established laboratory screening test for EC, making early detection challenging. This study introduces an innovative, minimally invasive, and cost-effective method utilizing three-dimensional fluorescence analysis combined with machine learning algorithms to enhance early EC detection. Intrinsic fluorescence of blood serum samples was measured using a luminescence spectrophotometer, which captured fluorescence spectra as synchronous excitation spectra and visualized them through wavelength contour matrices. The spectral data were processed using machine learning algorithms, including Random Forest (RF), Logistic Regression (LR), Support Vector Machine (SVM), and Stochastic Gradient Descent (SGD), along with exploratory techniques such as Principal Component Analysis (PCA) and Partial Least Squares Discriminant Analysis (PLS-DA). Fluorescence ratios R300/330 and R360/490, indicative of altered tryptophan metabolism and redox state changes, were identified as fluorescent spectral markers and represent key metabolic biomarkers. These ratios demonstrated high diagnostic efficacy with AUC values of 0.88 and 0.91, respectively. Among the ML algorithms, LR and RF exhibited high sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV), showing significant promise for clinical application. After optimization, LR achieved a sensitivity of 0.94, specificity of 0.89, and an impressive AUC value of 0.94. The application of this novel approach in laboratory diagnostics has the potential to significantly enhance early detection and improve prognosis for EC patients.

Reliability analysis of Multi-State System is one of fields, where the methods of the multiple-valued logic are used efficiently. Multi-State System is a mathematical model in reliability engineering, which allows considering some performance level in the system reliability behavior. The principal problem in the reliability engineering is identification of the system components that have the most influence on the system reliability. One of possible approaches, which can be used for this task, is to identify minimal cut sets (or minimal cut vectors (MCVs)). MCVs represent situations in which the repair of any damaged component causes the system improvement. In this paper, the new theoretical background for identification of MCVs is considered. The presented method is based on logical differential calculus.

One of the current issues of reliability analysis is investigation of complex systems consisting of many components. Investigation of such systems requires developing efficient methods for their representation. One of the possible ways is use of Binary Decision Diagrams (BDDs) that allow storing information about system topology in an efficient way. However, the main problem behind BDDs is how to create a good BDD. In this paper, we focus on construction of BDDs for common system structures such as series, parallel and k-out-of-n. Using these results, we present a method for creation of a good BDD for k-to-l-out-of-n systems, which are a typical instance of noncoherent systems. In the next phase, we use BDDs and logical differential calculus to develop an efficient method for importance analysis of k-to-l-out-of-n systems.