Vaccination Schedule under Conditions of Limited Vaccine Production Rate

The paper is devoted to optimal vaccination scheduling during a pandemic to minimize the probability of infection. The recent COVID-19 pandemic showed that the international community is not properly prepared to manage a crisis of this scale. Just after the vaccines had been approved by medical agencies, the policymakers needed to decide on the distribution strategy. To successfully fight the pandemic, the key is to find the equilibrium between the vaccine distribution schedule and the available supplies caused by limited production capacity. This is why society needs to be divided into stratified groups whose access to vaccines is prioritized. Herein, we present the problem of distributing protective actions (i.e., vaccines) and formulate two mixed-integer programs to solve it. The problem of distributing protective actions (PDPA) aims at finding an optimal schedule for a given set of social groups with a constant probability of infection. The problem of distributing protective actions with a herd immunity threshold (PDPAHIT) also includes a variable probability of infection, i.e., the situation when herd immunity is obtained. The results of computational experiments are reported and the potential of the models is illustrated with examples.

Effects of COVID-19 on Variations of Taxpayers in Tourism-Reliant Regions: The Case of the Mexican Caribbean

Given the tourism industry’s risk and vulnerability to pandemics and the need to better understand the impacts on tourism destinations, this research assesses the effect of the COVID-19 outbreak on the variation of taxpayer units in the Mexican Caribbean region, which includes some of the major sun-and-sand beach destinations in Latin America. Using monthly data of registered taxpayer entities at the state and national levels as the analysis variable, probability distributions and definite integrals are employed to determine variations of the year following the lockdown, compared with previous years’ data. Results indicate that despite the government’s measures to restrict businesses’ operations and a reduction in tourism activities, registered taxpayers at the regional level did not decrease for most of 2020. Further, as business activities and tourism recovered, taxpayer units increased at the end of 2020 and beginning of 2021. Surprisingly, such a pattern was not observed at the national level, which yielded no statistically significant variations. A discussion of factors influencing the resilience of the tourism region in the study (e.g., outbound markets’ geographic proximity, absence of travel restrictions, closure of competing destinations) and implications for public finances are presented.

Aircraft Fuselage Corrosion Detection Using Artificial Intelligence

Corrosion identification and repair is a vital task in aircraft maintenance to ensure continued structural integrity. Regarding fuselage lap joints, typically, visual inspections are followed by non-destructive methodologies, which are time-consuming. The visual inspection of large areas suffers not only from subjectivity but also from the variable probability of corrosion detection, which is aggravated by the multiple layers used in fuselage construction. In this paper, we propose a methodology for automatic image-based corrosion detection of aircraft structures using deep neural networks. For machine learning, we use a dataset that consists of D-Sight Aircraft Inspection System (DAIS) images from different lap joints of Boeing and Airbus aircrafts. We also employ transfer learning to overcome the shortage of aircraft corrosion images. With precision of over 93%, we demonstrate that our approach detects corrosion with a precision comparable to that of trained operators, aiding to reduce the uncertainties related to operator fatigue or inadequate training. Our results indicate that our methodology can support specialists and engineers in corrosion monitoring in the aerospace industry, potentially contributing to the automation of condition-based maintenance protocols.

THE EFFECT OF SYSTEMATIC RISK AND UNSYSTEMATIC RISK ON EXPECTED RETURN OF OPTIMAL PORTFOLIO

The purpose of this research is to search out empirical proof that the expected return of shares portfolio is influenced by the presence of systematic and unsystematic risk. The population in this study was a combination of shares portfolio of non-financial companies listed in the LQ45 stock index during the period 2015 - 2019. The technique for sampling in this research using the technique of purposive sampling with a sample of 7 companies combined into 120 samples. The results of the study were obtained from data that had been analyzed using a test of descriptive statistics, a test of classical assumption, determinant coefficients test, and analysis of multiple linear regression through the help of the SPSS application. The results of the research on the F-test showed that the simultaneous systematic risk (X1) and unsystematic risk (X2) have a significant and positive impact on the expected return of portfolio (Y). The results of the t-test showed that partially the systematic risk variable (X1) has a negative and significant impact on the optimal portfolio expected return (Y), and partially the unsystematic risk variable (X2) has a significant and positive impact on the expected return of optimal portfolio (Y). The variable probability of systematic and unsystematic risk has an impact of 53.5% on the expected return on the basis of the effects of the coefficient of determination in this analysis, while the remaining 46.5% is determined by other factors that are not tested.

Predicting the chances of live birth for couples undergoing IVF-ICSI: a novel instrument to advise patients and physicians before treatment

Background: In developed countries, the prevalence of infertility ranges from 3.5% to 16.7%. Therefore, the number of in vitro fertilization technique (IVF) and its subtype intracytoplasmic sperm injection (ICSI) treatments has been significantly increasing across Europe. Several factors affect the success rate of in vitro treatments, which can be used to calculate the probability of success for each couple. As these treatments are complicated and expensive with a variable probability of success, the most common question asked by IVF patients is ‘‘What are my chances of conceiving?”. The main aim of this study is to develop a validated model that estimates the chance of a live birth before they start their IVF non-donor cycle. Methods: A logistic regression model was developed based on the retrospective study of 737 IVF cycles. Each couple was characterized by 14 variables (woman’s and man’s age, duration of infertility, cause of infertility, woman’s and man’s body mass index (BMI), anti-Müllerian hormone (AMH), antral follicle count (AFC), woman’s and man’s ethnicity, woman’s and man’s smoking status and woman’s and man’s previous live children) and described with the outcome of the treatment "Live birth" or "No live birth". Results: The model results showed that from the 14 variables acquired before starting the IVF procedures, only male factor, man’s BMI, man's mixed ethnicity and level of AMH were statistically significant. The interactions between infertility duration and woman’s age, infertility duration and man’s BMI, AFC and AMH, AFC and woman’s age, AFC and woman’s BMI and AFC and disovulation were also statistically significant. The area under the receiver operating characteristic (AUROC) curve test for the discriminatory ability of the final prediction model is 0.700 (95% confidence interval (CI) 0.660–0.741). Conclusions: This model might result in a new validated decision support system to help physicians to manage couples’ expectations.

Sharpness of the Satisfiability Threshold for Non-Uniform Random k-SAT

We study a more general model to generate random instances of Propositional Satisfiability (SAT) with n Boolean variables, m clauses, and exactly k variables per clause. Additionally, our model is given an arbitrary probability distribution (p_1, ..., p_n) on the variable occurrences. Therefore, we call it non-uniform random k-SAT. The number m of randomly drawn clauses at which random formulas go from asymptotically almost surely (a.a.s.) satisfiable to a.a.s. unsatisfiable is called the satisfiability threshold. Such a threshold is called sharp if it approaches a step function as n increases. We identify conditions on the variable probability distribution (p_1, ..., p_n) under which the satisfiability threshold is sharp if its position is already known asymptotically. This result generalizes Friedgut’s sharpness result from uniform to non-uniform random k -SAT and implies sharpness for thresholds of a wide range of random k -SAT models with heterogeneous probability distributions, for example such models where the variable probabilities follow a power-law.

Probability Density Functions

This chapter builds on probability distributions. Its focus is on general concepts associated with probability density functions (pdf’s), which are distributions associated with continuous random variables. The continuous uniform and normal distributions are highlighted as examples of pdf’s. These and other pdf’s can be used to specify prior distributions, likelihoods, and/or posterior distributions in Bayesian inference. Although this chapter specifically focuses on the continuous uniform and normal distributions, the concepts discussed in this chapter will apply to other continuous probability distributions. By the end of the chapter, the reader should be able to define and use the following terms for a continuous random variable: random variable, probability distribution, parameter, probability density, likelihood, and likelihood profile.

INVESTIGATION OF THE PARAMETERS OF RELIABILITY OF LOW VOLTAGE COMMUTATION DEVICES ON OPERATING DATA OF INDUSTRIAL ENTERPRISES

The article presents an algorithm for estimating reliability parameters - probability of failure-free operation time and failure rate of low-voltage switching devices based on statistical data on failures of circuit breakers installed in control and protection circuits of such consumers as compressors, pumps and fans in industrial enterprises. The theoretical and statistical functions of the probability of the failure-free operation time of automatic circuit breakers depending on the service life and the number of operation cycles have been investigated and a hypothesis has been put forward and confirmed on the normal distribution law of the random variable (probability of failure-free operation o automatic circuit breakers) using the "agreement criteria" - the Kolmogorov test and Pearson's criterion.