Spline smoothing is a technique used to filter out noise in time series observations when predicting nonparametric regression models. Its performance depends on the choice of the smoothing parameter. Most of the existing smoothing methods applied to time series data tend to over fit in the presence of autocorrelated errors. This study aims to determine the optimum performance value, goodness of fit and model overfitting properties of the proposed Smoothing Method (PSM), Generalized Maximum Likelihood (GML), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR) smoothing parameter selection methods. A Monte Carlo experiment of 1,000 trials was carried out at three different sample sizes (20, 60, and 100) and three levels of autocorrelation (0.2, 05, and 0.8). The four smoothing methods' performances were estimated and compared using the Predictive Mean Squared Error (PMSE) criterion. The findings of the study revealed that: for a time series observation with autocorrelated errors, provides the best-fit smoothing method for the model, the PSM does not over-fit data at all the autocorrelation levels considered ( the optimum value of the PSM was at the weighted value of 0.04 when there is autocorrelation in the error term, PSM performed better than the GCV, GML, and UBR smoothing methods were considered at all-time series sizes (T = 20, 60 and 100). For the real-life data employed in the study, PSM proved to be the most efficient among the GCV, GML, PSM, and UBR smoothing methods compared. The study concluded that the PSM method provides the best fit as a smoothing method, works well at autocorrelation levels (ρ=0.2, 0.5, and 0.8), and does not over fit time-series observations. The study recommended that the proposed smoothing is appropriate for time series observations with autocorrelation in the error term and econometrics real-life data. This study can be applied to; non – parametric regression, non – parametric forecasting, spatial, survival, and econometrics observations.Full article

The paper considers a specific type of such financial instrument as an option, namely an exotic barrier call option of the European type. Exotic options are gaining popularity among ordinary investors due to the development of information and telecommunication technologies, thanks to which such specific financial instruments as options have become readily available. We investigate the hedging problem for such options with some restrictions on the payment function and the availability of dividend payment on a risky asset in the classical Black-Scholes model. An analogue of the Black-Scholes formula for the mentioned variant of the exotic barrier is proved. In the future, it is planned to generalize the obtained results for put options and for more general payment functions.Full article

We study the theory of combinatorial games and find winning strategies for players. The algorithmic implementation of the winning strategies for the game TacTix is presented and the software implementation for this game in Python programming language is implemented. The program has a console interface and allows one to check the winning strategies in practice.Full article

The SARS-COV-2 rapid spread caused an international public health emergency with unprecedented rates of morbidity and mortality. Post COVID-19 condition occurs as a spectrum of symptoms that present four or more weeks after acute infection with SARS-CoV-2. Most published data to date state 50-70% of hospitalized patients experienced at least one post-acute COVID-19 symptom up to 3 months after discharge. Commonly reported symptoms include; neurocognitive post COVID-19 (fatigue, dizziness, inattention, and brain fog), respiratory post-COVID (dyspnea, chest pain, and cough), and mental health related symptoms (insomnia, depression, and post-traumatic stress disorder). Additionally, gastro-intestinal post COVID-19 (diarrhea, vomiting, and abdominal pain) along with decline in quality of life and decreased ability to perform activities of daily living were reported. The response to post COVID-19 symptoms is still in its infancy despite being an emerging crisis as scientific evidence and robust data are nonetheless required for clear definition, identification of time frame, classification and management of the condition. New studies are needed to identify total and individual incidence/prevalence rates of different clinical presentations of post COVID-19 symptoms. These future studies will help us to o improve early recognition of long term symptoms after acute infection of COVID-19.Full article

Many attempts have been made to repurpose existing and approved drugs for the treatment of COVID-19 infection. This involves anti-malarial drugs such as hydroxychloroquine and chloroquine, which have been shown to be less successful than initially believed, with a substantial risk of often fatal complications and interactions. This also involves Remdesivir, which has been shown to decrease recovery time significantly in hospitalized patients. However, for patients who are not yet hospitalized, there is no currently accepted treatment. Treating patients before they need to be admitted or even prophylactically could greatly decrease the load on hospitals, protect healthcare workers and reduce the spread of COVID-19. An in-vitro study indicated that Ivermectin was dynamic against COVID-19-infected cell. Ivermectin has antimicrobial, antiviral, and anticancer, immunomodulatory properties. This drug could reduce the viral load in COVID-9 infected patients, with potential effect on disease progression and spread. Therefore, Ivermectin may be a therapeutic choice for treatment of COVID-19, however, there is still a lack of evidence-based studies to support ivermectin treatment of patients with COVID-19.Full article