Про моделювання гаусового стаціонарного процесу Орнштейна-Уленбека з заданою точністю та надійністю в Lp-просторі

Even though the problem of modelling and simulation is not new it continues to be actual over time. Our computers are becoming more powerful and this allows us to use more sofisticated algorithms for more complicated problems. In this paper we constructed the model from the series decomposition of the Gaussian stationary Ornstein–Uhlenbeck process. The Ornstein-Uhlenbeck process is widely used to model reversal processes, exchange rates, asset price volatility, etc. Controlling the model’s accuracy and reliability with which it approximates the real process is important for applications. For this purpuse we have established the relation between the model’s erorr measured in the norm of Lp-space and accuracy and reliability. The classical methods and results from the general theory of stochastic processes and sub-Gaussian spaces of random variables were used in our research. Since Gaussian stochastic processes are sub-Gaussian as well, we can utilize them. For one particular case the calculations were made in order to show how our results can be used in the particular situations. The results from our paper can help to simulate and analyse the situations which the Ornstein–Uhlenbeck process fits well. Pages of the article in the issue: 51 - 56 Language of the article: EnglishНезважаючи на те, що задачі моделювання та симулювання процесів не є новими, вони залишаються актуальними і дотепер. Наші комп’ютери стають потужнішими, і це дозволяє нам використовувати складніші алгоритми для більш складних задач. У цій статті ми побудували модель на основі розкладу гаусового стаціонарного процесу Орнштейна–Уленбека в ряд. Процес Орнштейн-Уленбека широко використовується для моделювання реверсивних процесів, обмінних курсів, коливань цін на активи тощо. Контроль точності та надійності моделі, з якими вона апроксимує реальний процес, важливий для застосувань. З цією метою ми встановили співвідношення між похибкою моделі, виміряною в нормі Lp-простору, та точністю та надійністю. Класичні методи та результати із загальної теорії стохастичних процесів і субгаусових просторів випадкових величин були використаний у нашому дослідженні. Оскільки стохастичні процеси Гауса також є субгаусовими, ми можемо їх використовувати. Для одного конкретного випадку були зроблені розрахунки, щоб показати, як наші результати можуть бути використані в конкретних ситуаціях. Результати нашої статті можуть допомогти змоделювати та проаналізувати ситуації, для яких добре підходить процес Орнштейна–Уленбека

Bounds for the Tail Distributions of Suprema of Sub-Gaussian Type Random Fields

The paper presents bounds for the distributions of suprema for particular classes of ϕ-sub-Gaussian random fields. Results stated depend on representations of bounds for increments of the fields in different metrics. Several examples of applications are provided to illustrate the results, in particular, to random fields related to stochastic partial differential equations and partial differential equations with random initial conditions

Ensuring the Professional Work Capacity of Staff amid the New Socio-Economic Reality

The essence and factors of professional work capacity, as well as its role in ensuring high job performance, are analyzed. The main task of the study was to analyze factors influencing the working capacity of modern employees; to identify the level of their satisfaction with the conditions and management of work; and to substantiate the ways to improve work capacity at enterprises, taking into account current threats caused by the COVID-19 pandemic. Based on the survey, the satisfaction level of employees at Ukrainian enterprises as for the existing measures aimed at ensuring and maintaining the work capacity of staff at the workplace, e.g. working conditions and recreation and other measures, is analyzed. The subjective fatigue among employees has been assessed, revealing the absence of a system for monitoring the working capacity and general physical and mental state of employees at enterprises, which makes it impossible to introduce qualitative measures to maintain and improve working capacity and eliminate the effects of fatigue. The influence of the COVID-19 pandemic on the conditions and management of work at enterprises, on the employee’s working capacity and their sense of physical and psychological well-being have been identified. Based on the study, the main areas for improving the work capacity of staff at the workplace in the new socio-economic conditions, which would reflect the expectations and needs of employees, are systematized. Priority measures that should be implemented at enterprises to maintain and improve the professional work capacity of staff include the following: clear regulation of job responsibilities and rational distribution of workload among all workflow participants; reduction of the hazardous effect of working conditions on human body; protection of employees from the already existing and potential hazards; compensation of excessive workload by various financial incentives, intangible incentives, improvement of working conditions and recreation; taking into account employees’ individual attributes when planning workload; organization of psychological assistance and counseling for staff members, training sessions on Time-management and Team-building, improvement of social and psychological climate

Corrigendum: Every-Other-Day Feeding Decreases Glycolytic and Mitochondrial Energy-Producing Potentials in the Brain and Liver of Young Mice (Frontiers in Physiology, (2019), 10, 10.3389/fphys.2019.01432)

In the original article, there was a mistake in Figure 6 as published. The incorrect data on the level of ketone bodies in the liver and the cortex ofmice fed ad libitum(control) or subjected to an every- other-day feeding regimen (EODF) over 1month were placed instead of the corresponding data on b-hydroxybutyrate dehydrogenase activity. The corrected Figure 6 and the legend appear below. The authors apologize for this error and state that this does not change the scientific conclusions of the article in any way. The original article has been updated

Every-Other-Day Feeding Decreases Glycolytic and Mitochondrial Energy-Producing Potentials in the Brain and Liver of Young Mice

Intermittent fasting is used to reduce body mass in obese adult humans and animals. However, information on the impact of one type of intermittent fasting (IF) called every-other-day feeding (EODF) on young animals is scarce. In this study, 1-month-old mice of both sexes were subjected to a 4-week regimen of EODF using age-matched counterparts fed ad libitum as controls. At the end of EODF exposure, experimental male and female mice weighed 14 and 13% less than the control counterparts. The EODF regimen resulted in lower liver levels of glycogen, glucose, and lactate, but did not affect lactate level in mouse cerebral cortex of both sexes. Activities of key glycolytic enzymes (hexokinase, phosphofructokinase, and pyruvate kinase) in liver of experimental mice were lower than those in controls. In the cerebral cortex, only hexokinase and pyruvate kinase activities were lower than in controls, but phosphofructokinase activity was not affected in IF females and was higher in IF males as compared with ad libitum fed males. Mitochondria isolated from liver of IF mice had lower respiratory control ratios, but those from the cortex had the same values as control animals. The concentration of β-hydroxybutyrate and the activity of β-hydroxybutyrate dehydrogenase were lower in the IF mouse liver, but not changed or enhanced in the IF cerebral cortex. Thus, animal responses to IF do not depend significantly on sex and are directed to decrease energy metabolism to save resources, and the effects are more pronounced in the liver than in the brain