Copulas constructed from horizontal sections

In analogy with the study of copulas whose diagonal sections have been fixed, we study the set $\mathcal{C}_h$ of copulas for which a horizontal section $h$ has been given. We first show that this set is not empty, by explicitly writing one such copula, which we call \textit{horizontal copula}. Then we find the copulas that bound both below and above the set $\mathcal{C}_h$. Finally we determine the expressions for Kendall's tau and Spearman's rho for the horizontal and the bounding copulas

Sex-dependent differences in stress-induced depression in Wistar rats are accompanied predominantly by changes in phosphatidylcholines and sphingomyelins

With a high annual and lifetime prevalence, depression is becoming the leading contributor to the global disease burden. During the COVID-19 crisis, the depression and mood disorders accelerated significantly. Despite the growing evidence, the precise underlying mechanisms of depression disorders (DD) remain unknown. When studying DD in humans, there are many uncontrollable factors such as medication history, age of the patient or living conditions. In this regard, animal models provide an essential step for examining neural circuitry or molecular and cellular pathways in a controlled environment. As far as we know, women have a consistently higher prevalence of DD than men. Thus, the aim of our study was to evaluate sex-related changes in blood metabolites in a model of stress-induced depression in Wistar rats. Pregnant females were stressed using restriction of mobility in the final week of the pregnancy three times a day for 45 minutes each, three following days. After the birth, the progeny aged 60 days was stressed repeatedly. The perturbation in overall energy metabolism as well as in lipid metabolism was found. While in males, phosphatidylcholines (the most phosphatidylcholine with acyl-alkyl residue sum C40:4 - PC ae C40:4), sphingomyelins, and acylcarnitines were changed, in females, lipid metabolism perturbation was seen with the most critical alteration in hydroxysphingomyelin with acyl residue sum C16:1 (SM OH C16:1). Our results confirm that the animal model may be used further in the research of depression. Our results may provide an essential insight into the sex-dependent pathogenesis of depression and contribute to the search for effective treatment and prevention of depression with respect to sex

Atrasentan and renal events in patients with type 2 diabetes and chronic kidney disease (SONAR): a double-blind, randomised, placebo-controlled trial

Background: Short-term treatment for people with type 2 diabetes using a low dose of the selective endothelin A receptor antagonist atrasentan reduces albuminuria without causing significant sodium retention. We report the long-term effects of treatment with atrasentan on major renal outcomes. Methods: We did this double-blind, randomised, placebo-controlled trial at 689 sites in 41 countries. We enrolled adults aged 18–85 years with type 2 diabetes, estimated glomerular filtration rate (eGFR)25–75 mL/min per 1·73 m 2 of body surface area, and a urine albumin-to-creatinine ratio (UACR)of 300–5000 mg/g who had received maximum labelled or tolerated renin–angiotensin system inhibition for at least 4 weeks. Participants were given atrasentan 0·75 mg orally daily during an enrichment period before random group assignment. Those with a UACR decrease of at least 30% with no substantial fluid retention during the enrichment period (responders)were included in the double-blind treatment period. Responders were randomly assigned to receive either atrasentan 0·75 mg orally daily or placebo. All patients and investigators were masked to treatment assignment. The primary endpoint was a composite of doubling of serum creatinine (sustained for ≥30 days)or end-stage kidney disease (eGFR <15 mL/min per 1·73 m 2 sustained for ≥90 days, chronic dialysis for ≥90 days, kidney transplantation, or death from kidney failure)in the intention-to-treat population of all responders. Safety was assessed in all patients who received at least one dose of their assigned study treatment. The study is registered with ClinicalTrials.gov, number NCT01858532. Findings: Between May 17, 2013, and July 13, 2017, 11 087 patients were screened; 5117 entered the enrichment period, and 4711 completed the enrichment period. Of these, 2648 patients were responders and were randomly assigned to the atrasentan group (n=1325)or placebo group (n=1323). Median follow-up was 2·2 years (IQR 1·4–2·9). 79 (6·0%)of 1325 patients in the atrasentan group and 105 (7·9%)of 1323 in the placebo group had a primary composite renal endpoint event (hazard ratio [HR]0·65 [95% CI 0·49–0·88]; p=0·0047). Fluid retention and anaemia adverse events, which have been previously attributed to endothelin receptor antagonists, were more frequent in the atrasentan group than in the placebo group. Hospital admission for heart failure occurred in 47 (3·5%)of 1325 patients in the atrasentan group and 34 (2·6%)of 1323 patients in the placebo group (HR 1·33 [95% CI 0·85–2·07]; p=0·208). 58 (4·4%)patients in the atrasentan group and 52 (3·9%)in the placebo group died (HR 1·09 [95% CI 0·75–1·59]; p=0·65). Interpretation: Atrasentan reduced the risk of renal events in patients with diabetes and chronic kidney disease who were selected to optimise efficacy and safety. These data support a potential role for selective endothelin receptor antagonists in protecting renal function in patients with type 2 diabetes at high risk of developing end-stage kidney disease. Funding: AbbVie

Aggregation and related functions in fuzzy set theory: dualities and monotonicity-based generalizations

We discuss several extensions of binary Boolean functions acting on the domain [0, 1]. Formally, there are 16 disjoint classes of such functions, covering a majority of binary functions considered in fuzzy set theory. We introduce and discuss dualities in this framework, stressing the links between different subclasses of considered functions, e.g., the link between conjunctive and implication functions. Special classes of considered functions are characterized, among others, by particular kinds of monotonicity. Relaxing these constraints by considering monotonicity in one direction only, we generalize standard classes of aggregation functions, implications, semicopulas, etc., into larger classes called pre-aggregations, pre-implications, pre-semicopulas, etc. Note that the dualities discussed for the standard classes also relate the new extended classes of pre-functions

Інноваційна діяльність SPA-компаній Словаччини та Чехії в умовах пандемії Covid-19

У багатьох системах охорони здоров'я європейських країн санаторно-курортні послуги в даний час є частиною або доповненням до медичної допомоги. Чехія та Словаччина завдяки своїм природним лікувальним ресурсам і давнім традиціям належать до значущих європейських курортних країн. В обох країнах санаторно-курортний туризм також є одним із найважливіших видів туризму, а з огляду на його оцінку за кількістю ночівель і доходом займає значну частку в структурі туристичної галузі. Однією з найбільших проблем для SPA-бізнесу стала пандемія COVID-19, яка спричинила обмеження на подорожі, закриття підприємств і падіння попиту та доходів. Питання впливу пандемії на санаторно-курортний бізнес у досліджуваних країнах досі детально не розглядалося. Відповідно до вищесказаного, метою представленого внеску є оцінка інноваційної діяльності курортних компаній у Словаччині та Чехії в контексті пандемії COVID-19. Вибірку дослідження склали 122 санаторнокурортних підприємства обох республік. За результатами попередніх досліджень встановлено, що інновації загалом сприймаються як важливий елемент розвитку суспільства, антикризового управління, підвищення конкурентоспроможності та комерційного успіху. Основним методом дослідження виявлення та класифікації типів інновацій та інноваційних можливостей, що впроваджуються на санаторно-курортних підприємствах, було анкетне опитування. За результатами проведеного дослідження виявилося, що походження SPA-бізнесу не впливає на країну, на те, як люди сприймають тенденції. Підтверджено зв’язки між типами впроваджуваних інновацій та деякими вигодами від впровадження інновацій, а також бар’єрами, що перешкоджають впровадженню інновацій. Звідси випливає, наприклад, що компанії, які інвестують в інноваційні процеси, можуть покращити свою ефективність і конкурентоспроможність своєї команди, зменшити свої витрати на виробництво або надання послуг. З аналізу факторів, пов’язаних із впровадженням інновацій, виявилося, що найважливішими є ті фактори, які безпосередньо впливають на економічні результати та конкурентні переваги підприємств. З іншого боку, фактори, пов’язані з культурними, екологічними чи технічними аспектами інновацій, менш важливі. Певними обмеженнями проведеного дослідження був той факт, що, незважаючи на неодноразові дзвінки, не всі SPA-компанії, які працюють у SPA-індустрії Чеської та Словацької Республік, взяли участь.In many health systems in European countries, SPA services are currently part of or a supplement to health care. Owing to their natural healing resources and long-standing traditions, the Czech Republic and Slovak Republic are important European SPA countries. In both countries, SPA tourism is also one of the most important types of tourism, and with regard to its evaluation according to the number of overnight stays and income, it constitutes a significant share of the structure of the tourism industry. One of the greatest challenges for SPA businesses was the COVID-19 pandemic, which caused travel restrictions, business closures, and a decrease in demand and revenue. The impact of the pandemic on SPA businesses in the studied countries has not yet been examined in detail. Accordingly, the aim of the present study is to evaluate the innovative activities of SPA companies in Slovakia and the Czech Republic in the context of the COVID-19 pandemic. The research sample consists of 122 SPA enterprises from both republics. Based on the results of previous research, innovation is generally perceived as an important element in the development of society, crisis management, increasing competitiveness and commercial success. The main research method for identifying and classifying the types of innovations and innovation capabilities implemented in SPA enterprises was a questionnaire survey. The results of the conducted research revealed that the origin of SPA businesses does not affect the country or how people perceive trends. The connections between the types of introduced innovations and some benefits from the introduction of innovations as well as the barriers affecting the introduction of innovations were confirmed. It follows, for example, that companies that invest in innovation processes can improve their performance and the competitiveness of their team and reduce their costs for production or service provision. From the analysis of factors related to the introduction of innovations, it emerged that the most important factors are those that have a direct impact on economic results and the competitive advantage of businesses. On the other hand, those factors related to cultural, environmental or technical aspects of innovation are less important. Despite repeated calls, not all SPA companies operating in the SPA industry in the Czech Republic and Slovak Republic participated

Measure-preserving transformations, copulae and compatibility

We study the relationship between copulas and measure-preserving transformations on the Borel sets of the u it interval. This also allows to investigate the connection with a restricted compatibility problem for copulas. To this end, in order to construct a 3-copula from two given 2-copulas A and B, we modify the *-operation introduced by Darsow et al., show that A*B is always compatible with A and B, and study the set D(A,B) of all copulas comaptible with A and

Discrete copulas

In this paper we will discuss the structure and properties of discrete copulas in a specialcase when both marginal discrete distribution functions coincide, i.e., they correspond to the uniform probability distribution on the set {0, 1/n, 2/n, . . . , (n−1)/n } and thus F(i/n)= G(i/n) = i/n, i = 0, 1, . . . , n