S-Restricted Compositions Revisited

An S-restricted composition of a positive integer n is an ordered partition of n where each summand is drawn from a given subset S of positive integers. There are various problems regarding such compositions which have received attention in recent years. This paper is an attempt at finding a closed- form formula for the number of S-restricted compositions of n. To do so, we reduce the problem to finding solutions to corresponding so-called interpreters which are linear homogeneous recurrence relations with constant coefficients. Then, we reduce interpreters to Diophantine equations. Such equations are not in general solvable. Thus, we restrict our attention to those S-restricted composition problems whose interpreters have a small number of coefficients, thereby leading to solvable Diophantine equations. The formalism developed is then used to study the integer sequences related to some well-known cases of the S-restricted composition problem

Homocysteine, vitamin B12 and folate levels in premature coronary artery disease

BACKGROUND: Hyperhomocysteinemia is known as an independent risk factor of atherosclerosis, but the probable role of hyperhomocysteinemia in premature Coronary Artery Disease (CAD) is not well studied. The aim of this study was to assess the role of hyperhomocysteinemia, folate and Vitamin B12 deficiency in the development of premature CAD. METHODS: We performed an analytical case-control study on 294 individuals under 45 years (225 males and 69 females) who were admitted for selective coronary angiography to two centers in Tehran. RESULTS: After considering the exclusion criteria, a total number of 225 individuals were enrolled of which 43.1% had CAD. The mean age of participants was 39.9 +/- 4.3 years (40.1 +/- 4.2 years in males and 39.4 +/- 4.8 years in females). Compared to the control group, the level of homocysteine measured in the plasma of the male participants was significantly high (14.9 +/- 1.2 versus 20.3 +/- 1.9 micromol/lit, P = 0.01). However there was no significant difference in homocysteine level of females with and without CAD (11.8 +/- 1.3 versus 11.5 ± 1.1 micromol/lit, P = 0.87). Mean plasma level of folic acid and vitamin B12 in the study group were 6.3 +/- 0.2 and 282.5 +/- 9.1 respectively. Based on these findings, 10.7% of the study group had folate deficiency while 26.6% had Vitamin B12 deficiency. Logistic regression analysis for evaluating independent CAD risk factors showed hyperhomocysteinemia as an independent risk factor for premature CAD in males (OR = 2.54 0.95% CI 1.23 to 5.22, P = 0.01). Study for the underlying causes of hyperhomocysteinemia showed that male gender and Vitamin B12 deficiency had significant influence on incidence of hyperhomocysteinemia. CONCLUSION: We may conclude that hyperhomocysteinemia is an independent risk factor for CAD in young patients (bellow 45 years old) – especially in men -and vitamin B12 deficiency is a preventable cause of hyperhomocysteinemia

Global, regional, and national incidence, prevalence, and years lived with disability for 354 diseases and injuries for 195 countries and territories, 1990-2017: a systematic analysis for the Global Burden of Disease Study 2017.

The Global Burden of Diseases, Injuries and Risk Factors 2017 includes a comprehensive assessment of incidence, prevalence, and years lived with disability (YLDs) for 354 causes in 195 countries and territories from 1990 to 2017. Previous GBD studies have shown how the decline of mortality rates from 1990 to 2016 has led to an increase in life expectancy, an ageing global population, and an expansion of the non-fatal burden of disease and injury. These studies have also shown how a substantial portion of the world's population experiences non-fatal health loss with considerable heterogeneity among different causes, locations, ages, and sexes. Ongoing objectives of the GBD study include increasing the level of estimation detail, improving analytical strategies, and increasing the amount of high-quality data. METHODS: We estimated incidence and prevalence for 354 diseases and injuries and 3484 sequelae. We used an updated and extensive body of literature studies, survey data, surveillance data, inpatient admission records, outpatient visit records, and health insurance claims, and additionally used results from cause of death models to inform estimates using a total of 68 781 data sources. Newly available clinical data from India, Iran, Japan, Jordan, Nepal, China, Brazil, Norway, and Italy were incorporated, as well as updated claims data from the USA and new claims data from Taiwan (province of China) and Singapore. We used DisMod-MR 2.1, a Bayesian meta-regression tool, as the main method of estimation, ensuring consistency between rates of incidence, prevalence, remission, and cause of death for each condition. YLDs were estimated as the product of a prevalence estimate and a disability weight for health states of each mutually exclusive sequela, adjusted for comorbidity. We updated the Socio-demographic Index (SDI), a summary development indicator of income per capita, years of schooling, and total fertility rate. Additionally, we calculated differences between male and female YLDs to identify divergent trends across sexes. GBD 2017 complies with the Guidelines for Accurate and Transparent Health Estimates Reporting

Global, regional, and national incidence, prevalence, and years lived with disability for 354 diseases and injuries for 195 countries and territories, 1990-2017: a systematic analysis for the Global Burden of Disease Study 2017

The Global Burden of Diseases, Injuries, and Risk Factors Study 2017 (GBD 2017) includes a comprehensive assessment of incidence, prevalence, and years lived with disability (YLDs) for 354 causes in 195 countries and territories from 1990 to 2017. Previous GBD studies have shown how the decline of mortality rates from 1990 to 2016 has led to an increase in life expectancy, an ageing global population, and an expansion of the non-fatal burden of disease and injury. These studies have also shown how a substantial portion of the world's population experiences non-fatal health loss with considerable heterogeneity among different causes, locations, ages, and sexes. Ongoing objectives of the GBD study include increasing the level of estimation detail, improving analytical strategies, and increasing the amount of high-quality data.; We estimated incidence and prevalence for 354 diseases and injuries and 3484 sequelae. We used an updated and extensive body of literature studies, survey data, surveillance data, inpatient admission records, outpatient visit records, and health insurance claims, and additionally used results from cause of death models to inform estimates using a total of 68 781 data sources. Newly available clinical data from India, Iran, Japan, Jordan, Nepal, China, Brazil, Norway, and Italy were incorporated, as well as updated claims data from the USA and new claims data from Taiwan (province of China) and Singapore. We used DisMod-MR 2.1, a Bayesian meta-regression tool, as the main method of estimation, ensuring consistency between rates of incidence, prevalence, remission, and cause of death for each condition. YLDs were estimated as the product of a prevalence estimate and a disability weight for health states of each mutually exclusive sequela, adjusted for comorbidity. We updated the Socio-demographic Index (SDI), a summary development indicator of income per capita, years of schooling, and total fertility rate. Additionally, we calculated differences between male and female YLDs to identify divergent trends across sexes. GBD 2017 complies with the Guidelines for Accurate and Transparent Health Estimates Reporting. Globally, for females, the causes with the greatest age-standardised prevalence were oral disorders, headache disorders, and haemoglobinopathies and haemolytic anaemias in both 1990 and 2017. For males, the causes with the greatest age-standardised prevalence were oral disorders, headache disorders, and tuberculosis including latent tuberculosis infection in both 1990 and 2017. In terms of YLDs, low back pain, headache disorders, and dietary iron deficiency were the leading Level 3 causes of YLD counts in 1990, whereas low back pain, headache disorders, and depressive disorders were the leading causes in 2017 for both sexes combined. All-cause age-standardised YLD rates decreased by 3·9% (95% uncertainty interval [UI] 3·1-4·6) from 1990 to 2017; however, the all-age YLD rate increased by 7·2% (6·0-8·4) while the total sum of global YLDs increased from 562 million (421-723) to 853 million (642-1100). The increases for males and females were similar, with increases in all-age YLD rates of 7·9% (6·6-9·2) for males and 6·5% (5·4-7·7) for females. We found significant differences between males and females in terms of age-standardised prevalence estimates for multiple causes. The causes with the greatest relative differences between sexes in 2017 included substance use disorders (3018 cases [95% UI 2782-3252] per 100 000 in males vs s1400 [1279-1524] per 100 000 in females), transport injuries (3322 [3082-3583] vs 2336 [2154-2535]), and self-harm and interpersonal violence (3265 [2943-3630] vs 5643 [5057-6302]). Global all-cause age-standardised YLD rates have improved only slightly over a period spanning nearly three decades. However, the magnitude of the non-fatal disease burden has expanded globally, with increasing numbers of people who have a wide spectrum of conditions. A subset of conditions has remained globally pervasive since 1990, whereas other conditions have displayed more dynamic trends, with different ages, sexes, and geographies across the globe experiencing varying burdens and trends of health loss. This study emphasises how global improvements in premature mortality for select conditions have led to older populations with complex and potentially expensive diseases, yet also highlights global achievements in certain domains of disease and injury

S-Restricted Compositions Revisited

An S-restricted composition of a positive integer n is an ordered partition of n where each summand is drawn from a given subset S of positive integers. There are various problems regarding such compositions which have received attention in recent years. This paper is an attempt at finding a closed- form formula for the number of S-restricted compositions of n. To do so, we reduce the problem to finding solutions to corresponding so-called interpreters which are linear homogeneous recurrence relations with constant coefficients. Then, we reduce interpreters to Diophantine equations. Such equations are not in general solvable. Thus, we restrict our attention to those S-restricted composition problems whose interpreters have a small number of coefficients, thereby leading to solvable Diophantine equations. The formalism developed is then used to study the integer sequences related to some well-known cases of the S-restricted composition problem

doi:10.1093/comjnl/bxm014 Service Availability in Concurrent Systems- Part I: A Theory of Hierarchical Services of Interacting Processes

A novel formal model is introduced that is tailored to the treatment of the service availability problem in concurrent systems. This model, called hierarchical services of interacting processes (HSIP), incorporates the hierarchy of services, processes, shared variables, and dense time to reason about services quantitatively. The underlying concept is that a service, via its hierarchy, relates to a number of so-called ‘atomic services ’ at the bottom of the hierarchy that are the outcomes of actions having no subaction within. The services in a hierarchy are the results Mof processes acting and interacting with each other to provide the service at the top of the hierarchy. These processes can completely be described by actions resulting in atomic services. The main features of HSIP are twofold. First, through this model, a wide range of quasi-isolated problems such as mutual exclusion, system reconfiguration, fault tolerance, resource allocation, denial of service, and quality of service can be stated and analyzed in a cohesive manner. Second, it retains the use of shared variables, but resolves the main shortcoming of the shared-variable approach, which is the implicitness of interactions among system components