The M/G/1 retrial queue: an information theoretic approach

In this paper, we give a survey of the use of information theoretic techniques for the estimation of the main performance characteristics of the M/G/1 retrial queue. We focus on the limiting distribution of the system state, the length of a busy period and the waiting time. Numerical examples are given to illustrate the accuracy of the maximum entropy estimations when they are compared versus the classical solutions.Peer Reviewe

Entropy maximization and the busy period of some single-server vacation models

In this paper, information theoretic methodology for system modeling is applied to investigate the probability density function of the busy period in M/G/1 vacation models operating under the N-, T- and D-policies. The information about the density function is limited to a few mean value constraints (usually the first moments). By using the maximum entropy methodology one obtains the least biased probability density function satisfying the system's constraints. The analysis of the three controllable M/G/1 queueing models provides a parallel numerical study of the solution obtained via the maximum entropy approach versus “classical” solutions. The maximum entropy analysis of a continuous system descriptor (like the busy period) enriches the current body of literature which, in most cases, reduces to discrete queueing measures (such as the number of customers in the system)

The busy period and the waiting time analysis of a MAP/M/c queue with finite retrial group

We concentrate on the analysis of the busy period and the waiting time distribution of a multi-server retrial queue in which primary arrivals occur according to a Markovian arrival process (MAP). Since the study of a model with an infinite retrial group seems intractable, we deal with a system having a finite buffer for the retrial group. The system is analyzed in steady state by deriving expressions for (a) the Laplace–Stieltjes transforms of the busy period and the waiting time; (b) the probabiliy generating functions for the number of customers served during a busy period and the number of retrials made by a customer; and (c) various moments of quantites of interest. Some illustrative numerical examples are discussed

Food sources of nutrients in the diet of Spanish children: the Four Provinces Study

The aim of the present study was to assess the principal food sources of energy and nutrients among Spanish children. We used a cross-sectional study design, based on results obtained from a food-frequency questionnaire. The sample included 1112 children, aged 6-7 years, from Cadiz, Madrid, Orense and Murcia, Spain. Children were selected through random cluster-sampling in schools. We analysed the percentage contributed by each food item to total energy and nutrient intake. The most important food sources were: white bread in the case of carbohydrate (13.4 %); olive oil in the case of total lipids (18.3 %) and monounsaturated fatty acids (29.2 %); whole milk in the case of protein (10.2 %) and saturated fatty acids (14.9 %); chips (French fried potatoes) in the case of polyunsaturated fatty acids (30.4 %). The greatest proportion of Na, consumed in excess, came from salt added to meals. Ham ranked second as a source of saturated fats. Fruits and green leafy vegetables proved to have great relevance as sources of fibre and vitamins, though with regard to the latter, it was observed that fortified foods (breakfast cereals, dairy products, fruit juices, etc.) had come to play a relevant role in many cases. In conclusion, the nutritional profile of Spanish school-aged children aged 6-7 years could be improved by nutritional policies targeted at limiting their consumption of ham (cured or cooked) and of salt added to meals, replacing whole milk with semi-skimmed milk, encouraging the consumption of products rich in complex carbohydrates already present in children's diets (bread, pasta, rice) and promoting less fatty ways of cooking food.This study was partly funded by grants from the Inter-national Olive Oil Board (Consejo Oleı ́cola Internacional),Madrid Regional Authority (Comunidad de Madrid), PedroBarrie ́de la Maza Foundation and Eugenio Rodrı ́guezPascual FoundationS

Achievement of treatment goals for primary prevention of cardiovascular disease in clinical practice across Europe: the EURIKA study

Aims: Most studies on the primary prevention of cardiovascular disease (CVD) have been limited to patients at high CVD risk. We assessed the achievement of treatment goals for CVD risk factors among patients with a substantial variation in CVD risk. Methods and results: This study was conducted with 7641 outpatients aged ≥50 years, free of clinical CVD and with at least one major CVD risk factor, selected from 12 European countries in 2009. Risk factor definition and treatment goals were based on the 2007 European guidelines on CVD prevention. Cholesterol fractions and glycated haemoglobin (HbA1c) were measured in a central laboratory. Cardiovascular disease risk was estimated with the SCORE equation. Patients' mean age was 63 years (48% men), and 40.1% had a high CVD risk. Among treated hypertensives (94.2%), only 38.8% achieved the blood pressure target of <140/90 mmHg [between-country range (BCR): 32.1–47.5%]. Among treated dyslipidaemic patients (74.4%), 41.2% attained both the total- and LDL-cholesterol target of <5 and <3 mmol/L, respectively (BCR: 24.3–68.4%). Among treated type 2 diabetic patients (87.2%), 36.7% achieved the <6.5% HbA1c target (BCR: 23.4–48.4%). Among obese patients on non-pharmacological treatment (92.2%), 24.7% reached the body mass index target of <30 kg/m2 (BCR: 12.7–37.1%). About one-third of controlled patients on treatment were still at high remaining CVD risk. Although most patients were advised to reduce excess weight and to follow a low-calorie diet, less than half received written recommendations. Conclusions: In Europe, a large proportion of patients in primary prevention have CVD risk factors that remain uncontrolled, and lifestyle counselling is not well implemented; moreover, there is substantial between-country variation, which indicates additional room for improvement. Raised residual CVD risk is relatively frequent among patients despite control of their primary risk factors and should be addressed

Stochastic descriptors to study the fate and potential of naive T cell clonotypes in the periphery

The population of naive T cells in the periphery is best described by determining both its T cell receptor diversity, or number of clonotypes, and the sizes of its clonal subsets. In this paper, we make use of a previously introduced mathematical model of naive T cell homeostasis, to study the fate and potential of naive T cell clonotypes in the periphery. This is achieved by the introduction of several new stochastic descriptors for a given naive T cell clonotype, such as its maximum clonal size, the time to reach this maximum, the number of proliferation events required to reach this maximum, the rate of contraction of the clonotype during its way to extinction, as well as the time to a given number of proliferation events. Our results show that two fates can be identified for the dynamics of the clonotype: extinction in the short-term if the clonotype experiences too hostile a peripheral environment, or establishment in the periphery in the long-term. In this second case the probability mass function for the maximum clonal size is bimodal, with one mode near one and the other mode far away from it. Our model also indicates that the fate of a recent thymic emigrant (RTE) during its journey in the periphery has a clear stochastic component, where the probability of extinction cannot be neglected, even in a friendly but competitive environment. On the other hand, a greater deterministic behaviour can be expected in the potential size of the clonotype seeded by the RTE in the long-term, once it escapes extinction

Mediterranean lifestyle index and 24-h systolic blood pressure and heart rate in community-dwelling older adults

Specifc foods, nutrients, dietary patterns, and physical activity are associated with lower blood pressure (BP) and heart rate (HR), but little is known about the joint efect of lifestyle factors captured in a multidimensional score. We assessed the association of a validated Mediterranean-lifestyle (MEDLIFE) index with 24-h-ambulatory BP and HR in everyday life among community-living older adults. Data were taken from 2,184 individuals (51% females, mean age: 71.4 years) from the SeniorsENRICA-2 cohort. The MEDLIFE index consisted of 29 items arranged in three blocks: 1) Food consumption; 2) Dietary habits; and 3) Physical activity, rest, and conviviality. A higher MEDLIFE score (0–29 points) represented a better Mediterranean lifestyle adherence. 24-h-ambulatory BP and HR were obtained with validated oscillometric devices. Analyses were performed with linear regression adjusted for the main confounders. The MEDLIFEhighest quintile (vs Q1) was associated with lower nighttime systolic BP (SBP) (-3.17 mmHg [95% CI: -5.25, -1.08]; p-trend=0.011), greater nocturnal-SBP fall (1.67% [0.51, 2.83]; p-trend=0.052), and lower HR (-2.04 bpm [daytime], -2.33 bpm [nighttime], and -1.93 bpm [24-h]; all p-trend<0.001). Results were similar for each of the three blocks of MEDLIFE and by hypertension status (yes/no). Among older adults, higher adherence to MEDLIFE was associated with lower nighttime SBP, greater nocturnal-SBP fall, and lower HR in their everyday life. These results suggest a synergistic BP-related protection from the components of the Mediterranean lifestyle. Future studies should determine whether these results replicate in older adults from other Mediterranean and non-Mediterranean countriesThis work was supported by FIS grants 19/319, 20/00896, and 22/1164 from the Carlos III Health Institute, the Secretary of R+D+I, and the European Regional Development Fund/European Social Fund; and by International; REACT EU Program. Comunidad de Madrid and European Regional Development Fund (ERDF), European Union: FACINGLCOVID-CM project, Comunidad de Madrid and European Regional Development Fund (ERDF), European Union. MSP holds a Ramón y Cajal contract (RYC2018–025069-I) from the Spanish Ministry of Science, Innovation and Universitie

Towns with extremely low mortality due to ischemic heart disease in Spain

BACKGROUND: The cause of coronary disease inframortality in Spain is unknown. The aim of this study is to identify Spanish towns with very low ischemic heart disease mortality, describe their health and social characteristics, and analyze the relationship with a series of contextual factors. METHODS: We obtained the number of deaths registered for each of 8,122 Spanish towns in the periods 1989-1998 and 1999-2003. Expected deaths, standardized mortality ratio (SMR), smoothed Relative Risk (RR), and Posterior Probability (PP) of RR > 1 were calculated using Bayesian hierarchical models. Inframortality was defined as any town that displayed an RR below the 10th percentile, an SMR of under 1 for both sexes, and a PP of RR > 1 less than or equal to 0.002 for male and 0.005 for female mortality, during the two periods covered. All the remaining towns, except for those with high mortality classified as "tourist towns", were selected as controls. The association among socioeconomic, health, dietary, lifestyle and vascular risk factors was analyzed using sequential mixed logistic regression models, with province as the random-effects variable. RESULTS: We identified 32 towns in which ischemic heart disease mortality was half the national rate and four times lower than the European Union rate, situated in lightly populated provinces spread across the northern half of Spain, and revealed a surprising pattern of geographic aggegation for 23 of the 32 towns. Variables related with inframortality were: a less aged population (OR 0.93, 95% CI 0.89-0.99); a contextual dietary pattern marked by a high fish content (OR 2.13, 95% CI 1.38-3.28) and wine consumption (OR 1.50, 95% CI 1.08-2.07); and a low prevalence of obesity (OR 0.47, 95% CI 0.22-1.01); and, in the case of towns of over 1000 inhabitants, a higher physician-population ratio (OR 3.80, 95% CI 1.17-12.3). CONCLUSIONS: Results indicate that dietary and health care factors have an influence on inframortality. The geographical aggregation suggests that other factors with a spatial pattern, e.g., genetic or environmental might also be implicated. These results will have to be confirmed by studies in situ, with objective measurements at an individual level.This study was funded by research study grant no. PI06/0656 from Spain's Health Research Fund (Fondo de Investigación Sanitaria).S

Low Rates of Both Lipid-Lowering Therapy Use and Achievement of Low-Density Lipoprotein Cholesterol Targets in Individuals at High-Risk for Cardiovascular Disease across Europe

Aims To analyse the treatment and control of dyslipidaemia in patients at high and very high cardiovascular risk being treated for the primary prevention of cardiovascular disease (CVD) in Europe. Methods and Results Data were assessed from the European Study on Cardiovascular Risk Prevention and Management in Usual Daily Practice (EURIKA, ClinicalTrials.gov identifier: NCT00882336), which included a randomly sampled population of primary CVD prevention patients from 12 European countries (n = 7641). Patients’ 10-year risk of CVD-related mortality was calculated using the Systematic Coronary Risk Evaluation (SCORE) algorithm, identifying 5019 patients at high cardiovascular risk (SCORE 5% and/or receiving lipid-lowering therapy), and 2970 patients at very high cardiovascular risk (SCORE 10% or with diabetes mellitus). Among high-risk individuals, 65.3% were receiving lipid-lowering therapy, and 61.3% of treated patients had uncontrolled low-density lipoprotein cholesterol (LDL-C) levels ( 2.5 mmol/L). For very-high-risk patients (uncontrolled LDL-C levels defined as 1.8 mmol/L) these figures were 49.5% and 82.9%, respectively. Excess 10-year risk of CVD-related mortality (according to SCORE) attributable to lack of control of dyslipidaemia was estimated to be 0.72%and 1.61% among high-risk and very-high-risk patients, respectively. Among high-risk individuals with uncontrolled LDL-C levels, only 8.7% were receiving a high-intensity statin (atorvastatin 40 mg/day or rosuvastatin 20 mg/day). Among veryhigh- risk patients, this figure was 8.4%. Conclusions There is a considerable opportunity for improvement in rates of lipid-lowering therapy use and achievement of lipid-level targets in high-risk and very-high-risk patients being treated for primary CVD prevention in EuropeWriting support was provided by Oxford PharmaGenesis Ltd, Oxford, UK, and was funded by AstraZenec