Near-optimal mean value estimates for multidimensional Weyl sums

We obtain sharp estimates for multidimensional generalisations of Vinogradov’s mean value theorem for arbitrary translation-dilation invariant systems, achieving constraints on the number of variables approaching those conjectured to be the best possible. Several applications of our bounds are discussed.

A mean value for pairs of integrals

Se prueba que para dos funciones continuas reales, una determinada ecuación posee solució única. Se presenta también una generalización a integrales con peso.

Maximum principle, mean value operators and quasi boundedness in non-euclidean settings

This work deals with some classes of linear second order partial differential operators with non-negative characteristic form and underlying non- Euclidean structures. These structures are determined by families of locally Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot- Carath´eodory type. The Carnot-Carath´eodory metric related to a family {Xj}j=1,...,m is the control distance obtained by minimizing the time needed to go from two points along piecewise trajectories of vector fields. We are mainly interested in the causes in which a Sobolev-type inequality holds with respect to the X-gradient, and/or the X-control distance is Doubling with respect to the Lebesgue measure in RN. This study is divided into three parts (each corresponding to a chapter), and the subject of each one is a class of operators that includes the class of the subsequent one. In the first chapter, after recalling “X-ellipticity” and related concepts introduced by Kogoj and Lanconelli in [KL00], we show a Maximum Principle for linear second order differential operators for which we only assume a Sobolev-type inequality together with a lower terms summability. Adding some crucial hypotheses on measure and on vector fields (Doubling property and Poincar´e inequality), we will be able to obtain some Liouville-type results. This chapter is based on the paper [GL03] by Guti´errez and Lanconelli. In the second chapter we treat some ultraparabolic equations on Lie groups. In this case RN is the support of a Lie group, and moreover we require that vector fields satisfy left invariance. After recalling some results of Cinti [Cin07] about this class of operators and associated potential theory, we prove a scalar convexity for mean-value operators of L-subharmonic functions, where L is our differential operator. In the third chapter we prove a necessary and sufficient condition of regularity, for boundary points, for Dirichlet problem on an open subset of RN related to sub-Laplacian. On a Carnot group we give the essential background for this type of operator, and introduce the notion of “quasi-boundedness”. Then we show the strict relationship between this notion, the fundamental solution of the given operator, and the regularity of the boundary points.

Functional equations and the Cauchy mean value theorem

The aim of this note is to characterize all pairs of sufficiently smooth functions for which the mean value in the Cauchy mean value theorem is taken at a point which has a well-determined position in the interval. As an application of this result, a partial answer is given to a question posed by Sahoo and Riedel.

Mean-value identities as an opportunity for Monte Carlo error reduction

In the Monte Carlo simulation of both lattice field theories and of models of statistical mechanics, identities verified by exact mean values, such as Schwinger-Dyson equations, Guerra relations, Callen identities, etc., provide well-known and sensitive tests of thermalization bias as well as checks of pseudo-random-number generators. We point out that they can be further exploited as control variates to reduce statistical errors. The strategy is general, very simple, and almost costless in CPU time. The method is demonstrated in the twodimensional Ising model at criticality, where the CPU gain factor lies between 2 and 4.

A Quantile-Based Probabilistic Mean Value Theorem

For non-negative random variables with finite means we introduce an analogous of the equilibrium residual-lifetime distribution based on the quantile function. This allows us to construct new distributions with support (0, 1), and to obtain a new quantile-based version of the probabilistic generalization of Taylor's theorem. Similarly, for pairs of stochastically ordered random variables we come to a new quantile-based form of the probabilistic mean value theorem. The latter involves a distribution that generalizes the Lorenz curve. We investigate the special case of proportional quantile functions and apply the given results to various models based on classes of distributions and measures of risk theory. Motivated by some stochastic comparisons, we also introduce the “expected reversed proportional shortfall order”, and a new characterization of random lifetimes involving the reversed hazard rate function.

A Mean Value Theorem for non Differentiable Mappings in Banach Spaces

We prove that if f is a real valued lower semicontinuous function on a Banach space X and if there exists a C^1, real valued Lipschitz continuous function on X with bounded support and which is not identically equal to zero, then f is Lipschitz continuous of constant K provided all lower subgradients of f are bounded by K. As an application, we give a regularity result of viscosity supersolutions (or subsolutions) of Hamilton-Jacobi equations in infinite dimensions which satisfy a coercive condition. This last result slightly improves some earlier work by G. Barles and H. Ishii.

Some Mean-Value Theorems of the Cauchy Type

2000 Mathematics Subject Classification: Primary 26A24, 26D15; Secondary 41A05

Integrating postoperative value of cardiac Troponin I for a better correlation with in-hospital outcomes after congenital heart surgery.

Objective: Cardiac Troponin-I (cTnI) is a well-recognized early postoperative marker for myocardial damage in adults and children after heart surgery. The present study was undertaken to evaluate whether the integrated value (area under the curve(AUC)) of postoperative cTnI is a better mode to predict long-term outcome than post operative cTnI maximum value, after surgery for congenital heart defects (CHD). Methods: retrospective cohort study. 279 patients (mean age 4.6 years; range 0-17 years-old, 185 males) with congenital heart defect repair on cardiopulmonary by-pass were retrieved from our database including postoperative cTnI values. Maximal post operative cTnI value, post operative cTnI AUC value at 48h and total post operative cTnI AUC value were calculated and then correlated with duration of intubation, duration of ICU stay and mortality. Results: the mean duration of mechanical ventilation was 5.1+/-7.2 days and mean duration of ICU stay was 11.0+/- 13.3 days,11 patients (3.9%) died in post operative period. When comparing survivor and deceased groups, there was a significant difference in the mean value for max cTnI (16.7+/- 21.8 vs 59.2+/-41.4 mcg/l, p+0.0001), 48h AUC cTnI (82.0+/-110.7 vs 268.8+/-497.7 mcg/l, p+0.0001) and total AUC cTnI (623.8+/-1216.7 vs 2564+/-2826.0, p+0.0001). Analyses for duration of mechanical ventilation and duration of ICU stay by linear regression demonstrated a better correlation for 48h AUC cTnI (ventilation time r+0.82, p+0.0001 and ICU stay r+0.74, p+0.0001) then total AUC cTnI (ventilation time r+0.65, p+0.0001 and ICU stay r+0.60, p+0.0001) and max cTnI (ventilation time r+0.64, p+0.0001 and ICU stay r+0.60, p+0.0001). Conclusion: Cardiac Troponin I is a specific and sensitive marker of myocardial injury after congenital heart surgery and it may predict early in-hospital outcomes. Integration of post operative value of cTnI by calculation of AUC improves prediction of early in-hospital outcomes. It probably takes into account, not only the initial surgical procedure, but probably also incorporates the occurrence of hypoxic-ischemic phenomena in the post-operative period.

Value of sTREM-1, procalcitonin and CRP as laboratory parameters for postmortem diagnosis of sepsis.

OBJECTIVES: Triggering receptor expressed on myeloid cells-1 (TREM-1) was reported to be up-regulated in various inflammatory diseases as well as in bacterial sepsis. Increased cell-surface TREM-1 expression was also shown to result in marked plasma elevation of the soluble form of this molecule (sTREM-1) in patients with bacterial infections. In this study, we investigated sTREM-1, procalcitonin and C-reactive protein in postmortem serum in a series of sepsis-related fatalities and control individuals who underwent medico-legal investigations. sTREM-1 was also measured in pericardial fluid and urine. METHODS: Two study groups were prospectively formed, a sepsis-related fatalities group and a control group. The sepsis-related fatalities group consisted of sixteen forensic autopsy cases. Eight of these had a documented clinical diagnosis of sepsis in vivo. The control group consisted of sixteen forensic autopsy cases with various causes of death. RESULTS: Postmortem serum sTREM-1 concentrations were higher in the sepsis group with a mean value of 173.6 pg/ml in septic cases and 79.2 pg/ml in control individuals. The cutoff value of 90 pg/ml provided the best sensitivity and specificity. Pericardial fluid sTREM-1 values were higher in the septic group, with a mean value of 296.7 pg/ml in septic cases and 100.9 pg/ml in control individuals. The cutoff value of 135 pg/ml provided the best sensitivity and specificity. Mean urine sTREM-1 concentration was 102.9 pg/ml in septic cases and 89.3 pg/ml in control individuals. CONCLUSIONS: Postmortem serum sTREM-1, individually considered, did not provide better sensitivity and specificity than procalcitonin in detecting sepsis. However, simultaneous assessment of procalcitonin and sTREM-1 in postmortem serum can be of help in clarifying contradictory postmortem findings. sTREM-1 determination in pericardial fluid can be an alternative to postmortem serum in those situations in which biochemical analyses are required and blood collected during autopsy proves insufficient.

Electrical colonic stimulation reduces mean transit time in a porcine model.

Abstract Electrical stimulation is a new way to treat digestive disorders such as constipation. Colonic propulsive activity can be triggered by battery operated devices. This study aimed to demonstrate the effect of direct electrical colonic stimulation on mean transit time in a chronic porcine model. The impact of stimulation and implanted material on the colonic wall was also assessed. Three pairs of electrodes were implanted into the caecal wall of 12 anaesthetized pigs. Reference colonic transit time was determined by radiopaque markers for each pig before implantation. It was repeated 4 weeks after implantation with sham stimulation and 5 weeks after implantation with electrical stimulation. Aboral sequential trains of 1-ms pulse width (10 V; 120 Hz) were applied twice daily for 6 days, using an external battery operated stimulator. For each course of markers, a mean value was computed from transit times obtained from individual pig. Microscopic examination of the caecum was routinely performed after animal sacrifice. A reduction of mean transit time was observed after electrical stimulation (19 +/- 13 h; mean +/- SD) when compared to reference (34 +/- 7 h; P = 0.045) and mean transit time after sham stimulation (36 +/- 9 h; P = 0.035). Histological examination revealed minimal chronic inflammation around the electrodes. Colonic transit time measured in a chronic porcine model is reduced by direct sequential electrical stimulation. Minimal tissue lesion is elicited by stimulation or implanted material. Electrical colonic stimulation could be a promising approach to treat specific disorders of the large bowel.

The mean corpuscular volume and hydroxyurea in brazilian patients with sickle cell anemia: a surrogate marker of compliance

The suppression of erythropoiesis by Hydroxyurea (HU) therapy is associated with increase in mean corpuscular volume, in addition to the increase in Hb F. Monitoring the mean corpuscular volume values and the presence of macrocytosis are effective tools of adherence to the treatment with HU in patients with sickle cell anemia. The aim of this study is to monitor the mean corpuscular volume values after starting treatment with HU to determine if macrocytosis can be used as a surrogate marker of compliance with therapy. We conducted a prospective cohort study over one year with measurements of blood counts and mean corpuscular volume after starting therapy with HU in 95 patients with sickle cell anemia who were regularly followed in our ambulatory outpatient unit. In one-year of successful use of HU the mean value of the mean corpuscular volume increased significantly. The Andersen and Gill model demonstrated that the increase of one unit of MCV implies a 5% reduction in the risk of visiting the emergency room. Monitoring mean corpuscular volume values after prescribing HU alerts the provider of noncompliance in order to counsel the patient in question for better adherence to the use of HU that could improve the quality of care and to reduce morbidity and the frequency of acute pain crises and associated healthcare costs.

Moral reasoning in sport: validation of the Portuguese version of the RSBH value-judgement inventory in adolescents

The purpose of this study was to examine the validity and reliability of the Portuguese version of the Rudd Stoll Beller Hahm Value-judgement Inventory (RSBHVI) in a sample of adolescents. The RSBHVI, which measures moral and social reasoning, was translated using a back translation method. A sample of 238 10th to 12th grade high school students (age mean value 16.93 years, s = 1.34) completed the Portuguese versions of RSBH, and the Task and Ego-orientation Questionnaire. Partial support for the original structure of the moral reasoning scale, but not the social reasoning scale, was found. Females, and non-athletes and individual sport athletes scored significantly higher than males and team sport athletes in moral reasoning, respectively. Moral reasoning was negatively correlated with ego-orientation (r = −30; p <. 001) and uncorrelated with task-orientation (r = .10, p > .05). Participants who were low-ego scored higher in moral reasoning than those who were high-ego. It is suggested that decreasing levels of ego-orientation may be necessary to improve athletes’ moral reasoning.