A singular function and its relation with the number systems involved in its definition

Minkowski's ?(x) function can be seen as the confrontation of two number systems: regular continued fractions and the alternated dyadic system. This way of looking at it permits us to prove that its derivative, as it also happens for many other non-decreasing singular functions from [0,1] to [0,1], when it exists can only attain two values: zero and infinity. It is also proved that if the average of the partial quotients in the continued fraction expansion of x is greater than k* =5.31972, and ?'(x) exists then ?'(x)=0. In the same way, if the same average is less than k**=2 log2(F), where F is the golden ratio, then ?'(x)=infinity. Finally some results are presented concerning metric properties of continued fraction and alternated dyadic expansions.

Satisfaction in choice as a function of the number of alternatives: When "goods satiate" but "bads escalate"

Whereas people are typically thought to be better off with more choices, studiesshow that they often prefer to choose from small as opposed to large sets of alternatives.We propose that satisfaction from choice is an inverted U-shaped function of thenumber of alternatives. This proposition is derived theoretically by considering thebenefits and costs of different numbers of alternatives and is supported by fourexperimental studies. We also manipulate the perceptual costs of information processingand demonstrate how this affects the resulting satisfaction function. We furtherindicate that satisfaction when choosing from a given set is diminished if people aremade aware of the existence of other choice sets. The role of individual differences insatisfaction from choice is documented by noting effects due to gender and culture. Weconclude by emphasizing the need to have an explicit rationale for knowing how muchchoice is enough.

Cost efficiency in primary care contracting: A stochastic frontier cost function approach

The principal aim of this paper is to estimate a stochastic frontier costfunction and an inefficiency effects model in the analysis of the primaryhealth care services purchased by the public authority and supplied by 180providers in 1996 in Catalonia. The evidence from our sample does not supportthe premise that contracting out has helped improve purchasing costefficiency in primary care. Inefficient purchasing cost was observed in thecomponent of this purchasing cost explicitly included in the contract betweenpurchaser and provider. There are no observable incentives for thecontracted-out primary health care teams to minimise prescription costs, whichare not explicitly included in the present contracting system.

A new light on Minkowski's? $(x)$ function

The well--known Minkowski's? $(x)$ function is presented as the asymptotic distribution function of an enumeration of the rationals in (0,1] based on their continued fraction representation. Besides, the singularity of ?$(x)$ is clearly proved in two ways: by exhibiting a set of measure one in which ?ï$(x)$ = 0; and again by actually finding a set of measure one which is mapped onto a set of measure zero and viceversa. These sets are described by means of metrical properties of different systems for real number representation.

Glutamine Stimulates Biosynthesis and Secretion of Insulin-like Growth Factor 2 (IGF2), an Autocrine Regulator of Beta Cell Mass and Function.

IGF2 is an autocrine ligand for the beta cell IGF1R receptor and GLP-1 increases the activity of this autocrine loop by enhancing IGF1R expression, a mechanism that mediates the trophic effects of GLP-1 on beta cell mass and function. Here, we investigated the regulation of IGF2 biosynthesis and secretion. We showed that glutamine rapidly and strongly induced IGF2 mRNA translation using reporter constructs transduced in MIN6 cells and primary islet cells. This was followed by rapid secretion of IGF2 via the regulated pathway, as revealed by the presence of mature IGF2 in insulin granule fractions and by inhibition of secretion by nimodipine and diazoxide. When maximally stimulated by glutamine, the amount of secreted IGF2 rapidly exceeded its initial intracellular pool and tolbutamide, and high K(+) increased IGF2 secretion only marginally. This indicates that the intracellular pool of IGF2 is small and that sustained secretion requires de novo synthesis. The stimulatory effect of glutamine necessitates its metabolism but not mTOR activation. Finally, exposure of insulinomas or beta cells to glutamine induced Akt phosphorylation, an effect that was dependent on IGF2 secretion, and reduced cytokine-induced apoptosis. Thus, glutamine controls the activity of the beta cell IGF2/IGF1R autocrine loop by increasing the biosynthesis and secretion of IGF2. This autocrine loop can thus integrate changes in feeding and metabolic state to adapt beta cell mass and function.

Abnormal Lung Function and Risk for Heart Failure in the Elderly: The Health, Aging, and Body Composition Study

Background: Chronic obstructive pulmonary disease (COPD) has been associated with increased risk for heart failure (HF). The impact of subclinical abnormal spirometric findings on HF risk among older adults without history of COPD is not well elucidated. Methods: We evaluated 2125 participants (age 73.6±2.9 years; 50.5% men; 62.3% white; 45.6/9.4% past/current smokers; body mass index [BMI] 27.2±4.6 kg/m2) without prevalent COPD or HF who underwent baseline spirometry in the Health ABC Study. Abnormal lung function was defined either as forced vital capacity (FVC) below lower limit of normal (LLN) or forced expiratory volume in 1st sec (FEV1) to FVC ratio below LLN. Results: On follow-up (median, 9.4 years), 68 of 350 (19.4%) participants with abnormal lung function developed HF, as compared to 172 of 1775 (9.7%) participants with normal lung function (hazard ratio [HR], 2.31; 95% confidence interval [CI], 1.74 -3.06; P<.001). This increased risk persisted after adjusting for all other independent predictors of HF in the Health ABC Study, BMI, incident coronary events, and several inflammatory markers (HR, 1.82; 95% CI, 1.30 -2.54; P<.001), and remained constant over time. Baseline FVC and FEV1 had a linear association with HF risk (Figure). In adjusted models, HF risk increased by 21% (95% CI, 10 -36%) per 10% decrease in FVC and 18% (95% CI, 10 -28%) per 10% decrease in FEV1 (both P<.001); this association persisted among participants with normal lung function at baseline. Findings were consistent across sex, race, and smoking status. Conclusions: Subclinical abnormal spirometric findings are prevalent among older adults and are independently associated with risk for incident HF.

Identification of an agrin mutation that causes congenital myasthenia and affects synapse function.

We report the case of a congenital myasthenic syndrome due to a mutation in AGRN, the gene encoding agrin, an extracellular matrix molecule released by the nerve and critical for formation of the neuromuscular junction. Gene analysis identified a homozygous missense mutation, c.5125G>C, leading to the p.Gly1709Arg variant. The muscle-biopsy specimen showed a major disorganization of the neuromuscular junction, including changes in the nerve-terminal cytoskeleton and fragmentation of the synaptic gutters. Experiments performed in nonmuscle cells or in cultured C2C12 myotubes and using recombinant mini-agrin for the mutated and the wild-type forms showed that the mutated form did not impair the activation of MuSK or change the total number of induced acetylcholine receptor aggregates. A solid-phase assay using the dystrophin glycoprotein complex showed that the mutation did not affect the binding of agrin to alpha-dystroglycan. Injection of wild-type or mutated agrin into rat soleus muscle induced the formation of nonsynaptic acetylcholine receptor clusters, but the mutant protein specifically destabilized the endogenous neuromuscular junctions. Importantly, the changes observed in rat muscle injected with mutant agrin recapitulated the pre- and post-synaptic modifications observed in the patient. These results indicate that the mutation does not interfere with the ability of agrin to induce postsynaptic structures but that it dramatically perturbs the maintenance of the neuromuscular junction.

Regulation of endothelial cell integrin function and angiogenesis by COX-2, cAMP and Protein Kinase A.

Angiogenesis, the development of new blood vessels from preexisting vessels, is a key step in tumor growth, invasion and metastasis formation. Inhibition of tumor angiogenesis is considered as an attractive approach to suppress cancer progression and spreading. Adhesion receptors of the integrin family promote tumor angiogenesis by mediating cell migration, proliferation and survival of angiogenic endothelial cells. Integrins up regulated and highly expressed on neovascular endothelial cells, such as alphaVbeta3 and alpha5beta1, have been considered as relevant targets for anti-angiogenic therapies. Small molecular integrin antagonists or blocking antibodies suppress angiogenesis and tumor progression in many animal models, and some of them are currently being tested in cancer clinical trials as anti-angiogenic agents. COX-2 inhibitors exert anti-cancer effects, at least in part, by inhibiting tumor angiogenesis. We have recently shown that COX-2 inhibitors suppress endothelial cell migration and angiogenesis by preventing alphaVbeta3-mediated and cAMP/PKA-dependent activation of the small GTPases Rac and Cdc42. Here we will review the evidence for the involvement of vascular integrins in mediating angiogenesis and the role of COX-2 metabolites in modulating the cAMP/Protein Kinase A pathway and alphaVbeta3-dependent Rac activation in endothelial cells.

Phenotype and function of protective T cell immune responses in HIV.

PURPOSE OF REVIEW: Definition of T cell immune correlates in HIV infection remains a lofty goal towards our understanding of the HIV-specific immune response. This review will focus upon recent developments and controversies in our understanding of protective T cell responses against HIV. RECENT FINDINGS: It has become clear that multiple functions and phenotypic markers of T cells must be assessed to accurately characterize the complexity of CD4 and CD8 T cell responses. While evidence indicates that a hallmark of protective immune responses in HIV infection is the presence of 'polyfunctional' T cell responses, a disconnect remains between the function and phenotype of effective HIV-specific T cells. Moreover, there may be inherent differences in the ability of specific human leukocyte antigen class I families to promote CD8 T cell effector versus polyfunctional responses. It remains to be determined how polyfunctional responses arise in HIV infection, which functions are important for control, and whether surface phenotype markers provide an indication of protective capacity. SUMMARY: Polyfunctional and phenotypic assessment of T cell responses have clearly advanced our understanding of HIV specific immune responses. Critical questions remain, however, especially whether polyfunctional T cell responses control, or are controlled by, HIV replication.

How to Preserve Renal Function in Transcatheter Aortic Valve Therapies

Background: Transcatheter aortic valve implantations (TAVI) are indicated in high risk patients requiring aortic valve replacement (AVR). However, CT-scans, coronary angiograms and intraoperative aortographies can induce contrast-related nephro-toxicity with a concrete risk of acute postoperative renal failure, especially in severely diseased patients. To prevent this complication, we routinely perform transapical (TA) TAVI guided by transesophageal echocardiogram and fluoroscopy without angiography. Material and Methods: From November 2008 to December 2009, 31 high-risk patients suffering from severe symptomatic aortic stenosis underwent TA-TAVI in our institution. The preoperative imaging assessment (cardiac CT-scan and coronary angiogram) was performed no less than 10 days before the TA-TAVI in all patients (to recover the renal function) with a low-dose protocol for injected contrast medium (equivalent to the patient's weight for the CT-scan). During the TA-TAVI, the stent-valve positioning was performed without any contrast injection. Results: 32 consecutive stent-valve were successfully positioned in 31 patients (mean age 80.76 8 8.3 years; mean EuroSCORE: 32.2 8 12.9%) through a transapical access (1 patient required 2 valves for valve embolisation). The mean preoperative creatinine and urea blood levels were 102.6 8 67.7 _ g/dl (range 53-339 _ g/dl) and 8.45 8 4.9 mmol/l, respectively. A chronic renal insufficiency affected 12 patients (38.7%) with 1 patient in pre-dialysis. Postoperatively, no patient developed acute myocardial infarction, atrio-ventricular block or acute renal insufficiency (mean creatinine level: 89.7 8 64.55 _ g/dl; urea level: 7.11 8 3.47 mmol/l) and the 30-days mortality was 9.67% (3 patients). Conclusion: Specific preoperative and intraoperative protocols that require lowdoses or absence of contrast medium are useful to preserve the renal function in high risk patients operated for TAVI.

Autosomal Recessive Posterior Microphthalmos/Nanophthalmos is Caused by Loss-of-function Mutations in LOC646960, a Novel Gene Encoding a Trypsin-like Serine Protease

Purpose: Posterior microphthalmos (MCOP)/nanophthalmos (NNO) is a developmental anomaly characterized by extreme hyperopia due to short axial length. The population of the Faroe Islands shows a high prevalence of an autosomal recessive form (arMCOP). The gene mutated in arMCOP is not yet known.Methods: Genetic mapping by linkage analysis using microsatellite and single nucleotide polymorphisms, mutation analysis by PCR and sequencing, molecular modellingResults: Having refined the position of the disease locus (MCOP6) in an interval of 250 kb in chromosome 2q37.1 in Faroese families, we detected 3 mutations in a novel gene, LOC646960: Patients of 10 different Faroese families were either homozygous (n=22) for c.926G>C (p.Trp309Ser) or compound heterozygous (n=6) for c.926G>C and c.526C>G (p.Arg176Gly), whereas a homozygous 1 bp duplication (c.1066dupC) was identified in patients with arNNO from a Tunisian family. In two unrelated patients with MCOP, no LOC646960 mutation was found. LOC646960 is expressed in the human adult retina and RPE. The expression of the mouse homologue in the eye can be first detected at E17 and is highest in adults. The predicted protein is a 603 amino acid long secreted trypsin-like serine peptidase. c.1066dupC should result in a functional null allele. Molecular modelling of the p.Trp309Ser mutant suggests that both affinity and reactivity of the enzyme towards in vivo substrates are substantially reduced.Conclusions: Postnatal growth of the eye is important for proper development of the refractive components (emmetropization), and is mainly due to elongation of the posterior segment from 10-11 mm at birth to 15-16 mm at the age of 13 years. Optical defocus leads to changes in axial length by moving the retina towards the image plane. arMCOP may theoretically be explained, in line with the expression pattern of LOC646960, by a postnatal growth retardation of the posterior segment.

Tapering for marathon and cardiac autonomic function.

The purpose of this study was to investigate changes in post-exercise heart rate recovery (HRR) and heart rate variability (HRV) during an overload-tapering paradigm in marathon runners and examine their relationship with running performance. 9 male runners followed a training program composed of 3 weeks of overload followed by 3 weeks of tapering (-33±7%). Before and after overload and during tapering they performed an exhaustive running test (Tlim). At the end of this test, HRR variables (e.g. HRR during the first 60 s; HRR60 s) and vagal-related HRV indices (e.g. RMSSD5-10 min) were examined. Tlim did not change during the overload training phase (603±105 vs. 614±132 s; P=0.992), but increased (727±185 s; P=0.035) during the second week of tapering. Compared with overload, RMSSD5-10 min (7.6±3.3 vs. 8.6±2.9 ms; P=0.045) was reduced after the 2(nd) week of tapering. During tapering, the improvements in Tlim were negatively correlated with the change in HRR60 s (r=-0.84; P=0.005) but not RMSSD5-10 min (r=-0.21; P=0.59). A slower HRR during marathon tapering may be indicative of improved performance. In contrast, the monitoring of changes in HRV as measured in the present study (i.e. after exercise on a single day), may have little or no additive value.

Small airways function declines after allogeneic haematopoietic stem cell transplantation.

Bronchiolitis obliterans (BO) following allogeneic haematopoietic stem cell transplantation (HSCT) affects peripheral airways. Detection of BO is presently delayed by the low sensitivity of spirometry. We examined the relationship between peripheral airway function and time since HSCT, and compared it with spirometry and clinical indices in 33 clinically stable allogeneic HSCT recipients. The following measurements were performed: lung function, exhaled nitric oxide, forced oscillatory respiratory system resistance and reactance, acinar (S(acin)) and conductive airways ventilation heterogeneity and lung clearance index (LCI) measured by multiple breath nitrogen washout. 22 patients underwent repeat visits from which short-term changes were examined. Median time post HSCT was 12 months. Eight patients were clinically diagnosed as having BO. In multivariate analysis, time since HSCT was predicted by S(acin) and forced expiratory volume in 1 s % predicted. 20 patients had abnormal S(acin) with normal spirometry, whereas none had airflow obstruction with normal S(acin). S(acin) and LCI were the only measures to change significantly between two visits, with both worsening. Change in S(acin) was the only parameter to correlate with change in chronic graft-versus-host disease grade. In conclusion, peripheral airways ventilation heterogeneity worsens with time after HSCT. S(acin) may be more sensitive than spirometry in detecting BO at an early stage, which needs confirmation in a prospective study.

Regional coronary endothelial function is closely related to local early coronary atherosclerosis in patients with mild coronary artery disease: pilot study.

BACKGROUND: Coronary endothelial function is abnormal in patients with established coronary artery disease and was recently shown by MRI to relate to the severity of luminal stenosis. Recent advances in MRI now allow the noninvasive assessment of both anatomic and functional (endothelial function) changes that previously required invasive studies. We tested the hypothesis that abnormal coronary endothelial function is related to measures of early atherosclerosis such as increased coronary wall thickness. METHODS AND RESULTS: Seventeen arteries in 14 healthy adults and 17 arteries in 14 patients with nonobstructive coronary artery disease were studied. To measure endothelial function, coronary MRI was performed before and during isometric handgrip exercise, an endothelial-dependent stressor, and changes in coronary cross-sectional area and flow were measured. Black blood imaging was performed to quantify coronary wall thickness and indices of arterial remodeling. The mean stress-induced change in cross-sectional area was significantly higher in healthy adults (13.5%±12.8%, mean±SD, n=17) than in those with mildly diseased arteries (-2.2%±6.8%, P<0.0001, n=17). Mean coronary wall thickness was lower in healthy subjects (0.9±0.2 mm) than in patients with coronary artery disease (1.4±0.3 mm, P<0.0001). In contrast to healthy subjects, stress-induced changes in cross-sectional area, a measure of coronary endothelial function, correlated inversely with coronary wall thickness in patients with coronary artery disease (r=-0.73, P=0.0008). CONCLUSIONS: There is an inverse relationship between coronary endothelial function and local coronary wall thickness in patients with coronary artery disease but not in healthy adults. These findings demonstrate that local endothelial-dependent functional changes are related to the extent of early anatomic atherosclerosis in mildly diseased arteries. This combined MRI approach enables the anatomic and functional investigation of early coronary disease.

Nrf2 links epidermal barrier function with antioxidant defense.

The skin provides an efficient permeability barrier and protects from microbial invasion and oxidative stress. Here, we show that these essential functions are linked through the Nrf2 transcription factor. To test the hypothesis that activation of Nrf2 provides skin protection under stress conditions, we determined the consequences of pharmacological or genetic activation of Nrf2 in keratinocytes. Surprisingly, mice with enhanced Nrf2 activity in keratinocytes developed epidermal thickening, hyperkeratosis and inflammation resembling lamellar ichthyosis. This resulted from upregulation of the cornified envelope proteins small proline-rich proteins (Sprr) 2d and 2h and of secretory leukocyte peptidase inhibitor (Slpi), which we identified as novel Nrf2 targets in keratinocytes. Since Sprrs are potent scavengers of reactive oxygen species and since Slpi has antimicrobial activities, their upregulation contributes to Nrf2's protective function. However, it also caused corneocyte fragility and impaired desquamation, followed by alterations in the epidermal lipid barrier, inflammation and overexpression of mitogens that induced keratinocyte hyperproliferation. These results identify an unexpected role of Nrf2 in epidermal barrier function, which needs to be considered for pharmacological use of Nrf2 activators.