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.

Nonlinear models and small sample performance of the generalized method of moments

In this paper I explore the issue of nonlinearity (both in the datageneration process and in the functional form that establishes therelationship between the parameters and the data) regarding the poorperformance of the Generalized Method of Moments (GMM) in small samples.To this purpose I build a sequence of models starting with a simple linearmodel and enlarging it progressively until I approximate a standard (nonlinear)neoclassical growth model. I then use simulation techniques to find the smallsample distribution of the GMM estimators in each of the models.

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.