Clarke critical values of subanalytic Lipschitz continuous functions

We prove that any subanalytic locally Lipschitz function has the Sard property. Such functions are typically nonsmooth and their lack of regularity necessitates the choice of some generalized notion of gradient and of critical point. In our framework these notions are defined in terms of the Clarke and of the convex-stable subdifferentials. The main result of this note asserts that for any subanalytic locally Lipschitz function the set of its Clarke critical values is locally finite. The proof relies on Pawlucki's extension of the Puiseuxlemma. In the last section we give an example of a continuous subanalytic function which is not constant on a segment of "broadly critical" points, that is, points for which we can find arbitrarily short convex combinations of gradients at nearby points.

Investor protection, risk sharing and inequality

This paper studies the relationship between investor protection, financial risk sharing and income inequality. In the presence of market frictions, better protection makes investors more willing to take on entrepreneurial risk while lending to firms. This implies lower cost of external finance and better risk sharing between financiers and entrepreneurs. Investor protection, by boosting the market for risk sharing plays the twofold role of encouraging agents to undertake risky enterprises and providing them with insurance. By increasing the number of risky projects, it raises income inequality. By extending insurance to more agents, it reduces it. As a result, the relationship between the size of the market for risk sharing and income inequality is hump-shaped. Empirical evidence from a cross-section of sixty-eight countries, and a panel of fifty countries over the period 1976-2000, supports the predictions of the model.

Heritability, determinants and reference values of renal length: a family-based population study.

OBJECTIVES: In this population-based study, reference values were generated for renal length, and the heritability and factors associated with kidney length were assessed. METHODS: Anthropometric parameters and renal ultrasound measurements were assessed in randomly selected nuclear families of European ancestry (Switzerland). The adjusted narrow sense heritability of kidney size parameters was estimated by maximum likelihood assuming multivariate normality after power transformation. Gender-specific reference centiles were generated for renal length according to body height in the subset of non-diabetic non-obese participants with normal renal function. RESULTS: We included 374 men and 419 women (mean ± SD, age 47 ± 18 and 48 ± 17 years, BMI 26.2 ± 4 and 24.5 ± 5 kg/m(2), respectively) from 205 families. Renal length was 11.4 ± 0.8 cm in men and 10.7 ± 0.8 cm in women; there was no difference between right and left renal length. Body height, weight and estimated glomerular filtration rate (eGFR) were positively associated with renal length, kidney function negatively, age quadratically, whereas gender and hypertension were not. The adjusted heritability estimates of renal length and volume were 47.3 ± 8.5 % and 45.5 ± 8.8 %, respectively (P < 0.001). CONCLUSION: The significant heritability of renal length and volume highlights the familial aggregation of this trait, independently of age and body size. Population-based references for renal length provide a useful guide for clinicians. KEY POINTS: • Renal length and volume are heritable traits, independent of age and size. • Based on a European population, gender-specific reference values/percentiles are provided for renal length. • Renal length correlates positively with body length and weight. • There was no difference between right and left renal lengths in this study. • This negates general teaching that the left kidney is larger and longer.

Olympic education experiences: the sponsorship in the promotion of Olympic values

This text was presented at the 16th International Seminar on Olympic Studies for Postgraduate Students that was organised by the International Olympic Academy in Ancient Olympia, from 1st to 30th July 2008. First here are reported, fundamental concepts on Olympics such as the Olympic values and the educational mandate of Pierre de Coubertin, the Olympic brand and symbols, the sponsorship and the Olympic partner programme. Then there is a chapter regarding the Top sponsors educational initiatives on Olympic values, and specially, describing the Olympic sponsors involvement in education and Top sponsors educational activities. And finally, the author analyses the sponsorship role in the promotion of Olympic Values Education, providing conclusions, comments on future and perspectives and some recommendations.

Role of secretory immunoglobulin A and secretory component in the protection of mucosal surfaces.

The contribution of secretory immunoglobulin A (SIgA) antibodies in the defense of mucosal epithelia plays an important role in preventing pathogen adhesion to host cells, therefore blocking dissemination and further infection. This mechanism, referred to as immune exclusion, represents the dominant mode of action of the antibody. However, SIgA antibodies combine multiple facets, which together confer properties extending from intracellular and serosal neutralization of antigens, activation of non-inflammatory pathways and homeostatic control of the endogenous microbiota. The sum of these features suggests that future opportunities for translational application from research-based knowledge to clinics include the mucosal delivery of bioactive antibodies capable of preserving immunoreactivity in the lung, gastrointestinal tract, the genito-urinary tract for the treatment of infections. This article covers topics dealing with the structure of SIgA, the dissection of its mode of action in epithelia lining different mucosal surfaces and its potential in immunotherapy against infectious pathogens.

The new role of the mass media in the construction of sport and Olympic values

This paper was presented in the International Symposium on Toward the Creation of New-Sport Cultures, undertaken in Osaka, Japan, in January 28, 1996. The main purpose is to make an interpretation of the cultural values of sport and Olympism in contemporary society, considering the enormous influence that the media have on them.

Parental Leave and Mothers' Careers: The Relative Importance of Job Protection and Cash Benefits

Job protection and cash benefits are key elements of parental leave (PL) systems. We study how these two policy instruments affect return-to-work and medium-run labour market outcomes of mothers of newborn children. Analysing a series of major PL policy changes in Austria, we find that longer cash benefits lead to a significant delay in return-to-work, particularly so in the period that is job-protected. Prolonged parental leave absence induced by these policy changes does not appear to hurt mothers' labour market outcomes in the medium run. We build a non-stationary model of job search after childbirth to isolate the role of the two policy instruments. The model matches return-to-work and return to same employer profiles under the various factual policy configurations. Counterfactual policy simulations indicate that a system that combines cash with protection dominates other systems in generating time for care immediately after birth while maintaining mothers' medium-run labour market attachment.

Earnings management and cultural values

Using theory and empirical data from social psychology to measure for cultural differences between countries, we study the effect of individualism as defined by Hofstede (1980) and egalitarianism as defined by Schwartz (1994, 1999, 2004) on earnings management. We find a significant influence of both cultural measures. In line with Licht et al. (2004), who argue that individualistic societies may be less susceptible to corruption, we find that countries scoring high on individualism tend to have lower levels of earnings management. In addition, we find that egalitarianism, defined as a society's cultural orientation with respect to intolerance for abuses of market and political power, is negatively related with earnings management. Our results are robust to different specifications and controls. The main message of this paper is that besides formal institutions, cultural differences are relevant to explain earnings management behaviour. We think that our work adds to the understanding of the importance of cultural values in managerial behaviour across countries contributing to the literature on earnings management and law and institutions.

Dividends and weighted values in games with externalities

We consider cooperative environments with externalities (games in partition function form) and provide a recursive definition of dividends for each coalition and any partition of the players it belongs to. We show that with this definition and equal sharing of these dividends the averaged sum of dividends for each player, over all the coalitions that contain the player, coincides with the corresponding average value of the player. We then construct weighted Shapley values by departing from equal division of dividends and finally, for each such value, provide a bidding mechanism implementing it.