Time of ruin in a risk model with generalized Erlang (n) interclaim times and a constant dividend barrier

In this paper we analyze the time of ruin in a risk process with the interclaim times being Erlang(n) distributed and a constant dividend barrier. We obtain an integro-differential equation for the Laplace Transform of the time of ruin. Explicit solutions for the moments of the time of ruin are presented when the individual claim amounts have a distribution with rational Laplace transform. Finally, some numerical results and a compare son with the classical risk model, with interclaim times following an exponential distribution, are given.

P value and the theory of hypothesis testing: an explanation for new researchers.

In the 1920s, Ronald Fisher developed the theory behind the p value and Jerzy Neyman and Egon Pearson developed the theory of hypothesis testing. These distinct theories have provided researchers important quantitative tools to confirm or refute their hypotheses. The p value is the probability to obtain an effect equal to or more extreme than the one observed presuming the null hypothesis of no effect is true; it gives researchers a measure of the strength of evidence against the null hypothesis. As commonly used, investigators will select a threshold p value below which they will reject the null hypothesis. The theory of hypothesis testing allows researchers to reject a null hypothesis in favor of an alternative hypothesis of some effect. As commonly used, investigators choose Type I error (rejecting the null hypothesis when it is true) and Type II error (accepting the null hypothesis when it is false) levels and determine some critical region. If the test statistic falls into that critical region, the null hypothesis is rejected in favor of the alternative hypothesis. Despite similarities between the two, the p value and the theory of hypothesis testing are different theories that often are misunderstood and confused, leading researchers to improper conclusions. Perhaps the most common misconception is to consider the p value as the probability that the null hypothesis is true rather than the probability of obtaining the difference observed, or one that is more extreme, considering the null is true. Another concern is the risk that an important proportion of statistically significant results are falsely significant. Researchers should have a minimum understanding of these two theories so that they are better able to plan, conduct, interpret, and report scientific experiments.

Peroxisome Proliferator-Activated Receptor beta/delta in the Brain: Facts and Hypothesis.

peroxisome proliferator-activated receptors (PPARs) are nuclear receptors acting as lipid sensors. Besides its metabolic activity in peripheral organs, the PPAR beta/delta isotype is highly expressed in the brain and its deletion in mice induces a brain developmental defect. Nevertheless, exploration of PPARbeta action in the central nervous system remains sketchy. The lipid content alteration observed in PPARbeta null brains and the positive action of PPARbeta agonists on oligodendrocyte differentiation, a process characterized by lipid accumulation, suggest that PPARbeta acts on the fatty acids and/or cholesterol metabolisms in the brain. PPARbeta could also regulate central inflammation and antioxidant mechanisms in the damaged brain. Even if not fully understood, the neuroprotective effect of PPARbeta agonists highlights their potential benefit to treat various acute or chronic neurological disorders. In this perspective, we need to better understand the basic function of PPARbeta in the brain. This review proposes different leads for future researches.

Lag-one autocorrelation in short series: Estimation and hypothesis testing

In the first part of the study, nine estimators of the first-order autoregressive parameter are reviewed and a new estimator is proposed. The relationships and discrepancies between the estimators are discussed in order to achieve a clear differentiation. In the second part of the study, the precision in the estimation of autocorrelation is studied. The performance of the ten lag-one autocorrelation estimators is compared in terms of Mean Square Error (combining bias and variance) using data series generated by Monte Carlo simulation. The results show that there is not a single optimal estimator for all conditions, suggesting that the estimator ought to be chosen according to sample size and to the information available of the possible direction of the serial dependence. Additionally, the probability of labelling an actually existing autocorrelation as statistically significant is explored using Monte Carlo sampling. The power estimates obtained are quite similar among the tests associated with the different estimators. These estimates evidence the small probability of detecting autocorrelation in series with less than 20 measurement times.

A comparison of mean phase difference and generalized least squares for analyzing single-case data

The present study focuses on single-case data analysis and specifically on two procedures for quantifying differences between baseline and treatment measurements The first technique tested is based on generalized least squares regression analysis and is compared to a proposed non-regression technique, which allows obtaining similar information. The comparison is carried out in the context of generated data representing a variety of patterns (i.e., independent measurements, different serial dependence underlying processes, constant or phase-specific autocorrelation and data variability, different types of trend, and slope and level change). The results suggest that the two techniques perform adequately for a wide range of conditions and researchers can use both of them with certain guarantees. The regression-based procedure offers more efficient estimates, whereas the proposed non-regression procedure is more sensitive to intervention effects. Considering current and previous findings, some tentative recommendations are offered to applied researchers in order to help choosing among the plurality of single-case data analysis techniques.

The Uncertain generalized probabilistic weighted average and its application in the theory of expertons

A new model for dealing with decision making under risk by considering subjective and objective information in the same formulation is here presented. The uncertain probabilistic weighted average (UPWA) is also presented. Its main advantage is that it unifies the probability and the weighted average in the same formulation and considering the degree of importance that each case has in the analysis. Moreover, it is able to deal with uncertain environments represented in the form of interval numbers. We study some of its main properties and particular cases. The applicability of the UPWA is also studied and it is seen that it is very broad because all the previous studies that use the probability or the weighted average can be revised with this new approach. Focus is placed on a multi-person decision making problem regarding the selection of strategies by using the theory of expertons.

On the success of generalized food deception in orchids : the role of sympatric rewarding species and pollinators

Résumé : La production de nectar assure aux plantes entomophiles un important succès reproducteur. Malgré cela, de nombreuses espèces d'orchidées ne produisent pas de nectar. La majorité de ces orchidées dites trompeuses exploitent simplement l'instinct des pollinisateurs généralistes, qui les pousse à chercher du nectar dans les fleurs. Afin d'optimiser la récolte de nectar, les pollinisateurs apprennent à différencier les fleurs trompeuses des nectarifères, et à concentrer leurs visites sur ces dernières, au détriment des plantes trompeuses. Chez les orchidées non autogames, la reproduction est assurée uniquement par les pollinisateurs. L'apprentissage des pollinisateurs a donc un impact négatif sur la reproduction des orchidées trompeuses. Cependant, les caractéristiques d'une espèce trompeuse et des espèces nectarifères au sein d'une communauté végétale peuvent affecter l'apprentissage et le taux de visite des pollinisateurs aux plantes trompeuses. J'ai réalisé des expériences en milieu naturel et en milieu contrôlé, pour déterminer si les caractéristiques florales, spatiales et temporelles des communautés affectent le taux de visite et le succès reproducteur de plantes trompeuses. Une agrégation spatiale élevée des plantes trompeuses et des plantes nectarifères diminue le succès reproducteur des plantes trompeuses. De plus, les pollinisateurs visitent plus souvent l'espèce trompeuse Iorsque ses fleurs sont de couleur similaire à celles de l'espèce nectarifère. Cet effet bénéfique de la similarité pour la couleur des fleurs s'accentue si les deux espèces sont mélangées et proches spatialement, ou si l'espèce trompeuse fleurit après l'espèce nectarifère. Enfin, le comportement des pollinisateurs n'est pas tout de suite affecté lorsque les caractéristiques de la communauté changent. Les caractéristiques des communautés végétales affectent donc la reproduction des espèces trompeuses. Bien que L'absence de coûts associés à la production de nectar, l'exportation efficace de pollen et la production de graines de qualité dont bénéficient les orchidées trompeuses favorisent Ieur maintien, les caractéristiques de la communauté peuvent aussi y contribuer. Mon étude fournit donc une explication alternative et complémentaire au maintien des orchidées trompeuses. Je conclus par une discussion des implications possibles de ces résultats sur le maintien et l'évolution des orchidées trompeuses, en tenant compte de la dynamique des caractéristiques des communautés végétales naturelles. Abstract : Despite the importance of producing food to ensure a high reproductive success, many orchid species lack such rewards. The majority of deceptive orchids simply exploit the instinctive food-foraging behaviour of generalist pollinators. This strategy is termed generalized food deception. To optimize their foraging efficiency, pollinators can learn to discriminate deceptive from rewarding flowers and to focus their visits to the rewarding plants, to the disadvantage of the deceptive plants. Because the reproductive success of non-autogamous orchids entirely relies on pollinator visitation rate, pollinator learning decreases the reproductive success of deceptive orchids. However, the characteristics of deceptive and rewarding plants within a community may affect pollinator learning and visitation rate to a deceptive orchid. Therefore, the biological characteristics of natural plant communities may be crucial to the maintenance of generalized food deceptive orchids. My study focused on the floral, spatial and temporal characteristics of plant communities. I used both in and ex sitar experiments to investigate whether these characteristics influence pollinator visitation rates and the reproductive success of deceptive orchids. A high spatial aggregation of both deceptive and rewarding species decreased the reproductive success of the deceptive species. Also, being of similar flower colour to rewarding sympatric species increased pollinator visitation rates to a deceptive species. The beneficial effect of flower colour similarity was even more pronounced when both species were spatially closely mingled or when the deceptive species flowered after the rewarding species. Finally, pollinator behaviour was unaffected in the short term by a change in the characteristics of plant communities, indicating that pollinators need time to learn under new conditions. Thus, the characteristics of plant communities may crucially affect the reproductive success of deceptive orchids. Although the absence of costs associated with nectar production, the efficient pollen export and the high seed quality of deceptive orchids may favour their maintenance, the characteristics of plant communities may also contribute to it. Therefore, my study provides an alternative yet complementary explanation to the maintenance of generalized food deceptive orchids in natural populations. I discuss the possible implications for the maintenance and the evolution of generalized food deceptive orchids with regards to the floral and temporal dynamics of natural plant communities.

Changes in the foraging strategy of female South American sea lions (Carnivora: Pinnipedia) after parturition.

This study tests the hypothesis that female South American sea lions shift from off-shore, pelagic prey to coastal, benthic prey after parturition in order to reduce the foraging trip duration and hence the time pups remain unattended on the beach during early lactation. The δ13C and δ15N values of the serum and blood cells of 26 South American sea lion suckling pups from northern Patagonia were used to track the dietary changes of their mothers from late pregnancy to early lactation, after correction for differential isotopic fractionation between tissues. Primary producers and potential prey species were also analysed to establish a baseline for interpreting the stable isotope concentration of serum and blood cells. Isotopic ratios revealed a generalized increase in the consumption of coastal-benthic prey after parturition. Such a generalized post-partum shift will allow females to spend more time on land and look after their pups. The effects of this foraging strategy on the nutritional quality of the female"s diet are discussed.

Residence time, expansion toward the equator in the invaded range and native range size matter to climatic niche shifts in non-native species

Aim Identifying climatic niche shifts and their drivers is important to accurately predict the risk of biological invasions. The niches of non-native plants and birds have recently been assessed in large-scale multi-species studies, but such large-scale tests are lacking for non-native reptiles and amphibians (herpetofauna). Furthermore, little is known about the factors contributing to niche shifts when they occur. Based on the occurrence of 71 reptile and amphibian species, we compared native and non-native realized niches in 101 invaded ranges at a worldwide scale and identified the factors that affect niche shifts. Location The world except the Antarctic. Methods We assessed climatic niche dynamics in a gridded environmental space allowing the quantification of niche overlap and expansion into climatic conditions not colonized by the species in their native range. We analyzed the factors affecting niche shifts using a model averaging approach based on generalized linear mixed-effects models. Results Approximately 57% of the invaded ranges (51% for amphibians and 61% for reptiles) showed niche shifts (≥10% expansion in the realized climatic niche). Island endemics, species introduced to Oceania and invaded ranges outside the native biogeographic realm showed a higher proportion of niche shifts. Niche shifts were more likely for species that had smaller native range sizes, were introduced earlier into a new range or invaded areas located at lower latitudes than the native range. Main conclusions The proportion of niche shifts for non-native herpetofauna was higher than those for Holarctic non-native plants and European non-native birds. The 'climate matching hypothesis' should be used with caution for species shifting their niche because it could underestimate the risk of their establishment.

Interpolating and sampling sequences in finite Riemann surfaces

We provide a description of the interpolating and sampling sequences on a space of holomorphic functions on a finite Riemann surface, where a uniform growth restriction is imposed on the holomorphic functions.

La funció Z de Riemann

El novembre de 1859 Riemann envià un manuscrit de sis fulls a l’Acadèmia de Berlín titulat Sobre el nombre de primers menors que una quantitat donada, el qual seria l’única publicació dedicada a la teoria de nombres de tota la seva producció científica. Aquest treball, sens dubte una de les peces mestres de les matemàtiques de tots els temps, és pioner en l’aplicació de tècniques analítiques per a l’estudi de problemes aritmètics. En ell Riemann introdueix la funció Z i en dóna diverses propietats, de les quals en treu conseqüències sobre l’acumulació dels nombres primers. També hi enuncia la famosa conjectura sobre els seus zeros que ha passat a la història amb el nom d’hipòtesi de Riemann, i que, havent resistit els esforços de molts dels millors matemàtics del segle xx, és considerada avui dia el problema obert més important de les matemàtiques. L’objectiu d’aquestes notes és explicar el contingut del treball de Riemann i el paper fonamental que ha jugat en l’estudi de la distribució dels nombres primers.

A Generalized Model Study of Scour Around Bridge Piers and Abutments, HR-24, 1953

Four classes of variables are apparent in the problem of scour around bridge piers and abutments--geometry of piers and abutments, stream-flow characteristics, sediment characteristics, and geometry of site. The laboratory investigation, from its inception, has been divided into four phases based on these classes. In each phase the variables in three of the classes are held constant and those in the pertinent class are varied. To date, the first three phases have been studied. Typical scour bole patterns related to the geometry of the pier or abutment have been found. For equilibrium conditions of scour with uniform sand, the velocity of flow and the sand size do not appear to have any measurable effects on the depth of scour. This result is especially encouraging in the search for correlation between model and prototype since it would indicate that, primarily, only the depth of flow might be involved in the scale effect. The technique of model testing has been simplified, therefore, because rate of sediment transportation does not need to be scaled. Prior to the establishment of equilibrium conditions, however, depths of scour in excess of those for equilibrium conditions have been found. A concept of active scour as an imbalance between sediment transport capacity and rate of sediment supply has been used to explain the laboratory observations.