Gap probabilities for the cardinal sine

We study the zero set of random analytic functions generated by a sum of the cardinal sine functions which form an orthogonal basis for the Paley-Wiener space. As a model case, we consider real-valued Gaussian coefficients. It is shown that the asymptotic probability that there is no zero in a bounded interval decays exponentially as a function of the length.

Perturbation expansions of multilocus fixation probabilities for frequency-dependent selection with applications to the Hill-Robertson effect and to the joint evolution of helping and punishment.

Natural populations are of finite size and organisms carry multilocus genotypes. There are, nevertheless, few results on multilocus models when both random genetic drift and natural selection affect the evolutionary dynamics. In this paper we describe a formalism to calculate systematic perturbation expansions of moments of allelic states around neutrality in populations of constant size. This allows us to evaluate multilocus fixation probabilities (long-term limits of the moments) under arbitrary strength of selection and gene action. We show that such fixation probabilities can be expressed in terms of selection coefficients weighted by mean first passages times of ancestral gene lineages within a single ancestor. These passage times extend the coalescence times that weight selection coefficients in one-locus perturbation formulas for fixation probabilities. We then apply these results to investigate the Hill-Robertson effect and the coevolution of helping and punishment. Finally, we discuss limitations and strengths of the perturbation approach. In particular, it provides accurate approximations for fixation probabilities for weak selection regimes only (Ns < or = 1), but it provides generally good prediction for the direction of selection under frequency-dependent selection.

Identification concept and the use of probabilities in forensic odontology--an approach by philosophical discussion.

This paper questions the practitioners' deterministic approach(es) in forensic identification and notes the limits of their conclusions in order to encourage a discussion to question current practices. With this end in view, a hypothetical discussion between an expert in dentistry and an enthusiastic member of a jury, eager to understand the scientific principles of evidence interpretation, is presented. This discussion will lead us to regard any argument aiming at identification as probabilistic.

Salience theory of choice under risk

We present a theory of choice among lotteries in which the decision maker's attention is drawn to (precisely defined) salient payoffs. This leads the decision maker to a context-dependent representation of lotteries in which true probabilities are replaced by decision weights distorted in favor of salient payoffs. By endogenizing decision weights as a function of payoffs, our model provides a novel and unified account of many empirical phenomena, including frequent risk-seeking behavior, invariance failures such as the Allais paradox, and preference reversals. It also yields new predictions, including some that distinguish it from Prospect Theory, which we test.

Transition probabilities and duration analysis among disability states: Some evidence from Spanish data

In this paper we study the disability transition probabilities (as well as the mortalityprobabilities) due to concurrent factors to age such as income, gender and education. Althoughit is well known that ageing and socioeconomic status influence the probability ofcausing functional disorders, surprisingly little attention has been paid to the combined effectof those factors along the individuals' life and how this affects the transition from one degreeof disability to another. The assumption that tomorrow's disability state is only a functionof the today's state is very strong, since disability is a complex variable that depends onseveral other elements than time. This paper contributes into the field in two ways: (1) byattending the distinction between the initial disability level and the process that leads tohis course (2) by addressing whether and how education, age and income differentially affectthe disability transitions. Using a Markov chain discrete model and a survival analysis, weestimate the probability by year and individual characteristics that changes the state of disabilityand the duration that it takes its progression in each case. We find that people withan initial state of disability have a higher propensity to change and take less time to transitfrom different stages. Men do that more frequently than women. Education and incomehave negative effects on transition. Moreover, we consider the disability benefits associatedto those changes along different stages of disability and therefore we offer some clues onthe potential savings of preventive actions that may delay or avoid those transitions. Onpure cost considerations, preventive programs for improvement show higher benefits thanthose for preventing deterioration, and in general terms, those focussing individuals below65 should go first. Finally the trend of disability in Spain seems not to change among yearsand regional differences are not found.

Evolution in heterogeneous populations: from migration models to fixation probabilities.

Although dispersal is recognized as a key issue in several fields of population biology (such as behavioral ecology, population genetics, metapopulation dynamics or evolutionary modeling), these disciplines focus on different aspects of the concept and often make different implicit assumptions regarding migration models. Using simulations, we investigate how such assumptions translate into effective gene flow and fixation probability of selected alleles. Assumptions regarding migration type (e.g. source-sink, resident pre-emption, or balanced dispersal) and patterns (e.g. stepping-stone versus island dispersal) have large impacts when demes differ in sizes or selective pressures. The effects of fragmentation, as well as the spatial localization of newly arising mutations, also strongly depend on migration type and patterns. Migration rate also matters: depending on the migration type, fixation probabilities at an intermediate migration rate may lie outside the range defined by the low- and high-migration limits when demes differ in sizes. Given the extreme sensitivity of fixation probability to characteristics of dispersal, we underline the importance of making explicit (and documenting empirically) the crucial ecological/ behavioral assumptions underlying migration models.

Integrating detection probabilities in species distribution models of amphibians breeding in Mediterranean temporary ponds

Aim  The imperfect detection of species may lead to erroneous conclusions about species-environment relationships. Accuracy in species detection usually requires temporal replication at sampling sites, a time-consuming and costly monitoring scheme. Here, we applied a lower-cost alternative based on a double-sampling approach to incorporate the reliability of species detection into regression-based species distribution modelling.Location  Doñana National Park (south-western Spain).Methods  Using species-specific monthly detection probabilities, we estimated the detection reliability as the probability of having detected the species given the species-specific survey time. Such reliability estimates were used to account explicitly for data uncertainty by weighting each absence. We illustrated how this novel framework can be used to evaluate four competing hypotheses as to what constitutes primary environmental control of amphibian distribution: breeding habitat, aestivating habitat, spatial distribution of surrounding habitats and/or major ecosystems zonation. The study was conducted on six pond-breeding amphibian species during a 4-year period.Results  Non-detections should not be considered equivalent to real absences, as their reliability varied considerably. The occurrence of Hyla meridionalis and Triturus pygmaeus was related to a particular major ecosystem of the study area, where suitable habitat for these species seemed to be widely available. Characteristics of the breeding habitat (area and hydroperiod) were of high importance for the occurrence of Pelobates cultripes and Pleurodeles waltl. Terrestrial characteristics were the most important predictors of the occurrence of Discoglossus galganoi and Lissotriton boscai, along with spatial distribution of breeding habitats for the last species.Main conclusions  We did not find a single best supported hypothesis valid for all species, which stresses the importance of multiscale and multifactor approaches. More importantly, this study shows that estimating the reliability of non-detection records, an exercise that had been previously seen as a naïve goal in species distribution modelling, is feasible and could be promoted in future studies, at least in comparable systems.

The Effect of a threshold proportional reinsurance strategy on ruin probabilities

[spa] En un modelo de Poisson compuesto, definimos una estrategia de reaseguro proporcional de umbral : se aplica un nivel de retención k1 siempre que las reservas sean inferiores a un determinado umbral b, y un nivel de retención k2 en caso contrario. Obtenemos la ecuación íntegro-diferencial para la función Gerber-Shiu, definida en Gerber-Shiu -1998- en este modelo, que nos permite obtener las expresiones de la probabilidad de ruina y de la transformada de Laplace del momento de ruina para distintas distribuciones de la cuantía individual de los siniestros. Finalmente presentamos algunos resultados numéricos.

Pauli distorted double folded potential

The enhancement in the production of even-Z nuclei observed in nuclear fission has also been observed in fragments produced from heavy ion collsions. Beams of 40Ar, 40Cl, and 40Ca at 25 MeV/nucleon were impinged on 58Fe and 58Ni targets. The resulting fragments were detected using the MSU 4pi detector array, which had additional silicon detectors for better isotopic resolution. Comparison of the ratios of yields for each element showed enhancement of even-Z fragment production. The enhancement was more pronounced for reactions with a greater difference in the N/Z of the compound system. However, this effect was less for systems that were more neutron rich. The average N/Z for fragments also displayed an odd-even effect with a lower average N/Z for the even-Z fragments. This is related to the greater availability of neutron-poor isotopes for even-Z nuclei

Distorted-wave calculation of cross sections for inner-shell ionization by electron and positron impact

The relativistic distorted-wave Born approximation is used to calculate differential and total cross sections for inner shell ionization of neutral atoms by electron and positron impact. The target atom is described within the independent-electron approximation using the self-consistent Dirac-Fock-Slater potential. The distorting potential for the projectile is also set equal to the Dirac-Fock-Slater potential. For electrons, this guarantees orthogonality of all the orbitals involved and simplifies the calculation of exchange T-matrix elements. The interaction between the projectile and the target electrons is assumed to reduce to the instantaneous Coulomb interaction. The adopted numerical algorithm allows the calculation of differential and total cross sections for projectiles with kinetic energies ranging from the ionization threshold up to about ten times this value. Algorithm accuracy and stability are demonstrated by comparing differential cross sections calculated by our code with the distorting potential set to zero with equivalent results generated by a more robust code that uses the conventional plane-wave Born approximation. Sample calculation results are presented for ionization of K- and L-shells of various elements and compared with the available experimental data.

On the efficient evaluation of ruin probabilities for completely monotone claim size distributions

In this paper we propose a highly accurate approximation procedure for ruin probabilities in the classical collective risk model, which is based on a quadrature/rational approximation procedure proposed in [2]. For a certain class of claim size distributions (which contains the completely monotone distributions) we give a theoretical justification for the method. We also show that under weaker assumptions on the claim size distribution, the method may still perform reasonably well in some cases. This in particular provides an efficient alternative to a related method proposed in [3]. A number of numerical illustrations for the performance of this procedure is provided for both completely monotone and other types of random variables.