Choosing a random distribution with prescribed risks

We describe several simulation algorithms that yield random probability distributions with given values of risk measures. In case of vanilla risk measures, the algorithms involve combining and transforming random cumulative distribution functions or random Lorenz curves obtained by simulating rather general random probability distributions on the unit interval. A new algorithm based on the simulation of a weighted barycentres array is suggested to generate random probability distributions with a given value of the spectral risk measure.

The von Mises-Fisher distribution of the first exit point from the hypersphere of the drifted Brownian motion and the density of the first exit time

A characterization is provided for the von Mises–Fisher random variable, in terms of first exit point from the unit hypersphere of the drifted Wiener process. Laplace transform formulae for the first exit time from the unit hypersphere of the drifted Wiener process are provided. Post representations in terms of Bell polynomials are provided for the densities of the first exit times from the circle and from the sphere.

Massive Boson Production at Small qT in Soft-Collinear Effective Theory

We study the differential cross sections for electroweak gauge-boson and Higgs production at small and very small transverse-momentum qT. Large logarithms are resummed using soft-collinear effective theory. The collinear anomaly generates a non-perturbative scale q⁎, which protects the processes from receiving large long-distance hadronic contributions. A numerical comparison of our predictions with data on the transverse-momentum distribution in Z-boson production at the Tevatron and LHC is given.

Voter Participation in the 1998 Bundestag Elections: A Theoretical Modification and Empirical Application of Downs’ Theory of Voter Participation

This article seeks to contribute to the illumination of the so-called 'paradox of voting' using the German Bundestag elections of 1998 as an empirical case. Downs' model of voter participation will be extended to include elements of the theory of subjective expected utility (SEU). This will allow a theoretical and empirical exploration of the crucial mechanisms of individual voters' decisions to participate, or abstain from voting, in the German general election of 1998. It will be argued that the infinitely low probability of an individual citizen's vote to decide the election outcome will not necessarily reduce the probability of electoral participation. The empirical analysis is largely based on data from the ALLBUS 1998. It confirms the predictions derived from SEU theory. The voters' expected benefits and their subjective expectation to be able to influence government policy by voting are the crucial mechanisms to explain participation. By contrast, the explanatory contribution of perceived information and opportunity costs is low.

Parentage analysis with genetic markers in natural populations. I. The expected proportion of offspring with unambiguous paternity.

Recent studies indicate that polymorphic genetic markers are potentially helpful in resolving genealogical relationships among individuals in a natural population. Genetic data provide opportunities for paternity exclusion when genotypic incompatibilities are observed among individuals, and the present investigation examines the resolving power of genetic markers in unambiguous positive determination of paternity. Under the assumption that the mother for each offspring in a population is unambiguously known, an analytical expression for the fraction of males excluded from paternity is derived for the case where males and females may be derived from two different gene pools. This theoretical formulation can also be used to predict the fraction of births for each of which all but one male can be excluded from paternity. We show that even when the average probability of exclusion approaches unity, a substantial fraction of births yield equivocal mother-father-offspring determinations. The number of loci needed to increase the frequency of unambiguous determinations to a high level is beyond the scope of current electrophoretic studies in most species. Applications of this theory to electrophoretic data on Chamaelirium luteum (L.) shows that in 2255 offspring derived from 273 males and 70 females, only 57 triplets could be unequivocally determined with eight polymorphic protein loci, even though the average combined exclusionary power of these loci was 73%. The distribution of potentially compatible male parents, based on multilocus genotypes, was reasonably well predicted from the allele frequency data available for these loci. We demonstrate that genetic paternity analysis in natural populations cannot be reliably based on exclusionary principles alone. In order to measure the reproductive contributions of individuals in natural populations, more elaborate likelihood principles must be deployed.

Neutral biodiversity theory can explain the imbalance of phylogenetic trees but not the tempo of their diversification

Numerous evolutionary studies have sought to explain the distribution of diversity across the limbs of the tree of life. At the same time, ecological studies have sought to explain differences in diversity and relative abundance within and among ecological communities. Traditionally, these patterns have been considered separately, but models that consider processes operating at the level of individuals, such as neutral biodiversity theory (NBT), can provide a link between them. Here, we compare evolutionary dynamics across a suite of NBT models. We show that NBT can yield phylogenetic tree topologies with imbalance closely resembling empirical observations. In general, metacommunities that exhibit greater disparity in abundance are characterized by more imbalanced phylogenetic trees. However, NBT fails to capture the tempo of diversification as represented by the distribution of branching events through time. We suggest that population-level processes might therefore help explain the asymmetry of phylogenetic trees, but that tree shape might mislead estimates of evolutionary rates unless the diversification process is modeled explicitly.

Are cryptic host species also cryptic to parasites? Host specificity and geographical distribution of acanthocephalan parasites infecting freshwater Gammarus

Many parasites infect multiple host species. In coevolving host–parasite interactions, theory predicts that parasites should be adapted to locally common hosts, which could lead to regional shifts in host preferences. We studied the interaction between freshwater Gammarus (Crustacea, Amphipoda) and their acanthocephalan parasites using a large-scale field survey and experiments, combined with molecular identification of cryptic host and parasite species. Gammarus pulex is a common host for multiple species of Acanthocephala in Europe but, in Switzerland, is less common than two cryptic members of the Gammarus fossarum species complex (type A and type B). We found that natural populations of these cryptic species were frequently infected by Pomphorhynchus tereticollis and Polymorphus minutus. Four additional parasite species occurred only locally. Parasites were more common in G. fossarum type B than in type A. Infection experiments using several host and parasite sources confirmed consistently lower infection rates in G. pulex than in G. fossarum type A, suggesting a general difference in susceptibility between the two species. In conclusion, we could show that cryptic host species differ in their interactions with parasites, but that these differences were much less dramatic than differences between G. fossarum (type A) and G. pulex. Our data suggest that the acanthocephalans in Switzerland have adapted to the two most common Gammarus species in this region where host species frequencies differ from near-by regions in Europe.

Uniqueness of the Embedding Continuous Convolution Semigroup of a Gaussian Probability Measure on the Affine Group and an Application in Mathematical Finance

Let {μ(i)t}t≥0 ( i=1,2 ) be continuous convolution semigroups (c.c.s.) of probability measures on Aff(1) (the affine group on the real line). Suppose that μ(1)1=μ(2)1 . Assume furthermore that {μ(1)t}t≥0 is a Gaussian c.c.s. (in the sense that its generating distribution is a sum of a primitive distribution and a second-order differential operator). Then μ(1)t=μ(2)t for all t≥0 . We end up with a possible application in mathematical finance.

Redox front geochemistry and weathering: theory with application to the Osamu Utsumi uranium mine, Poços de Caldas, Brazil

Numerical calculations describing weathering of the Poços de Caldas alkaline complex (Minas Gerais, Brazil) by infiltrating groundwater are carried out for time spans up to two million years in the absence of pyrite, and up to 500,000 years with pyrite present. Deposition of uranium resulting from infiltration of oxygenated, uranium bearing groundwater through the hydrothermally altered phonolitic host rock at the Osamu Utsumi uranium mine is also included in the latter calculation. The calculations are based on the quasi-stationary state approximation to mass conservation equations for pure advective transport. This approximation enables the prediction of solute concentrations, mineral abundances and porosity as functions of time and distance over geologic time spans. Mineral reactions are described by kinetic rate laws for both precipitation and dissolution. Homogeneous equilibrium is assumed to be maintained within the aqueous phase. No other constraints are imposed on the calculations other than the initial composition of the unaltered host rock and the composition of the inlet fluid, taken as rainwater modified by percolation through a soil zone. The results are in qualitative agreement with field observations at the Osamu Utsumi uranium mine. They predict a lateritic cover followed by a highly porous saprolitic zone, a zone of oxidized rock with pyrite replaced by iron-hydroxide, a sharp redox front at which uranium is deposited, and the reduced unweathered host rock. Uranium is deposited in a narrow zone located on the reduced side of the redox front in association with pyrite, in agreement with field observations. The calculations predict the formation of a broad dissolution front of primary kaolinite that penetrates deep into the host rock accompanied by the precipitation of secondary illite. Secondary kaolinite occurs in a saprolitic zone near the surface and in the vicinity of the redox front. Gibbsite forms a bi-modal distribution consisting of a maximum near the surface followed by a thin tongue extending downward into the weathered profile in agreement with field observations. The results are found to be insensitive to the kinetic rate constants used to describe mineral reactions.

Variability of daily winter wind speed distribution over Northern Europe during the past millennium in regional and global climate simulations

We analyse the variability of the probability distribution of daily wind speed in wintertime over Northern and Central Europe in a series of global and regional climate simulations covering the last centuries, and in reanalysis products covering approximately the last 60 years. The focus of the study lies on identifying the link of the variations in the wind speed distribution to the regional near-surface temperature, to the meridional temperature gradient and to the North Atlantic Oscillation. Our main result is that the link between the daily wind distribution and the regional climate drivers is strongly model dependent. The global models tend to behave similarly, although they show some discrepancies. The two regional models also tend to behave similarly to each other, but surprisingly the results derived from each regional model strongly deviates from the results derived from its driving global model. In addition, considering multi-centennial timescales, we find in two global simulations a long-term tendency for the probability distribution of daily wind speed to widen through the last centuries. The cause for this widening is likely the effect of the deforestation prescribed in these simulations. We conclude that no clear systematic relationship between the mean temperature, the temperature gradient and/or the North Atlantic Oscillation, with the daily wind speed statistics can be inferred from these simulations. The understand- ing of past and future changes in the distribution of wind speeds, and thus of wind speed extremes, will require a detailed analysis of the representation of the interaction between large-scale and small-scale dynamics.

The Distribution of the Irreducibles in an Algebraic Number Field

The objective of this thesis is to study the distribution of the number of principal ideals generated by an irreducible element in an algebraic number field, namely in the non-unique factorization ring of integers of such a field. In particular we are investigating the size of M(x), defined as M ( x ) =∑ (α) α irred.|N (α)|≤≠ 1, where x is any positive real number and N (α) is the norm of α. We finally obtain asymptotic results for hl(x).

Are Shirking and Leisure Substitutable? An Empirical Test of Efficiency Wages Based on Urban Economic Theory

Recent theoretical work has examined the spatial distribution of unemployment using the efficiency wage model as the mechanism by which unemployment arises in the urban economy. This paper extends the standard efficiency wage model in order to allow for behavioral substitution between leisure time at home and effort at work. In equilibrium, residing at a location with a long commute affects the time available for leisure at home and therefore affects the trade-off between effort at work and risk of unemployment. This model implies an empirical relationship between expected commutes and labor market outcomes, which is tested using the Public Use Microdata sample of the 2000 U.S. Decennial Census. The empirical results suggest that efficiency wages operate primarily for blue collar workers, i.e. workers who tend to be in occupations that face higher levels of supervision. For this subset of workers, longer commutes imply higher levels of unemployment and higher wages, which are both consistent with shirking and leisure being substitutable.

The theory of runs with application to drought predictions

The primary interest was in predicting the distribution runs in a sequence of Bernoulli trials. Difference equation techniques were used to express the number of runs of a given length k in n trials under three assumptions (1) no runs of length greater than k, (2) no runs of length less than k, (3) no other assumptions about the length of runs. Generating functions were utilized to obtain the distributions of the future number of runs, future number of minimum run lengths and future number of the maximum run lengths unconditional on the number of successes and failures in the Bernoulli sequence. When applying the model to Texas hydrology data, the model provided an adequate fit for the data in eight of the ten regions. Suggested health applications of this approach to run theory are provided. ^

Prospective run theory for multinomial outcomes

The focus of this study was to generalize the theory of runs to multinomial outcomes using the generating function approach. Detailed discussion is provided for determining the probability distributions for all runs of length i in a sequence of n trials for the binomial and trinomial cases. The generalization to multinomial case is also presented. Application to data for patients from a long term disability care facility is presented to illustrate the use of Run Theory in determining the probability of a dominant state of treatment associated with a patient during his/her hospitalization. ^

Mineralogy and nannoplankton distribution in ODP Hole 194-1195A

Significant synchronous shifts in the chemistry, mineralogy, grain sizes and color of the sediments at 6 m below sea floor (mbsf) at ODP Site 1195 on the Marion Plateau (NE Australia) are interpreted to reflect a major regional paleoceanographic change: the initiation of the southern province of the Great Barrier Reef (GBR). The onset of this massive carbonate production centre nearby resulted primarily in increased deposition of carbonate-rich sediments of neritic origin. Both sedimentation rate and terrigenous input record a coincident decline attributed to inshore trapping of materials behind the reefs. Our best estimate places the development of reef framework in the southern part of the GBR between 560 and 670 kyr B.P., based on an age model combining magnetostratigraphic and biostratigraphic data. The proposed estimation agrees with previous studies reporting an age between 500 and 930 kyr B.P., constraining more tightly their results. However, it does not support research placing the birth of the GBR in Marine Isotope Stage (MIS) 11 (~400 kyr), nor the theory of a worldwide modern barrier reef development at that time.