Voting Power and Probability

Voting power is commonly measured using a probability. But what kind of probability is this? Is it a degree of belief or an objective chance or some other sort of probability? The aim of this paper is to answer this question. The answer depends on the use to which a measure of voting power is put. Some objectivist interpretations of probabilities are appropriate when we employ such a measure for descriptive purposes. By contrast, when voting power is used to normatively assess voting rules, the probabilities are best understood as classical probabilities, which count possibilities. This is so because, from a normative stance, voting power is most plausibly taken to concern rights and thus possibilities. The classical interpretation also underwrites the use of the Bernoulli model upon which the Penrose/Banzhaf measure is based.

Breakdown voltage of metal-oxide resistors in liquid argon

We characterized a sample of metal-oxide resistors and measured their breakdown voltage in liquid argon by applying high voltage (HV) pulses over a 3 second period. This test mimics the situation in a HV-divider chain when a breakdown occurs and the voltage across resistors rapidly rise from the static value to much higher values. All resistors had higher breakdown voltages in liquid argon than their vendor ratings in air at room temperature. Failure modes range from full destruction to coating damage. In cases where breakdown was not catastrophic, subsequent breakdown voltages were lower in subsequent measuring runs. One resistor type withstands 131 kV pulses, the limit of the test setup.

A logarithmic efficient estimator of the probability of ruin with recuperation for spectrally negative Lévy risk processes

This article provides an importance sampling algorithm for computing the probability of ruin with recuperation of a spectrally negative Lévy risk process with light-tailed downwards jumps. Ruin with recuperation corresponds to the following double passage event: for some t∈(0,∞)t∈(0,∞), the risk process starting at level x∈[0,∞)x∈[0,∞) falls below the null level during the period [0,t][0,t] and returns above the null level at the end of the period tt. The proposed Monte Carlo estimator is logarithmic efficient, as t,x→∞t,x→∞, when y=t/xy=t/x is constant and below a certain bound.

Hybrid Breakdown in Cichlid Fish

Studies from a wide diversity of taxa have shown a negative relationship between genetic compatibility and the divergence time of hybridizing genomes. Theory predicts the main breakdown of fitness to happen after the F1 hybrid generation, when heterosis subsides and recessive allelic (Dobzhansky-Muller) incompatibilities are increasingly unmasked. We measured the fitness of F2 hybrids of African haplochromine cichlid fish bred from species pairs spanning several thousand to several million years divergence time. F2 hybrids consistently showed the lowest viability compared to F1 hybrids and non-hybrid crosses (crosses within the grandparental species), in agreement with hybrid breakdown. Especially the short- and long-term survival (2 weeks to 6 months) of F2 hybrids was significantly reduced. Overall, F2 hybrids showed a fitness reduction of 21% compared to F1 hybrids, and a reduction of 43% compared to the grandparental, non-hybrid crosses. We further observed a decrease of F2 hybrid viability with the genetic distance between grandparental lineages, suggesting an important role for negative epistatic interactions in cichlid fish postzygotic isolation. The estimated time window for successful production of F2 hybrids resulting from our data is consistent with the estimated divergence time between the multiple ancestral lineages that presumably hybridized in three major adaptive radiations of African cichlids.

Saddlepoint Approximations to the Probability of Ruin in Finite Time for the Compound Poisson Risk Process Perturbed by Diffusion

A large deviations type approximation to the probability of ruin within a finite time for the compound Poisson risk process perturbed by diffusion is derived. This approximation is based on the saddlepoint method and generalizes the approximation for the non-perturbed risk process by Barndorff-Nielsen and Schmidli (Scand Actuar J 1995(2):169–186, 1995). An importance sampling approximation to this probability of ruin is also provided. Numerical illustrations assess the accuracy of the saddlepoint approximation using importance sampling as a benchmark. The relative deviations between saddlepoint approximation and importance sampling are very small, even for extremely small probabilities of ruin. The saddlepoint approximation is however substantially faster to compute.

Chlorophyll Breakdown in Senescent Arabidopsis Leaves. Characterization of Chlorophyll Catabolites and of Chlorophyll Catabolic Enzymes Involved in the Degreening Reaction

During senescence, chlorophyll (chl) is metabolized to colorless nonfluorescent chl catabolites (NCCs). A central reaction of the breakdown pathway is the ring cleavage of pheophorbide (pheide) a to a primary fluorescent chl catabolite. Two enzymes catalyze this reaction, pheide a oxygenase (PAO) and red chl catabolite reductase. Five NCCs and three fluorescent chl catabolites (FCCs) accumulated during dark-induced chl breakdown in Arabidopsis (Arabidopsis thaliana). Three of these NCCs and one FCC (primary fluorescent chl catabolite-1) were identical to known catabolites from canola (Brassica napus). The presence in Arabidopsis of two modified FCCs supports the hypothesis that modifications, as present in NCCs, occur at the level of FCC. Chl degradation in Arabidopsis correlated with the accumulation of FCCs and NCCs, as well as with an increase in PAO activity. This increase was due to an up-regulation of Pao gene expression. In contrast, red chl catabolite reductase is not regulated during leaf development and senescence. A pao1 knockout mutant was identified and analyzed. The mutant showed an age- and light-dependent cell death phenotype on leaves and in flowers caused by the accumulation of photoreactive pheide a. In the dark, pao1 exhibited a stay-green phenotype. The key role of PAO in chl breakdown is discussed.

Chlorophyll breakdown: Pheophorbide a oxygenase is a Rieske-type iron-sulfur protein, encoded by the accelerated cell death 1 gene

Chlorophyll (chl) breakdown during senescence is an integral part of plant development and leads to the accumulation of colorless catabolites. The loss of green pigment is due to an oxygenolytic opening of the porphyrin macrocycle of pheophorbide (pheide) a followed by a reduction to yield a fluorescent chl catabolite. This step is comprised of the interaction of two enzymes, pheide a oxygenase (PaO) and red chl catabolite reductase. PaO activity is found only during senescence, hence PaO seems to be a key regulator of chl catabolism. Whereas red chl catabolite reductase has been cloned, the nature of PaO has remained elusive. Here we report on the identification of the PaO gene of Arabidopsis thaliana (AtPaO). AtPaO is a Rieske-type iron–sulfur cluster-containing enzyme that is identical to Arabidopsis accelerated cell death 1 and homologous to lethal leaf spot 1 (LLS1) of maize. Biochemical properties of recombinant AtPaO were identical to PaO isolated from a natural source. Production of fluorescent chl catabolite-1 required ferredoxin as an electron source and both substrates, pheide a and molecular oxygen. By using a maize lls1 mutant, the in vivo function of PaO, i.e., degradation of pheide a during senescence, could be confirmed. Thus, lls1 leaves stayed green during dark incubation and accumulated pheide a that caused a light-dependent lesion mimic phenotype. Whereas proteins were degraded similarly in wild type and lls1, a chl-binding protein was selectively retained in the mutant. PaO expression correlated positively with senescence, but the enzyme appeared to be post-translationally regulated as well.

Breakdown of chlorophyll: A nonenzymatic reaction accounts for the formation of the colorless "nonfluorescent" chlorophyll catabolites

Senescent higher plants degrade their chlorophylls (Chls) to polar colorless tetrapyrrolic Chl catabolites, which accumulate in the vacuoles. In extracts from degreened leaves of the tree Cercidiphyllum japonicum an unpolar catabolite of this type was discovered. This tetrapyrrole was named Cj-NCC-2 and was found to be identical with the product of a stereoselective nonenzymatic isomerization of a “fluorescent” Chl catabolite. This (bio-mimetic) formation of the “nonfluorescent” catabolite Cj-NCC-2 took place readily at ambient temperature and at pH 4.9 in aqueous solution. The indicated nonenzymatic process is able to account for a crucial step during Chl breakdown in senescent higher plants. Once delivered to the acidic vacuoles, the fluorescent Chl catabolites are due to undergo a rapid, stereoselective isomerization to the ubiquitous nonfluorescent catabolites. The degradation of the Chl macrocycle is thus indicated to rely on just two known enzymes, one of which is senescence specific and cuts open the chlorin macroring. The two enzymes supply the fluorescent Chl catabolites, which are “programmed” to isomerize further rapidly in an acidic medium, as shown here. Indeed, only small amounts of the latter are temporarily observable during senescence in higher plants.

Chlorophyll Breakdown in Tobacco: On the Structure of Two Nonfluorescent Chlorophyll Catabolites

In extracts of senescent leaves of the tobacco plant Nicotiana rustica, two colorless compounds with UV/VIS characteristics of nonfluorescent chlorophyll catabolites (NCCs) were detected and tentatively identified as Nr-NCCs. These two polar NCCs were found in similar amounts in the fresh extracts, and their constitutions could be determined by spectroscopic analysis. The data showed both of the two Nr-NCCs to have the same tetrapyrrolic core structure, as reported previously for all other NCCs from senescent higher plants. In the less polar catabolite, named Nr-NCC-2, this core structure was conjugated with a glucopyranose unit, as similarly discovered earlier in Bn-NCC-2, an NCC from oilseed rape (Brassica napus). The more polar NCC from tobacco leaves, Nr-NCC-1, carried an additional malonyl substituent at the 6′-OH group of the glucopyranosyl moiety. Partial (enzyme-catalyzed) hydrolysis of Nr-NCC-1 gave Nr-NCC-2, while enzyme-catalyzed malonylation of Nr-NCC-2 gave Nr-NCC-1, establishing the identity of their basic tetrapyrrole structure. In earlier work (on the polar NCCs from oilseed rape), only separate glucopyranosyl and malonyl functionalities were detected. Nr-NCC-1, thus, represents a further variant of the structures of NCCs from senescent higher plants and exhibits an unprecedented peripheral refunctionalization in chlorophyll catabolites.