Regularity of solutions of the p-Laplace equation in the Heisenberg group

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Ergodicity and regularity of invariant measure for branching Markov processes with immigration

In this thesis we consider systems of finitely many particles moving on paths given by a strong Markov process and undergoing branching and reproduction at random times. The branching rate of a particle, its number of offspring and their spatial distribution are allowed to depend on the particle's position and possibly on the configuration of coexisting particles. In addition there is immigration of new particles, with the rate of immigration and the distribution of immigrants possibly depending on the configuration of pre-existing particles as well. In the first two chapters of this work, we concentrate on the case that the joint motion of particles is governed by a diffusion with interacting components. The resulting process of particle configurations was studied by E. Löcherbach (2002, 2004) and is known as a branching diffusion with immigration (BDI). Chapter 1 contains a detailed introduction of the basic model assumptions, in particular an assumption of ergodicity which guarantees that the BDI process is positive Harris recurrent with finite invariant measure on the configuration space. This object and a closely related quantity, namely the invariant occupation measure on the single-particle space, are investigated in Chapter 2 where we study the problem of the existence of Lebesgue-densities with nice regularity properties. For example, it turns out that the existence of a continuous density for the invariant measure depends on the mechanism by which newborn particles are distributed in space, namely whether branching particles reproduce at their death position or their offspring are distributed according to an absolutely continuous transition kernel. In Chapter 3, we assume that the quantities defining the model depend only on the spatial position but not on the configuration of coexisting particles. In this framework (which was considered by Höpfner and Löcherbach (2005) in the special case that branching particles reproduce at their death position), the particle motions are independent, and we can allow for more general Markov processes instead of diffusions. The resulting configuration process is a branching Markov process in the sense introduced by Ikeda, Nagasawa and Watanabe (1968), complemented by an immigration mechanism. Generalizing results obtained by Höpfner and Löcherbach (2005), we give sufficient conditions for ergodicity in the sense of positive recurrence of the configuration process and finiteness of the invariant occupation measure in the case of general particle motions and offspring distributions.

Evidence of oligogenic inheritance in nephronophthisis

Nephronophthisis is a recessive cystic renal disease that leads to end-stage renal failure in the first two decades of life. Twenty-five percent of nephronophthisis cases are caused by large homozygous deletions of NPHP1, but six genes responsible for nephronophthisis have been identified. Because oligogenic inheritance has been described for the related Bardet-Biedl syndrome, we evaluated whether mutations in more than one gene may also be detected in cases of nephronophthisis. Because the nephrocystins 1 to 4 are known to interact, we examined patients with nephronophthisis from 94 different families and sequenced all exons of the NPHP1, NPHP2, NPHP3, and NPHP4 genes. In our previous studies involving 44 families, we detected two mutations in one of the NPHP1-4 genes. Here, we detected in six families two mutations in either NPHP1, NPHP3, or NPHP4, and identified a third mutation in one of the other NPHP genes. Furthermore, we found possible digenic disease by detecting one individual who carried one mutation in NPHP2 and a second mutation in NPHP3. Finally, we detected the presence of a single mutation in nine families, suggesting that the second recessive mutation may be in another as yet unidentified NPHP gene. Our findings suggest that oligogenicity may occur in cases of nephronophthisis.

Endangering of Businesses by the German Inheritance Tax? – An Empirical Analysis

This contribution addresses the substantial tax privilege for businesses introduced by the German Inheritance Tax Act 2009. Advocates of the vast or even entire tax exemption for businesses stress the potential damage of the inheritance tax on businesses, as those often lack liquidity to meet tax liability. This submission tackles this issue empirically based on data of the German Inheritance Tax Statistics and the SOEP. The results indicate that former German inheritance tax law has not endangered transferred businesses. Hence, there is no need for the tremendous tax privilege for businesses in current German inheritance tax law. An alternative flat inheritance tax without tax privileges, which meets revenue neutrality per tax class according to current tax law, provokes in some cases relative high tax loads which might trouble businesses.

Trypanosomal TAC40 constitutes a novel subclass of mitochondrial -barrel proteins specialized in mitochondrial genome inheritance

Mitochondria cannot form de novo but require mechanisms allowing their inheritance to daughter cells. In contrast to most other eukaryotes Trypanosoma brucei has a single mitochondrion whose single-unit genome is physically connected to the flagellum. Here we identify a β-barrel mitochondrial outer membrane protein, termed tripartite attachment complex 40 (TAC40), that localizes to this connection. TAC40 is essential for mitochondrial DNA inheritance and belongs to the mitochondrial porin protein family. However, it is not specifically related to any of the three subclasses of mitochondrial porins represented by the metabolite transporter voltage-dependent anion channel (VDAC), the protein translocator of the outer membrane 40 (TOM40), or the fungi-specific MDM10, a component of the endoplasmic reticulum–mitochondria encounter structure (ERMES). MDM10 and TAC40 mediate cellular architecture and participate in transmembrane complexes that are essential for mitochondrial DNA inheritance. In yeast MDM10, in the context of the ERMES, is postulated to connect the mitochondrial genomes to actin filaments, whereas in trypanosomes TAC40 mediates the linkage of the mitochondrial DNA to the basal body of the flagellum. However, TAC40 does not colocalize with trypanosomal orthologs of ERMES components and, unlike MDM10, it regulates neither mitochondrial morphology nor the assembly of the protein translocase. TAC40 therefore defines a novel subclass of mitochondrial porins that is distinct from VDAC, TOM40, and MDM10. However, whereas the architecture of the TAC40-containing complex in trypanosomes and the MDM10-containing ERMES in yeast is very different, both are organized around a β-barrel protein of the mitochondrial porin family that mediates a DNA–cytoskeleton linkage that is essential for mitochondrial DNA inheritance.

Antipredator defences of young are independently determined by genetic inheritance, maternal effects and own early experience in mouthbrooding cichlids.

1. Predation is a prime force of natural selection. Vulnerability to predation is typically highest early in life, hence effective antipredator defences should work already shortly after birth. Such early defences may be innate, transmitted through non-genetic parental effects or acquired by own early experience. 2. To understand potential joint effects of these sources of antipredator defences on pheno- typic expression, they should be manipulated within the same experiment. We investigated innate, parental and individual experience effects within a single experiment. Females of the African cichlid Simochromis pleurospilus were exposed to the offspring predator Ctenochromis horei or a benign species until spawning. Eggs and larvae were hand-reared, and larvae were then exposed to odour cues signalling the presence or absence of predators in a split-brood design. 3. Shortly after independence of maternal care, S. pleurospilus undergo a habitat shift from a deeper, adult habitat to a shallow juvenile habitat, a phase where young are thought to be par- ticularly exposed to predation risk. Thus, maternal effects induced by offspring predators pres- ent in the adult habitat should take effect mainly shortly after independence, whereas own experience and innate antipredator responses should shape behaviour and life history of S. pleurospilus during the later juvenile period. 4. We found that the manipulated environmental components independently affected different offspring traits. (i) Offspring of predator-exposed mothers grew faster during the first month of life and were thus larger at termination of maternal care, when the young migrate from the adult to the juvenile habitat. (ii) The offspring’s own experience shortly after hatching exerted lasting effects on predator avoidance behaviour. (iii) Finally, our results suggest that S. pleuro- spilus possess a genetically inherited ability to distinguish dangerous from benign species. 5. In S. pleurospilus, maternal effects were limited to a short but critical time window, when young undergo a niche shift. Instead, own environmental sampling of predation risk combined with an innate predisposition to correctly identify predators appears to prepare the young best for the environment, in which they grow up as juveniles.

Minor inheritance inhibits the calibration of the 10Be production rate from the AD 1717 Val Ferret rock avalanche, European Alps

To calibrate the in situ 10Be production rate, we collected surface samples from nine large granitic boulders within the deposits of a rock avalanche that occurred in AD 1717 in the upper Ferret Valley, Mont Blanc Massif, Italy. The 10Be concentrations were extremely low and successfully measured within 10% analytical uncertainty or less. The concentrations vary from 4829 ± 448 to 5917 ± 476 at g−1. Using the historical age exposure time, we calculated the local and sea level-high latitude (i.e. ≥60°) cosmogenic 10Be spallogenic production rates. Depending on the scaling schemes, these vary between 4.60 ± 0.38 and 5.26 ± 0.43 at g−1 a−1. Although they correlate well with global values, our production rates are clearly higher than those from more recent calibration sites. We conclude that our 10Be production rate is a mean and an upper bound for production rates in the Massif region over the past 300 years. This rate is probably influenced by inheritance and will yield inaccurate (e.g. too young) exposure ages when applied to surface-exposure studies in the area. Other independently dated rock-avalanche deposits in the region that are approximately 103 years old could be considered as possible calibration sites.

Better than nothing? : dowry in the absence of the legal protection of women's inheritance rights

The practice of dowry is often thought to be the root cause of the unequal treatment of women in India. For women without inheritance rights, however, dowry may function as their only source of protection. Using a nationwide dataset and exploiting a natural experimental situation, this study explores the effects of dowry on women's empowerment in India, a society where women do not have inheritance rights. In such a society, dowry seems to enhance women's status in the marital household. The effects reverse when women have equal inheritance rights as their brothers. Empirical analysis suggests that the outright ban on dowry that ignores the context may not necessarily benefit women.

A first trial of retrospective collaboration for positional cloning in complex inheritance: Assay of the cytokine region on chromosome 5 by the Consortium on Asthma Genetics (COAG)

The central problem of complex inheritance is to map oligogenes for disease susceptibility, integrating linkage and association over samples that differ in several ways. Combination of evidence over multiple samples with 1,037 families supports loci contributing to asthma susceptibility in the cytokine region on 5q [maximum logarithm of odds (lod) = 2.61 near IL-4], but no evidence for atopy. The principal problems with retrospective collaboration on linkage appear to have been solved, providing far more information than a single study. A multipoint lod table evaluated at commonly agreed reference loci is required for both collaboration and metaanalysis, but variations in ascertainment, pedigree structure, phenotype definition, and marker selection are tolerated. These methods are invariant with statistical methods that increase the power of lods and are applicable to all diseases, motivating collaboration rather than competition. In contrast to linkage, positional cloning by allelic association has yet to be extended to multiple samples, a prerequisite for efficient combination with linkage and the greatest current challenge to genetic epidemiology.

Seeing properties of an invisible object: Feature inheritance and shine-through

We characterize a class of spatio-temporal illusions with two complementary properties. Firstly, if a vernier stimulus is flashed for a short time on a monitor and is followed immediately by a grating, the latter can express features of the vernier, such as its offset, its orientation, or its motion (feature inheritance). Yet the vernier stimulus itself remains perceptually invisible. Secondly, the vernier can be rendered visible by presenting gratings with a larger number of elements (shine-through). Under these conditions, subjects perceive two independent “objects” each carrying their own features. Transition between these two domains can be effected by subtle changes in the spatio-temporal layout of the grating. This should allow psychophysicists and electrophysiologists to investigate feature binding in a precise and quantitative manner.

Trials of the beta model for complex inheritance.

Theoretical advantages of nonparametric logarithm of odds to map polygenic diseases are supported by tests of the beta model that depends on a single logistic parameter and is the only model under which paternal and maternal transmissions to sibs of specified phenotypes are independent. Although it does not precisely describe recurrence risks in monozygous twins, the beta model has greater power to detect family resemblance or linkage than the more general delta model which describes the probability of 0, 1, or 2 alleles identical by descent (ibd) with two parameters. Available data on ibd in sibs are consistent with the beta model, but not with the equally parsimonious but less powerful gamma model that assumes a fixed probability of 1/2 for 1 allele ibd. Additivity of loci on the liability scale is not disproven. A simple equivalence extends the beta model to multipoint analysis.