Abstract:
We generalize the notion of Gaussian bridges by conditioning Gaussian processes given that certain linear functionals of the sample paths vanish. We show the equivalence of the laws of the unconditioned and the conditioned process and by an application of Girsanov's theorem, we show that the conditioned process follows a stochastic differential equation (SDE) whenever the unconditioned process does. In the Markovian case, we are able to determine the coefficients in the SDE of the conditioned process explicitly. Our main example is Brownian motion on $[0,1]$ pinned down in 0 at time 1 and conditioned to have vanishing area spanned by the sample paths.

Abstract:
Over the past years, risk measurement and therewith risk measures became more and more important in economics. While in the past risk measures were already adopted at the deposit of credit and shareholders equity, the approach now generates two hybrid decision models and applies them to the reinsurance business. The two introduced models implement a convex combination of risk measures and with it provide the possibility of modelling risk attitudes. By doing that, for the two hybrid decision models on the one hand can be shown, which risk attitude leads to the acceptance of a reinsurance contract and on the other hand, a deductible of which height an insurer is willing to undertake. Hence the possibility exists to identify the risk attitude of an insurer. In return, due to the knowledge of risk attitudes, under similar conditions the possibility arises to establish recommendations about the extent of the deductible at reinsurance contracts.

Abstract:
The total lepton asymmetry $l=\sum_f l_f$ in our universe is only poorly constrained by theories and experiments. It might be orders of magnitudes larger than the observed baryon asymmetry $b\simeq {\cal O}(10^{-10})$, $|l|/b \leq {\cal O}(10^{9})$. We found that the dynamics of the cosmic QCD transition changes for large asymmetries. Predictions for asymmetries in a single flavour $l_f$ allow even larger values. We find that asymmetries of $l_f\leq {\cal O}(1)$ in a single or two flavours change the relic abundance of WIMPs. However, large lepton and large individual lepton flavour asymmetries influences significantly the dynamics of the early universe.

Abstract:
Despite its age quantum theory remains ill-understood, which is partially to blame on its deep interwovenness with the mysterious concept of quantization. In this article we argue that a quantum theory recoursing to quantization algorithms is necessarily incomplete. To provide a new axiomatic foundation, we give a rigorous proof showing how the Schr\"odinger equation follows from the Madelung equations, which are formulated in the language of Newtonian mechanics. We show how the Schr\"odinger picture relates to this Madelung picture and how the "classical limit" is directly obtained. This suggests a reformulation of the correspondence principle, stating that a quantum theory must reduce to a probabilistic version of Newtonian mechanics for large masses. We then enhance the stochastic interpretation developed by Tsekov, which speculates that quantum mechanical behavior is caused by random vibrations in spacetime. A new, yet incomplete model of particle creation and annihilation is also proposed.

Abstract:
Calcium sparks represent local, rapid, and transient calcium release events from a cluster of ryanodine receptors (RyRs) in the sarcoplasmic reticulum. In arterial smooth muscle cells (SMCs), calcium sparks activate calcium-dependent potassium channels causing decrease in the global intracellular [Ca2

Abstract:
Salivary gland diseases are rare in childhood and adolescence. Their pattern of incidence differs very much from that of adults. Acute and chronic sialadenitis not responding to conservative treatment requires an appropriate surgical approach. The rareness of salivary gland tumors is particularly true for the malignant parotid tumors which are more frequent in juvenile patients, a fact that has to be considered in diagnosis and therapy.Diseases of the salivary glands are rare in infants and children (with the exception of diseases such as parotitis epidemica and cytomegaly) and the therapeutic regimen differs from that in adults. It is therefore all the more important to gain exact and extensive insight into general and special aspects of pathological changes of the salivary glands in these age groups. Previous studies [1-3] have dealt with the clinical distribution pattern of the various pathological entities in infants and older children.According to these studies, important pathologies in these age groups are acute and chronic sialadenitis (with special regard to chronic recurrent parotitis) and secondary inflammation associated with sialolithiasis [2,4-6]. The etiology and pathogenesis of these entities in young patients, however, are still not yet sufficiently understood, so that therapeutic strategies based on extensive clinical experience cannot be defined, particularly in view of the small number of patients in the relevant age groups. The acute forms of sialadenitis are mainly caused by viral or bacterial infections. The predominant cause of parotid swelling in infancy is parotitis epidemica [7]. This disease has its peak incidence between the ages of 2 and 14 [8]. Acute inflammation of the parotid gland, with evidence of Staphylococcus aureus, is often seen in neonates and in children with an underlying systemic disease accompanied by fever, dehydration, immunosuppression and general morbidity [4,9]. Acute inflammation of the submandibular gland, as oppose

Abstract:
We used three different algorithms (BestKeeper, geNorm and NormFinder) to validate the expression stability of nine candidate reference genes in different rose tissues from three different genotypes of Rosa hybrida and in leaves treated with various stress factors. The candidate genes comprised the classical "housekeeping genes" (Actin, EF-1α, GAPDH, Tubulin and Ubiquitin), and genes showing stable expression in studies in Arabidopsis (PP2A, SAND, TIP and UBC). The programs identified no single gene that showed stable expression under all of the conditions tested, and the individual rankings of the genes differed between the algorithms. Nevertheless the new candidate genes, specifically, PP2A and UBC, were ranked higher as compared to the other traditional reference genes. In general, Tubulin showed the most variable expression and should be avoided as a reference gene.Reference genes evaluated as suitable in experiments with Arabidopsis thaliana were stably expressed in roses under various experimental conditions. In most cases, these genes outperformed conventional reference genes, such as EF1-α and Tubulin. We identified PP2A, SAND and UBC as suitable reference genes, which in different combinations may be used for normalisation in expression analyses via qPCR for different rose tissues and stress treatments. However, the vast genetic variation found within the genus Rosa, including differences in ploidy levels, might also influence expression stability of reference genes, so that future research should also consider different genotypes and ploidy levels.Roses are one of the economically most important ornamentals worldwide. They are produced as cut and potted plants and garden and landscaping plants with a production value of 24 billion Euros from 1995 to 2007 [1]. Other, less prominent uses include medicinal applications or the consumption in teas and soups [2]. Apart from the beauty of their flowers, roses are also admired for their delicate scent. Their scent

Abstract:
Localization properties of scalar single particle states are analyzed by explicit calculational examples with a focus on the massless case. Problems arising from the non-existence of relativistic particle position operators respecting the causal structure of Minkowski spacetime are illustrated by exploring the conflicts arising from localization and causal properties commonly imposed on single particle states. These topics necessitate the introduction of quantum field theoretical localization concepts and are scarcely discussed and often misinterpreted in the literature.

Abstract:
We study the problem of stopping an $\alpha$-Brownian bridge as close as possible to its global maximum. This extends earlier results found for the Brownian bridge (the case $\alpha=1$). The exact behavior for $\alpha$ close to $0$ is investigated.

Abstract:
We study a simple decision problem on the scaling parameter in the $\alpha$-Brownian bridge $X^{(\alpha)}$ on the interval $[0,1]$: given two values $\alpha_0, \alpha_1 \geq 0$ with $\alpha_0 + \alpha_1 \geq 1$ and some time $0 \leq T \leq 1$ we want to test $H_0: \alpha = \alpha_0$ vs. $H_1: \alpha = \alpha_1$ based on the observation of $X^{(\alpha)}$ until time $T$. The likelihood ratio can be written as a functional of a quadratic form $\psi(X^{(\alpha)})$ of $X^{(\alpha)}$. In order to calculate the distribution of $\psi(X^{(\alpha)})$ under the null hypothesis, we generalize the Karhunen-Lo\`eve Theorem to positive finite measures on $[0,1]$ and compute the Karhunen-Lo\`eve expansion of $X^{(\alpha)}$ under such a measure. Based on this expansion, the distribution of $\psi(X^{(\alpha)})$ follows by Smirnov's formula.