Some distance bounds of branching processes and their diffusion limits

We compute exact values respectively bounds of "distances" - in the sense of (transforms of) power divergences and relative entropy - between two discrete-time Galton-Watson branching processes with immigration GWI for which the offspring as well as the immigration is arbitrarily Poisson-distributed (leading to arbitrary type of criticality). Implications for asymptotic distinguishability behaviour in terms of contiguity and entire separation of the involved GWI are given, too. Furthermore, we determine the corresponding limit quantities for the context in which the two GWI converge to Feller-type branching diffusion processes, as the time-lags between observations tend to zero. Some applications to (static random environment like) Bayesian decision making and Neyman-Pearson testing are presented as well.Comment: 45 page

Some Potential Means for Venture Valuation

In some modern venture valuation approaches, option pricing theory plays an important role. The aim of this paper is to present some tools and viewpoints which might be helpful for future investigations along this line. We model the value-dynamics Xt of an imbedded underlying X as a non-lognormally-distributed generalization of the geometric Brownian motion. In detail, Xt is supposed to be a solution of a stochastic differential equation of the form with non-constant volatility function ? (t) and Brownian motion Wt . For this, we discuss a certain decision problem concerning the size of the trend function b . Under some handy-toverify but far-reaching assumptions, we investigate the (average) reduction of decision risk that can be obtained by observing the sample path of X . Furthermore, we also show some connections with the valuation of call options on X

A precise bare simulation approach to the minimization of some distances. Foundations

In information theory -- as well as in the adjacent fields of statistics, machine learning, artificial intelligence, signal processing and pattern recognition -- many flexibilizations of the omnipresent Kullback-Leibler information distance (relative entropy) and of the closely related Shannon entropy have become frequently used tools. To tackle corresponding constrained minimization (respectively maximization) problems by a newly developed dimension-free bare (pure) simulation method, is the main goal of this paper. Almost no assumptions (like convexity) on the set of constraints are needed, within our discrete setup of arbitrary dimension, and our method is precise (i.e., converges in the limit). As a side effect, we also derive an innovative way of constructing new useful distances/divergences. To illustrate the core of our approach, we present numerous examples. The potential for widespread applicability is indicated, too; in particular, we deliver many recent references for uses of the involved distances/divergences and entropies in various different research fields (which may also serve as an interdisciplinary interface)

Induction of Immune Mediators in Glioma and Prostate Cancer Cells by Non-Lethal Photodynamic Therapy

BACKGROUND: Photodynamic therapy (PDT) uses the combination of photosensitizing drugs and harmless light to cause selective damage to tumor cells. PDT is therefore an option for focal therapy of localized disease or for otherwise unresectable tumors. In addition, there is increasing evidence that PDT can induce systemic anti-tumor immunity, supporting control of tumor cells, which were not eliminated by the primary treatment. However, the effect of non-lethal PDT on the behavior and malignant potential of tumor cells surviving PDT is molecularly not well defined. METHODOLOGY/PRINCIPAL FINDINGS: Here we have evaluated changes in the transcriptome of human glioblastoma (U87, U373) and human (PC-3, DU145) and murine prostate cancer cells (TRAMP-C1, TRAMP-C2) after non-lethal PDT in vitro and in vivo using oligonucleotide microarray analyses. We found that the overall response was similar between the different cell lines and photosensitizers both in vitro and in vivo. The most prominently upregulated genes encoded proteins that belong to pathways activated by cellular stress or are involved in cell cycle arrest. This response was similar to the rescue response of tumor cells following high-dose PDT. In contrast, tumor cells dealing with non-lethal PDT were found to significantly upregulate a number of immune genes, which included the chemokine genes CXCL2, CXCL3 and IL8/CXCL8 as well as the genes for IL6 and its receptor IL6R, which can stimulate proinflammatory reactions, while IL6 and IL6R can also enhance tumor growth. CONCLUSIONS: Our results indicate that PDT can support anti-tumor immune responses and is, therefore, a rational therapy even if tumor cells cannot be completely eliminated by primary phototoxic mechanisms alone. However, non-lethal PDT can also stimulate tumor growth-promoting autocrine loops, as seen by the upregulation of IL6 and its receptor. Thus the efficacy of PDT to treat tumors may be improved by controlling unwanted and potentially deleterious growth-stimulatory pathways

Some Divergence Properties of Asset Price Models

We consider asset price processes Xt which are weak solutions of one-dimensional stochastic differential equations of the form (equation (2)) Such price models can be interpreted as non-lognormally-distributed generalizations of the geometric Brownian motion. We study properties of the Iα-divergence between the law of the solution Xt and the corresponding drift-less measure (the special case α=1 is the relative entropy). This will be applied to some context in statistical information theory as well as to arbitrage theory and contingent claim valuation. For instance, the seminal option pricing theorems of Black-Scholes and Merton appear as a special case

On bounded entropy of solutions of multi-dimensional stochastic differential equations

The objects of consideration are weak solutions Xt of "classical" multi-dimensional stochastic differential equations of the form dXt = b(t, Xt) dt + dWt. We give stochastic and non-stochastic conditions which guarantee the boundedness of the entropy of Xt. It will be demonstrated by example that also exploding drifts b are covered in this scheme. A short application deals with the diffusion behaviour of the time reversal of Xt.Multi-dimensional stochastic differential equations Entropy Time reversal

Studien zur Optimierung der Strahlführung von K12 und P42 für zukünftige Beam-Dump-Experimente am CERN

Abweichender Titel nach Übersetzung der Verfasserin/des VerfassersDuring the beam operation years 2021-2025 at CERN the NA62 experiment is expected to reach its goal of making a more precise measurement of the branching ratio of the decay $K^+ \rightarrow \pi^+\nu\bar{\nu}$. There is a number of potential future experiments under consideration which could utilize the beam lines P42 and K12 that currently provide the beam for NA62. One possibility would be to operate the K12 beam line in a beam dump mode. The experiment taking data in such a beam line setting is called NA62 beam dump (NA62-BD) and would be able to use the NA62 detectors to search for dark matter decays downstream the beam dump thereby looking for physics beyond the Standard Model. Additionally, a possible off-axis experiment alongside the K12 beam line called SHADOWS is considered, which would be able to focus on the search for feebly interacting particles. Prior to these experiments preliminary studies need to be performed to optimize the setup and to reduce the backgrounds that blur the signals of the detectors. Therefore, simulations in the Geant4-based software BDSIM have been performed to gain insight on the expected backgrounds and to evaluate the possibilities for reducing them. The BDSIM model of the K12 beam line has been validated in beam dump mode and the simulation data is in good agreement with measurement data provided by NA62. It was confirmed that in beam dump mode the muon background will be the main background and that it needs to be minimized. An optimization study for the magnetic field configuration of BEND1, a dipole configuration near the beam dump in the K12 beam line, showed that the muon background for NA62-BD can be reduced by a factor of 20 compared to the setting that is currently used in $K^+$ mode. Furthermore, the simulations pointed out that the magnetic field optimization of BEND1 is not sufficient to minimize the muon background for SHADOWS and that an off-axis muon sweeping system will be necessary. Several possibilities for such a system have been evaluated and a configuration was found that achieves a muon background reduction by a factor of 7 compared to the simulations without a SHADOWS dedicated muon sweeping system.7