Convergence Rates for Inverse Problems with Impulsive Noise

We study inverse problems F(f) = g with perturbed right hand side g^{obs} corrupted by so-called impulsive noise, i.e. noise which is concentrated on a small subset of the domain of definition of g. It is well known that Tikhonov-type regularization with an L^1 data fidelity term yields significantly more accurate results than Tikhonov regularization with classical L^2 data fidelity terms for this type of noise. The purpose of this paper is to provide a convergence analysis explaining this remarkable difference in accuracy. Our error estimates significantly improve previous error estimates for Tikhonov regularization with L^1-fidelity term in the case of impulsive noise. We present numerical results which are in good agreement with the predictions of our analysis

Convergence Rates for Exponentially Ill-Posed Inverse Problems with Impulsive Noise

This paper is concerned with exponentially ill-posed operator equations with additive impulsive noise on the right hand side, i.e. the noise is large on a small part of the domain and small or zero outside. It is well known that Tikhonov regularization with an $L^1$ data fidelity term outperforms Tikhonov regularization with an $L^2$ fidelity term in this case. This effect has recently been explained and quantified for the case of finitely smoothing operators. Here we extend this analysis to the case of infinitely smoothing forward operators under standard Sobolev smoothness assumptions on the solution, i.e. exponentially ill-posed inverse problems. It turns out that high order polynomial rates of convergence in the size of the support of large noise can be achieved rather than the poor logarithmic convergence rates typical for exponentially ill-posed problems. The main tools of our analysis are Banach spaces of analytic functions and interpolation-type inequalities for such spaces. We discuss two examples, the (periodic) backwards heat equation and an inverse problem in gradiometry.Comment: to appear in SIAM J. Numer. Ana

Correction algorithm for finite sample statistics

Assume in a sample of size M one finds M_i representatives of species i with i=1...N^*. The normalized frequency p^*_i=M_i/M, based on the finite sample, may deviate considerably from the true probabilities p_i. We propose a method to infer rank-ordered true probabilities r_i from measured frequencies M_i. We show that the rank-ordered probabilities provide important informations on the system, e.g., the true number of species, the Shannon- and the Renyi-entropies.Comment: 11 pages, 9 figure

The Minority of Three-Game: An Experimental and Theoretical Analysis

We report experimental and theoretical results on the minority of three-game where three players have to choose one of two alternatives independently and the most rewarding alternative is the one chosen by a single player. This coordination game has many asymmetric equilibria in pure strategies that are non strict and payoff-asymmetric, and a unique symmetric mixed strategy equilibrium in which each player's behavior is based on the toss of a fair coin. We show that such a straightforward behavior is predicted by Harsanyi and Selten's (1988) equilibrium selection theory as well as alternative solution concepts like impulse balance equilibrium and sampling equilibrium. Our results indicate that participants rely on various decision rules, and that only a quarter of them decide according to the toss of a fair coin. Reinforcement learning is the most successful decision rule as it describes best the behavior of about a third of our participants.Coordination, Minority game, Mixed strategy, Learning models, Experiments

Inhibition of diacylglycerol–sensitive TRPC channels by synthetic and natural steroids

TRPC channels are a family of nonselective cation channels that regulate ion homeostasis and intracellular Ca2+ signaling in numerous cell types. Important physiological functions such as vasoregulation, neuronal growth, and pheromone recognition have been assigned to this class of ion channels. Despite their physiological relevance, few selective pharmacological tools are available to study TRPC channel function. We, therefore, screened a selection of pharmacologically active compounds for TRPC modulating activity. We found that the synthetic gestagen norgestimate inhibited diacylglycerol-sensitive TRPC3 and TRPC6 with IC50s of 3–5 µM, while half-maximal inhibition of TRPC5 required significantly higher compound concentrations (>10 µM). Norgestimate blocked TRPC-mediated vasopressin-induced cation currents in A7r5 smooth muscle cells and caused vasorelaxation of isolated rat aorta, indicating that norgestimate could be an interesting tool for the investigation of TRP channel function in native cells and tissues. The steroid hormone progesterone, which is structurally related to norgestimate, also inhibited TRPC channel activity with IC50s ranging from 6 to 18 µM but showed little subtype selectivity. Thus, TRPC channel inhibition by high gestational levels of progesterone may contribute to the physiological decrease of uterine contractility and immunosuppression during pregnancy

Hypoxia Tolerance of 10 Euphausiid Species in Relation to Vertical Temperature and Oxygen Gradients

Oxygen Minimum Zones prevail in most of the world’s oceans and are particularly extensive in Eastern Boundary Upwelling Ecosystems such as the Humboldt and the Benguela upwelling systems. In these regions, euphausiids are an important trophic link between primary producers and higher trophic levels. The species are known as pronounced diel vertical migrators, thus facing different levels of oxygen and temperature within a 24 h cycle. Declining oxygen levels may lead to vertically constrained habitats in euphausiids, which consequently will affect several trophic levels in the food web of the respective ecosystem. By using the regulation index (RI), the present study aimed at investigating the hypoxia tolerances of different euphausiid species from Atlantic, Pacific as well as from Polar regions. RI was calculated from 141 data sets and used to differentiate between respiration strategies using median and quartile (Q) values: low degree of oxyregulation (0.25 0.25 or Q3 > 0.75); and metabolic suppression (RI median, Q1 and Q3 0) was identified for the neritic temperate species Thysanoessa spinifera and the tropical species Euphausia lamelligera. RI values of Euphausia distinguenda and the Humboldt species Euphausia mucronata qualified these as metabolic suppressors. RI showed a significant impact of temperature on the respiration strategy of E. hanseni from oxyregulation to metabolic suppression. The species’ estimated hypoxia tolerances and the degree of oxyconformity vs. oxyregulation were linked to diel vertical migration behavior and the temperature experienced during migration. The results highlight that the euphausiid species investigated have evolved various strategies to deal with different levels of oxygen, ranging from species showing a high degree of oxyconformity to strong oxyregulation. Neritic species may be more affected by hypoxia, as these are often short-distance-migrators and only adapted to a narrow range of environmental conditions

Predator diversity and abundance provide little support for the enemies hypothesis in forests of high tree diversity

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