Convergence rates in expectation for Tikhonov-type regularization of Inverse Problems with Poisson data

In this paper we study a Tikhonov-type method for ill-posed nonlinear operator equations \gdag = F( ag) where \gdag is an integrable, non-negative function. We assume that data are drawn from a Poisson process with density t\gdag where $t>0$ may be interpreted as an exposure time. Such problems occur in many photonic imaging applications including positron emission tomography, confocal fluorescence microscopy, astronomic observations, and phase retrieval problems in optics. Our approach uses a Kullback-Leibler-type data fidelity functional and allows for general convex penalty terms. We prove convergence rates of the expectation of the reconstruction error under a variational source condition as $t\to\infty$ both for an a priori and for a Lepski{\u\i}-type parameter choice rule

Patients in a permanent vegetative state or minimally conscious state in the Maine-et-Loire county of France: A cross-sectional, descriptive study

PurposesTo determine how many patients in a permanent vegetative state or a minimally conscious state are living in healthcare institutions in the Maine-et-Loire county of western France. To evaluate patient management, physical complications, problems encountered by nursing staff and the patient care teams’ wishes. Patients and methods We performed a cross-sectional, descriptive study in physical medicine and rehabilitation departments, nursing homes, geriatric units and local hospitals. All patients and their medical records were examined by the same investigator. A questionnaire for carers was used to evaluate nursing tasks and a second questionnaire for head nurses served to assess staff needs and the patient care teams’ wishes. Results Thirteen patients were identified. Four were in a permanent vegetative state and nine were in a minimally conscious state. Ten patients were cared for in geriatric units, one in a physical medicine and rehabilitation department and two in local hospitals. All patients displayed limited joint angle ranges. All the patient care teams reported practical difficulties and ethical issues. Discussion Our survey highlighted the variety of care scenarios for patients in a permanent vegetative state or a minimally conscious state. It revealed practical difficulties and, above all, ethical questions. The present work could serve as a basis for implementation of a recently issued French government circular on defining specific wards for these patients

Regularization of statistical inverse problems and the Bakushinskii veto

In the deterministic context Bakushinskii's theorem excludes the existence of purely data driven convergent regularization for ill-posed problems. We will prove in the present work that in the statistical setting we can either construct a counter example or develop an equivalent formulation depending on the considered class of probability distributions. Hence, Bakushinskii's theorem does not generalize to the statistical context, although this has often been assumed in the past. To arrive at this conclusion, we will deduce from the classic theory new concepts for a general study of statistical inverse problems and perform a systematic clarification of the key ideas of statistical regularization.Comment: 20 page

General regularization schemes for signal detection in inverse problems

The authors discuss how general regularization schemes, in particular linear regularization schemes and projection schemes, can be used to design tests for signal detection in statistical inverse problems. It is shown that such tests can attain the minimax separation rates when the regularization parameter is chosen appropriately. It is also shown how to modify these tests in order to obtain (up to a $\log\log$ factor) a test which adapts to the unknown smoothness in the alternative. Moreover, the authors discuss how the so-called \emph{direct} and \emph{indirect} tests are related via interpolation properties

Similar Comparative Low and High Doses of Deltamethrin and Acetamiprid Differently Impair the Retrieval of the Proboscis Extension Reflex in the Forager Honey Bee (Apis mellifera)

In the present study, the effects of low (10 ng/bee) and high (100 ng/bee) doses of acetamiprid and deltamethrin insecticides on multi-trial learning and retrieval were evaluated in the honey bee Apis mellifera. After oral application, acetamiprid and deltamethrin at the concentrations used were not able to impair learning sessions. When the retention tests were performed 1 h, 6 h, and 24 h after learning, we found a significant difference between bees after learning sessions when drugs were applied 24 h before learning. Deltamethrin-treated bees were found to be more sensitive at 10 ng/bee and 100 ng/bee doses compared to acetamiprid-treated bees, only with amounts of 100 ng/bee and at 6 h and 24 h delays. When insecticides were applied during learning sessions, none of the tested insecticides was able to impair learning performance at 10 ng/bee or 100 ng/bee but retention performance was altered 24 h after learning sessions. Acetamiprid was the only one to impair retrieval at 10 ng/bee, whereas at 100 ng/bee an impairment of retrieval was found with both insecticides. The present results therefore suggest that acetamiprid and deltamethrin are able to impair retrieval performance in the honey bee Apis mellifera

Self-energy limited ion transport in sub-nanometer channels

The current-voltage characteristics of the alpha-Hemolysin protein pore during the passage of single-stranded DNA under varying ionic strength, C, are studied experimentally. We observe strong blockage of the current, weak super-linear growth of the current as a function of voltage, and a minimum of the current as a function of C. These observations are interpreted as the result of the ion electrostatic self-energy barrier originating from the large difference in the dielectric constants of water and the lipid bilayer. The dependence of DNA capture rate on C also agrees with our model.Comment: more experimental material is added. 4 pages, 7 figure

Digging into acceptor splice site prediction : an iterative feature selection approach

Feature selection techniques are often used to reduce data dimensionality, increase classification performance, and gain insight into the processes that generated the data. In this paper, we describe an iterative procedure of feature selection and feature construction steps, improving the classification of acceptor splice sites, an important subtask of gene prediction. We show that acceptor prediction can benefit from feature selection, and describe how feature selection techniques can be used to gain new insights in the classification of acceptor sites. This is illustrated by the identification of a new, biologically motivated feature: the AG-scanning feature. The results described in this paper contribute both to the domain of gene prediction, and to research in feature selection techniques, describing a new wrapper based feature weighting method that aids in knowledge discovery when dealing with complex datasets

Iteratively regularized Newton-type methods for general data misfit functionals and applications to Poisson data

We study Newton type methods for inverse problems described by nonlinear operator equations $F(u)=g$ in Banach spaces where the Newton equations $F'(u_n;u_{n+1}-u_n) = g-F(u_n)$ are regularized variationally using a general data misfit functional and a convex regularization term. This generalizes the well-known iteratively regularized Gauss-Newton method (IRGNM). We prove convergence and convergence rates as the noise level tends to 0 both for an a priori stopping rule and for a Lepski{\u\i}-type a posteriori stopping rule. Our analysis includes previous order optimal convergence rate results for the IRGNM as special cases. The main focus of this paper is on inverse problems with Poisson data where the natural data misfit functional is given by the Kullback-Leibler divergence. Two examples of such problems are discussed in detail: an inverse obstacle scattering problem with amplitude data of the far-field pattern and a phase retrieval problem. The performence of the proposed method for these problems is illustrated in numerical examples