Global Saturation of Regularization Methods for Inverse Ill-Posed Problems

In this article the concept of saturation of an arbitrary regularization method is formalized based upon the original idea of saturation for spectral regularization methods introduced by A. Neubauer in 1994. Necessary and sufficient conditions for a regularization method to have global saturation are provided. It is shown that for a method to have global saturation the total error must be optimal in two senses, namely as optimal order of convergence over a certain set which at the same time, must be optimal (in a very precise sense) with respect to the error. Finally, two converse results are proved and the theory is applied to find sufficient conditions which ensure the existence of global saturation for spectral methods with classical qualification of finite positive order and for methods with maximal qualification. Finally, several examples of regularization methods possessing global saturation are shown.Comment: 29 page

Generalized Qualification and Qualification Levels for Spectral Regularization Methods

The concept of qualification for spectral regularization methods for inverse ill-posed problems is strongly associated to the optimal order of convergence of the regularization error. In this article, the definition of qualification is extended and three different levels are introduced: weak, strong and optimal. It is shown that the weak qualification extends the definition introduced by Mathe and Pereverzev in 2003, mainly in the sense that the functions associated to orders of convergence and source sets need not be the same. It is shown that certain methods possessing infinite classical qualification, e.g. truncated singular value decomposition (TSVD), Landweber's method and Showalter's method, also have generalized qualification leading to an optimal order of convergence of the regularization error. Sufficient conditions for a SRM to have weak qualification are provided and necessary and sufficient conditions for a given order of convergence to be strong or optimal qualification are found. Examples of all three qualification levels are provided and the relationships between them as well as with the classical concept of qualification and the qualification introduced by Mathe and Perevezev are shown. In particular, spectral regularization methods having extended qualification in each one of the three levels and having zero or infinite classical qualification are presented. Finally several implications of this theory in the context of orders of convergence, converse results and maximal source sets for inverse ill-posed problems, are shown.Comment: 20 pages, 1 figur

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

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

Quinuclidine compounds differently act as agonists of Kenyon cell nicotinic acetylcholine receptors and induced distinct effect on insect ganglionic depolarizations

We have recently demonstrated that a new quinuclidine benzamide compound named LMA10203 acted as an agonist of insect nicotinic acetylcholine receptors. Its specific pharmacological profile on cockroach dorsal unpaired median neurons (DUM) helped to identify alpha-bungarotoxin-insensitive nAChR2 receptors. In the present study, we tested its effect on cockroach Kenyon cells. We found that it induced an inward current demonstrating that it bounds to nicotinic acetylcholine receptors expressed on Kenyon cells. Interestingly, LMA10203-induced currents were completely blocked by the nicotinic antagonist alpha-bungarotoxin. We suggested that LMA10203 effect occurred through the activation of alpha-bungarotoxin-sensitive receptors and did not involve alpha-bungarotoxin-insensitive nAChR2, previously identified in DUM neurons. In addition, we have synthesized two new compounds, LMA10210 and LMA10211, and compared their effects on Kenyon cells. These compounds were members of the 3-quinuclidinyl benzamide or benzoate families. Interestingly, 1 mM LMA10210 was not able to induce an inward current on Kenyon cells compared to LMA10211. Similarly, we did not find any significant effect of LMA10210 on cockroach ganglionic depolarization, whereas these three compounds were able to induce an effect on the central nervous system of the third instar M. domestica larvae. Our data suggested that these three compounds could bind to distinct cockroach nicotinic acetylcholine receptors

Towards a generic, comprehensive and participatory approach for assessing the impact of agricultural research in developing countries

International public agricultural research for development is increasingly requested to contribute to solving societal challenges related to food security, ecological transitions, climatic change and inequalities in development, among others. At the same time, in one strand of the scientific communities modalities and criteria to assess research are shifting towards demonstrating and explaining the causal link between research outputs and development impacts (Gaunand et al;, 2015). This paper describes a novel approach for impact assessment of agricultural research conducted in a developing country context adapted from the “impact pathways” and ASIRPA approaches (e.g. Douthwaite and Gummert 2010; Joly et al., 2015). A key methodological choice was to give an active role in the assessment to the multiple stakeholders involved in innovation and/or impacted by it. This was considered essential to identify impacts and indicators that evaluation teams might not have thought of by themselves, and to understand the complexity of innovation processes eventually leading to impact, particularly in a developing country context for which accountability towards end-users of research is weak and availability of or access to reliable quantitative data is a challenge. The resulting participatory methodology, called “Impress” (IMPact of RESearch in the South) focuses on establishing and explaining the relationships between the outputs produced by research, the outcomes that involve and affect the actors directly or indirectly interacting with research and ultimately the primary and secondary impacts for development. After developing it iteratively over several years, CIRAD is currently testing it by assessing 13 case studies throughout Africa, Asia and Latin America. Cases cover a wide diversity of innovation domains (plant breeding, post-harvest processing, pest and disease management, value chains, etc.), research approaches (from transfer of technology to action-research) and innovation trajectories, some of which were assessed ex-post and others in itinere). The perimeter of each case study includes suites of consecutive or closely related research or R&D projects which took place around a common theme in a given area over time. Evidence and indicators of impact are being identified, measured and validated through multi-stakeholders workshops, focus groups, semi-structured interviews and surveys with key concerned stakeholder groups. Initial results show a wide diversity of mostly positive impact types, including increases in production and incomes, improvement of the natural resources base, increased access to remunerative markets and at times changes in regulatory frameworks and policies, among others. Some impacts and indicators thereof were identified by the case stakeholders themselves, vindicating the choice of a participatory approach. Impacts seem linked among others to the development of and access to new knowledge and the strengthening of partnerships among stakeholders. Developing the capacities of stakeholders and of smallholder farmers in particular, also seems to have had a significant effect, which may have contributed to scaling out of some innovations. After cross-analysing this round of case studies and addressing the methodological lessons and challenges, CIRAD will release by end of 2016 an improved, user-friendlier version of IMPRESS which may be used within and outside CIRAD. It also hopes to encourage its researchers and Triomphe et al. Towards a generic, comprehensive and participatory approach... 3Southern partners to adopt an “impact culture” so that they can adjust their research planning and practices in an ex-ante fashion, and in doing so, improve the probability their future research work will indeed contribute to more and better impact. (Résumé d'auteur

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

Error bounds for computing the expectation by Markov chain Monte Carlo

We study the error of reversible Markov chain Monte Carlo methods for approximating the expectation of a function. Explicit error bounds with respect to different norms of the function are proven. By the estimation the well known asymptotical limit of the error is attained, i.e. there is no gap between the estimate and the asymptotical behavior. We discuss the dependence of the error on a burn-in of the Markov chain. Furthermore we suggest and justify a specific burn-in for optimizing the algorithm

Statistical analysis of the individual variability of 1D protein profiles as a tool in ecology: an application to parasitoid venom

International audienceUnderstanding the forces that shape eco-evolutionary patterns often requires linking phenotypes to genotypes, allowing characterization of these patterns at the molecular level. DNA-based markers are less informative in this aim compared to markers associated with gene expression and, more specifically, with protein quantities. The characterization of eco-evolutionary patterns also usually requires the analysis of large sample sizes to accurately estimate interindividual variability. However, the methods used to characterize and compare protein samples are generally expensive and time-consuming, which constrains the size of the produced data sets to few individuals. We present here a method that estimates the interindividual variability of protein quantities based on a global, semi-automatic analysis of 1D electrophoretic profiles, opening the way to rapid analysis and comparison of hundreds of individuals. The main original features of the method are the in silico normalization of sample protein quantities using pictures of electrophoresis gels at different staining levels, as well as a new method of analysis of electrophoretic profiles based on a median profile. We demonstrate that this method can accurately discriminate between species and between geographically distant or close populations, based on interindividual variation in venom protein profiles from three endoparasitoid wasps of two different genera (Psyttalia concolor, Psyttalia lounsburyi and Leptopili-na boulardi). Finally, we discuss the experimental designs that would benefit from the use of this method