Nutritional symbionts enhance structural defence against predation and fungal infection in a grain pest beetle

Many insects benefit from bacterial symbionts that provide essential nutrients and thereby extend the hosts’ adaptive potential and their ability to cope with challenging environments. However, the implications of nutritional symbioses for the hosts’ defence against natural enemies remain largely unstudied. Here, we investigated whether the cuticle-enhancing nutritional symbiosis of the saw-toothed grain beetle Oryzaephilus surinamensis confers protection against predation and fungal infection. We exposed age-defined symbiotic and symbiont-depleted (aposymbiotic) beetles to two antagonists that must actively penetrate the cuticle for a successful attack: wolf spiders (Lycosidae) and the fungal entomopathogen Beauveria bassiana. While young beetles suffered from high predation and fungal infection rates regardless of symbiont presence, symbiotic beetles were able to escape this period of vulnerability and reach high survival probabilities significantly faster than aposymbiotic beetles. To understand the mechanistic basis of these differences, we conducted a time-series analysis of cuticle development in symbiotic and aposymbiotic beetles by measuring cuticular melanisation and thickness. The results reveal that the symbionts accelerate their host's cuticle formation and thereby enable it to quickly reach a cuticle quality threshold that confers structural protection against predation and fungal infection. Considering the widespread occurrence of cuticle enhancement via symbiont-mediated tyrosine supplementation in beetles and other insects, our findings demonstrate how nutritional symbioses can have important ecological implications reaching beyond the immediate nutrient-provisioning benefits

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

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

Elastic-Net Regularization: Error estimates and Active Set Methods

This paper investigates theoretical properties and efficient numerical algorithms for the so-called elastic-net regularization originating from statistics, which enforces simultaneously l^1 and l^2 regularization. The stability of the minimizer and its consistency are studied, and convergence rates for both a priori and a posteriori parameter choice rules are established. Two iterative numerical algorithms of active set type are proposed, and their convergence properties are discussed. Numerical results are presented to illustrate the features of the functional and algorithms

Parameter identification in a semilinear hyperbolic system

We consider the identification of a nonlinear friction law in a one-dimensional damped wave equation from additional boundary measurements. Well-posedness of the governing semilinear hyperbolic system is established via semigroup theory and contraction arguments. We then investigte the inverse problem of recovering the unknown nonlinear damping law from additional boundary measurements of the pressure drop along the pipe. This coefficient inverse problem is shown to be ill-posed and a variational regularization method is considered for its stable solution. We prove existence of minimizers for the Tikhonov functional and discuss the convergence of the regularized solutions under an approximate source condition. The meaning of this condition and some arguments for its validity are discussed in detail and numerical results are presented for illustration of the theoretical findings