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We consider a linear ill-posed equation in the Hilbert space setting. Multiple independent unbiased measurements of the right-hand side are available. A natural approach is to take the average of the measurements as an approximation of the right-hand side and to estimate the data error as the inverse of the square root of the number of measurements. We calculate the optimal convergence rate (as the number of measurements tends to infinity) under classical source conditions and introduce a modified discrepancy principle, which asymptotically attains this rate.
Crenicichla is the largest and most widely distributed genus of Neotropical cichlids. The Crenicichla mandelburgeri species complex from the Middle Paraná departs from the ancestral and predominant ecomorphology of the large genus and shows parallel evolution of ecomorphs both within the complex and also to the unrelated C. missioneira species complex from the Uruguay River. Here, we formally describe a new species pair from the C. mandelburgeri species complex that has evolved a parallel morphological and ecological dichotomy to another species pair and also to species in the unrelated C. missioneira species complex. The new species pair is endemic to a single tributary (the Piray Guazú) of the Middle Paraná River where it is sympatric and partly syntopic. Mitochondrial DNA phylogeny shows the two new species as distantly related within the C. mandelburgeri species complex, each with a sister species in the Iguazú rather than in the neighbouring Paraná River tributaries. Nuclear DNA analyses demonstrate their sister-group relationship, which is however complicated by the reticulated origin of one of the new species. We present determination keys for all the currently formally described species of the C. mandelburgeri species complex including the new species described here.
We describe two new species of Ctenocerinae (Pompilidae) from Asia, i.e., Ctenocerus srilankae Shimizu sp. nov. from Sri Lanka and Paraclavelia arabiae Shimizu sp. nov. from Oman. These represent the first records of Ctenocerus Dahlbom, 1845 and Paraclavelia Haupt, 1930 in Asia. Two new combinations and a new synonymy are proposed: Ctenocerus fasciatus (Smith, 1851) (= Micropteryx fasciata Smith, 1851); Paraclavelia decipiens (Arnold, 1932) (= Clavelia decipiens Arnold, 1932); and Ctenocerus Dahlbom, 1845 (= Euclavelia Arnold, 1932). We discuss the difficulty of systematics of Ctenocerinae at generic level. The head and pronotal structures of Ctenocerus and Paraclavelia are presumably specialized for preying on trapdoor spiders. These structures are considered to have evolved independently of other unrelated parasitoid Pompilidae that have been confirmed or proposed to prey on trapdoor spiders. We also discuss the biogeographical distribution of these genera.