On the convergence of the no response test

The no response test is a new scheme in inverse problems for partial differential equations which was recently proposed in [D. R. Luke and R. Potthast, SIAM J. Appl. Math., 63 (2003), pp. 1292–1312] in the framework of inverse acoustic scattering problems. The main idea of the scheme is to construct special probing waves which are small on some test domain. Then the response for these waves is constructed. If the response is small, the unknown object is assumed to be a subset of the test domain. The response is constructed from one, several, or many particular solutions of the problem under consideration. In this paper, we investigate the convergence of the no response test for the reconstruction information about inclusions D from the Cauchy values of solutions to the Helmholtz equation on an outer surface $\partial\Omega$ with $\overline{D} \subset \Omega$. We show that the one‐wave no response test provides a criterion to test the analytic extensibility of a field. In particular, we investigate the construction of approximations for the set of singular points $N(u)$ of the total fields u from one given pair of Cauchy data. Thus, the no response test solves a particular version of the classical Cauchy problem. Also, if an infinite number of fields is given, we prove that a multifield version of the no response test reconstructs the unknown inclusion D. This is the first convergence analysis which could be achieved for the no response test.

A multiwave range test for obstacle reconstructions with unknown physical properties

We develop a new multiwave version of the range test for shape reconstruction in inverse scattering theory. The range test [R. Potthast, et al., A ‘range test’ for determining scatterers with unknown physical properties, Inverse Problems 19(3) (2003) 533–547] has originally been proposed to obtain knowledge about an unknown scatterer when the far field pattern for only one plane wave is given. Here, we extend the method to the case of multiple waves and show that the full shape of the unknown scatterer can be reconstructed. We further will clarify the relation between the range test methods, the potential method [A. Kirsch, R. Kress, On an integral equation of the first kind in inverse acoustic scattering, in: Inverse Problems (Oberwolfach, 1986), Internationale Schriftenreihe zur Numerischen Mathematik, vol. 77, Birkhäuser, Basel, 1986, pp. 93–102] and the singular sources method [R. Potthast, Point sources and multipoles in inverse scattering theory, Habilitation Thesis, Göttingen, 1999]. In particular, we propose a new version of the Kirsch–Kress method using the range test and a new approach to the singular sources method based on the range test and potential method. Numerical examples of reconstructions for all four methods are provided.

Spatangoid-produced ichnofabrics (Bateig Limestone, Miocene, Spain) and the preservation of spatangoid trace fossils

A spatangoid-produced ichnofabric is described from the Miocene Bateig Limestone, SE Spain. This ichnofabric is characterized by the dominant presence of large meniscate burrows (Bichordites) produced by irregular echinoids. This constitutes an unusual mode of occurrence for spatangoid bioturbation, as their traces are most typically preserved in bases and tops of sandstone event beds. In fact, despite their important role as burrowers in modern settings (that can be extended back to the Early Cretaceous based on their body fossil record), spatangoid trace fossils (Scolicia and Bichordites) are comparatively rare. Several factors play an important role in their preservation: mechanism of burrowing, sediment characteristics, early diagenesis and presence/absence of deep-tier burrowers. Spatangoid-produced ichnofabrics, such as those from the Bateig Limestone, characterize depositional settings with intermittent deposition of event beds where there is an absence of deeper-tier bioturbation. (C) 2008 Elsevier B.V. All rights reserved

Hiatal surfaces from the Miocene Globigerina Limestone Formation of Malta: Biostratigraphy, sedimentology, trace fossils and early diagenesis

The Miocene Globigerina Limestone of the Maltese islands contains widespread omission surfaces with very different characteristics and origins. The terminal Lower Globigerina Limestone hardground (TLGLHg) formed during a period of falling sea level. Coccolith assemblages suggest shallowness. Sedimentary structures and trace fossil assemblages, indicate increasing frequency of storm events and erosional episodes, towards the surface. Calcite cementation which took place around Thalassinoides burrows and formed irregular nodules was followed by dissolution of aragonite. It is suggested that lithification was linked to microbial reactions involving organic matter. In contrast two later surfaces, the terminal Middle Globigerina Limestone omissionground (TMGLOg), which marks the Lower to Middle Miocene boundary, and the Fomm-ir-Rih local hardground (FiRLHg) both contain early diagenetic dolomite. Lithification took place in two phases. The dolomite is interpreted to have formed beneath the sea floor: it was subsequently exhumed and partially corroded as the precipitation of calcitic and phosphatic cements took place around burrows open to the circulation of sea water. (C) 2008 Elsevier B.V. All rights reserved.

Inverse problems in dynamic cognitive modeling

Inverse problems for dynamical system models of cognitive processes comprise the determination of synaptic weight matrices or kernel functions for neural networks or neural/dynamic field models, respectively. We introduce dynamic cognitive modeling as a three tier top-down approach where cognitive processes are first described as algorithms that operate on complex symbolic data structures. Second, symbolic expressions and operations are represented by states and transformations in abstract vector spaces. Third, prescribed trajectories through representation space are implemented in neurodynamical systems. We discuss the Amari equation for a neural/dynamic field theory as a special case and show that the kernel construction problem is particularly ill-posed. We suggest a Tikhonov-Hebbian learning method as regularization technique and demonstrate its validity and robustness for basic examples of cognitive computations.

Ribose 2′-O-methylation provides a molecular signature for the distinction of self and non-self mRNA dependent on the RNA sensor Mda5

The 5'-cap-structures of higher eukaryote mRNAs are ribose 2'-O-methylated. Likewise, a number of viruses replicating in the cytoplasm of eukayotes have evolved 2'-O-methyltransferases to modify autonomously their mRNAs. However, a defined biological role of mRNA 2'-O-methylation remains elusive. Here we show that viral mRNA 2'-O-methylation is critically involved in subversion of type-I-interferon (IFN-I) induction. We demonstrate that human and murine coronavirus 2'-O-methyltransferase mutants induce increased IFN-I expression, and are highly IFN-I sensitive. Importantly, IFN-I induction by 2'-O-methyltransferase-deficient viruses is dependent on the cytoplasmic RNA sensor melanoma differentiation-associated gene 5 (MDA5). This link between MDA5-mediated sensing of viral RNA and mRNA 2'-O-methylation suggests that RNA modifications, such as 2'-O-methylation, provide a molecular signature for the discrimination of self and non-self mRNA.