Operator Theory and Its Applications: In Memory of V. B. Lidskii (1924-2008)

This book is a collection of articles devoted to the theory of linear operators in Hilbert spaces and its applications. The subjects covered range from the abstract theory of Toeplitz operators to the analysis of very specific differential operators arising in quantum mechanics, electromagnetism, and the theory of elasticity; the stability of numerical methods is also discussed. Many of the articles deal with spectral problems for not necessarily selfadjoint operators. Some of the articles are surveys outlining the current state of the subject and presenting open problems.

Root phenomics of crops: opportunities and challenges

Reliable techniques for screening large numbers of plants for root traits are still being developed, but include aeroponic, hydroponic and agar plate systems. Coupled with digital cameras and image analysis software, these systems permit the rapid measurement of root numbers, length and diameter in moderate ( typically <1000) numbers of plants. Usually such systems are employed with relatively small seedlings, and information is recorded in 2D. Recent developments in X-ray microtomography have facilitated 3D non-invasive measurement of small root systems grown in solid media, allowing angular distributions to be obtained in addition to numbers and length. However, because of the time taken to scan samples, only a small number can be screened (typically<10 per day, not including analysis time of the large spatial datasets generated) and, depending on sample size, limited resolution may mean that fine roots remain unresolved. Although agar plates allow differences between lines and genotypes to be discerned in young seedlings, the rank order may not be the same when the same materials are grown in solid media. For example, root length of dwarfing wheat ( Triticum aestivum L.) lines grown on agar plates was increased by similar to 40% relative to wild-type and semi-dwarfing lines, but in a sandy loam soil under well watered conditions it was decreased by 24-33%. Such differences in ranking suggest that significant soil environment-genotype interactions are occurring. Developments in instruments and software mean that a combination of high-throughput simple screens and more in-depth examination of root-soil interactions is becoming viable.

Spectral asymmetry of the massless Dirac operator on a 3-torus

Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double eigenvalue. The aim of the paper is to develop a perturbation theory for the eigenvalue with smallest modulus with respect to perturbations of the metric. Here the application of perturbation techniques is hindered by the fact that eigenvalues of the massless Dirac operator have even multiplicity, which is a consequence of this operator commuting with the antilinear operator of charge conjugation (a peculiar feature of dimension 3). We derive an asymptotic formula for the eigenvalue with smallest modulus for arbitrary perturbations of the metric and present two particular families of Riemannian metrics for which the eigenvalue with smallest modulus can be evaluated explicitly. We also establish a relation between our asymptotic formula and the eta invariant.

Molecular archaeology of Flaviviridae untranslated regions: duplicated RNA structures in the replication enhancer of flaviviruses and pestiviruses emerged via convergent evolution.

RNA secondary structures in the 3'untranslated regions (3'UTR) of the viruses of the family Flaviviridae, previously identified as essential (promoters) or beneficial (enhancers) for replication, have been analysed. Duplicated enhancer elements are revealed as a global feature in the evolution of the 3'UTR of distantly related viruses within the genera Flavivirus and Pestivirus. For the flaviviruses, duplicated structures occur in the 3'UTR of all four distantly related ecological virus subgroups (tick-borne, mosquito-borne, no known vector and insect-specific flaviviruses (ISFV). RNA structural differences distinguish tick-borne flaviviruses with discrete pathogenetic characteristics. For Aedes- and Culex-associated ISFV, secondary RNA structures with different conformations display numerous short ssRNA direct repeats, exposed as loops and bulges. Long quadruplicate regions comprise almost the entire 3'UTR of Culex-associated ISFV. Extended duplicated sequence and associated RNA structures were also discovered in the 3'UTR of pestiviruses. In both the Flavivirus and Pestivirus genera, duplicated RNA structures were localized to the enhancer regions of the 3'UTR suggesting an adaptive role predominantly in wild-type viruses. We propose sequence reiteration might act as a scaffold for dimerization of proteins involved in assembly of viral replicase complexes. Numerous nucleotide repeats exposed as loops/bulges might also interfere with host immune responses acting as a molecular sponge to sequester key host proteins or microRNAs.

Challenges of operational river forecasting

Skillful and timely streamflow forecasts are critically important to water managers and emergency protection services. To provide these forecasts, hydrologists must predict the behavior of complex coupled human–natural systems using incomplete and uncertain information and imperfect models. Moreover, operational predictions often integrate anecdotal information and unmodeled factors. Forecasting agencies face four key challenges: 1) making the most of available data, 2) making accurate predictions using models, 3) turning hydrometeorological forecasts into effective warnings, and 4) administering an operational service. Each challenge presents a variety of research opportunities, including the development of automated quality-control algorithms for the myriad of data used in operational streamflow forecasts, data assimilation, and ensemble forecasting techniques that allow for forecaster input, methods for using human-generated weather forecasts quantitatively, and quantification of human interference in the hydrologic cycle. Furthermore, much can be done to improve the communication of probabilistic forecasts and to design a forecasting paradigm that effectively combines increasingly sophisticated forecasting technology with subjective forecaster expertise. These areas are described in detail to share a real-world perspective and focus for ongoing research endeavors.

An overview on the urban boundary-layer atmosphere network in Helsinki

The Helsinki Urban Boundary-Layer Atmosphere Network (UrBAN: http://urban.fmi.fi) is a dedicated research-grade observational network where the physical processes in the atmosphere above the city are studied. Helsinki UrBAN is the most poleward intensive urban research observation network in the world and thus will allow studying some unique features such as strong seasonality. The network's key purpose is for the understanding of the physical processes in the urban boundary layer and associated fluxes of heat, momentum, moisture, and other gases. A further purpose is to secure a research-grade database, which can be used internationally to validate and develop numerical models of air quality and weather prediction. Scintillometers, a scanning Doppler lidar, ceilometers, a sodar, eddy-covariance stations, and radiometers are used. This equipment is supplemented by auxiliary measurements, which were primarily set up for general weather and/or air-quality mandatory purposes, such as vertical soundings and the operational Doppler radar network. Examples are presented as a testimony to the potential of the network for urban studies, such as (i) evidence of a stable boundary layer possibly coupled to an urban surface, (ii) the comparison of scintillometer data with sonic anemometry above an urban surface, (iii) the application of scanning lidar over a city, and (iv) combination of sodar and lidar to give a fuller range of sampling heights for boundary layer profiling.