Wegner estimate for Landau-breather Hamiltonians

We consider Landau Hamiltonians with a weak coupling random electric potential of breather type. Under appropriate assumptions we prove a Wegner estimate. It implies the Hoelder continuity of the integrated density of states. The main challenge is the problem how to deal with non-linear dependence on the random parameters

Harmonic Analysis and Random Schrödinger Operators

The present volume contains the Proceedings of the International Conference on Spectral Theory and Mathematical Physics held in Santiago de Chile in November 2014

Protecting points from operator pencils

We classify all sets of the form $\bigcup_{t\in\mathbb{R}}\mathrm{spec}(A+tB)$ where $A$ and $B$ are self-adjoint operators and $B$ is bounded, non-negative, and non-zero. We show that these sets are exactly the complements of discrete subsets of $\mathbb{R}$, that is, of at most countable subsets of $\mathbb{R}$ that contain none of their accumulation points.Comment: 6 pages; a counterexample for sign-indefinite perturbations and some references have been added, some editorial change

Scale-free uncertainty principles and Wegner estimates for random breather potentials

We present new scale-free quantitative unique continuation principles for Schr\"odinger operators. They apply to linear combinations of eigenfunctions corresponding to eigenvalues below a prescribed energy, and can be formulated as an uncertainty principle for spectral projectors. This extends recent results of Rojas-Molina & Veseli\'c, and Klein. We apply the scale-free unique continuation principle to obtain a Wegner estimate for a random Schr\"odinger operator of breather type. It holds for arbitrarily high energies. Schr\"odinger operators with random breather potentials have a non-linear dependence on random variables. We explain the challenges arising from this non-linear dependence

D'Alembert sums for vibrating bar with viscous ends

We describe a new method for finding analytic solutions to some initial-boundary problems for partial differential equations with constant coefficients. The method is based on expanding the denominator of the Laplace transformed Green's function of the problem into a convergent geometric series. If the denominator is a linear combination of exponents with real powers one obtains a closed form solution as a sum with finite but time dependent number of terms. We call it a d'Alembert sum. This representation is computationally most effective for small evolution times, but it remains valid even when the system of eigenmodes is incomplete and the eigenmode expansion is unavailable. Moreover, it simplifies in such cases. In vibratory problems d'Alembert sums represent superpositions of original and partially reflected traveling waves. They generalize the d'Alembert type formulas for the wave equation, and reduce to them when original waves can undergo only finitely many reflections in the entire course of evolution. The method is applied to vibrations of a bar with dampers at each end and at some internal point. The results are illustrated by computer simulations and comparisons to modal and FEM solutions.Comment: 18 pages, 8 figure

Rapid KRAS, EGFR, BRAF and PIK3CA Mutation Analysis of Fine Needle Aspirates from Non-Small-Cell Lung Cancer Using Allele-Specific qPCR

Endobronchial Ultrasound Guided Transbronchial Needle Aspiration (EBUS-TBNA) and Trans-esophageal Ultrasound Scanning with Fine Needle Aspiration (EUS-FNA) are important, novel techniques for the diagnosis and staging of non-small cell lung cancer (NSCLC) that have been incorporated into lung cancer staging guidelines. To guide and optimize treatment decisions, especially for NSCLC patients in stage III and IV, EGFR and KRAS mutation status is often required. The concordance rate of the mutation analysis between these cytological aspirates and histological samples obtained by surgical staging is unknown. Therefore, we studied the extent to which allele-specific quantitative real-time PCR with hydrolysis probes could be reliably performed on EBUS and EUS fine needle aspirates by comparing the results with histological material from the same patient. We analyzed a series of 43 NSCLC patients for whom cytological and histological material was available. We demonstrated that these standard molecular techniques can be accurately applied on fine needle cytological aspirates from NSCLC patients. Importantly, we show that all mutations detected in the histological material of primary tumor were also identified in the cytological samples. We conclude that molecular profiling can be reliably performed on fine needle cytology aspirates from NSCLC patients

National records of 3000 European bee and hoverfly species: A contribution to pollinator conservation

Pollinators play a crucial role in ecosystems globally, ensuring the seed production of most flowering plants. They are threatened by global changes and knowledge of their distribution at the national and continental levels is needed to implement efficient conservation actions, but this knowledge is still fragmented and/or difficult to access. As a step forward, we provide an updated list of around 3000 European bee and hoverfly species, reflecting their current distributional status at the national level (in the form of present, absent, regionally extinct, possibly extinct or non-native). This work was attainable by incorporating both published and unpublished data, as well as knowledge from a large set of taxonomists and ecologists in both groups. After providing the first National species lists for bees and hoverflies for many countries, we examine the current distributional patterns of these species and designate the countries with highest levels of species richness. We also show that many species are recorded in a single European country, highlighting the importance of articulating European and national conservation strategies. Finally, we discuss how the data provided here can be combined with future trait and Red List data to implement research that will further advance pollinator conservation