Constructing solutions to the Bj\"orling problem for isothermic surfaces by structure preserving discretization

In this article, we study an analog of the Bj\"orling problem for isothermic surfaces (that are more general than minimal surfaces): given a real analytic curve $\gamma$ in ${\mathbb R}^3$, and two analytic non-vanishing orthogonal vector fields $v$ and $w$ along $\gamma$, find an isothermic surface that is tangent to $\gamma$ and that has $v$ and $w$ as principal directions of curvature. We prove that solutions to that problem can be obtained by constructing a family of discrete isothermic surfaces (in the sense of Bobenko and Pinkall) from data that is sampled along $\gamma$, and passing to the limit of vanishing mesh size. The proof relies on a rephrasing of the Gauss-Codazzi-system as analytic Cauchy problem and an in-depth-analysis of its discretization which is induced from the geometry of discrete isothermic surfaces. The discrete-to-continuous limit is carried out for the Christoffel and the Darboux transformations as well.Comment: 29 pages, some figure

Processing methods for photoacoustic Doppler flowmetry with a clinical ultrasound scanner

Photoacoustic flowmetry (PAF) based on time-domain cross correlation of photoacoustic signals is a promising technique for deep tissue measurement of blood flow velocity. Signal processing has previously been developed for single element transducers. Here, the processing methods for acoustic resolution PAF using a clinical ultrasound transducer array are developed and validated using a 64-element transducer array with a -6 dB detection band of 11 to 17 MHz. Measurements were performed on a flow phantom consisting of a tube (580  μm inner diameter) perfused with human blood flowing at physiological speeds ranging from 3 to 25  mm  /  s. The processing pipeline comprised: image reconstruction, filtering, displacement detection, and masking. High-pass filtering and background subtraction were found to be key preprocessing steps to enable accurate flow velocity estimates, which were calculated using a cross-correlation based method. In addition, the regions of interest in the calculated velocity maps were defined using a masking approach based on the amplitude of the cross-correlation functions. These developments enabled blood flow measurements using a transducer array, bringing PAF one step closer to clinical applicability

Terbium to Quantum Dot FRET Bioconjugates for Clinical Diagnostics: Influence of Human Plasma on Optical and Assembly Properties

Förster resonance energy transfer (FRET) from luminescent terbium complexes (LTC) as donors to semiconductor quantum dots (QDs) as acceptors allows extraordinary large FRET efficiencies due to the long Förster distances afforded. Moreover, time-gated detection permits an efficient suppression of autofluorescent background leading to sub-picomolar detection limits even within multiplexed detection formats. These characteristics make FRET-systems with LTC and QDs excellent candidates for clinical diagnostics. So far, such proofs of principle for highly sensitive multiplexed biosensing have only been performed under optimized buffer conditions and interactions between real-life clinical media such as human serum or plasma and LTC-QD-FRET-systems have not yet been taken into account. Here we present an extensive spectroscopic analysis of absorption, excitation and emission spectra along with the luminescence decay times of both the single components as well as the assembled FRET-systems in TRIS-buffer, TRIS-buffer with 2% bovine serum albumin, and fresh human plasma. Moreover, we evaluated homogeneous LTC-QD FRET assays in QD conjugates assembled with either the well-known, specific biotin-streptavidin biological interaction or, alternatively, the metal-affinity coordination of histidine to zinc. In the case of conjugates assembled with biotin-streptavidin no significant interference with the optical and binding properties occurs whereas the histidine-zinc system appears to be affected by human plasma

Mycorrhization of fagaceae forests within mediterranean ecosystems

Mediterranean Fagaceae forests are valuable due to their ecological and socioeconomic aspects. Some profitable plant species, such as Castanea (timber and chestnut), Quercus (timber and cork), and Fagus (timber), encounter in this habitat the excellent edaphoclimatic conditions to develop. All Fagaceae plants are commonly associated to ECM fungal species, which are found in these forests in quite stable communities, mainly enriched in Russulaceae and Telephoraceae species. Currently, the Mediterranean Basin is considered as one of the global biodiversity hotspots, since many of their endemic plant species are not found elsewhere and are now under threat. Due to climate changing and introduction of disease agents, Fagaceae forests are facing an adaptation challenge to both biotic and abiotic threats. Although ECM communities are highly disturbed by climate factors and tree disease incidence, they could play an important role in increasing water availability to the plant and also improving plant tree defense against pathogens. Recent advances, namely, on genomics and transcriptomics, are providing tools for increasing the understanding of Fagaceae mycorrhization process and stress responses to biotic and abiotic stresses. Such studies can provide new information for the implementation of the most adequate management policies for protecting threaten Mediterranean forests.info:eu-repo/semantics/publishedVersio