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Analysis and computation of the transmission eigenvalues with a conductive boundary condition
(2022)
We provide a new analytical and computational study of the transmission eigenvalues with a conductive boundary condition. These eigenvalues are derived from the scalar inverse scattering problem for an inhomogeneous material with a conductive boundary condition. The goal is to study how these eigenvalues depend on the material parameters in order to estimate the refractive index. The analytical questions we study are: deriving Faber–Krahn type lower bounds, the discreteness and limiting behavior of the transmission eigenvalues as the conductivity tends to infinity for a sign changing contrast. We also provide a numerical study of a new boundary integral equation for computing the eigenvalues. Lastly, using the limiting behavior we will numerically estimate the refractive index from the eigenvalues provided the conductivity is sufficiently large but unknown.
Deoxyribonucleic acid (DNA) and protein recognition are now standard tools in biology. In addition, the special optical properties of microsphere resonators expressed by the high quality factor (Q-factor) of whispering gallery modes (WGMs) or morphology dependent resonances (MDRs) have attracted the attention of the biophotonic community. Microsphere-based biosensors are considered as powerful candidates to achieve label-free recognition of single molecules due to the high sensitivity of their WGMs. When the microsphere surface is modified with biomolecules, the effective refractive index and the effective size of the microsphere change resulting in a resonant wavelength shift. The transverse electric (TE) and the transverse magnetic (TM) elastic light scattering intensity of electromagnetic waves at 600 and 1400 nm are numerically calculated for DNA and unspecific binding of proteins to the microsphere surface. The effect of changing the optical properties was studied for diamond (refractive index 2.34), glass (refractive index 1.50), and sapphire (refractive index 1.75) microspheres with a 50 µm radius. The mode spacing, the linewidth of WGMs, and the shift of resonant wavelength due to the change in radius and refractive index, were analyzed by numerical simulations. Preliminary results of unspecific binding of biomolecules are presented. The calculated shift in WGMs can be used for biomolecules detection.
Analysis of the long-term effect of the MBST® nuclear magnetic resonance therapy on gonarthrosis
(2016)
In this paper, we provide an analytical study of the transmission eigenvalue problem with two conductivity parameters. We will assume that the underlying physical model is given by the scattering of a plane wave for an isotropic scatterer. In previous studies, this eigenvalue problem was analyzed with one conductive boundary parameter whereas we will consider the case of two parameters. We prove the existence and discreteness of the transmission eigenvalues as well as study the dependence on the physical parameters. We are able to prove monotonicity of the first transmission eigenvalue with respect to the parameters and consider the limiting procedure as the second boundary parameter vanishes. Lastly, we provide extensive numerical experiments to validate the theoretical work.
Application of a (bio-)chemical sensor (ISFET) for the detection of physical parameters in liquids
(2003)
Multi-analyte biosensors may offer the opportunity to perform cost-effective and rapid analysis with reduced sample volume, as compared to electrochemical biosensing of each analyte individually. This work describes the development of an enzyme-based biosensor system for multi-parametric determination of four different organic acids. The biosensor array comprises five working electrodes for simultaneous sensing of ethanol, formate, d-lactate, and l-lactate, and an integrated counter electrode. Storage stability of the biosensor was evaluated under different conditions (stored at +4 °C in buffer solution and dry at −21 °C, +4 °C, and room temperature) over a period of 140 days. After repeated and regular application, the individual sensing electrodes exhibited the best stability when stored at −21 °C. Furthermore, measurements in silage samples (maize and sugarcane silage) were conducted with the portable biosensor system. Comparison with a conventional photometric technique demonstrated successful employment for rapid monitoring of complex media.
The chemical imaging sensor was applied to in-situ pH imaging of the solution in the vicinity of a corroding surface of stainless steel under potentiostatic polarization. A test piece of polished stainless steel was placed on the sensing surface leaving a narrow gap filled with artificial seawater and the stainless steel was corroded under polarization. The pH images obtained during polarization showed correspondence between the region of lower pH and the site of corrosion. It was also found that the pH value in the gap became as low as 2 by polarization, which triggered corrosion.
Malaria infection remains a significant risk for much of the population of tropical and subtropical areas, particularly in developing countries. Therefore, it is of high importance to develop sensitive, accurate and inexpensive malaria diagnosis tests. Here, we present a novel aptamer-based electrochemical biosensor (aptasensor) for malaria detection by impedance spectroscopy, through the specific recognition between a highly discriminatory DNA aptamer and its target Plasmodium falciparum lactate dehydrogenase (PfLDH). Interestingly, due to the isoelectric point (pI) of PfLDH, the aptasensor response showed an adjustable detection range based on the different protein net-charge at variable pH environments. The specific aptamer recognition allows sensitive protein detection with an expanded detection range and a low detection limit, as well as a high specificity for PfLDH compared to analogous proteins. The specific feasibility of the aptasensor is further demonstrated by detection of the target PfLDH in human serum. Furthermore, the aptasensor can be easily regenerated and thus applied for multiple usages. The robustness, sensitivity, and reusability of the presented aptasensor make it a promising candidate for point-of-care diagnostic systems.
We study the estimation of some linear functionals which are based on an unknown lifetime distribution. The observations are assumed to be generated under the semi-parametric random censorship model (SRCM), that is, a random censorship model where the conditional expectation of the censoring indicator given the observation belongs to a parametric family. Under this setup a semi-parametric estimator of the survival function was introduced by the author. If the parametric model assumption is correct, it is known that the estimated functional which is based on this semi-parametric estimator is asymptotically at least as efficient as the corresponding one which rests on the nonparametric Kaplan–Meier estimator.
In this paper we show that the estimated functional which is based on this semi-parametric estimator is asymptotically efficient with respect to the class of all regular estimators under this semi-parametric model.
Sleep scoring is a necessary and time-consuming task in sleep studies. In animal models (such as mice) or in humans, automating this tedious process promises to facilitate long-term studies and to promote sleep biology as a data-driven f ield. We introduce a deep neural network model that is able to predict different states of consciousness (Wake, Non-REM, REM) in mice from EEG and EMG recordings with excellent scoring results for out-of-sample data. Predictions are made on epochs of 4 seconds length, and epochs are classified as artifactfree or not. The model architecture draws on recent advances in deep learning and in convolutional neural networks research. In contrast to previous approaches towards automated sleep scoring, our model does not rely on manually defined features of the data but learns predictive features automatically. We expect deep learning models like ours to become widely applied in different fields, automating many repetitive cognitive tasks that were previously difficult to tackle.