On a class of integral systems. - In: Complex analysis and operator theory, ISSN 1661-8262, Bd. 15 (2021), 6, 103, insges. 39 S.
We study spectral problems for two-dimensional integral system with two given non-decreasing functions R, W on an interval [0, b) which is a generalization of the Krein string. Associated to this system are the maximal linear relation Tmax and the minimal linear relation Tmin in the space L2(dW) which are connected by Tmax=T*min. It is shown that the limit point condition at b for this system is equivalent to the strong limit point condition for the linear relation Tmax. In the limit circle case the Evans-Everitt condition is proved to hold on a subspace T*N of Tmax characterized by the Neumann boundary condition at b. The notion of the principal Titchmarsh-Weyl coefficient of this integral system is introduced. Boundary triple for the linear relation Tmax in the limit point case (and for T*N in the limit circle case) is constructed and it is shown that the corresponding Weyl function coincides with the principal Titchmarsh-Weyl coefficient of the integral system. The notion of the dual integral system is introduced by reversing the order of R and W and the formula relating the principal Titchmarsh-Weyl coefficients of the direct and the dual integral systems is proved. For every integral system with the principal Titchmarsh-Weyl coefficients q a canonical system is constructed so that its Titchmarsh-Weyl coefficient Q is the unwrapping transform of q: Q(z)=zq(z2).
https://doi.org/10.1007/s11785-021-01148-w
A meshfree method for a PDE-constrained optimization problem. - In: SIAM journal on numerical analysis, ISSN 1095-7170, Bd. 59 (2021), 4, S. 1896-1917
We describe a new approximation method for solving a PDE-constrained optimization problem numerically. Our method is based on the adjoint formulation of the optimization problem, leading to a system of weakly coupled, elliptic PDEs. These equations are then solved using kernel-based collocation. We derive an error analysis and give numerical examples.
https://doi.org/10.1137/20M1363510
Cost-effective sensor for flow monitoring in biologic microreactors. - In: IEEE sensors journal, ISSN 1558-1748, Bd. 21 (2021), 19, S. 21314-21321
https://doi.org/10.1109/JSEN.2021.3102262
A pre-registered short-term forecasting study of COVID-19 in Germany and Poland during the second wave. - In: Nature Communications, ISSN 2041-1723, Bd. 12 (2021), 5173, S. 1-16
Disease modelling has had considerable policy impact during the ongoing COVID-19 pandemic, and it is increasingly acknowledged that combining multiple models can improve the reliability of outputs. Here we report insights from ten weeks of collaborative short-term forecasting of COVID-19 in Germany and Poland (12 October-19 December 2020). The study period covers the onset of the second wave in both countries, with tightening non-pharmaceutical interventions (NPIs) and subsequently a decay (Poland) or plateau and renewed increase (Germany) in reported cases. Thirteen independent teams provided probabilistic real-time forecasts of COVID-19 cases and deaths. These were reported for lead times of one to four weeks, with evaluation focused on one- and two-week horizons, which are less affected by changing NPIs. Heterogeneity between forecasts was considerable both in terms of point predictions and forecast spread. Ensemble forecasts showed good relative performance, in particular in terms of coverage, but did not clearly dominate single-model predictions. The study was preregistered and will be followed up in future phases of the pandemic.
https://doi.org/10.1038/s41467-021-25207-0
Antitumor efficiency of the natural alkaloid berberine complexed with C60 fullerene in Lewis lung carcinoma in vitro and in vivo. - In: Cancer nanotechnology, ISSN 1868-6966, Bd. 12 (2021), 24, insges. 18 S.
Berberine (Ber) is a herbal alkaloid with pharmacological activity in general and a high anticancer potency in particular. However, due to its low bioavailability, the difficulty in reaching a target and choosing the right dose, there is a need to improve approaches of Ber use in anticancer therapy. In this study, Ber, noncovalently bound to a carbon nanostructure C60 fullerene (C60) at various molar ratios of the components, was explored against Lewis lung carcinoma (LLC).
https://doi.org/10.1186/s12645-021-00096-6
Neurochirurgische Planung mittels automatisierter Bilderkennung und optimaler Pfadplanung :
Neurosurgery planning based on automated image recognition and optimal path design. - In: Automatisierungstechnik, ISSN 2196-677X, Bd. 69 (2021), 8, S. 708-721
Stereotactic neurosurgery requires a careful planning of cannulae paths to spare eloquent areas of the brain that, if damaged, will result in loss of essential neurological function such as sensory processing, linguistic ability, vision, or motor function. We present an approach based on modelling, simulation, and optimization to set up a computational assistant tool. Thereby, we focus on the modeling of the brain topology, where we construct ellipsoidal approximations of voxel clouds based on processed MRI data. The outcome is integrated in a path-planning problem either via constraints or by penalization terms in the objective function. The surgical planning problem with obstacle avoidance is solved for different types of stereotactic cannulae using numerical simulations. We illustrate our method with a case study using real MRI data.
https://doi.org/10.1515/auto-2021-0044
C60 fullerene against SARS-CoV-2 coronavirus: an in silico insight. - In: Scientific reports, ISSN 2045-2322, Bd. 11 (2021), 17748, S. 1-12
Based on WHO reports the new SARS-CoV-2 coronavirus is currently widespread all over the world. So far > 162 million cases have been confirmed, including > 3 million deaths. Because of the pandemic still spreading across the globe the accomplishment of computational methods to find new potential mechanisms of virus inhibitions is necessary. According to the fact that C60 fullerene (a sphere-shaped molecule consisting of carbon) has shown inhibitory activity against various protein targets, here the analysis of the potential binding mechanism between SARS-CoV-2 proteins 3CLpro and RdRp with C60 fullerene was done; it has resulted in one and two possible binding mechanisms, respectively. In the case of 3CLpro, C60 fullerene interacts in the catalytic binding pocket. And for RdRp in the first model C60 fullerene blocks RNA synthesis pore and in the second one it prevents binding with Nsp8 co-factor (without this complex formation, RdRp can't perform its initial functions). Then the molecular dynamics simulation confirmed the stability of created complexes. The obtained results might be a basis for other computational studies of 3CLPro and RdRp potential inhibition ways as well as the potential usage of C60 fullerene in the fight against COVID-19 disease.
https://doi.org/10.1038/s41598-021-97268-6
Bismuth selenide nanosheets confined in thin carbon layers as anode materials for advanced potassium-ion batteries. - In: Inorganic chemistry frontiers, ISSN 2052-1553, Bd. 8 (2021), 18, S. 4267-4275
Metal selenides as promising anode materials for potassium ion batteries (PIBs) have attracted great research attention. However, it is still a challenge to promote its practical application due to the unsatisfactory cyclability resulting from large volume variation and sluggish kinetics. Herein, we tackle this issue by focusing on a promising but undemonstrated anode, bismuth selenide for PIBs which possesses a high theoretical capacity and good electronic conductivity. Benefitting from the carbon layer coating, Bi2Se3C has the capability to inhibit self-aggregation and buffer the volume expansion, leading to outstanding potassium-ion storage capability. It exhibits a very high reversible capacity of 526 mA h g^-1 at 50 mA g^-1, as well as superior cyclability and rate capability while maintaining a high capacity of 214 mA h g^-1 at 1.0 A g^-1 after 1000 cycles. Furthermore, its fast and reversible ion storage mechanism was verified, which first involves conversion and subsequent alloying redox reactions. This work enriches the understanding and development of stable conversion/alloying-based anodes for high-performance potassium-ion batteries.
https://doi.org/10.1039/D1QI00672J
Micro flow photochemical synthesis of Ca-sensitive fluorescent sensor particles. - In: Engineering in life sciences, ISSN 1618-2863, Bd. 21 (2021), 8/9, S. 518-526
Fluorescence probes have widely been used for detecting and imaging Ca2+-enriched parts of cells but more rarely for quantitative determination of concentrations. In this study we show how this can be achieved by a novel approach using hydrogel particles. In a microfluidic co-flow arrangement spherical droplets were generated from an aqueous solution of acrylamide, N,N'-methylenebisacrylamide crosslinker and photoinitiator and subsequently photo-cured in situ yielding gel particles in a sub millimeter range. These particles were separated, dried under reduced pressure and re-swollen in water containing Rhod-5N tri potassium salt as calcium ion selective fluorescence probe. After that the particles were dried again and stored for further investigations. Upon exposure of dried particles to calcium chloride solutions they swell and take up Ca2+-ions forming a strong fluorescing complex with Rhod-5N. Thus, fluorescence intensity increases with calcium ion concentration. Up to ca. 0.50 mM the enhancement effect is strong and then becomes considerably weaker. The intensity-concentration-dependence is well described by an equation derived from the equilibrium of the formation of a 1:1 Ca2+:Rhod-5N complex. The particles allow for a fast optical determination of Ca2+-concentrations up to 0.50 mM in analyte volumes down to below 10 [my]L.
https://doi.org/10.1002/elsc.202100023
Metal nanoparticles as free-floating electrodes. - In: Encyclopedia, ISSN 2673-8392, Bd. 1 (2021), 3, S. 551-565
Colloidal metal nanoparticles in an electrolyte environment are not only electrically charged but also electrochemically active objects. They have the typical character of metal electrodes with ongoing charge transfer processes on the metal/liquid interface. This picture is valid for the equilibrium state and also during the formation, growth, aggregation or dissolution of nanoparticles. This behavior can be understood in analogy to macroscopic mixed-electrode systems with a free-floating potential, which is determined by the competition between anodic and cathodic partial processes. In contrast to macroscopic electrodes, the small size of nanoparticles is responsible for significant effects of low numbers of elementary charges and for self-polarization effects as they are known from molecular systems, for example. The electrical properties of nanoparticles can be estimated by basic electrochemical equations. Reconsidering these fundamentals, the assembly behavior, the formation of nonspherical assemblies of nanoparticles and the growth and the corrosion behavior of metal nanoparticles, as well as the formation of core/shell particles, branched structures and particle networks, can be understood. The consequences of electrochemical behavior, charging and self-polarization for particle growth, shape formation and particle/particle interaction are discussed.
https://doi.org/10.3390/encyclopedia1030046