Bandlimited approximations to the truncated Gaussian and applications

In this paper we extend the theory of optimal approximations of functions $f: \R \to \R$ in the $L^1(\R)$-metric by entire functions of prescribed exponential type (bandlimited functions). We solve this problem for the truncated and the odd Gaussians using explicit integral representations and fine properties of truncated theta functions obtained via the maximum principle for the heat operator. As applications, we recover most of the previously known examples in the literature and further extend the class of truncated and odd functions for which this extremal problem can be solved, by integration on the free parameter and the use of tempered distribution arguments. This is the counterpart of the work \cite{CLV}, where the case of even functions is treated.Comment: to appear in Const. Appro

Some extremal functions in Fourier analysis, III

We obtain the best approximation in $L^1(\R)$, by entire functions of exponential type, for a class of even functions that includes $e^{-\lambda|x|}$, where $\lambda >0$, $\log |x|$ and $|x|^{\alpha}$, where $-1 < \alpha < 1$. We also give periodic versions of these results where the approximating functions are trigonometric polynomials of bounded degree.Comment: 26 pages. Submitte

Direct cell mass measurements expand the role of small microorganisms in nature.

Microbial biomass is a key parameter needed for the quantification of microbial turnover rates and their contribution to the biogeochemical element cycles. However, estimates of microbial biomass rely on empirically-derived mass-to-volume relationships and large discrepancies exist between the available empirical conversion factors. Here we report a significant non-linear relationship between carbon mass and cell volume (mcarbon = 197 × V0.46.; R2 = 0.95) based on direct cell mass, volume and elemental composition measurements of twelve prokaryotic species with average volumes between 0.011 – 0.705 μm3. The carbon mass density of our measured cells ranged from 250 to 1800 fg C μm-3 for the measured cell volumes. Compared to other currently used models, our relationship yielded up to 300 % higher carbon mass values. A compilation of our and previously published data showed that cells with larger volumes (> 0.5 μm3) display a constant (carbon) mass-to-volume ratio whereas cells with volumes below 0.5 μm3 exhibit a nonlinear increase in (carbon) mass density with decreasing volume. Small microorganisms dominate marine and freshwater bacterioplankton as well as soils and marine and terrestrial subsurface. The application of our experimentally-determined conversion factors will help to quantify the true contribution of these microorganisms to ecosystem functions and global microbial biomass

The NY-Ålesund TurbulencE Fiber Optic eXperiment (NYTEFOX): investigating the Arctic boundary layer, Svalbard

The NY-Ålesund TurbulencE Fiber Optic eXperiment (NYTEFOX) was a field experiment at the Ny-Ålesund Arctic site (78.9◦ N, 11.9◦ E) and yielded a unique meteorological data set. These data describe the distribution of heat, airflows, and exchange in the Arctic boundary layer for a period of 14 d from 26 February to 10 March 2020. NYTEFOX is the first field experiment to investigate the heterogeneity of airflow and its transport of temperature, wind, and kinetic energy in the Arctic environment using the fiber-optic distributed sensing (FODS) technique for horizontal and vertical observations. FODS air temperature and wind speed were observed at a spatial resolution of 0.127 m and a temporal resolution of 9 s along a 700 m horizontal array at 1 m above ground level (a.g.l.) and along three 7 m vertical profiles. Ancillary data were collected from three sonic anemometers and an acoustic profiler (minisodar; sodar is an acronym for “sound detection and ranging”) yielding turbulent flow statistics and vertical profiles in the lowest 300 m a.g.l., respectively. The observations from this field campaign are publicly available on Zenodo (https://doi.org/10.5281/zenodo.4756836, Huss et al., 2021) and supplement the meteorological data set operationally collected by the Baseline Surface Radiation Network (BSRN) at Ny-Ålesund, Svalbard

A conceptual basis for surveying fouling communities at exposed and protected sites at sea: Feasible designs with exchangeable test bodies for in-situ biofouling collection

The enhanced inertia load caused by biofouling on device components, such as the foundations of wind turbines or other structures at sea, modifies the hydrodynamic properties, and increases the stress to structures, predominantly in upper water layers with high impact from wave dynamics. This compromises the stability, functioning, operation as well as the durability of these devices especially in exposed environments. A main challenge is the quantification of the impact of hydrodynamic forces on irregular bodies being overgrown by soft- and hard-bodied biofouling organisms. Therefore, test bodies from the upper 1–5 m water depth and thus exposed to the strongest wave actions close to the surface shall be overgrown by biofouling and used in measurement trials in a wave and current flume. These measurements shall shed light on the varying roughness and its influence on the load bearing capacity of foundation piles. Consequently, the main aims of the present work were the development of two independent test stations as holding devices for artificial test bodies for the collection of biofouling organisms during field studies: a carrying unit floating at the surface in an exposed area (System A) and a sampling device with access from a land-based facility (System B). Both systems are relatively easy to access, exhibit straightforward handling, and are reasonable cost-effective. A Test Body Support Unit (TBSU, System A) was designed and mounted on a spare buoy to carry the test bodies (cylinders), which serve as substrate for the fouling. The system was sufficiently robust to withstand several periods of rough sea conditions over the first two years. This system can only be accessed by vessels. System B (MareLift) provided the robustness and functionality needed for areas exhibiting harsh conditions but can be operated from land. The here used test bodies (steel panels) exhibited a sound basis for the monitoring of succession processes in the biofouling development. System B offered the possibility to analyse two habitats (intertidal and subtidal) and revealed clear differences in the composition and development of their fouling communities. Overall, both systems provide advantages in obtaining standardized biofouling samples compared to previous approaches. Such test stations play an important role in the risk management of marine sectors as they could help characterising biofouling communities over different geographical areas. System A and B provide a sound basis for biofouling research but potentially also for other potential research approaches in exposed areas as they provide space for future developments

Nitrate respiration and diel migration patterns of diatoms are linked in sediments underneath a microbial mat

Diatoms are among the few eukaryotes known to store nitrate (NO3−) and to use it as an electron acceptor for respiration in the absence of light and O2. Using microscopy and 15N stable isotope incubations, we studied the relationship between dissimilatory nitrate/nitrite reduction to ammonium (DNRA) and diel vertical migration of diatoms in phototrophic microbial mats and the underlying sediment of a sinkhole in Lake Huron (USA). We found that the diatoms rapidly accumulated NO3− at the mat-water interface in the afternoon and 40% of the population migrated deep into the sediment, where they were exposed to dark and anoxic conditions for ~75% of the day. The vertical distribution of DNRA rates and diatom abundance maxima coincided, suggesting that DNRA was the main energy generating metabolism of the diatom population. We conclude that the illuminated redox-dynamic ecosystem selects for migratory diatoms that can store nitrate for respiration in the absence of light. A major implication of this study is that the dominance of DNRA over denitrification is not explained by kinetics or thermodynamics. Rather, the dynamic conditions select for migratory diatoms that perform DNRA and can outcompete sessile denitrifiers

Cobalt containing glass fibres and their synergistic effect on the HIF-1 pathway for wound healing applications

Introduction and Methods: Chronic wounds are a major healthcare problem, but their healing may be improved by developing biomaterials which can stimulate angiogenesis, e.g. by activating the Hypoxia Inducible Factor (HIF) pathway. Here, novel glass fibres were produced by laser spinning. The hypothesis was that silicate glass fibres that deliver cobalt ions will activate the HIF pathway and promote the expression of angiogenic genes. The glass composition was designed to biodegrade and release ions, but not form a hydroxyapatite layer in body fluid. Results and Discussion: Dissolution studies demonstrated that hydroxyapatite did not form. When keratinocyte cells were exposed to conditioned media from the cobalt-containing glass fibres, significantly higher amounts of HIF-1α and Vascular Endothelial Growth Factor (VEGF) were measured compared to when the cells were exposed to media with equivalent amounts of cobalt chloride. This was attributed to a synergistic effect of the combination of cobalt and other therapeutic ions released from the glass. The effect was also much greater than the sum of HIF-1α and VEGF expression when the cells were cultured with cobalt ions and with dissolution products from the Co-free glass, and was proven to not be due to a rise in pH. The ability of the glass fibres to activate the HIF-1 pathway and promote VEGF expression shows the potential for their use in chronic wound dressings