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

The rate and fate of N-2 and C fixation by marine diatom-diazotroph symbioses

N-2 fixation constitutes an important new nitrogen source in the open sea. One group of filamentous N-2 fixing cyanobacteria (Richelia intracellularis, hereafter Richelia) form symbiosis with a few genera of diatoms. High rates of N-2 fixation and carbon (C) fixation have been measured in the presence of diatom-Richelia symbioses. However, it is unknown how partners coordinate C fixation and how the symbiont sustains high rates of N-2 fixation. Here, both the N-2 and C fixation in wild diatom-Richelia populations are reported. Inhibitor experiments designed to inhibit host photosynthesis, resulted in lower estimated growth and depressed C and N-2 fixation, suggesting that despite the symbionts ability to fix their own C, they must still rely on their respective hosts for C. Single cell analysis indicated that up to 22% of assimilated C in the symbiont is derived from the host, whereas 78-91% of the host N is supplied from their symbionts. A size-dependent relationship is identified where larger cells have higher N-2 and C fixation, and only N-2 fixation was light dependent. Using the single cell measures, the N-rich phycosphere surrounding these symbioses was estimated and contributes directly and rapidly to the surface ocean rather than the mesopelagic, even at high estimated sinking velocities (<10 m d(-1)). Several eco-physiological parameters necessary for incorporating symbiotic N-2 fixing populations into larger basin scale biogeochemical models (i.e., N and C cycles) are provided

Biofilms on glacial surfaces: hotspots for biological activity

Glaciers are important constituents in the Earth’s hydrological and carbon cycles, with predicted warming leading to increases in glacial melt and the transport of nutrients to adjacent and downstream aquatic ecosystems. Microbial activity on glacial surfaces has been linked to the biological darkening of cryoconite particles, affecting albedo and increased melt. This phenomenon, however, has only been demonstrated for alpine glaciers and the Greenland Ice Sheet, excluding Antarctica. In this study, we show via confocal laser scanning microscopy that microbial communities on glacial surfaces in Antarctica persist in biofilms. Overall, ~35% of the cryoconite sediment surfaces were covered by biofilm. Nanoscale scale secondary ion mass spectrometry measured significant enrichment of 13C and 15N above background in both Bacteroidetes and filamentous cyanobacteria (i.e., Oscillatoria) when incubated in the presence of 13C–NaHCO3 and 15NH4. This transfer of newly synthesised organic compounds was dependent on the distance of heterotrophic Bacteroidetes from filamentous Oscillatoria. We conclude that the spatial organisation within these biofilms promotes efficient transfer and cycling of nutrients. Further, these results support the hypothesis that biofilm formation leads to the accumulation of organic matter on cryoconite minerals, which could influence the surface albedo of glaciers

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

Highly porous scaffolds of PEDOT:PSS for bone tissue engineering.

UNLABELLED: Conjugated polymers have been increasingly considered for the design of conductive materials in the field of regenerative medicine. However, optimal scaffold properties addressing the complexity of the desired tissue still need to be developed. The focus of this study lies in the development and evaluation of a conductive scaffold for bone tissue engineering. In this study PEDOT:PSS scaffolds were designed and evaluated in vitro using MC3T3-E1 osteogenic precursor cells, and the cells were assessed for distinct differentiation stages and the expression of an osteogenic phenotype. Ice-templated PEDOT:PSS scaffolds presented high pore interconnectivity with a median pore diameter of 53.6±5.9µm and a total pore surface area of 7.72±1.7m2·g-1. The electrical conductivity, based on I-V curves, was measured to be 140µS·cm-1 with a reduced, but stable conductivity of 6.1µS·cm-1 after 28days in cell culture media. MC3T3-E1 gene expression levels of ALPL, COL1A1 and RUNX2 were significantly enhanced after 4weeks, in line with increased extracellular matrix mineralisation, and osteocalcin deposition. These results demonstrate that a porous material, based purely on PEDOT:PSS, is suitable as a scaffold for bone tissue engineering and thus represents a promising candidate for regenerative medicine. STATEMENT OF SIGNIFICANCE: Tissue engineering approaches have been increasingly considered for the repair of non-union fractions, craniofacial reconstruction or large bone defect replacements. The design of complex biomaterials and successful engineering of 3-dimensional tissue constructs is of paramount importance to meet this clinical need. Conductive scaffolds, based on conjugated polymers, present interesting candidates to address the piezoelectric properties of bone tissue and to induce enhanced osteogenesis upon implantation. However, conductive scaffolds have not been investigated in vitro in great measure. To this end, we have developed a highly porous, electrically conductive scaffold based on PEDOT:PSS, and provide evidence that this purely synthetic material is a promising candidate for bone tissue engineering

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

Responses of the coastal bacterial community to viral infection of the algae <i>Phaeocystis globosa</i>

The release of organic material upon algal cell lyses has a key role in structuring bacterial communities and affects the cycling of biolimiting elements in the marine environment. Here we show that already before cell lysis the leakage or excretion of organic matter by infected yet intact algal cells shaped North Sea bacterial community composition and enhanced bacterial substrate assimilation. Infected algal cultures of Phaeocystis globosa grown in coastal North Sea water contained gamma-and alphaproteobacterial phylotypes that were distinct from those in the non-infected control cultures 5 h after infection. The gammaproteobacterial population at this time mainly consisted of Alteromonas sp. cells that were attached to the infected but still intact host cells. Nano-scale secondary-ion mass spectrometry (nanoSIMS) showed similar to 20% transfer of organic matter derived from the infected C-13- and N-15-labelled P. globosa cells to Alteromonas sp. cells. Subsequent, viral lysis of P. globosa resulted in the formation of aggregates that were densely colonised by bacteria. Aggregate dissolution was observed after 2 days, which we attribute to bacteriophage-induced lysis of the attached bacteria. Isotope mass spectrometry analysis showed that 40% of the particulate C-13-organic carbon from the infected P. globosa culture was remineralized to dissolved inorganic carbon after 7 days. These findings reveal a novel role of viruses in the leakage or excretion of algal biomass upon infection, which provides an additional ecological niche for specific bacterial populations and potentially redirects carbon availability

Latent class analysis of diagnostic tests for adenovirus, Bordetella pertussis and influenza virus infections in German adults with longer lasting coughs

Laboratory tests in adult outpatients with longer lasting coughs to identify a potential causal pathogen are rarely performed, and there is no gold standard for these diagnostic tests. While the diagnostic validity of serological tests for pertussis is well established their potential contribution for diagnosing adenovirus and influenza virus A and B infections is unclear. A sentinel study into the population-based incidence of longer lasting coughs in adults was done in Rostock (former East Germany) and Krefeld (former West Germany). A total of 971 outpatients who consulted general practitioners or internists were included. Inclusion criteria were coughing for 51 week and no chronic respiratory diseases. We evaluated the performance of polymerase chain reaction (PCR) as well as IgG and IgA serology, applying a latent class model for diagnosing infections with adenovirus, B. pertussis, and influenza virus A and B. The adult outpatients first sought medical attention when they had been coughing for a median of 3 weeks. In this situation, direct detection of infectious agents by PCR had a low sensitivity. Modelling showed that additional serological tests equally improved sensitivity and specificity for diagnosis for adenovirus, B. pertussis and influenza virus A and B infections. The combination of serology and PCR may improve the overall performance of diagnostic tests for B. pertussis and also for adenovirus, and influenza virus A and B infections