Smooth, invariant orthonormal basis for singular potential Schroedinger operators

In a recent contribution we showed that there exists a smooth, dense domain for singular potential Schr\"odinger operators on the real line which is invariant under taking derivatives of arbitrary order and under multiplication by positive and negative integer powers of the coordinate. Moreover, inner products between basis elements of that domain were shown to be easily computable analytically. A task left open was to construct an orthonormal basis from elements of that domain by using Gram-Schmidt orthonormalisation. We perform that step in the present manuscript. We also consider the application of these methods to the positive real line for which one can no longer perform the integrals analytically but for which one can give tight analytical estimates.Comment: 5

Challenges in using mid-infrared spectroscopy for the determination of soil physical, chemical, and biochemical properties on undisturbed soil samples

Diffuse reflectance infrared Fourier transform (DRIFT) spectroscopy in the mid-infrared range (MIR) has become an established analytical tool for quantitative and qualitative analysis of soil samples. The heterogeneity of soil requires sample preparation procedures to optimize the reproducibility and accuracy of the spectroscopic measurement. These procedures have not been standardized. Generally, soil is dried and ground before measurement to avoid reflections of surface water films and minimize the intra- and inter-particle variability, respectively. Additionally, the sample surface is levelled to a plain surface for an ideal reflection. These sample preparation techniques are limited to disturbed samples only. Thus, a potential DRIFT mapping of undisturbed soil samples requires an adjusted calibration to allow for an accurate prediction of soil properties. In this study, we developed a method for calibrating the prediction of DRIFT spectra collected from undisturbed soil samples. In a first step, differences of spectral information measured from undisturbed and ground soil samples have been evaluated. Therefore, we record the DRIFT spectra of 120 German and 120 West-African chemically well characterized soils. DRIFT spectra of both, ground and sieved only soil samples are recorded and both calibrated against different physio-chemical soil properties, such as texture, CEC, organic carbon, pH, or iron oxides. In preliminary experiments, we found that spectra of sieved and ground samples significantly differed in specific spectral regions representing clay minerals, as well as organic matter. It can be assumed that the prediction of surface related soil parameters could be superior using sieved soil spectra, as grounding alters the surface structure of the soil. In a further step, microtopgraphy effects on spectra quality from disturbed and undisturbed soil samples have been evaluated. Therefore, spectral information has been taken from two dimensional disturbed and undisturbed soil samples at a high spatial resolution. The spectra quality was significantly higher in the disturbed soils since microtopography was absent in these samples. Thus, a digital elevation model (DEM) will be constructed using close-range digital photogrammetry to correct these topography effects. With this new method, there is a potential of imaging soil parameters on a microscale that can help considerably in locating and understanding soil processes on a small scale

Влияние электронно-пучковой обработки на фазовый состав поверхностных слоев системы "покрытие из тантала-основа из никелида титана"

The evolution of the structural phase states in the Tantalum coatings formed on the NiTi substrate and their change after low energy high-current pulsed electron beam (LEHCPEB) treatment has been investigated by using X-ray diffraction technique. It was found that after LEHCPEB at E=15 J/cm{2} of coated samples alfa-Ta phase of the coating remains. In addition to the B2 phase of the substrate the[beta]-Ta[2]O[5] phase andmartensitephase B19' were detected in the surface layer. The appearance of martensite probably occurred due to the partial dissolution of Ta in TiNi

In cis TP53 and RAD51C pathogenic variants may predispose to sebaceous gland carcinomas

Pathogenic variants in TP53 have been classically thought to cause Li-Fraumeni syndrome (LFS), a cancer predisposition with high risks for various childhood- and adult-onset malignancies. However, increased genetic testing has lately revealed, that pathogenic variant carriers exhibit a broader range of phenotypes and that penetrance may be dependent both on variant type and modifiers. Using next generation sequencing and short tandem repeat analysis, we identified germline pathogenic variants in TP53 and RAD51C located in cis on chromosome 17 in a 43-year-old male, who has developed a rare sebaceous gland carcinoma (SGC) but so far no tumors of the LFS spectrum. This course mirrors a Trp53-Rad51c-double-mutant cis mouse-model, which similarly develops SGC, while the characteristic Trp53-associated tumor spectrum occurs with significantly lower frequency. Therefore, we propose that co-occurent pathogenic variants in RAD51C and TP53 may predispose to SGC, reminiscent of Muir-Torre syndrome. Further, this report supports the diversity of clinical presentations associated with germline TP53 alterations, and thus, the proposed expansion of LFS to heritable TP53-related cancer syndrome

A unique coral biomineralization pattern has resisted 40 million years of major ocean chemistry change

Today coral reefs are threatened by changes to seawater conditions associated with rapid anthropogenic global climate change. Yet, since the Cenozoic, these organisms have experienced major fluctuations in atmospheric CO2 levels (from greenhouse conditions of high pCO2 in the Eocene to low pCO2 ice-house conditions in the Oligocene-Miocene) and a dramatically changing ocean Mg/Ca ratio. Here we show that the most diverse, widespread, and abundant reef-building coral genus Acropora (20 morphological groups and 150 living species) has not only survived these environmental changes, but has maintained its distinct skeletal biomineralization pattern for at least 40 My: Well-preserved fossil Acropora skeletons from the Eocene, Oligocene, and Miocene show ultra-structures indistinguishable from those of extant representatives of the genus and their aragonitic skeleton Mg/Ca ratios trace the inferred ocean Mg/Ca ratio precisely since the Eocene. Therefore, among marine biogenic carbonate fossils, well-preserved acroporid skeletons represent material with very high potential for reconstruction of ancient ocean chemistry

High-throughput imaging of ATG9A distribution as a diagnostic functional assay for adaptor protein complex 4-associated hereditary spastic paraplegia

Adaptor protein complex 4-associated hereditary spastic paraplegia is caused by biallelic loss-of-function variants in AP4B1, AP4M1, AP4E1 or AP4S1, which constitute the four subunits of this obligate complex. While the diagnosis of adaptor protein complex 4-associated hereditary spastic paraplegia relies on molecular testing, the interpretation of novel missense variants remains challenging. Here, we address this diagnostic gap by using patient-derived fibroblasts to establish a functional assay that measures the subcellular localization of ATG9A, a transmembrane protein that is sorted by adaptor protein complex 4. Using automated high-throughput microscopy, we determine the ratio of the ATG9A fluorescence in the trans-Golgi-network versus cytoplasm and ascertain that this metric meets standards for screening assays (Z'-factor robust >0.3, strictly standardized mean difference >3). The `ATG9A ratio' is increased in fibroblasts of 18 well-characterized adaptor protein complex 4-associated hereditary spastic paraplegia patients [mean: 1.54 +/- 0.13 versus 1.21 +/- 0.05 (standard deviation) in controls] and receiver-operating characteristic analysis demonstrates robust diagnostic power (area under the curve: 0.85, 95% confidence interval: 0.849-0.852). Using fibroblasts from two individuals with atypical clinical features and novel biallelic missense variants of unknown significance in AP4B1, we show that our assay can reliably detect adaptor protein complex 4 function. Our findings establish the 'ATG9A ratio' as a diagnostic marker of adaptor protein complex 4-associated hereditary spastic paraplegia

Intrinsic activity in the fly brain gates visual information during behavioral choices

The small insect brain is often described as an input/output system that executes reflex-like behaviors. It can also initiate neural activity and behaviors intrinsically, seen as spontaneous behaviors, different arousal states and sleep. However, less is known about how intrinsic activity in neural circuits affects sensory information processing in the insect brain and variability in behavior. Here, by simultaneously monitoring Drosophila's behavioral choices and brain activity in a flight simulator system, we identify intrinsic activity that is associated with the act of selecting between visual stimuli. We recorded neural output (multiunit action potentials and local field potentials) in the left and right optic lobes of a tethered flying Drosophila, while its attempts to follow visual motion (yaw torque) were measured by a torque meter. We show that when facing competing motion stimuli on its left and right, Drosophila typically generate large torque responses that flip from side to side. The delayed onset (0.1-1 s) and spontaneous switch-like dynamics of these responses, and the fact that the flies sometimes oppose the stimuli by flying straight, make this behavior different from the classic steering reflexes. Drosophila, thus, seem to choose one stimulus at a time and attempt to rotate toward its direction. With this behavior, the neural output of the optic lobes alternates; being augmented on the side chosen for body rotation and suppressed on the opposite side, even though the visual input to the fly eyes stays the same. Thus, the flow of information from the fly eyes is gated intrinsically. Such modulation can be noise-induced or intentional; with one possibility being that the fly brain highlights chosen information while ignoring the irrelevant, similar to what we know to occur in higher animals