Spectral Theory for Perturbed Krein Laplacians in Nonsmooth Domains

We study spectral properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the perturbed Laplacian $-\Delta+V$ defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class $C^{1,r}$, $r>1/2$. In particular, in the aforementioned context we establish the Weyl asymptotic formula #\{j\in\mathbb{N} | \lambda_{K,\Omega,j}\leq\lambda\} = (2\pi)^{-n} v_n |\Omega| \lambda^{n/2}+O\big(\lambda^{(n-(1/2))/2}\big) {as} \lambda\to\infty, where $v_n=\pi^{n/2}/ \Gamma((n/2)+1)$ denotes the volume of the unit ball in $\mathbb{R}^n$, and $\lambda_{K,\Omega,j}$, $j\in\mathbb{N}$, are the non-zero eigenvalues of $H_{K,\Omega}$, listed in increasing order according to their multiplicities. We prove this formula by showing that the perturbed Krein Laplacian (i.e., the Krein--von Neumann extension of $-\Delta+V$ defined on $C^\infty_0(\Omega)$) is spectrally equivalent to the buckling of a clamped plate problem, and using an abstract result of Kozlov from the mid 1980's. Our work builds on that of Grubb in the early 1980's, who has considered similar issues for elliptic operators in smooth domains, and shows that the question posed by Alonso and Simon in 1980 pertaining to the validity of the above Weyl asymptotic formula continues to have an affirmative answer in this nonsmooth setting.Comment: 60 page

On the Breeds of Cattle—Historic and Current Classifications

Classification of cattle breeds contributes to our understanding of the history of cattle and is essential for an effective conservation of genetic diversity. Here we review the various classifications over the last two centuries and compare the most recent classifications with genetic data. The classifications devised during the 19th to the late 20th century were in line with the Linnaean taxonomy and emphasized cranial or horn morphology. Subsequent classifications were based on coat color, geographic origin or molecular markers. Several theories were developed that linked breed characteristics either to a supposed ancestral aurochs subspecies or to a presumed ethnic origin. Most of the older classifications have now been discarded, but have introduced several Latin terms that are still in use. The most consistent classification was proposed in 1995 by Felius and emphasizes the geographic origin of breeds. This is largely in agreement with the breed clusters indicated by a biochemical and molecular genetic analysis, which reflect either groups of breeds with a common geographic origin or single breeds that have expanded by export and/or crossbreeding. We propose that this information is also relevant for managing the genetic diversity of cattl

Testing of the CubeSat Laser Infrared CrosslinK (CLICK-A) Payload

The CubeSat Laser Infrared CrosslinK (CLICK-A) is a risk-reduction mission that will demonstrate a miniaturized optical transmitter capable of ≥10 Mbps optical downlinks from a 3U CubeSat to aportable 30 cm optical ground telescope. The payload is jointly developed by MIT and NASA ARC, and is on schedule for a 2020 bus integration and 2021 launch. The mission purpose is to reduce risk to its follow-up in 2022, called CLICK-B/C, that plans to demonstrate ≥20 Mbps intersatellite optical crosslinks and precision ranging between two 3U CubeSats. The 1.4U CLICK-A payload will fly on a Blue Canyon Technologies 3U bus inserted into a 400 km orbit. The payload will demonstrate both the transmitter optoelectronics and the fine-pointing system based on a MEMS fast steering mirror, which enables precision pointing of its 1300 μrad full-width half-maximum (FWHM) downlink beam with anestimated error of 136.9 μrad (3-σ) for a pointing loss of -0.134 dB (3-σ) at the time of link closure. We present recent test results of the CLICK-A payload, including results from thermal-vacuum testing, beam characterization, functional testing of the transmitter, and thermal analyses including measurement of deformation due to the thermal loading of the MEMS FSM

Postoperative Spinal Epidural Hematoma: Risk Factor and Clinical Outcome

We report a series of epidural hematomas which cause neurologic deterioration after spinal surgery, and have taken risk factors and prognostic factors into consideration. We retrospectively reviewed the database of 3720 cases of spine operation in a single institute over 7 years (1998 April-2005 July). Nine patients who demonstrated neurologic deterioration after surgery and required surgical decompression were identified. Factors postulated to increase the postoperative epidural hematoma and to improve neurologic outcome were investigated. The incidence of postoperative epidural hematoma was 0.24%. Operation sites were cervical 3 cases, thoracic 2 cases, and lumbar 4 cases. Their original diagnoses were tumor 3 cases, cervical stenosis 2 cases, lumbar stenosis 3 cases and herniated lumbar disc 1case. The symptoms of epidural hematomas were neurologic deterioration and pain. After decompression, clinical outcome revealed complete recovery in 3 cases (33.3%), incomplete recovery in 5 cases (55.6%) and no change in 1 case (11.1%). Factors increasing the risk of postoperative epidural hematoma were coagulopathy from medical illness or anticoagulation therapy (4 cases, 44.4%) and highly vascularized tumor (3 cases, 33.3%). The time interval to evacuation of complete recovery group (29.3 hours) was shorter than incomplete recovery group (66.3 hours). Patients with coagulopathy and highly vascularized tumor were more vulnerable to spinal epidural hematoma. The postoperative outcome was related to the preoperative neurological deficit and the time interval to the decompression

From DNA sequence to application: possibilities and complications

The development of sophisticated genetic tools during the past 15 years have facilitated a tremendous increase of fundamental and application-oriented knowledge of lactic acid bacteria (LAB) and their bacteriophages. This knowledge relates both to the assignments of open reading frames (ORF’s) and the function of non-coding DNA sequences. Comparison of the complete nucleotide sequences of several LAB bacteriophages has revealed that their chromosomes have a fixed, modular structure, each module having a set of genes involved in a specific phase of the bacteriophage life cycle. LAB bacteriophage genes and DNA sequences have been used for the construction of temperature-inducible gene expression systems, gene-integration systems, and bacteriophage defence systems. The function of several LAB open reading frames and transcriptional units have been identified and characterized in detail. Many of these could find practical applications, such as induced lysis of LAB to enhance cheese ripening and re-routing of carbon fluxes for the production of a specific amino acid enantiomer. More knowledge has also become available concerning the function and structure of non-coding DNA positioned at or in the vicinity of promoters. In several cases the mRNA produced from this DNA contains a transcriptional terminator-antiterminator pair, in which the antiterminator can be stabilized either by uncharged tRNA or by interaction with a regulatory protein, thus preventing formation of the terminator so that mRNA elongation can proceed. Evidence has accumulated showing that also in LAB carbon catabolite repression in LAB is mediated by specific DNA elements in the vicinity of promoters governing the transcription of catabolic operons. Although some biological barriers have yet to be solved, the vast body of scientific information presently available allows the construction of tailor-made genetically modified LAB. Today, it appears that societal constraints rather than biological hurdles impede the use of genetically modified LAB.

Once is an Instance, Twice is a Hobby: Multiple Optical and Near-Infrared Changing-Look Events in NGC 5273

NGC 5273 is a known optical and X-ray variable AGN. We analyze new and archival IR, optical, UV, and X-ray data in order to characterize its long-term variability from 2000 to 2022. At least one changing-look event occurred between 2011 and 2014, when the AGN changed from a Type 1.8/1.9 Seyfert to a Type 1. It then faded considerably at all wavelengths, followed by a dramatic but slow increase in UV/optical brightness between 2021 and 2022. We propose that NGC 5273 underwent multiple changing-look events between 2000 and 2022 -- starting as a Type 1.8/1.9, NGC 5273 changes-look to a Type 1 only temporarily in 2002 and again in 2014, reverting back to a Type 1.8/1.9 by 2005 and 2017, respectively. In 2022, it is again a Type 1 Seyfert with optical and NIR broad emission lines. We characterize the changing-look events and their connection to the dynamic accretion and radiative processes in NGC 5273.Comment: 18 pages, 13 figures, 4 tables, submitting to MNRA

Reproducibility of shear wave elastography measuresof the Achilles tendon.

OBJECTIVE To assess the reproducibility of shear wave elastography (SWE) measures in the Achilles tendon (AT) in vivo. MATERIALS AND METHODS Shear wave velocity (SWV) of 14 healthy volunteers [7 males, 7 females; mean age 26.5 ± 3.8 years, mean height 171.6 ± 10.9 cm, mean Victorian Institute of Sports Assessment Achilles questionnaire (VISA-A) score 99.4 ± 1.2] was measured with the foot relaxed and fixed at 90°. Data were collected over five consecutive measures and 5 consecutive days. RESULTS Mean SWV values ranged from 7.91 m/s-9.56 m/s ± 0.27-0.50 m/s. Coefficient of variation (CV), correlations and intra-class correlation coefficient (ICC) scores ranged from 2.9%-6.3%, 0.4-0.7 and 0.54-0.85 respectively. No significant differences were noted for longitudinal or transverse data with respect to protocol or time and no significant differences were noted for foot position in transverse data. Significant differences in SWV values were noted between foot positions for longitudinal scanning (p = <0.05), with a relaxed foot position providing SWV values on average 0.47 m/s faster than a fixed position. Increased reproducibility was obtained with the foot relaxed. ICC between operators was 0.70 for transverse and 0.80 for longitudinal scanning. CONCLUSIONS Reproducible SWE measures were obtained over a 1-h period as well as a period of 5 consecutive days with more reliable measures obtained from a longitudinal plane using a relaxed foot position. SWE also has a high level of agreement between operators making SWE a reproducible technique for quantitatively assessing the mechanical properties of the human AT in vivo

WISE J072003.20-084651.2B Is A Massive T Dwarf

We present individual dynamical masses for the nearby M9.5+T5.5 binary WISE J072003.20$-$084651.2AB, a.k.a. Scholz's star. Combining high-precision CFHT/WIRCam photocenter astrometry and Keck adaptive optics resolved imaging, we measure the first high-quality parallactic distance ($6.80_{-0.06}^{+0.05}$ pc) and orbit ($8.06_{-0.25}^{+0.24}$ yr period) for this system composed of a low-mass star and brown dwarf. We find a moderately eccentric orbit ($e = 0.240_{-0.010}^{+0.009}$), incompatible with previous work based on less data, and dynamical masses of $99\pm6$ $M_{\rm Jup}$ and $66\pm4$ $M_{\rm Jup}$ for the two components. The primary mass is marginally inconsistent (2.1$\sigma$) with the empirical mass$-$magnitude$-$metallicity relation and models of main-sequence stars. The relatively high mass of the cold ($T_{\rm eff} = 1250\pm40$ K) brown dwarf companion indicates an age older than a few Gyr, in accord with age estimates for the primary star, and is consistent with our recent estimate of $\approx$70 $M_{\rm Jup}$ for the stellar/substellar boundary among the field population. Our improved parallax and proper motion, as well as an orbit-corrected system velocity, improve the accuracy of the system's close encounter with the solar system by an order of magnitude. WISE J0720$-$0846AB passed within $68.7\pm2.0$ kAU of the Sun $80.5\pm0.7$ kyr ago, passing through the outer Oort cloud where comets can have stable orbits.Comment: accepted to A