Virtual knot groups and almost classical knots

We define a group-valued invariant of virtual knots and relate it to various other group-valued invariants of virtual knots, including the extended group of Silver-Williams and the quandle group of Manturov and Bardakov-Bellingeri. A virtual knot is called almost classical if it admits a diagram with an Alexander numbering, and in that case we show that the group factors as a free product of the usual knot group and Z. We establish a similar formula for mod p almost classical knots, and we use these results to derive obstructions to a virtual knot K being mod p almost classical. Viewed as knots in thickened surfaces, almost classical knots correspond to those that are homologically trivial. We show they admit Seifert surfaces and relate their Alexander invariants to the homology of the associated infinite cyclic cover. We prove the first Alexander ideal is principal, recovering a result first proved by Nakamura et al. using different methods. The resulting Alexander polynomial is shown to satisfy a skein relation, and its degree gives a lower bound for the Seifert genus. We tabulate almost classical knots up to 6 crossings and determine their Alexander polynomials and virtual genus.Comment: 44 page

Chromatic transit light curves of disintegrating rocky planets

Context. Kepler observations have revealed a class of short period exoplanets, of which Kepler-1520 b is the prototype, which have comet-like dust tails thought to be the result of small, rocky planets losing mass. The shape and chromaticity of the transits constrain the properties of the dust particles originating from the planet's surface, offering a unique opportunity to probe the composition and geophysics of rocky exoplanets. Aims. We aim to approximate the average Kepler long-cadence light curve of Kepler-1520 b and investigate how the optical thickness and transit cross-section of a general dust tail can affect the observed wavelength dependence and depth of transit light curves. Methods. We developed a new 3D model that ejects sublimating particles from the planet surface to build up a dust tail, assuming it to be optically thin, and used 3D radiative transfer computations that fully treat scattering using the distribution of hollow spheres (DHS) method, to generate transit light curves between 0.45 and 2.5 $\mu$m. Results. We show that the transit depth is wavelength independent for optically thick tails, potentially explaining why only some observations indicate a wavelength dependence. From the 3D nature of our simulated tails, we show that their transit cross-sections are related to the component of particle ejection velocity perpendicular to the planet's orbital plane and use this to derive a minimum ejection velocity of 1.2 kms$^{-1}$. To fit the average transit depth of Kepler-1520 b of 0.87%, we require a high dust mas-loss rate of 7 $-$ 80 M$_\oplus$ Gyr$^{-1}$ which implies planet lifetimes that may be inconsistent with the observed sample. Therefore, these mass-loss rates should be considered to be upper limits.Comment: 22 pages, 22 figures, accepted for publication in A&

The Use of NVivo in the Different Stages of Qualitative Research

When researchers take their first steps in qualitative research, they face the great lack of models to follow regarding the method to use in the analysis of data, on some occasions falling into the temptation of coveting the high level of systematisation employed by researchers working with quantitative data. This article offers a basic theoretical contribution that allows researcher to approach qualitative data analysis and the use of the NVivo software, highlighting its advantages and describing the main functions at each moment of a qualitative investigation, placing particular emphasis on the analysis process

Dusty tails of evaporating exoplanets. II. Physical modelling of the KIC 12557548b light curve

Evaporating rocky exoplanets, such as KIC 12557548b, eject large amounts of dust grains, which can trail the planet in a comet-like tail. When such objects occult their host star, the resulting transit signal contains information about the dust in the tail. We aim to use the detailed shape of the Kepler light curve of KIC 12557548b to constrain the size and composition of the dust grains that make up the tail, as well as the mass loss rate of the planet. Using a self-consistent numerical model of the dust dynamics and sublimation, we calculate the shape of the tail by following dust grains from their ejection from the planet to their destruction due to sublimation. From this dust cloud shape, we generate synthetic light curves (incorporating the effects of extinction and angle-dependent scattering), which are then compared with the phase-folded Kepler light curve. We explore the free-parameter space thoroughly using a Markov chain Monte Carlo method. Our physics-based model is capable of reproducing the observed light curve in detail. Good fits are found for initial grain sizes between 0.2 and 5.6 micron and dust mass loss rates of 0.6 to 15.6 M_earth/Gyr (2-sigma ranges). We find that only certain combinations of material parameters yield the correct tail length. These constraints are consistent with dust made of corundum (Al2O3), but do not agree with a range of carbonaceous, silicate, or iron compositions. Using a detailed, physically motivated model, it is possible to constrain the composition of the dust in the tails of evaporating rocky exoplanets. This provides a unique opportunity to probe to interior composition of the smallest known exoplanets.Comment: 18 pages, 11 figures, A&A accepte

Symmetric Versus Nonsymmetric Structure of the Phosphorus Vacancy on InP(110)

The atomic and electronic structure of positively charged P vacancies on InP(110) surfaces is determined by combining scanning tunneling microscopy, photoelectron spectroscopy, and density-functional theory calculations. The vacancy exhibits a nonsymmetric rebonded atomic configuration with a charge transfer level 0.75+-0.1 eV above the valence band maximum. The scanning tunneling microscopy (STM) images show only a time average of two degenerate geometries, due to a thermal flip motion between the mirror configurations. This leads to an apparently symmetric STM image, although the ground state atomic structure is nonsymmetric.Comment: 5 pages including 3 figures. related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

Search for gas from the disintegrating rocky exoplanet K2-22b

[Abridged] Aims. We searched for circumplanetary sodium and ionized calcium gas around the disintegrating rocky exoplanet K2-22 b to constrain its gas-loss and sublimation processes. Methods. We observed four transits of K2-22 b with X-shooter on ESO's Very Large Telescope to obtain time-series of intermediate-resolution (R $\sim$ 11400) spectra. Our analysis focused on the two sodium D lines (588.995 nm and 589.592 nm) and the Ca$^{+}$ triplet (849.802 nm, 854.209 nm and 866.214 nm). Planet-related absorption is searched for in the velocity rest frame of the planet, which changes from $\pm$66 kms$^{-1}$ during the transit. Results. Since K2-22 b exhibits highly variable transit depths, we analyzed the individual nights and their average. By injecting signals we reached 5$\sigma$ upper-limits on the individual nights that ranged from 11% - 13% and 1.7% - 2.0% for the tail's sodium and ionized calcium absorption, respectively. Night 1 was contaminated by its companion star so we considered weighted averages with and without Night 1 and quote conservative 5$\sigma$ limits without Night 1 of 9% and 1.4%, respectively. Assuming their mass fractions to be similar to those in the Earth's crust, these limits correspond to scenarios in which 0.04% and 35% of the transiting dust is sublimated and observed as absorbing gas. However, this assumes the gas to be co-moving with the planet. We show that for the high irradiation environment of K2-22 b, sodium and ionized calcium could be quickly accelerated to 100s of km s$^{-1}$ due to radiation pressure and entrainment by the stellar wind, making them much more difficult to detect. No evidence for such possibly broad and blue-shifted signals are seen in our data. Conclusions. Future observations aimed at observing circumplanetary gas should take into account the possible broad and blue-shifted velocity field of atomic and ionized species.Comment: Accepted on 7 June 2019 for publication in Astronomy and Astrophysics (A&A). 17 pages, 11 figures. Submission updated after language editing by A&

Search for an exosphere in sodium and calcium in the transmission spectrum of exoplanet 55 Cancri e

[Abridged] The aim of this work is to search for an absorption signal from exospheric sodium (Na) and singly ionized calcium (Ca$^+$) in the optical transmission spectrum of the hot rocky super-Earth 55 Cancri e. Although the current best-fitting models to the planet mass and radius require a possible atmospheric component, uncertainties in the radius exist, making it possible that 55 Cancri e could be a hot rocky planet without an atmosphere. High resolution (R$\sim$110000) time-series spectra of five transits of 55 Cancri e, obtained with three different telescopes (UVES/VLT, HARPS/ESO 3.6m & HARPS-N/TNG) were analysed. Targeting the sodium D lines and the calcium H and K lines, the potential planet exospheric signal was filtered out from the much stronger stellar and telluric signals, making use of the change of the radial component of the orbital velocity of the planet over the transit from -57 to +57 km/sec. Combining all five transit data sets, we detect a signal potentially associated with sodium in the planet exosphere at a statistical significance level of 3$\sigma$. Combining the four HARPS transits that cover the calcium H and K lines, we also find a potential signal from ionized calcium (4.1 $\sigma$). Interestingly, this latter signal originates from just one of the transit measurements - with a 4.9$\sigma$ detection at this epoch. Unfortunately, due to the low significance of the measured sodium signal and the potentially variable Ca$^+$ signal, we estimate the p-values of these signals to be too high (corresponding to <4$\sigma$) to claim unambiguous exospheric detections. By comparing the observed signals with artificial signals injected early in the analysis, the absorption by Na and Ca$^+$ are estimated to be at a level of approximately 2.3$\times 10^{-3}$ and 7.0$\times 10^{-2}$ respectively, relative to the stellar spectrum.Comment: 15 pages, 8 figures, submission updated after English language editing, submission updated to correct a mistaken cross-reference noticed in A&A proo

Cancer-Associated Fibroblasts Suppress CD8⁺ T-cell Infiltration and Confer Resistance to Immune-Checkpoint Blockade

\ua92022 The Authors. Immune-checkpoint blockade (ICB) promotes antitumor immune responses and can result in durable patient benefit. However, response rates in breast cancer patients remain modest, stimulating efforts to discover novel treatment options. Cancer-associated fibroblasts (CAF) represent a major component of the breast tumor microenvironment and have known immunosuppressive functions in addition to their well-established roles in directly promoting tumor growth and metastasis. Here we utilized paired syngeneic mouse mammary carcinoma models to show that CAF abundance is associated with insensitivity to combination aCTLA4 and aPD-L1 ICB. CAF-rich tumors exhibited an immunologically cold tumor microenvironment, with transcriptomic, flow cytometric, and quantitative histopathologic analyses demonstrating a relationship between CAF density and a CD8+ T-cell–excluded tumor phenotype. The CAF receptor Endo180 (Mrc2) is predominantly expressed on myofibroblastic CAFs, and its genetic deletion depleted a subset of aSMA-expressing CAFs and impaired tumor progression in vivo. The addition of wild-type, but not Endo180-deficient, CAFs in coimplantation studies restricted CD8+ T-cell intratumoral infiltration, and tumors in Endo180 knockout mice exhibited increased CD8+ T-cell infiltration and enhanced sensitivity to ICB compared with tumors in wild-type mice. Clinically, in a trial of melanoma patients, high MRC2 mRNA levels in tumors were associated with a poor response to aPD-1 therapy, highlighting the potential benefits of therapeutically targeting a specific CAF subpopulation in breast and other CAF-rich cancers to improve clinical responses to immunotherapy