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We present the database of potential targets for the Large Interferometer For Exoplanets (LIFE), a space-based mid-infrared nulling interferometer mission proposed for the Voyage 2050 science program of the European Space Agency (ESA). The database features stars, their planets and disks, main astrophysical parameters, and ancillary observations. It allows users to create target lists based on various criteria to predict, for instance, exoplanet detection yields for the LIFE mission. As such, it enables mission design trade-offs, provides context for the analysis of data obtained by LIFE, and flags critical missing data. Work on the database is in progress, but given its relevance to LIFE and other space missions, including the Habitable Worlds Observatory (HWO), we present its main features here. A preliminary version of the LIFE database is publicly available on the German Astrophysical Virtual Observatory (GAVO)., Comment: RNAAS published, 3 pages, 1 figure

Machine learning (ML) models benefit from large datasets. Collecting data in biomedical domains is costly and challenging, hence, combining datasets has become a common practice. However, datasets obtained under different conditions could present undesired site-specific variability. Data harmonization methods aim to remove site-specific variance while retaining biologically relevant information. This study evaluates the effectiveness of popularly used ComBat-based methods for harmonizing data in scenarios where the class balance is not equal across sites. We find that these methods struggle with data leakage issues. To overcome this problem, we propose a novel approach PrettYharmonize, designed to harmonize data by pretending the target labels. We validate our approach using controlled datasets designed to benchmark the utility of harmonization. Finally, using real-world MRI and clinical data, we compare leakage-prone methods with PrettYharmonize and show that it achieves comparable performance while avoiding data leakage, particularly in site-target-dependence scenarios.

Recent research provides compelling evidence that the decay of short-lived radioisotopes (SLRs), such as 26Al, provided the bulk of energy for heating and desiccation of volatile-rich planetesimals in the early Solar System. However, it remains unclear whether the early Solar System was highly enriched relative to other planetary systems with similar formation characteristics. While the Solar System possesses an elevated level of SLR enrichment compared to the interstellar medium, determining SLR enrichment of individual protoplanetary disks observationally has not been performed and is markedly more difficult. We use N-body simulations to estimate enrichment of SLRs in star-forming regions through two likely important SLR sources, stellar winds from massive stars and supernovae. We vary the number of stars and the radii of the star-forming regions and implement two models of stellar wind SLR propagation for the radioisotopes 26Al and 60Fe. We find that for 26Al enrichment the Solar System is at the upper end of the expected distribution, while for the more supernovae dependent isotope 60Fe we find that the Solar System is comparatively very highly enriched. Furthermore, combined with our previous research, these results suggest that the statistical role of 26Al-driven desiccation on exoplanet bulk composition may be underestimated in typical interpretations of the low-mass exoplanet census, and that 60Fe is even less influential as a source of heating than previously assumed., Comment: 15 pages, 6 figures, 1 table

The increased brightness temperature of young rocky protoplanets during their magma ocean epoch makes them potentially amenable to atmospheric characterization to distances from the solar system far greater than thermally equilibrated terrestrial exoplanets, offering observational opportunities for unique insights into the origin of secondary atmospheres and the near surface conditions of prebiotic environments. The Large Interferometer For Exoplanets (LIFE) mission will employ a space-based mid-infrared nulling interferometer to directly measure the thermal emission of terrestrial exoplanets. Here, we seek to assess the capabilities of various instrumental design choices of the LIFE mission concept for the detection of cooling protoplanets with transient high-temperature magma ocean atmospheres, in young stellar associations in particular. Using the LIFE mission instrument simulator (LIFEsim) we assess how specific instrumental parameters and design choices, such as wavelength coverage, aperture diameter, and photon throughput, facilitate or disadvantage the detection of protoplanets. We focus on the observational sensitivities of distance to the observed planetary system, protoplanet brightness temperature using a blackbody assumption, and orbital distance of the potential protoplanets around both G- and M-dwarf stars. Our simulations suggest that LIFE will be able to detect (S/N $\geq$ 7) hot protoplanets in young stellar associations up to distances of $\approx$100 pc from the solar system for reasonable integration times (up to $\sim$hours). Detection of an Earth-sized protoplanet orbiting a solar-sized host star at 1 AU requires less than 30 minutes of integration time. M-dwarfs generally need shorter integration times. The contribution from wavelength regions $<$6 $\mu$m is important for decreasing the detection threshold and discriminating emission temperatures., Comment: 18 pages, 19 figures; accepted for publication in A&A

The distribution of different types of atmospheres and surfaces on rocky planets is one of the major questions in exoplanet astronomy, but there are currently no published unambiguous detections of atmospheres on any rocky exoplanets. The MIRI instrument on JWST can measure thermal emission from tidally locked rocky exoplanets orbiting small, cool stars. This emission is a function of their surface and atmospheric properties, potentially allowing the detection of atmospheres. One technique is to measure day-side emission to search for lower thermal emission than expected for a black-body planet due to atmospheric absorption features. Another technique is to measure phase curves of thermal emission to search for night-side emission due to atmospheric heat redistribution. In this work we compare strategies for detecting atmospheres on rocky exoplanets using these techniques. We simulate secondary eclipse and phase curve observations in the MIRI F1500W and F1280W filters, for a range of surfaces and atmospheres on thirty exoplanets selected for their F1500W signal-to-noise ratio. Our results show that secondary eclipse observations are highly degenerate between surfaces and atmospheres, given the wide range of potential surface albedos. We also show that thick atmospheres can support emission consistent with a black-body planet in these filters. These two results make it difficult to unambiguously detect or rule out atmospheres using their photometric day-side emission, except in a subset of CO$_{2}$-dominated atmospheres. We suggest that an F1500W phase curve could instead be observed for a similar sample of planets, allowing the unambiguous detection of atmospheres by night-side emission.

Many super-Earths are on very short orbits around their host star and, therefore, more likely to be tidally locked. Because this locking can lead to a strong contrast between the dayside and nightside surface temperatures, these super-Earths could exhibit mantle convection patterns and tectonics that could differ significantly from those observed in the present-day solar system. The presence of an atmosphere, however, would allow transport of heat from the dayside towards the nightside and thereby reduce the surface temperature contrast between the two hemispheres. On rocky planets, atmospheric and geodynamic regimes are closely linked, which directly connects the question of atmospheric thickness to the potential interior dynamics of the planet. Here, we study the interior dynamics of super-Earth GJ 486b ($R=1.34$ $R_{\oplus}$, $M=3.0$ $M_{\oplus}$, T$_\mathrm{eq}\approx700$ K), which is one of the most suitable M-dwarf super-Earth candidates for retaining an atmosphere produced by degassing from the mantle and magma ocean. We investigate how the geodynamic regime of GJ 486b is influenced by different surface temperature contrasts by varying possible atmospheric circulation regimes. We also investigate how the strength of the lithosphere affects the convection pattern. We find that hemispheric tectonics, the surface expression of degree-1 convection with downwellings forming on one hemisphere and upwelling material rising on the opposite hemisphere, is a consequence of the strong lithosphere rather than surface temperature contrast. Anchored hemispheric tectonics, where downwellings und upwellings have a preferred (day/night) hemisphere, is favoured for strong temperature contrasts between the dayside and nightside and higher surface temperatures., Comment: 36 pages, 13 figures, resubmitted to JGR: Planets

An increasing number of media streaming services have expanded their offerings to include entities of multiple content types. For instance, audio streaming services that started by offering music only, now also offer podcasts, merchandise items, and videos. Ranking items across different content types into a single slate poses a significant challenge for traditional learning-to-rank (LTR) algorithms due to differing user engagement patterns for different content types. We explore a simple method for cross-content-type ranking, called multinomial blending (MB), which can be used in conjunction with most existing LTR algorithms. We compare MB to existing baselines not only in terms of ranking quality but also from other industry-relevant perspectives such as interpretability, ease-of-use, and stability in dynamic environments with changing user behavior and ranking model retraining. Finally, we report the results of an A/B test from an Amazon Music ranking use-case., Comment: To appear in 18th ACM Conference on Recommender Systems (RecSys24), Bari, Italy. ACM, New York, NY, USA, 3 pages

PLATO (PLAnetary Transits and Oscillations of stars) is ESA's M3 mission designed to detect and characterise extrasolar planets and perform asteroseismic monitoring of a large number of stars. PLATO will detect small planets (down to <2 R_(Earth)) around bright stars (<11 mag), including terrestrial planets in the habitable zone of solar-like stars. With the complement of radial velocity observations from the ground, planets will be characterised for their radius, mass, and age with high accuracy (5 %, 10 %, 10 % for an Earth-Sun combination respectively). PLATO will provide us with a large-scale catalogue of well-characterised small planets up to intermediate orbital periods, relevant for a meaningful comparison to planet formation theories and to better understand planet evolution. It will make possible comparative exoplanetology to place our Solar System planets in a broader context. In parallel, PLATO will study (host) stars using asteroseismology, allowing us to determine the stellar properties with high accuracy, substantially enhancing our knowledge of stellar structure and evolution. The payload instrument consists of 26 cameras with 12cm aperture each. For at least four years, the mission will perform high-precision photometric measurements. Here we review the science objectives, present PLATO's target samples and fields, provide an overview of expected core science performance as well as a description of the instrument and the mission profile at the beginning of the serial production of the flight cameras. PLATO is scheduled for a launch date end 2026. This overview therefore provides a summary of the mission to the community in preparation of the upcoming operational phases.

The issue of popularity bias -- where popular items are disproportionately recommended, overshadowing less popular but potentially relevant items -- remains a significant challenge in recommender systems. Recent advancements have seen the integration of general-purpose Large Language Models (LLMs) into the architecture of such systems. This integration raises concerns that it might exacerbate popularity bias, given that the LLM's training data is likely dominated by popular items. However, it simultaneously presents a novel opportunity to address the bias via prompt tuning. Our study explores this dichotomy, examining whether LLMs contribute to or can alleviate popularity bias in recommender systems. We introduce a principled way to measure popularity bias by discussing existing metrics and proposing a novel metric that fulfills a series of desiderata. Based on our new metric, we compare a simple LLM-based recommender to traditional recommender systems on a movie recommendation task. We find that the LLM recommender exhibits less popularity bias, even without any explicit mitigation., Comment: Accepted at Gen-IR@SIGIR24 workshop

In the last few years astronomical surveys have expanded the reach of planetary science into the realm of small and dense extrasolar worlds. These share a number of characteristics with the terrestrial and icy planetary objects of the Solar System, but keep stretching previous understanding of the known limits of planetary thermodynamics, material properties, and climate regimes. Improved compositional and thermal constraints on exoplanets below $\sim$2 Earth radii suggest efficient accretion of atmosphere-forming volatile elements in a fraction of planetary systems, pointing to rapid formation, planet-scale melting, and chemical equilibration between the core, mantle, and atmosphere of rocky and volatile-rich exoplanets. Meaningful interpretation of novel observational data from these worlds necessitates cross-disciplinary expansion of known material properties under extreme thermodynamic, non-solar conditions, and accounting for dynamic feedbacks between interior and atmospheric processes. Exploration of the atmosphere and surface composition of individual, short-period super-Earths in the next few years will enable key inferences on magma ocean dynamics, the redox state of rocky planetary mantles, and mixing between volatile and refractory phases in planetary regimes that are absent from the present-day Solar System, and reminiscent of the conditions of the prebiotic Earth. The atmospheric characterization of climate diversity and the statistical search for biosignatures on terrestrial exoplanets on temperate orbits will require space-based direct imaging surveys, capable of resolving emission features of major and trace gases in both shortwave and mid-infrared wavelengths., Comment: 39 pages, 11 figures; review chapter accepted for publication in Treatise on Geochemistry, 3rd edition

Whilst the formation of Solar system planets is constrained by meteoritic evidence, the geophysical history of low-mass exoplanets is much less clear. The bulk composition and climate states of rocky exoplanets may vary significantly based on the composition and properties of the planetesimals they form from. An important factor influenced by planetesimal composition is water content, where the desiccation of accreting planetesimals impacts the final water content of the resultant planets. While the inner planets of the Solar system are comparatively water-poor, recent observational evidence from exoplanet bulk densities and planetary formation models suggest that rocky exoplanets engulfed by substantial layers of high-pressure ices or massive steam atmospheres could be widespread. Here we quantify variations in planetesimal desiccation due to potential fractionation of the two short-lived radioisotopes 26Al and 60Fe relevant for internal heating on planetary formation timescales. We focus on how order of magnitude variations in 60Fe can affect the water content of planetesimals, and how this may alter the formation of extrasolar ocean worlds. We find that heating by 26Al is the dominant cause of planetesimal heating in any Solar system analogue scenario, thus validating previous works focussing only on this radioisotope. However, 60Fe can become the primary heating source in the case of high levels of supernova enrichment in massive star-forming regions. These diverging scenarios can affect the formation pathways, bulk volatile budget, and climate diversity of low-mass exoplanets., Comment: 12 pages, 13 figures

It is found that subtle changes in the external magnetic field and temperature result in dramatic changes in the ultrafast response of spins to a femtosecond laser excitation in a ferrimagnetic Gd/FeCo multilayer. A total of six distinct types of spin dynamics were observed and explained by considering the spin-flop transition to the noncollinear phase and the concept of a tricritical point in the $H$-$T$ phase diagram. A particularly interesting type of dynamics is the exchange-driven reversal. These exchange-driven dynamics provide new insights into the tricritical point, which is shown to separate two thermodynamically distinct noncollinear phases with the transition-metal magnetization pointing on adjacent sides of the anisotropy plane., Comment: 21 pages, 11 figures

Mildly irradiated mini-Neptunes have densities potentially consistent with them hosting substantial liquid water oceans (`Hycean' planets). The presence of CO2 and simultaneous absence of ammonia (NH3) in their atmospheres has been proposed as a fingerprint of such worlds. JWST observations of K2-18b, the archetypal Hycean, have found the presence of CO2 and the depletion of NH3 to <100 ppm; hence, it has been inferred that this planet may host liquid water oceans. In contrast, climate modelling suggests that many of these mini-Neptunes, including K2-18b, may likely be too hot to host liquid water. We propose a solution to this discrepancy between observation and climate modelling by investigating the effect of a magma ocean on the atmospheric chemistry of mini-Neptunes. We demonstrate that atmospheric NH3 depletion is a natural consequence of the high solubility of nitrogen species in magma at reducing conditions; precisely the conditions prevailing where a thick hydrogen envelope is in communication with a molten planetary surface. The magma ocean model reproduces the present JWST spectrum of K2-18b to < 3 sigma, suggesting this is as credible an explanation for current observations as the planet hosting a liquid water ocean. Spectral areas that could be used to rule out the magma ocean model include the >4um region, where CO2 and CO features dominate: Magma ocean models suggest a systematically lower CO2/CO ratio than estimated from free chemistry retrieval, indicating that deeper observations of this spectral region may be able to distinguish between oceans of liquid water and magma on mini-Neptunes., Comment: 13 pages, 5 figures, Published in The Astrophysical Journal Letters; corrects error on y-axis of Figure 2

We study the problem of determining the configuration of $n$ points by using their distances to $m$ nodes, referred to as anchor nodes. One sampling scheme is Nystrom sampling, which assumes known distances between the anchors and between the anchors and the $n$ points, while the distances among the $n$ points are unknown. For this scheme, a simple adaptation of the Nystrom method, which is often used for kernel approximation, is a viable technique to estimate the configuration of the anchors and the $n$ points. In this manuscript, we propose a modified version of Nystrom sampling, where the distances from every node to one central node are known, but all other distances are incomplete. In this setting, the standard Nystrom approach is not applicable, necessitating an alternative technique to estimate the configuration of the anchors and the $n$ points. We show that this problem can be framed as the recovery of a low-rank submatrix of a Gram matrix. Using synthetic and real data, we demonstrate that the proposed approach can exactly recover configurations of points given sufficient distance samples. This underscores that, in contrast to methods that rely on global sampling of distance matrices, the task of estimating the configuration of points can be done efficiently via structured sampling with well-chosen reliable anchors. Finally, our main analysis is grounded in a specific centering of the points. With this in mind, we extend previous work in Euclidean distance geometry by providing a general dual basis approach for points centered anywhere., Comment: 20 pages. Introduced a new sampling model. Experimental results on both synthetic and real data. A new optimization program for structured distance geometry based on low-rank recovery. The analysis of the previous sampling model is also discussed. Made changes to improve the clarity and presentation of the paper

Ultra-cool dwarf stars are abundant, long-lived, and uniquely suited to enable the atmospheric study of transiting terrestrial companions with JWST. Amongst them, the most prominent is the M8.5V star TRAPPIST-1 and its seven planets. While JWST Cycle 1 observations have started to yield preliminary insights into the planets, they have also revealed that their atmospheric exploration requires a better understanding of their host star. Here, we propose a roadmap to characterize the TRAPPIST-1 system -- and others like it -- in an efficient and robust manner. We notably recommend that -- although more challenging to schedule -- multi-transit windows be prioritized to mitigate the effects of stellar activity and gather up to twice more transits per JWST hour spent. We conclude that, for such systems, planets cannot be studied in isolation by small programs, but rather need large-scale, jointly space- and ground-based initiatives to fully exploit the capabilities of JWST for the exploration of terrestrial planets.

Long-term magma ocean phases on rocky exoplanets orbiting closer to their star than the runaway greenhouse threshold - the inner edge of the classical habitable zone - may offer insights into the physical and chemical processes that distinguish potentially habitable worlds from others. Thermal stratification of runaway planets is expected to significantly inflate their atmospheres, potentially providing observational access to the runaway greenhouse transition in the form of a "habitable zone inner edge discontinuity" in radius-density space. Here, we use Bioverse, a statistical framework combining contextual information from the overall planet population with a survey simulator, to assess the ability of ground- and space-based telescopes to test this hypothesis. We find that the demographic imprint of the runaway greenhouse transition is likely detectable with high-precision transit photometry for sample sizes $\gtrsim 100$ planets if at least ~10 % of those orbiting closer than the habitable zone inner edge harbor runaway climates. Our survey simulations suggest that in the near future, ESA's PLATO mission will be the most promising survey to probe the habitable zone inner edge discontinuity. We determine survey strategies that maximize the diagnostic power of the obtained data and identify as key mission design drivers: 1. A follow-up campaign of planetary mass measurements and 2. The fraction of low-mass stars in the target sample. Observational constraints on the runaway greenhouse transition will provide crucial insights into the distribution of atmospheric volatiles among rocky exoplanets, which may help to identify the nearest potentially habitable worlds., Comment: For a video abstract, see https://youtu.be/acgKcdTTv9c. All source code is available at https://github.com/matiscke/hz-inner-edge-discontinuity. 29 pages, 12 figures, 1 table. Typos corrected, references added. Published in The Planetary Science Journal

"Clipping" (a.k.a. importance weight truncation) is a widely used variance-reduction technique for counterfactual off-policy estimators. Like other variance-reduction techniques, clipping reduces variance at the cost of increased bias. However, unlike other techniques, the bias introduced by clipping is always a downward bias (assuming non-negative rewards), yielding a lower bound on the true expected reward. In this work we propose a simple extension, called $\textit{double clipping}$, which aims to compensate this downward bias and thus reduce the overall bias, while maintaining the variance reduction properties of the original estimator., Comment: Presented at CONSEQUENCES '23 workshop at RecSys 2023 conference in Singapore

Line attributes such as width and dashing are commonly used to encode information. However, many questions on the perception of line attributes remain, such as how many levels of attribute variation can be distinguished or which line attributes are the preferred choices for which tasks. We conducted three studies to develop guidelines for using stylized lines to encode scalar data. In our first study, participants drew stylized lines to encode uncertainty information. Uncertainty is usually visualized alongside other data. Therefore, alternative visual channels are important for the visualization of uncertainty. Additionally, uncertainty -- e.g., in weather forecasts -- is a familiar topic to most people. Thus, we picked it for our visualization scenarios in study 1. We used the results of our study to determine the most common line attributes for drawing uncertainty: Dashing, luminance, wave amplitude, and width. While those line attributes were especially common for drawing uncertainty, they are also commonly used in other areas. In studies 2 and 3, we investigated the discriminability of the line attributes determined in study 1. Studies 2 and 3 did not require specific application areas; thus, their results apply to visualizing any scalar data in line attributes. We evaluated the just-noticeable differences (JND) and derived recommendations for perceptually distinct line levels. We found that participants could discriminate considerably more levels for the line attribute width than for wave amplitude, dashing, or luminance., Comment: 11 pages, 9 figures, to be published in IEEE Transactions on Visualization and Computer Graphics The supplemental material for this paper is available at https://www.doi.org/10.17605/OSF.IO/7SCF8

The presence of short-lived radioisotopes (SLRs) 26-Al and 60-Fe in the Solar system places constraints on the initial conditions of our planetary system. Most theories posit that the origin of 26-Al and 60-Fe is in the interiors of massive stars, and they are either delivered directly to the protosolar disc from the winds and supernovae of the massive stars, or indirectly via a sequential star formation event. However, massive stars that produce SLRs also emit photoionising far and extreme ultraviolet radiation, which can destroy the gas component of protoplanetary discs, possibly precluding the formation of gas giant planets like Jupiter and Saturn. Here, we perfom N-body simulations of star-forming regions and determine whether discs that are enriched in SLRs can retain enough gas to form Jovian planets. We find that discs are enriched and survive the photoionising radiation only when the dust radius of the disc is fixed and not allowed to move inwards due to the photoevaporation, or outwards due to viscous spreading. Even in this optimal scenario, not enough discs survive until the supernovae of the massive stars and so have zero or very little enrichment in 60-Fe. We therefore suggest that the delivery of SLRs to the Solar system may not come from the winds and supernovae of massive stars., Comment: 13 pages, 4 figures, accepted for publication in MNRAS

The ultra-short-period super-Earth 55 Cancri e has a measured radius of 1.8 Earth radii. Previous thermal phase curve observations suggest a strong temperature contrast between the dayside and nightside of around 1000 K with the hottest point shifted $41\pm12$ degrees east from the substellar point, indicating some degree of heat circulation. The dayside (and potentially even the nightside) is hot enough to harbour a magma ocean. We use results from general circulation models (GCMs) of atmospheres to constrain the surface temperature contrasts. There is still a large uncertainty on the vigour and style of mantle convection in super-Earths, especially those that experience stellar irradiation large enough to harbour a magma ocean. In this work, we aim to constrain the mantle dynamics of the tidally locked lava world 55 Cancri e. Using the surface temperature contrasts as boundary condition, we model the mantle flow of 55 Cancri e using 2D mantle convection simulations and investigate how the convection regimes are affected by the different climate models. We find that large super-plumes form on the dayside if that hemisphere is covered by a magma ocean and the nightside remains solid or only partially molten. Cold material descends into the deep interior on the nightside, but no strong downwellings form. In some cases, the super-plume also moves several tens of degrees towards the terminator. A convective regime where the upwelling is preferentially on the dayside might lead to preferential outgassing on that hemisphere which could lead to the build-up of atmospheric species that could be chemically distinct from the nightside., Comment: 20 pages, 11 figures, accepted for publication in A&A

Super-Earths span a wide range of bulk densities, indicating a diversity in interior conditions beyond that seen in the solar system. In particular, an emerging population of low-density super-Earths may be explained by volatile-rich interiors. Among these, low-density lava worlds have dayside temperatures high enough to evaporate their surfaces, providing a unique opportunity to probe their interior compositions and test for the presence of volatiles. In this work, we investigate the atmospheric observability of low-density lava worlds. We use a radiative-convective model to explore the atmospheric structures and emission spectra of these planets, focusing on three case studies with high observability metrics and sub-stellar temperatures spanning $\sim$1900-2800 K: HD 86226c, HD 3167b and 55 Cnce. Given the possibility of mixed volatile and silicate interior compositions for these planets, we consider a range of mixed volatile and rock vapor atmospheric compositions. This includes a range of volatile fractions and three volatile compositions: water-rich (100% H$_2$O), water with CO$_2$ (80% H$_2$O+20% CO$_2$), and a desiccated O-rich scenario (67% O$_2$+33%CO$_2$). We find that spectral features due to H$_2$O, CO$_2$, SiO and SiO$_2$ are present in the infrared emission spectra as either emission or absorption features, depending on dayside temperature, volatile fraction and volatile composition. We further simulate JWST secondary eclipse observations for each of the three case studies, finding that H$_2$O and/or CO$_2$ could be detected with as few as $\sim$5 eclipses. Detecting volatiles in these atmospheres would provide crucial independent evidence that volatile-rich interiors exist among the super-Earth population., Comment: Accepted for publication in ApJ. 26 pages, 12 figures, 2 tables

In recent years, the use of expressive surface visualizations in the representation of vascular structures has gained significant attention. These visualizations provide a comprehensive understanding of complex anatomical structures and are crucial for treatment planning and medical education. However, to aid decision-making, physicians require visualizations that accurately depict anatomical structures and their spatial relationships in a clear and well-perceivable manner. This work extends a previous paper and presents a thorough examination of common techniques for encoding distance information of 3D vessel surfaces and provides an implementation of these visualizations. A Unity environment and detailed implementation instructions for sixteen different visualizations are provided. These visualizations can be classified into four categories: fundamental, surface-based, auxiliary, and illustrative. Furthermore, this extension includes tools to generate endpoint locations for vascular models. Overall this framework serves as a valuable resource for researchers in the field of vascular surface visualization by reducing the barrier to entry and promoting further research in this area. By providing an implementation of various visualizations, this paper aims to aid in the development of accurate and effective visual representations of vascular structures to assist in treatment planning and medical education.

The abundance of the short-lived radioisotopes 26-Al and 60-Fe in the early Solar system is usually explained by the Sun either forming from pre-enriched material, or the Sun's protosolar disc being polluted by a nearby supernova explosion from a massive star. Both hypotheses suffer from significant drawbacks: the former does not account for the dynamical evolution of star-forming regions, while in the latter the time for massive stars to explode as supernovae can be similar to, or even longer than, the lifetime of protoplanetary discs. In this paper, we extend the disc enrichment scenario to include the contribution of 26-Al from the winds of massive stars before they explode as supernovae. We use N-body simulations and a post-processing analysis to calculate the amount of enrichment in each disc, and we vary the stellar density of the star-forming regions. We find that stellar winds contribute to disc enrichment to such an extent that the Solar system's 26-Al/60-Fe ratio is reproduced in up to 50 per cent of discs in dense (rho = 1000Msun pc^-3) star-forming regions. When winds are a significant contributor to the SLR enrichment, we find that Solar system levels of enrichment can occur much earlier (before 2.5 Myr) than when enrichment occurs from supernovae, which start to explode at later ages (>4 Myr). We find that Solar system levels of enrichment all but disappear in low-density star-forming regions (rho < 10Msun pc^-3), implying that the Solar system must have formed in a dense, populous star-forming region if 26-Al and 60-Fe were delivered directly to the protosolar disc from massive-star winds and supernovae., Comment: 16 pages, 10 figures, 1 appendix with 3 further figures, accepted for publication in MNRAS

Classical multidimensional scaling (CMDS) is a technique that embeds a set of objects in a Euclidean space given their pairwise Euclidean distances. The main part of CMDS involves double centering a squared distance matrix and using a truncated eigendecomposition to recover the point coordinates. In this paper, motivated by a study in Euclidean distance geometry, we explore a dual basis approach to CMDS. We give an explicit formula for the dual basis vectors and fully characterize the spectrum of an essential matrix in the dual basis framework. We make connections to a related problem in metric nearness., Comment: 7 pages. The proof of dual basis representation is now compact. It is not constructive compared to the previous version, but it uses bi-orthogonality relation to establish the result more directly. A minor error in the proof of the spectrum of the dual basis has been fixed. We also made few changes for better clarity and presentation