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This brief examines how specific college affordability policies and practices at the federal, state, and institutional levels can be strengthened to close racial equity gaps in college affordability and completion and to support widespread diversity and representation in higher education. By increasing access to financial aid and shifting the way colleges and universities equitably award and disburse funds, we can leverage financial aid as a marketing, recruitment, enrollment, and retainment tool for both low-income and minoritized students, and to counteract the chilling effect of the Supreme Court of the United States (SCOTUS) decision curtailing the use of race-conscious admissions in higher education. Socio-economic status is not a perfect proxy for race, but affordability policies are a critical lever for equity, given that Latinx, Black, Native Hawaiians and Pacific Islanders (NHPI), and American Indian and Alaska Native (AIAN) students receive multiple forms of grant aid at higher percentages than their white counterparts. The recommendations made in this paper will help close racial/ethnic and economic equity gaps in higher education without violating the SCOTUS decision. [Eileen and Harold Brown provided additional funding for this series of briefs.]

We report on the discovery of a very prominent mid-infrared (18-25 {\mu}m) excess associated with the trans-Neptunian dwarf planet (136472) Makemake. The excess, detected by the MIRI instrument of the James Webb Space Telescope, along with previous measurements from the Spitzer and Herschel space telescopes, indicates the occurrence of temperatures of about 150 K, much higher than what solid surfaces at Makemake's heliocentric distance could reach by solar irradiation. We identify two potential explanations: a continuously visible, currently active region, powered by subsurface upwelling and possibly cryovolcanic activity, covering <1% of Makemake's surface, or an as yet undetected ring containing very small carbonaceous dust grains, which have not been seen before in trans-Neptunian or Centaur rings. Both scenarios point to unprecedented phenomena among trans-Neptunian objects and could greatly impact our understanding of these distant worlds., Comment: Accepted for publication in The Astrophysical Journal Letters

We present new observations from CHEOPS and TESS to clarify the architecture of the planetary system hosted by the old Galactic thick disk star TOI-561. Our global analysis, which also includes previously published photometric and radial velocity data, incontrovertibly proves that TOI-561 is hosting at least four transiting planets with periods of 0.44 days (TOI-561 b), 10.8 days (TOI-561 c), 25.7 days (TOI-561 d), and 77.1 days (TOI-561 e) and a fifth non-transiting candidate, TOI-561f with a period of 433 days. The precise characterisation of TOI-561's orbital architecture is interesting since old and metal-poor thick disk stars are less likely to host ultra-short period Super-Earths like TOI-561 b. The new period of planet -e is consistent with the value obtained using radial velocity alone and is now known to be $77.14399\pm0.00025$ days, thanks to the new CHEOPS and TESS transits. The new data allowed us to improve its radius ($R_p = 2.517 \pm 0.045 R_{\oplus}$ from 5$\%$ to 2$\%$ precision) and mass ($M_p = 12.4 \pm 1.4 M_{\oplus}$) estimates, implying a density of $\rho_p = 0.778 \pm 0.097 \rho_{\oplus}$. Thanks to recent TESS observations and the focused CHEOPS visit of the transit of TOI-561 e, a good candidate for exomoon searches, the planet's period is finally constrained, allowing us to predict transit times through 2030 with 20-minute accuracy. We present an updated version of the internal structure of the four transiting planets. We finally performed a detailed stability analysis, which confirmed the long-term stability of the outer planet TOI-561 f., Comment: 13 pages, 10 Figures. Accepted on MNRAS. Updated the author list

Sputtering by solar wind ions is a key process driving the ejection of high-energy particles into the exospheres of airless bodies like asteroids, Mercury and the Moon. In view of upcoming missions which will deliver new in-situ data on these exospheres like the Artemis program at the Moon and BepiColombo at Mercury, a deeper understanding of sputtering effects is crucial. In this work, we combine sensitive quartz crystal microbalance measurements and numerical simulations to quantify sputter yields of Apollo soil 68501 under solar wind relevant conditions. We find that none of the commonly used simulation codes can reliably predict laboratory sputter yields without experimental benchmarks. All of the employed packages significantly overestimate the sputter yields of flat samples by at least a factor of 2 for the case of hydrogen. When accounting for surface roughness and regolith-like porosity, sputter yields are decreased even further to 7.3E-3 atoms\ion and 7.6E-2 atoms\ion for H and He at solar wind energies of 1 keV\amu, respectively. The reduced yields of porous regolith structures are largely independent of the ion incidence angle, making them applicable across a wide range of lunar latitudes. This study highlights the need for experimental validation of sputtering models to ensure accurate predictions for space weathering and lunar exosphere composition.

Gaussian Processes (GPs) are widely used to model dependency in spatial statistics and machine learning, yet the exact computation suffers an intractable time complexity of $O(n^3)$. Vecchia approximation allows scalable Bayesian inference of GPs in $O(n)$ time by introducing sparsity in the spatial dependency structure that is characterized by a directed acyclic graph (DAG). Despite the popularity in practice, it is still unclear how to choose the DAG structure and there are still no theoretical guarantees in nonparametric settings. In this paper, we systematically study the Vecchia GPs as standalone stochastic processes and uncover important probabilistic properties and statistical results in methodology and theory. For probabilistic properties, we prove that the conditional distributions of the Mat\'{e}rn GPs, as well as the Vecchia approximations of the Mat\'{e}rn GPs, can be characterized by polynomials. This allows us to prove a series of results regarding the small ball probabilities and RKHSs of Vecchia GPs. For statistical methodology, we provide a principled guideline to choose parent sets as norming sets with fixed cardinality and provide detailed algorithms following such guidelines. For statistical theory, we prove posterior contraction rates for applying Vecchia GPs to regression problems, where minimax optimality is achieved by optimally tuned GPs via either oracle rescaling or hierarchical Bayesian methods. Our theory and methodology are demonstrated with numerical studies, where we also provide efficient implementation of our methods in C++ with R interfaces.

In this paper, we study the cardinality of the smallest set of lines of the finite projective spaces $\operatorname{PG}(n,q)$ such that every plane is incident with at least one line of the set. This is the first main open problem concerning the minimum size of $(s,t)$-blocking sets in $\operatorname{PG}(n,q)$, where we set $s=2$ and $t=1$. In $\operatorname{PG}(n,q)$, an $(s,t)$-blocking set refers to a set of $t$-spaces such that each $s$-space is incident with at least one chosen $t$-space. This is a notoriously difficult problem, as it is equivalent to determining the size of certain $q$-Tur\'an designs and $q$-covering designs. We present an improvement on the upper bounds of Etzion and of Metsch via a refined scheme for a recursive construction, which in fact enables improvement in the general case as well., Comment: 21 pages

The QCD cross-over line in the temperature ($T$) -- baryo-chemical potential ($\mu_B$) plane has been computed by several lattice groups by calculating the chiral order parameter and its susceptibility at finite values of $\mu_B$. In this work we focus on the deconfinement aspect of the transition between hadronic and Quark Gluon Plasma (QGP) phases. We define the deconfinement temperature as the peak position of the static quark entropy ($S_Q(T,\mu_B)$) in $T$, which is based on the renormalized Polyakov loop. We extrapolate $S_Q(T,\mu_B)$ based on high statistics finite temperature ensembles on a $16^3\times 8$ lattice to finite density by means of a Taylor expansion to eighth order in $\mu_B$ (NNNLO) along the strangeness neutral line. For the simulations the 4HEX staggered action was used with 2+1 flavors at physical quark masses. In this setup the phase diagram can be drawn up to unprecedentedly high chemical potentials. Our results for the deconfinement temperature are in rough agreement with phenomenological estimates of the freeze-out curve in relativistic heavy ion collisions. In addition, we study the width of the deconfinement crossover. We show that up to $\mu_B \approx 400$ MeV, the deconfinement transition gets broader at higher densities, disfavoring the existence of a deconfinement critical endpoint in this range. Finally, we examine the transition line without the strangeness neutrality condition and observe a hint for the narrowing of the crossover towards large $\mu_B$., Comment: 14 pages, 8 figures

We initiate the study of quantum property testing in sparse directed graphs, and more particularly in the unidirectional model, where the algorithm is allowed to query only the outgoing edges of a vertex. In the classical unidirectional model the problem of testing $k$-star-freeness, and more generally $k$-source-subgraph-freeness, is almost maximally hard for large $k$. We prove that this problem has almost quadratic advantage in the quantum setting. Moreover, we prove that this advantage is nearly tight, by showing a quantum lower bound using the method of dual polynomials on an intermediate problem for a new, property testing version of the $k$-collision problem that was not studied before. To illustrate that not all problems in graph property testing admit such a quantum speedup, we consider the problem of $3$-colorability in the related undirected bounded-degree model, when graphs are now undirected. This problem is maximally hard to test classically, and we show that also quantumly it requires a linear number of queries.

We present a lattice calculation of the $\eta$ and $\eta^{\prime}$ meson masses at the physical point and in the continuum limit, based on $N_f = 2+1+1$ flavors of rooted staggered quarks. Our analysis includes gauge ensembles at the physical pion and kaon masses spread over six lattice spacings in the range [0.064-0.1315]~fm. Our main results read $m_{\eta} = 543.5(5.6)~$MeV and $m_{\eta^{\prime}} = 986(38)~$MeV, consistent with the experimental values. This is an important numerical test that supports the validity of the fourth root procedure used in the staggered quark formalism. This calculation was the first step towards extracting the pseudoscalar transition form factors of the $\eta$ and $\eta^{\prime}$ mesons that play a crucial role in the hadronic light-by-light contribution to the muon $g-2$., Comment: 19 pages, 12 figures

Hot Jupiters are giant planets subject to intense stellar radiation. The physical and chemical properties of their atmosphere makes them the most amenable targets for the atmospheric characterization. In this paper we analyze the photometry collected during the secondary eclipses of the hot Jupiter WASP-3 b by CHEOPS, TESS and Spitzer. Our aim is to characterize the atmosphere of the planet by measuring the secondary eclipse depth in several passbands and constrain the planetary dayside spectrum. Our update of the stellar and planetary properties is consistent with previous works. The analysis of the occultations returns an eclipse depth of 92+-21 ppm in the CHEOPS passband, 83+-27 ppm for TESS and >2000 ppm in the IRAC 1-2-4 Spitzer passbands. Using the eclipse depths in the Spitzer bands we propose a set of likely emission spectra which constrain the emission contribution in the \cheops and TESS passbands to approximately a few dozens of parts per million. This allowed us to measure a geometric albedo of 0.21+-0.07 in the CHEOPS passband, while the TESS data lead to a 95\% upper limit of $\sim$0.2. WASP-3 b belongs to the group of ultra-hot Jupiters which are characterized by low Bond albedo (<0.3+-0.1), as predicted by different atmospheric models. On the other hand, it unexpectedly seems to efficiently recirculate the absorbed stellar energy, unlike similar highly irradiated planets. To explain this inconsistency, we propose that other energy recirculation mechanisms may be at play other than advection (for example, dissociation and recombination of H_2). Another possibility is that the observations in different bandpasses probe different atmospheric layers, making the atmospheric analysis difficult without an appropriate modeling of the thermal emission spectrum of WASP-3 b, which is not feasible with the limited spectroscopic data available to date.

Routinely-implemented deterministic approximations of posterior distributions from, e.g., Laplace method, variational Bayes and expectation-propagation, generally rely on symmetric approximating densities, often taken to be Gaussian. This choice facilitates optimization and inference, but typically affects the quality of the overall approximation. In fact, even in basic parametric models, the posterior distribution often displays asymmetries that yield bias and reduced accuracy when considering symmetric approximations. Recent research has moved towards more flexible approximating densities that incorporate skewness. However, current solutions are model-specific, lack general supporting theory, increase the computational complexity of the optimization problem, and do not provide a broadly-applicable solution to include skewness in any symmetric approximation. This article addresses such a gap by introducing a general and provably-optimal strategy to perturb any off-the-shelf symmetric approximation of a generic posterior distribution. Crucially, this novel perturbation is derived without additional optimization steps, and yields a similarly-tractable approximation within the class of skew-symmetric densities that provably enhances the finite-sample accuracy of the original symmetric approximation, and, under suitable assumptions, improves its convergence rate to the exact posterior by at least a $\sqrt{n}$ factor, in asymptotic regimes. These advancements are illustrated in numerical studies focusing on skewed perturbations of state-of-the-art Gaussian approximations.

For any real $k\geq 2$ and large prime $q$, we prove a lower bound on the $2k$-th moment of the Dirichlet character sum \begin{equation*} \frac{1}{\phi(q)} \sum_{\substack{\chi \text{ mod }q\\ \chi\neq \chi_0}} \Big| \sum_{n\leq x} \chi(n)\Big|^{2k}, \end{equation*} where $1\leq x\leq q$, and $\chi$ is summed over the set of non-trivial Dirichlet characters mod $q$. Our bound is known to be optimal up to a constant factor under the Generalised Riemann Hypothesis. We also get a sharp lower bound on moments of theta functions using the same method.

K2-24 is a planetary system composed of two transiting low-density Neptunians locked in an almost perfect 2:1 resonance and showing large TTVs, i.e., an excellent laboratory to search for signatures of planetary migration. Previous studies performed with K2, Spitzer and RV data tentatively claimed a significant non-zero eccentricity for one or both planets, possibly high enough to challenge the scenario of pure disk migration through resonant capture. With 13 new CHEOPS light curves (seven of planet -b, six of planet -c), we carried out a global photometric and dynamical re-analysis by including all the available literature data as well. We got the most accurate set of planetary parameters to date for the K2-24 system, including radii and masses at 1% and 5% precision (now essentially limited by the uncertainty on stellar parameters) and non-zero eccentricities $e_b=0.0498_{-0.0018}^{+0.0011}$, $e_c=0.0282_{-0.0007}^{+0.0003}$ detected at very high significance for both planets. Such relatively large values imply the need for an additional physical mechanism of eccentricity excitation during or after the migration stage. Also, while the accuracy of the previous TTV model had drifted by up to 0.5 days at the current time, we constrained the orbital solution firmly enough to predict the forthcoming transits for the next ~15 years, thus enabling an efficient follow-up with top-level facilities such as JWST or ESPRESSO., Comment: 19 pages, 11 figures, 8 tables. Accepted for publication in A&A on September 4, 2024. Typos corrected

Variational ab-initio methods in quantum chemistry stand out among other methods in providing direct access to the wave function. This allows in principle straightforward extraction of any other observable of interest, besides the energy, but in practice this extraction is often technically difficult and computationally impractical. Here, we consider the electron density as a central observable in quantum chemistry and introduce a novel method to obtain accurate densities from real-space many-electron wave functions by representing the density with a neural network that captures known asymptotic properties and is trained from the wave function by score matching and noise-contrastive estimation. We use variational quantum Monte Carlo with deep-learning ans\"atze (deep QMC) to obtain highly accurate wave functions free of basis set errors, and from them, using our novel method, correspondingly accurate electron densities, which we demonstrate by calculating dipole moments, nuclear forces, contact densities, and other density-based properties., Comment: 12 pages, 9 figures in the main text

The progenitor system(s) as well as the explosion mechanism(s) of thermonuclear (Type Ia) supernovae are long-standing issues in astrophysics. Here we present ejecta masses and other physical parameters for 28 recent Type Ia supernovae inferred from multiband photometric and optical spectroscopic data. Our results confirm that the majority of SNe Ia show {\it observable} ejecta masses below the Chandrasekhar-limit (having a mean $M_{\rm ej} \approx 1.1 \pm 0.3$ M$_\odot$), consistent with the predictions of recent sub-M$_{\rm Ch}$ explosion models. They are compatible with models assuming either single- or double-degenerate progenitor configurations. We also recover a sub-sample of supernovae within $1.2 $ M$_\odot$ $< M_{\rm {ej}} < 1.5$ M$_\odot$ that are consistent with near-Chandrasekhar explosions. Taking into account the uncertainties of the inferred ejecta masses, about half of our SNe are compatible with both explosion models. We compare our results with those in previous studies, and discuss the caveats and concerns regarding the applied methodology.

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.

We formulate scalar electrodynamics in the braided $L_\infty$-algebra formalism and study its perturbative expansion in the algebraic framework of Batalin-Vilkovisky quantization. We confirm that UV/IR mixing is absent at one-loop order in this noncommutative field theory, and that the non-anomalous Ward-Takahashi identities for the braided gauge symmetry are satisfied., Comment: 48 pages; v2: minor changes

The Pan-STARRS 3$\pi$ survey has detected hundreds of thousands of variable stars thanks to its coverage and 4-year time span, even though the sampling of the light curves is relatively sparse. These light curves contain only 10-15 detections in each of the five filters (g,r,i,z,y). During the K2 mission, the Kepler space telescope observed with a high sampling frequency, although only for about 80 days in each of its campaigns. Crossmatching and investigating the RR Lyrae stars observed by both K2 and Pan-STARRS can serve as a valuable tool to validate the classification and period determination of the survey. We used the Sesar catalogue of RR Lyrae stars detected by Pan-STARRS. After determining the overlap, we also considered the Gaia DR3 RR Lyrae catalogue data for these stars wherever it was available. The frequencies of the light variations were calculated by applying the Lomb-Scargle periodogram method on the K2 light curves that were prepared with autoEAP photometry. The calculated frequencies of the stars then were compared with those given in the Sesar catalogue and the Gaia DR3 RR Lyrae catalogue. We found that for the majority of the stars, the classification (95.6%) and the frequency determination (90.1%) of the PanSTARRS RR Lyrae stars were consistent within 0.03 d-1 with those that we derived from the K2 autoEAP light curves. For a significant subset of the sample, 7.4%, however, an offset of 1 or 2 d-1 was found in the frequencies. These are the result of the sampling of the detections, because Pan-STARRS observations are affected by diurnal cycles, whereas Kepler carried out measurements quasicontinuously. We found that RRc subtypes are significantly more affected (25.3%) than RRab subtypes (3.7%), which is most likely caused by RRc stars having less sharp light curve features. Validation via space-based data will be important for future ground-based surveys, as well., Comment: 9 pages, 5 figures, 2 tables, 1 appendix table, accepted for publication in A&A

Computing education widely applies general learning theories and pedagogical practices. However, computing also includes specific disciplinary knowledge and skills, e.g., programming and software development methods, for which there has been a long history of development and application of specific pedagogical practices. In recent years, there has also been substantial interest in developing computing-specific theoretical models, which seek to describe and explain the complex interactions within teaching and learning computing in various contexts. In this paper, we explore connections between computing-specific pedagogies and theoretical models as reported in the literature. Our goal is to enrich computing education research and practice by illustrating how explicit use of field-specific theories and pedagogies can further the whole field. We have collected a list of computing-specific pedagogical practices and theoretical models from a literature search, identifying source papers where they have been first introduced or well described. We then searched for papers in the ACM digital library that cite source papers from each list, and analyzed the type of interaction between the model and pedagogy in each paper. We developed a categorization of how theoretical models and pedagogies have supported or discounted each other, have been used together in empirical studies or used to build new artefacts. Our results showed that pair programming and parsons problems have had the most interactions with theoretical models in the explored papers, and we present findings of the analysis of these interactions.

Liebeck, Nikolov, and Shalev conjectured that for every subset A of a finite simple group S with |A|>1, there exist O( log|S| / log|A| ) conjugates of A whose product is S. This paper is a companion to [Lifshitz: Completing the proof of the Liebeck-Nikolov-Shalev conjecture] and together they prove the conjecture. In this paper we prove the conjecture in the regime where $|A|>|S|^c$ for an absolute constant c>0. We also prove that the following Skew Product Theorem holds for all finite simple groups. Namely we show that either the product of two conjugates of A has size at least $|A|^{1.49}$, or S is the product of boundedly many conjugates of A., Comment: Citation added. Supporting grant numbers corrected

In this paper we present a theoretical analysis of the faster than light communication possibility based on entangled photons. We analyze designs that may be capable to solve the problem of direct information transfer between members of an entangled photon pairs. We consider that experimental verifications can confirm or even refute this. Our hypothesis was that most proofs of the nocommunication theorem are based on a certain set of conditions, and it is possible to provide a broader set of conditions that allow the establishment of entangled states as quantum information channels, without using a classical channel. One basic unit of the proposed design transforms the polarization state of one member of an entangled photon pair into a spatial superposition state. Thus, after the polarization measurement performed on one member, which eliminates the entanglement, the quantum information is maintained in the spatial superposition state of the other member. This can be recovered by a particular measurement based on spatial interference. We have shown that solutions with so-called symmetric functions lead to average results that corresponds to the nocommunication theorem. However, using asymmetric functions the averaged measurement results calculated in a prescribed time window can distinguish the types of measurements performed on the other member of the pair. This can establish a communication code that enables faster-than-light information sharing under specific conditions. There may be also further theoretical consequences: a significant extension of the quantum mechanical nonlocality principle.

The \textit{Vera C. Rubin} Observatory will start operations in 2025. During the first two years, too few visits per target per band will be available, meaning that mean magnitude measurements of variable stars will not be precise and thus, standard candles like RR Lyrae (RRL) will not be usable. Light curve templates (LCTs) can be adopted to estimate the mean magnitude of a variable star with few magnitude measurements, provided that their period (plus amplitude and reference epoch, depending on how the LCT is applied) is known. LSST will provide precise RRL periods within the first six months, allowing to exploit RRLs if LCTs were available. We aim to build LCTs in the LSST bands to enhance the early science with LSST. Using them will provide a 1-2 years advantage with respect to a classical approach, concerning distance measurements. We collected $gri$-band data from the ZTF survey and $z$-band data from DECam to build the LCTs of RRLs. We also adopted synthetic $griz$-band data in the LSST system from pulsation models, plus SDSS, \gaia and OGLE photometry, inspecting the light amplitude ratios in different photometric systems to provide useful conversions to apply the LCTs. We have built LCTs of RRLs in the $griz$ bands of the LSST photometric system; for the $z$ band, we could build only fundamental-mode RRL LCTs. We quantitatively demonstrated that LCTs built with ZTF and DECam data can be adopted on the LSST photometric system. LCTs will decrease by a factor of at least two the uncertainty on distance estimates of RRLs, with respect to a simple average of the available measurements. Finally, within our tests, we have found a brand new behavior of amplitude ratios in the Large Magellanic Cloud., Comment: Accepted for publication in A&A

We prove the Geometric P=W conjecture in rank 3 on the three-punctured sphere. We describe the topology at infinity of the related character variety. We use asymptotic abelianization of harmonic bundles away from the ramification divisor and an equivariant approach near the branch points to find the WKB (also known as Liouville--Green or phase-integral) expansion of the involved maps. We analyze the Stokes phenomenon governing their behavior., Comment: 66 pages, 7 figures; v2: expanded Section 6

We report the spectroscopic confirmation and fundamental properties of TOI-757 b, a mini-Neptune on a 17.5-day orbit transiting a bright star ($V = 9.7$ mag) discovered by the TESS mission. We acquired high-precision radial velocity measurements with the HARPS, ESPRESSO, and PFS spectrographs to confirm the planet detection and determine its mass. We also acquired space-borne transit photometry with the CHEOPS space telescope to place stronger constraints on the planet radius, supported with ground-based LCOGT photometry. WASP and KELT photometry were used to help constrain the stellar rotation period. We also determined the fundamental parameters of the host star. We find that TOI-757 b has a radius of $R_{\mathrm{p}} = 2.5 \pm 0.1 R_{\oplus}$ and a mass of $M_{\mathrm{p}} = 10.5^{+2.2}_{-2.1} M_{\oplus}$, implying a bulk density of $\rho_{\text{p}} = 3.6 \pm 0.8$ g cm$^{-3}$. Our internal composition modeling was unable to constrain the composition of TOI-757 b, highlighting the importance of atmospheric observations for the system. We also find the planet to be highly eccentric with $e$ = 0.39$^{+0.08}_{-0.07}$, making it one of the very few highly eccentric planets among precisely characterized mini-Neptunes. Based on comparisons to other similar eccentric systems, we find a likely scenario for TOI-757 b's formation to be high eccentricity migration due to a distant outer companion. We additionally propose the possibility of a more intrinsic explanation for the high eccentricity due to star-star interactions during the earlier epoch of the Galactic disk formation, given the low metallicity and older age of TOI-757., Comment: Accepted for publication in MNRAS; 26 pages, 14 figures, 6 tables

Building Information Modeling (BIM) describes a central data pool covering the entire life cycle of a construction project. Similarly, Building Energy Modeling (BEM) describes the process of using a 3D representation of a building as a basis for thermal simulations to assess the building's energy performance. This paper explores the intersection of BIM and BEM, focusing on the challenges and methodologies in converting BIM data into BEM representations for energy performance analysis. BEMTrace integrates 3D data wrangling techniques with visualization methodologies to enhance the accuracy and traceability of the BIM-to-BEM conversion process. Through parsing, error detection, and algorithmic correction of BIM data, our methods generate valid BEM models suitable for energy simulation. Visualization techniques provide transparent insights into the conversion process, aiding error identification, validation, and user comprehension. We introduce context-adaptive selections to facilitate user interaction and to show that the BEMTrace workflow helps users understand complex 3D data wrangling processes., Comment: 9 pages and 2 pages references, 12 figures

We present a new lattice QCD calculation of the leading order hadronic vacuum polarization contribution to the muon anomalous magnetic moment $a_\mu$. We reduce uncertainties compared to our earlier computation by $40\%$, arXiv:2002.12347. We perform simulations on finer lattices allowing for an even more accurate continuum extrapolation. We also include a small, long-distance contribution obtained using input from experiments in a low-energy regime where they all agree. Combined with other standard model contributions our result leads to a prediction that differs from the measurement of $a_\mu$ by only 0.9 standard deviations. This provides a remarkable validation of the standard model to 0.37ppm., Comment: 55 pages, 31 figures

Three-dimensional doped Dirac insulators foster simply connected (in both topological and trivial regimes) and annular (deep inside the topological regime) Fermi surfaces (FSs) in the normal state, and allow on-site repulsions among fermions with opposite spin ($U_1$) and parity ($U_2$) eigenvalues. From an unbiased leading-order (one-loop) renormalization group analysis, controlled by a suitable $\epsilon$ expansion, we show that this system develops strong propensity toward the nucleation of scalar $s$-wave and odd-parity pseudoscalar $p$-wave pairings, favored by repulsive $U_1$ and $U_2$ interactions, respectively, irrespective of the underlying FS topology. Our results can be pertinent for the observed superconductivity in various doped narrow gap semiconductors, and the theoretical foundation can readily be applied to investigate similar phenomenon in various doped topological materials., Comment: 5 Pages, 1 Figure, 2 Tables (Supplemental Material as ancillary file)

Among the thousands of exoplanets discovered to date, approximately a few hundred gas giants on short-period orbits are classified as "lonely" and only a few are in a multi-planet system with a smaller companion on a close orbit. The processes that formed multi-planet systems hosting gas giants on close orbits are poorly understood, and only a few examples of this kind of system have been observed and well characterised. Within the contest of multi-planet system hosting gas-giant on short orbits, we characterise TOI-1130 system by measuring masses and orbital parameters. This is a 2-transiting planet system with a Jupiter-like planet (c) on a 8.35 days orbit and a Neptune-like planet (b) on an inner (4.07 days) orbit. Both planets show strong anti-correlated transit timing variations (TTVs). Furthermore, radial velocity (RV) analysis showed an additional linear trend, a possible hint of a non-transiting candidate planet on a far outer orbit. Since 2019, extensive transit and radial velocity observations of the TOI-1130 have been acquired using TESS and various ground-based facilities. We present a new photo-dynamical analysis of all available transit and RV data, with the addition of new CHEOPS and ASTEP+ data that achieve the best precision to date on the planetary radii and masses and on the timings of each transit. We were able to model interior structure of planet b constraining the presence of a gaseous envelope of H/He, while it was not possible to assess the possible water content. Furthermore, we analysed the resonant state of the two transiting planets, and we found that they lie just outside the resonant region. This could be the result of the tidal evolution that the system underwent. We obtained both masses of the planets with a precision less than 1.5%, and radii with a precision of about 1% and 3% for planet b and c, respectively., Comment: 22 pages, 10 figures, Accepted for publication by Astronomy and Astrophysics

We investigate subsets with small sumset in arbitrary abelian groups. For an abelian group $G$ and an $n$-element subset $Y \subseteq G$ we show that if $m \ll s^2/(\log n)^2$, then the number of subsets $A \subseteq Y$ with $|A| = s$ and $|A + A| \leq m$ is at most \[2^{o(s)}\binom{\frac{m+\beta}{2}}{s},\] where $\beta$ is the size of the largest subgroup of $G$ of size at most $\left(1+o(1)\right)m$. This bound is sharp for $\mathbb{Z}$ and many other groups. Our result improves the one of Campos and nearly bridges the remaining gap in a conjecture of Alon, Balogh, Morris, and Samotij. We also explore the behaviour of uniformly chosen random sets $A \subseteq \{1,\ldots,n\}$ with $|A| = s$ and $|A + A| \leq m$. Under the same assumption that $m \ll s^2/(\log n)^2$, we show that with high probability there exists an arithmetic progression $P \subseteq \mathbb{Z}$ of size at most $m/2 + o(m)$ containing all but $o(s)$ elements of $A$. Analogous results are obtained for asymmetric sumsets, improving results by Campos, Coulson, Serra, and W\"otzel. The main tool behind our proofs is a graph container theorem combined with a variant of an asymmetric hypergraph container theorem., Comment: 36 pages (including appendix)

In this paper, we study several generalizations of multiway cut where the terminals can be chosen as \emph{representatives} from sets of \emph{candidates} $T_1,\ldots,T_q$. In this setting, one is allowed to choose these representatives so that the minimum-weight cut separating these sets \emph{via their representatives} is as small as possible. We distinguish different cases depending on (A) whether the representative of a candidate set has to be separated from the other candidate sets completely or only from the representatives, and (B) whether there is a single representative for each candidate set or the choice of representative is independent for each pair of candidate sets. For fixed $q$, we give approximation algorithms for each of these problems that match the best known approximation guarantee for multiway cut. Our technical contribution is a new extension of the CKR relaxation that preserves approximation guarantees. For general $q$, we show $o(\log q)$-inapproximability for all cases where the choice of representatives may depend on the pair of candidate sets, as well as for the case where the goal is to separate a fixed node from a single representative from each candidate set. As a positive result, we give a $2$-approximation algorithm for the case where we need to choose a single representative from each candidate set. This is a generalization of the $(2-2/k)$-approximation for k-cut, and we can solve it by relating the tree case to optimization over a gammoid.

Reinforcement learning (RL) -- finding the optimal behaviour (also referred to as policy) maximizing the collected long-term cumulative reward -- is among the most influential approaches in machine learning with a large number of successful applications. In several decision problems, however, one faces the possibility of policy switching -- changing from the current policy to a new one -- which incurs a non-negligible cost (examples include the shifting of the currently applied educational technology, modernization of a computing cluster, and the introduction of a new webpage design), and in the decision one is limited to using historical data without the availability for further online interaction. Despite the inevitable importance of this offline learning scenario, to our best knowledge, very little effort has been made to tackle the key problem of balancing between the gain and the cost of switching in a flexible and principled way. Leveraging ideas from the area of optimal transport, we initialize the systematic study of policy switching in offline RL. We establish fundamental properties and design a Net Actor-Critic algorithm for the proposed novel switching formulation. Numerical experiments demonstrate the efficiency of our approach on multiple benchmarks of the Gymnasium.

Off-policy evaluation (OPE) is crucial for assessing a target policy's impact offline before its deployment. However, achieving accurate OPE in large state spaces remains challenging. This paper studies state abstractions -- originally designed for policy learning -- in the context of OPE. Our contributions are three-fold: (i) We define a set of irrelevance conditions central to learning state abstractions for OPE, and derive a backward-model-irrelevance condition for achieving irrelevance in %sequential and (marginalized) importance sampling ratios by constructing a time-reversed Markov decision process (MDP). (ii) We propose a novel iterative procedure that sequentially projects the original state space into a smaller space, resulting in a deeply-abstracted state, which substantially simplifies the sample complexity of OPE arising from high cardinality. (iii) We prove the Fisher consistencies of various OPE estimators when applied to our proposed abstract state spaces., Comment: 56 pages, 5 figures

Solar wind turbulence is a dynamical phenomenon that evolves with heliocentric distance. Orbiting Mars since September 2014, Mars Atmosphere and Volatile EvolutioN (MAVEN) offers a unique opportunity to explore some of its main properties beyond ~1.38 au. Here, we analyze solar wind turbulence upstream of Mars's bow shock, utilizing more than five years of magnetic field and plasma measurements. This analysis is based on two complementary methodologies: 1) the computation of magnetohydrodynamic (MHD) invariants characterizing incompressible fluctuations; 2) the estimation of the incompressible energy cascade rate at MHD scales (i.e., $\langle\varepsilon^{T}\rangle_{MHD}$). Our results show the solar wind incompressible fluctuations are primarily in a magnetically dominated regime, with the component travelling away from the Sun having a higher median pseudo-energy. Moreover, turbulent fluctuations have a total energy per mass of up to ~300 km2 s-2, a range smaller than reported at 1 au. For these conditions, we determine the probability distribution function of $\langle\varepsilon^{T}\rangle_{MHD}$ ranges mainly between ~-1x10-16 and ~1x10-16 J m-3 s-1, with a median equal to -1.8x10-18 J m-3 s-1, suggesting back-transfer of energy. Our results also suggest that $|\langle\varepsilon^{T}\rangle_{MHD}|$ is correlated with the total energy per mass of fluctuations and that the median of $\langle\varepsilon^{T}\rangle_{MHD}$ does not vary significantly with the cross-helicity. We find, however, that the medians of the inward and outward pseudo-energy cascade rates vary with the solar wind cross-helicity. Finally, we discuss these results and their implications for future studies that can provide further insight into the factors affecting solar wind energy transfer rate., Comment: 5 figures, 1 table, Submitted to the Astrophysical Journal

Multiplanetary systems spanning the radius valley are ideal testing grounds for exploring the proposed explanations for the observed bimodality in the radius distribution of close-in exoplanets. One such system is HIP 29442 (TOI-469), an evolved K0V star hosting two super-Earths and a sub-Neptune. We observe HIP 29442 with CHEOPS for a total of 9.6 days, which we model jointly with 2 sectors of TESS data to derive planetary radii of $3.410\pm0.046$, $1.551\pm0.045$ and $1.538\pm0.049$ R$_\oplus$ for planets b, c and d, which orbit HIP 29442 with periods of 13.6, 3.5 and 6.4 days. For planet d, this value deviates by more than 3 sigma from the median value reported in the discovery paper, leading us to conclude that caution is required when using TESS photometry to determine the radii of small planets with low per-transit S/N and large gaps between observations. Given the high precision of these new radii, combining them with published RVs from ESPRESSO and HIRES provides us with ideal conditions to investigate the internal structure and formation pathways of the planets in the system. We introduce the publicly available code plaNETic, a fast and robust neural network-based Bayesian internal structure modelling framework. We then apply hydrodynamic models to explore the upper atmospheric properties of these inferred structures. Finally, we identify planetary system analogues in a synthetic population generated with the Bern model for planet formation and evolution. Based on this analysis, we find that the planets likely formed on opposing sides of the water iceline from a protoplanetary disk with an intermediate solid mass. We finally report that the observed parameters of the HIP 29442 system are compatible with both a scenario where the second peak in the bimodal radius distribution corresponds to sub-Neptunes with a pure H/He envelope as well as a scenario with water-rich sub-Neptunes., Comment: 30 pages, 17 figures, accepted for publication in A&A

Approximated functional renormalization group (FRG) equations lead to regulator-dependent $\beta$-functions, in analogy to the scheme-dependence of the perturbative renormalization group (pRG) approach. A scheme transformation redefines the couplings to relate the $\beta$-functions of the FRG method with an arbitrary regulator function to the pRG ones obtained in a given scheme. Here, we consider a periodic sine-Gordon scalar field theory in $d=2$ dimensions and show that the relation of the FRG and pRG approaches is intricate. Although, both the FRG and the pRG methods are known to be sufficient to obtain the critical frequency $\beta_c^2 =8\pi$ of the model independently of the choice of the regulator and the renormalization scheme, we show that one has to go beyond the standard pRG method (e.g., using an auxiliary mass term) or the Coulomb-gas representation in order to obtain the $\beta$-function of the wave function renormalization. This aspect makes the scheme transformation non-trivial. Comparing flow equations of the two-dimensional sine-Gordon theory without any scheme-transformation, i.e., redefinition of couplings, we find that the auxiliary mass pRG $\beta$-functions of the minimal subtraction scheme can be recovered within the FRG approach with the choice of the power-law regulator with $b=2$, therefore constitutes a preferred choice for the comparison of FRG and pRG flows., Comment: 17 pages, 1 figure, final version, to appear in J.Phys.G

Due to their flexibility and theoretical tractability Gaussian process (GP) regression models have become a central topic in modern statistics and machine learning. While the true posterior in these models is given explicitly, numerical evaluations depend on the inversion of the augmented kernel matrix $ K + \sigma^2 I $, which requires up to $ O(n^3) $ operations. For large sample sizes n, which are typically given in modern applications, this is computationally infeasible and necessitates the use of an approximate version of the posterior. Although such methods are widely used in practice, they typically have very limtied theoretical underpinning. In this context, we analyze a class of recently proposed approximation algorithms from the field of Probabilistic numerics. They can be interpreted in terms of Lanczos approximate eigenvectors of the kernel matrix or a conjugate gradient approximation of the posterior mean, which are particularly advantageous in truly large scale applications, as they are fundamentally only based on matrix vector multiplications amenable to the GPU acceleration of modern software frameworks. We combine result from the numerical analysis literature with state of the art concentration results for spectra of kernel matrices to obtain minimax contraction rates. Our theoretical findings are illustrated by numerical experiments.

We investigate a simple variant of spin ice whose degenerate ground states are densely packed monopole configurations. An applied field drives this model through a Z2 confinement transition, in absence of any local order parameter. Instead, this hidden order turns out to be diagnosed by a string order invisible to any local probe. We describe the transition in terms of a bosonic field theory with a pairing term, as well as a Kramers-Wannier duality into a 3D Ising model, which establishes its Z2 nature. This topological transition can be thought of as a variant of the celebrated U(1) Kasteleyn transition; but instead of the traditional '3/2'-order kink, the system shows critical scaling expected near a 3D Ising transition. Remarkably, however, the magnetic response scales with the critical exponent not of the susceptibility, but of the specific heat.

For each nonnegative integer m we show that any closed, oriented topological four-manifold with fundamental group Z_{4m+2} and odd intersection form, with possibly seven exceptions, either admits no smooth structure or admits infinitely many distinct smooth structures up to diffeomorphism. Moreover, we construct infinite families of non-complex irreducible fake projective planes with diverse fundamental groups., Comment: 32 pages

Kernel methods underpin many of the most successful approaches in data science and statistics, and they allow representing probability measures as elements of a reproducing kernel Hilbert space without loss of information. Recently, the kernel Stein discrepancy (KSD), which combines Stein's method with the flexibility of kernel techniques, gained considerable attention. Through the Stein operator, KSD allows the construction of powerful goodness-of-fit tests where it is sufficient to know the target distribution up to a multiplicative constant. However, the typical U- and V-statistic-based KSD estimators suffer from a quadratic runtime complexity, which hinders their application in large-scale settings. In this work, we propose a Nystr\"om-based KSD acceleration -- with runtime $\mathcal O\left(mn+m^3\right)$ for $n$ samples and $m\ll n$ Nystr\"om points -- , show its $\sqrt{n}$-consistency with a classical sub-Gaussian assumption, and demonstrate its applicability for goodness-of-fit testing on a suite of benchmarks., Comment: Broader applicability of main result, consistency of quadratic time estimator

Today's programmers can choose from an exceptional range of programming languages, each with its own traits, purpose, and complexity. A key aspect of a language's complexity is how hard it is to compile programs in the language. While most programmers have an intuition about compilation hardness for different programming languages, no metric exists to quantify it. We introduce the compilation quotient (CQ), a metric to quantify the compilation hardness of compiled programming languages. The key idea is to measure the compilation success rates of programs sampled from context-free grammars. To this end, we fairly sample over 12 million programs in total. CQ ranges between 0 and 100, where 0 indicates that no programs compile, and 100 means that all programs compile. Our findings on 12 popular compiled programming languages show high variation in CQ. C has a CQ of 48.11, C++ has 0.60, Java has 0.27 and Haskell has 0.13. Strikingly, Rust's CQ is nearly 0, and for C, even a large fraction of very sizable programs compile. We believe CQ can help understand the differences of compiled programming languages better and help language designers.

We formulate scalar field theories in a curved braided $L_\infty$-algebra formalism and analyse their correlation functions using Batalin-Vilkovisky quantization. We perform detailed calculations in cubic braided scalar field theory up to two-loop order and three-point multiplicity. The divergent tadpole contributions are eliminated by a suitable choice of central curvature for the $L_\infty$-structure, and we confirm the absence of UV/IR mixing. The calculations of higher loop and higher multiplicity correlators in homological perturbation theory are facilitated by the introduction of a novel diagrammatic calculus. We derive an algebraic version of the Schwinger-Dyson equations based on the homological perturbation lemma, and use them to prove the braided Wick theorem., Comment: 41 pages; v2: typos corrected; v3: minor changes and typos fixed; v4: Final version to be published in Fortschritte der Physik

CHEOPS is a space telescope specifically designed to monitor transiting exoplanets orbiting bright stars. In September 2023, CHEOPS completed its nominal mission and remains in excellent operational conditions. The mission has been extended until the end of 2026. Scientific and instrumental data have been collected throughout in-orbit commissioning and nominal operations, enabling a comprehensive analysis of the mission's performance. In this article, we present the results of this analysis with a twofold goal. First, we aim to inform the scientific community about the present status of the mission and what can be expected as the instrument ages. Secondly, we intend for this publication to serve as a legacy document for future missions, providing insights and lessons learned from the successful operation of CHEOPS. To evaluate the instrument performance in flight, we developed a comprehensive monitoring and characterisation programme. It consists of dedicated observations that allow us to characterise the instrument's response. In addition to the standard collection of nominal science and housekeeping data, these observations provide input for detecting, modelling, and correcting instrument systematics, discovering and addressing anomalies, and comparing the instrument's actual performance with expectations. The precision of the CHEOPS measurements has enabled the mission objectives to be met and exceeded. Careful modelling of the instrumental systematics allows the data quality to be significantly improved during the light curve analysis phase, resulting in more precise scientific measurements. CHEOPS is compliant with the driving scientific requirements of the mission. Although visible, the ageing of the instrument has not affected the mission's performance., Comment: Accepted for publication in Astronomy and Astrophysics

Ultra-hot Jupiters (UHJs) orbiting pulsating A/F stars represent an important subset of the exoplanetary demographic, as they are excellent candidates for the study of exoplanetary atmospheres, as well as being astrophysical laboratories for the investigation of planet-to-star interactions. We analyse the \texttt{TESS} (Transiting Exoplanet Survey Satellite) light curve of the WASP-167 system, consisting of an F1V star and a substellar companion on a $\sim 2.02$ day orbit. We model the combination of the ellipsoidal variability and the Doppler beaming to measure the mass of WASP-167b, and the reflection effect to obtain constraints on the geometric albedo, while placing a special emphasis on noise separation. We implement a basic model to determine the dayside ($T_{\rm Day}$), nightside ($T_{\rm Night}$) and intrinsic ($T_{\rm Internal}$) temperatures of WASP-167b and put a constraint on its Bond albedo. We confirm the transit parameters of the planet seen in the literature. We find that a resonant $\sim 2P^{-1}$ stellar signal (which may originate from planet-to-star interactions) interferes with the phase curve analysis. After considerate treatment of this signal, we find $M_p = 0.34 \pm 0.22$~$M_J$. We measure a dayside temperature of $2790 \pm 100$ K, classifying WASP-167b as an UHJ. We find a $2\sigma$ upper limit of $0.51$ on its Bond albedo, and determine the geometric albedo at $0.34 \pm 0.11$ ($1 \sigma$ uncertainty). With an occultation depth of $106.8 \pm 27.3$ ppm in the \texttt{TESS} passband, the UHJ WASP-167b will be an excellent target for atmospheric studies, especially those at thermal wavelength ranges, where the stellar pulsations are expected to be be less influential., Comment: 19 pages, 15 figures, resubmitted to Astronomy and Astrophysics after minor revision

HIP 41378 d is a long-period planet that has only been observed to transit twice, three years apart, with K2. According to stability considerations and a partial detection of the Rossiter-McLaughlin effect, $P_\mathrm{d} = 278.36$ d has been determined to be the most likely orbital period. We targeted HIP 41378 d with CHEOPS at the predicted transit timing based on $P_\mathrm{d}= 278.36$ d, but the observations show no transit. We find that large ($>22.4$ hours) transit timing variations (TTVs) could explain this non-detection during the CHEOPS observation window. We also investigated the possibility of an incorrect orbital solution, which would have major implications for our knowledge of this system. If $P_\mathrm{d} \neq 278.36$ d, the periods that minimize the eccentricity would be $101.22$ d and $371.14$ d. The shortest orbital period will be tested by TESS, which will observe HIP 41378 in Sector 88 starting in January 2025. Our study shows the importance of a mission like CHEOPS, which today is the only mission able to make long observations (i.e., from space) to track the ephemeris of long-period planets possibly affected by large TTVs., Comment: Accepted for publication in Astronomy and Astrophysics

We introduce several improvements to the penalty-based variational quantum Monte Carlo (VMC) algorithm for computing electronic excited states of Entwistle $\textit{et al.}$ [M. T. Entwistle $\textit{et al.}$, Nat. Commun. $\textbf{14}$, 274 (2023)], and demonstrate that the accuracy of the updated method is competitive with other available excited-state VMC approaches. A theoretical comparison of the computational aspects of these algorithms is presented, where several benefits of the penalty-based method are identified. Our main contributions include an automatic mechanism for tuning the scale of the penalty terms, an updated form of the overlap penalty with proven convergence properties, and a new term that penalizes the spin of the wave function, enabling the selective computation of states with a given spin. With these improvements, along with the use of the latest self-attention-based ansatz, the penalty-based method achieves a mean absolute error below 1 kcal/mol for the vertical excitation energies of a set of 26 atoms and molecules, without relying on variance matching schemes. Considering excited states along the dissociation of the carbon dimer, the accuracy of the penalty-based method is on par with that of natural-excited-state (NES) VMC, while also providing results for larger sections of the potential energy surface. Additionally, the accuracy of the original penalty-based method is improved for a conical intersection of ethylene, with the predicted angle of the intersection agreeing well with both NES-VMC and multi-reference configuration interaction., Comment: 18 pages, 7 figures

We classify equivariant $\mathbb{C}^*$-actions on moduli spaces of Higgs bundles corresponding to the Painlev\'e equations. We deduce the Floer-theoretic filtrations on the cohomology of these spaces, introduced by Ritter and the second author in arXiv:2304.13026. Filtration is then compared with the $``P=W"$ and the filtration obtained by multiplicities of the irreducible components of the nilpotent cone, for all the 2-dimensional Higgs moduli., Comment: 21 pages, 5 figures

Given a homomorphism $\tau$ from a suitable finite group $\mathsf{\Gamma}$ to $\mathsf{SU}(4)$ with image $\mathsf{\Gamma}^\tau$, we construct a cohomological gauge theory on a noncommutative resolution of the quotient singularity $\mathbb{C}^4/\mathsf{\Gamma}^\tau$ whose BRST fixed points are $\mathsf{\Gamma}$-invariant tetrahedron instantons on a generally non-effective orbifold. The partition function computes the expectation values of complex codimension one defect operators in rank $r$ cohomological Donaldson-Thomas theory on a flat gerbe over the quotient stack $[\mathbb{C}^4/\,\mathsf{\Gamma}^\tau]$. We describe the generalized ADHM parametrization of the tetrahedron instanton moduli space, and evaluate the orbifold partition functions through virtual torus localization. If $\mathsf{\Gamma}$ is an abelian group the partition function is expressed as a combinatorial series over arrays of $\mathsf{\Gamma}$-coloured plane partitions, while if $\mathsf{\Gamma}$ is non-abelian the partition function localizes onto a sum over torus-invariant connected components of the moduli space labelled by lower-dimensional partitions. When $\mathsf{\Gamma}=\mathbb{Z}_n$ is a finite abelian subgroup of $\mathsf{SL}(2,\mathbb{C})$, we exhibit the reduction of Donaldson-Thomas theory on the toric Calabi-Yau four-orbifold $\mathbb{C}^2/\,\mathsf{\Gamma}\times\mathbb{C}^2$ to the cohomological field theory of tetrahedron instantons, from which we express the partition function as a closed infinite product formula. We also use the crepant resolution correpondence to derive a closed formula for the partition function on any polyhedral singularity., Comment: 79 pages; v2: minor changes and corrections

The TOI-178 system consists of a nearby late K-dwarf transited by six planets in the super-Earth to mini-Neptune regime, with radii ranging from 1.2 to 2.9 earth radius and orbital periods between 1.9 and 20.7 days. All planets but the innermost one form a chain of Laplace resonances. The fine-tuning and fragility of such orbital configurations ensure that no significant scattering or collision event has taken place since the formation and migration of the planets in the protoplanetary disc, hence providing important anchors for planet formation models. We aim to improve the characterisation of the architecture of this key system, and in particular the masses and radii of its planets. In addition, since this system is one of the few resonant chains that can be characterised by both photometry and radial velocities, we aim to use it as a test bench for the robustness of the planetary mass determination with each technique. We perform a global analysis of all available photometry and radial velocity. We also try different sets of priors on the masses and eccentricity, as well as different stellar activity models, to study their effects on the masses estimated by each method. We show how stellar activity is preventing us from obtaining a robust mass estimation for the three outer planets using radial velocity data alone. We also show that our joint photo-dynamical and radial velocity analysis resulted in a robust mass determination for planets c to g, with precision of 12% for the mass of planet c, and better than 10% for planets d to g. The new precisions on the radii range from 2 to 3%. The understanding of this synergy between photometric and radial velocity measurements will be valuable during the PLATO mission. We also show that TOI-178 is indeed currently locked in the resonant configuration, librating around an equilibrium of the chain.