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Thermal nonequilibrium (TNE) is a condition of the plasma in the solar corona in which the local rate of energy loss due to radiation increases to the point that it cannot be sustained by the various heating terms acting on the plasma, precluding the existence of a steady state. The limit cycles of precipitation and evaporation that result from TNE have been simulated in 1D models of coronal loops, as well as 2D and 3D models of the solar chromosphere and lower corona. However, a careful study of TNE in the solar wind has not been performed until now. Here we demonstrate that for suitable combinations of local and global heating rates it is possible for the plasma to exhibit a TNE condition, even in the context of a transonic solar wind with appreciable mass and energy fluxes. This implies limits on the amount of foot-point heating that can be withstood under steady-state conditions in the solar wind, and may help to explain the variability of solar wind streams that emanate from regions of highly concentrated magnetic flux on the solar surface. The implications of this finding pertain to various sources of high-density solar wind, including plumes that form above regions of mixed magnetic polarity in polar coronal holes and the slow solar wind (SSW) that emanates from coronal hole boundaries.

This paper introduces distribution-based prediction, a novel approach to using Large Language Models (LLMs) as predictive tools by interpreting output token probabilities as distributions representing the models' learned representation of the world. This distribution-based nature offers an alternative perspective for analyzing algorithmic fidelity, complementing the approach used in silicon sampling. We demonstrate the use of distribution-based prediction in the context of recent United States presidential election, showing that this method can be used to determine task specific bias, prompt noise, and algorithmic fidelity. This approach has significant implications for assessing the reliability and increasing transparency of LLM-based predictions across various domains., Comment: 17 pages, 10 Figures, Pre-print

The rapid advances of multi-modal agents built on large foundation models have largely overlooked their potential for language-based communication between agents in collaborative tasks. This oversight presents a critical gap in understanding their effectiveness in real-world deployments, particularly when communicating with humans. Existing agentic benchmarks fail to address key aspects of inter-agent communication and collaboration, particularly in scenarios where agents have unequal access to information and must work together to achieve tasks beyond the scope of individual capabilities. To fill this gap, we introduce a novel benchmark designed to evaluate the collaborative performance of multimodal multi-agent systems through language communication. Our benchmark features a variety of scenarios, providing a comprehensive evaluation across four key categories of agentic capability in a communicative collaboration setting. By testing both agent-agent and agent-human collaborations using open-source and closed-source models, our findings reveal surprising weaknesses in state-of-the-art models, including proprietary models like GPT-4o. These models struggle to outperform even a simple random agent baseline in agent-agent collaboration and only surpass the random baseline when a human is involved.

We consider a general reaction--nonlinear-diffusion equation with a region of negative diffusivity, and show how a nonlinear regularisation selects a shock position. Negative diffusivity can model population aggregation, but leads to shock-fronted solutions for population density. In general the shock position is non-unique. Previous studies have defined shock selection criteria such as the equal area rule, and shown how these arise from specific regularisations to the reaction--diffusion equation. In this work, we show that a nonlinear regularisation leads to travelling wave solutions where the shock is selected according to a modified equal area rule. Adjusting the nonlinearity in the regularisation moves the shock location. We focus on attaining shocks that conserve diffusivity across the shock, and demonstrate that this condition yields the longest possible shock length. Using geometric singular perturbation theory, we prove the existence of shock-fronted travelling wave solutions with continuous diffusivity, show how to construct them, and demonstrate that they correspond to a unique wave speed. Numerical solutions align with theoretical predictions for shock position and wave speed, confirming that a single regularisation term can vary the shock position and attain shocks with continuous diffusivity., Comment: 31 pages, 14 figures

A graph $G$ is $k$-critical (list $k$-critical, DP $k$-critical) if $\chi(G)= k$ ($\chi_\ell(G)= k$, $\chi_\mathrm{DP}(G)= k$) and for every proper subgraph $G'$ of $G$, $\chi(G')\left(3 + \frac{1}{5} \right) \frac{n}{2}. $$ This is the first bound on $f_\mathrm{DP}(n,4)$ that is asymptotically better than the well-known bound $f(n,4)\geq \left(3 + \frac{1}{13} \right) \frac{n}{2}$ by Gallai from 1963. The result also yields a better bound on $f_{\ell}(n,4)$ than the one known before., Comment: 23 pages. arXiv admin note: substantial text overlap with arXiv:2409.00937

In this paper we explore the extent to which discretely self-similar (DSS) solutions to the 3D Navier-Stokes equations with rough data almost have the same asymptotics as DSS flows with smoother data. In a previous work, we established algebraic spatial decay rates for data in $L^q_{loc}(\mathbb{R}^3\setminus\{0\})$ for $q\in (3,\infty]$. The optimal rate occurs when $q=\infty$ and rates degrade as $q$ decreases. In this paper, we show that these solutions can be further decomposed into a term satisfying the optimal $q=\infty$ decay rate -- i.e.~have asymptotics like $(|x|+\sqrt t)^{-1}$ -- and a term with the $q<\infty$ decay rate multiplied by a prefactor which can be taken to be arbitrarily small. This smallness property is new and implies the $q<\infty$ asymptotics should be understood in a little-o sense. The decay rates in our previous work broke down when $q=3$, in which case spatial asymptotics have not been explored. The second result of this paper shows that DSS solutions with data in $L^3_{loc}(\mathbb{R}^3\setminus\{0\})$ can be expanded into a term satisfying the $(|x|+\sqrt t)^{-1}$ decay rate and a term that can be taken to be arbitrarily small in a scaling invariant class. A Besov space version of this result is also included., Comment: 30 pages

We provide a short proof of $L^3$-asymptotic stability around vector fields that are small in weak-$L^3$, including small Landau solutions. We show that asymptotic stability also holds for vector fields in the range of Lorentz spaces strictly between $L^3$ and weak-$L^3$, as well as in the closure of the test functions in weak-$L^3$. To provide a comprehensive perspective on the matter, we observe that asymptotic stability of Landau solutions does not generally extend to weak-$L^3$ via a counterexample., Comment: 13 pages

We present observations of wave steepening and signatures of shock formation during expansion of ultracold neutral plasmas formed with an initial density distribution that is centrally peaked and decays exponentially with distance. The plasma acceleration and velocity decrease at large distance from the plasma center, leading to central ions overtaking ions in the outer regions and the development of a steepening front that is narrow compared to the size of the plasma. The density and velocity change dramatically across the front, and significant heating of the ions is observed in the region of steepest gradients. For a reasonable estimate of electron temperature, the relative velocity of ions on either side of the front modestly exceeds the local sound speed (Mach number $M \gtrsim 1$). This indicates that by sculpting steep density gradients, it is possible to create the conditions for shock formation, or very close to it, opening a new avenue of research for ultracold neutral plasmas., Comment: 7 pages, 6 figures

A Reflective Intelligent Surface (RIS) consists of many small reflective elements whose reflection properties can be adjusted to change the wireless propagation environment. Envisioned implementations require that each RIS element be connected to a controller, and as the number of RIS elements on a surface may be on the order of hundreds or more, the number of required electrical connectors creates a difficult wiring problem, especially at high frequencies where the physical space between the elements is limited. A potential solution to this problem was previously proposed by the authors in which "biasing transmission lines" carrying standing waves are sampled at each RIS location to produce the desired bias voltage for each RIS element. This solution has the potential to substantially reduce the complexity of the RIS control. This paper presents models for the RIS elements that account for mutual coupling and realistic varactor characteristics, as well as circuit models for sampling the transmission line to generate the RIS control signals. For the latter case, the paper investigates two techniques for conversion of the transmission line standing wave voltage to the varactor bias voltage, namely an envelope detector and a sample-and-hold circuit. The paper also develops a modal decomposition approach for generating standing waves that are able to generate beams and nulls in the resulting RIS radiation pattern that maximize either the Signal-to-Noise Ratio (SNR) or the Signal-to-Leakage-plus-Noise Ratio (SLNR). Extensive simulation results are provided for the two techniques, together with a discussion of computational complexity., Comment: 20 pages, 25 figures, 2 tables

A graph $G$ is $k$-critical (list $k$-critical, DP $k$-critical) if $\chi(G)= k$ ($\chi_\ell(G)= k$, $\chi_\mathrm{DP}(G)= k$) and for every proper subgraph $G'$ of $G$, $\chi(G')\left(k - 1 + \left \lceil \frac{k^2 - 7}{2k-7} \right \rceil^{-1}\right)\frac{n}{2}.$$ This is the first bound on $f_\mathrm{DP}(n,k)$ that is asymptotically better than the well-known bound on $f(n,k)$ by Gallai from 1963. The result also yields a slightly better bound on $f_{\ell}(n,k)$ than the ones known before., Comment: 24 pages

Alon and Krivelevich conjectured that if $G$ is a bipartite graph of maximum degree $\Delta$, then the choosability (or list chromatic number) of $G$ satisfies $\chi_{\ell}(G) = O \left ( \log \Delta \right )$. Currently, the best known upper bound for $\chi_{\ell}(G)$ is $(1 + o(1)) \frac{\Delta}{\log \Delta}$, which also holds for the much larger class of triangle-free graphs. We prove that for $\varepsilon = 10^{-3}$, every bipartite graph $G$ of sufficiently large maximum degree $\Delta$ satisfies $\chi_{\ell}(G) < (\frac{4}{5} -\varepsilon) \frac{\Delta}{\log \Delta}$. This improved upper bound suggests that list coloring is fundamentally different for bipartite graphs than for triangle-free graphs and hence gives a step toward solving the conjecture of Alon and Krivelevich., Comment: 8 pages

Ramanujan's Master Theorem is a decades-old theorem in the theory of Mellin transforms which has wide applications in both mathematics and high energy physics. The unconventional method of Ramanujan in his proof of the theorem left convergence issues which were later settled by Hardy. Here we extend Ramanujan's theorem to meromorphic functions with poles of arbitrary order and observe that the new theorem produces analogues of Ramanujan's famous theorem. Moreover, we find that the theorem produces integral representations for meromorphic functions which are shown to satisfy interesting properties, opening up an avenue for further study., Comment: 25 pages

We consider the flexible list coloring problem, in which we have a graph $G$, a color list assignment $L:V(G) \rightarrow 2^{\mathbb N}$, and a set $U \subseteq V(G)$ of vertices such that each $u \in U$ has a preferred color $p(u) \in L(u)$. Given a constant $\varepsilon > 0$, the problem asks for an $L$-coloring of $G$ in which at least $\varepsilon |U|$ vertices in $U$ receive their preferred color. We use a method of reducible subgraphs to approach this problem. We develop a vertex-partitioning tool that, when used with a new reducible subgraph framework, allows us to define large reducible subgraphs. Using this new tool, we show that if $G$ has maximum average degree less than $\frac{11}{3}$, a list $L(v)$ of size $4$ at each $v \in V(G)$, and a set $U \subseteq V(G)$ of vertices with preferred colors, then there exists an $L$-coloring of $G$ for which at least $2^{-145} |U|$ vertices of $U$ receive their preferred color., Comment: 34 pages + appendix

We address a class of definite integrals known as Berndt-type integrals, highlighting their role as specialized instances within the integral representation framework of the Barnes-zeta function. Building upon the foundational insights of Xu and Zhao, who adeptly evaluate these integrals using rational linear combinations of Lambert-type series and derive closed-form expressions involving products of $\Gamma^4(1/4)$ and $\pi^{-1}$, we uncover direct evaluations of the Barnes-zeta function. Moreover, our inquiry leads us to establish connections between Berndt-type integrals and Jacobi elliptic functions, as well as moment polynomials investigated by Lomont and Brillhart, a relationship elucidated through the seminal contributions of Kuznetsov. In this manner, we extend and integrate these diverse mathematical threads, unveiling deeper insights into the intrinsic connections and broader implications of Berndt-type integrals in special function and integration theory., Comment: 27 pages, 1 table

The 2nd SNMMI Artificial Intelligence (AI) Summit, organized by the SNMMI AI Task Force, took place in Bethesda, MD, on February 29 - March 1, 2024. Bringing together various community members and stakeholders, and following up on a prior successful 2022 AI Summit, the summit theme was: AI in Action. Six key topics included (i) an overview of prior and ongoing efforts by the AI task force, (ii) emerging needs and tools for computational nuclear oncology, (iii) new frontiers in large language and generative models, (iv) defining the value proposition for the use of AI in nuclear medicine, (v) open science including efforts for data and model repositories, and (vi) issues of reimbursement and funding. The primary efforts, findings, challenges, and next steps are summarized in this manuscript.

A visual-language model (VLM) pre-trained on natural images and text pairs poses a significant barrier when applied to medical contexts due to domain shift. Yet, adapting or fine-tuning these VLMs for medical use presents considerable hurdles, including domain misalignment, limited access to extensive datasets, and high-class imbalances. Hence, there is a pressing need for strategies to effectively adapt these VLMs to the medical domain, as such adaptations would prove immensely valuable in healthcare applications. In this study, we propose a framework designed to adeptly tailor VLMs to the medical domain, employing selective sampling and hard-negative mining techniques for enhanced performance in retrieval tasks. We validate the efficacy of our proposed approach by implementing it across two distinct VLMs: the in-domain VLM (MedCLIP) and out-of-domain VLMs (ALBEF). We assess the performance of these models both in their original off-the-shelf state and after undergoing our proposed training strategies, using two extensive datasets containing mammograms and their corresponding reports. Our evaluation spans zero-shot, few-shot, and supervised scenarios. Through our approach, we observe a notable enhancement in Recall@K performance for the image-text retrieval task.

The study examines the heating profile of hot solar transition region loops, particularly focusing on transient brightenings observed in IRIS 1400{\AA} slit-jaw images. The findings challenge the adequacy of simplistic, singular heating mechanisms, revealing that the heating is temporally impulsive and requires a spatially complex profile with multiple heating scales. A forward modeling code is utilized to generate synthetic IRIS emission spectra of these loops based on HYDRAD output, confirming that emitting ions are out of equilibrium. The modeling further indicates that density-dependent dielectronic recombination rates must be included to reproduce the observed line ratios. Collectively, this evidence substantiates that the loops are subject to impulsive heating and that the components of the transiently brightened plasma are driven far from thermal equilibrium. Heating events such as these are ubiquitous in the transition region and the analysis described above provides a robust observational diagnostic tool for characterizing the plasma., Comment: 11 Pages, 4 Figures, 3 Tables

This paper considers the existence of short synchronizing words in deterministic finite automata (DFAs). In particular, we define a general strategy, which we call the \emph{cornering strategy}, for generating short synchronizing words in well-structured DFAs. We show that a DFA is synchronizable if and only if this strategy can be applied. Using the cornering strategy, we prove that all DFAs consisting of $n$ points in $\mathbb{R}^d$ with bidirectional connected edge sets in which each edge $(\mb x, \mb y)$ is labeled $\mb y - \mb x$ are synchronizable. We also give sufficient conditions for such DFAs to have synchronizing words of length at most $(n-1)^2$ and thereby satisfy \v{C}ern\'y's conjecture. Using similar ideas, we generalise a result of Ananichev and Volkov \cite{ananichev2004synchronizing} from monotonic automata to a wider class of DFAs admitting well-behaved partial orders. Finally, we consider how the cornering strategy can be applied to the problem of simultaneously synchronizing a DFA $G$ to an initial state $u$ and a DFA $H$ to an initial state $v$. We do not assume that DFAs $G$ and $H$ or states $u$ and $v$ are related beyond sharing the same edge labels., Comment: 17 pages, 6 figures

$\textbf{Purpose}$: Automatic quantification of longitudinal changes in PET scans for lymphoma patients has proven challenging, as residual disease in interim-therapy scans is often subtle and difficult to detect. Our goal was to develop a longitudinally-aware segmentation network (LAS-Net) that can quantify serial PET/CT images for pediatric Hodgkin lymphoma patients. $\textbf{Materials and Methods}$: This retrospective study included baseline (PET1) and interim (PET2) PET/CT images from 297 patients enrolled in two Children's Oncology Group clinical trials (AHOD1331 and AHOD0831). LAS-Net incorporates longitudinal cross-attention, allowing relevant features from PET1 to inform the analysis of PET2. Model performance was evaluated using Dice coefficients for PET1 and detection F1 scores for PET2. Additionally, we extracted and compared quantitative PET metrics, including metabolic tumor volume (MTV) and total lesion glycolysis (TLG) in PET1, as well as qPET and $\Delta$SUVmax in PET2, against physician measurements. We quantified their agreement using Spearman's $\rho$ correlations and employed bootstrap resampling for statistical analysis. $\textbf{Results}$: LAS-Net detected residual lymphoma in PET2 with an F1 score of 0.606 (precision/recall: 0.615/0.600), outperforming all comparator methods (P<0.01). For baseline segmentation, LAS-Net achieved a mean Dice score of 0.772. In PET quantification, LAS-Net's measurements of qPET, $\Delta$SUVmax, MTV and TLG were strongly correlated with physician measurements, with Spearman's $\rho$ of 0.78, 0.80, 0.93 and 0.96, respectively. The performance remained high, with a slight decrease, in an external testing cohort. $\textbf{Conclusion}$: LAS-Net demonstrated significant improvements in quantifying PET metrics across serial scans, highlighting the value of longitudinal awareness in evaluating multi-time-point imaging datasets., Comment: There are 6 figures and 4 tables in the main text. The supplementary material is appended to the main text

The widely popular transformer network popularized by the generative pre-trained transformer (GPT) has a large field of applicability, including predicting text and images, classification, and even predicting solutions to the dynamics of physical systems. In the latter context, the continuous analog of the self-attention mechanism at the heart of transformer networks has been applied to learning the solutions of partial differential equations and reveals a convolution kernel nature that can be exploited by the Fourier transform. It is well known that many quantum algorithms that have provably demonstrated a speedup over classical algorithms utilize the quantum Fourier transform. In this work, we explore quantum circuits that can efficiently express a self-attention mechanism through the perspective of kernel-based operator learning. In this perspective, we are able to represent deep layers of a vision transformer network using simple gate operations and a set of multi-dimensional quantum Fourier transforms. We analyze the computational and parameter complexity of our novel variational quantum circuit, which we call Self-Attention Sequential Quantum Transformer Channel (SASQuaTCh), and demonstrate its utility on simplified classification problems., Comment: 11 pages, 4 figures

The paintability of a graph is a coloring parameter defined in terms of an online list coloring game. In this paper we ask, what is the paintability of a graph $G$ of maximum degree $\Delta$ and chromatic number $r$? By considering the Alon-Tarsi number of $G$, we prove that the paintability of $G$ is at most $\left(1 - \frac{1}{4r+1} \right ) \Delta + 2$. We also consider the DP-paintability of $G$, which is defined in terms of an online DP-coloring game. By considering the strict type $3$ degeneracy parameter recently introduced by Zhou, Zhu, and Zhu, we show that when $r$ is fixed and $\Delta$ is sufficiently large, the DP-paintability of $G$ is at most $\Delta - \Omega( \sqrt{\Delta \log \Delta})$., Comment: 13 pages, a terminology error was corrected

Mechanistic understanding of organic reactions can facilitate reaction development, impurity prediction, and in principle, reaction discovery. While several machine learning models have sought to address the task of predicting reaction products, their extension to predicting reaction mechanisms has been impeded by the lack of a corresponding mechanistic dataset. In this study, we construct such a dataset by imputing intermediates between experimentally reported reactants and products using expert reaction templates and train several machine learning models on the resulting dataset of 5,184,184 elementary steps. We explore the performance and capabilities of these models, focusing on their ability to predict reaction pathways and recapitulate the roles of catalysts and reagents. Additionally, we demonstrate the potential of mechanistic models in predicting impurities, often overlooked by conventional models. We conclude by evaluating the generalizability of mechanistic models to new reaction types, revealing challenges related to dataset diversity, consecutive predictions, and violations of atom conservation., Comment: 105 pages, 9 figures

Recent observations of reflected propagating and standing slow-mode waves in hot flaring coronal loops have spurred our investigation into their underlying excitation and damping mechanisms. To understand these processes, we conduct 2.5D magnetohydrodynamic (MHD) simulations using an arcade active region model that includes a hot and dense loop. Our simulations allow for in-depth parametric investigations complementing and expanding our previous 3D MHD modeling results. We excite these waves in two distinct models as motivated by observations from the SDO/AIA. Model 1 incorporates classical compressive viscosity coefficient, while Model 2 adopts a 10-times enhanced viscosity coefficient. We find that: (1) Our 2.5D MHD simulations reinforce previous conclusions derived from 1D and 3D MHD models that significantly enhanced viscosity is crucial for the rapid excitation of standing slow waves with damping times consistent with observations by Wang et al. (2015). (2) We uncover that nonlinearity in Model 1 delays the conversion of a reflected propagating wave into a standing wave. In contrast, Model 2 exhibits a much weak influence of nonlinearity. (3) Our results reveal that the transverse temperature structure holds more influence on wave behavior than the density structure. In Model 1, increased loop temperature contrast significantly enhances wave trapping within the structure, mitigating the impact of temperature-dependent viscous damping. Conversely, in Model 2, the impact of temperature structure on wave behavior weakens in comparison to the effect of viscosity. (4) Model 1 displays evident nonlinear coupling to the fast and kink magnetoacoustic waves and pronounced wave leakage into the corona. However, analyzing three observed wave events by SDO/AIA aligns with Model 2 predictions, providing further support for the substantial viscosity increase., Comment: 44 pages, 19 figures, 3 tables, accepted for publication in Solar Physics

Nanoflares are thought to be one of the prime candidates that can heat the solar corona to its multi-million kelvin temperature. Individual nanoflares are difficult to detect with the present generation instruments, however their presence can be inferred by comparing simulated nanoflare-heated plasma emissions with the observed emission. Using HYDRAD coronal loop simulations, we model the emission from an X-ray bright point (XBP) observed by the Marshall Grazing Incidence X-ray Spectrometer (MaGIXS), along with nearest-available observations from the Atmospheric Imaging Assembly (AIA) onboard Solar Dynamics Observatory (SDO) and X-Ray Telescope (XRT) onboard Hinode observatory. The length and magnetic field strength of the coronal loops are derived from the linear-force-free extrapolation of the observed photospheric magnetogram by Helioseismic and Magnetic Imager (HMI) onboard SDO. Each loop is assumed to be heated by random nanoflares, whose magnitude and frequency are determined by the loop length and magnetic field strength. The simulation results are then compared and matched against the measured intensity from AIA, XRT, and MaGIXS. Our model results indicate the observed emissions from the XBP under study could be well matched by a distribution of nanoflares with average delay times 1500 s to 3000 s, which suggest that the heating is dominated by high-frequency events. Further, we demonstrate the high sensitivity of MaGIXS and XRT to diagnose the heating frequency using this method, while AIA passbands are found to be the least sensitive., Comment: Accepted for publication in the Astrophysical Journal (ApJ)

Recently, strong evidence has accumulated that some solutions to the Navier-Stokes equations in physically meaningful classes are not unique. The primary purpose of this paper is to establish necessary properties for the error of hypothetical non-unique Navier-Stokes flows under conditions motivated by the scaling of the equations. Our first set of results show that some scales are necessarily active -- comparable in norm to the full error -- as solutions separate. `Scale' is interpreted in several ways, namely via algebraic bounds, the Fourier transform and discrete volume elements. These results include a new type of uniqueness criteria which is stated in terms of the error. The second result is a conditional predictability criteria for the separation of small perturbations. An implication is that the error necessarily activates at larger scales as flows de-correlate. The last result says that the error of the hypothetical non-unique Leray-Hopf solutions of Jia and Sverak locally grows in a self-similar fashion. Consequently, within the Leray-Hopf class, energy can de-correlate at a rate which is faster than linear. This contrasts numerical work on predictability which identifies a linear rate. This discrepancy can likely be explained by the fact that non-uniqueness can be viewed as a perturbation of a singular flow., Comment: 23 pages

Blue large-amplitude pulsators (BLAPs) make up a rare class of hot pulsating stars with effective temperatures of $\approx$30,000 K and surface gravities of 4.0 - 5.0 dex (cgs). The evolutionary origin and current status of BLAPs is not well understood, largely based on a lack of spectroscopic observations and no available mass constraints. However, several theoretical models have been proposed that reproduce their observed properties, including studies that identify them as pulsating helium-core pre-white dwarfs (He-core pre-WDs). We present here follow-up high-speed photometry and phase-resolved spectroscopy of one of the original 14 BLAPs, OGLE-BLAP-009, discovered during the Optical Gravitational Lensing Experiment. We aim to explore its pulsation characteristics and determine stellar properties such as mass and radius in order to test the consistency of these results with He-core pre-WD models. Using the mean atmospheric parameters found using spectroscopy, we fit a spectral energy distribution to obtain a preliminary estimate of the radius, luminosity and mass by making use of the Gaia parallax. We then compare the consistency of these results to He-core pre-WD models generated using MESA, with predicted pulsation periods implemented using GYRE. We find that our mass constraints are in agreement with a low-mass He-core pre-WD of $\approx$0.30 M$_{\odot}$., Comment: Accepted for publication in MNRAS, 15 pages, 11 figures, 5 tables