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Given a uniform algebra A on a compact Hausdorff space X and a point x in X, denote by M_x the ideal of functions in A that vanish at x and by J_x the ideal of functions in A that vanish on a neighborhood of x. It is shown that for each integer m greater than or equal to 2, there exists a compact plane set K containing the origin such that in R(K) the closure of J_x contains M_x for every x in K minus {0} and the closure of J_0 contains M_0^m but does not contain M_0^{m-1}. This result establishes a recent conjecture of Alexander Izzo. For the proof we introduce a construction that could be described as taking square roots of Swiss cheeses.

The upcoming Vera C. Rubin Legacy Survey of Space and Time (LSST) will discover tens of thousands of astrophysical transients per night, far outpacing available spectroscopic follow-up capabilities. Carefully prioritising candidates for follow-up observations will maximise the scientific return from small telescopes with a single-object spectrograph. We introduce AAS2RTO, an astrophysical transient candidate prioritisation tool written in Python. AAS2RTO is flexible in that any number of criteria that consider observed properties of transients can be implemented. The visibility of candidates from a given observing site is also considered. The prioritised list of candidates provided by AAS2RTO is continually updated when new transient data are made available. Therefore, it can be applied to observing campaigns with a wide variety of scientific motivations. AAS2RTO uses a greedy algorithm to prioritise candidates. Candidates are represented by a single numerical value, or `score'. Scores are computed by constructing simple numerical factors which individually consider the competing facets of a candidate which make it suitable for follow-up observation. AAS2RTO is currently configured to work primarily with photometric data from the Zwicky Transient Facility (ZTF), distributed by certified LSST community brokers. We provide an example of how AAS2RTO can be used by defining a set of criteria to prioritise observations of type Ia supernovae (SNe Ia) close to peak brightness, in preparation for observations with the spectrograph at the Danish-1.54m telescope. Using a sample of archival alerts from ZTF, we evaluate the criteria we have designed to estimate the number of SNe Ia that we will be able to observe with a 1.5m telescope. Finally, we evaluate the performance of our criteria when applied to mock LSST observations of SNe Ia., Comment: 18 pages, 11 figures

We report precision mass measurements of $^{74-76}$Sr performed with the TITAN Multiple-Reflection Time-of-Flight Mass Spectrometer. This marks a first time mass measurement of $^{74}$Sr and gives increased mass precision to both $^{75}$Sr and $^{76}$Sr which were previously measured using storage ring and Penning trap methods, respectively. This completes the A = 74, T = 1 isospin triplet and gives increased precision to the A = 75, T = 1/2 isospin doublet which are both the heaviest experimentally evaluated triplets and doublets to date. The new data allow us to evaluate coefficients of the isobaric multiplet mass equation for the first time at A = 74, and with increased precision at A = 75. With increased precision of 75Sr, we confirm the recent measurement reported by CSRe which was used to remove a staggering anomaly in the doublets. New ab initio valence-space in-medium similarity renormalization group calculations of the T = 1 triplet are presented at A = 74. We also investigate the impact of the new mass data on the reaction flow of the rapid proton capture process in type I x-ray bursts using a single-zone model., Comment: 7 pages, 3 figures, 1 table

Direct observation of proton emission with very small emission energy is often unfeasible due to the long partial half-lives associated with tunneling through the Coulomb barrier. Therefore proton emitters with very small Q-values may require masses of both parent and daughter nuclei to establish them as proton unbound. Nuclear mass models have been used to predict the proton drip-line of the thulium (Tm) isotopic chain ($Z=69$), but up until now the proton separation energy has not been experimentally tested. Mass measurements were therefore performed using a Multiple Reflection Time-Of-Flight Mass Spectrometer (MR-TOF-MS) at TRIUMF's TITAN facility to definitively map the limit of proton-bound Tm. The masses of neutron-deficient, $^{149}$Tm and $^{150}$Tm, combined with measurements of $^{149m,g}$Er (which were found to deviate from literature by $\sim$150 keV), provide the first experimental confirmation that $^{149}$Tm is the first proton-unbound nuclide in the Tm chain. Our measurements also enable the strength of the $N=82$ neutron shell gap to be determined at the Tm proton drip-line, providing evidence supporting its continued existence.

Recently, a class of mechanical lattices with reconfigurable, zero-stiffness structures has been proposed, called Totimorphic structures. In this work, we introduce a computational framework that allows continuous reprogramming of a Totimorphic lattice's effective properties, such as mechanical and optical properties, via continuous geometric changes alone. Our approach is differentiable and guarantees valid Totimorphic lattice configurations throughout the optimisation process, thus providing not only specific configurations with desired properties but also trajectories through configuration space connecting them. It enables re-programmable structures where actuators are controlled via automatic differentiation on an objective-dependent cost function, altering the lattice structure at all times to achieve a given objective - which is interchangeable to achieve different functionalities. Our main interest lies in deep space applications where harsh, extreme, and resource-constrained environments demand solutions that offer flexibility, resource efficiency, and autonomy. We illustrate our framework through two proofs of concept: a re-programmable metamaterial as well as a space telescope mirror with adjustable focal length, both made from Totimorphic structures. The introduced framework is easily adjustable to a variety of Totimorphic designs and objectives, providing a light-weight model for endowing physical prototypes of Totimorphic structures with autonomous self-configuration and self-repair capabilities.

Referring Expression Comprehension (REC) aims to identify a particular object in a scene by a natural language expression, and is an important topic in visual language understanding. State-of-the-art methods for this task are based on deep learning, which generally requires expensive and manually labeled annotations. Some works tackle the problem with limited-supervision learning or relying on Large Vision and Language Models. However, the development of techniques to synthesize labeled data is overlooked. In this paper, we propose a novel framework that generates artificial data for the REC task, taking into account both textual and visual modalities. At first, our pipeline processes existing data to create variations in the annotations. Then, it generates an image using altered annotations as guidance. The result of this pipeline is a new dataset, called Harlequin, made by more than 1M queries. This approach eliminates manual data collection and annotation, enabling scalability and facilitating arbitrary complexity. We pre-train three REC models on Harlequin, then fine-tuned and evaluated on human-annotated datasets. Our experiments show that the pre-training on artificial data is beneficial for performance., Comment: Accepted to ICPR 2024