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AniMAIRE (Anisotropic Model for Atmospheric Ionising Radiation Effects) is a new model and Python toolkit for calculating radiation dose rates experienced by aircraft during anisotropic solar energetic particle events. AniMAIRE expands the physics of the MAIRE+ model such that dose rate calculations can be performed for anisotropic solar energetic particle conditions by supplying a proton or alpha particle rigidity spectrum, a pitch angle distribution, and the conditions of Earth's magnetosphere. In this paper, we describe the algorithm and top-level structure of AniMAIRE and showcase AniMAIRE's capabilities by analysing the dose rate maps that AniMAIRE produces when the time-dependent spectra and pitch angle distribution for GLE71 are inputted. We find that the dose rates AniMAIRE produces for the event fall between the dose rates produced by the WASAVIES and CRAC:DOMO models. Dose rate maps that evolve throughout the event are also shown, and it is found that each peak in the inputted pitch angle distribution generates a dose rate hotspot in each of the polar regions. AniMAIRE has been made available openly online so that it can be downloaded and run freely on local machines and so that the space weather community can easily contribute to it using Github forking., Comment: 22 pages, 7 figures, manuscript submitted to Space Weather Journal. The previous version of this had the incorrect abstract and title, this has been fixed in this version

We discuss three proof evaluation activities meant to promote the acquisition of sociomathematical skills in an introductory undergraduate proof-writing course. Sociomathematical norms include meta-mathematical learning behaviors of professional mathematics, for example the ability to read and discuss mathematics critically, reach a consensus on correctness and clarity as a group, and verbalize what qualities ``good" proofs possess. The first of these activities involves peer review, the second focuses on evaluating the quality of internet resources, and the third emphasizes the progression of proof ideas and the brainstorm-sketch-revise process of professional mathematics. All three of the activities involve groupwork and meta-mathematical discussion questions to develop students' sociomathematical skills., Comment: 21 pages, plus appendices with original proof evaluation activities. Comments are welcome!

We describe our team's contribution to the STRICT-SMALL track of the BabyLM Challenge. The challenge requires training a language model from scratch using only a relatively small training dataset of ten million words. We experiment with three variants of cognitively-motivated curriculum learning and analyze their effect on the performance of the model on linguistic evaluation tasks. In the vocabulary curriculum, we analyze methods for constraining the vocabulary in the early stages of training to simulate cognitively more plausible learning curves. In the data curriculum experiments, we vary the order of the training instances based on i) infant-inspired expectations and ii) the learning behavior of the model. In the objective curriculum, we explore different variations of combining the conventional masked language modeling task with a more coarse-grained word class prediction task to reinforce linguistic generalization capabilities. Our results did not yield consistent improvements over our own non-curriculum learning baseline across a range of linguistic benchmarks; however, we do find marginal gains on select tasks. Our analysis highlights key takeaways for specific combinations of tasks and settings which benefit from our proposed curricula. We moreover determine that careful selection of model architecture, and training hyper-parameters yield substantial improvements over the default baselines provided by the BabyLM challenge.

Let $p$ be an odd prime and $R$ a $p$-torsion-free commutative $\mathbb{Z}_{(p)}$-algebra. We compute the periodic cyclic homology over $R$ of the universal differential graded algebra $R//p$ which is obtained from $R$ by universally killing $p$. We furthermore compute the cyclic and negative cyclic homologies of $R//p$ over $R$ in infinitely many degrees., Comment: 20 pages

The recent release of very large language models such as PaLM and GPT-4 has made an unprecedented impact in the popular media and public consciousness, giving rise to a mixture of excitement and fear as to their capabilities and potential uses, and shining a light on natural language processing research which had not previously received so much attention. The developments offer great promise for education technology, and in this paper we look specifically at the potential for incorporating large language models in AI-driven language teaching and assessment systems. We consider several research areas and also discuss the risks and ethical considerations surrounding generative AI in education technology for language learners. Overall we find that larger language models offer improvements over previous models in text generation, opening up routes toward content generation which had not previously been plausible. For text generation they must be prompted carefully and their outputs may need to be reshaped before they are ready for use. For automated grading and grammatical error correction, tasks whose progress is checked on well-known benchmarks, early investigations indicate that large language models on their own do not improve on state-of-the-art results according to standard evaluation metrics. For grading it appears that linguistic features established in the literature should still be used for best performance, and for error correction it may be that the models can offer alternative feedback styles which are not measured sensitively with existing methods. In all cases, there is work to be done to experiment with the inclusion of large language models in education technology for language learners, in order to properly understand and report on their capacities and limitations, and to ensure that foreseeable risks such as misinformation and harmful bias are mitigated., Comment: Accepted at the AIED2023 workshop: Empowering Education with LLMs - the Next-Gen Interface and Content Generation

A geometric interpretation of the vanishing of Milnor's higher order linking numbers remains an important open problem in the study of link concordance. In the 1990's, works of Cochran-Orr and Livingston exhibit a potential resolution to this problem in the form of homology boundary links. They exhibit the first known links with vanishing Milnor's invariants that are not concordant to boundary links. It remains unknown whether every link with vanishing Milnor's invariants is concordant to a homology boundary link. In this paper we present an obstruction to concordance to a homology boundary link and a potential path to the construction of links with vanishing Milnor's invariants which are not concordant to a homology boundary link. Our obstructions and examples fit into the language of the solvable filtration due to Cochran-Orr-Teichner. Along the way we demonstrate that every homology boundary link is equivalent to a boundary link modulo the 0.5 term of the solvable filtration, in contrast to the results of Cochran-Orr and Livingston. Finally we exhibit highly solvable homology boundary links that are not concordant to boundary links, pushing the work of Cochran-Orr and Livingston deep into the solvable filtration.

In a groundbreaking work A. Levine proved the surprising result that there exist knots in homology spheres which are not smoothly concordant to any knot in $S^3$, even if one allows for concordances in homology cobordisms. Since then subsequent works due to Hom-Levine-Lidman and Zhou have strengthened this result showing that there are many knots in homology spheres which are not smoothly concordant to knots in $S^3$. In this paper we present evidence that the opposite is true topologically. We study the Whitney tower filtration of concordance due to Cochran-Orr-Teichner and prove that modulo any term in this filtration every knot (or link) in a homology sphere is equivalent to a knot (or link) in $S^3$. As an application we recover the main result of [Davis2019], namely that the solvable filtration similarly fails to distinguish links in homology spheres from links in $S^3$., Comment: 16 pages, 10 Figures

The geographic structure of radiation dose rates at aircraft altitudes in Earth's atmosphere during the irradiation of Earth by proton spectra from incoming solar particle events is examined using the recently developed MAIRE+ software. Conditions are examined under two incoming proton spectra, a low/hard spectral index and a high/soft spectral index spectra, which are representative of some of the solar particle events that have caused reasonably sized Ground-Level Enhancements/Events (GLEs) over the past 70 years. It is found through the use of `cut-throughs' of the atmosphere, that the atmosphere can be divided into three volumes; a high dose rate polar region, a low dose rate equatorial region, and a transition region between the two. The location of these regions as a function of latitude, longitude and altitude is characterised. It is also found that the location of the transition region changes for different magnetospheric disturbance levels, implying that the total radiation dose rate an aircraft will experience if it passes through the transition region will be subject to large systematic uncertainties, particularly during the currently unknown levels of magnetospheric disturbance that a major solar event could cause. The impact that various magnetospheric conditions might have on dose rates that specific flight routes might experience is also discussed., Comment: 26 pages, 17 figures

Both active and passive magnetic shielding have been used extensively during past and current X-ray astronomy missions to shield detectors from soft protons and electrons entering through telescope optics. However, simulations performed throughout the past decade have discovered that a significant proportion of X-ray-like background originates from secondary electrons produced in spacecraft shielding surrounding X-ray detectors, which hit detectors isotropically from all directions. Here, the results from Geant4 simulations of a simple Helmholtz coil-like magnetic field surrounding a detector are presented, and it is found that a Helmholtz coil-like magnetic field is extremely effective at preventing secondary electrons from reaching the detector. This magnetic shielding method could remove almost all background associated with both backscattering electrons and fully absorbed soft electrons, which together are expected to account for approximately two thirds of the expected off-axis background in silicon-based X-ray detectors of several hundred microns in thickness. The magnetic field structure necessary for doing this could easily be produced using a set of solenoids or neodymium magnets providing that power requirements can be sufficiently optimised or neodymium fluorescence lines can be sufficiently attenuated, respectively., Comment: 20 pages, 6 figures

Targeted studies testing knowledge of subject-verb agreement (SVA) indicate that pre-trained language models encode syntactic information. We assert that if models robustly encode subject-verb agreement, they should be able to identify when agreement is correct and when it is incorrect. To that end, we propose grammatical error detection as a diagnostic probe to evaluate token-level contextual representations for their knowledge of SVA. We evaluate contextual representations at each layer from five pre-trained English language models: BERT, XLNet, GPT-2, RoBERTa, and ELECTRA. We leverage public annotated training data from both English second language learners and Wikipedia edits, and report results on manually crafted stimuli for subject-verb agreement. We find that masked language models linearly encode information relevant to the detection of SVA errors, while the autoregressive models perform on par with our baseline. However, we also observe a divergence in performance when probes are trained on different training sets, and when they are evaluated on different syntactic constructions, suggesting the information pertaining to SVA error detection is not robustly encoded., Comment: CoNLL 2022

In groundbreaking work from 2004, Cimasoni gave a geometric computation of the multivariable Conway potential function in terms of a generalization of a Seifert surface for a link called a C-complex. Lemma 3 of that paper provides a family of moves which relates any two C-complexes for a fixed link. This allows for an approach to studying links from the point of view of C-complexes and in following papers it has been used to derive invariants. This lemma is false. We present counterexamples, a correction with detailed proof, and an analysis of the consequences of this error on subsequent works that rely on this lemma., Comment: 18 pages, 14 figures

Contents Legislative Authority for the District of Columbia Retention of Congressional Authority Regular Local Lawmaking Process Council Mayor Congress Special Legislation Congressional Disapproval Process Introduction and Referral of a Joint [...]

We introduce a geometric operation, which we call the relative Whitney trick, that removes a single double point between properly immersed surfaces in a $4$-manifold with boundary. Using the relative Whitney trick we prove that every link in a homology sphere is homotopic to a link that is topologically slice in a contractible topological $4$-manifold. We further prove that any link in a homology sphere is order $k$ Whitney tower concordant to a link in $S^3$ for all $k$. Finally, we explore the minimum Gordian distance from a link in $S^3$ to a homotopically trivial link. Extending this notion to links in homology spheres, we use the relative Whitney trick to make explicit computations for 3-component links and establish bounds in general., Comment: Corrected a technical error in Section 2. Improved exposition throughout. To appear in Selecta Mathematica

Binary supermassive black holes (BSBHs) are expected to be a generic byproduct from hierarchical galaxy formation. The final coalescence of BSBHs is thought to be the loudest gravitational wave (GW) siren, yet no confirmed BSBH is known in the GW-dominated regime. While periodic quasars have been proposed as BSBH candidates, the physical origin of the periodicity has been largely uncertain. Here we report discovery of a periodicity (P=1607$\pm$7 days) at 99.95% significance (with a global p-value of ~$10^{-3}$ accounting for the look elsewhere effect) in the optical light curves of a redshift 1.53 quasar, SDSS J025214.67-002813.7. Combining archival Sloan Digital Sky Survey data with new, sensitive imaging from the Dark Energy Survey, the total ~20-yr time baseline spans ~4.6 cycles of the observed 4.4-yr (restframe 1.7-yr) periodicity. The light curves are best fit by a bursty model predicted by hydrodynamic simulations of circumbinary accretion disks. The periodicity is likely caused by accretion rate modulation by a milli-parsec BSBH emitting GWs, dynamically coupled to the circumbinary accretion disk. A bursty hydrodynamic variability model is statistically preferred over a smooth, sinusoidal model expected from relativistic Doppler boost, a kinematic effect proposed for PG1302-102. Furthermore, the frequency dependence of the variability amplitudes disfavors Doppler boost, lending independent support to the circumbinary accretion variability hypothesis. Given our detection rate of one BSBH candidate from circumbinary accretion variability out of 625 quasars, it suggests that future large, sensitive synoptic surveys such as the Vera C. Rubin Observatory Legacy Survey of Space and Time may be able to detect hundreds to thousands of candidate BSBHs from circumbinary accretion with direct implications for Laser Interferometer Space Antenna., Comment: Accepted to MNRAS, 17 pages, 9 figures

We show that in a prime, closed, oriented 3-manifold M, equivalent knots are isotopic if and only if the orientation preserving mapping class group is trivial. In the case of irreducible, closed, oriented $3$-manifolds we show the more general fact that every orientation preserving homeomorphism which preserves free homotopy classes of loops is isotopic to the identity. In the case of $S^1\times S^2$, we give infinitely many examples of knots whose isotopy classes are changed by the Gluck twist., Comment: 37 pages, 16 figures

Strong lenses are extremely useful probes of the distribution of matter on galaxy and cluster scales at cosmological distances, but are rare and difficult to find. The number of currently known lenses is on the order of 1,000. We wish to use crowdsourcing to carry out a lens search targeting massive galaxies selected from over 442 square degrees of photometric data from the Hyper Suprime-Cam (HSC) survey. We selected a sample of $\sim300,000$ galaxies with photometric redshifts in the range $0.2 < z_{phot} < 1.2$ and photometrically inferred stellar masses $\log{M_*} > 11.2$. We crowdsourced lens finding on this sample of galaxies on the Zooniverse platform, as part of the Space Warps project. The sample was complemented by a large set of simulated lenses and visually selected non-lenses, for training purposes. Nearly 6,000 citizen volunteers participated in the experiment. In parallel, we used YattaLens, an automated lens finding algorithm, to look for lenses in the same sample of galaxies. Based on a statistical analysis of classification data from the volunteers, we selected a sample of the most promising $\sim1,500$ candidates which we then visually inspected: half of them turned out to be possible (grade C) lenses or better. Including lenses found by YattaLens or serendipitously noticed in the discussion section of the Space Warps website, we were able to find 14 definite lenses, 129 probable lenses and 581 possible lenses. YattaLens found half the number of lenses discovered via crowdsourcing. Crowdsourcing is able to produce samples of lens candidates with high completeness and purity, compared to currently available automated algorithms. A hybrid approach, in which the visual inspection of samples of lens candidates pre-selected by discovery algorithms and/or coupled to machine learning is crowdsourced, will be a viable option for lens finding in the 2020s., Comment: Published version

Fix an odd prime $p$. The results in this paper are modeled after work of Hesselholt and Hesselholt-Madsen on the $p$-typical absolute de Rham-Witt complex in mixed characteristic. We have two primary results. The first is an exact sequence which describes the kernel of the restriction map on the de Rham-Witt complex over $A$, where $A$ is the ring of integers in an algebraic extension of $\mathbb{Q}_p$, or where $A$ is a $p$-torsion-free perfectoid ring. The second result is a description of the $p$-power torsion (and related objects) in the de Rham-Witt complex over $A$, where $A$ is a $p$-torsion-free perfectoid ring containing a compatible system of $p$-power roots of unity. Both of these results are analogous to results of Hesselholt and Madsen. Our main contribution is the extension of their results to certain perfectoid rings. We also provide algebraic proofs of these results, whereas the proofs of Hesselholt and Madsen used techniques from topology.

Robust atmospheric and radiative transfer modeling will be required to properly interpret reflected light and thermal emission spectra of terrestrial exoplanets. This will help break observational degeneracies between the numerous atmospheric, planetary, and stellar factors that drive planetary climate. Here we simulate the climates of Earth-like worlds around the Sun with increasingly slow rotation periods, from Earth-like to fully Sun-synchronous, using the ROCKE-3D general circulation model. We then provide these results as input to the Spectral Planet Model (SPM), which employs the SMART radiative transfer model to simulate the spectra of a planet as it would be observed from a future space-based telescope. We find that the primary observable effects of slowing planetary rotation rate are the altered cloud distributions, altitudes, and opacities which subsequently drive many changes to the spectra by altering the absorption band depths of biologically-relevant gas species (e.g., H2O, O2, and O3). We also identify a potentially diagnostic feature of synchronously rotating worlds in mid-infrared H2O absorption/emission lines., Comment: Accepted to The Astrophysical Journal

We construct links of arbitrarily many components each component of which is slice and yet are not concordant to any link with even one unknotted component. The only tool we use comes from the Alexander modules., Comment: 6 pages, 6 figures

January 24, 2024 The Congressional Review Act (CRA, 5 U.S.C. [section][section]801-808) is an oversight tool that Congress may use to consider a joint resolution overturning a rule issued by a [...]