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It is fundamental in number theory to calculate lower bounds for height functions. Grizzard studied lower bounds for the Weil height in a relative setting. Vidaux and Videla introduced the Northcott number for a set $A\subset\bar{\mathbb{Q}}$. It bounds the Weil height on $A$ from below, outside the zero-height points and the finitely many small-height points. Pazuki, Technau, and Widmer introduced the weighted Weil heights. These heights generalize both the absolute and relative Weil heights. In this paper, we introduce a relative version of the Northcott number related to the weighted Weil height. We also give a field extension whose Northcott number equals a given positive number. The work is a relative version of the previous work of the author and Sano on the Northcott numbers for the weighted Weil heights., Comment: 12 pages

We study various conjectural dual descriptions of a stack of M2-branes in M-theory including ADHM, ABJ(M), BLG, discrete gauge theories and quiver Chern-Simons (CS) theories and propose several new dualities of the M2-brane SCFTs by analyzing flavored supersymmetric indices in detail. The mapping of local operators, Coulomb, Higgs and mixed branch operators as well as global symmetries under the dualities are obtained from the precise matching of the indices. Furthermore, we find closed form expressions for the Coulomb limit of the indices of the $U(N)$ ADHM theory and the dual quiver CS theory for arbitrary $N$ and propose a refined generating function for plane partitions with trace $N$. For the quiver CS theories we also find an infinite-sum expression for the Higgs limit of the indices which is more useful than the original expression., Comment: 126 pages, 5 figures, v2: published version in JHEP

Logical table-to-text generation is a task that involves generating logically faithful sentences from tables, which requires models to derive logical level facts from table records via logical inference. It raises a new challenge on the logical-level content planning of table-to-text models. However, directly learning the logical inference knowledge from table-text pairs is very difficult for neural models because of the ambiguity of natural language and the scarcity of parallel data. Hence even large-scale pre-trained language models present low logical fidelity on logical table-to-text. In this work, we propose a PLOG (Pretrained Logical Form Generator) framework to improve the generation fidelity. Specifically, PLOG is first pretrained on a table-to-logic-form generation (table-to-logic) task, then finetuned on downstream table-to-text tasks. The formal definition of logical forms enables us to collect large amount of accurate logical forms from tables without human annotation. In addition, PLOG can learn logical inference from table-logic pairs much more definitely than from table-text pairs. To evaluate our model, we further collect a controlled logical table-to-text dataset CONTLOG based on an existing dataset. On two benchmarks, LOGICNLG and CONTLOG, PLOG outperforms strong baselines by a large margin on the logical fidelity, demonstrating the effectiveness of table-to-logic pretraining., Comment: EMNLP'22

Different methods have been proposed to develop meta-embeddings from a given set of source embeddings. However, the source embeddings can contain unfair gender-related biases, and how these influence the meta-embeddings has not been studied yet. We study the gender bias in meta-embeddings created under three different settings: (1) meta-embedding multiple sources without performing any debiasing (Multi-Source No-Debiasing), (2) meta-embedding multiple sources debiased by a single method (Multi-Source Single-Debiasing), and (3) meta-embedding a single source debiased by different methods (Single-Source Multi-Debiasing). Our experimental results show that meta-embedding amplifies the gender biases compared to input source embeddings. We find that debiasing not only the sources but also their meta-embedding is needed to mitigate those biases. Moreover, we propose a novel debiasing method based on meta-embedding learning where we use multiple debiasing methods on a single source embedding and then create a single unbiased meta-embedding., Comment: Findings of EMNLP 2022

Morphology of nova ejecta is essential for fully understanding the physical processes involved in nova eruptions. We studied the 3D morphology of the expanding ejecta of the extremely slow nova V1280 Sco with a unique light curve. Synthetic line profile spectra were compared to the observed [O III] 4959, 5007 and [N II] 5755 emission line profiles in order to find the best-fit morphology, inclination angle, and maximum expansion velocity of the ejected shell. We derive the best fitting expansion velocity, inclination, and squeeze as $V_{\rm exp} = 2100^{+100}_{-100}$ \,km\,s$^{-1}$, $i = 80^{+1}_{-3}$ deg, and $squ = 1.0^{+0.0}_{-0.1}$ using [O III] line profiles, and $V_{\rm exp} = 1600^{+100}_{-100}$ \,km\,s$^{-1}$, $i = 81^{+2}_{-4}$ deg, and $squ = 1.0^{+0.0}_{-0.1}$ using [N II] 5755 line profile. A high inclination angle is consistent with the observational results showing multiple absorption lines originating from clumpy gases which are produced in dense and slow equatorially focused outflows. Based on additional observational features such as optical flares near the maximum light and dust formation on V1280 Sco, a model of internal shock interaction between slow ejecta and fast wind proposed for the $\gamma$-ray emission detected in other novae seems to be applicable to this extremely slow and peculiar nova. Increasing the sample size of novae whose morphology is studied will be helpful in addressing long-standing mysteries in novae such as the dominant energy source to power the optical light at the maximum, optical flares near the maximum, clumpiness of the ejecta, and dust formation., Comment: 21 pages, 8 figures, accepted for publication in ApJ

The layered perovskite Sr$_2$RuO$_4$ is a most intensively studied superconductor, but its pairing mechanism, which is often coupled intimately with magnetic fluctuations in correlated materials, is still an open question. Here we present a systematic evolution of the Seebeck coefficient in Co- and Mn-substituted Sr$_2$RuO$_4$ single crystals, in which ferromagnetic and antiferromagnetic glassy states respectively emerge in proximity to the superconducting phase of the parent compound. We find that the Seebeck coefficient $S$ divided by temperature $T$, $S/T$, shows a maximum near characteristic temperatures seen in the irreversible magnetization $M_{\rm ir}$ in both of the Co- and Mn-substituted crystals, demonstrating both of the ferromagnetic and antiferromagnetic fluctuations to enhance the Seebeck coefficient. Interestingly, $S/T$ increases with lowering temperature in the parent compound, reminiscent of non-Fermi-liquid behavior, indicating an essential role of coexisting ferromagnetic and antiferromagnetic fluctuations for the itinerant electrons in Sr$_2$RuO$_4$., Comment: 7 pages, 4 figures

Masked Language Models (MLMs) pre-trained by predicting masked tokens on large corpora have been used successfully in natural language processing tasks for a variety of languages. Unfortunately, it was reported that MLMs also learn discriminative biases regarding attributes such as gender and race. Because most studies have focused on MLMs in English, the bias of MLMs in other languages has rarely been investigated. Manual annotation of evaluation data for languages other than English has been challenging due to the cost and difficulty in recruiting annotators. Moreover, the existing bias evaluation methods require the stereotypical sentence pairs consisting of the same context with attribute words (e.g. He/She is a nurse). We propose Multilingual Bias Evaluation (MBE) score, to evaluate bias in various languages using only English attribute word lists and parallel corpora between the target language and English without requiring manually annotated data. We evaluated MLMs in eight languages using the MBE and confirmed that gender-related biases are encoded in MLMs for all those languages. We manually created datasets for gender bias in Japanese and Russian to evaluate the validity of the MBE. The results show that the bias scores reported by the MBE significantly correlates with that computed from the above manually created datasets and the existing English datasets for gender bias., Comment: NAACL 2022

We answer the question of Vidaux and Videla about the distribution of the Northcott numbers for the Weil height. We solve the same problem for the weighted Weil heights. These heights generalize both the absolute and relative Weil height. Our results also refine those of Pazuki, Technau, and Widmer., Comment: 16 pages

There is a correspondence between the protected local operators in the 3d SCFTs describing the geometry $\mathbb{C}^2$ probed by a stack of $N$ M2-branes and plane partitions of trace $N$. We give combinatorial expressions of the indices which count the local operators parametrizing $\mathbb{C}^2/\mathbb{Z}_k$ probed by $N$ M2-branes in the canonical and grand canonical ensembles in terms of generating functions for plane partitions. We derive the asymptotic behaviors of the grand potential in the high-temperature limit and the scaling dimension in the large $N$ limit., Comment: 30 pages, v3: published version in JHEP

Formality style transfer (FST) is a task that involves paraphrasing an informal sentence into a formal one without altering its meaning. To address the data-scarcity problem of existing parallel datasets, previous studies tend to adopt a cycle-reconstruction scheme to utilize additional unlabeled data, where the FST model mainly benefits from target-side unlabeled sentences. In this work, we propose a simple yet effective semi-supervised framework to better utilize source-side unlabeled sentences based on consistency training. Specifically, our approach augments pseudo-parallel data obtained from a source-side informal sentence by enforcing the model to generate similar outputs for its perturbed version. Moreover, we empirically examined the effects of various data perturbation methods and propose effective data filtering strategies to improve our framework. Experimental results on the GYAFC benchmark demonstrate that our approach can achieve state-of-the-art results, even with less than 40% of the parallel data., Comment: ACL 2022 main conference

Subword regularizations use multiple subword segmentations during training to improve the robustness of neural machine translation models. In previous subword regularizations, we use multiple segmentations in the training process but use only one segmentation in the inference. In this study, we propose an inference strategy to address this discrepancy. The proposed strategy approximates the marginalized likelihood by using multiple segmentations including the most plausible segmentation and several sampled segmentations. Because the proposed strategy aggregates predictions from several segmentations, we can regard it as a single model ensemble that does not require any additional cost for training. Experimental results show that the proposed strategy improves the performance of models trained with subword regularization in low-resource machine translation tasks., Comment: Findings of ACL 2022

Grammatical Error Correction (GEC) should not focus only on high accuracy of corrections but also on interpretability for language learning. However, existing neural-based GEC models mainly aim at improving accuracy, and their interpretability has not been explored. A promising approach for improving interpretability is an example-based method, which uses similar retrieved examples to generate corrections. In addition, examples are beneficial in language learning, helping learners understand the basis of grammatically incorrect/correct texts and improve their confidence in writing. Therefore, we hypothesize that incorporating an example-based method into GEC can improve interpretability as well as support language learners. In this study, we introduce an Example-Based GEC (EB-GEC) that presents examples to language learners as a basis for a correction result. The examples consist of pairs of correct and incorrect sentences similar to a given input and its predicted correction. Experiments demonstrate that the examples presented by EB-GEC help language learners decide to accept or refuse suggestions from the GEC output. Furthermore, the experiments also show that retrieved examples improve the accuracy of corrections., Comment: ACL 2022

The Cherenkov Telescope Array (CTA) is the next-generation ground-based very-high-energy gamma-ray observatory. The Large-Sized Telescope (LST) of CTA is designed to detect gamma rays between 20 GeV and a few TeV with a 23-meter diameter mirror. We have developed the focal plane camera of the first LST, which has 1855 photomultiplier tubes (PMTs) and the readout system which samples a PMT waveform at GHz with switched capacitor arrays, Domino Ring Sampler ver4 (DRS4). To measure the precise pulse charge and arrival time of Cherenkov signals, we developed a method to calibrate the output voltage of DRS4 and the sampling time interval, as well as an analysis method to correct the spike noise of DRS4. Since the first LST was inaugurated in 2018, we have performed the commissioning tests and calibrated the camera. We characterised the camera in terms of the charge pedestal under various conditions of the night sky background, the charge resolution of each pixel, the charge uniformity of the whole camera, and the time resolutions with a test pulse and calibration laser., Comment: 14 pages, 13 figures, Proceedings of the SPIE Astronomical Telescopes + Instrumentation, 114470H (2020)

We study the mechanism of the exceptionally large anomalous Hall effect (AHE) in the noncentrosymmetric antiferromagnet $\mathrm{Co}\mathrm{Nb}_3\mathrm{S}_6$ by angle-resolved photoemission spectroscopy (ARPES) and magnetotransport measurements. From ARPES measurements of $\mathrm{Co}\mathrm{Nb}_3\mathrm{S}_6$ and its family compounds ($\mathrm{Fe}\mathrm{Nb}_3\mathrm{S}_6$ and $\mathrm{Ni}\mathrm{Nb}_3\mathrm{S}_6$), we find a band dispersion unique to the Co intercalation existing near the Fermi level. We further demonstrate that a slight deficiency of sulfur in $\mathrm{Co}\mathrm{Nb}_3\mathrm{S}_6$ eliminates the ferromagnetism and the AHE simultaneously while hardly changing the band structure, indicating that the weak ferromagnetism is responsible for the emergence of the large AHE. Based on our results, we propose Weyl points near the Fermi level to cause the large AHE., Comment: 7+28 pages, 4+18 figures, Physical Review B accepted

A method for obtaining appropriate reaction coordinates is required to identify transition states distinguishing product and reactant in complex molecular systems. Recently, abundant research has been devoted to obtaining reaction coordinates using artificial neural networks from deep learning literature, where many collective variables are typically utilized in the input layer. However, it is difficult to explain the details of which collective variables contribute to the predicted reaction coordinates owing to the complexity of the nonlinear functions in deep neural networks. To overcome this limitation, we used Explainable Artificial Intelligence (XAI) methods of the Local Interpretable Model-agnostic Explanation (LIME) and the game theory-based framework known as Shapley Additive exPlanations (SHAP). We demonstrated that XAI enables us to obtain the degree of contribution of each collective variable to reaction coordinates that is determined by nonlinear regressions with deep learning for the committor of the alanine dipeptide isomerization in vacuum. In particular, both LIME and SHAP provide important features to the predicted reaction coordinates, which are characterized by appropriate dihedral angles consistent with those previously reported from the committor test analysis. The present study offers an AI-aided framework to explain the appropriate reaction coordinates, which acquires considerable significance when the number of degrees of freedom increases., Comment: 9 pages, 5 figures, 2 tables, to appear in J. Chem. Phys

We have measured the electrical resistivity and the thermopower of the electron-doped perovskite cobaltites LaCo$_{1-y}$Te$_y$O$_3$. In contrast to the hole-doped systems such as metallic ferromagnets La$_{1-x}M_x$CoO$_3$ ($M$ = Ca, Sr, Ba), the electron-doped samples show an insulating behavior even in a heavily doped range due to a spin-state blockade mechanism that an electron hopping from high-spin Co$^{2+}$ to low-spin Co$^{3+}$ site is energetically suppressed. We find that, despite the electron doping, the thermopower shows relatively large positive values above $y=0.05$, strikingly distinct from the hole-doped case where it comes close to zero with doping. This prominent electron-hole asymmetry seen in the thermopower originates from a bipolar conduction which consists of a slight amount of mobile holes and the main immobile electrons, demonstrating an impact of spin-state blockade on thermoelectric transport., Comment: 6 pages, 4 figures

We performed third-order electrical conductivity measurements on the organic conductor $\alpha$-(BEDT-TTF)$_2$I$_3$ using an ac bridge technique sensitive to nonlinear signals. Third-order conductance $G_3$ is clearly observed even at low electric fields, and interestingly, $G_3$ is critically enhanced above the charge-order transition temperature $T_{\rm CO}=136$~K. The observed frequency dependence of $G_3$ is incompatible with a percolation model, in which a Joule heating in a random resistor network is relevant to the nonlinear conduction. We instead argue the nonlinearity of the relaxation time according to a phenomenological model on the mobility in materials with large dielectric constants, and find that the third-order conductance $G_3$ corresponds to the third-order electric susceptibility $\chi_3$. Since the nonlinear susceptibility is known as a probe for higher-order multipole ordering, the present observation of the divergent behavior of $G_3$ above $T_{\rm CO}$ reveals an underlying quadrupole instability at the charge-order transition of the organic system., Comment: 5 pages, 3 figures

South and North Korea both use the Korean language. However, Korean NLP research has focused on South Korean only, and existing NLP systems of the Korean language, such as neural machine translation (NMT) models, cannot properly handle North Korean inputs. Training a model using North Korean data is the most straightforward approach to solving this problem, but there is insufficient data to train NMT models. In this study, we create data for North Korean NMT models using a comparable corpus. First, we manually create evaluation data for automatic alignment and machine translation. Then, we investigate automatic alignment methods suitable for North Korean. Finally, we verify that a model trained by North Korean bilingual data without human annotation can significantly boost North Korean translation accuracy compared to existing South Korean models in zero-shot settings., Comment: 8 pages, 1 figures, 8 tables

Neural models trained with large amount of parallel data have achieved impressive performance in abstractive summarization tasks. However, large-scale parallel corpora are expensive and challenging to construct. In this work, we introduce a low-cost and effective strategy, ExtraPhrase, to augment training data for abstractive summarization tasks. ExtraPhrase constructs pseudo training data in two steps: extractive summarization and paraphrasing. We extract major parts of an input text in the extractive summarization step, and obtain its diverse expressions with the paraphrasing step. Through experiments, we show that ExtraPhrase improves the performance of abstractive summarization tasks by more than 0.50 points in ROUGE scores compared to the setting without data augmentation. ExtraPhrase also outperforms existing methods such as back-translation and self-training. We also show that ExtraPhrase is significantly effective when the amount of genuine training data is remarkably small, i.e., a low-resource setting. Moreover, ExtraPhrase is more cost-efficient than the existing approaches.