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Field-induced superconductivity is a rare phenomenon where an applied magnetic field enhances or induces superconductivity. This fascinating effect arises from a complex interplay between magnetism and superconductivity, and it offers the tantalizing technological possibility of an infinite magnetoresistance superconducting spin valve. Here, we demonstrate field-induced superconductivity at a record-high temperature of T=9K in two samples of the ferromagnetic superconductor Eu(Fe$_{0.88}$Co$_{0.12}$)$_{2}$As$_{2}$. We combine tunable uniaxial stress and applied magnetic field to shift the temperature range of the zero-resistance state between 4K and 10K. We use x-ray diffraction and spectroscopy measurements under stress and field to demonstrate that stress tuning of the nematic order and field tuning of the ferromagnetism act as independent tuning knobs of the superconductivity. Finally, DFT calculations and analysis of the Eu dipole field reveal the electromagnetic mechanism of the field-induced superconductivity., Comment: Main text: 15 pages, 5 figures; Supplement: 15 pages, 10 supplementary figures

This work presents a machine learning approach to predict novel perovskite oxide materials in the Pr-Al-O and Pr-Sc-O compound families with the potential for photoluminescence applications. The predicted materials exhibit a large bandgap and high Debye temperature, and have remained unexplored thus far. The predicted compounds (Pr$_3$AlO$_6$, Pr$_4$Al$_2$O$_9$, Pr$_3$ScO$_6$ and Pr$_3$Sc$_5$O$_{12}$) are screened using machine learning approach, which are then confirmed by density functional theory calculations. The study includes the calculation of the bandgap and density of states to determine electronic properties, and the optical absorption and emission spectra to determine optical properties. Mechanical stability of the predicted compounds, as demonstrated by satisfying the Born-Huang criterion. By combining machine learning and density functional theory, this work offers a more efficient and comprehensive approach to materials discovery and design.

Establishing the fundamental chemical principles that govern molecular electronic quantum decoherence has remained an outstanding challenge. Fundamental questions such as how solvent and intramolecular vibrations or chemical functionalization contribute to the decoherence remain unanswered and are beyond the reach of state-of-the-art theoretical and experimental approaches. Here we address this challenge by developing a strategy to isolate electronic decoherence pathways for molecular chromophores immersed in condensed phase environments that enables elucidating how electronic quantum coherence is lost. For this, we first identify resonance Raman spectroscopy as a general experimental method to reconstruct molecular spectral densities with full chemical complexity at room temperature, in solvent, and for fluorescent and non-fluorescent molecules. We then show how to quantitatively capture the decoherence dynamics from the spectral density and identify decoherence pathways by decomposing the overall coherence loss into contributions due to individual molecular vibrations and solvent modes. We illustrate the utility of the strategy by analyzing the electronic decoherence pathways of the DNA base thymine in water. Its electronic coherences decay in ~ 30 fs. The early-time decoherence is determined by intramolecular vibrations while the overall decay by solvent. Chemical substitution of thymine modulates the decoherence with hydrogen-bond interactions of the thymine ring with water leading to the fastest decoherence. Increasing temperature leads to faster decoherence as it enhances the importance of solvent contributions but leaves the early-time decoherence dynamics intact. The developed strategy opens key opportunities to establish the connection between molecular structure and quantum decoherence as needed to develop chemical strategies to rationally modulate it., Comment: Main text 8 pages, 6 figures (Figures 5 and 6 have been changed) SI 9 pages, 5 figures, 6 tables

Respiratory sound contains crucial information for the early diagnosis of fatal lung diseases. Since the COVID-19 pandemic, there has been a growing interest in contact-free medical care based on electronic stethoscopes. To this end, cutting-edge deep learning models have been developed to diagnose lung diseases; however, it is still challenging due to the scarcity of medical data. In this study, we demonstrate that the pretrained model on large-scale visual and audio datasets can be generalized to the respiratory sound classification task. In addition, we introduce a straightforward Patch-Mix augmentation, which randomly mixes patches between different samples, with Audio Spectrogram Transformer (AST). We further propose a novel and effective Patch-Mix Contrastive Learning to distinguish the mixed representations in the latent space. Our method achieves state-of-the-art performance on the ICBHI dataset, outperforming the prior leading score by an improvement of 4.08%., Comment: INTERSPEECH 2023, Code URL: https://github.com/raymin0223/patch-mix_contrastive_learning

Infusing deep learning with structural engineering has received widespread attention for both forward problems (structural simulation) and inverse problems (structural health monitoring). Based on Fourier Neural Operator, this study proposes VINO (Vehicle-bridge Interaction Neural Operator) to serve as the digital twin of bridge structures. VINO learns mappings between structural response fields and damage fields. In this study, VBI-FE dataset was established by running parametric finite element (FE) simulations considering a random distribution of structural initial damage field. Subsequently, VBI-EXP dataset was produced by conducting an experimental study under four damage scenarios. After VINO was pre-trained by VBI-FE and fine-tuned by VBI-EXP from the bridge at the healthy state, the model achieved the following two improvements. First, forward VINO can predict structural responses from damage field inputs more accurately than the FE model. Second, inverse VINO can determine, localize, and quantify damages in all scenarios, suggesting the practicality of data-driven approaches., Comment: 20 pages, 10 figures, uses NJDapacite.sty

We inspect the microlensing data of the KMTNet survey collected during the 2018--2020 seasons in order to find lensing events produced by binaries with brown-dwarf companions. In order to pick out binary-lens events with candidate BD lens companions, we conduct systematic analyses of all anomalous lensing events observed during the seasons. By applying the selection criterion with mass ratio between the lens components of $0.03\lesssim q\lesssim 0.1$, we identify four binary-lens events with candidate BD companions, including KMT-2018-BLG-0321, KMT-2018-BLG-0885, KMT-2019-BLG-0297, and KMT-2019-BLG-0335. For the individual events, we present the interpretations of the lens systems and measure the observables that can constrain the physical lens parameters. The masses of the lens companions estimated from the Bayesian analyses based on the measured observables indicate that the probabilities for the lens companions to be in the brown-dwarf mass regime are high: 59\%, 68\%, 66\%, and 66\% for the four events respectively., Comment: 10 pages, 8 figures

Vision transformers (ViTs) that model an image as a sequence of partitioned patches have shown notable performance in diverse vision tasks. Because partitioning patches eliminates the image structure, to reflect the order of patches, ViTs utilize an explicit component called positional embedding. However, we claim that the use of positional embedding does not simply guarantee the order-awareness of ViT. To support this claim, we analyze the actual behavior of ViTs using an effective receptive field. We demonstrate that during training, ViT acquires an understanding of patch order from the positional embedding that is trained to be a specific pattern. Based on this observation, we propose explicitly adding a Gaussian attention bias that guides the positional embedding to have the corresponding pattern from the beginning of training. We evaluated the influence of Gaussian attention bias on the performance of ViTs in several image classification, object detection, and semantic segmentation experiments. The results showed that proposed method not only facilitates ViTs to understand images but also boosts their performance on various datasets, including ImageNet, COCO 2017, and ADE20K., Comment: 11 pages, 7 Figures

We present an extensive and well-characterized Chandra X-ray Galaxy Catalog (CGC) of 8557 galaxy candidates in the redshift range z ~ 0.04 - 0.7, optical luminosity 1010 - 1011 Lro, and X-ray luminosity (0.5-7 keV) LX = 2x1040 - 2x1043 erg s-1. We estimate ~5% false match fraction and contamination by QSOs. The CGC was extracted from the Chandra Source Catalog version 2 (CSC2) by cross-correlating with optical and IR all-sky survey data, including SDSS, PanSTARRS, DESI Legacy, and WISE. Our selection makes use of two main criteria that we have tested on the subsample with optical spectroscopical identification. (1) A joint selection based on X-ray luminosity (LX) and X-ray to optical flux ratio (FXO), which recovers 63% of the spectroscopically classified galaxies with a small contamination fraction (7%), a significant improvement over methods using LX or FXO alone (< 50% recovery). (2) A joint W1-W2 (W12) WISE color and LX selection that proves effective in excluding QSOs and improves our selection by recovering 72% of the spectroscopically classified galaxies and reducing the contamination fraction (4%). Of the CGC, 24% was selected by means of optical spectroscopy; 30% on the basis of LX, FXO, and W12; and 46% by using either the LX-FXO or the LX-W12 selection criteria. We have individually examined the data for galaxies with z < 0.1, which may include more than one CSC2 X-ray source, leading to the exclusion of 110 local galaxies. Our catalog also includes near-IR and UV data and galaxy morphological types., Comment: Accepted in ApJS, 37 pages, 11 figures; Minor revisions

X-ray bright optically normal galaxies (XBONGs) are galaxies with X-ray luminosities consistent with those of active galactic nuclei (AGNs) but no evidence of AGN optical emission lines. Crossmatching the Chandra Source Catalog version 2 (CSC2) with the Sloan Digital Sky Survey (SDSS) sample of spectroscopically classified galaxies, we have identified 817 XBONG candidates with LX > 1042 erg s-1 and X-ray to optical flux ratio FXO > 0.1. Comparisons with WISE colors and NIR, optical, UV, and radio luminosities show that the loci of XBONGs are in-between those of control samples of normal galaxies and quasars and are consistent with low-luminosity quasars. We find that 43% of the XBONG sample have X-ray colors suggesting NH > 1022 cm-2, double the fraction in the QSO sample, suggesting that a large fraction of XBONG are highly obscured AGNs. However, ~50% of the XBONGs are not obscured and have X-ray colors harder than those of normal galaxies. Some of these XBONGs have spatially extended X-ray emission. These characteristics suggest that they may be unidentified galaxy groups and clusters. Using the X-ray luminosity functions of QSOs and galaxies/groups/clusters, we estimate the approximate fraction of extended XBONGs to be < 20%. We also assess the approximate fraction of XBONGs whose AGN signatures are diluted by stellar light of host galaxies to be ~30%, based on their redshift and deviation from the extrapolation of the QSO LX-Lr relation., Comment: Accepted in ApJ. 33 pages, 17 figures; minor revisions

Nitrogen-doped lutetium hydride has recently been proposed as a near-ambient-conditions superconductor. Interestingly, the sample transforms from blue to pink to red as a function of pressure, but only the pink phase is claimed to be superconducting. Subsequent experimental studies have failed to reproduce the superconductivity, but have observed pressure-driven colour changes including blue, pink, red, violet, and orange. However, discrepancies exist among these experiments regarding the sequence and pressure at which these colour changes occur. Given the claimed relationship between colour and superconductivity, understanding colour changes in nitrogen-doped lutetium hydride may hold the key to clarifying the possible superconductivity in this compound. Here, we present a full microscopic theory of colour in lutetium hydride, revealing that hydrogen-deficient LuH$_2$ is the only phase which exhibits colour changes under pressure consistent with experimental reports, with a sequence blue-violet-pink-red-orange. The concentration of hydrogen vacancies controls the precise sequence and pressure of colour changes, rationalising seemingly contradictory experiments. Nitrogen doping also modifies the colour of LuH$_2$ but it plays a secondary role compared to hydrogen vacancies. Therefore, we propose hydrogen-deficient LuH$_2$ as the key phase for exploring the superconductivity claim in the lutetium-hydrogen system. Finally, we find no phonon-mediated superconductivity near room temperature in the pink phase., Comment: 3 figures + Supplementary Information, published version

We investigate how feedback and environment shapes the X-ray scaling relations of early-type galaxies (ETGs), especially at the low-mass end. We select central-ETGs from the IllustrisTNG-100 box that have stellar masses $\log_{10}(M_{\ast}/\mathrm{M_{\odot}})\in[10.7, 11.9]$. We derive mock X-ray luminosity ($L_{\mathrm{X, 500}}$) and spectroscopic-like temperature ($T_{\mathrm{sl, 500}}$) of hot gas within $R_{500}$ of the ETG haloes using the MOCK-X pipeline. The scaling between $L_{\mathrm{X, 500}}$ and the total mass within 5 effective radii ($M_{5R_{\rm e}}$) agrees well with observed ETGs from Chandra. IllustrisTNG reproduces the observed increase in scatter of $L_{\mathrm{X, 500}}$ towards lower masses, and we find that ETGs with $\log_{10} (M_{5R_{\rm e}}/\mathrm{M_{\odot}}) \leqslant 11.5$ with above-average $L_{\mathrm{X, 500}}$ experienced systematically lower cumulative kinetic AGN feedback energy historically (vice versa for below-average ETGs). This leads to larger gas mass fractions and younger stellar populations with stronger stellar feedback heating, concertedly resulting in the above-average $L_{\mathrm{X, 500}}$. The $L_{\mathrm{X, 500}}$--$T_{\mathrm{sl, 500}}$ relation shows a similar slope to the observed ETGs but the simulation systematically underestimates the gas temperature. Three outliers that lie far below the $L_{\rm X}$--$T_{\rm sl}$ relation all interacted with larger galaxy clusters recently and demonstrate clear features of environmental heating. We propose that the distinct location of these backsplash ETGs in the $L_{\rm X}$--$T_{\rm sl}$ plane could provide a new way of identifying backsplash galaxies in future X-ray surveys., Comment: 16 pages, 10 figures. Submitted to MNRAS

We propose a deep learning-based LiDAR odometry estimation method called LoRCoN-LO that utilizes the long-term recurrent convolutional network (LRCN) structure. The LRCN layer is a structure that can process spatial and temporal information at once by using both CNN and LSTM layers. This feature is suitable for predicting continuous robot movements as it uses point clouds that contain spatial information. Therefore, we built a LoRCoN-LO model using the LRCN layer, and predicted the pose of the robot through this model. For performance verification, we conducted experiments exploiting a public dataset (KITTI). The results of the experiment show that LoRCoN-LO displays accurate odometry prediction in the dataset. The code is available at https://github.com/donghwijung/LoRCoN-LO., Comment: 4 pages, ICEIC 2023

We study the impact of galaxy mergers on stellar population profiles/gradients of early-type galaxies (ETGs) using ETGs at $z<0.055$ in the Stripe 82 region of the Sloan Digital Sky Survey and MaNGA integral field unit spectroscopic data. Tidal features around ETGs, which are detected from deep coadded images, are regarded as direct observational evidence for recent mergers. We find that ETGs with tidal features have less negative metallicity gradients and more positive age gradients than ETGs without tidal features at $M_\mathrm{star}\gtrsim10^{10.6}M_\odot$. Moreover, when integrating all the resolved stellar populations, ETGs with tidal features have lower metallicities by $\sim0.07$ dex and younger ages by $\sim1$ - $2$ Gyr than ETGs without tidal features. Analyzing star formation histories, we discover that the mass fraction of young stellar populations with age $<5$ Gyr is higher in the central regions of ETGs with tidal features than in the same regions of the counterparts without tidal features. Compared to normal ETGs, ETGs with tidal features have a slow metal-enrichment history in the early universe, but they have been accelerating the metal enrichment through recently formed stars over the last few billion years. Many of our results can be explained if the effects of recently occurred mergers are different from those in the early universe, which are more likely to be rich in gas., Comment: 22 pages, 14 figures, 1 table, accepted for publication in the ApJ

We report the analysis of microlensing event OGLE-2017-BLG-1038, observed by the Optical Gravitational Lensing Experiment, Korean Microlensing Telescope Network, and Spitzer telescopes. The event is caused by a giant source star in the Galactic Bulge passing over a large resonant binary lens caustic. The availability of space-based data allows the full set of physical parameters to be calculated. However, there exists an eightfold degeneracy in the parallax measurement. The four best solutions correspond to very-low-mass binaries near ($M_1 = 170^{+40}_{-50} M_J$ and $M_2 = 110^{+20}_{-30} M_J$), or well below ($M_1 = 22.5^{+0.7}_{-0.4} M_J$ and $M_2 = 13.3^{+0.4}_{-0.3} M_J$) the boundary between stars and brown dwarfs. A conventional analysis, with scaled uncertainties for Spitzer data, implies a very-low-mass brown dwarf binary lens at a distance of 2 kpc. Compensating for systematic Spitzer errors using a Gaussian process model suggests that a higher mass M-dwarf binary at 6 kpc is equally likely. A Bayesian comparison based on a galactic model favors the larger-mass solutions. We demonstrate how this degeneracy can be resolved within the next ten years through infrared adaptive-optics imaging with a 40 m class telescope., Comment: 20 pages, 11 figures, 4 tables

For the stable optimization of deep neural networks, regularization methods such as dropout and batch normalization have been used in various tasks. Nevertheless, the correct position to apply dropout has rarely been discussed, and different positions have been employed depending on the practitioners. In this study, we investigate the correct position to apply dropout. We demonstrate that for a residual network with batch normalization, applying dropout at certain positions increases the performance, whereas applying dropout at other positions decreases the performance. Based on theoretical analysis, we provide the following guideline for the correct position to apply dropout: apply one dropout after the last batch normalization but before the last weight layer in the residual branch. We provide detailed theoretical explanations to support this claim and demonstrate them through module tests. In addition, we investigate the correct position of dropout in the head that produces the final prediction. Although the current consensus is to apply dropout after global average pooling, we prove that applying dropout before global average pooling leads to a more stable output. The proposed guidelines are validated through experiments using different datasets and models., Comment: 10 pages, 4 figures

We systematically inspect the microlensing data acquired by the KMTNet survey during the previous seasons in order to find anomalous lensing events for which the anomalies in the lensing light curves cannot be explained by the usual binary-lens or binary-source interpretations. From the inspection, we find that interpreting the three lensing events OGLE-2018-BLG-0584, KMT-2018-BLG-2119, and KMT-2021-BLG-1122 requires four-body (lens+source) models, in which either both the lens and source are binaries (2L2S event) or the lens is a triple system (3L1S event). Following the analyses of the 2L2S events presented in \citet{Han2023}, here we present the 3L1S analysis of the KMT-2021-BLG-1122. It is found that the lens of the event KMT-2021-BLG-1122 is composed of three masses, in which the projected separations (normalized to the angular Einstein radius) and mass ratios between the lens companions and the primary are $(s_2, q_2)\sim (1.4, 0.53)$ and $(s_3, q_3) \sim (1.6, 0.24)$. By conducting a Bayesian analysis, we estimate that the masses of the individual lens components are $(M_1, M_2, M_3)\sim (0.47\,M_\odot, 0.24\,M_\odot, 0.11\,M_\odot)$. The companions are separated in projection from the primary by $(a_{\perp,2}, a_{\perp,3})\sim (3.5, 4.0)$~AU. The lens of KMT-2018-BLG-2119 is the first triple stellar system detected via microlensing., Comment: 8 pages, 7 figures, 2 tables

Recently, various normalization layers have been proposed to stabilize the training of deep neural networks. Among them, group normalization is a generalization of layer normalization and instance normalization by allowing a degree of freedom in the number of groups it uses. However, to determine the optimal number of groups, trial-and-error-based hyperparameter tuning is required, and such experiments are time-consuming. In this study, we discuss a reasonable method for setting the number of groups. First, we find that the number of groups influences the gradient behavior of the group normalization layer. Based on this observation, we derive the ideal number of groups, which calibrates the gradient scale to facilitate gradient descent optimization. Our proposed number of groups is theoretically grounded, architecture-aware, and can provide a proper value in a layer-wise manner for all layers. The proposed method exhibited improved performance over existing methods in numerous neural network architectures, tasks, and datasets., Comment: 10 pages, 2 figures

We present the observations and analysis of a high-magnification microlensing planetary event, KMT-2022-BLG-0440, for which the weak and short-lived planetary signal was covered by both the KMTNet survey and follow-up observations. The binary-lens models with a central caustic provide the best fits, with a planet/host mass ratio, $q = 0.75$--$1.00 \times 10^{-4}$ at $1\sigma$. The binary-lens models with a resonant caustic and a brown-dwarf mass ratio are both excluded by $\Delta\chi^2 > 70$. The binary-source model can fit the anomaly well but is rejected by the ``color argument'' on the second source. From Bayesian analyses, it is estimated that the host star is likely a K or M dwarf located in the Galactic disk, the planet probably has a Neptune-mass, and the projected planet-host separation is $1.9^{+0.6}_{-0.7}$ or $4.6^{+1.4}_{-1.7}$ au, subject to the close/wide degeneracy. This is the third $q < 10^{-4}$ planet from a high-magnification planetary signal ($A \gtrsim 65$). Together with another such planet, KMT-2021-BLG-0171Lb, the ongoing follow-up program for the KMTNet high-magnification events has demonstrated its ability in detecting high-magnification planetary signals for $q < 10^{-4}$ planets, which are challenging for the current microlensing surveys., Comment: MNRAS accepted

We report on the observation of quantum criticality forming at the transition point between topological Anderson insulator phases in a one-dimensional photonic quantum walk with spin. The walker's probability distribution reveals a time-staggered profile of the dynamical spin-susceptibility, recently suggested as a smoking gun signature for topological Anderson criticality in the chiral symmetry class AIII. Controlled breaking of phase coherence removes the signal, revealing its origin in quantum coherence.

We have observed the z=4.3 protocluster SPT2349-56 with ATCA with the aim of detecting radio-loud active galactic nuclei (AGN) amongst the ~30 submillimeter galaxies identified in the structure. We detect the central complex of SMGs at 2.2\,GHz with a luminosity of L_2.2=(4.42pm0.56)x10^{25} W/Hz. The ASKAP also detects the source at 888 MHz, constraining the radio spectral index to alpha=-1.6pm0.3, consistent with ATCA non-detections at 5.5 and 9GHz, and implying L_1.4(rest)=(2.4pm0.3)x10^{26}W/Hz. This radio luminosity is about 100 times higher than expected from star formation, assuming the usual FIR-radio correlation, which is a clear indication of an AGN driven by a forming brightest cluster galaxy (BCG). None of the SMGs in SPT2349-56 show signs of AGN in any other diagnostics available to us (notably 12CO out to J=16, OH163um, CII/IR, and optical spectra), highlighting the radio continuum as a powerful probe of obscured AGN in high-z protoclusters. No other significant radio detections are found amongst the cluster members, consistent with the FIR-radio correlation. We compare these results to field samples of radio sources and SMGs, along with the 22 SPT-SMG gravitational lenses also observed in the ATCA program, as well as powerful radio galaxies at high redshifts. Our results allow us to better understand the effects of this gas-rich, overdense environment on early supermassive black hole (SMBH) growth and cluster feedback. We estimate that (3.3pm0.7)x10^{38} W of power are injected into the growing ICM by the radio-loud AGN, whose energy over 100Myr is comparable to the binding energy of the gas mass of the central halo. The AGN power is also comparable to the instantaneous energy injection from supernova feedback from the 23 catalogued SMGs in the core region of 120kpc projected radius. The SPT2349-56 radio-loud AGN may be providing strong feedback on a nascent ICM., Comment: 31 pages, submitted to ApJ, Dec17,2022

We conduct a systematic investigation of the microlensing data collected during the previous observation seasons for the purpose of reanalyzing anomalous lensing events with no suggested plausible models. We find that two anomalous lensing events OGLE-2018-BLG-0584 and KMT-2018-BLG-2119 cannot be explained with the usual models based on either a binary-lens single-source (2L1S) or a single-lens binary-source (1L2S) interpretation. We test the feasibility of explaining the light curves with more sophisticated models by adding an extra lens (3L1S model) or a source (2L2S model) component to the 2L1S lens-system configuration. We find that a 2L2S interpretation well explains the light curves of both events, for each of which there are a pair of solutions resulting from the close and wide degeneracy. For the event OGLE-2018-BLG-0584, the source is a binary composed of two K-type stars, and the lens is a binary composed of two M dwarfs. For KMT-2018-BLG-2119, the source is a binary composed of two dwarfs of G and K spectral types, and the lens is a binary composed of a low-mass M dwarf and a brown dwarf., Comment: 9 pages, 9 figures

Aside from graph neural networks (GNNs) attracting significant attention as a powerful framework revolutionizing graph representation learning, there has been an increasing demand for explaining GNN models. Although various explanation methods for GNNs have been developed, most studies have focused on instance-level explanations, which produce explanations tailored to a given graph instance. In our study, we propose Prototype-bAsed GNN-Explainer (PAGE), a novel model-level GNN explanation method that explains what the underlying GNN model has learned for graph classification by discovering human-interpretable prototype graphs. Our method produces explanations for a given class, thus being capable of offering more concise and comprehensive explanations than those of instance-level explanations. First, PAGE selects embeddings of class-discriminative input graphs on the graph-level embedding space after clustering them. Then, PAGE discovers a common subgraph pattern by iteratively searching for high matching node tuples using node-level embeddings via a prototype scoring function, thereby yielding a prototype graph as our explanation. Using six graph classification datasets, we demonstrate that PAGE qualitatively and quantitatively outperforms the state-of-the-art model-level explanation method. We also carry out systematic experimental studies by demonstrating the relationship between PAGE and instance-level explanation methods, the robustness of PAGE to input data scarce environments, and the computational efficiency of the proposed prototype scoring function in PAGE., Comment: 18 pages, 12 figures, 5 tables; to appear in the IEEE Transactions on Pattern Analysis and Machine Intelligence (Please cite our journal version that will appear in an upcoming issue. Its two-page extended summary was presented in the AAAI-22 Student Abstract and Poster Program.)