Miracle-dz/UniFAR-FTUs huggingface dataset:
Integer Colorings with No Rainbow 3-Term Arithmetic Progression

In this paper, we study the rainbow Erdős-Rothschild problem with respect to 3-term arithmetic progressions. We obtain the asymptotic number of $r$-colorings of $[n]$ without rainbow 3-term arithmetic progressions, and we show that the typical colorings with this property are 2-colorings. We also prove that $[n]$ attains the maximum number of rainbow 3-term arithmetic progression-free $r$-colorings among all subsets of $[n]$. Moreover, the exact number of rainbow 3-term arithmetic progression-free $r$-colorings of $\mathbb{Z}_p$ is obtained, where $p$ is any prime and $\mathbb{Z}_p$ is the cyclic group of order $p$.
Stability analysis of a hyperbolic stochastic Galerkin formulation for the Aw-Rascle-Zhang model with relaxation

We investigate the propagation of uncertainties in the Aw-Rascle-Zhang model, which belongs to a class of second order traffic flow models described by a system of nonlinear hyperbolic equations. The stochastic quantities are expanded in terms of wavelet-based series expansions. Then, they are projected to obtain a deterministic system for the coefficients in the truncated series. Stochastic Galerkin formulations are presented in conservative form and for smooth solutions also in the corresponding non-conservative form. This allows to obtain stabilization results, when the system is relaxed to a first-order model. Computational tests illustrate the theoretical results.
Knowledge Hypergraph Embedding Meets Relational Algebra

Embedding-based methods for reasoning in knowledge hypergraphs learn a representation for each entity and relation. Current methods do not capture the procedural rules underlying the relations in the graph. We propose a simple embedding-based model called ReAlE that performs link prediction in knowledge hypergraphs (generalized knowledge graphs) and can represent high-level abstractions in terms of relational algebra operations. We show theoretically that ReAlE is fully expressive and provide proofs and empirical evidence that it can represent a large subset of the primitive relational algebra operations, namely renaming, projection, set union, selection, and set difference. We also verify experimentally that ReAlE outperforms state-of-the-art models in knowledge hypergraph completion, and in representing each of these primitive relational algebra operations. For the latter experiment, we generate a synthetic knowledge hypergraph, for which we design an algorithm based on the Erdos-R'enyi model for generating random graphs.
Grid Cell Path Integration For Movement-Based Visual Object Recognition

Grid cells enable the brain to model the physical space of the world and navigate effectively via path integration, updating self-position using information from self-movement. Recent proposals suggest that the brain might use similar mechanisms to understand the structure of objects in diverse sensory modalities, including vision. In machine vision, object recognition given a sequence of sensory samples of an image, such as saccades, is a challenging problem when the sequence does not follow a consistent, fixed pattern - yet this is something humans do naturally and effortlessly. We explore how grid cell-based path integration in a cortical network can support reliable recognition of objects given an arbitrary sequence of inputs. Our network (GridCellNet) uses grid cell computations to integrate visual information and make predictions based on movements. We use local Hebbian plasticity rules to learn rapidly from a handful of examples (few-shot learning), and consider the task of recognizing MNIST digits given only a sequence of image feature patches. We compare GridCellNet to k-Nearest Neighbour (k-NN) classifiers as well as recurrent neural networks (RNNs), both of which lack explicit mechanisms for handling arbitrary sequences of input samples. We show that GridCellNet can reliably perform classification, generalizing to both unseen examples and completely novel sequence trajectories. We further show that inference is often successful after sampling a fraction of the input space, enabling the predictive GridCellNet to reconstruct the rest of the image given just a few movements. We propose that dynamically moving agents with active sensors can use grid cell representations not only for navigation, but also for efficient recognition and feature prediction of seen objects.
Less is More: Pre-training a Strong Siamese Encoder Using a Weak Decoder

Many real-world applications use Siamese networks to efﬁciently match text sequences at scale, which require high-quality sequence encodings. This paper pre-trains language models dedicated to sequence matching in Siamese architectures. We ﬁrst hypothesize that a representation is better for sequence matching if the entire sequence can be reconstructed from it, which, however, is un-likely to be achieved in standard autoencoders: A strong decoder can rely on its capacity and natural language patterns to reconstruct and bypass the needs of better sequence encodings. Therefore we propose a new self-learning method that pre-trains the encoder with a weak decoder, which reconstructs the original sequence from the encoder’s [CLS] representations but is restricted in both capacity and attention span. In our experiments on web search and recommendation, the pre-trained SEED-Encoder, “SiamEsE oriented encoder by reconstructing from weak decoder”, shows signiﬁcantly better generalization ability when ﬁne-tuned in Siamese networks, improving overall accuracy and few-shot performances. Our code and models will be released.
Combinatorial optimization and reasoning with graph neural networks

Combinatorial optimization is a well-established area in operations research and computer science. Until recently, its methods have mostly focused on solving problem instances in isolation, ignoring the fact that they often stem from related data distributions in practice. However, recent years have seen a surge of interest in using machine learning, especially graph neural networks, as a key building block for combinatorial tasks, either directly as solvers or by enhancing the former. This paper presents a conceptual review of recent key advancements in this emerging field, aiming at researchers in both optimization and machine learning.
Dense and Warm Neutral Gas in BR 1202-0725 at z = 4.7 as Traced by the [O I] 145 μm Line

We report the detection of [O i] 145.5 μm in the BR 1202-0725 system, a compact group at z = 4.7 consisting of a quasar (QSO), a submillimeter-bright galaxy (SMG), and three faint Lyα emitters. By taking into account the previous detections and upper limits, the [O i] /[C ii] line ratios of the now five known high-z galaxies are higher than or on the high end of the observed values in local galaxies ([O i] /[C ii] ≳ 0.13). The high [O i] /[C ii] ratios and the joint analysis with previous detection of [N ii] lines for both of the QSO and the SMG suggest the presence of warm and dense neutral gas in these highly star-forming galaxies. This is further supported by new CO (12–11) line detections and a comparison with cosmological simulations. There is a possible positive correlation between the [N ii] 122/205 line ratio and the [O i] /[C ii] ratio when all local and high-z sources are taken into account, indicating that the denser the ionized gas, the denser and warmer the neutral gas (or vice versa). The detection of the [O i] line in the BR 1202-0725 system with a relatively short amount of integration with Atacama Large Millimeter/submillimeter Array (ALMA) demonstrates the great potential of this line as a dense gas tracer for high-z galaxies.
On the origin of GeV spectral break for Fermi blazars: 3C 454.3

The GeV break in spectra of the blazar 3C 454.3 is a special observation feature that has been discovered by the Fermi-LAT. The origin of the GeV break in the spectra is still under debate. In order to explore the possible source of GeV spectral break in 3C 454.3, a one-zone homogeneous leptonic jet model, as well as the McFit technique are utilized for fitting the quasi-simultaneous multi-waveband spectral energy distribution (SED) of 3C 454.3. The outside border of the broad-line region (BLR) and inner dust torus are chosen to contribute radiation in the model as external, seed photons to the external-Compton process, considering the observed W-ray radiation. The combination of two components, namely the Compton-scattered BLR and dust torus radiation, assuming a broken power-law distribution of emitted particles, provides a proper fitting to the multi-waveband SED of 3C 454.3 detected 2008 Aug 3 Sept 2 and explains the GeV spectral break. We propose that the spectral break of 3C 454.3 may originate from an inherent break in the energy distribution of the emitted particles and the Klein-Nishina effect. A comparison is performed between the energy density of the ‘external’ photon field for the whole BLR *BLR achieved via model fitting and that constrained from the BLR data. The distance from the position of the W-ray radiation area of 3C 454.3 to the central black hole could be constrained at ∼ 0.78pc (∼ 4.00'BLR, the size of the BLR).
Constraints on interacting dark energy model from lensed quasars: Relieving the H0 tension from 5.3σ to 1.7σ

Measurements for strong gravitational lensing time delays between multiple images of background quasars can provide an independent probe to explore the expansion history of the late-time universe. In this paper, we employ the new results of the time-delay (TD) measurements for six strong gravitational lens systems to constrain interacting dark energy (IDE) model. We mainly focus on the model of vacuum energy (with w = −1) interacting with cold dark matter, and consider four typical cases of the interaction form. Our main findings include: (i) the IDE models with Q ∝ ρde have an advantage in alleviating the H0 tension between the cosmic microwave background and TD observations; (ii) when the TD data are combined with the latest local distance-ladder result, the H0 tension can be alleviated from 5. 3σ (in the standard ΛCDM cosmology) to 1. 7σ in the IDE model with the interaction term Q = βHρde; (iii) the coupling parameter β in all the considered IDE models are preferred to be positive around 1σ range when the late-universe measurements (TD+SN) are used to perform constraint, implying a mild preference for the case of cold dark matter decaying into dark energy by the late-universe observations.
Can effective four-dimensional scalar theory be asymptotically free in a spacetime with extra dimensions?

We trace what happens with asymptotically free behavior of the running coupling in φ3 theory in six-dimensional spacetime, if to compactify two spatial dimensions on a 2D closed manifold. The result can be considered as an effective 4D theory of infinitely many KKtype scalar fields with triple interactions. The effective dimensional coupling constant inherits running to zero at high mass scales in a modified form depending on the size of the compact manifold. Some physical implications are discussed. Freedom is not worth having if it does not include the freedom to make mistakes. Mahatma Gandhi.
The Diverse Morphology, Stellar Population, and Black Hole Scaling Relations of the Host Galaxies of Nearby Quasars

We present rest-frame B and I imaging of 35 low-redshift ( ) Palomar–Green quasars using the Hubble Space Telescope Wide Field Camera 3. We perform multicomponent two-dimensional image decomposition to separate the host galaxy from its bright active nucleus, characterize its morphology, and measure its photometric properties. Special care is devoted to quantifying the structural parameters of the galaxy bulge, determining its B − I color, and estimating its stellar mass. Roughly half of the sample, comprising the less luminous ( ) but most high Eddington ratio quasars, reside in disk galaxies that are often barred and possess pseudo bulges. The large stellar masses, large effective radii, and faint surface brightnesses suggest that the host galaxies of the most luminous quasars are mostly ellipticals. Major mergers constitute only a small percentage (≲20%) of our sample. Our quasar sample roughly obeys the scaling relations between black hole mass and host galaxy (bulge, core, total) stellar mass. Hosts with black holes more massive than behave similarly to classical bulges and early-type galaxies, while those with less massive black holes, particularly the narrow-line Seyfert 1s, are consistent with pseudo bulges in late-type galaxies. The host galaxy bulges, irrespective of whether they are classical or pseudo, follow a relatively tight inverse relation between the effective radius and the mean effective surface brightness of inactive classical bulges and ellipticals. We argue that pseudo bulges experience recent or ongoing nuclear star formation.
Edinburgh Research Explorer A systematic review of natural language processing applied to radiology reports

Background: Natural language processing (NLP) has a signiﬁcant role in advancing healthcare and has been found to be key in extracting structured information from radiology reports. Understanding recent developments in NLP application to radiology is of signiﬁcance but recent reviews on this are limited. This study systematically assesses and quantiﬁes recent literature in NLP applied to radiology reports. Methods: We conduct an automated literature search yielding 4,836 results using automated ﬁltering, metadata enriching steps and citation search combined with manual review. Our analysis is based on 21 variables including radiology characteristics, NLP methodology, performance, study, and clinical application characteristics. Results: We present a comprehensive analysis of the 164 publications retrieved with publications in 2019 almost triple those in 2015. Each publication is categorised into one of 6 clinical application categories. Deep learning use increases in the period but conventional machine learning approaches are still prevalent. Deep learning remains challenged when data is scarce and there is little evidence of adoption into clinical practice. Despite 17% of studies reporting greater than 0.85 F1 scores, it is hard to comparatively evaluate these approaches given that most of them use diﬀerent datasets. Only 14 studies made their data and 15 their code available with 10 externally validating results. Conclusions: Automated understanding of clinical narratives of the radiology reports has the potential to enhance the healthcare process and we show that research in this ﬁeld continues to grow. Reproducibility and explainability of models are important if the domain is to move applications into clinical use. More could be done to share code enabling validation of methods on diﬀerent institutional data and to reduce heterogeneity in reporting of study properties allowing inter-study comparisons. Our results have signiﬁcance for researchers in the ﬁeld providing a systematic synthesis of existing work to build on, identify gaps, opportunities for collaboration and avoid duplication.
Optimal Spectrum Partitioning and Licensing in Tiered Access Under Stochastic Market Models

We consider the problem of partitioning a spectrum band into <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> channels of equal bandwidth, and then further assigning these <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> channels into <inline-formula> <tex-math notation="LaTeX">$P$ </tex-math></inline-formula> licensed channels and <inline-formula> <tex-math notation="LaTeX">$M-P$ </tex-math></inline-formula> unlicensed channels. Licensed channels can be accessed both for licensed and opportunistic use following a tiered structure that has a higher priority for licensed use. Unlicensed channels can be accessed only for opportunistic use. We address the following question in this paper. Given a market setup, what values of <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$P$ </tex-math></inline-formula> maximize the net spectrum utilization of the spectrum band? While this problem is fundamental, it is highly relevant practically, e.g., in the context of partitioning the recently proposed Citizens Broadband Radio Service band. If <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> is too high or too low, it may decrease spectrum utilization due to limited channel capacity or due to wastage of channel capacity, respectively. If <inline-formula> <tex-math notation="LaTeX">$P$ </tex-math></inline-formula> is too high (low), it will not incentivize the wireless operators who are primarily interested in unlicensed channels (licensed channels) to join the market. These tradeoffs are captured in our optimization problem which manifests itself as a two-stage Stackelberg game. We design an algorithm to solve the Stackelberg game and hence find the optimal <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$P$ </tex-math></inline-formula>. The algorithm design also involves an efficient Monte Carlo integrator to evaluate the expected value of the involved random variables like spectrum utilization and operators’ revenue. We also benchmark our algorithms using numerical simulations.
On adapting Nesterov's scheme to accelerate iterative methods for linear problems

Nesterov's well‐known scheme for accelerating gradient descent in convex optimization problems is adapted to accelerating stationary iterative solvers for linear systems. Compared with classical Krylov subspace acceleration methods, the proposed scheme requires more iterations, but it is trivial to implement and retains essentially the same computational cost as the unaccelerated method. An explicit formula for a fixed optimal parameter is derived in the case where the stationary iteration matrix has only real eigenvalues, based only on the smallest and largest eigenvalues. The fixed parameter and corresponding convergence factor are shown to maintain their optimality when the iteration matrix also has complex eigenvalues that are contained within an explicitly defined disk in the complex plane. A comparison to Chebyshev acceleration based on the same information of the smallest and largest real eigenvalues (dubbed restricted information Chebyshev acceleration) demonstrates that Nesterov's scheme is more robust in the sense that it remains optimal over a larger domain when the iteration matrix does have some complex eigenvalues. Numerical tests validate the efficiency of the proposed scheme. This work generalizes and extends the results of [14, lemmas 3.1 and 3.2 and theorem 3.3].
K2-138 g: Spitzer Spots a Sixth Planet for the Citizen Science System

K2 greatly extended Kepler’s ability to find new planets, but it was typically limited to identifying transiting planets with orbital periods below 40 days. While analyzing K2 data through the Exoplanet Explorers project, citizen scientists helped discover one super-Earth and four sub-Neptune sized planets in the relatively bright (V = 12.21, K = 10.3) K2-138 system, all which orbit near 3:2 mean-motion resonances. The K2 light curve showed two additional transit events consistent with a sixth planet. Using Spitzer photometry, we validate the sixth planet’s orbital period of 41.966 ± 0.006 days and measure a radius of , solidifying K2-138 as the K2 system with the most currently known planets. There is a sizeable gap between the outer two planets, since the fifth planet in the system, K2-138 f, orbits at 12.76 days. We explore the possibility of additional nontransiting planets in the gap between f and g. Due to the relative brightness of the K2-138 host star, and the near resonance of the inner planets, K2-138 could be a key benchmark system for both radial velocity and transit-timing variation mass measurements, and indeed radial velocity masses for the inner four planets have already been obtained. With its five sub-Neptunes and one super-Earth, the K2-138 system provides a unique test bed for comparative atmospheric studies of warm to temperate planets of similar size, dynamical studies of near-resonant planets, and models of planet formation and migration.
Implications of Abdominal Adipose Tissue Distribution on Nonalcoholic Fatty Liver Disease and Metabolic Syndrome: A Chinese General Population Study

INTRODUCTION: Visceral adipose tissue (VAT) has been found to play a critical role in the development of metabolic syndrome and nonalcoholic fatty liver disease (NAFLD) independent of generalized obesity. METHODS: In this secondary study of prospectively acquired data, 625 participants underwent magnetic resonance spectroscopy and chemical shift fat–water separation MRI (2-point Dixon) of the liver and whole abdomen, respectively, in a 3 Tesla magnet. Whole abdominal VAT and subcutaneous adipose tissue (SAT) were extracted from the 2-point Dixon image series using an automated method. Clinical/anthropometric/blood biochemistry parameters were measured. Using region-specific body mass index, participants were classified into 3 paired subgroups (lean, overweight, and obese) and presence of NAFLD (liver fat content ≥ 5.5%). RESULTS: All relevant clinical/anthropometric/blood biochemistry characteristics and liver enzymes were statistically significant between groups (P < 0.001). NAFLD was found in 12.1%, 43.8%, and 68.3% and metabolic syndrome in 51.1%, 61.9%, and 65% of the lean, overweight, and obese, respectively. Odds ratio for metabolic syndrome and NAFLD was increased by 2.73 (95% confidence interval [CI] 2.18–3.40) and 2.53 (95% CI 2.04–3.12), respectively, for 1SD increase in VAT volume while prevalence of metabolic syndrome was increased by 2.26 (95% CI 1.83–2.79) for 1SD increase in liver fat content (%). VAT/SAT ratio in the lean with fatty liver showed the highest ratio (0.54) among all the subgroups, without a significant difference between the lean and obese with NAFLD (P = 0.127). DISCUSSION: Increased VAT volume/disproportional distribution of VAT/SAT may be vital drivers to the development of metabolic syndrome and NAFLD irrespective of body mass index category.
Investigation of the Ligand Exchange Behavior of Square‐Planar Nickel(II) Complexes by X‐ray Absorption Spectroscopy and X‐ray Diffraction

The local structure of nickel and bromine in three square-planar nickel(II) complexes [(2,2′-bipyridyl)(bromo)(mesityl)nickel(II)] (1), [(bromo)(N,N-diisopropyl-1,2-ethanediimine)(mesityl)nickel(II)] (2), [(bromo)(mesityl)bis(triphenylphosphane)nickel(II) (3)] and their ligand exchange behavior towards several solvents has been determined by means of X-ray Absorption Near Edge Spectroscopy (XANES), Extended X-ray Absorption Fine Structure Spectroscopy (EXAFS), X-ray Diffraction (XRD), multinuclear NMR and UV/Vis spectroscopy. Several square-planar and octahedral nickel(II) complexes were prepared and spectroscopically characterized as reference compounds. The exchange behavior strongly depends on the nature of the incoming donor ligand (solvent molecule). In some cases the substitution of one or more ligands was accompanied by conservation of the square-planar geometry. In other solvents the geometry changed from square-planar to octahedral. The structural information obtained is important to the further development of such nickel(II) complexes as catalysts for various applications. (© Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2003)