ShantanuT01/DACTYL-Pretraining huggingface dataset:
In 1989, Erd\H{o}s conjectured that for a sufficiently large $n$ it is impossible to place $n$ points in general position in a plane such that for every $1\le i \le n-1$ there is a distance that occurs exactly $i$ times. For small $n$ this is possible and in his paper he provided constructions for $n\leq 8$. The one for $n=5$ was due to Pomerance while Pal\'{a}sti came up with the constructions for $n=7,8$. Constructions for $n=9$ and above remain undiscovered, and little headway has been made toward a proof that for sufficiently large $n$ no configuration exists. In this paper we consider a natural generalization to higher dimensions and provide a construction which shows that for any given $n$ there exists a sufficiently large dimension $d$ such that there is a configuration in $d$-dimensional space meeting Erd\H{o}s' criteria.
We investigate model independent top-quark corrections to $\Delta F = 2$ processes for the down-type quarks within the framework of the Standard Model Effective Field Theory. Dimension-six $\Delta F = 1$ operators contribute to them through renormalization group evolutions and matching conditions. We provide a complete one-loop matching formula from the top quarks for $\Delta F=2$ transitions. We also demonstrate these corrections on $\Delta M_{B_s}$ in the left-right symmetric model, which are compared with the conventional calculation.
Let $f(z)=\sum_{n=1}^{\infty}a(n) e^{2\pi i nz}$ be a normalized Hecke eigenform in $S_{2k}^{\text{new}}(\Gamma_0(N))$ with integer Fourier coefficients. We prove that there exists a constant $C(f)>0$ such that any integer is a sum of at most $C(f)$ coefficients $a(n) $. It holds $C(f)\ll_{\varepsilon,k}N^{\frac{6k-3}{16}+\varepsilon}$.
It is well-known that the action of a quantum channel on a state can be represented, using an auxiliary space, as the partial trace of an associated bipartite state. Recently, it was observed that for the bipartite state associated with the optimal average input of the channel, the entanglement of formation is simply the entropy of the reduced density matrix minus the Holevo capacity. It is natural to ask if every bipartite state can be associated with some channel in this way. We show that the answer is negative.
(Context) In recent years, our understanding of the cool cores of galaxy clusters has changed. Once thought to be relatively simple places where gas cools and flows toward the centre, now they are believed to be very dynamic places where heating from the central Active Galactic Nucleus (AGN) and cooling, as inferred from active star formation, molecular gas, and Halpha nebulosity, find an uneasy energetic balance. (Aims) We want to characterize the X-ray properties of the nearby cool-core cluster Zw1742+3306, selected because it is bright at X-ray (with a flux greater than 1e-11 erg/s/cm2 in the 0.1-2.4 keV band) and Halpha wavelengths (Halpha luminosity > 1e40 erg/s). (Methods) We used Chandra data to analyze the spatial and spectral properties of the cool core of Zw1742+3306, a galaxy cluster at z=0.0757 that emits in Halpha and presents the brightest central galaxy located in a diffuse X-ray emission with multiple peaks in surface brightness. (Results) We show that the X-ray cool core of the galaxy cluster Zw1742+3306 is thermodynamically very active with evidence of cold fronts and a weak shock in the surface brightness map and of an apparently coherent, elongated structure with metallicity greater than the value measured in the surrounding ambient gas by about 50 per cent. This anisotropic structure is 280 x 90 kpc2 and is aligned with the cold fronts and with the X-ray emission on larger scales. We suggest that all these peculiarities in the X-ray emission of Zw1742+3306 are either a very fine-tuned output of a sloshing gas in the cluster core or the product of a metal-rich outflow from the central AGN.
RX J1914.4+2456 is a candidate double-degenerate binary (AM CVn) with a putative 569 s orbital period. If this identification is correct, then it has one of the shortest binary orbital periods known, and gravitational radiation should drive the orbital evolution and mass transfer if the binary is semi-detached. Here we report the results of a coherent timing study of the archival ROSAT and ASCA data for RX J1914.4+2456. We performed a phase coherent timing analysis using all five ROSAT observations spanning a 4.6 year period. We demonstrate that all the data can be phase connected, and we show evidence that the 1.756 mHz orbital frequency is increasing at a rate of 8 +- 3 e-18 Hz/s, consistent with the expected loss of angular momentum from the binary system via gravitational radiation. In addition to providing evidence for the emission of gravitational waves, our measurement of the orbital decay constrains models for the X-ray emission and the nature of the secondary. If stable mass accretion drives the X-ray flux, then orbital decay is inconsistent with a degenerate donor. A helium burning dwarf is compatible if indeed such systems can have periods as short as that of RX J1914.4+2456, an open theoretical question. Our measurement is consistent with the unipolar induction model of Wu et al. which does not require accretion to drive the X-ray flux. We discuss how future timing measurements of RX J1914.4+2456 (and systems like it) with for example, Chandra and XMM-Newton, can provide a unique probe of the interaction between mass loss and gravitational radiation. We also discuss the importance of such measurements in the context of gravitational wave detection from space, such as is expected in the future with the LISA mission.
In this paper, we propose a modified Density Matrix Renormalization Group (DMRG) algorithm to preferentially select minimum entropy states (minimally entangled states) in finite systems with asymptotic ground state degeneracy. The algorithm adds a "quench" process to the conventional DMRG method, which mimics the decoherence of physical systems, and collapses non-locally entangled states such as Schr\"odinger cats. We show that the method works for representative models with ground state degeneracy arising from either topological order or spontaneous discrete symmetry breaking. In the minimal entropy states thus obtained, properties associated with thermodynamic limit, such as topological entanglement entropy and magnetic order parameters, can be obtained directly and efficiently.
Poor modelling of the surface regions of solar-like stars causes a systematic discrepancy between the observed and model pulsation frequencies. We aim to characterise this frequency discrepancy for main sequence solar-like oscillators for a wide range of initial masses and metallicities. We fit stellar models to the observed mode frequencies of the 67 stars, including the Sun, in the $Kepler$ LEGACY sample, using three different empirical surface corrections. The three surface corrections we analyse are a frequency power-law, a cubic frequency term divided by the mode inertia, and a linear combination of an inverse and cubic frequency term divided by the mode inertia. We construct a grid of stellar evolution models using the stellar evolution code MESA and calculate mode frequencies using GYRE. We scale the frequencies of each stellar model by an empirical calculated homology coefficient, which greatly improves the robustness of our grid. We calculate stellar parameters and surface corrections for each star using the average of the best-fitting models from each evolutionary track, weighted by the likelihood of each model. The resulting model stellar parameters agree well with an independent reference, the $\texttt{BASTA}$ pipeline. However, we find that the adopted physics of the stellar models has a greater impact on the fitted stellar parameters than the choice of correction method. We find that scaling the frequencies by the mode inertia improves the fit between the models and observations. The inclusion of the inverse frequency term produces substantially better model fits to lower surface gravity stars.
Object cutout is a fundamental operation for image editing and manipulation, yet it is extremely challenging to automate it in real-world images, which typically contain considerable background clutter. In contrast to existing cutout methods, which are based mainly on low-level image analysis, we propose a more holistic approach, which considers the entire shape of the object of interest by leveraging higher-level image analysis and learnt global shape priors. Specifically, we leverage a deep neural network (DNN) trained for objects of a particular class (chairs) for realizing this mechanism. Given a rectangular image region, the DNN outputs a probability map (P-map) that indicates for each pixel inside the rectangle how likely it is to be contained inside an object from the class of interest. We show that the resulting P-maps may be used to evaluate how likely a rectangle proposal is to contain an instance of the class, and further process good proposals to produce an accurate object cutout mask. This amounts to an automatic end-to-end pipeline for catergory-specific object cutout. We evaluate our approach on segmentation benchmark datasets, and show that it significantly outperforms the state-of-the-art on them.
We study the shuttling instability in an array of three quantum dots the central one of which is movable. We extend the results by Armour and MacKinnon on this problem to a broader parameter regime. The results obtained by an efficient numerical method are interpreted directly using the Wigner distributions. We emphasize that the instability should be viewed as a crossover phenomenon rather than a clear-cut transition.
We study the possibility of generalising the Einstein--Straus model to anisotropic settings, by considering the matching of locally cylindrically symmetric static regions to the set of $G_4$ on $S_3$ locally rotationally symmetric (LRS) spacetimes. We show that such matchings preserving the symmetry are only possible for a restricted subset of the LRS models in which there is no evolution in one spacelike direction. These results are applied to spatially homogeneous (Bianchi) exteriors where the static part represents a finite bounded interior region without holes. We find that it is impossible to embed finite static strings or other locally cylindrically symmetric static objects (such as bottle or coin-shaped objects) in reasonable Bianchi cosmological models, irrespective of the matter content. Furthermore, we find that if the exterior spacetime is assumed to have a perfect fluid source satisfying the dominant energy condition, then only a very particular family of LRS stiff fluid solutions are compatible with this model.   Finally, given the interior/exterior duality in the matching procedure, our results have the interesting consequence that the Oppenheimer-Snyder model of collapse cannot be generalised to such anisotropic cases.
Using the Very Large Telescope's Spectrograph for INtegral Field Observation in the Near-Infrared (VLT/SINFONI), we have obtained repeated AO-assisted, NIR spectroscopy of the six central luminous, Wolf-Rayet (WR) stars in the core of the very young (~1 Myr), massive and dense cluster R136, in the Large Magellanic Cloud (LMC). We also de-archived available images that were obtained with the Hubble Space Telescope's Space Telescope Imaging Spectrograph (HST/STIS), and extracted high-quality, differential photometry of our target stars to check for any variability related to binary motion.   Previous studies, relying on spatially unresolved, integrated, optical spectroscopy, had reported that one of these stars was likely to be a 4.377-day binary. Our study set out to identify the culprit and any other short-period system among our targets. However, none displays significant photometric variability, and only one star, BAT99-112 (R136c), located on the outer fringe of R136, displays a marginal variability in its radial velocities; we tentatively report an 8.2-day period. The binary status of BAT99-112 is supported by the fact that it is one of the brightest X-ray sources among all known WR stars in the LMC, consistent with it being a colliding-wind system. Follow-up observations have been proposed to confirm the orbital period of this potentially very massive system.
We consider a system of independent one-dimensional random walks in a common random environment under the condition that the random walks are transient with positive speed $v_P$. We give upper bounds on the quenched probability that at least one of the random walks started in the interval $[An, Bn]$ has traveled a distance of less than $(v_P - \epsilon)n$. This leads to both a uniform law of large numbers and a hydrodynamic limit. We also identify a family of distributions on the configuration of particles (parameterized by particle density) which are stationary under the (quenched) dynamics of the random walks and show that these are the limiting distributions for the system when started from a certain natural collection of distributions.
We present the high angular resolution and high sensitivity images of the "Circum-Nuclear Disk (CND)" and its surrounding region of Milky Way Galaxy in the CS J=2-1, SiO v=0 J=2-1, H^13CO^+ J=1-0, C^34S J=2-1, and CH_3OH J_{K_a, K_c}=2_{1,1}-1_{1,0}A_{--} emission lines using ALMA. The CND is recognized as a torus-like molecular gas with gaps in these emission lines except for the CH_3OH emission line. The inner and outer radii of the CND are estimated to be R_in~1.5 and R_out~2 pc, respectively. The velocities of the rotation and radial motion are estimated to be V_rot~115 km s^-1 and V_rad~23 km s^-1, respectively. The LTE molecular gas mass is estimated to be M_LTE~3x10^4 Mo. We also found some anomalous molecular clouds in the surrounding region. One of the molecular clouds is positionally connected to a part of the CND adjacent to the "Western Arc". However, the cloud is seen to rotate in the opposite direction to the CND. The molecular cloud would be falling currently from the outer region to the CND and being disrupted by the tidal shear of Sagittarius A*(Sgr A*) because the velocity is not yet assimilated into that of the CND. Another molecular cloud is continuously connected to the tip of the "Eastern Arm (EA)". The velocity of this cloud is consistent with that of the ionized gas in the EA. These facts suggest that the molecular cloud is falling from the outer region to the vicinity of Sgr A*, being disrupted by the tidal shear, and ionized by strong UV emission from the Central Cluster because the impact parameter of the cloud is smaller than the first cloud. These falling clouds would play an important role in transferring material from the outer region to the CND and/or the vicinity of Sgr A*.
CONTEXT. The maximum size of the Galactic stellar disk is not yet known. Some studies have suggested an abrupt drop-off of the stellar density of the disk at Galactocentric distances $R\gtrsim 15$ kpc, which means that in practice no disk stars or only very few of them should be found beyond this limit. However, stars in the Milky Way plane are detected at larger distances. In addition to the halo component, star counts have placed the end of the disk beyond 20 kpc, although this has not been spectroscopically confirmed so far.   AIMS. Here, we aim to spectroscopically confirm the presence of the disk stars up to much larger distances.   METHODS. With data from the LAMOST and SDSS-APOGEE spectroscopic surveys, we statistically derived the maximum distance at which the metallicity distribution of stars in the Galactic plane is distinct from that of the halo populations.   RESULTS. Our analysis reveals the presence of disk stars at R>26 kpc (99.7% C.L.) and even at R>31 kpc (95.4% C.L.).
We propose a very fast and effective one-step restoring method for blurry face images. In the last decades, many blind deblurring algorithms have been proposed to restore latent sharp images. However, these algorithms run slowly because of involving two steps: kernel estimation and following non-blind deconvolution or latent image estimation. Also they cannot handle face images in small size. Our proposed method restores sharp face images directly in one step using Convolutional Neural Network. Unlike previous deep learning involved methods that can only handle a single blur kernel at one time, our network is trained on totally random and numerous training sample pairs to deal with the variances due to different blur kernels in practice. A smoothness regularization as well as a facial regularization are added to keep facial identity information which is the key to face image applications. Comprehensive experiments demonstrate that our proposed method can handle various blur kenels and achieve state-of-the-art results for small size blurry face images restoration. Moreover, the proposed method shows significant improvement in face recognition accuracy along with increasing running speed by more than 100 times.
Context: Solar eruptions, such as coronal mass ejections (CMEs), are often accompanied by accelerated electrons that can in turn emit radiation at radio wavelengths. This radiation is observed as solar radio bursts. The main types of bursts associated with CMEs are type II and type IV bursts that can sometimes show movement in the direction of the CME expansion, either radially or laterally. However, the propagation of radio bursts with respect to CMEs has only been studied for individual events. Aims: Here, we perform a statistical study of 64 moving bursts with the aim to determine how often CMEs are accompanied by moving radio bursts. This is done in order to ascertain the usefulness of using radio images in estimating the early CME expansion. Methods: Using radio imaging from the Na\c{c}ay Radioheliograph (NRH), we constructed a list of moving radio bursts, defined as bursts that move across the plane of sky at a single frequency. We define their association with CMEs and the properties of associated CMEs using white-light coronagraph observations. We also determine their connection to classical type II and type IV radio burst categorisation. Results: We find that just over a quarter of type II and half of type IV bursts that occurred during the NRH observing windows in Solar Cycle 24 are accompanied by moving radio emission. All but one of the moving radio bursts are associated with white--light CMEs and the majority of moving bursts (90%) are associated with wide CMEs (>60 degrees in width). In particular, all but one of the moving bursts corresponding to type IIs are associated with wide CMEs; however, and unexpectedly, the majority of type II moving bursts are associated with slow white-light CMEs (<500 km/s). On the other hand, the majority of moving type IV bursts are associated with fast CMEs (>500 km/s).
We present a novel generalized zero-shot algorithm to recognize perceived emotions from gestures. Our task is to map gestures to novel emotion categories not encountered in training. We introduce an adversarial, autoencoder-based representation learning that correlates 3D motion-captured gesture sequence with the vectorized representation of the natural-language perceived emotion terms using word2vec embeddings. The language-semantic embedding provides a representation of the emotion label space, and we leverage this underlying distribution to map the gesture-sequences to the appropriate categorical emotion labels. We train our method using a combination of gestures annotated with known emotion terms and gestures not annotated with any emotions. We evaluate our method on the MPI Emotional Body Expressions Database (EBEDB) and obtain an accuracy of $58.43\%$. This improves the performance of current state-of-the-art algorithms for generalized zero-shot learning by $25$--$27\%$ on the absolute.
This paper presents a new deep learning approach for video-based scene classification. We design a Heterogeneous Deep Discriminative Model (HDDM) whose parameters are initialized by performing an unsupervised pre-training in a layer-wise fashion using Gaussian Restricted Boltzmann Machines (GRBM). In order to avoid the redundancy of adjacent frames, we extract spatiotemporal variation patterns within frames and represent them sparsely using Sparse Cubic Symmetrical Pattern (SCSP). Then, a pre-initialized HDDM is separately trained using the videos of each class to learn class-specific models. According to the minimum reconstruction error from the learnt class-specific models, a weighted voting strategy is employed for the classification. The performance of the proposed method is extensively evaluated on two action recognition datasets; UCF101 and Hollywood II, and three dynamic texture and dynamic scene datasets; DynTex, YUPENN, and Maryland. The experimental results and comparisons against state-of-the-art methods demonstrate that the proposed method consistently achieves superior performance on all datasets.
It is proved that in order to obtain a model of the accelerated cosmic expansion the thing one only need to do is to add a perturbation term to the Einstein-Hilbert Lagrangian. This term leads to some symmetry breaking terms in the fields equation, which makes the cosmic expansion accelerating. A vacuum de Sitter solution is obtained. A new explanation of the acceleration of the cosmic expansion is presented. In this model the changing of the expansion from decelerating to accelerating is an intrinsic property of the universe without need of an exotic dark energy. The acceleration of the cosmic expansion is induced by the symmetry breaking perturbation of the gravitational energy. The cosmological constant problem, the coincidence problem and the problem of phantom divide line crossing are naturally solved. The results of the model are roughly consistent with the observations.
Apart from offering explanations not only for the distinctive fermion mass and mixing patterns but also for the actual values of the mass and mixing parameters, the dual colour solution to the generation puzzle gives numerous detailed predictions ranging from rare FCNC meson decays and $\mu$-$e$ conversions in nuclei at low energies to cosmic ray air showers with energies beyond $10^{20}$ eV at the extreme end of the experimental range. Besides, it predicts a new class of flavour-violating phenomena (called transmutations) due to the rotating fermion mass matrix which are unambiguously calculable. Comparison with experiment of these many ``parameter-free'' predictions reveals no violation of existing bounds but identifies several striking effects which can be tested with present experimental sensitivity.
GX 339-4 is an unusual black hole candidate in that it is a persistent source, being detected by X-ray telescopes most of the time, but it also has nova-like flaring states. In 1996 we performed radio, optical, X-ray, and gamma-ray observations of GX 339-4 when it was in a hard state (= soft X-ray low state). Here we present a brief summary of some of the results.
For more than 40 years E.Schmutzer has developed a new approach to the (5-dimensional) projective relativistic theory which he later called Projective Unified Field Theory (PUFT). In the present paper we introduce a new axiomatics for Schmutzer's theory. By means of this axiomatics we can give a new geometrical interpretation of the physical concept of the PUFT.