ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let $Q$ be a transition probability on a measurable space $E$, let $(X\_n)\_n$ be a Markov chain associated to $Q$, and let $\xi$ be a real-valued measurable function on $E$, and $S\_n = \sum\_{k=1}^{n} \xi(X\_k)$. Under functional hypotheses on the action of $Q$ and its Fourier kernels $Q(t)$, we investigate the rate of convergence in the central limit theorem for the sequence $(\frac{S\_n}{\sqrt n})\_n$. According to the hypotheses, we prove that the rate is, either $O(n^{-\frac{\tau}{2}})$ for all $\tau<1$, or $O(n^{-{1/2}})$. We apply the spectral method of Nagaev which is improved by using a perturbation theorem of Keller and Liverani and a method of martingale difference reduction. When $E$ is not compact or $\xi$ is not bounded, the conditions required here are weaker than the ones usually imposed when the standard perturbation theorem is used. For example, in the case of $V$-geometric ergodic chains or Lipschitz iterative models, the rate of convergence in the c.l.t is $O(n^{-{1/2}})$ under a third moment condition on $\xi$.
We find the entropy of Kehagias-Sfetsos black hole in the deformed Ho\v{r}ava-Lifshitz gravity by using the first law of thermodynamics. When applying generalized uncertainty principle (GUP) to Schwarzschild black hole, the entropy $S=A/4+(\pi/\omega)\ln(A/4)$ may be interpreted as the GUP-inspired black hole entropy. Hence, it implies that the duality in the entropy between the Kehagias-Sfetsos black hole and GUP-inspired Schwarzschild black hole is present.
Tremendous efforts have been made on instance segmentation but the mask quality is still not satisfactory. The boundaries of predicted instance masks are usually imprecise due to the low spatial resolution of feature maps and the imbalance problem caused by the extremely low proportion of boundary pixels. To address these issues, we propose a conceptually simple yet effective post-processing refinement framework to improve the boundary quality based on the results of any instance segmentation model, termed BPR. Following the idea of looking closer to segment boundaries better, we extract and refine a series of small boundary patches along the predicted instance boundaries. The refinement is accomplished by a boundary patch refinement network at higher resolution. The proposed BPR framework yields significant improvements over the Mask R-CNN baseline on Cityscapes benchmark, especially on the boundary-aware metrics. Moreover, by applying the BPR framework to the PolyTransform + SegFix baseline, we reached 1st place on the Cityscapes leaderboard.
The Asynchronous Time-based Image Sensor (ATIS) and the Spiking Neural Network Architecture (SpiNNaker) are both neuromorphic technologies that "unconventionally" use binary spikes to represent information. The ATIS produces spikes to represent the change in light falling on the sensor, and the SpiNNaker is a massively parallel computing platform that asynchronously sends spikes between cores for processing. In this demonstration we show these two hardware used together to perform a visual tracking task. We aim to show the hardware and software architecture that integrates the ATIS and SpiNNaker together in a robot middle-ware that makes processing agnostic to the platform (CPU or SpiNNaker). We also aim to describe the algorithm, why it is suitable for the "unconventional" sensor and processing platform including the advantages as well as challenges faced.
Observations and modeling suggest that the dust abundance (gas-to-dust ratio, G/D) depends on (surface) density. The variations of the G/D provide constraints on the timescales for the different processes involved in the lifecycle of metals in galaxies. Recent G/D measurements based on Herschel data suggest a factor 5---10 decrease in the dust abundance between the dense and diffuse interstellar medium (ISM) in the Magellanic Clouds. However, the relative nature of the Herschel measurements precludes definitive conclusions on the magnitude of those variations. We investigate the variations of the dust abundance in the LMC and SMC using all-sky far-infrared surveys, which do not suffer from the limitations of Herschel on their zero-point calibration. We stack the dust spectral energy distribution (SED) at 100, 350, 550, and 850 microns from IRAS and Planck in intervals of gas surface density, model the stacked SEDs to derive the dust surface density, and constrain the relation between G/D and gas surface density in the range 10---100 \Msu pc$^{-2}$ on $\sim$ 80 pc scales. We find that G/D decreases by factors of 3 (from 1500 to 500) in the LMC and 7 (from 1.5$\times 10^4$ to 2000) in the SMC between the diffuse and dense ISM. The surface density dependence of G/D is consistent with elemental depletions and with simple modeling of the accretion of gas-phase metals onto dust grains. This result has important implications for the sub-grid modeling of galaxy evolution, and for the calibration of dust-based gas mass estimates, both locally and at high-redshift.
In the present paper we take a step towards the generalization of the post-Newtonian formalism to tensor-multi-scalar theories. These are theories where we have more than one scalar field being mediators of the gravitational interaction in addition to the spacetime metric. They are very natural extensions of Einstein's gravity allowing for the existence of new classes of compact objects and offering interesting phenomenology reaching far beyond the single scalar field theories. We calculate the expansion up to 2.5 post-Newtonian order in the near zone using the so-called direct integration of the relaxed Einstein equations formalism and derive the equation of motion. This work is the first step towards the calculation of gravitational waveforms in tensor-multi-scalar theories.
We introduce stochastic models of chemotaxis generalizing the deterministic Keller-Segel model. These models include fluctuations which are important in systems with small particle numbers or close to a critical point. Following Dean's approach, we derive the exact kinetic equation satisfied by the density distribution of cells. In the mean field limit where statistical correlations between cells are neglected, we recover the Keller-Segel model governing the smooth density field. We also consider hydrodynamic and kinetic models of chemotaxis that take into account the inertia of the particles and lead to a delay in the adjustment of the velocity of cells with the chemotactic gradient. We make the connection with the Cattaneo model of chemotaxis and the telegraph equation.
The profiles of emission lines formed in the corona contain information on the dynamics and the heating of the hot plasma. Only recently has data with sufficiently high spectral resolution become available for investigating the details of the profiles of emission lines formed well above 10^6 K. These show enhanced emission in the line wings, which has not been understood yet. Line profiles of Fe XV formed at 2.5 MK acquired by the Extreme ultraviolet Imaging Spectrometer (EIS) onboard the Hinode solar space observatory are studied using multi Gaussian fits, with emphasis on the resulting line widths and Doppler shifts. In the major part of the active region, the spectra are best fit by a narrow line core and a broad minor component. The latter contributes some 10% to 20% to the total emission, is about a factor of 2 broader than the core, and shows strong blueshifts of up to 50 km/s. On average, the line width increases from the footpoints to the loop top for both components. A component with high upflow speeds can be found also in small restricted areas. The coronal structures consist of at least two classes that are not resolved spatially but only spectroscopically and that are associated with the line core and the minor component. Because of their huge line width and strong upflows, it is proposed that the major part of the heating and the mass supply to the corona is actually located in source regions of the minor component. The siphon flows and draining loops seen in the line core component are consistent with structures found in a 3D MHD coronal model. Despite the quite different appearance of the large active region corona and small network elements seen in transition region lines, both show similar line profile characteristics. This indicates that the same processes govern the heating and dynamics of the transition region and the corona.
Given an action of an algebraic torus on a normal affine variety, we describe all open subsets admitting a complete orbit space.
We consider a variant of the radial spanning tree introduced by Baccelli and Bordenave. Like the original model, our model is a tree rooted at the origin, built on the realization of a planar Poisson point process. Unlike it, the paths of our model have independent jumps. We show that locally our diffusively rescaled tree, seen as the collection of the paths connecting its sites to the root, converges in distribution to the Brownian Bridge Web, which is roughly speaking a collection of coalescing Brownian bridges starting from all the points of a planar strip perpendicular to the time axis, and ending at the origin.
We investigate the ionized gas excitation and kinematics in the inner $4.3 \times 6.2$ kpc$^{2}$ of the merger radio galaxy 4C +29.30. Using optical integral field spectroscopy with the Gemini North Telescope, we present flux distributions, line-ratio maps, peak velocities and velocity dispersion maps as well as channel maps with a spatial resolution of $\approx 955$ pc. We observe high blueshifts of up to $\sim -650$ km s$^{-1}$, in a region $\sim 1''$ south of the nucleus (the southern knot, SK), which also presents high velocity dispersions ($\sim 250$ km s$^{-1}$), which we attribute to an outflow. A possible redshifted counterpart is observed north from the nucleus (the northern knot, NK). We propose that these regions correspond to a bipolar outflow possibly due to the interaction of the radio jet with the ambient gas. We estimate a total ionized gas mass outflow rate of $\dot{M}_{out} = 25.4 \substack{+11.5 \\ -7.5}$ M$_\odot$ yr$^{-1}$ with a kinetic power of $\dot{E} = 8.1 \substack{+10.7 \\ -4.0} \times 10^{42}$ erg s$^{-1}$, which represents $5.8 \substack{+7.6 \\ -2.9} \%$ of the AGN bolometric luminosity. These values are higher than usually observed in nearby active galaxies with the same bolometric luminosities and could imply a significant impact of the outflows in the evolution of the host galaxy. The excitation is higher in the NK (that correlates with extended X-ray emission, indicating the presence of hotter gas) than in the SK, supporting a scenario in which an obscuring dust lane is blocking part of the AGN radiation to reach the southern region of the galaxy.
We propose and prove a family of generalized Lieb-Schultz-Mattis (LSM) theorems for symmetry protected topological (SPT) phases on boson/spin models in any dimensions. The "conventional" LSM theorem, applicable to e.g. any translation invariant system with an odd number of spin-1/2 particles per unit cell, forbids a symmetric short-range-entangled ground state in such a system. Here we focus on systems with no LSM anomaly, where global/crystalline symmetries and fractional spins within the unit cell ensure that any symmetric SRE ground state must be a nontrivial SPT phase with anomalous boundary excitations. Depending on models, they can be either strong or "higher-order" crystalline SPT phases, characterized by nontrivial surface/hinge/corner states. Furthermore, given the symmetry group and the spatial assignment of fractional spins, we are able to determine all possible SPT phases for a symmetric ground state, using the real space construction for SPT phases based on the spectral sequence of cohomology theory. We provide examples in one, two and three spatial dimensions, and discuss possible physical realization of these SPT phases based on condensation of topological excitations in fractionalized phases.
In a previous article, we reduced the unsolved problem of the convergence of Collatz sequences, to convergence of Collatz sequences of odd numbers, that are divisible by 3. In this article, we further reduce this set to odd numbers that are congruent to 21 mod 24. We also show that either the Collatz sequence of a given odd number or an equivalent Collatz sequence reverses to a multiple of 3. Moreover, we construct a network composed of Collatz sequences of all odd numbers.
Double coronal hard X-ray (HXR) sources are believed to be critical observational evidence of bi-directional energy release through magnetic reconnection in a large-scale current sheet in solar ares. Here we present a study on double coronal sources observed in both HXR and microwave regimes, revealing new characteristics distinct from earlier reports. This event is associated with a footpoint-occulted X1.3-class flare (25 April 2014, starting at 00:17 UT) and a coronal mass ejection that are likely triggered by the magnetic breakout process, with the lower source extending upward from the top of the partially-occulted flare loops and the upper source co-incident with rapidly squeezing-in side lobes (at a speed of ~250 km/s on both sides). The upper source can be identified at energies as high as 70-100 keV. The X-ray upper source is characterized by flux curves different from the lower source, a weak energy dependence of projected centroid altitude above 20 keV, a shorter duration and a HXR photon spectrum slightly-harder than those of the lower source. In addition, the microwave emission at 34 GHz also exhibits a similar double source structure and the microwave spectra at both sources are in line with gyro-synchrotron emission given by non- thermal energetic electrons. These observations, especially the co-incidence of the very-fast squeezing-in motion of side lobes and the upper source, indicate that the upper source is associated with (possibly caused by) this fast motion of arcades. This sheds new lights on the origin of the corona double-source structure observed in both HXRs and microwaves.
The electride Sr$_3$CrN$_3$ has a one-dimensional channel of electron density, which is a rare feature that offers great potential for fast ion conduction. Using density functional theory, we find that Sr$_3$CrN$_3$ is an excellent hydride conductor within this channel, with a diffusion barrier as low as 0.30 eV and an estimated diffusion coefficient of $5.37\times 10^{-8}$ cm$^2$/s. This diffusion barrier is lower than those reported for the best hydride conductors to date. We also show the most-stable amount of hydride in the host material under standard conditions and the corresponding change in electronic structure from metal to wide-gap insulator. Our results highlight the potential offered by 1D electride materials for ion-transport applications such as energy storage or gas separation.
We illustrate how the measurements of the CP asymmetries in $B^0_{d,s}$-decays together with a measurement of $Br(K_L\to \pi^\circ\nu\bar\nu)$ or $Br(K^+\to \pi^+\nu\bar\nu)$ and the known value of $\mid V_{us}\mid $ can determine all elements of the Cabibbo-Kobayashi-Maskawa matrix essentially without any hadronic uncertainties. An analysis using the ratio $x_d/x_s$ of $B_d-\bar B_d$ to $B_s-\bar B_s$ mixings is also presented.
The most peculiar radio characteristics of the TeV emitting high-mass X-ray binary LS I +61{\deg}303 are two periodicities: A large periodic outburst which exhibits the same period as the orbit (phase \Phi) and a second periodicity of 1667 days (phase \Theta) which modulates the orbital phase and amplitude of the large outburst. Recent analysis of the radio spectral index present strong evidence for the presence of the critical transition from optically thick emission (related to a steady jet) to an optically thin outburst (related to a transient jet) as in other microquasars. In parallel, a switch from a low/hard X-ray state to a transitional state (e.g. steep power law state) would be expected. We show how the critical transition from optically thick emission to an optically thin outburst is modulated by \Theta. Folding over a too large \Theta-interval mixes up important information about the outbursts and can yield a false picture of the emission behaviour of the source along the orbit. We therefore analyse the implications of this long period for treatment of hard X-ray/high energy data obtained from LS I +61{\deg}303, e.g. with Fermi-LAT or INTEGRAL, taking into account this long-term periodicity.
We report discovery of actively star forming elliptical galaxies in a morphologically classified sample of bright galaxies at a low redshift obtained from the Sloan Digital Sky Survey. The emission lines of these galaxies do not show the characteristics of active galactic nuclei, and thus their strong H$\alpha$ emission is ascribed to star formation with a rate nearly as high as that is seen in typical late spiral galaxies. This is taken as evidence against the traditional view that all elliptical galaxies formed early and now evolve only passively. The frequency of such star forming elliptical galaxies is a few tenths of a percent in the sample, but increases to 3% if we include active S0 galaxies. We may identify these galaxies as probable progenitors of so-called E+A galaxies that show the strong Balmer absorption feature of A stars superimposed on an old star population. The approximate match of the abundance of active elliptical plus S0 galaxies with that of E+A galaxies indicates that the duration of such late star formation episodes is of the order of $\gsim 1$ Gyr. If we interpret these galaxies as new additions to the early-type galaxy population, and if we assume a power law for their number evolution, the abundance of early-type galaxies at $z=1$ is about 30% less than that at $z=0$.
In this article, we prove that finite semidistributive lattices are dismantlable if and only if they are planar. This extends a well-known result by Kelly and Rival that states the same property for finite distributive lattices. Moreover, we show how the breadth of finite semidistributive lattices can be computed with the help of canonical join representations. We use this result to conclude that the breadth of a finite semidistributive dismantlable lattice cannot exceed $2$.
Computer vision leveraging deep learning has achieved significant success in the last decade. Despite the promising performance of the existing deep models in the recent literature, the extent of models' reliability remains unknown. Structural health monitoring (SHM) is a crucial task for the safety and sustainability of structures, and thus prediction mistakes can have fatal outcomes. This paper proposes Bayesian inference for deep vision SHM models where uncertainty can be quantified using the Monte Carlo dropout sampling. Three independent case studies for cracks, local damage identification, and bridge component detection are investigated using Bayesian inference. Aside from better prediction results, mean class softmax variance and entropy, the two uncertainty metrics, are shown to have good correlations with misclassifications. While the uncertainty metrics can be used to trigger human intervention and potentially improve prediction results, interpretation of uncertainty masks can be challenging. Therefore, surrogate models are introduced to take the uncertainty as input such that the performance can be further boosted. The proposed methodology in this paper can be applied to future deep vision SHM frameworks to incorporate model uncertainty in the inspection processes.
We solve the problem of characteristic numbers of elliptic curves in any dimensional projective space The answers are given in the form of effective recursions. Many numerical examples are provided. A C++ program implementing all the recursions is available upon request.
Matching information across image and text modalities is a fundamental challenge for many applications that involve both vision and natural language processing. The objective is to find efficient similarity metrics to compare the similarity between visual and textual information. Existing approaches mainly match the local visual objects and the sentence words in a shared space with attention mechanisms. The matching performance is still limited because the similarity computation is based on simple comparisons of the matching features, ignoring the characteristics of their distribution in the data. In this paper, we address this limitation with an efficient learning objective that considers the discriminative feature distributions between the visual objects and sentence words. Specifically, we propose a novel Adversarial Discriminative Domain Regularization (ADDR) learning framework, beyond the paradigm metric learning objective, to construct a set of discriminative data domains within each image-text pairs. Our approach can generally improve the learning efficiency and the performance of existing metrics learning frameworks by regulating the distribution of the hidden space between the matching pairs. The experimental results show that this new approach significantly improves the overall performance of several popular cross-modal matching techniques (SCAN, VSRN, BFAN) on the MS-COCO and Flickr30K benchmarks.
The single-degenerate model for the progenitors of type Ia supernovae (SNe Ia) is one of the two most popular models, in which a carbon-oxygen white dwarf (CO WD) accretes hydrogen-rich material from its companion, increases its mass to the Chandrasekhar mass limit, and then explodes as a SN Ia. Incorporating the prescription of Hachisu et al. (1999a) for the accretion efficiency into Eggleton's stellar evolution code and assuming that the prescription is valid for \emph{all} metallicities, we carried out a detailed binary evolution study with different metallicities. We show the initial and final parameter space for SNe Ia in a ($\log P-M_{\rm 2}$) plane. The positions of some famous recurrent novae in the ($\log P-M_{\rm 2}$) plane, as well as a supersoft X-ray source (SSS), RX J0513.9-6951 are well explained by our model, and our model can also explain the space velocity and mass of Tycho G, which is now suggested to be the companion star of Tycho's supernova . Our study indicates that the SSS, V Sge, is a potential progenitor of supernovae like SN 2002ic if the delayed dynamical-instability model in Han & Podsiadlowski (2006) is appropriate.
Electronic energy-eigen-states of graphene in an orthogonal electromagnetic field with relative magnitude beta=E/vf*B>=1 or in a pure electric field are obtained by a differential-equation method. Gaussian wave packets of probability density are constructed and found to transform form two-dimensional solitons into one-dimension ones at beta=1, when beta increases form beta<1 into beta>1. The maximum number of one-dimensional solitons of a finite graphene in the field is used to determine the electronic energy levels. These energy levels and the velocity of solitons lead to nonlinear dependence of the current on the Hall voltage for the field with beta>1 and nonlinear current-voltage curves for the pure electric field including the step-like ones at low temperatures, according to the ballistic transport of solitons.
We present results concerning when the joint distribution of an exchangeable sequence is determined by the marginal distributions of its partial sums. The question of whether or not this determination occurs was posed by David Aldous. We then consider related uniqueness problems, including a continuous time analog to the Aldous problem and a randomized univariate moment problem.