ShantanuT01/DACTYL-Pretraining huggingface dataset:
Quantum systems carry information. Quantum theory supports at least two distinct kinds of information (classical and quantum), and a variety of different ways to encode and preserve information in physical systems. A system's ability to carry information is constrained and defined by the noise in its dynamics. This paper introduces an operational framework, using information-preserving structures to classify all the kinds of information that can be perfectly (i.e., with zero error) preserved by quantum dynamics. We prove that every perfectly preserved code has the same structure as a matrix algebra, and that preserved information can always be corrected. We also classify distinct operational criteria for preservation (e.g., "noiseless", "unitarily correctible", etc.) and introduce two new and natural criteria for measurement-stabilized and unconditionally preserved codes. Finally, for several of these operational critera, we present efficient (polynomial in the state-space dimension) algorithms to find all of a channel's information-preserving structures.
We report detailed inelastic neutron scattering measurements on single crystals of the frustrated two-leg ladder BiCu2PO6, whose ground state is described as a spin liquid phase with no long-range order down to 6 K. Two branches of steeply dispersing long-lived spin excitations are observed with excitation gaps of \Delta_1 = 1.90(9) meV and \Delta_2 = 3.95(8) meV. Significant frustrating next-nearest neighbour interactions along the ladder leg drive the minimum of each excitation branch to incommensurate wavevectors \zeta_1 = 0.574\pi and \zeta_2 = 0.553\pi for the lower and upper energy branches respectively. The temperature dependence of the excitation spectrum near the gap energy is consistent with thermal activation into singly and doubly degenerate excited states. The observed magnetic excitation spectrum as well as earlier thermodynamic data could be consistently explained by the presence of strong anisotropic interactions in the ground state Hamiltonian.
In this paper we describe a computer implementation of Abramovich, Temkin, and Wlodarczyk's algorithm for resolving singularities in characteristic zero. Their "weighted resolution" algorithm proceeds by repeatedly blowing up along centers that are independent of the history of the past blowing ups, distinguishing weighted resolution from previous resolution algorithms, which all rely on history. We compare our implementation of weighted resolution with that of Villamayor's resolution algorithm, experimentally verifying that weighted resolution is remarkably efficient.
We demonstrate the coherent control and electrical readout of the nuclear spins of ionized phosphorus donors in natural silicon. By combining pulsed illumination with coherent electron spin manipulation, we selectively ionize the donor depending on its nuclear spin state, exploiting a spin-dependent recombination process via a spin pair at the Si/SiO2 interface. The nuclear-spin coherence time of the ionized donor is 18 ms, two orders of magnitude longer than in the neutral donor state, rendering the ionized donor a potential resource as a quantum memory. The presented experimental techniques allow for spectroscopy of ionized-donor nuclear spins, increase the sensitivity of electrically detected electron nuclear double resonance by more than two orders of magnitude, and give experimental access to the lifetime of parallel electron spin pairs.
We discuss inelastic collisions of two rotating disks by using the conservation laws for baryonic mass and angular momentum. In particular, we formulate conditions for the formation of a new disk after the collision and calculate the total energy loss to obtain upper limits for the emitted gravitational energy.
We develop certain aspects of the theory of shifted multiple Dirichlet series and study their meromorphic continuations. These continuations are used to obtain explicit spectral first and second moments of Rankin-Selberg convolutions. One consequence is a Weyl type estimate for the Rankin-Selberg convolution of a holomorphic cusp form and a Maass form with spectral parameter $|t_j|\le T$, namely: $$   \left| L\left(\frac{1}{2}+ir, f\times u_j\right) \right|   \ll_N T^{2/3+\epsilon}, $$ uniformly, for $|r| \le T^{2/3}$, with the implied constant depending only on $f$ and the level $N$.
Regular spaceborne measurements have revealed that solar brightness varies on multiple timescales, variations on timescales greater than a day being attributed to surface magnetic field. Independently, ground-based and spaceborne measurements suggest that Sun-like stars show a similar, but significantly broader pattern of photometric variability.   To understand whether the broader pattern of stellar variations is consistent with the solar paradigm we assess relative contributions of faculae and spots to solar magnetically-driven brightness variability. We investigate how the solar brightness variability as well as its facular and spot contributions depend on the wavelength, timescale of variability, and position of the observer relative to the ecliptic plane.   We perform calculations with the SATIRE model, which returns solar brightness with daily cadence from solar disc area coverages of various magnetic features.   Moving the observer away from the ecliptic plane increases the amplitude of 11-year variability as it would be seen in Str\"omgren $(b+y)/2$ photometry, but decreases the amplitude of the rotational brightness variations as it would appear in Kepler and CoRoT passbands. The spot and facular contributions to the 11-year solar variability in the Str\"omgren $(b+y)/2$ photometry almost fully compensate each other so that the Sun appears anomalously quiet with respect to its stellar cohort. Such a compensation does not occur on the rotational timescale.   The rotational solar brightness variability as it would appear in Kepler and CoRoT passband from the ecliptic plane is spot-dominated but the relative contribution of faculae increases for out-of-ecliptic viewing so that the apparent brightness variations are faculae-dominated for inclinations less than about $i=45^{\circ}$.
Madelung's hydrodynamical forms of the Schrodinger equation and the Klein-Gordon equation are presented. The physical nature of the quantum potential is explored. It is demonstrated that the geometrical origin of the quantum potential is in the scalar curvature of the of the metric that defines the kinetic energy density for an extended particle and that the quantization of circulation (Bohr-Sommerfeld) is a consequence of associating an SO(2)-reduction of the Lorentz frame bundle with wave motion. The Madelung equations are then cast in a basis-free form in terms of exterior differential forms in such a way that they represent the equations for a timelike solution to the conventional wave equations whose rest mass density satisfies a differential equation of the "Klein-Gordon minus nonlinear term" type. The role of non-zero vorticity is briefly examined.
We introduce SimBAL, a novel spectral-synthesis procedure that uses large grids of ionic column densities generated by the photoionization code Cloudy and a Bayesian model calibration to forward-model broad absorption line quasar spectra. We used SimBAL to analyze the HST COS spectrum of the low-redshift BALQ SDSS J085053.12+445122.5. SimBAL analysis yielded velocity-resolved information about the physical conditions of the absorbing gas. We found that the ionization parameter and column density increase, and the covering fraction decreases as a function of velocity. The total log column density is 22.9 (22.4) [cm^-2] for solar (Z=3Z_\odot) metallicity. The outflow lies 1--3 parsecs from the central engine, consistent with the estimated location of the torus. The mass outflow rate is 17--28 M_\odot yr^-1, the momentum flux is consistent with L_Bol/c, and the ratio of the kinematic to bolometric luminosity is 0.8--0.9%. The outflow velocity is similar to the escape velocity at the absorber's location, and force multiplier analysis indicates that part of the outflow could originate in resonance-line driving. The location near the torus suggests that dust scattering may play a role in the acceleration, although the lack of reddening in this UV-selected object indictes a relatively dust-free line of sight. The low accretion rate (0.06 L_Edd) and compact outflow suggests that SDSS~J0850+4451 might be a quasar past its era of feedback, although since its mass outflow is about 8 times the accretion rate, the wind is likely integral to the accretion physics of the central engine.
Texture analysis plays an important role in many image processing applications to describe the image content or objects. On the other hand, visual surface defect detection is a highly research field in the computer vision. Surface defect refers to abnormalities in the texture of the surface. So, in this paper a dual purpose benchmark dataset is proposed for texture image analysis and surface defect detection titled stone texture image (STI dataset). The proposed benchmark dataset consist of 4 different class of stone texture images. The proposed benchmark dataset have some unique properties to make it very near to real applications. Local rotation, different zoom rates, unbalanced classes, variation of textures in size are some properties of the proposed dataset. In the result part, some descriptors are applied on this dataset to evaluate the proposed STI dataset in comparison with other state-of-the-art datasets.
Optimal transport theory has been a powerful tool for the analysis of parabolic equationsviewed as gradient flows of volume forms according to suitable transportation metrics.In this paper, we present an example of gradient flows for closed (d-1)-forms in theEuclidean space R^d. In spite of its apparent complexity, the resulting verydegenerate parabolic system is fully integrable and can be viewed as the Eulerianversion of the heat equation for curves in the Euclidean space.We analyze this system in terms of "relative entropy" and "dissipative solutions" and provide global existence and weak-strong uniqueness results.
Vacuum polarization in external fields is treated by way of calculating - exactly and then perturbatively - the phase of the quantum scattering matrix in the Shale-Stinespring approach to field theory. The link between the Shale-Stinespring method and the Epstein-Glaser renormalization procedure is highlighted.
From the one-dimensional consolidation of fine-grained soils with threshold gradient, it can be derived a special type of Stefan problems where the seepage front, due to the presence of this threshold gradient, exhibits the features of a moving boundary. In this kind of problems, in contrast with the classical Stefan problem, the latent heat is considered to depend inversely with the rate of change of the seepage front. In this paper a one-phase Stefan problem with a latent heat that not only depends on the rate of change of the free boundary but also on its position is studied. The aim of this analysis is to extend prior results, finding an analytical solution that recovers, by specifying some parameters, the solutions that have already been examined in the literature regarding Stefan problems with variable latent heat. Computational examples will be presented in order to examine the effect of this parameters on the free boundary.
We give a complete proof of the so called $8n^2$-inequality, a local inequality for the self-intersection of a movable linear system at an isolated centre of a non canonical singularity. The inequality was suggested and several times published by I.Cheltsov but some of his arguments are faulty. We explain the mistake and replace the faulty piece by a correct argument.
This manual is intended to provide a detailed description of the DIML/CVL RGB-D dataset. This dataset is comprised of 2M color images and their corresponding depth maps from a great variety of natural indoor and outdoor scenes. The indoor dataset was constructed using the Microsoft Kinect v2, while the outdoor dataset was built using the stereo cameras (ZED stereo camera and built-in stereo camera). Table I summarizes the details of our dataset, including acquisition, processing, format, and toolbox. Refer to Section II and III for more details.
Tight-binding molecular dynamics simulations shed light into the fracture mechanisms and the ideal strength of tetrahedral amorphous carbon and of nanocomposite carbon containing diamond crystallites, two of the hardest materials. It is found that fracture in the nanocomposites, under tensile or shear load, occurs inter-grain and so their ideal strength is similar to the pure amorphous phase. The onset of fracture takes place at weakly bonded sp^3 sites in the amorphous matrix. On the other hand, the nanodiamond inclusions significantly enhance the elastic moduli, which approach those of diamond.
Visual localization is critical to many applications in computer vision and robotics. To address single-image RGB localization, state-of-the-art feature-based methods match local descriptors between a query image and a pre-built 3D model. Recently, deep neural networks have been exploited to regress the mapping between raw pixels and 3D coordinates in the scene, and thus the matching is implicitly performed by the forward pass through the network. However, in a large and ambiguous environment, learning such a regression task directly can be difficult for a single network. In this work, we present a new hierarchical scene coordinate network to predict pixel scene coordinates in a coarse-to-fine manner from a single RGB image. The network consists of a series of output layers, each of them conditioned on the previous ones. The final output layer predicts the 3D coordinates and the others produce progressively finer discrete location labels. The proposed method outperforms the baseline regression-only network and allows us to train compact models which scale robustly to large environments. It sets a new state-of-the-art for single-image RGB localization performance on the 7-Scenes, 12-Scenes, Cambridge Landmarks datasets, and three combined scenes. Moreover, for large-scale outdoor localization on the Aachen Day-Night dataset, we present a hybrid approach which outperforms existing scene coordinate regression methods, and reduces significantly the performance gap w.r.t. explicit feature matching methods.
A quantum walk whose continuous limit coincides with Dirac equation is usually called a Dirac Quantum Walk (DQW). A new systematic method to build DQWs coupled to electromagnetic (EM) fields is introduced and put to test on several examples of increasing difficulty. It is first used to derive the EM coupling of a well-known $3D$ walk on the cubic lattice. Recently introduced DQWs on the triangular and honeycomb lattice are then re-derived, showing for the first time that these are the only DQWs that can be defined with spinors living on the vertices of these lattices. As a third example of the method's effectiveness, a new $3D$ walk on a parallelepiped lattice is derived. As a fourth, negative example, it is shown that certain lattices like the rhombohedral lattice cannot be used to build DQWs. The effect of changing representation in the Dirac equation is also discussed.
Context. While the halo mass function is theoretically a very sensitive measure of cosmological models, masses of dark-matter halos are poorly defined, global, and unobservable quantities.   Aims. We argue that local, observable quantities such as the X-ray temperatures of galaxy clusters can be directly compared to theoretical predictions without invoking masses. We derive the X-ray temperature function directly from the statistics of Gaussian random fluctuations in the gravitational potential.   Methods. We derive the abundance of potential minima constrained by the requirement that they belong to linearly collapsed structures. We then use the spherical-collapse model to relate linear to non-linear perturbations, and the virial theorem to convert potential depths to temperatures. No reference is made to mass or other global quantities in the derivation.   Results. Applying a proper high-pass filter that removes large enough modes from the gravitational potential, we derive an X-ray temperature function that agrees very well with the classical Press-Schechter approach on relevant temperature scales, but avoids the necessity of measuring masses.   Conclusions. TThis first study shows that and how an X-ray temperature function of galaxy clusters can be analytically derived, avoiding the introduction of poorly defined global quantities such as halo masses. This approach will be useful for reducing scatter in observed cluster distributions and thus in cosmological conclusions drawn from them.
We present a general method to obtain a closed, finite formula for the exponential map from the Lie algebra to the Lie group, for the defining representation of the orthogonal groups. Our method is based on the Hamilton-Cayley theorem and some special properties of the generators of the orthogonal group, and is also independent of the metric. We present an explicit formula for the exponential of generators of the $SO_+(p,q)$ groups, with $p+q = 6$, in particular we are dealing with the conformal group $SO_+(2,4)$, which is homomorphic to the $SU(2,2)$ group. This result is needed in the generalization of U(1) gauge transformations to spin gauge transformations, where the exponential plays an essential role. We also present some new expressions for the coefficients of the secular equation of a matrix.
Clustering of the abundant SiO molecules has been discussed as a possible mechanism of seed particle formation for silicate dust in stellar outflows with an oxygen rich element mixture. Previous results indicated that condensation temperatures based on this mechanism are significant lower than what is really observed. This negative result strongly rests on experimental data on vapour pressure of SiO. New determinations show the older data to be seriously in error. Here we aim to check with improved data the possibility that SiO nucleation triggers the cosmic silicate dust formation. First we present results of our measurements of vapour pressure of solid SiO. Second, we use the improved vapour pressure data to re-calibrate existing experimental data on SiO nucleation from the literature. Third, we use the re-calibrated data on SiO nucleation in a simple model for dust-driven winds to determine the condensation temperature of silicate in stellar outflows from AGB stars. We show that onset of nucleation under circumstellar conditions commences at higher temperature than was previously found. Calculated condensation temperatures are still by about 100 K lower than observed ones, but this may be due to the greenhouse effect of silicate dust temperatures. The assumption that the onset of silicate dust formation in late-type M stars is triggered by cluster formation of SiO is compatible with dust condensation temperatures derived from IR observations.
The exceptional zero conjecture relates the first derivative of the $p$-adic $L$-function of a rational elliptic curve with split multiplicative reduction at $p$ to its complex $L$-function. Teitelbaum formulated an analogue of Mazur and Tate's refined (multiplicative) version of this conjecture for elliptic curves over the rational function field $\FQ(T)$ with split multiplicative reduction at two places $\fp$ and $\infty$, avoiding the construction of a $\fp$-adic $L$-function. This article proves Teitelbaum's conjecture up to roots of unity by developing Darmon's theory of double integrals over arbitrary function fields. A function field version of Darmon's period conjecture is also obtained.
Existing online multiple object tracking (MOT) algorithms often consist of two subtasks, detection and re-identification (ReID). In order to enhance the inference speed and reduce the complexity, current methods commonly integrate these double subtasks into a unified framework. Nevertheless, detection and ReID demand diverse features. This issue would result in an optimization contradiction during the training procedure. With the target of alleviating this contradiction, we devise a module named Global Context Disentangling (GCD) that decouples the learned representation into detection-specific and ReID-specific embeddings. As such, this module provides an implicit manner to balance the different requirements of these two subtasks. Moreover, we observe that preceding MOT methods typically leverage local information to associate the detected targets and neglect to consider the global semantic relation. To resolve this restriction, we develop a module, referred to as Guided Transformer Encoder (GTE), by combining the powerful reasoning ability of Transformer encoder and deformable attention. Unlike previous works, GTE avoids analyzing all the pixels and only attends to capture the relation between query nodes and a few self-adaptively selected key samples. Therefore, it is computationally efficient. Extensive experiments have been conducted on the MOT16, MOT17 and MOT20 benchmarks to demonstrate the superiority of the proposed MOT framework, namely RelationTrack. The experimental results indicate that RelationTrack has surpassed preceding methods significantly and established a new state-of-the-art performance, e.g., IDF1 of 70.5% and MOTA of 67.2% on MOT20.
We present observations of [NII] 205 $\mu$m, [OIII] 88 $\mu$m and dust emission in a strongly-lensed, submillimeter galaxy (SMG) at $z=6.0$, G09.83808, with the Atacama Large Millimeter/submillimeter Array (ALMA). Both [NII] and [OIII] line emissions are detected at $>12\sigma$ in the 0.8$"$-resolution maps. Lens modeling indicates that the spatial distribution of the dust continuum emission is well characterized by a compact disk with an effective radius of 0.64$\pm$0.02 kpc and a high infrared surface brightness of $\Sigma_\mathrm{IR}=(1.8\pm0.3)\times10^{12}~L_\odot$ kpc$^{-2}$. This result supports that G09.83808 is the progenitors of compact quiescent galaxies at $z\sim4$, where the majority of its stars are expected to be formed through a strong and short burst of star formation. G09.83808 and other lensed SMGs show a decreasing trend of the [NII] line to infrared luminosity ratio with increasing continuum flux density ratio between 63 $\mu$m and 158 $\mu$m, as seen in local luminous infrared galaxies (LIRGs). The decreasing trend can be reproduced by photoionization models with increasing ionization parameters. Furthermore, by combining the [NII]/[OIII] luminosity ratio with far-infrared continuum flux density ratio in G09.83808, we infer that the gas phase metallicity is already $Z\approx 0.5-0.7~Z_\odot$. G09.83808 is likely one of the earliest galaxies that has been chemically enriched at the end of reionization.
Time crystals form when arbitrary physical states of a periodically driven system spontaneously break discrete time-translation symmetry. We introduce one-dimensional time-crystalline topological superconductors, for which time-translation symmetry breaking and topological physics intertwine---yielding anomalous Floquet Majorana modes that are not possible in free-fermion systems. Such a phase exhibits a bulk magnetization that returns to its original form after two drive periods, together with Majorana end modes that recover their initial form only after four drive periods. We propose experimental implementations and detection schemes for this new state.
Researchers try to model the aesthetic quality of photographs into low and high- level features, drawing inspiration from art theory, psychology and marketing. We attempt to describe every feature extraction measure employed in the above process. The contribution of this literature review is the taxonomy of each feature by its implementation complexity, considering real-world applications and integration in mobile apps and digital cameras. Also, we discuss the machine learning results along with some unexplored research areas as future work.