ShantanuT01/DACTYL-Pretraining huggingface dataset:
In studies of the environmental dependence of structure formation, the large scale environment is often thought of as providing an effective background cosmology: e.g. the formation of structure in voids is expected to be just like that in a less dense universe with appropriately modified Hubble and cosmological constants. However, in the excursion set description of structure formation which is commonly used to model this effect, no explicit mention is made of the effective cosmology. Rather, this approach uses the spherical evolution model to compute an effective linear theory growth factor, which is then used to predict the growth and evolution of nonlinear structures. We show that these approaches are, in fact, equivalent: a consequence of Birkhoff's theorem. We speculate that this equivalence will not survive in models where the gravitational force law is modified from an inverse square, potentially making the environmental dependence of clustering a good test of such models.
Flajolet and Salvy pointed out that every Euler sum is a $\mathbb{Q}$-linear combination of multiple zeta values. However, in the literature, there is no formula completely revealing this relation. In this paper, using permutations and compositions, we establish two explicit formulas for the Euler sums, and show that all the Euler sums are indeed expressible in terms of MZVs. Moreover, we apply this method to the alternating Euler sums, and show that all the alternating Euler sums are reducible to alternating MZVs. Some famous results, such as the Euler theorem, the Borwein--Borwein--Girgensohn theorems, and the Flajolet--Salvy theorems can be obtained directly from our theory. Some other special cases, such as the explicit expressions of $S_{r^m,q}$, $S_{r^m,\bar{q}}$, $S_{\bar{r}^m,q}$ and $S_{\bar{r}^m,\bar{q}}$, are also presented here. The corresponding Maple programs are developed to help us compute all the sums of weight $w\leq 11$ for non-alternating case and of weight $w\leq 6$ for alternating case.
A Bott tower of height $r$ is a sequence of projective bundles $$X_r \overset{{\pi_r}}\longrightarrow X_{r-1} \overset{\pi_{r-1}}\longrightarrow \cdots \overset{\pi_2}\longrightarrow X_1=\mathbb P^1 \overset{\pi_1} \longrightarrow X_0=\{pt\}, $$ where $X_i=\mathbb P (\mathcal O_{X_{i-1}}\oplus \mathcal L_{i-1})$ for a line bundle $\mathcal L_{i-1}$ over $X_{i-1}$ for all $1\leq i\leq r$ and $\mathbb P(-)$ denotes the projectivization. These are smooth projective toric varieties and we refer to the top object $X_{r}$ also as a Bott tower. In this article, we study the Mori cone and numerically effective (nef) cone of Bott towers, and we classify Fano, weak Fano and log Fano Bott towers. We prove some vanishing theorems for the cohomology of tangent bundle of Bott towers.
The goal of this paper is to apply the recently developed theory of buckling of arbitrary slender bodies to a tractable yet non-trivial example of buckling in axially compressed circular cylindrical shells, regarded as three-dimensional hyperelastic bodies. The theory is based on a mathematically rigorous asymptotic analysis of the second variation of 3D, fully nonlinear elastic energy, as the shell's slenderness parameter goes to zero. Our main results are a rigorous proof of the classical formula for buckling load and the explicit expressions for the relative amplitudes of displacement components in single Fourier harmonics buckling modes, whose wave numbers are described by Koiter's circle. This work is also a part of an effort to quantify the sensitivity of the buckling load of axially compressed cylindrical shells to imperfections of load and shape.
We present a spectroscopic study of the tidal tails and core of the Milky Way satellite Tucana III, collectively referred to as the Tucana III stream, using the 2dF+AAOmega spectrograph on the Anglo-Australian Telescope and the IMACS spectrograph on the Magellan/Baade Telescope. In addition to recovering the brightest 9 previously known member stars in the Tucana III core, we identify 22 members in the tidal tails. We observe strong evidence for a velocity gradient of 8.0 km/s/deg (or 18.3 km/s/kpc over at least 3$^{\circ}$ (or 1.3 kpc) on the sky. Based on the continuity in velocity we confirm that the Tucana III tails are real tidal extensions of Tucana III. The large velocity gradient of the stream implies that Tucana III is likely on a radial orbit. We successfully obtain metallicities for 4 members in the core and 12 members in the tails. We find that members close to the ends of the stream tend to be more metal-poor than members in the core, indicating a possible metallicity gradient between the center of the progenitor halo and its edge. The spread in metallicity suggests that the progenitor of the Tucana III stream is a dwarf galaxy rather than a star cluster. Furthermore, we find that with the precise photometry of the Dark Energy Survey data, there is a discernible color offset between metal-rich disk stars and metal-poor stream members. This metallicity-dependent color offers a more efficient method to recognize metal-poor targets and will increase the selection efficiency of stream members for future spectroscopic follow-up programs on stellar streams.
The caloric curve for mononuclear configurations is studied with a schematic model. We investigate the dependence of the entropy on the density and effective mass profiles. A plateau in the caloric curve is a direct result of decreasing density and the destruction of correlations with increasing excitation. The mononuclear regime is metastable with respect to binary fission at low excitation energy and unstable with respect to multifragmentation at high excitation. The statistical framework presented here is suitable to treat scenarios where experimental conditions are set to favor population of highly excited mononuclear states.
We conduct a search for z>~7 dropout galaxies behind 11 massive lensing clusters using 21 arcmin**2 of deep HST NICMOS, ACS, and WFPC2 image data. In total, over this entire area, we find only one robust z~7 z-dropout candidate (previously reported around Abell 1689). Four less robust z-dropout and J-dropout candidates are also found. The nature of the four weaker candidates could not be precisely determined due to the limited depth of the available optical data, but detailed simulations suggest that all four could be low-redshift interlopers. We compare these numbers with what we might expect using the z~7 UV luminosity function (LF) determined from field searches. We predict 2.7 z~7 z-dropouts and 0.3 z~9 J-dropouts over our cluster search area, in reasonable agreement with our observational results, given the small numbers. The number of z>~7 candidates we find in the present search are much lower than has been reported in several previous studies of the prevalence of z>~7 galaxies behind lensing clusters. To understand these differences, we examined z>~7 candidates in other studies and conclude that only a small fraction are likely to be z>~7 galaxies. Our findings support models that show that gravitational lensing from clusters is of the most value for detecting galaxies at magnitudes brighter than L* (H<~ 27) where the LF is expected to be very steep. Use of these clusters to constrain the faint-end slope or determine the full LF is likely of less value due to the shallower effective slope measured for the LF at fainter magnitudes, as well as significant uncertainties introduced from modelling both the gravitational lensing and incompleteness.
We present a new open-source program, DCore, that implements dynamical mean-field theory (DMFT). DCore features a user-friendly interface based on text and HDF5 files. It allows DMFT calculations of tight-binding models to be performed on predefined lattices as well as \textit{ab initio} models constructed by external density functional theory codes through the Wannier90 package. Furthermore, DCore provides interfaces to many advanced quantum impurity solvers such as quantum Monte Carlo and exact diagonalization solvers. This paper details the structure and usage of DCore and shows some applications.
Vanishing of the Fefferman-Graham obstruction tensor was used by Andersson and Chru{\'s}ciel to show stability of the asymptotically de Sitter spaces in even dimensions. However, existing proofs of hyperbolicity of this equation contain gaps. We show in this paper that it is indeed a well-posed hyperbolic system with unique up to diffeomorphism and conformal transformations smooth development for smooth Cauchy data. Our method applies also to equations defined by various versions Graham-Jenne-Mason-Sparling operators. In particular, we use one of these operators to propagate Gover's condition of being almost conformally Einstein. This allows to study initial data also for Cauchy surfaces which cross conformal boundary. As a by-product we show that on globally hyperbolic manifolds one can always choose conformal factor such that Branson Q-curvature vanishes.
In this paper we tackle a very novel problem, namely height estimation from a single monocular remote sensing image, which is inherently ambiguous, and a technically ill-posed problem, with a large source of uncertainty coming from the overall scale. We propose a fully convolutional-deconvolutional network architecture being trained end-to-end, encompassing residual learning, to model the ambiguous mapping between monocular remote sensing images and height maps. Specifically, it is composed of two parts, i.e., convolutional sub-network and deconvolutional sub-network. The former corresponds to feature extractor that transforms the input remote sensing image to high-level multidimensional feature representation, whereas the latter plays the role of a height generator that produces height map from the feature extracted from the convolutional sub-network. Moreover, to preserve fine edge details of estimated height maps, we introduce a skip connection to the network, which is able to shuttle low-level visual information, e.g., object boundaries and edges, directly across the network. To demonstrate the usefulness of single-view height prediction, we show a practical example of instance segmentation of buildings using estimated height map. This paper, for the first time in the remote sensing community, attempts to estimate height from monocular vision. The proposed network is validated using a large-scale high resolution aerial image data set covered an area of Berlin. Both visual and quantitative analysis of the experimental results demonstrate the effectiveness of our approach.
We present a method, the dynamical cumulant expansion, that allows to calculate quantum corrections for time-dependent quantities of interacting spin systems or single spins with anisotropy. This method is applied to the quantum-spin model \hat{H} = -H_z(t)S_z + V(\bf{S}) with H_z(\pm\infty) = \pm\infty and \Psi (-\infty)=|-S> we study the quantity P(t)=(1-<S_z>_t/S)/2. The case V(\bf{S})=-H_x S_x corresponds to the standard Landau-Zener-Stueckelberg model of tunneling at avoided-level crossing for N=2S independent particles mapped onto a single-spin-S problem, P(t) being the staying probability. Here the solution does not depend on S and follows, e.g., from the classical Landau-Lifshitz equation. A term -DS_z^2 accounts for particles' interaction and it makes the model nonlinear and essentially quantum mechanical. The 1/S corrections obtained with our method are in a good accord with a full quantum-mechanical solution if the classical motion is regular, as for D>0.
We prove a version of Bagchi's Theorem and of Voronin's Universality Theorem for family of primitive cusp forms of weight $2$ and prime level, and discuss under which conditions the argument will apply to general reasonable family of automorphic $L$-functions.
I have proposed that long Halpha fibrils are caused by heating events of which the tracks are afterwards outlined by contrails of cooling gas with extraordinary Halpha opacity and yet larger opacity at the ALMA wavelengths. Here I detail the radiative transfer background.
We have analyzed archival HST/WFPC2 time-series data of the central parts of globular clusters M13, M30 and NGC 6712 in search of variable objects. Among a total of 21 identified variables there are 15 new discoveries. The sample includes nine RR Lyr stars, two SX Phe stars and seven W UMa-type contact binaries. One object is preliminarily classified as a detached eclipsing binary and another as an ellipsoidal variable.
The four-year X-ray all-sky survey (eRASS) of the eROSITA telescope aboard the Spektrum-Roentgen-Gamma satellite will detect ~3 million active galactic nuclei (AGN) with a median redshift of z~1 and a typical luminosity of L_(0.5-2.0 keV) ~ 10^(44) erg/s. We show that this unprecedented AGN sample, complemented with redshift information, will supply us with outstanding opportunities for large-scale structure research. For the first time, detailed redshift- and luminosity-resolved studies of the bias factor for X-ray selected AGN will become possible. The eRASS AGN sample will not only improve the redshift- and luminosity-resolution of these studies, but will also expand their luminosity range beyond L_(0.5-2.0 keV) ~ 10^(44) erg/s, thus enabling a direct comparison of the clustering properties of luminous X-ray AGN and optical quasars. These studies will dramatically improve our understanding of the AGN environment, triggering mechanisms, the growth of supermassive black holes and their co-evolution with dark matter halos.   The eRASS AGN sample will become a powerful cosmological probe. It will enable detecting baryonic acoustic oscillations (BAOs) for the first time with X-ray selected AGN. With the data from the entire extragalactic sky, BAO will be detected at a >~10sigma confidence level in the full redshift range and with ~8sigma confidence in the 0.8 < z < 2.0 range, which is currently not covered by any existing BAO surveys. To exploit the full potential of the eRASS AGN sample, photometric and spectroscopic surveys of large areas and a sufficient depth will be needed.
The Large Area Telescope (LAT) on the Fermi Gamma-ray Space Telescope (formerly GLAST), with its improved sensitivity relative to previous generation gamma-ray telescopes, is significantly increasing the number of known gamma-ray sources in the sky, including pulsars. In addition to searching for gamma-ray emission from known radio pulsars, it is now possible to successfully perform blind searches for pulsars on the gamma-ray data alone, with the goal of uncovering a new population of potentially radio-quiet (Geminga-like) pulsars. We describe our methods and some recent results from our searches, performed using the time-differencing technique, which have resulted in the discovery of a large number of new gamma-ray pulsars.
Learning invariant representations is a critical task in computer vision. In this paper, we propose the Theta-Restricted Boltzmann Machine ({\theta}-RBM in short), which builds upon the original RBM formulation and injects the notion of rotation-invariance during the learning procedure. In contrast to previous approaches, we do not transform the training set with all possible rotations. Instead, we rotate the gradient filters when they are computed during the Contrastive Divergence algorithm. We formulate our model as an unfactored gated Boltzmann machine, where another input layer is used to modulate the input visible layer to drive the optimisation procedure. Among our contributions is a mathematical proof that demonstrates that {\theta}-RBM is able to learn rotation-invariant features according to a recently proposed invariance measure. Our method reaches an invariance score of ~90% on mnist-rot dataset, which is the highest result compared with the baseline methods and the current state of the art in transformation-invariant feature learning in RBM. Using an SVM classifier, we also showed that our network learns discriminative features as well, obtaining ~10% of testing error.
Yearslong time series of high-precision brightness measurements have been assembled for thousands of stars with telescopes operating in space. Such data have allowed astronomers to measure the physics of stellar interiors via nonradial oscillations, opening a new avenue to study the stars in the Universe. Asteroseismology, the interpretation of the characteristics of oscillation modes in terms of the physical properties of the stellar interior, brought entirely new insights in how stars rotate and how they build up their chemistry throughout their evolution. Data-driven space asteroseismology delivered a drastic increase in the reliability of computer models mimicking the evolution of stars born with a variety of masses and metallicities. Such models are critical ingredients for modern physics as a whole, because they are used throughout various contemporary and multidisciplinary research fields in space science, including the search for life outside the solar system, archaeological studies of the Milky Way, and the study of single and binary supernova progenitors, among which are future gravitational wave sources. The specific role and potential of asteroseismology for those modern research fields are illustrated. The review concludes with current limitations of asteroseismology and highlights how they can be overcome with ongoing and future large infrastructures for survey astronomy combined with new theoretical research in the era of high-performance computing. This review presents results obtained through major community efforts over the past decade. These breakthroughs were achieved in a collaborative and inclusive spirit that is characteristic of the asteroseismology community. The review's aim is to make this research field accessible to graduate students and readers coming from other fields of physics, with incentives to join future applications in this domain of astrophysics.
We investigate the cold and warm dust properties during galaxy interactions using a merging galaxy sample ordered into a chronological sequence from pre- to post-mergers. Our sample comprises a total of 29 merging systems selected to have far-infrared and sub-millimeter observations. The sub-millimeter data are mainly culled from the literature while for 5 galaxies (NGC 3597, NGC 3690, NGC 6090, NGC 6670 and NGC 7252) the sub-millimeter observations are presented here for the first time. We use the 100-to-850 micron flux density ratio, f_{100}/f_{850}, as a proxy to the mass fraction of the warm and the cold dust in these systems. We find evidence for an increase in f_{100}/f_{850} along the merging sequence from early to advanced mergers and interpret this trend as an increase of the warm relative to the cold dust mass. We argue that the two key parameters affecting the f_{100}/f_{850} flux ratio is the star-formation rate and the dust content of individual systems relative to the stars. Using a sophisticated model for the absorption and re-emission of the stellar UV radiation by dust we show that these parameters can indeed explain both the increase and the observed scatter in the f_{100}/f_{850} along the merging galaxy sequence. We also discuss our results under the hypothesis that elliptical galaxies are formed via disc galaxy mergers.
In this paper, we propose a new query-based detection framework for crowd detection. Previous query-based detectors suffer from two drawbacks: first, multiple predictions will be inferred for a single object, typically in crowded scenes; second, the performance saturates as the depth of the decoding stage increases. Benefiting from the nature of the one-to-one label assignment rule, we propose a progressive predicting method to address the above issues. Specifically, we first select accepted queries prone to generate true positive predictions, then refine the rest noisy queries according to the previously accepted predictions. Experiments show that our method can significantly boost the performance of query-based detectors in crowded scenes. Equipped with our approach, Sparse RCNN achieves 92.0\% $\text{AP}$, 41.4\% $\text{MR}^{-2}$ and 83.2\% $\text{JI}$ on the challenging CrowdHuman \cite{shao2018crowdhuman} dataset, outperforming the box-based method MIP \cite{chu2020detection} that specifies in handling crowded scenarios. Moreover, the proposed method, robust to crowdedness, can still obtain consistent improvements on moderately and slightly crowded datasets like CityPersons \cite{zhang2017citypersons} and COCO \cite{lin2014microsoft}. Code will be made publicly available at https://github.com/megvii-model/Iter-E2EDET.
The first Herschel Hi-Gal images of the galactic plane unveil the far-infrared diffuse emission of the interstellar medium with an unprecedented angular resolution and sensitivity. In this paper, we present the first analysis of these data in combination with that of Spitzer Glimpse & Mipsgal. We selected a relatively diffuse and low excitation region of the l~59\,^{\circ} Hi-Gal Science Demonstration Phase field to perform a pixel by pixel fitting of the 8 to 500 microns SED using the DustEM dust emission model. We derived maps of the Very Small Grains (VSG) and PAH abundances from the model. Our analysis allows us to illustrate that the Aromatic Infrared Bands (AIB) intensity does not trace necessarily the PAH abundance but rather the product of "abundance x column density x intensity of the exciting radiation field". We show that the spatial structure of PACS70microns map resembles the shorter wavelengths (e.g. IRAC8microns) maps, because they trace both the intensity of exciting radiation field and column density. We also show that the modeled VSG contribution to PACS70microns (PACS160microns) band intensity can be up to 50% (7%). The interpretation of diffuse emission spectra at these wavelengths must take stochastically heated particles into account. Finally, this preliminary study emphasizes the potential of analyzing the full dust SED sampled by Herschel and Spitzer data, with a physical dust model (DustEM) to reach the properties of the dust at simultaneously large and small scales.
We present initial results on some of the properties of open clusters NGC 6791 and NGC 6819 derived from asteroseismic data obtained by NASA's Kepler mission. In addition to estimating the mass, radius and log g of stars on the red-giant branch of these clusters, we estimate the distance to the clusters and their ages. Our model-independent estimate of the distance modulus of NGC 6791 is (m-M)_0= 13.11\pm 0.06. We find (m-M)_0= 11.85\pm 0.05 for NGC 6819. The average mass of stars on the red-giant branch of NGC 6791 is 1.20 \pm 0.01 M_sun, while that of NGC 6819 is 1.68\pm 0.03M_sun. It should be noted that we do not have data that cover the entire red-giant branch and the actual mass will be somewhat lower. We have determined model-dependent estimates of ages of these clusters. We find ages between 6.8 and 8.6 Gyr for NGC 6791, however, most sets of models give ages around 7Gyr. We obtain ages between 2 and 2.4 Gyr for NGC 6819.
The problem of feedback control of quantum systems by means of weak measurements is investigated in detail. When weak measurements are made on a set of identical quantum systems, the single-system density matrix can be determined to a high degree of accuracy while affecting each system only slightly. If this information is fed back into the systems by coherent operations, the single-system density matrix can be made to undergo an arbitrary nonlinear dynamics, including for example a dynamics governed by a nonlinear Schr\"odinger equation. We investigate the implications of such nonlinear quantum dynamics for various problems in quantum control and quantum information theory, including quantum computation. The nonlinear dynamics induced by weak quantum feedback could be used to create a novel form of quantum chaos in which the time evolution of the single-system wave function depends sensitively on initial conditions.