ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the complete gravitational collapse of a class of spherically symmetric inhomogeneous perfect fluid models obtained by introducing small radial perturbations in an otherwise homogeneous matter cloud. Our aim here is to study the genericity and stability of the formation of black holes and locally naked singularities in collapse. While the occurrence of naked singularities is known for many models of collapse, the key issue now in focus is genericity and stability of these outcomes. Towards this purpose, we study how the introduction of a somewhat general class of small inhomogeneities in homogeneous collapse leading to a black hole can change the final outcome to a naked singularity. The key feature that we assume for the perturbation profile is that of a mass profile that is separable in radial and temporal coordinates. The known models of dust and homogeneous perfect fluid collapse can be obtained from this choice of the mass profile as special cases. This choice is very general and physically well motivated and we show that this class of collapse models leads to the formation of a naked singularity as the final state.
We consider the problem of optimal incomplete transportation between the empirical measure on an i.i.d. uniform sample on the d-dimensional unit cube $[0,1]^d$ and the true measure. This is a family of problems lying in between classical optimal transportation and nearest neighbor problems. We show that the empirical cost of optimal incomplete transportation vanishes at rate $O_P(n^{-1/d})$, where n denotes the sample size. In dimension $d\geq3$ the rate is the same as in classical optimal transportation, but in low dimension it is (much) higher than the classical rate.
Compensated isocurvature perturbations are opposite spatial fluctuations in the baryon and dark matter (DM) densities. They arise in the curvaton model and some models of baryogenesis. While the gravitational effects of baryon fluctuations are compensated by those of DM, leaving no observable impacts on the cosmic microwave background (CMB) at first order, they modulate the sound horizon at recombination, thereby correlating CMB anisotropies at different multipoles. As a result, CIPs can be reconstructed using quadratic estimators similarly to CMB detection of gravitational lensing. Because of these similarities, however, the CIP estimators are biased with lensing contributions that must be subtracted. These lensing contributions for CMB polarization measurement of CIPs are found to roughly triple the noise power of the total CIP estimator on large scales. In addition, the cross power with temperature and $E$-mode polarization are contaminated by lensing-ISW (integrated Sachs-Wolfe) correlations and reionization-lensing correlations respectively. For a cosmic-variance-limited (CVL) temperature and polarization experiment measuring out to multipoles $l_{\max} = 2500$, the lensing noise raises the detection threshold by a factor of 1.5, leaving a $2.7\sigma$ detection possible for the maximal CIP signal in the curvaton model.
Cluster decays of rare-earth nuclei are studied with a view to look for neutron magic shells for the $_{50}$Sn nucleus as the daughter product always. The $^{100}$Sn and $^{132}$Sn radioactivities are studied to find the most probable cluster decays and the possibility, if any, of new neutron shells. For a wide range of parent nuclei considered here (from Ba to Pt) $^{12}$C from $^{112}$Ba and $^{78}$Ni from $^{210}$Pt parent are predicted to be the most probable clusters (minimum decay half-life) referring to $^{100}$Sn and $^{132}$Sn daughters, respectively. Also, $^{22}$Mg decay of $^{122}$Sm is indicated at the second best possibilty for $^{100}$Sn-daughter decay. In addition to these well known magic shells (Z=50, N=50 and 82), a new magic shell at Z=50, N=66 ($^{116}$Sn daughter) is indicated for the $^{64}$Ni decay from $^{180}$Pt parent.
Antiferromagnet Mn$_3$P with Neel temperature $T_N=30$ K is composed of Mn-tetrahedrons and zigzag chains formed by three inequivalent Mn sites. Due to the nearly frustrated lattice with many short Mn-Mn bonds, competition of the exchange interactions is expected. We here investigate the magnetic structure and physical properties including pressure effect in single crystals of this material, and reveal a complex yet well-ordered helimagnetic structure. The itinerant character of this materials is strong, and the ordered state with small magnetic moments is easily suppressed under pressure, exhibiting a quantum critical point at $\sim1.6$ GPa. The remarkable mass renormalization, even in the ordered state, and an incoherent-coherent crossover in the low-temperature region, characterize an unusual electronic state in Mn$_3$P, which is most likely effected by the underlying frustration effect.
Magnetometry and magnetic imaging with nitrogen-vacancy (NV) defects in diamond rely on the optical detection of electron spin resonance (ESR). However, this technique is inherently limited to magnetic fields that are weak enough to avoid electron spin mixing. Here we focus on the high off-axis magnetic field regime for which spin mixing alters the NV defect spin dynamics. We first study in a quantitative manner the dependence of the NV defect optical properties on the magnetic field vector B. Magnetic-field-dependent time-resolved photoluminescence (PL) measurements are compared to a seven-level model of the NV defect that accounts for field-induced spin mixing. The model reproduces the decreases in (i) ESR contrast, (ii) PL intensity and (iii) excited level lifetime with an increasing off-axis magnetic field. We next demonstrate that those effects can be used to perform all-optical magnetic imaging in the high off-axis magnetic field regime. Using a scanning NV defect microscope, we map the stray field of a magnetic hard disk through both PL and fluorescence lifetime imaging. This all-optical method for high magnetic field imaging at the nanoscale might be of interest in the field of nanomagnetism, where samples producing fields in excess of several tens of milliteslas are typical.
We consider the problem of counting the occurrences of patterns of the form $xy-z$ within flattened permutations of a given length. Using symmetric functions, we find recurrence relations satisfied by the distributions on $\mathcal{S}_n$ for the patterns 12-3, 21-3, 23-1 and 32-1, and develop a unified approach to obtain explicit formulas. By these recurrences, we are able to determine simple closed form expressions for the number of permutations that, when flattened, avoid one of these patterns as well as expressions for the average number of occurrences. In particular, we find that the average number of 23-1 patterns and the average number of 32-1 patterns in $\text{Flatten}(\pi)$, taken over all permutations $\pi$ of the same length, are equal, as are the number of permutations avoiding either of these patterns. We also find that the average number of 21-3 patterns in $\text{Flatten}(\pi)$ over all $\pi$ is the same as it is for 31-2 patterns.
We give a bijective proof of Hurwitz formula for the number of simple branched coverings of the sphere by itself. Our approach extends to double Hurwitz numbers and yields new properties for them. In particular we prove for double Hurwitz numbers a conjecture of Kazarian and Zvonkine, and we give an expression that in a sense interpolates between two celebrated polynomiality properties: polynomiality in chambers for double Hurwitz numbers, and a new analog for almost simple genus 0 Hurwitz numbers of the polynomiality up to normalization of simple Hurwitz numbers of genus $g$. Some probabilistic implications of our results for random branched coverings are briefly discussed in conclusion.
Spin systems with frustrated anisotropic interactions are of significant interest due to possible exotic ground states. We have explored their phase diagram on a nearest-neighbor triangular lattice using the density-matrix renormalization group and mapped out the topography of the region that can harbor a spin liquid. We find that this spin-liquid phase is continuously connected to a previously discovered spin-liquid phase of the isotropic $J_1\!-\!J_2$ model. The two limits show nearly identical spin correlations, making the case that their respective spin liquids are isomorphic to each other.
Given an elliptic fibration $f \colon X \to S$ over the spectrum of a complete discrete valuation ring with algebraically closed residue field, we use a Hochschild--Serre spectral sequence to express the torsion in $R^1f_\ast \mathscr{O}_X$ as the first group cohomology $H^1(G,H^0(S^\prime, \mathscr{O}_{S^\prime}))$. Here, $G$ is the Galois group of the maximal extension $K^\prime / K$ such that the normalization of $X \times_S S^\prime$ induces an \'etale covering of $X$, where $S^\prime$ is the normalization of $S$ in $K^\prime$. The case where $S$ is a Dedekind scheme is easily reduced to the local case. Moreover, we generalize to higher-dimensional fibrations.
We perform classic molecular dynamics simulations to comparatively investigate the mechanical properties of single-layer MoS2 and a graphene/MoS2/graphene heterostructure under uniaxial tension. We show that the lattice mismatch between MoS2 and graphene will lead to an spontaneous strain energy in the interface. The Young's modulus of MoS2 can be enhanced by a factor of five by sandwiching it between two graphene layers. While the stiffness is enhanced, the yield strain of the MoS2 is reduced due to lateral buckling of the outer graphene layers due to the applied mechanical tension.
Multi-target multi-camera tracking (MTMCT), i.e., tracking multiple targets across multiple cameras, is a crucial technique for smart city applications. In this paper, we propose an effective and reliable MTMCT framework for vehicles, which consists of a traffic-aware single camera tracking (TSCT) algorithm, a trajectory-based camera link model (CLM) for vehicle re-identification (ReID), and a hierarchical clustering algorithm to obtain the cross camera vehicle trajectories. First, the TSCT, which jointly considers vehicle appearance, geometric features, and some common traffic scenarios, is proposed to track the vehicles in each camera separately. Second, the trajectory-based CLM is adopted to facilitate the relationship between each pair of adjacently connected cameras and add spatio-temporal constraints for the subsequent vehicle ReID with temporal attention. Third, the hierarchical clustering algorithm is used to merge the vehicle trajectories among all the cameras to obtain the final MTMCT results. Our proposed MTMCT is evaluated on the CityFlow dataset and achieves a new state-of-the-art performance with IDF1 of 74.93%.
Domain adversarial learning aligns the feature distributions across the source and target domains in a two-player minimax game. Existing domain adversarial networks generally assume identical label space across different domains. In the presence of big data, there is strong motivation of transferring deep models from existing big domains to unknown small domains. This paper introduces partial domain adaptation as a new domain adaptation scenario, which relaxes the fully shared label space assumption to that the source label space subsumes the target label space. Previous methods typically match the whole source domain to the target domain, which are vulnerable to negative transfer for the partial domain adaptation problem due to the large mismatch between label spaces. We present Partial Adversarial Domain Adaptation (PADA), which simultaneously alleviates negative transfer by down-weighing the data of outlier source classes for training both source classifier and domain adversary, and promotes positive transfer by matching the feature distributions in the shared label space. Experiments show that PADA exceeds state-of-the-art results for partial domain adaptation tasks on several datasets.
We use high-resolution UV spectra of the radio-quiet QSO H1821+643 (z_em = 0.297), obtained with STIS and FUSE, to study the ionization and metallicity of an intervening O VI absorption line system at z(abs) = 0.1212. This absorber has the following notable properties: (1) Several galaxies are close to the sight line at the absorber redshift, including an actively star-forming galaxy at a projected distance of 144 kpc. (2) There is a complex cluster of H I lya absorption lines near the O VI redshift, including at least five components spread over a velocity range of ~700 km/s . (3) The strongest lya line in the cluster appears to be composed of a mildly saturated component with a typical b-value blended with a broad component with b = 85 km/s . (4) The O VI absorption is not aligned with the strongest H I absorption, but instead is well-aligned with the broad component. (5) The only detected species (>4sigma) are O VI and H I despite coverage of strong transitions of other abundant elements. Based on these constraints, we find that the absorption line properties can be produced in collisionally ionized gas with roughly 5.3 < log T < 5.6 and -1.8 < [O/H] < -0.6. However, we find that photoionization is also viable if the pathlength l through the absorbing gas is long enough; simple photoionization models require 85 < l < 1900 kpc and -1.1 < [O/H] < -0.3. We briefly discuss how observations of X-ray absorption lines due to O VII and O VIII could be used, in principle, to break the ionization mechanism degeneracy.
We construct and validate the selection function of the MARD-Y3 sample. This sample was selected through optical follow-up of the 2nd ROSAT faint source catalog (2RXS) with Dark Energy Survey year 3 (DES-Y3) data. The selection function is modeled by combining an empirically constructed X-ray selection function with an incompleteness model for the optical follow-up. We validate the joint selection function by testing the consistency of the constraints on the X-ray flux--mass and richness--mass scaling relation parameters derived from different sources of mass information: (1) cross-calibration using SPT-SZ clusters, (2) calibration using number counts in X-ray, in optical and in both X-ray and optical while marginalizing over cosmological parameters, and (3) other published analyses. We find that the constraints on the scaling relation from the number counts and SPT-SZ cross-calibration agree, indicating that our modeling of the selection function is adequate. Furthermore, we apply a largely cosmology independent method to validate selection functions via the computation of the probability of finding each cluster in the SPT-SZ sample in the MARD-Y3 sample and vice-versa. This test reveals no clear evidence for MARD-Y3 contamination, SPT-SZ incompleteness or outlier fraction. Finally, we discuss the prospects of the techniques presented here to limit systematic selection effects in future cluster cosmological studies.
Dynamic phase transition of charged dilaton black holes is investigated in this paper. We introduce the Gibbs free energy landscape and calculate the corresponding $G_L$ for the dilaton black hole. On the one hand, we numerically solve the Fokker-Planck equation constrained by only the reflecting boundary condition. The effects of dilaton gravity on the probabilistic evolution of dilaton black holes are quite obvious. Firstly, the horizon radius difference between the large dilaton black hole and small dilaton black hole increases with the parameter $\alpha$. Secondly, with the increasing of $\alpha$, the system needs much more time to achieve a stationary distribution. Thirdly, the value which $\rho(r_l,t)$ and $\rho(r_s,t)$ finally attain varies with the parameter $\alpha$. On the other hand, resolving Fokker-Planck equation constrained by both the reflecting boundary condition and absorbing boundary condition, we investigate the first passage process of dilaton black holes. The initial peak decays more slowly with the increase of $\alpha$, which can also be witnessed from the slow down of the decay of $\Sigma(t)$ (the sum of the probability that the black hole system having not finished a first passage by time $t$). Moreover, the time corresponding to the single peak of the first passage time distribution is also found to increase with the parameter $\alpha$. Considering all the observations mentioned above, the dilaton field does slow down the dynamic phase transition process between the large black hole and small black hole.
Two-dimensional spinless Falicov-Kimball model (FKM) with correlated hopping is studied perturbatively in the limit of large on-site Coulomb interaction $U$. In the neutral case the effective Hamiltonian in spin variables is derived up to terms proportional to $U^{-3}$. Unlike the simplest FKM case, it contains odd parity terms (resulting from the correlated hopping) in addition to even parity ones. The ground-state phase diagram of the effective Hamiltonian is examined in the $(a/t, h)$ plane, where $a/t$ is a parameter characterizing strength of the correlated hopping and $h$ is a difference of chemical potentials of two sorts of particles present in the system. It appears to be asymmetric with respect to the change $h\to -h$ and a new ordered phase is found for a certain interval of $a/t$.
We present a study of the stellar populations of galaxies in the cluster RXJ0152.7-1357 at a redshift of 0.83. The study is based on new high S/N spectroscopy of 29 cluster members covering the wavelength range 5000-10000A as well as r'i'z' photometry of the cluster. The scaling relations between velocity dispersions, luminosities and Balmer line strengths appear to be in agreement with pure passive evolution of the stellar populations with a formation redshift z=4. However, the strengths of the D4000 indices and the metal indices do not support this interpretation. Compared to z=0, the metal indices (C4668, Fe4383, CN3883, G4300 and CN2) show that at least half of the non-emission line galaxies in RXJ0152.7-1357 have [alpha/Fe] of 0.2 dex higher, and about half of the galaxies have significantly lower metal content. The differences in stellar populations of the galaxies are associated with the location of the galaxies relative to the X-ray emission. The galaxies with weak C4668 and G4300, as well as galaxies with weak [OII] emission, are located in areas of low X-ray luminosity. It is possible that these galaxies are experiencing the effect of the cluster merger taking place in RXJ0152.7-1357 as (short) episodes of star formation, while the galaxies in the cores of the X-ray sub-clumps are unaffected by the merger. The spectroscopy of the RXJ0152.7-1357 galaxies shows for the first time galaxies in a rich cluster at intermediate redshift that cannot evolve passively into the present day galaxy population in rich clusters. Additional physical processes may be at work and we speculate that merging with infalling (disk) galaxies in which stars have formed over an extended period might produce the required reduction in [alpha/Fe]. (abridged)
Spectral functions relevant in the context of quantum field theory under the influence of spherically symmetric external conditions are analysed. Examples comprise heat-kernels, determinants and spectral sums needed for the analysis of Casimir energies. First, we summarize that a convenient way of handling them is to use the associated zeta function. A way to determine all its needed properties is derived. Using the connection with the mentioned spectral functions, we provide: i.) a method for the calculation of heat-kernel coefficients of Laplace-like operators on Riemannian manifolds with smooth boundaries and ii.) an analysis of vacuum energies in the presence of spherically symmetric boundaries and external background potentials.
We study here the spherical gravitational collapse assuming initial data to be necessarily smooth, as motivated by the requirements based on physical reasonableness. A tangential pressure model is constructed and analyzed in order to understand the final fate of collapse explicitly in terms of the density and pressure parameters at the initial epoch from which the collapsedevelops. It is seen that both black holes and naked singularities are produced as collapse end states even when the initial data is smooth. We show that the outcome is decided entirely in terms of the initial data, as given by density, pressure and velocity profiles at the initial epoch, from which the collapse evolves.
Many of the fundamental properties of early-type galaxies (ellipticals and lenticulars) can only be accessed by venturing beyond their oft-studied centers into their large-radius halo regions. Advances in observations of kinematical tracers allow early-type halos to be increasingly well probed. This review focuses on recent findings on angular momentum and dark matter content, and discusses some possible implications for galaxy structure and formation.
We probe the radial clumping stratification of OB stars in the intermediate and outer wind regions (r>~2 R*) to derive upper limits for mass-loss rates, and compare to current mass-loss implementation. Together with archival multi-wavelength data, our new far-infrared continuum observations for a sample of 25 OB stars (including 13 B Supergiants) uniquely constrain the clumping properties of the intermediate wind region. We derive the minimum radial stratification of the clumping factor through the stellar wind, fclmin(r), and the corresponding maximum mass-loss rate, Mdotmax, normalising clumping factors to the outermost wind region (clfar=1). The clumping degree for r>~2 R* decreases or stays constant with increasing radius for almost the whole sample. There is a dependence on luminosity class and spectral type at the intermediate region relative to the outer ones: O Supergiants (OSGs) present a factor 2 larger clumping factors than B Supergiants (BSGs). The maximum clumping of roughly 1/3 of the OB Supergiants occurs close to the wind base (r<~2 R*) and then decreases monotonically. This contrasts with the more frequent case where the lowermost clumping increases towards a maximum, and needs to be addressed by theoretical models. Additionally, the estimated Mdotmax for BSGs is at least one order of magnitude lower than theoretical values, whereas for OSGs our results and predictions agree within errors. Assuming values of clfar=4-9 from hydrodynamical models would imply a reduction of mass-loss rates included in stellar evolution models by a factor 2-3 for OSGs and by factors 6-200 for BSGs below the first bi-stability jump. This implies large reductions of mass-loss rates applied in evolution-models for BSGs, independently of the actual clumping properties of these winds, and a thorough re-investigation of BSG mass-loss rates and their effects on stellar evolution.
The Reference-based Super-resolution (RefSR) super-resolves a low-resolution (LR) image given an external high-resolution (HR) reference image, where the reference image and LR image share similar viewpoint but with significant resolution gap x8. Existing RefSR methods work in a cascaded way such as patch matching followed by synthesis pipeline with two independently defined objective functions, leading to the inter-patch misalignment, grid effect and inefficient optimization. To resolve these issues, we present CrossNet, an end-to-end and fully-convolutional deep neural network using cross-scale warping. Our network contains image encoders, cross-scale warping layers, and fusion decoder: the encoder serves to extract multi-scale features from both the LR and the reference images; the cross-scale warping layers spatially aligns the reference feature map with the LR feature map; the decoder finally aggregates feature maps from both domains to synthesize the HR output. Using cross-scale warping, our network is able to perform spatial alignment at pixel-level in an end-to-end fashion, which improves the existing schemes both in precision (around 2dB-4dB) and efficiency (more than 100 times faster).