ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, we study two PDEs that generalize the urban crime model proposed by Short \emph{et al}. [Math. Models Methods Appl. Sci., 18 (2008), pp. 1249-1267]. Our modifications are made under assumption of the spatial heterogeneity of both the near-repeat victimization effect and the dispersal strategy of criminal agents. We investigate pattern formations in the reaction-advection-diffusion systems with nonlinear diffusion over multi-dimensional bounded domains subject to homogeneous Neumann boundary conditions. It is shown that the positive homogeneous steady state loses its stability as the intrinsic near-repeat victimization rate $\epsilon$ decreases and spatially nonconstant solutions emerge through bifurcation. Moreover, we find the wavemode selection mechanism through rigorous stability analysis of these nontrivial patterns, which shows that the only stable pattern must have wavenumber that maximizes the bifurcation value. Based on this wavemode selection mechanism, we will be able to precisely predict the formation of stable aggregates of the house attractiveness and criminal population density, at least when the diffusion rate $\epsilon$ is around the principal bifurcation value. Our theoretical results also suggest that large domains support more stable aggregates than small domains. Finally, we perform extensive numerical simulations over 1D intervals and 2D squares to illustrate and verify our theoretical findings. Our numerics also include some interesting phenomena such as the merging of two interior spikes and the emerging of new spikes, etc. These nontrivial solutions can model the well observed aggregation phenomenon in urban criminal activities.
We study the infrared perturbative properties of a class of non supersymmetric gauge theories with the same field content of N=4 Super Yang-Mills and we show that the N=4 supersymmetric model represents an IR unstable fixed point for the renormalization group equations.
We present a study of the kinematics of the remote globular cluster NGC5694 based on GIRAFFE@VLT medium resolution spectra. A sample of 165 individual stars selected to lie on the Red Giant Branch in the cluster Color Magnitude Diagram was considered. Using radial velocity and metallicity from Calcium triplet, we were able to select 83 bona-fide cluster members. The addition of six previously known members leads to a total sample of 89 cluster giants with typical uncertainties <1.0 km/s in their radial velocity estimates. The sample covers a wide range of projected distances from the cluster center, from ~0.2 arcmin to 6.5 arcmin = 23 half-light radii (r_h). We find only very weak rotation, as typical of metal-poor globular clusters. The velocity dispersion gently declines from a central value of sigma=6.1 km/s to sigma = 2.5 km/s at ~2 arcmin = 7.1= r_h, then it remainins flat out to the next (and last) measured point of the dispersion profile, at ~4 arcmin = 14.0 r_h, at odds with the predictions of isotropic King models. We show that both isotropic single-mass non-collisional models and multi-mass anisotropic models can reproduce the observed surface brightness and velocity dispersion profiles.
The Mordell-Weil group of an elliptically fibered Calabi-Yau threefold X contains information about the abelian sector of the six-dimensional theory obtained by compactifying F-theory on X. After examining features of the abelian anomaly coefficient matrix and U(1) charge quantization conditions of general F-theory vacua, we study Calabi-Yau threefolds with Mordell-Weil rank-one as a first step towards understanding the features of the Mordell-Weil group of threefolds in more detail. In particular, we generate an interesting class of F-theory models with U(1) gauge symmetry that have matter with both charges 1 and 2. The anomaly equations --- which relate the Neron-Tate height of a section to intersection numbers between the section and fibral rational curves of the manifold --- serve as an important tool in our analysis.
Electromagnetic properties of off-shell particles are discussed on the basis of a purely electromagnetic reaction: virtual Compton scattering off a proton. It is shown that the definition of off-shell electromagnetic form factors is not gauge invariant and that these cannot be investigated in practice. Using only fundamental requirements of gauge invariance it is demonstrated that off-shell effects are cancelled in the longitudinal components of the total conserved current by the minimal contact current, while the off-shellness appears only in the the transverse (gauge invariant) non-pole part. This provides the possibility to introduce an on-shell extrapolated form factor F_1^+(q^2) in a gauge invariant way for the unphysical time-like region, 4m_e^2<q^2, 4M_N^2.
Hubble Space Telescope V,I photometry of stars in the Large Magellanic Cloud Cluster NGC 1866 shows a well defined cluster main sequence down to V=25 mag, with little contamination from field or foreground stars. We use the main sequence fitting procedure to link the distance of NGC 1866 to the Hipparcos determination of the distance for the Hyades MS stars, making use of evolutionary prescriptions to allow for differences in the chemical composition. On this basis we find a true distance modulus for NGC 1866 of 18.35 +/- 0.05 mag. If the cluster is assumed to lie in the LMC plane then the LMC modulus is 0.02 mag less.
With adiabatic techniques, it is possible to create quantum superposition states with high fidelity while exercising limited control over the parameters of a system. However, because these techniques are slow compared to other timescales in the system, they are usually not suitable for creating highly unstable states or performing time-critical processes. Both of these situations arise in quantum information processing, where entangled states may only be isolated from the environment for a short time and where quantum computers require high-fidelity operations to be performed quickly. Recently it has been shown that techniques like optimal control and shortcuts to adiabaticity may be used to prepare quantum states non-adiabatically with high fidelity. Here we present two examples of how these techniques can be used to create maximally entangled many-body NOON states in one-dimensional Tonks--Girardeau gases.
In this work, we have performed large-scale shell-model calculations for the first-forbidden $\beta ^{-}$ decay of $^{207}$Hg into the one-proton-hole nucleus $^{207}$Tl corresponding to the recently available experimental data from ISOLDE-CERN [T. A. Berry et al., Phys. Rev. C 101, 054311 (2020)]. We have used the one-particle one-hole ($1p$-$1h$) truncation for both protons and neutrons simultaneously across the doubly-shell closure at $^{208}$Pb in the final states of $^{207}$Tl. In our calculations, we have also considered the effect of mesonic enhancement $\epsilon _{\mathrm{mec}}=2.01\pm 0.05$ in the rank-0 for the axial-charge matrix element $\gamma _{5}$. Here, we have calculated the $\log ft$ values from the ground-state of $^{207}$Hg to the several excited states of $^{207}$Tl and obtained a good agreement between the calculated and the experimental data. In the experimental data spin and parity for some states are not yet confirmed, thus based on the shell-model results for the $\log ft$ values we have given the prediction for these states. This is the first theoretical calculation for the $\log ft$ values for these transitions.
Let the sign components of the maximal covectors of a simple oriented matroid M be represented by the real numbers -1 and 1. Consider the vertex set V(R) of a symmetric cycle R of adjacent topes in the tope graph of M as a subposet of the tope poset of M. If B is the bottom element of the tope poset then B is equal to the unweighted sum of the members of the set min V(R) of minimal elements of the subposet V(R); if B is the positive tope then the set min V(R) is a critical tope committee for the acyclic oriented matroid M.
The ratio of electric to magnetic proton form factors G_E/G_M as measured in polarization transfer experiments shows a characteristic linear decrease with increasing momentum transfer Q^2. We present a simple argument how such a decrease arises naturally in chiral soliton models. For a detailed comparison of model results with experimentally determined form factors it is necessary to employ a boost from the soliton rest frame to the Breit frame. To enforce asymptotic counting rules for form factors, the model must be supplemented by suitably chosen interpolating powers n in the boost prescription. Within the minimal pi-rho-omega soliton model, with the same n for both, electric and magnetic form factors, it is possible to obtain a very satisfactory fit to all available proton data for the magnetic form factor and to the recent polarization results for the ratio G_E/G_M. At the same time the small and very sensitive neutron electric form factor is reasonably well reproduced. The results show a systematic discrepancy with presently available data for the neutron magnetic form factor G_M^n for Q^2 > 1 (GeV/c)^2. We additionally comment on the possibility to extract information about the form factors in the time-like region and on two-photon exchange contributions to unpolarized elastic scattering which specifically arise in soliton models.
Extensions to higher-dimensions are given for a convolution estimate used by Klainerman and Machedon in their study of uniqueness of solutions for the Gross-Pitaevskii hierarchy. Such estimates determine more general forms of Stein-Weiss integrals involving restriction to smooth submanifolds.
A Maxwell-Stefan system for fluid mixtures with driving forces depending on Cahn-Hilliard-type chemical potentials is analyzed. The corresponding parabolic cross-diffusion equations contain fourth-order derivatives and are considered in a bounded domain with no-flux boundary conditions. The main difficulty of the analysis is the degeneracy of the diffusion matrix, which is overcome by proving the positive definiteness of the matrix on a subspace and using the Bott--Duffin matrix inverse. The global existence of weak solutions and a weak-strong uniqueness property are shown by a careful combination of (relative) energy and entropy estimates, yielding $H^2(\Omega)$ bounds for the densities, which cannot be obtained from the energy or entropy inequalities alone.
We discuss the properties of the Liouville theory coupled to the c=1 matter when perturbed by an operator, the screening operator of the $SL(2;R)$ current algebra, which is supposed to generate the mass of the two-dimensional black hole. Mimicking the standard KPZ scaling theory of the Liouville system perturbed by the cosmological constant operator, we develop a scaling theory of correlation functions as functions of the mass of the black hole. Contrary to the case of KPZ, the present theory does not have the $c=1$ barrior and seems somewhat insensitive to the delatils of the matter content of the theory; the string succeptibility equals 1 independent of the matter central charge. It turns out that our scaling exponents agree with those of the deformed matrix model proposed recently by Jevicki and Yoneya.
Quarkyonic matter is a new phase of QCD at finite temperature and density which is distinct from the confined and de-confined phases. Its existence is unambiguously argued in the large number of colors limit in QCD. Hints of its existence for 3 color QCD are shown in lattice Monte-Carlo data and heavy ion experiments.
Tracking has traditionally been the art of following interest points through space and time. This changed with the rise of powerful deep networks. Nowadays, tracking is dominated by pipelines that perform object detection followed by temporal association, also known as tracking-by-detection. In this paper, we present a simultaneous detection and tracking algorithm that is simpler, faster, and more accurate than the state of the art. Our tracker, CenterTrack, applies a detection model to a pair of images and detections from the prior frame. Given this minimal input, CenterTrack localizes objects and predicts their associations with the previous frame. That's it. CenterTrack is simple, online (no peeking into the future), and real-time. It achieves 67.3% MOTA on the MOT17 challenge at 22 FPS and 89.4% MOTA on the KITTI tracking benchmark at 15 FPS, setting a new state of the art on both datasets. CenterTrack is easily extended to monocular 3D tracking by regressing additional 3D attributes. Using monocular video input, it achieves 28.3% AMOTA@0.2 on the newly released nuScenes 3D tracking benchmark, substantially outperforming the monocular baseline on this benchmark while running at 28 FPS.
We present the mass distribution for all S/N > 15 pure DA white dwarfs detected in the Sloan Digital Sky Survey up to Data Release 12, fitted with Koester models for ML2/alpha=0.8, and with Teff > 10 000 K, and for DBs with S/N >10, fitted with ML2/alpha=1.25, for Teff > 16 000 K. These mass distributions are for log g > 6.5 stars, i.e., excluding the Extremely Low Mass white dwarfs. We also present the mass distributions corrected by volume with the 1/Vmax approach, for stars brighter than g=19. Both distributions have a maximum at M=0.624 Msun but very distinct shapes. From the estimated z-distances, we deduce a disk scale height of 300 pc. We also present 10 probable halo white dwarfs, from their galactic U, V, W velocities.
We calculate $^3$He+$p$ scattering phase shifts in two different microscopic cluster models, Model T and Model C, in order to show the effects of tensor force as well as $D$-wave components in the cluster wave function. Model T employs a realistic nucleon-nucleon potential and includes the $D$-wave, whereas Model C employs an effective potential in which the tensor-force effect is considered to be renormalized into the central force and includes only the $S$-wave for the cluster intrinsic motion. The $S$- and $P$-wave elastic scattering phase shifts are obtained in the \{$^3$He+$p$\}+\{$d$ + 2$p$\} coupled-channels calculation. In Model T, the $d$ + 2$p$ channel plays a significant role in producing the $P$-wave resonant phase shifts but hardly affects the $S$-wave non-resonant phase shifts. In Model C, however, the effect of the $d$ + 2$p$ channel is suppressed in both of the $S$- and $P$-wave phase shifts, suggesting that it is renormalized mostly as the $^3$He(1/2$^+$)+$p$ channel in the resonance region.
We show that universal holonomic quantum computation (HQC) can be achieved fault-tolerantly by adiabatically deforming the gapped stabilizer Hamiltonian of the surface code, where quantum information is encoded in the degenerate ground space of the system Hamiltonian. We explicitly propose procedures to perform each logical operation, including logical state initialization, logical state measurement, logical CNOT, state injection and distillation,etc. In particular, adiabatic braiding of different types of holes on the surface leads to a topologically protected, non-Abelian geometric logical CNOT. Throughout the computation, quantum information is protected from both small perturbations and low weight thermal excitations by a constant energy gap, and is independent of the system size. Also the Hamiltonian terms have weight at most four during the whole process. The effect of thermal error propagation is considered during the adiabatic code deformation. With the help of active error correction, this scheme is fault-tolerant, in the sense that the computation time can be arbitrarily long for large enough lattice size. It is shown that the frequency of error correction and the physical resources needed can be greatly reduced by the constant energy gap.
Human action recognition is a quite hugely investigated area where most remarkable action recognition networks usually use large-scale coarse-grained action datasets of daily human actions as inputs to state the superiority of their networks. We intend to recognize our small-scale fine-grained Tai Chi action dataset using neural networks and propose a transfer-learning method using NTU RGB+D dataset to pre-train our network. More specifically, the proposed method first uses a large-scale NTU RGB+D dataset to pre-train the Transformer-based network for action recognition to extract common features among human motion. Then we freeze the network weights except for the fully connected (FC) layer and take our Tai Chi actions as inputs only to train the initialized FC weights. Experimental results show that our general model pipeline can reach a high accuracy of small-scale fine-grained Tai Chi action recognition with even few inputs and demonstrate that our method achieves the state-of-the-art performance compared with previous Tai Chi action recognition methods.
We present an endpoint box regression module(epBRM), which is designed for predicting precise 3D bounding boxes using raw LiDAR 3D point clouds. The proposed epBRM is built with sequence of small networks and is computationally lightweight. Our approach can improve a 3D object detection performance by predicting more precise 3D bounding box coordinates. The proposed approach requires 40 minutes of training to improve the detection performance. Moreover, epBRM imposes less than 12ms to network inference time for up-to 20 objects.   The proposed approach utilizes a spatial transformation mechanism to simplify the box regression task. Adopting spatial transformation mechanism into epBRM makes it possible to improve the quality of detection with a small sized network.   We conduct in-depth analysis of the effect of various spatial transformation mechanisms applied on raw LiDAR 3D point clouds. We also evaluate the proposed epBRM by applying it to several state-of-the-art 3D object detection systems.   We evaluate our approach on KITTI dataset, a standard 3D object detection benchmark for autonomous vehicles. The proposed epBRM enhances the overlaps between ground truth bounding boxes and detected bounding boxes, and improves 3D object detection. Our proposed method evaluated in KITTI test server outperforms current state-of-the-art approaches.
Ark 564 is an extreme high-Eddington Narrow-line Seyfert 1 galaxy, known for being one of the brightest, most rapidly variable soft X-ray AGN, and for having one of the lowest temperature coronae. Here we present a 410-ks NuSTAR observation and two 115-ks XMM-Newton observations of this unique source, which reveal a very strong, relativistically broadened iron line. We compute the Fourier-resolved time lags by first using Gaussian processes to interpolate the NuSTAR gaps, implementing the first employment of multi-task learning for application in AGN timing. By fitting simultaneously the time lags and the flux spectra with the relativistic reverberation model RELTRANS, we constrain the mass at $2.3^{+2.6}_{-1.3} \times 10^6M_\odot$, although additional components are required to describe the prominent soft excess in this source. These results motivate future combinations of machine learning, Fourier-resolved timing, and the development of reverberation models.
We propose nonlinear parabolic equations of Monge--Amp\'ere (M--A) type that admit regional, single poin, and global blow-up of similarity type. A similar model is derived for a fourth-order M--A flow.
We present C and X-band radio observations of the famous utraluminous X-ray source (ULX) Holmberg IX X-1, previously discovered to be associated with an optical emission line nebula several hundred pc in extent. Our recent infrared study of the ULX suggested that a jet could be responsible for the infrared excess detected at the ULX position. The new radio observations, performed using the Karl G. Jansky Very Large Array (VLA) in B-configuration, reveal the presence of a radio counterpart to the nebula with a spectral slope of -0.56 similar to other ULXs. Importantly, we find no evidence for an unresolved radio source associated with the ULX itself, and we set an upper limit on any 5 GHz radio core emission of 6.6 $\mu$Jy ($4.1\times10^{32}$ erg s$^{-1}$). This is 20 times fainter than what we expect if the bubble is energized by a jet. If a jet exists its core component is unlikely to be responsible for the infrared excess unless it is variable. Strong winds which are expected in super-Eddington sources could also play an important role in inflating the radio bubble. We discuss possible interpretations of the radio/optical bubble and we prefer the jet+winds-blown bubble scenario similar to the microquasar SS 433.
For a line bundle L on a smooth surface S, it is now known that the degree of the Severi variety of cogenus-d curves is given by a universal polynomial in the Chern classes of L and S if L is d-very ample. For S rational, we relax the latter condition substantially: it suffices that three key loci be of codimension more than d. As corollaries, we prove that the condition conjectured by G\"ottsche suffices if S is P^2 or S is any Hirzebruch surface, and that a similar condition suffices if S is any classical del Pezzo surface.
We give a strong approximation of Rosenblatt process via transport processes and we give the rate of convergence.
A fully self-consistent density-functional theory (DFT) with improved functionals is used to provide a comprehensive account of structural, electronic, and optical properties of C$_{3}$N$_{4}$ polymorphs. Using our recently developed van Leeuwen-Baerends (vLB) corrected local-density approximation (LDA), we implemented LDA+vLB within full-potential N$^{th}$-order muffin-tin orbital (FP-NMTO) method and show that it improves structural properties and band gaps compared to semi-local functionals (LDA/GGA). We demonstrate that the LDA+vLB predicts band-structure and work-function for well-studied 2D-graphene and bulk-Si in very good agreement with experiments, and more exact hybrid functional (HSE) calculations as implemented in the Quantum-Espresso (QE) package. The structural and electronic-structure (band gap) properties of C$_{3}$N$_{4}$ polymorphs calculated using FP-NMTO-LDA+vLB is compared with more sophisticated hybrid-functional calculations. We also perform detailed investigation of photocatalytic behavior using QE-HSE method of C$_{3}$N$_{4}$ polymorphs through work-function, band (valence and conduction) position with respect to water reduction and oxidation potential. Our results show $\gamma$-C$_{3}$N$_{4}$ as the best candidate for photocatalysis among all the C$_{3}$N$_{4}$~polymorphs but it is dynamically unstable at `zero' pressure. We show that $\gamma$-C$_{3}$N$_{4}$ can be stabilized under hydrostatic-pressure, which improves its photocatalytic behavior relative to water reduction and oxidation potentials.