ShantanuT01/DACTYL-Pretraining huggingface dataset:
We prove existence, uniqueness and regularity of weak solutions of a coupled parabolic-elliptic model in two dimensions; we consider the standard equations of magnetohydrodynamics with the advective terms removed from the velocity equation. Despite the apparent simplicity of the model, the proof requires results that are at the limit of what is available, including elliptic regularity in $L^{1}$ and a strengthened form of the Ladyzhenskaya inequality   \[ \| f \|_{L^{4}} \leq c \| f \|_{L^{2,\infty}}^{1/2} \| \nabla f \|_{L^{2}}^{1/2}, \] which we derive using the theory of interpolation. The model has applications to the method of magnetic relaxation, introduced by Moffatt (J. Fluid. Mech. 159, 359-378, 1985), to construct stationary Euler flows with non-trivial topology.
In this paper we are concerned with the SIR (Susceptible-Infective-Removed) epidemic on open clusters of bond percolation on the squared lattice. For the SIR model, a susceptible vertex is infected at rate proportional to the number of infective neighbors while an infective vertex becomes removed at a constant rate. A removed vertex will never be infected again. We assume that there is only one infective vertex at $t=0$ and define the critical value of the model as the maximum of the infection rates with which infective vertices die out with probability one, then we show that the critical value is $\big(1+o(1)\big)/(2dp)$ as $d\rightarrow+\infty$, where $d$ is the dimension of the lattice and $p$ is the probability that a given edge is open. Our result is a counterpart of the main theorem in \cite{Hol1981} for the contact process.
Indoor positioning aims at navigation inside areas with no GPS-data availability and could be employed in many applications such as augmented reality, autonomous driving specially inside closed areas and tunnels. In this paper, a deep neural network-based architecture has been proposed to address this problem. In this regard, a tandem set of convolutional neural networks, as well as a Pix2Pix GAN network have been leveraged to perform as the scene classifier, scene RGB image to point cloud converter, and position regressor, respectively. The proposed architecture outperforms the previous works, including our recent work, in the sense that it makes data generation task easier and more robust against scene small variations, whilst the accuracy of the positioning is remarkably well, for both Cartesian position and quaternion information of the camera.
The stable marriage problem has been introduced in order to describe a complex system where individuals attempt to optimise their own satisfaction, subject to mutually conflicting constraints. Due to the potential large applicability of such model to describe all the situation where different objects has to be matched pairwise, the statistical properties of this model have been extensively studied. In this paper we present a generalization of this model, introduced in order to take into account the presence of correlations in the lists and the effects of distance when the player are supposed to be represented by a position in space.
IGR J16493-4348 is a supergiant high mass X-ray binary discovered by INTEGRAL in 2004. The source is detected at a significance level of $\sim21$ standard deviations in the Swift-BAT survey data collected during the first 54 months of the Swift mission. The timing analysis reveals an orbital period of $\sim$6.78 days and the presence of a full eclipse of the compact ob\ ject. The dynamical range (variability up to a factor $\sim$20) observed during the BAT monitoring suggests that IGR J16493-4348 is a wind-fed system. The derived semi-major axis of the binary system is $\sim55 R_{\sun}$ with an orbit eccentr\ icity lower than 0.15.
We compute the Chow ring of an arbitrary heavy/light Hassett space $\bar{M}_{0, w}$. These spaces are moduli spaces of weighted pointed stable rational curves, where the associated weight vector $w$ consists of only heavy and light weights. Work of Cavalieri et al. exhibits these spaces as tropical compactifications of hyperplane arrangement complements. The computation of the Chow ring then reduces to intersection theory on the toric variety of the Bergman fan of a graphic matroid. Keel has calculated the Chow ring $A^*(\bar{M}_{0, n})$ of the moduli space $\bar{M}_{0, n}$ of stable nodal $n$-marked rational curves; his presentation is in terms of divisor classes of stable trees of $\mathbb{P}^1$'s having one nodal singularity. Our presentation of the ideal of relations for the Chow ring $A^*(\bar{M}_{0, w})$ is analogous. We show that pulling back under Hassett's birational reduction morphism $\rho_w: \bar{M}_{0, n} \to \bar{M}_{0, w}$ identifies the Chow ring $A^*(\bar{M}_{0, w})$ with the subring of $A^*(\bar{M}_{0, n})$ generated by divisors of $w$-stable trees, which are those trees which remain stable in $\bar{M}_{0, w}$.
We introduce a new class of dynamic point process models with simple and intuitive dynamics that are based on the Voronoi tessellations generated by the processes. Under broad conditions, these processes prove to be ergodic and produce, on stabilisation, a wide range of clustering patterns. In the paper, we present results of simulation studies of three statistical measures (Thiel's redundancy, van Lieshout and Baddeley's $J$-function and the empirical distribution of the Voronoi nearest neighbours' numbers) for inference on these models from the clustering behaviour in the stationary regime. In particular, we make comparisons with the area-interaction processes of Baddeley and van Lieshout.
We study the weak limits of solutions to SDEs \[dX_n(t)=a_n\bigl(X_n(t)\bigr)\,dt+dW(t),\] where the sequence $\{a_n\}$ converges in some sense to $(c_- 1\mkern-4.5mu\mathrm{l}_{x<0}+c_+ 1\mkern-4.5mu\mathrm{l}_{x>0})/x+\gamma\delta_0$. Here $\delta_0$ is the Dirac delta function concentrated at zero. A limit of $\{X_n\}$ may be a Bessel process, a skew Bessel process, or a mixture of Bessel processes.
Differences in the stellar populations of galaxies can be used to quantify the effect of environment on the star formation history. We target a sample of early-type galaxies from the Sloan Digital Sky Survey in two different environmental regimes: close pairs and a general sample where environment is measured by the mass of their host dark matter halo. We apply a blind source separation technique based on principal component analysis, from which we define two parameters that correlate, respectively, with the average stellar age (eta) and with the presence of recent star formation (zeta) from the spectral energy distribution of the galaxy. We find that environment leaves a second order imprint on the spectra, whereas local properties - such as internal velocity dispersion - obey a much stronger correlation with the stellar age distribution.
We introduce an ansatz of the PMNS matrix that consists of specific types of transformations. Bi-maximal mixing is taken for the neutrino masses, while a single-angle rotation in the 1-2 block is taken for the charged lepton masses. Motivated by the implications of the recent results on neutrino oscillations, $\theta_{23}$ in the first octant and non-zero $\theta_{13}$ are predicted by the ansatz. Three physical mixing angles are expressed in terms of a single variable, the 1-2 angle of charged leptons, so that a simple relation among the angles has been obtained: $\tan\theta_{13}=\sqrt{2}(\sin\theta_{23}-\sin\theta_{12})$. It follows that a model of the inverted hierarchy that can produce the given ansatz is proposed.
Motivated by the immense success of random walk and Markov chain methods in the design of classical algorithms, we consider_quantum_ walks on graphs. We analyse in detail the behaviour of unbiased quantum walk on the line, with the example of a typical walk, the ``Hadamard walk''. We show that after t time steps, the probability distribution on the line induced by the Hadamard walk is almost uniformly distributed over the interval [-t/sqrt(2),t/sqrt(2)]. This implies that the same walk defined on the circle mixes in_linear_ time. This is in direct contrast with the quadratic mixing time for the corresponding classical walk. We conclude by indicating how our techniques may be applied to more general graphs.
We introduce spectral Hirzebruch-Milnor classes for singular hypersurfaces. These can be identified with Steenbrink spectra in the isolated singularity case, and may be viewed as their global analogues in general. Their definition uses vanishing cycles of mixed Hodge modules and the Todd class transformation. These are compatible with the pushforward by proper morphisms, and the classes can be calculated by using resolutions of singularities. Formulas for Hirzebruch-Milnor classes of projective hypersurfaces in terms of these classes are given in the case where the multiplicity of a generic hyperplane section is not 1. These formulas using hyperplane sections instead of hypersurface ones are easier to calculate in certain cases. Here we use the Thom-Sebastiani theorem for the underlying filtered $D$-modules of vanishing cycles, from which we can deduce the Thom-Sebastiani type theorem for spectral Hirzebruch-Milnor classes. For the Chern classes after specializing to $y=-1$, we can give a relatively simple formula for the localized Milnor classes, which implies a new formula for the Euler numbers of projective hypersurfaces, using iterated hyperplane sections. Applications to log canonical thresholds and Du Bois singularities are also explained; for instance, the latter can be detected by using Hirzebruch-Milnor classes in the projective hypersurface case.
In this letter we study the self-energy of a point-like charge for the electromagnetic field in a non minimal Lorentz symmetry breaking scenario in a $n+1$ dimensional space time. We consider two variations of a model where the Lorentz violation is caused by a background vector $d^{\nu}$ that appears in a higher derivative interaction. We restrict our attention to the case where $d^{\mu}$ is a time-like background vector, namely $d^{2}=d^{\mu}d_{\mu}>0$, and we verify that the classical self-energy is finite for any odd spatial dimension $n$ and diverges for even $n$. We also make some comments regarding obstacles in the quantization of the proposed model.
I report the discovery that the 9th-magnitude Galactic-halo star BD+14$^\circ$3061 is a member of the rare class of luminous metal-poor "yellow post-AGB" stars. Its Gaia DR2 parallax implies an absolute magnitude of $M_V=-3.44\pm0.27$, and it is a very high-velocity star moving in a retrograde Galactic orbit. BD+14$^\circ$3061 is a field analog of the half-dozen yellow PAGB stars known in Galactic globular clusters, which have closely similar absolute magnitudes. These objects are the visually brightest members of old stellar populations; their apparently narrow luminosity function makes them potentially useful as Population II standard candles. The spectral-energy distribution of BD+14$^\circ$3061 out to $22\,\mu$m shows no evidence for circumstellar dust. The star is a low-amplitude semi-regular pulsating variable, with typical periods of 30-32 days. A radial-velocity study suggests that it is a spectroscopic binary with a period of 429.6 days, making it similar to known binary yellow PAGB stars such as HD 46703 and BD+39$^\circ$4926.
We prove that the Veronese embedding of P^n of degree d with n\ge 2, d\ge 3 does not satisfy property N_p (according to Green and Lazarsfeld) if p\ge 3d-2.   We conjecture that the converse holds. This is true for n=2 and for n=d=3.
Ultraluminous X-ray sources (ULXs) with Lx > 10^{39} ergs/s have been discovered in great numbers in external galaxies with ROSAT, Chandra, and XMM. The central question regarding this important class of sources is whether they represent an extension in the luminosity function of binary X-ray sources containing neutron stars and stellar-mass black holes (BHs), or a new class of objects, e.g., systems containing intermediate-mass black holes (100-1000 Msun). We have carried out a theoretical study to test whether a large fraction of the ULXs, especially those in galaxies with recent star formation activity, can be explained with binary systems containing stellar-mass black holes. To this end, we have applied a unique set of binary evolution models for black-hole X-ray binaries, coupled to a binary population synthesis code, to model the ULXs observed in external galaxies. We find that for donor stars with initial masses >10 Msun the mass transfer driven by the normal nuclear evolution of the donor star is sufficient to potentially power most ULXs. This is the case during core hydrogen burning and, to an even more pronounced degree, while the donor star ascends the giant branch, though the latter phases lasts only ~5% of the main sequence phase. We show that with only a modest violation of the Eddington limit, e.g., a factor of ~10, both the numbers and properties of the majority of the ULXs can be reproduced. One of our conclusions is that if stellar-mass black-hole binaries account for a significant fraction of ULXs in star-forming galaxies, then the rate of formation of such systems is ~3 x 10^{-7} per year normalized to a core-collapse supernova rate of 0.01 per year.
Analytical treatment of black hole accretion generally presumes the stability of the stationary configuration. Various authors in the past several decades demonstrated the validity of such an assumption for inviscid hydrodynamic flow. Inviscid assumption is a reasonable approximation for low angular^M momentum advection dominated flow in connection to certain^M supermassive black holes at the^M centres of the galaxies (including our own) fed from a number of stellar donors.^M Introduction of a weak viscosity, however, may sometimes provide a more detail understanding of the observed spectrum. Recently it has been demonstrated that introduction of small amount of viscosity in the form of quasi-viscous flow makes a stationary accretion disc -- where the geometric configuration of matter is described by axisymmetric flow in hydrostatic equilibrium -- unstable. We perform similar analysis for other disc models (for all three possible geometric configurations of matter) for quasi-viscous models under the post-Newtonian scheme. We introduced perturbations on the stationary flow solution particularly in standing wave form and studied their time evolution to observe whether they grow with time. Our analysis shows that same sort of secular instability exists in other disc models too. We further argued that with sufficiently low value of viscosity in the realistic astrophysical perspective, the instability does not effectively jeopardize the stationary condition.
This work addresses a novel and challenging problem of estimating the full 3D hand shape and pose from a single RGB image. Most current methods in 3D hand analysis from monocular RGB images only focus on estimating the 3D locations of hand keypoints, which cannot fully express the 3D shape of hand. In contrast, we propose a Graph Convolutional Neural Network (Graph CNN) based method to reconstruct a full 3D mesh of hand surface that contains richer information of both 3D hand shape and pose. To train networks with full supervision, we create a large-scale synthetic dataset containing both ground truth 3D meshes and 3D poses. When fine-tuning the networks on real-world datasets without 3D ground truth, we propose a weakly-supervised approach by leveraging the depth map as a weak supervision in training. Through extensive evaluations on our proposed new datasets and two public datasets, we show that our proposed method can produce accurate and reasonable 3D hand mesh, and can achieve superior 3D hand pose estimation accuracy when compared with state-of-the-art methods.
We study Bose-Einstein condensates with purely dipolar interactions in oblate (pancake) traps. We find that the condensate always becomes unstable to collapse when the number of particles is sufficiently large. We analyze the instability, and find that it is the trapped-gas analogue of the ``roton-maxon'' instability previously reported for a gas that is unconfined in two dimensions. In addition, we find that under certain circumstances, the condensate wave function attains a biconcave shape, with its maximum density away from the center of the gas. These biconcave condensates become unstable due to azimuthl excitation - an angular roton.
A Wigner-Poisson kinetic equation describing charge transport in doped semiconductor superlattices is proposed. Electrons are supposed to occupy the lowest miniband, exchange of lateral momentum is ignored and the electron-electron interaction is treated in the Hartree approximation. There are elastic collisions with impurities and inelastic collisions with phonons, imperfections, etc. The latter are described by a modified BGK (Bhatnagar-Gross-Krook) collision model that allows for energy dissipation while yielding charge continuity. In the hyperbolic limit, nonlocal drift-diffusion equations are derived systematically from the kinetic Wigner-Poisson-BGK system by means of the Chapman-Enskog method. The nonlocality of the original quantum kinetic model equations implies that the derived drift-diffusion equations contain spatial averages over one or more superlattice periods. Numerical solutions of the latter equations show self-sustained oscillations of the current through a voltage biased superlattice, in agreement with known experiments.
We investigate the behaviour of parallel Faddeev-Hopf vortices under energy minimization in a system with physically relevant, but unusual boundary conditions. The homotopy classification is no longer provided by the Hopf invariant, but rather by the set of integer homotopy invariants proposed by Pontrjagin. The nature of these invariants depends on the boundary conditions. A set of tightly wound parallel vortices of the usual Hopfion structure is observed to form a bunch of intertwined vortices or unwind completely, depending on the boundary conditions.
The differential spectra in the reaction $pp\to K^+\bar K^0 d$ for different reasonable versions of the production amplitude are discussed at the initial proton energy $T_p=2.645$ GeV.
In algebraic geometry there is the notion of a height pairing of algebraic cycles, which lies at the confluence of arithmetic, Hodge theory and topology. After explaining a motivating example situation, we introduce new directions in this subject.
In this paper, we investigate the half-metallicity of Heusler alloys Fe2Co1-xCrxSi by first principles calculations and anisotropy magnetoresistance measurements. It is found that, with the increase of Cr content x, the Fermi level of Fe2Co1-xCrxSi moves from the top of valence band to the bottom of conduction band, and a large half-metallic band gap of 0.75 eV is obtained for x=0.75. We then successfully synthesized a series Heusler Fe2Co1-xCrxSi polycrystalline ribbon samples. The results of X-ray diffraction indicate that the Fe2Co1-xCrxSi series of samples are pure phase with a high degree of order and the saturation magnetic moment follows half-metallic Slater-Pauling rule. Except for the two end members, Fe2CoSi and Fe2CrSi, the anisotropic magnetoresistance of Fe2Co1-xCrxSi (x=0.25, 0.5, 0.75) show a negative value suggesting they are stable half-metallic ferromagnets.
Recent observations of the black hole (BH) - bulge scaling relations usually report positive redshift evolution, with higher redshift galaxies harboring more massive BHs than expected from the local relations. All of these studies focus on broad line quasars with BH mass estimated from virial estimators based on single-epoch spectra. Since the sample selection is largely based on quasar luminosity, the cosmic scatter in the BH-bulge relation introduces a statistical bias leading to on average more massive BHs given galaxy properties at high redshift (Lauer et al. 2007). We here emphasize a previously under-appreciated statistical bias resulting from the uncertainty of single-epoch virial BH mass estimators and the shape of the underlying (true) BH mass function, which leads to on average overestimation of the true BH masses at the high-mass end (Shen et al. 2008). We demonstrate that the latter virial mass bias can contribute a substantial amount to the observed excess in BH mass at fixed bulge properties, comparable to the Lauer et al. bias. The virial mass bias is independent of the Lauer et al. bias, hence if both biases are at work, they can largely (or even fully) account for the observed BH mass excess at high redshift.
We systematically investigated native defects and reconstructions of TiO2 anatase (101) using USPEX and VASP codes. For lightly reduced samples, the coverage of O vacancies at surface depends on its concentration in bulk, while Ti interstitials prefer to dissolve in bulk. Atomic configurations of reconstructed TiO2 anatase (101) structures were given for severe reduced samples at the first time. Increasing the reduction degree, the Fermi level can be modulated in the whole bandgap. For O-rich samples, due to the indirect-to-direct bandgap transition and bandgap narrowing, O interstitials are responsible for visible light photoactivity. In a word, stoichiometry deviations of TiO2 anatase (101) have broad implications for photocatalytic reactions.
We give a complete classification of equivariant vector bundles of rank two over smooth complete toric surfaces and construct moduli spaces of such bundles. This note is a direct continuation of an earlier note where we developed a general description of equivariant sheaves on toric varieties. Here we give a first application of that description.
We present high spatial resolution (5.1" x 2.7") OVRO millimeter array observations of HCN (J=1-0) and HCO+ (J=1-0) emission in the inner 3 pc of the galaxy. The HCN and HCO+ emission of the circumnuclear disk (CND) is distributed in a well-defined ring with a peak at a radius of 1.6pc. The HCO+/HCN emission ratio is typically ~0.4 but with significant variations. The HCN emission is well correlated with the H_2 emission at 2.12 microns both in the main emission lobes of the CND and also in four filaments. Multiple areas of interaction between the ionized gas and the CND are also seen - the western arm of the minispiral is spatially and kinematically consistent with being the ionized inner edge of the CND, and the northern arm may be connected to the CND northeastern extension. With the enhanced spatial resolution of the HCN map, we resolve numerous dense molecular gas cores within the CND with characteristic diameter of 7" (0.25pc). For 26 of the more isolated cores, we measure sizes, velocity widths, and integrated fluxes. We estimate three masses for each core: a virial mass, an optically thick mass, and a lower limit mass assuming optically thin HCN emission. The virial and optically thick masses are in good agreement with a typical mass of (2-3)x10^4 M_sun and a total CND gas mass of 10^6 M_sun. The internal densities implied by these core masses are on average (3-4)x10^7 cm^-3, high enough to be stable against tidal disruption from Sgr A* and the central stellar concentration. This tidal stability suggests a longer lifetime for the CND. The higher densities and masses within the cores might support star formation either in the CND itself or within a core infalling toward the inner parsec, thus providing a mechanism for the formation of the young stellar population in the inner arcseconds of the galaxy.
We prove that there are infinitely many integers $n$ such that the total number of prime factors of $(n+h_{1})(n+h_{2})...(n+h_{\kappa})$ is at most $(1/2)\kappa\log\kappa+O(\kappa)$, provided $\kappa$ is sufficiently large.