ShantanuT01/DACTYL-Pretraining huggingface dataset:
Learned 3D representations of human faces are useful for computer vision problems such as 3D face tracking and reconstruction from images, as well as graphics applications such as character generation and animation. Traditional models learn a latent representation of a face using linear subspaces or higher-order tensor generalizations. Due to this linearity, they can not capture extreme deformations and non-linear expressions. To address this, we introduce a versatile model that learns a non-linear representation of a face using spectral convolutions on a mesh surface. We introduce mesh sampling operations that enable a hierarchical mesh representation that captures non-linear variations in shape and expression at multiple scales within the model. In a variational setting, our model samples diverse realistic 3D faces from a multivariate Gaussian distribution. Our training data consists of 20,466 meshes of extreme expressions captured over 12 different subjects. Despite limited training data, our trained model outperforms state-of-the-art face models with 50% lower reconstruction error, while using 75% fewer parameters. We also show that, replacing the expression space of an existing state-of-the-art face model with our autoencoder, achieves a lower reconstruction error. Our data, model and code are available at http://github.com/anuragranj/coma
Let $G$ be a simple graph with $2n$ vertices and a perfect matching. We denote by $f(G)$ and $F(G)$ the minimum and maximum forcing number of $G$, respectively.   Hetyei obtained that the maximum number of edges of graphs $G$ with a unique perfect matching is $n^2$. We know that $G$ has a unique perfect matching if and only if $f(G)=0$. Along this line, we generalize the classical result to all graphs $G$ with $f(G)=k$ for $0\leq k\leq n-1$, and characterize corresponding extremal graphs as well. Hence we get a non-trivial lower bound of $f(G)$ in terms of the order and size. For bipartite graphs, we gain corresponding stronger results. Further, we obtain a new upper bound of $F(G)$. For bipartite graphs $G$, Che and Chen (2013) obtained that $f(G)=n-1$ if and only if $G$ is complete bipartite graph $K_{n,n}$. We completely characterize all bipartite graphs $G$ with $f(G)= n-2$.
Reply to Comments by Lambrecht, Jaekel, and Reynaud, and by Garcia and Levanyuk, submitted to Physical Review Letters.
We present an update to the ultraviolet-to-radio database of global broadband photometry for the 79 nearby galaxies that comprise the union of the KINGFISH (Key Insights on Nearby Galaxies: A Far-Infrared Survey with Herschel) and SINGS (Spitzer Infrared Nearby Galaxies Survey) samples. The 34-band dataset presented here includes contributions from observational work carried out with a variety of facilities including GALEX, SDSS, PS, NOAO, 2MASS, WISE, Spitzer, Herschel, Planck, JCMT, and the VLA. Improvements of note include recalibrations of previously-published SINGS BVRcIc and KINGFISH far-infrared/submillimeter photometry. Similar to previous results in the literature, an excess of submillimeter emission above model predictions is seen primarily for low-metallicity dwarf/irregular galaxies. This 34-band photometric dataset for the combined KINGFISH$+$SINGS sample serves as an important multi-wavelength reference for the variety of galaxies observed at low redshift. A thorough analysis of the observed spectral energy distributions is carried out in a companion paper.
A method which we have developed for determining corotation radii, has allowed us to map in detail the radial resonant structures of barred spiral galaxies. Here we have combined this information with new determinations of the bar strength and the pitch angle of the innermost segment of the spiral arms to find relationships between these parameters of relevance to the dynamical evolution of the galaxies. We show how (1) the bar mass fraction, (2) the scaled bar angular momentum, (3) the pitch angle, and (4) the shear parameter vary along the Hubble sequence, and we also plot along the Hubble sequence (5) the scaled bar length, (6) the ratio of bar corotation radius to bar length, (7) the scaled bar pattern speed, and (8) the bar strength. It is of interest to note that the parameters (2), (5), (6), (7), and (8) all show breaks in their behaviour at type Scd. We find that bars with high shear have only small pitch angles, while bars with large pitch angles must have low shear; we also find a generally inverse trend of pitch angle with bar strength. An inference which at first seems counter-intuitive is that the most massive bars rotate most slowly but have the largest angular momenta. Among a further set of detailed results we pick out here the 2:1 ratio between the number of spiral arms and the number of corotations ouside that of the bar. These results give a guideline to theories of disc-bar evolution.
We report the manipulation of nitrogen vacancy (NV) spins in diamond when nearby ferrimagnetic insulator, yttrium iron garnet, is driven into precession. The change in NV spin polarization, as measured by changes in photoluminescence, is comparable in magnitude to that from conventional optically detected magnetic resonance, but relies on a distinct mechanism as it occurs at a microwave frequency far removed from the magnetic resonance frequency of the NV spin. This observation presents a new approach to transferring ferromagnetic spin information into a paramagnet and then transducing the response into a robust optical signal. It also opens new avenues for studying ferromagnetism and spin transport at the nanoscale.
Let $G$ be a simple, finite graph with vertex set $V(G)$ and edge set $E(G)$, where each vertex is either colored blue or white. Define the standard zero forcing process on $G$ with the following color-change rule: let $S$ be the set of all initially blue vertices of $G$ and let $u \in S$. If $v$ is the unique white vertex adjacent to $u$ in $G$, color $v$ blue and update $S$ by adding $v$ to $S$. If $S = V(G)$ after a finite number of iterations of the color-change rule, we say that $S$ is a zero forcing set for $G$. Otherwise, we say that $S$ is a failed zero forcing set. In this paper, we construct maximal failed zero forcing sets for graph products such as Cartesian products, strong products, lexicographic products, and coronas. In particular, we consider products of two paths, two cycles, and two complete graphs.
The effects of a minimal length are investigated within an algebraically extended theory of General Relativity (GR). Former attempts, to include a minimal length in GR are first resumed, with a conformal factor of the metric as a consequence. Effective potentials for various black hole masses (as ratios to the minimal length) are deduced. It is found that the existence of a minimal length has, for a small mass black hole, important effects on the effective potential near the event horizon, creating barriers which inhibit that particles can pass the event horizon. Further, a new limit for the minimal mass of a black hole is derive
In this work we present a mathematical model for the mechanical response of the Brazilian Mario SCHENBERG gravitational wave (GW) detector to such waves. We found the physical parameters that are involved in this response assuming a linear elastic theory. Adopting this approach we determined the system's resonance frequencies for the case when six $i$-mode mechanical resonators are coupled to the antenna surface according to the arrangement suggested by Johnson and Merkowitz: the truncated icosahedron configuration. This configuration presents special symmetries that allow for the derivation of an analytic expression for the mode channels, which can be experimentally monitored and which are directly related to the tensorial components of the GW. Using this model we simulated how the system behaves under a gravitational sinewave quadrupolar force and found the relative amplitudes that result from this excitation. The mechanical resonators made the signal $\approx 5340$ times stronger. We found $i+1$ degenerate triplets plus $i$ non-degenerate system mode resonances within a band around ${3.17-3.24\rm{kHz}}$ that are sensitive to signals higher than ${\tilde h\sim 10^{-22}\rm{Hz}^{-1/2}}$ when we considerate the effects of thermal noise only.
In the paper will be presented a safety and security system based on fingerprint technology. The results suggest a new scenario where the new cars can use a fingerprint sensor integrated in car handle to allow access and in the dashboard as starter button.
This monograph presents a comprehensive treatment of second order divergence form elliptic operators with bounded measurable t-independent coefficients in spaces of fractional smoothness, in Besov and weighted Sobolev classes.   We establish mapping properties for the double and single layer potentials, as well as the Newton potential, on Besov spaces. We prove extrapolation-type solvability results: that is, we show that solvability of the Dirichlet or Neumann boundary value problem at any given L^p space automatically assures their solvability in an extended range of Besov spaces. We also establish well-posedness for non-homogeneous boundary value problems.   In particular, we prove well-posedness of the non-homogeneous Dirichlet problem with data in Besov spaces for operators with real, not necessarily symmetric coefficients.
The effects of high magnetic fields applied perpendicular to the spontaneous ferroelectric polarization on single crystals of BiFeO$_3$ were investigated through magnetization, magnetostriction, and neutron diffraction measurements. The magnetostriction measurements revealed lattice distortion of $2\times 10^{-5}$, during the reorientation process of the cycloidal spin order by applied magnetic fields. Furthermore, anomalous changes in magnetostriction and electric polarization at a larger field demonstrate an intermediate phase between cycloidal and canted antiferromagnetic states, where a large magnetoelectric effect was observed. Neutron diffraction measurements clarified that incommensurate spin modulation along [110] direction in the cycloidal phase becomes commensurate in the intermediate phase. Theoretical calculations based on the standard spin Hamiltonian of this material suggest an antiferromagnetic cone-type spin order in the intermediate phase.
We study linear polarization of optical emission from white dwarf (WD) binary system AR~Scorpii. The optical emission from this binary is modulating with the beat frequency of the system, and it is highly polarized, with the degree of the polarization reaching $\sim 40$\%. The angle of the polarization monotonically increases with the spin phase, and the total swing angle can reach $360^{\circ}$ over one spin phase. It is also observed that the morphology of the pulse profile and the degree of linear polarization evolve with the orbital phase. These polarization properties can constrain the scenario for nonthermal emission from AR Scorpii. In this paper, we study the polarization properties predicted by the emission model, in which (i) the pulsed optical emission is produced by the synchrotron emission from relativistic electrons trapped by magnetic field lines of the WD and (ii) the emission is mainly produced at magnetic mirror points of the electron motion. We find that this model can reproduce the large swing of the polarization angle, provided that the distribution of the initial pitch angle of the electrons that are leaving the M-type star is biased to a smaller angle rather than a uniform distribution. The observed direction of the swing suggests that the Earth viewing angle is less than $90^{\circ}$ measured from the WD spin axis. The current model prefers an Earth viewing angle of $50^{\circ}-60^{\circ}$ and a magnetic inclination angle of $50^{\circ}-60^{\circ}$ (or $120^{\circ}-130^{\circ}$). We discuss that the different contribution of the emission from M-type star to total emission causes a large variation in the pulsed fraction and the degree of the linear polarization along the orbital phase.
Clathrates are lightweight, cage-like, fully-sp3 three dimensional (3D) structures that are experimentally-available for several host elements of the IV group. However, carbon clathrates are as yet hypothetical structures. Herein, the mechanical properties of Type-I-C46 Type-II-C34 and Type-H-C34 carbon clathrates are explored by first-principles calculations. It is revealed that those carbon clathrates show distinct anisotropic patterns in ideal tensile/shear strengths and critical tensile/shear strains, with maximum ideal tensile strength of Type-I carbon clathrate that is superior over that of diamond in <111> direction. However, it is identified isotropy in shear Youngs modulus, and in terms of tensile/shear Youngs moduli, they are sorted as Type-I > Type-II > Type-H carbon clathrates. There are distinct critical load-bearing bond configurations that explain their distinct mechanical behaviors. Moreover, those carbon clathrates are intrinsically indirect semiconductors, and their electronic properties can be greatly dictated by mechanical strain. Carbon clathrates can be potentially utilized as lightweight technically robust engineering metastructures and in electromechanical devices.
We compute the large-dimensional asymptotics for the average number of equilibria with a fixed number of unstable directions for random Gaussian ODEs on a sphere. We also discuss the effects that the value of the Lagrange multiplier of the vector field has on the number of such equilibria. This was a problem posed by Fyodorov.
It is pointed out that the third of five low-lying P11 states predicted by a constituent quark model can be identified with the third of four states in a solution from a three-channel analysis by the Zagreb group. This is one of the so-called ``missing'' resonances, predicted at 1880 MeV. The fit of the Zagreb group to the pi N -> eta N data is the crucial element in finding this fourth resonance in the P11 partial wave.
We propose a novel formalism for inflation from a 5D vacuum state which could explain both, seeds of matter and magnetic fields in the early universe.
We show that a quantum channel $\mathcal{N}$ constructed by averaging over $\mathcal{O}(\log d/\epsilon^2)$ randomly chosen unitaries gives a local $\epsilon$-randomizing map with non-negative probability. The idea comes from a small $\epsilon$-net construction on the higher dimensional unit sphere or quantum pure states. By exploiting the net, we analyze the concentrative phenomenon of an output reduced density matrix of the channel, and this analysis imply that there exists a local random unitary channel, with relatively small unitaries, generically.
We explore the role played by the quantum relative phase in a well-known model of atom-field interaction, namely, the Dicke model. We introduce an appropriate polar decomposition of the atom-field relative amplitudes that leads to a truly Hermitian relative-phase operator, whose eigenstates correctly describe the phase properties, as we demonstrate by studying the positive operator-valued measure derived from it. We find the probability distribution for this relative phase and, by resorting to a numerical procedure, we study its time evolution.
We present results on the rates of interlayer energy transfer between excitons in two-dimensional transition metal dichalcogenides (TMDs). We consider both radiative (mediated by real photons) and non-radiative (mediated by virtual photons) mechanisms of energy transfer using a unified Green's function approach that takes into account modification of the exciton energy dispersions as a result of interactions. The large optical oscillator strengths associated with excitons in TMDs result in very fast energy transfer rates. The energy transfer times depend on the exciton momentum, exciton linewidth, and the interlayer separation and can range from values less than 100 femtoseconds to more than tens of picoseconds. Whereas inside the light cone the energy transfer rates of longitudinal and transverse excitons are comparable, outside the light cone the energy transfer rates of longitudinal excitons far exceed those of transverse excitons. Average energy transfer times for a thermal ensemble of longitudinal and transverse excitons is temperature dependent and can be smaller than a picosecond at room temperature for interlayer separations smaller than 10 nm. Energy transfer times of localized excitons range from values less than a picosecond to several tens of picoseconds. When the exciton scattering and dephasing rates are small, energy transfer dynamics exhibit coherent oscillations. Our results show that electromagnetic interlayer energy transfer can be an efficient mechanism for energy exchange between TMD monolayers.
Stellar dynamos generate magnetic fields that are of fundamental importance to the variability and evolution of Sun-like and low-mass stars, and for the development of their planetary systems. We report measurements of surface-average magnetic fields in 292 M dwarfs from a comparison with radiative transfer calculations; for 260 of them, this is the first measurement of this kind. Our data were obtained from more than 15,000 high-resolution spectra taken during the CARMENES project. They reveal a relation between average field strength, <B>, and Rossby number, $Ro$, resembling the well-studied rotation-activity relation. Among the slowly rotating stars, we find that magnetic flux, $\Phi_\textrm{B}$, is proportional to rotation period, $P$, and among the rapidly rotating stars that average surface fields do not grow significantly beyond the level set by the available kinetic energy. Furthermore, we find close relations between nonthermal coronal X-ray emission, chromospheric H$\alpha$ and Ca H&K emission, and magnetic flux. Taken together, these relations demonstrate empirically that the rotation-activity relation can be traced back to a dependence of the magnetic dynamo on rotation. We advocate the picture that the magnetic dynamo generates magnetic flux on the stellar surface proportional to rotation rate with a saturation limit set by the available kinetic energy, and we provide relations for average field strengths and nonthermal emission that are independent of the choice of the convective turnover time. We also find that Ca H&K emission saturates at average field strengths of $\langle B \rangle \approx 800$ G while H$\alpha$ and X-ray emission grow further with stronger fields in the more rapidly rotating stars. This is in conflict with the coronal stripping scenario predicting that in the most rapidly rotating stars coronal plasma would be cooled to chromospheric temperatures.
A model of damped lyman alpha systems is presented based on randomly moving clouds in spherical halos. We use the Press-Schechter model for the abundance of halos, and assume that each halo has a similar population of clouds, with total mass and spatial distribution constrained to fit observations of the column density distribution. We show that the kinematics of the multiple absorbing components revealed in absorption profiles of the low-ionization lines, presented by Prochaska & Wolfe, are consistent with our spherical halo model.   The presence of multiple absorbing components with a large covering factor, combined with the small impact parameters of the systems predicted in our analytical model and in numerical simulations, implies a high rate of energy dissipation in cloud collisions. We calculate the rate of energy dissipation in our model, and show that it is far greater than the rate at which energy can be supplied by gravitational mergers of halos. This poses a problem for the model of merging protogalactic clumps of Haehnelt et al., based on numerical simulations. We also present new constraints on the amplitude of the power spectrum in hierarchical theories required to account for the observed velocity dispersion in the absorbers. We find that the linearly extrapolated rms fluctuation on spheres of radius HR = 100 km/s at z=4 must be greater than 0.75. Although this limit is obtained only for our specific model of the absorbing components, it should not be highly model-dependent because the velocity dispersion of the absorbers is essentially determined by the velocity dispersion of the halos where the gas is moving.
The tracking-by-detection framework consists of two stages, i.e., drawing samples around the target object in the first stage and classifying each sample as the target object or as background in the second stage. The performance of existing trackers using deep classification networks is limited by two aspects. First, the positive samples in each frame are highly spatially overlapped, and they fail to capture rich appearance variations. Second, there exists extreme class imbalance between positive and negative samples. This paper presents the VITAL algorithm to address these two problems via adversarial learning. To augment positive samples, we use a generative network to randomly generate masks, which are applied to adaptively dropout input features to capture a variety of appearance changes. With the use of adversarial learning, our network identifies the mask that maintains the most robust features of the target objects over a long temporal span. In addition, to handle the issue of class imbalance, we propose a high-order cost sensitive loss to decrease the effect of easy negative samples to facilitate training the classification network. Extensive experiments on benchmark datasets demonstrate that the proposed tracker performs favorably against state-of-the-art approaches.
Self-similar and semi-analytical solutions are found for the height-averaged equations govern the dynamical behavior of a polytropic, self-gravitating disk under the effects of winds, around the nascent object. In order to describe time evolution of the system, we adopt a radius dependent mass loss rate, then highlight its importance on both the traditional $\alpha$ and innovative $\beta$ models of viscosity prescription. In agreement with some other studies, our solutions represent that Toomre parameter is less than one in most regions on the $\beta$-disk which indicate that in such disks gravitational instabilities can occur in various distances from the central accretor and so the $\beta$-disk model might provide a good explanation of how the planetary systems form. The purpose of the present work is twofold. First, examining the structure of disk with wind in comparison to no-wind solution; and second, to see if the adopted viscosity prescription affects significantly the dynamical behavior of the disk-wind system. We also considered the temperature distribution in our disk by a polytropic condition. The solutions imply that, under our boundary conditions, the radial velocity is larger for $\alpha$-disks and increases as wind becomes stronger in both viscosity models. Also, we noticed that the disk thickness increases by amplifying the wind or adopting larger values for polytropic exponent $\gamma$. It also may globally decrease if one prescribe $\beta$-model for the viscosity. Moreover, in both viscosity models, surface density and mass accretion rate reduce as wind gets stronger or $\gamma$ increases.
In two-dimensional (2D) insulating magnets, the thermal Hall effect of magnons is believed to be a consequence of topological magnon insulator with separated magnon bands and a well-defined Chern number. Due to broken time-reversal symmetry the thermal Hall effect vanishes in Dirac magnons. In this paper, we show that periodically driven semi-Dirac magnon in 2D insulating honeycomb ferromagnet results in a photoinduced Dirac magnon at the topological phase transition between a photoinduced topological and trivial magnon insulator. Remarkably, the photoinduced Dirac magnon and the photoinduced trivial magnon insulator possess a nonzero Berry curvature and exhibit a finite thermal Hall effect. These intriguing properties of periodically driven 2D insulating magnets originate from the bosonic nature of magnons. Hence, they are not expected to exist in 2D electronic Floquet systems.