ShantanuT01/DACTYL-Pretraining huggingface dataset:
Measurements of switching via spin-orbit coupling (SOC) mechanisms are discussed for a pair of inverted Pt/Co/Pt stacks with asymmetrical Pt thicknesses. Taking into account the planar Hall effect contribution, effective fields of spin-orbit torques (SOT) are evaluated using lock-in measurements of the first and second harmonics of the Hall voltage. Reversing the stack structure leads to significant asymmetries in the switching behavior, including clear evidence of a nonlinear current dependence of the transverse effective field. Our results demonstrate potentially complex interplay in devices with all-metallic interfaces utilizing SOT.
The cluster cumulant formula of Kubo is derived by appealing only to elementary properties of subsets and binomial coefficients. It is shown to be a binomial transform of the grand potential. Extensivity is proven without introducing cumulants. A combinatorial inversion is used to reformulate the expansion in the activity to one in occupation probabilities, which explicitly control the convergence. The classical virial expansion is recovered to third order as an example.
The escape process of particles accelerated at supernova remnant (SNR) shocks is one of the poorly understood aspects of the shock acceleration theory. Here we adopt a phenomenological approach to study the particle escape and its impact on the gamma-ray spectrum resulting from hadronic collisions both inside and outside of a middle-aged SNR. Under the assumption that in the spatial region immediately outside of the remnant the diffusion coefficient is suppressed with respect to the average Galactic one, we show that a significant fraction of particles are still located inside the SNR long time after their nominal release from the acceleration region. This fact results into a gamma-ray spectrum that resembles a broken power law, similar to those observed in several middle-aged SNRs. Above the break, the spectral steepening is determined by the diffusion coefficient outside of the SNR and by the time dependence of maximum energy. Consequently, the comparison between the model prediction and actual data will contribute to determining these two quantities, the former being particularly relevant within the predictions of the gamma-ray emission from the halo of escaping particles around SNRs which could be detected with future Cherenkov telescope facilities. We also calculate the spectrum of run-away particles injected into the Galaxy by an individual remnant. Assuming that the acceleration stops before the SNR enters the snowplow phase, we show that the released spectrum can be a featureless power law only if the accelerated spectrum has a slope alpha > 4.
This paper addresses the problem of 3D human pose estimation from single images. While for a long time human skeletons were parameterized and fitted to the observation by satisfying a reprojection error, nowadays researchers directly use neural networks to infer the 3D pose from the observations. However, most of these approaches ignore the fact that a reprojection constraint has to be satisfied and are sensitive to overfitting. We tackle the overfitting problem by ignoring 2D to 3D correspondences. This efficiently avoids a simple memorization of the training data and allows for a weakly supervised training. One part of the proposed reprojection network (RepNet) learns a mapping from a distribution of 2D poses to a distribution of 3D poses using an adversarial training approach. Another part of the network estimates the camera. This allows for the definition of a network layer that performs the reprojection of the estimated 3D pose back to 2D which results in a reprojection loss function. Our experiments show that RepNet generalizes well to unknown data and outperforms state-of-the-art methods when applied to unseen data. Moreover, our implementation runs in real-time on a standard desktop PC.
In this paper I discuss whether superluminal particles exist in the general relativistic theory of gravity. It seems that the answer to this question is negative. In truth the result may only represent a difficulty to {\bf special} but not general relativity, the later allowing both Lorentzian and Euclidian metrics. An Euclidian metric does not restrict speed. Although only the Lorentzian metric is stable \cite{Yahaloma}, an Euclidian metric can be created under special gravitational circumstances and persist in a limited region of space-time causing possible superluminality.
We shall give an explicit pair of birational projective Calabi--Yau threefolds which are rigid, non-homeomorphic, but are connected by projective flat deformation over some connected base scheme.
We derive asymptotically optimal upper bounds on the number of L-rational torsion points on a given elliptic curve or Drinfeld module defined over a finitely generated field K, as a function of the degree [L:K]. Our main tool is the adelic openness of the image of Galois representations attached to elliptic curves and Drinfeld modules, due to Serre and Pink-Ruetsche, respectively. Our approach is to prove a general result for certain Galois modules, which applies simultaneously to elliptic curves and to Drinfeld modules.
This is the third paper in a series describing a numerical implementation of the conformal Einstein equation. This paper describes a scheme to calculate (three) dimensional data for the conformal field equations from a set of free functions. The actual implementation depends on the topology of the spacetime. We discuss the implementation and exemplary calculations for data leading to spacetimes with one spherical null infinity (asymptotically Minkowski) and for data leading to spacetimes with two toroidal null infinities (asymptotically A3). We also outline the (technical) modifications of the implementation needed to calculate data for spacetimes with two and more spherical null infinities (asymptotically Schwarzschild and asymptotically multiple black holes).
Small and bright stellar disks with scale lengths of few tens of parsec are known to reside in the center of galaxies. They are believed to have formed in a dissipational process as the end result of star formation in gas either accreted in a merging (or acquisition) event or piled up by the secular evolution of a nuclear bar. Only few of them have been studied in detail to date. Using archival Hubble Space Telescope (HST) imaging, we investigated the photometric parameters of the nuclear stellar disks hosted by three early-type galaxies in the Virgo cluster, NGC 4458, NGC4478, and NGC4570. We aimed at constraining the process of formation of their stars. The central surface brightness, scale length, inclination, and position angle of the nuclear disks were derived by adopting the photometric decomposition method introduced by Scorza & Bender and assuming the disks to be infinitesimally thin and exponential. The location, orientation, and size of the nuclear disks is the same in all the images obtained with the Wide Field Planetary Camera 2 and Advanced Camera for Survey and available in the HST Science Archive. The scale length, inclination, and position angle of each disk are constant within the errors in the observed U, B, V, and I passbands, independently of their values and of the properties of the host spheroid. We interpret the absence of color gradients in the stellar population of the nuclear disks as the signature that star formation homogeneously occurred all through their extension. A inside-out formation scenario is, instead, expected to produce color gradients and therefore is ruled out.
We study the asymptotic behavior of zero-drift random walks confined to multidimensional convex cones, when the endpoint is close to the boundary. We derive a local limit theorem in the fluctuation regime.
We present extensive optical photometric and spectroscopic observations of the high-velocity (HV) Type Ia supernova (SN Ia) 2017fgc, covering the phase from $\sim$ 12 d before to $\sim 389$ d after maximum brightness. SN 2017fgc is similar to normal SNe Ia, with an absolute peak magnitude of $M_{\rm max}^{B} \approx$ $-19.32 \pm 0.13$ mag and a post-peak decline of ${\Delta}m_{15}(B)$ = $1.05 \pm 0.07$ mag. Its peak bolometric luminosity is derived as $1.32 \pm 0.13) \times 10^{43} $erg s$^{-1}$, corresponding to a $^{56}$Ni mass of $0.51 \pm 0.03 M_{\odot}$. The light curves of SN 2017fgc are found to exhibit excess emission in the $UBV$ bands in the early nebular phase and pronounced secondary shoulder/maximum features in the $RrIi$ bands. Its spectral evolution is similar to that of HV SNe Ia, with a maximum-light Si II velocity of $15,000 \pm 150 $km s$^{-1}$ and a post-peak velocity gradient of $\sim$ $120 \pm 10 $km s$^{-1} $d$^{-1}$. The Fe II and Mg II lines blended near 4300 {\AA} and the Fe II, Si II, and Fe III lines blended near 4800 {\AA} are obviously stronger than those of normal SNe Ia. Inspecting a large sample reveals that the strength of the two blends in the spectra, and the secondary peak in the $i/r$-band light curves, are found to be positively correlated with the maximum-light Si II velocity. Such correlations indicate that HV SNe~Ia may experience more complete burning in the ejecta and/or that their progenitors have higher metallicity. Examining the birthplace environment of SN 2017fgc suggests that it likely arose from a stellar environment with young and high-metallicity populations.
Hadron production in semi-inclusive deep-inelastic scattering of leptons from nuclei is an ideal tool to determine and constrain the transport coefficient in cold nuclear matter. The leading-order computations for hadron multiplicity ratios are performed by means of the SW quenching weights and the analytic parameterizations of quenching weights based on BDMPS formalism. The theoretical results are compared to the HERMES positively charged pions production data with the quarks hadronization occurring outside the nucleus. With considering the nuclear geometry effect on hadron production, our predictions are in good agreement with the experimental measurements. The extracted transport parameter from the global fit is shown to be $\hat{q} = 0.74\pm0.03 GeV^2/fm$ for the SW quenching weight without the finite energy corrections. As for the analytic parameterization of BDMPS quenching weight without the quark energy E dependence, the computed transport coefficient is $\hat{q} = 0.20\pm0.02 GeV^2/fm$. It is found that the nuclear geometry effect has a significant impact on the transport coefficient in cold nuclear matter. It is necessary to consider the detailed nuclear geometry in studying the semi-inclusive hadron production in deep inelastic scattering on nuclear targets.
Truly stable metastable states are an artifact of the mean-field approximation or the zero temperature limit. If such appealing concepts in glass theory as configurational entropy are to have a meaning beyond these approximations, one needs to cast them in a form involving states with finite lifetimes.   Starting from elementary examples and using results of Gaveau and Schulman, we propose a simple expression for the configurational entropy and revisit the question of taking flat averages over metastable states. The construction is applicable to finite dimensional systems, and we explicitly show that for simple mean-field glass models it recovers, justifies and generalises the known results. The calculation emphasises the appearance of new dynamical order parameters.
Following the procedure described in Pol et al., we update the Galactic double neutron star (DNS) merger rate by including the new, highly eccentric DNS system J0509+3801 (Lynch et al.). This leads to a new Galactic DNS merger rate of $\mathcal{R}_{\rm MW} = 37^{+24}_{-11}$ Myr$^{-1}$, where the errors represent 90% confidence intervals. The corresponding DNS merger detection rate for Advanced LIGO is $\mathcal{R} = 1.9^{+1.2}_{-0.6} \times \left( D_{\rm r} / 100 \ \rm Mpc \right)^3 \rm yr^{-1},$ where $D_{\rm r}$ is the range distance. Using the LIGO O3 range distance of 130 Mpc (Abbott et al.), we predict that LIGO will detect anywhere between three and seven DNS mergers per year of observing at O3 sensitivity.
Let $p$ be an odd prime. For each integer $a$ with $p\nmid a$, the famous Zolotarev's Lemma says that the Legendre symbol $(\frac{a}{p})$ is the sign of the permutation of $\Z/p\Z$ induced by multiplication by $a$. The extension of Zolotarev's result to the case of odd integers was shown by Frobenius. After that, Lerch extended these to all positive integers. In this paper we explore some applications of Lerch's result. For instance, we study permutations involving arbitrary $k$-th power residue modulo $p$ and primitive roots of a power of $p$. Finally, we discuss some permutation problems concerning quadratic residues modulo $p$. In particular, we confirm some conjectures posed by Sun.
We present an exploration of the expected detection of the earliest Active Galactic Nuclei (AGN) in the Universe from state-of-art galaxy formation and evolution semi-analytic models and hydro-dynamical simulations. We estimate the number and radiative characteristics of Super Massive Black Holes (SMBHs) at $z\geq 6$, a redshift range that will be intensively explored by the next generation of telescopes, in particular in the radio through the Square Kilometre Array (SKA) and at high energies with ESA's Athena X-ray Observatory. We find that Athena will be able to observe over 5000 AGN/$\rm deg^2$ at the Epoch of Re-ionization (EoR), $6\leq z \leq 10$. Similarly, for the same redshift range the models/simulations suggest that SKA will detect at least 400 AGN/$\rm deg^2$. Additionally, we stress the importance of the volume of the simulation box as well as the initial physical conditions of the models/simulations on their effect on the luminosity functions (LFs) and the creation of the most massive SMBHs that we currently observe at the EoR. Furthermore, following the evolution of the accretion mode of the SMBHs in each model/simulation, we show that, while the quasar dominates over the radio mode at the EoR, detection at radio wavelengths still reaches significant numbers even at the highest redshifts. Finally, we present the effect that the radiative efficiency has on the LFs by comparing results produced with a constant value for the radiative efficiency and more complex calculations based on the spin of each SMBH.
The influence of the spin-orbit interactions on the energy spectrum of two-electron laterally coupled quantum dots is investigated. The effective Hamiltonian for a spin qubit pair proposed in F. Baruffa et al., Phys. Rev. Lett. 104, 126401 (2010) is confronted with exact numerical results in single and double quantum dots in zero and finite magnetic field. The anisotropic exchange Hamiltonian is found quantitatively reliable in double dots in general. There are two findings of particular practical importance: i) The model stays valid even for maximal possible interdot coupling (a single dot), due to the absence of a coupling to the nearest excited level, a fact following from the dot symmetry. ii) In a weak coupling regime, the Heitler-London approximation gives quantitatively correct anisotropic exchange parameters even in a finite magnetic field, although this method is known to fail for the isotropic exchange. The small discrepancy between the analytical model (which employes the linear Dresselhaus and Bychkov-Rashba spin-orbit terms) and the numerical data for GaAs quantum dots is found to be mostly due to the cubic Dresselhaus term.
Cylindric skew Schur functions, which are a generalisation of skew Schur functions, arise naturally in the study of P-partitions. Also, recent work of A. Postnikov shows they have a strong connection with a problem of considerable current interest: that of finding a combinatorial proof of the non-negativity of the 3-point Gromov-Witten invariants. After explaining these motivations, we study cylindric skew Schur functions from the point of view of Schur-positivity. Using a result of I. Gessel and C. Krattenthaler, we generalise a formula of A. Bertram, I. Ciocan-Fontanine and W. Fulton, thus giving an expansion of an arbitrary cylindric skew Schur function in terms of skew Schur functions. While we show that no non-trivial cylindric skew Schur functions are Schur-positive, we conjecture that this can be reconciled using the new concept of cylindric Schur-positivity.
This is the third of a series of papers studying real algebraic threefolds, but the methods are mostly independent from the previous two. Let $f:X\to S$ be a map of a smooth projective real algebraic 3-fold to a surface $S$ whose general fibers are rational curves.   Assume that the set of real points of $X$ is an orientable 3-manifold $M$. The aim of the paper is to give a topological description of $M$. It is shown that $M$ is either Seifert fibered or a connected sum of lens spaces. Much stronger results hold if $S$ is rational.
In the framework of the rigged Hilbert space, unstable quantum systems associated with first order poles of the analytically continued S-matrix can be described by Gamow vectors which are generalized vectors with exponential decay and a Breit-Wigner energy distribution. This mathematical formalism can be generalized to quasistationary systems associated with higher order poles of the S-matrix, which leads to a set of Gamow vectors of higher order with a non-exponential time evolution. One can define a state operator from the set of higher order Gamow vectors which obeys the exponential decay law. We shall discuss to what extend the requirement of an exponential time evolution determines the form of the state operator for a quasistationary microphysical system associated with a higher order pole of the S-matrix.
Geodesic regression has been proposed for fitting the geodesic curve. However, it cannot automatically choose the dimensionality of data. In this paper, we develop a Bayesian geodesic regression model on Riemannian manifolds (BGRM) model. To avoid the overfitting problem, we add a regularization term to control the effectiveness of the model. To automatically select the dimensionality, we develop a prior for the geodesic regression model, which can automatically select the number of relevant dimensions by driving unnecessary tangent vectors to zero. To show the validation of our model, we first apply it in the 3D synthetic sphere and 2D pentagon data. We then demonstrate the effectiveness of our model in reducing the dimensionality and analyzing shape variations of human corpus callosum and mandible data.
We explain how the constraints from present experimental data can be used to obtain the nPDF in the framework of LO DGLAP evolution. We will also compare the only two available sets of this type and comment on the important information that neutrino factories could provide.
Normalization constant in the eigenstate appearing in the eigenvalue problem of the su(1,1)-algebra is discussed. This normalization constant is expressed in terms of the Gauss' hypergeometric series which is not absolutely convergent. It is proved that this series is obtained as a certain limit of an absolutely convergent series, which was conjectured in the previous paper.
We study the asymptotic behavior of a Markov chain on $\mathbb{Z}^2$ that corresponds to the two-dimensional marginals of a reinforcement process on $\mathbb{Z}^{\mathbb{N}}$. Three distinct asymptotic regimes are identified, depending on the scaling of the reinforcement parameter $\Delta$ with respect to the number of steps performed by the chain.
A sequence $\left(x_1,x_2,\ldots,x_{2n}\right)$ of even length is a repetition if $\left(x_1,\ldots,x_n\right) = \left(x_{n+1},\ldots,x_{2n}\right)$. We prove existence of a constant $C < 10^{4 \cdot 10^7}$ such that given any planar drawing of a graph $G$, and a list $L(v)$ of $C$ permissible colors for each vertex $v$ in $G$, there is a choice of a permissible color for each vertex such that the sequence of colors of the vertices on any facial simple path in $G$ is not a repetition.
Pyrochlore dielectric materials such as (Bi$_{1.5}$Zn$_{0.5}$)(Nb$_{1.5}$Zn$_{0.5}$)O$_7$ (BZN) have generated interest because they combine high dielectric constants with small dielectric loss tangents and yet are cubic at all temperatures. The recent low-temperature preparation and structural characterization of Bi$_2$Ti$_2$O$_7$, which remains cubic down to 2 K, has provided a good model system for understanding the properties of Bi-based pyrochlores. In this contribution, the electronic structure of cubic Bi$_2$Ti$_2$O$_7$ is visualized and compared with the electronic structure of the Aurivillius phase ferroelectric SrBi$_2$Ta$_2$O$_9$ (SBT), which displays a ferroelectric distortion below 608 K associated with the tendency of lone pair active Bi$^{3+}$ to move off-center. Such coherent off-centering distortions are frustrated on the pyrochlore lattice, and this prevents a ferroelectric-paraelectric phase transition in Bi$_2$Ti$_2$O$_7$. Instead, Bi$^{3+}$ ions in Bi$_2$Ti$_2$O$_7$ are obliged to off-center in an \textit{incoherent} manner, that is compatible with the cubic structure being retained. Frustrated lone pair behavior in the defect pyrochlore Pb$_2$Sn$_2$O$_6$ is also described. Parallels between the well-studied frustration of certain types of \textit{magnetism} in pyrochlore compounds (spin-ice) and the striking paucity of ferroelectric pyrochlores, arising from the corner-connected tetrahedral topology of the pyrochlore lattice are pointed out.
3D Morphable Model (3DMM) fitting has widely benefited face analysis due to its strong 3D priori. However, previous reconstructed 3D faces suffer from degraded visual verisimilitude due to the loss of fine-grained geometry, which is attributed to insufficient ground-truth 3D shapes, unreliable training strategies and limited representation power of 3DMM. To alleviate this issue, this paper proposes a complete solution to capture the personalized shape so that the reconstructed shape looks identical to the corresponding person. Specifically, given a 2D image as the input, we virtually render the image in several calibrated views to normalize pose variations while preserving the original image geometry. A many-to-one hourglass network serves as the encode-decoder to fuse multiview features and generate vertex displacements as the fine-grained geometry. Besides, the neural network is trained by directly optimizing the visual effect, where two 3D shapes are compared by measuring the similarity between the multiview images rendered from the shapes. Finally, we propose to generate the ground-truth 3D shapes by registering RGB-D images followed by pose and shape augmentation, providing sufficient data for network training. Experiments on several challenging protocols demonstrate the superior reconstruction accuracy of our proposal on the face shape.
We consider the process of partial sums of moving averages of finite order with a regular varying memory function, constructed from a stationary sequence, variance of the sum of which is a regularly varying function. We study the Gaussian approximation of this process of partial sums with the aid of a certain class of Gaussian processes, and obtain sufficient conditions for the $C$-convergence in the invariance principle in the Donsker form