ShantanuT01/DACTYL-Pretraining huggingface dataset:
A k-connected graph such that deleting any edge / deleting any vertex / contracting any edge results in a graph which is not k-connected is called minimally / critically / contraction-critically k-connected. These three classes play a prominent role in graph connectivity theory, and we give a brief introduction with a light emphasis on reduction- and construction theorems for classes of k-connected graphs.
The gesture recognition using motion capture data and depth sensors has recently drawn more attention in vision recognition. Currently most systems only classify dataset with a couple of dozens different actions. Moreover, feature extraction from the data is often computational complex. In this paper, we propose a novel system to recognize the actions from skeleton data with simple, but effective, features using deep neural networks. Features are extracted for each frame based on the relative positions of joints (PO), temporal differences (TD), and normalized trajectories of motion (NT). Given these features a hybrid multi-layer perceptron is trained, which simultaneously classifies and reconstructs input data. We use deep autoencoder to visualize learnt features, and the experiments show that deep neural networks can capture more discriminative information than, for instance, principal component analysis can. We test our system on a public database with 65 classes and more than 2,000 motion sequences. We obtain an accuracy above 95% which is, to our knowledge, the state of the art result for such a large dataset.
We consider a company that receives capital injections so as to avoid ruin. Differently from the classical bail-out settings where the underlying process is restricted to stay at or above zero, we study the case bail-out can only be made at independent Poisson times. Namely, we study a version of the reflected process that is pushed up to zero only on Poisson observation times at which the process is below zero. We also study the case with additional classical reflection above so as to model a company that pays dividends according to a barrier strategy. Focusing on the spectrally negative L\'evy case, we compute, using the scale function, various fluctuation identities including capital injections and dividends.
We construct a series of bosonic symmetry protected topological (BSPT) states beyond group cohomology classification using "decorated defects" approach. This construction is based on topological defects of ordinary Landau order parameters, decorated with the bosonic short range entangled (BSRE) states in $(4k+3)d$ and $(4k+5)d$ space-time (with $k$ being nonnegative integers), which do not need any symmetry. This approach not only gives these BSPT states an intuitive physical picture, it also allows us to derive the effective field theory for all these BSPT states beyond group cohomology.
We apply the slave-boson approach of Kotliar and Ruckenstein to the two-band Hubbard model with an Ising like Hund's rule coupling and bands of different widths. On the mean-field level of this approach we investigate the Mott transition and observe both separate and joint transitions of the two bands depending on the choice of the inter- and intraorbital Coulomb interaction parameters. The mean-field calculations allow for a simple physical interpretation and can confirm several aspects of previous work. Beside the case of two individually half-filled bands we also examine what happens if the original metallic bands possess fractional filling either due to finite doping or due to a crystal field which relatively shifts the atomic energy levels of the two orbitals. For appropriate values of the interaction and of the crystal field we can observe a a band insulating state and a ferromagnetic metal.
We carry out three-body-model calculations for a proton-rich Borromean nucleus $^{17}$Ne by assuming a $^{15}$O + $p$ + $p$ structure. To this end, we use a density-dependent contact interaction between the valence protons, explicitly treating also the Coulomb interaction. We find that the two-particle density distribution for $^{17}$Ne is similar to that for $^{16}$C, which has two valence neutrons outside the $N$ = 8 core. That is, the two protons take a spatially compact configuration, while the Coulomb repulsion plays a minor role. This indicates that there is a strong diproton correlation in the ground state of the $^{17}$Ne nucleus. We also show that the Coulomb interaction reduces the expectation value of the proton-proton interaction by about 14\%.
We present cosmological parameter constraints from a blinded joint analysis of galaxy-galaxy weak lensing, $\Delta\!\Sigma(R)$, and projected correlation function, $w_\mathrm{p}(R)$, measured from the first-year HSC (HSC-Y1) data and SDSS spectroscopic galaxies over $0.15<z<0.7$. We use luminosity-limited samples as lens samples for $\Delta\!\Sigma$ and as large-scale structure tracers for $w_\mathrm{p}$ in three redshift bins, and use the HSC-Y1 galaxy catalog to define a secure sample of source galaxies at $z_\mathrm{ph}>0.75$ for the $\Delta\!\Sigma$ measurements, selected based on their photometric redshifts. For theoretical template, we use the "minimal bias" model for the cosmological clustering observables for the flat $\Lambda$CDM cosmological model. We compare the model predictions with the measurements in each redshift bin on large scales, $R>12$ and $8~h^{-1}\mathrm{Mpc}$ for $\Delta\!\Sigma(R)$ and $w_\mathrm{p}(R)$, respectively, where the perturbation theory-inspired model is valid. When we employ weak priors on cosmological parameters, without CMB information, we find $S_8=0.936^{+0.092}_{-0.086}$, $\sigma_8=0.85^{+0.16}_{-0.11}$, and $\Omega_\mathrm{m}=0.283^{+0.12}_{-0.035}$ for the flat $\Lambda$CDM model. Although the central value of $S_8$ appears to be larger than those inferred from other cosmological experiments, we find that the difference is consistent with expected differences due to sample variance, and our results are consistent with the other results to within the statistical uncertainties. (abriged)
Riemannian coordinates for flat metrics corresponding to three--dimensional conformal Poisson--Lie T--dualizable sigma models are found by solving partial differential equations that follow from the transformations of the connection components. They are then used for finding general forms of the dilaton fields satisfying the vanishing beta equations of the sigma models.
In this paper we provide a basic introduction of the core ideas and theories surrounding fault-tolerant quantum computation. These concepts underly the theoretical framework of large-scale quantum computation and communications and are the driving force for many recent experimental efforts to construct small to medium sized arrays of controllable quantum bits. We examine the basic principals of redundant quantum encoding, required to protect quantum bits from errors generated from both imprecise control and environmental interactions and then examine the principals of fault-tolerance from largely a classical framework. As quantum fault-tolerance essentially is avoiding the uncontrollable cascade of errors caused by the interaction of quantum-bits, these concepts can be directly mapped to quantum information.
Terrestrial gravity noise, also known as Newtonian noise, produced by ambient seismic and infrasound fields will pose one of the main sensitivity limitations in low-frequency, ground-based, gravitational-wave (GW) detectors. It was estimated that this noise foreground needs to be suppressed by about 3 -- 5 orders of magnitude in the frequency band 10\,mHz to 1\,Hz, which will be extremely challenging. In this article, we present a new approach that greatly facilitates cancellation of gravity noise in full-tensor GW detectors. The method uses optimal combinations of tensor channels and environmental sensors such as seismometers and microphones to reduce gravity noise. It makes explicit use of the direction of propagation of a GW, and can therefore either be implemented in directional searches for GWs or in observations of known sources. We show that suppression of the Newtonian-noise foreground is greatly facilitated using the extra strain channels in full-tensor GW detectors. Only a modest number of auxiliary, high-sensitivity environmental sensors are required to achieve noise suppression by a few orders of magnitude.
We present the analysis of the first set of low-redshift Type Ia supernovae (SNe Ia) by the Carnegie Supernova Project. Well-sampled, high-precision optical (ugriBV) and near-infrared (NIR; YJHKs) light curves obtained in a well-understood photometric system are used to provide light-curve parameters, and ugriBVYJH template light curves. The intrinsic colors at maximum light are calibrated to compute optical--NIR color excesses for the full sample, thus allowing the properties of the reddening law in the host galaxies to be studied. A low value of Rv~1.7, is derived when using the entire sample of SNe. However, when the two highly reddened SNe in the sample are excluded, a value Galactic standard of Rv~3.2 is obtained. The colors of these two events are well matched by a reddening model due to circumstellar dust. The peak luminosities are calibrated using a two-parameter linear fit to the decline rates and the colors, or alternatively, the color excesses. In both cases, dispersions in absolute magnitude of 0.12--0.16 mag are obtained, depending on the filter-color combination. In contrast to the results obtained from color excesses, these fits give Rv~1--2, even when the two highly reddened SNe are excluded. This discrepancy suggests that, beyond the "normal" interstellar reddening produced in the host galaxies, there is an intrinsic dispersion in the colors of SNe Ia which is correlated with luminosity but independent of the decline rate. Finally, a Hubble diagram is produced by combining the results of the fits for each filter. The resulting scatter of 0.12 mag appears to be limited by peculiar velocities as evidenced by the strong correlation between the distance-modulus residuals among the different filters. The implication is that the actual precision of SN Ia distances is 3--4%.
Diffractive vector meson photoproduction accompanied by proton dissociation is studied for large momentum transfer. The process is described by the non-forward BFKL equation, for which a complete analytical solution is found. The scattering amplitudes for all combinations of helicity are presented.
Origin of the magnetic field ubiquitous in the Universe is studied based on the Biermann mechanism, which is expected to work in the non-barotropic region. We perform a series of two-dimensional MHD simulations of the first generation supernova remnant (SNR) expanding in the inhomogeneous interstellar matter (ISM) and study the Biermann mechanism working in the interior of the SNR. Especially, we pay attention to the relaxation process of electron and ion temperatures via the Coulomb interaction. In the early SNR in which the electron temperature is much lower than the ion temperature, the Biermann mechanism is ineffective, since the gradient of electron pressure is small. Magnetic fields begin to be generated just behind the shock front when the electron temperature is sufficiently relaxed. Assuming the explosion energy of 10^52 erg, the total magnetic energy generated reaches about 10^26 erg and does not depend strongly on the parameters of either SNR or ISM. Analytic expression to estimate the magnetic total energy is presented and it is shown this agrees well with our numerical results. Finally we evaluate the expected amplitude of magnetic fields in protogalaxies as ~10^-19 G, which is sufficient for seed fields of the observed galactic magnetic fields.
Let $\X = \X[a, b] = \{x: a<|x|<b\}\subset \R^n$ with $0<a<b<\infty$ fixed be an open annulus and consider the energy functional, \begin{equation*} {\mathbb F} [u; \X] = \frac{1}{2} \int_\X \frac{|\nabla u|^2}{|u|^2} \, dx, \end{equation*} over the space of admissible incompressible Sobolev maps \begin{equation*} {\mathcal A}_\phi(\X) = \bigg\{ u \in W^{1,2}(\X, \R^n) : \det \nabla u = 1 \text{ {\it a.e.} in $\X$ and $u|_{\partial \X} = \phi$} \bigg\}, \end{equation*} where $\phi$ is the identity map of $\overline \X$. Motivated by the earlier works \cite{TA2, TA3} in this paper we examine the {\it twist} maps as extremisers of ${\mathbb F}$ over ${\mathcal A}_\phi(\X)$ and investigate their minimality properties by invoking the coarea formula and a symmetrisation argument. In the case $n=2$ where ${\mathcal A}_\phi(\X)$ is a union of infinitely many disjoint homotopy classes we establish the minimality of these extremising twists in their respective homotopy classes a result that then leads to the latter twists being $L^1$-local minimisers of ${\mathbb F}$ in ${\mathcal A}_\phi(\X)$. We discuss variants and extensions to higher dimensions as well as to related energy functionals.
By measuring the thermoelectric effect in high-mobility quantum wells with two occupied subbands in perpendicular magnetic field, we detect magnetophonon oscillations due to interaction of electrons with acoustic phonons. These oscillations contain specific features identified as combined resonances caused by intersubband phonon-assisted transitions of electrons in the presence of Landau quantization. The quantum theory of phonon-drag magnetothermoelectric effect, generalized to the case of multi-subband occupation, describes our experimental findings.
The opacity of spiral galaxies is examined by modelling the dust and stellar content of individual galaxies. The model is applied to five late-type spiral galaxies (NGC 4013, IC 2531, UGC 1082, NGC 5529 and NGC 5907). Having analyzed a total of seven galaxies thus far, the five galaxies mentioned above plus UGC 2048 and NGC 891 presented in (Xilouris et al. 1997, 1998), we are able to draw some general conclusions, the most significant of which are: 1) The face-on central optical depth is less than one in all optical bands indicating that typical spiral galaxies like the ones that we have modelled would be completely transparent if they were to be seen face-on. 2) The dust scaleheight is about half that of the stars, which means that the dust is more concentrated near the plane of the disk. 3) The dust scalelength is about 1.4 times larger than that of the stars and the dust is more radially extended than the stars. 4) The dust mass is found to be about an order of a magnitude more than previously measured using the IRAS fluxes, indicating the existence of a cold dust component. The gas-to-dust mass ratio calculated is close to the value derived for our Galaxy. 5) The derived extinction law matches quite well the Galactic extinction law, indicating a universal dust behaviour.
The effects of the orbital diffusion of stars and clusters on the galactic abundance gradient have been modelled. For a single generation of field stars, the results confirm previous analyses based upon the assumption of a linear gradient with galactocentric distance. Though the dispersion in metallicity at a given radius grows with time, the underlying slope across the disk remains unchanged. For a disk dominated by a discontinuity in [Fe/H] beyond the solar circle, but no gradient within the inner or outer disk, a gradient is derived for any sample whose galactocentric baseline overlaps the discontinuity. The consequence of orbital diffusion is to shift the observable edge of the transition in [Fe/H] to smaller galactocentric distance. In contrast, star clusters of a single generation evaporate so quickly that the small surviving sample of the oldest clusters is statistically insufficient to define any but a linear gradient. Inclusion of multiple generations of stars and clusters with a plausible age-metallicity relation enhances these patterns by expanding the metallicity range at a given galactocentric distance through the inclusion of stars with a wide range in both age and galactocentric origin. For field stars, the metallicity distribution of stars in the solar neighborhood is virtually indistinguishable for the two cases modelled. Because ages, abundances, and distances can be reliably determined for clusters and any sample of clusters is invariably dominated by clusters formed over the last 2 Gyrs, the cluster population offers a means for finding detailed structure within the recent galactic abundance gradient. Using clusters to extend the galactocentric baseline would supply an additional critical test of the discontinuity.
We present an approach to generating 3D human models from images. The key to our framework is that we predict double-sided orthographic depth maps and color images from a single perspective projected image. Our framework consists of three networks. The first network predicts normal maps to recover geometric details such as wrinkles in the clothes and facial regions. The second network predicts shade-removed images for the front and back views by utilizing the predicted normal maps. The last multi-headed network takes both normal maps and shade-free images and predicts depth maps while selectively fusing photometric and geometric information through multi-headed attention gates. Experimental results demonstrate that our method shows visually plausible results and competitive performance in terms of various evaluation metrics over state-of-the-art methods.
We prove that the purely imaginary square well generates an infinite number of bound states with real energies. In the strong-coupling limit, our exact PT symmetric solutions coincide, utterly unexpectedly, with their textbook, well known Hermitian predecessors.
We review and complete the kinetic theory of spatially inhomogeneous stellar systems when collective effects (dressing of the stars by their polarization cloud) are neglected. We start from the BBGKY hierarchy issued from the Liouville equation and consider an expansion in powers of 1/N in a proper thermodynamic limit. For $N\rightarrow +\infty$, we obtain the Vlasov equation describing the evolution of collisionless stellar systems like elliptical galaxies. At the order 1/N, we obtain a kinetic equation describing the evolution of collisional stellar systems like globular clusters. This equation does not suffer logarithmic divergences at large scales since spatial inhomogeneity is explicitly taken into account. Making a local approximation, and introducing an upper cut-off at the Jeans length, it reduces to the Vlasov-Landau equation which is the standard kinetic equation of stellar systems. Our approach provides a simple and pedagogical derivation of these important equations from the BBGKY hierarchy which is more rigorous for systems with long-range interactions than the two-body encounters theory. Making an adiabatic approximation, we write the generalized Landau equation in angle-action variables and obtain a Landau-type kinetic equation that is valid for fully inhomogeneous stellar systems and is free of divergences at large scales. This equation is less general than the Lenard Balescu-type kinetic equation recently derived by Heyvaerts (2010) since it neglects collective effects, but it is substantially simpler and could be useful as a first step. We discuss the evolution of the system as a whole and the relaxation of a test star in a bath of field stars. We derive the corresponding Fokker-Planck equation in angle-action variables and provide expressions for the diffusion coefficient and friction force.
We discuss the work of Hans Bethe and others in formulating a theoretical foundation for the nuclear shell model. Written for a general audience, this article describes the evolution from Brueckner's reaction matrix theory to the Moszkowski-Scott separation method and ultimately to the Reference Spectrum method of Bethe, Brandow, and Petschek. We also discuss connections with the recently developed low momentum nucleon-nucleon interactions.
We obtain a more precise version of an asymptotic formula of A. Dubickas for the number of monic Eisenstein polynomials of fixed degree $d$ and of height at most $H$, as $H\to \infty$. In particular, we give an explicit bound for the error term. We also obtain an asymptotic formula for arbitrary Eisenstein polynomials of height at most $H$.
We investigate optical transitions of non-interacting electron systems consisting of two symmetric energy bands touching each other at the Fermi energy (e.g. graphene at half filling). Optical conductivity is obtained using Kubo formula at zero temperature. We show that for particles whose pseudospin direction is determined solely by the direction of their momentum, the optical conductivity has power law frequency dependence with the exponent $(d-2)/z$ where $d$ is the dimension of the system and $z$ is the dynamical exponent. According to our result two-dimensional systems with the above pseudospin characteristics always exhibit frequency-independent optical conductivity.
From stellar evolution simulations (using MESA) we conclude that the fatal common envelope evolution (CEE) channel for the formation of Type IIb core collapse supernova (SN IIb) progenitors can indeed account for some SNe IIb. In the fatal CEE channel for SNe IIb a low mass main sequence secondary star inspirals inside the giant envelope of the massive primary star and removes most of the giant envelope before it merges with the giant core. The key ingredient of the scenario studied here is that the tidally destroyed secondary star forms a new giant envelope. The mass-loss process in a wind during the evolution from the merger process until core collapse, i.e., until the explosion, leaves little hydrogen mass at explosion as inferred from observations of SNe IIb. In the case of a massive primary star with a zero age main sequence mass of M(ZAMS)=16Mo that during its giant phase swallows a main sequence star of mass M2=0.5Mo, we find at explosion a hydrogen mass of M(H)=0.02-0.09Mo, depending on the rotation we assume. We find similar values for M(ZAMS)=12Mo.
We present the analysis of the onset of the new 2010s' OH flaring event detected in the OH ground-state main line at 1665~MHz towards o Ceti and compare its characteristics with those of the 1990s' flaring event. This is based on a series of complementary single-dish and interferometric observations both in OH and H2O obtained with the Nancay Radio telescope (NRT), the Medicina and Effelsberg Telescopes, the European VLBI Network (EVN), and (e)Multi-Element Radio Linked Interferometer Network ((e)MERLIN). We compare the overall characteristics of o Ceti's flaring events with those which have been observed towards other thin-shell Miras, and explore the implication of these events with respect to the standard OH circumstellar-envelope model. The role of binarity in the specific characteristics of o Ceti's flaring events is also investigated. The flaring regions are found to be less than ~400$ +/- 40 mas (i.e., ~40 +/- 4$ AU) either side of o Ceti, with seemingly no preferential location with respect to the direction to the companion Mira B. Contrary to the usual expectation that the OH maser zone is located outside the H2O maser zone, the coincidence of the H2O and OH maser velocities suggests that both emissions arise at similar distances from the star. The OH flaring characteristics of Mira are similar to those observed in various Mira variables before, supporting the earlier results that the regions where the transient OH maser emission occurs are different from the standard OH maser zone.