ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper we prove the existence and uniqueness of very weak solutions to linear diffusion equations involving a singular absorption potential and/or an unbounded convective flow on a bounded open set of $\mathbb R^N$. In most of the paper we consider homogeneous Dirichlet boundary conditions but we prove that when the potential function grows faster than the distance to the boundary to the power -2 then no boundary condition is required to get the uniqueness of very weak solutions. This result is new in the literature and must be distinguished from other previous results in which such uniqueness of solutions without any boundary condition was proved for degenerate diffusion operators (which is not our case). Our approach, based on the treatment on some distance to the boundary weighted spaces, uses a suitable regularity of the solution of the associated dual problem which is here established. We also consider the delicate question of the differentiability of the very weak solution and prove that some suitable additional hypothesis on the data is required since otherwise the gradient of the solution may not be integrable on the domain.
Throughout the evolution of the neural networks more specialized cells were added to the set of basic building blocks. These cells aim to improve training convergence, increase the overall performance, and reduce the number of required labels, all while preserving the expressive power of the universal network. Inspired by the partitioning of the human visual perception system between the eyes and the cerebral cortex, we present TPNET, which offloads universal and application-specific CNN from the bulk processing of the high resolution pixel data and performs the translation-variant image correction while delegating all non-linear decision making to the network.   In this work, we explore application of TPNET to 3D perception with a narrow-baseline (0.0001-0.0025) quad stereo camera and prove that a trained network provides a disparity prediction from the 2D phase correlation output by the Tile Processor (TP) that is twice as accurate as the prediction from a carefully hand-crafted algorithm. The TP in turn reduces the dimensions of the input features of the network and provides instrument-invariant and translation-invariant data, making real-time high resolution stereo 3D perception feasible and easing the requirement to have a complete end-to-end network.
Two different realistic $F(R)$ modified gravity models are considered in the framework of the Friedmann-Lemetre-Robertson-Walker universe. The parameters of these two models are adjusted to reach coherence with the most recent and accurate observations of the current universe. A study of the growth of matter density perturbations is done, and several parametrizations of the growth index are developed for both models. The ansatz for the growth index given by $\gamma = \gamma_0 + \gamma_1 z/(1+z)$ seems to be the best parametrization for the two models considered. Finally, the values obtained for $\gamma_0$ and $\gamma_1$ can be used in order to characterize these two models and to differentiate them from others such as the Hu-Sawicki model.
The High Altitude Water Cherenkov (HAWC) telescope recently observed extended emission around the Geminga and PSR~B0656+14 pulsar wind nebulae (PWNe). These observations have been used to estimate cosmic-ray (CR) diffusion coefficients near the PWNe that appear to be more than two orders of magnitude smaller than that typically derived for the interstellar medium from the measured abundances of secondary species in CRs. Two-zone diffusion models have been proposed as a solution to this discrepancy, where the slower diffusion zone (SDZ) is confined to a small region around the PWN. Such models are shown to successfully reproduce the HAWC observations of the Geminga PWN while retaining consistency with other CR data. It is found that the size of the SDZ influences the predicted positron flux and the spectral shape of the extended $\gamma$-ray emission at lower energies that can be observed with the {\it Fermi} Large Area Telescope ({\it Fermi} LAT). If the two observed PWNe are not unique, then it is likely that there are similar pockets of slow diffusion around many CR sources elsewhere in the Milky Way. The consequences of such picture for Galactic CR propagation is explored.
Abhyankar showed that for a finite tame extension $L_1/K$ and a finite extension $L_2/K$ of $\mathfrak{P}$-adic fields, the condition $[\nu L_1 : \nu K]$ divides $[\nu L_2 : \nu K]$ is sufficient to eliminate ramification, that is, $L_1 \cdot L_2 / L_2$ is unramified. In this paper, we show that the above condition is not sufficient in the case of an arbitrary henselian valued field. We construct a counterexample illustrating that fact. We also give a necessary and sufficient condition for the elimination of tame ramification of a henselian field after a finite extension of the base field.
In this paper we use ultra-violet (UV) and optical HST photometry in five bands, and an extensive set of spectral evolutionary synthesis scenarios to investigate the age and masses of 124 star clusters in the luminous blue compact galaxy ESO338-IG04 (Tololo 1924-416). The very small internal reddening makes ESO 338-IG04 an excellent laboratory for studying the formation of massive star clusters. We have used the star clusters to trace the temporal and spatial evolution of the starburst, and to put constraints on the star formation activity over a cosmological time-scale. The present starburst has been active for about 40 Myr. A standard Salpeter initial mass function (IMF) extending up to 120 solar masses provides the best fit to the data, although a flatter IMF cannot be excluded. The compact star clusters provide 30-40 percent of the UV luminosity and star formation activity. We find no evidence for dust obscuration even among the youngest (< 1 Myr) clusters. The fraction of stellar mass contained in compact star clusters is found to be several percent, which is an unusually high value. The intermediate age clusters show a flattened space distribution which agrees with the isophotal shape of the galaxy, whereas the oldest clusters seem to have a spherical distribution.(abridged)
Facial expressions convey nonverbal cues which play an important role in interpersonal relations, and are widely used in behavior interpretation of emotions, cognitive science, and social interactions. In this paper we analyze different ways of representing geometric feature and present a fully automatic facial expression recognition (FER) system using salient geometric features. In geometric feature-based FER approach, the first important step is to initialize and track dense set of facial points as the expression evolves over time in consecutive frames. In the proposed system, facial points are initialized using elastic bunch graph matching (EBGM) algorithm and tracking is performed using Kanade-Lucas-Tomaci (KLT) tracker. We extract geometric features from point, line and triangle composed of tracking results of facial points. The most discriminative line and triangle features are extracted using feature selective multi-class AdaBoost with the help of extreme learning machine (ELM) classification. Finally the geometric features for FER are extracted from the boosted line, and triangles composed of facial points. The recognition accuracy using features from point, line and triangle are analyzed independently. The performance of the proposed FER system is evaluated on three different data sets: namely CK+, MMI and MUG facial expression data sets.
We studied the surface structures of chemical vapor deposited (CVD) graphene on Cu(103). The graphene covered Cu surface had (103) facets parallel to the Cu[010] direction, on which triangular patterns were formed. In contrast, the bare Cu surface showed no facets. Post-growth thermal annealing in an ultra-high vacuum induced surface changes on the Cu(103) facets. The reorganization of the Cu surface by the post-growth thermal annealing led to a change in the lattice strain and hole doping level of the CVD-grown graphene.
Color separations (most often cyan, magenta, yellow, and black) are commonly used in printing to reproduce multi-color images. For mechanical reasons, these color separations are generally not perfectly aligned with respect to each other when they are rendered by their respective imaging stations. This phenomenon, called color plane misregistration, causes gap and halo artifacts in the printed image. Color trapping is an image processing technique that aims to reduce these artifacts by modifying the susceptible edge boundaries to create small, unnoticeable overlaps between the color planes. We propose three low-complexity algorithms for automatic color trapping which hide the effects of small color plane mis-registrations. Our algorithms are designed for software or embedded firmware implementation. The trapping method they follow is based on a hardware-friendly technique proposed by J. Trask (JTHBCT03) which is too computationally expensive for software or firmware implementation. The first two algorithms are based on the use of look-up tables (LUTs). The first LUT-based algorithm corrects all registration errors of one pixel in extent and reduces several cases of misregistration errors of two pixels in extent using only 727 Kbytes of storage space. This algorithm is particularly attractive for implementation in the embedded firmware of low-cost formatter-based printers. The second LUT-based algorithm corrects all types of misregistration errors of up to two pixels in extent using 3.7 Mbytes of storage space. The third algorithm is a hybrid one that combines LUTs and feature extraction to minimize the storage requirements (724 Kbytes) while still correcting all misregistration errors of up to two pixels in extent. This algorithm is suitable for both embedded firmware implementation on low-cost formatter-based printers and software implementation on host-based printers.
The nature of the progenitors of type Ia supernovae is still under controversial debate. KPD 1930+2752 is one of the best SN Ia progenitor candidates known today. The object is a double degenerate system consisting of a subluminous B star (sdB) and a massive white dwarf (WD). Maxted et al. (2000) conclude that the system mass exceeds the Chandrasekhar mass. This conclusion, however, rests on the assumption that the sdB mass is 0.5 Mo. However, recent binary population synthesis calculations suggest that the mass of an sdB star may range from 0.3 Mo to more than 0.7 Mo. It is therefore important to measure the mass of the sdB star simultaneously with that of the white dwarf. Since the rotation of the sdB star is tidally locked to the orbit the inclination of the system can be constrained if the sdB radius and the projected rotational velocity can be measured with high precision. An analysis of the ellipsoidal variations in the light curve allows to tighten the constraints derived from spectroscopy. We derive the mass-radius relation for the sdB star from a quantitative spectral analysis of 150 low-resolution spectra. The projected rotational velocity is determined for the first time from 200 high-resolution spectra. In addition a reanalysis of the published light curve is performed. The atmospheric and orbital parameters are measured with unprecedented accuracy. In particular the projected rotational velocity is determined. A neutron star companion can be ruled out and the mass of the sdB is limited between 0.45 Mo and 0.52 Mo. The total mass of the system ranges from 1.36 Mo to 1.48 Mo and hence is likely to exceed the Chandrasekhar mass. So KPD 1930+2752 qualifies as an excellent double degenerate supernova Ia progenitor candidate.
A perfect cuboid is a rectangular parallelepiped whose edges, whose face diagonals, and whose space diagonal are of integer lengths. The second cuboid conjecture specifies a subclass of perfect cuboids described by one Diophantine equation of tenth degree and claims their non-existence within this subclass. This Diophantine equation has two parameters. Previously asymptotic expansions and estimates for roots of this equation were obtained in the case where the first parameter is fixed and the other tends to infinity. In the present paper reverse asymptotic expansions and estimates are derived in the case where the second parameter is fixed and the first one tends to infinity. Their application to the perfect cuboid problem is discussed.
The ladder-rainbow truncation of the set of Dyson-Schwinger equations is used to study the pion and kaon electromagnetic form factors and the $\gamma^\star \pi^0 \gamma$ transition form factor in impulse approximation. With model parameters previously fixed by the pseudoscalar meson masses and decay constants, the obtained form factors are in good agreement with the data.
For dynamical dark energy cosmologies we carry out a series of N-body gravitational simulations, achieving percent level accuracy in the relative mass power spectra at any redshift. Such accuracy in the power spectrum is necessary for next generation cosmological mass probes. Our matching procedure reproduces the CMB distance to last scattering and delivers subpercent level power spectra at z=0 and z~3. We discuss the physical implications for probing dark energy with surveys of large scale structure.
The Weyl anomaly in the Holographic Renormalisation Group as implemented using Hamilton-Jacobi language is studied in detail. We investigate the breakdown of the descent equations in order to isolate the Weyl anomaly of the dual field theory close to the (UV) fixed point. We use the freedom of adding finite terms to the renormalised effective action in order to bring the anomalies in the expected form. We comment on different ways of describing the bare and renormalised schemes, and on possible interpretations of the descent equations as describing the renormalisation group flow non-perturbatively. We find that under suitable assumptions these relations may lead to a class of c-functions.
In the multi-fractal analysis of large scale matter distribution, the scale of transition to homogeneity is defined as the scale above which the fractal dimension of underlying point distribution is equal to the ambient dimension of the space in which points are distributed. With finite sized weakly clustered distribution of tracers obtained from galaxy redshift surveys it is difficult to achieve this equality. Recently we have defined the scale of homogeneity to be the scale above which the deviation of fractal dimension from the ambient dimension becomes smaller than the statistical dispersion. In this paper we use the relation between the fractal dimensions and the correlation function to compute the dispersion for any given model in the limit of weak clustering amplitude. We compare the deviation and dispersion for the LCDM model and discuss the implication of this comparison for the expected scale of homogeneity in the concordant model of cosmology. We estimate the upper limit to the scale of homogeneity to be close to 260 Mpc/h for the LCDM model. Actual estimates of the scale of homogeneity should be smaller than this as we have considered only statistical contribution to the dispersion in fractal dimension and we have ignored cosmic variance and contributions due to survey geometry and the selection function. We find that as long as non linear correction are insignificant, scale of homogeneity as defined above does not change with epoch. The scale of homogeneity depends very weakly on the choice of tracer of the density field. Thus the suggested definition of the scale of homogeneity is fairly robust.
We have studied the phase diagram of the one dimensional XXZ model with Dzyaloshinskii-Moriya (DM) interaction. We have applied the quantum renormalization group (QRG) approach to get the stable fixed points, critical point and the scaling of coupling constants. This model has three phases, ferromagnetic, spin-fluid and N\'{e}el phases which are separated by a critical line which depends on the DM coupling constant. We have shown that the staggered magnetization is the order parameter of the system and investigated the influence of DM interaction on the chiral ordering as a helical magnetic order.
We investigate the geometry of the Simpson moduli space M of stable sheaves on P_3 with Hilbert polynomial H(m)=3m+1 and describe explicitly the two smooth, rational components, their 11-dimensional smooth, transversal intersection and the relation between M and the Hilbert scheme Hilb_H(P_3) of cubic space curves. We also compute the Betti numbers of the Chow groups of the moduli space M.
We study double line structures in projective spaces and quadric hypersurfaces, and investigate the geometry of irreducible components of Hilbert scheme of curves and moduli of stable sheaves of pure dimension 1 on a smooth quadric threefold.
1H0323+342 is one of narrow-line radio-loud Seyfert 1 galaxies (RL-NLS1), which is a new class of gamma-ray emitting AGNs. Narrow-line Seyfert 1 galaxies (NLS1) have a small-mass black hole, but its mass accretion rate is almost as high as Eddington limit. Therefore, by observing NLS1s, we can know the evolution of supermassive black holes at the center of galaxies. Some of NLS1s are radio-loud and we call them RL-NLS1. From past observations, multi-wavelength spectrum of RL-NLS1s is similar to that of typical blazars; the synchrotron emission in the lower energy band up to the optical band, and inverse Compton scattering of low energy photons from disk, torus, and broad line region. X-ray band is a transittion region between the synchrotron and inverse Compton, and also there is a possible disk/corona emission. Therefore, we studied the energy-dependence of time variability of the X-ray emission of 1H0323+342, which have been observed by Suzaku in 2009 and 2013, in order to constrain the emission mechanism. We found that the lower energy below 1 keV and the higher energy above 7 keV show a different variability from the middle energy band, indicating at least two emission components in the X-ray band. X-ray spectrum is not a simple power-law, but requires an additional features; a broken power-law plus flat hard component, or a power-law plus a relativistic reflection component. Each spectral component seems to vary independently.
Polarization phenomena are essential for the understanding of elementary processes, and are typically large in the threshold region. The selection rules with respect to P-parity, angular momentum, isotopic spin and the Pauli principle allow to parametrize in a model independent way, the spin structure of the matrix elements for the near-threshold heavy meson production in NN-collisions in terms of a small number of partial amplitudes. Such parametrization is very powerful for the analysis of polarization phenomena and possible $t-$exchange mechanisms.
A class of $AdS_2\times \Sigma_2$, with $\Sigma_2$ being a two-sphere or a hyperbolic space, solutions within four-dimensional $N=4$ gauged supergravity coupled to three-vector multiplets with dyonic gauging is identified. The gauged supergravity has non-semisimple $SO(3)\ltimes (\mathbf{T}^3,\hat{\mathbf{T}}^3)$ gauge group and can be obtained from a consistent truncation of eleven-dimensional supergravity on a tri-sasakian manifold. The maximally symmetric vacua contain $AdS_4$ geometries with $N=1,3$ supersymmetry corresponding to $N=1$ and $N=3$ superconformal field theories (SCFTs) in three dimensions. We find supersymmetric solutions of the form $AdS_2\times \Sigma_2$ preserving two supercharges. These solutions describe twisted compactifications of the dual $N=1$ and $N=3$ SCFTs and should arise as near horizon geometries of dyonic black holes in asymptotically $AdS_4$ space-time. Most solutions have hyperbolic horizons although some of them exhibit spherical horizons. These provide a new class of $AdS_2\times \Sigma_2$ geometries with known M-theory origin.
We have investigated direct and pulsed current induced electroresistance in two manganites with different electronic and magnetic ground states: charge-orbital ordered 50 % Ca doped NdMnO3 and 50 % Mn doped LaNiO3. It has been shown that negative differential resistance observed at high current density in these compounds is related to Joule heating. However, bi-level and multi-level resistivity switching induced by variations in pulse width and pulse period at low current density can not be attributable to Joule heating alone. We discuss possible origins.
Vortex flows can foster a variety of wave modes. A recent oscillatory analysis of a persistent 1.7 h vortex flow with a significant substructure has suggested the existence of various types of waves within it. We investigate the nature and characteristics of waves within this quiet-Sun vortex flow to better understand its physics and dynamics. We used a cross-wavelet spectral analysis between pairs of Ha and Ca II 8542 intensity time series at different wavelengths and, hence, atmospheric heights, acquired with CRISP/SST, as well as the derived Ha Doppler velocity and full width at half maximum (FWHM) time series. We constructed halftone frequency-phase difference plots and investigated the existence and propagation characteristics of different wave modes. Our analysis suggests the existence of upwards propagating Alfvenic type waves with phase speeds of ~20-30 km/s. The dominant wave mode seems to be the fast kink wave mode; however, our analysis also suggests the existence of localised Alfvenic torsional waves related to the dynamics of individual chromospheric swirls that characterise the substructure of the vortex flow. The Ha V-I phase difference analysis seems to imply the existence of a standing wave pattern possibly arising from the interference of upwards propagating kink waves with downwards propagating ones that are reflected at the transition region or the corona. Moreover, the results provide further evidence that the central chromospheric swirl drives the dynamics of the vortex flow. This is the first exhaustive phase difference analysis within a vortex flow that explores the nature and dynamics of different wave modes within it. The questions, however, of whether, and how, the dissipation of the derived wave modes occurs and if vortex flows ultimately play a role in the energy budget of the upper layers of the solar atmosphere remain open.
We provide a definition of the quantum distances of correlated many fermion wave functions in terms of the expectation values of certain operators that we call exchange operators. We prove that the distances satisfy the triangle inequalities. We apply our formalism to the one-dimensional t-V model, which we solve numerically by exact diagonalisation. We compute the distance matrix and illustrate that it shows clear signatures of the metal-insulator transition.
We report the discovery of a new exceptional young lithium-rich giant, KIC 9821622, in the \textit{Kepler} field that exhibits an unusually large enhancement of $\alpha$, Fe-peak, and \textit{r}-process elements. From high-resolution spectra obtained with GRACES at Gemini North, we derived fundamental parameters and detailed chemical abundances of 23 elements from equivalent widths and synthesis analysis. By combining atmospheric stellar parameters with available asteroseismic data, we obtained the stellar mass, radius, and age. The data analysis reveals that KIC 9821622 is a Li-rich (A(Li)$_{NLTE}$ = 1.80 $\pm$ 0.2) intermediate-mass giant star ($M$ = 1.64 $M_{\odot}$) located at the red giant branch near the luminosity bump. We find unexpectedly elevated abundances of Fe-peak and \textit{r}-process elements. In addition, as previously reported, we find that this is a young star (2.37 Gyr) with unusually high abundances of $\alpha$-elements ([$\alpha$/Fe] = 0.31). The evolutionary status of KIC 9821622 suggests that its Li-rich nature is the result of internal fresh Li that is synthesized through the Cameron-Fowler mechanism near the luminosity bump. However, its peculiar enhancement of $\alpha$, Fe-peak, and \textit{r}-process elements opens the possibility of external contamination by material enriched by a supernova explosion. Although it is less likely, planet accretion cannot be ruled out.