ShantanuT01/DACTYL-Pretraining huggingface dataset:
Real-world data processing problems often involve various image modalities associated with a certain scene, including RGB images, infrared images or multi-spectral images. The fact that different image modalities often share certain attributes, such as certain edges, textures and other structure primitives, represents an opportunity to enhance various image processing tasks. This paper proposes a new approach to construct a high-resolution (HR) version of a low-resolution (LR) image given another HR image modality as reference, based on joint sparse representations induced by coupled dictionaries. Our approach, which captures the similarities and disparities between different image modalities in a learned sparse feature domain in \emph{lieu} of the original image domain, consists of two phases. The coupled dictionary learning phase is used to learn a set of dictionaries that couple different image modalities in the sparse feature domain given a set of training data. In turn, the coupled super-resolution phase leverages such coupled dictionaries to construct a HR version of the LR target image given another related image modality. One of the merits of our sparsity-driven approach relates to the fact that it overcomes drawbacks such as the texture copying artifacts commonly resulting from inconsistency between the guidance and target images. Experiments on real multimodal images demonstrate that incorporating appropriate guidance information via joint sparse representation induced by coupled dictionary learning brings notable benefits in the super-resolution task with respect to the state-of-the-art. Of particular relevance, the proposed approach also demonstrates better robustness than competing deep-learning-based methods in the presence of noise.
Assuming the Riemann hypothesis, we prove that $$ N_k(T) = \frac{T}{2\pi}\log \frac{T}{4\pi e} + O_k\left(\frac{\log{T}}{\log\log{T}}\right), $$ where $N_k(T)$ is the number of zeros of $\zeta^{(k)}(s)$ in the region $0<\Im s\le T$. We further apply our method and obtain a zero counting formula for the derivative of Selberg zeta functions, improving earlier work of Luo.
We perform Differential Emission Measure (DEM) analysis of an M7.7 flare that occurred on 2012 July 19 and was well observed by the Atmospheric Imaging Assembly (AIA) aboard the Solar Dynamic Observatory. Using the observational data with unprecedented high temporal and spatial resolution from six AIA coronal passbands, we calculate the DEM of the flare and derive the time series of maps of DEM-weighted temperature and emission measure (EM). It is found that, during the flare, the highest EM region is located in the flare loop top with a value varying between 8.4 10^28 cm^-5 and 2.5 10^30 cm^-5. The temperature there rises from 8 MK at about 04:40 UT (the initial rise phase) to a maximum value of 13 MK at about 05:20 UT (the hard X-ray peak). Moreover, we find a hot region that is above the flare loop top with a temperature even up to 16 MK. We also analyze the DEM properties of the reconnection site. The temperature and density there are not as high as that in the loop top and the flux rope, indicating that the main heating may not take place inside the reconnection site. In the end, we examine the dynamic behavior of the flare loops. Along the flare loop, both the temperature and the EM are the highest in the loop top and gradually decrease towards the footpoints. In the northern footpoint, an upward force appears with a biggest value in the impulsive phase, which we conjecture originates from chromospheric evaporation.
The decay constants of pseudoscalar mesons are calculated in a relativistic quark model which assumes that mesons are made of a valence quark antiquark pair and of an effective vacuum like component. The results are given in terms of quark masses and of some free parameters entering the expression of the internal wave functions of the mesons. By using the pion and kaon decay constants $F_{\pi^+}=130.7~MeV,~F_{K^+}=159.8~MeV$ to fix the parameters of the model one gets $60~MeV\leq F_{D^+}\leq 185~MeV,~95~MeV\leq F_{D_s}\leq230~MeV,~80~MeV\leq F_{B^+}\leq205~MeV$ for the light quark masses $m_u=5.1~MeV,~m_d=9.3~MeV,~m_s=175~MeV$ and the heavy quark masses in the range: $1.~GeV\leq m_c\leq1.6~GeV,~4.1~GeV\leq m_b\leq4.5~GeV$. In the case of light neutral mesons one obtains with the same set of parameters $F_{\pi^0}\approx 138~MeV,~F_\eta\approx~130~MeV,F_{\eta'} \approx~78~MeV$. The values are in agreement with the experimental data and other theoretical results.
We use a sample of 706 galaxies, selected as [OII]$\lambda$3727 ([OII]) emitters in the Survey for High-$z$ Absorption Red and Dead Sources (SHARDS) on the CANDELS/GOODS-N field, to study the differential attenuation of the nebular emission with respect to the stellar continuum. The sample includes only galaxies with a counterpart in the infrared and $\mathrm{log}_{10}(M_{*}/\mathrm{M}_{\odot})$ $>$ 9, over the redshift interval 0.3 $\lesssim$ $z$ $\lesssim$ 1.5. Our methodology consists in the comparison of the star formation rates inferred from [OII] and H$\alpha$ emission lines with a robust quantification of the total star-forming activity (${SFR}_{\mathrm{TOT}}$) that is independently estimated based on both infrared and ultraviolet (UV) luminosities. We obtain $f$$=$$E(B-V)_{\mathrm{stellar}}$/$E(B-V)_{\mathrm{nebular}}$ $=$ 0.69$^{0.71}_{0.69}$ and 0.55$^{0.56}_{0.53}$ for [OII] and H$\alpha$, respectively. Our resulting $f$-factors display a significant positive correlation with the UV attenuation and shallower or not-significant trends with the stellar mass, the $SFR_{\mathrm{TOT}}$, the distance to the main sequence, and the redshift. Finally, our results favour an average nebular attenuation curve similar in shape to the typical dust curve of local starbursts.
We present new atomic hydrogen (HI) observations of the collisional ring galaxy NGC 922 obtained using the Australia Telescope Compact Array. Our observations reveal for the first time the vast extent of the HI disc of this galaxy. The HI morphology and kinematics of NGC 922 show that this galaxy is not the product of a simple drop-through interaction, but has a more complex interaction history. The integrated HI flux density of NGC 922 from our observations is 24.7 Jy km s$^{-1}$, which is within the error of the flux value obtained using the $64$-m Parkes radio telescope. This flux density translates to a total HI mass of $1.1*10^{10}$ M$_{\circ}$ and corresponds to an HI to total mass fraction (M$_{HI}$/M$_{tot}$) of approximately $0.11$. The gaseous structures of NGC 922 are more extended to the north and include an HI tail that has a projected physical length of $8$ kpc. Gas warps are also evident in the velocity field of NGC 922 and are more prominent on the approaching and the western side of the disc. In comparison with a large sample of star-forming galaxies in the local Universe, NGC 922 possesses a high gas fraction relative to galaxies with a similar stellar mass of ~$10^{10.4}$ M$_{\circ}$, and exhibits a high specific star formation rate.
In this note, we study the problem of existence of sequences of consecutive 1's in the periodic part of the continued fractions expansions of square roots of primes. We prove unconditionally that, for a given $N\gg 1$, there are at least $N\log^{-3/2}N$ prime numbers $p\leq N$ such that the continued fraction expansion of $\sqrt{p}$ contains three consecutive 1's on the beginning of the periodic part. We also present results of our computations related to the considered problem and some related problems, formulate several open questions and conjectures and get some results under the assumption of Hypothesis H of Schinzel.
The aim of this work is to prove by a perturbation method the existence of solutions of the coupled Einstein-Dirac equations for a static, spherically symmetric system of two fermions in a singlet spinor state. We relate the solutions of our equations to those of the nonlinear Choquard equation and we show that the nondegenerate solution of Choquard's equation generates solutions for Einstein-Dirac equations.
The rotational behaviour of T=0 and T=1 bands in the odd-odd N=Z nucleus 62Ga is studied theoretically using the spherical shell model (laboratory frame) and the cranked Nilsson-Strutinsky model (intrinsic frame). Both models give a good description of available experimental data. The role of isoscalar and isovector pairing in the T=0 and T=1 bands as functions of angular momentum is studied in the shell model. The observed backbending in the T=0 band is interpreted as an unpaired band-crossing between two configurations with different deformation. The two configurations differ by 2p-2h and are found to terminate the rotational properties at I\pi=9+ and I\pi=17+, respectively. E2-decay matrix elements and spectroscopic quadrupole moments are calculated. From the CNS calculation, supported by shell model results, it is suggested that the low spin parts of the bands with T=0 and T=1 correspond to triaxially deformed states with the rotation taking place around the shortest axis (positive \gamma) and intermediate axis (negative \gamma), respectively. At lower spins the configuration space pf_{5/2}g_{9/2}, used in the shell model calculation, is found sufficient while also f_{7/2} becomes important above the backbending.
In order to test the $^{16}$C internal wave function, we perform microscopic coupled-channels (MCC) calculations of the $^{16}$C($0_1^+ \to 2_1^+$) inelastic scattering by $^{208}$Pb target at $E/A$=52.7 MeV using the antisymmetrized molecular dynamics (AMD) wave functions of $^{16}$C, and compare the calculated differential cross sections with the measured ones. The MCC calculations with AMD wave functions reproduce the experimental data fairly well, although they slightly underestimate the magnitude of the cross sections. The absolute magnitude of calculated differential cross sections is found to be sensitive to the neutron excitation strength. We prove that the MCC method is a useful tool to connect the inelastic scattering data with the internal wave functions.
We considered real, p-adic and adelic noncommutative scalar solitons and obtained some new results.
In contrast to the generic object, aerial targets are often non-axis aligned with arbitrary orientations having the cluttered surroundings. Unlike the mainstreamed approaches regressing the bounding box orientations, this paper proposes an effective adaptive points learning approach to aerial object detection by taking advantage of the adaptive points representation, which is able to capture the geometric information of the arbitrary-oriented instances. To this end, three oriented conversion functions are presented to facilitate the classification and localization with accurate orientation. Moreover, we propose an effective quality assessment and sample assignment scheme for adaptive points learning toward choosing the representative oriented reppoints samples during training, which is able to capture the non-axis aligned features from adjacent objects or background noises. A spatial constraint is introduced to penalize the outlier points for roust adaptive learning. Experimental results on four challenging aerial datasets including DOTA, HRSC2016, UCAS-AOD and DIOR-R, demonstrate the efficacy of our proposed approach. The source code is availabel at: https://github.com/LiWentomng/OrientedRepPoints.
We have performed a first principles study of structural, mechanical, electronic, and optical properties of orthorhombic Sb2S3 and Sb2Se3 compounds. The calculations have been carried out within the local density approximation using norm conserving pseudopotentials. The lattice parameters, bulk modulus, and its pressure derivatives of the these compounds have been obtained. The second-order elastic constants have been calculated, and the other related quantities such as the Young's modulus, shear modulus, Poisson's ratio, anisotropy factor, sound velocities and Debye temperature have also been estimated in the present work. The linear photon-energy dependent dielectric functions and some optical properties such as the energy-loss function, the effective number of valance electrons and the effective optical dielectric constant are calculated. Our structural estimation and some other results are in agreement with the available experimental and theoretical data.
We present a novel approach for model-based 6D pose refinement in color data. Building on the established idea of contour-based pose tracking, we teach a deep neural network to predict a translational and rotational update. At the core, we propose a new visual loss that drives the pose update by aligning object contours, thus avoiding the definition of any explicit appearance model. In contrast to previous work our method is correspondence-free, segmentation-free, can handle occlusion and is agnostic to geometrical symmetry as well as visual ambiguities. Additionally, we observe a strong robustness towards rough initialization. The approach can run in real-time and produces pose accuracies that come close to 3D ICP without the need for depth data. Furthermore, our networks are trained from purely synthetic data and will be published together with the refinement code to ensure reproducibility.
Anderson proved that the finite generation of the value semigroup $\Gamma_{Y_\bullet}(D)$ in the construction of the Newton-Okounkov body $\Delta_{Y_\bullet}(D)$ induces a toric degeneration of the corresponding variety $X$ to some toric variety $X_0$. In this case the normalization of $X_0$ is the normal toric variety corresponding to the rational polytope $\Delta_{Y_\bullet}(D)$. Since $X_0$ is not normal in general this correspondence is rather implicit. In this article we investigate in conditions to assure that $X_0$ is normal, by comparing the Hilbert polynomial with the Ehrhart polynomial.   In the case of del Pezzo surfaces this will result in an algorithm which outputs for a given divisor $D$ a flag $Y_\bullet$ such that the value semigroup in question is indeed normal. Furthermore, we will find flags on del Pezzo surfaces and on some particular weak del Pezzo surfaces which induce normal toric degenerations for all possible divisors at once. We will prove that in this case the global value semigroup $\Gamma_{Y_\bullet}(X)$ is finitely generated and normal.
We study the bifurcation diagram of the Onsager free-energy func- tional for liquid crystals with orientation parameter on the sphere in three dimensions. In particular, we concentrate on a very general class of two- body interaction potentials including the Onsager kernel. The problem is reformulated as a non-linear eigenvalue problem for the kernel operator, and a general method to find the corresponding eigenvalues and eigenfunctions is presented. Our main tools for this analysis are spherical harmonics and a special algorithm for computing expansions of products of spherical harmon- ics in terms of spherical harmonics. We find an explicit expression for the set of all bifurcation points. Using a Lyapunov-Schmidt reduction, we derive a bifurcation equation depending on five state variables. The dimension of this state space is further reduced to two dimensions by using the rotational symmetry of the problem and the theory of invariant polynomials. On the basis of these result, we show that the first bifurcation occurring in case of the Onsager interaction potential is a transcritical bifurcation and that the corresponding solution is uniaxial. In addition, we prove some global proper- ties of the bifurcation diagram such as the fact that the trivial solution is the unique local minimiser for high temperatures, that it is not a local minimiser if the temperature is low, the boundedness of all equilibria of the functional and that the bifurcation branches are either unbounded or that they meet another bifurcation branch.
We study the interaction between single apex atoms in a metallic contact, using the break junction geometry. By carefully 'training' our samples, we create stable junctions in which no further atomic reorganization takes place. This allows us to study the relation between the so-called jump out of contact (from contact to tunnelling regime) and jump to contact (from tunnelling to contact regime) in detail. Our data can be fully understood within a relatively simple elastic model, where the elasticity k of the electrodes is the only free parameter. We find 5 < k < 32 N/m. Furthermore, the interaction between the two apex atoms on both electrodes, observed as a change of slope in the tunnelling regime, is accounted for by the same model.
We consider a class of wave equations of the type $\partial_{tt} u + Lu + B\partial_{t} u = 0$, with a self-adjoint operator $L$, and various types of local damping represented by $B$. By establishing appropriate and raher precise estimates on the resolvent of an associated operator $A$ on the imaginary axis of ${{\Bbb C}}$, we prove polynomial decay of the semigroup $\exp(-tA)$ generated by that operator. We point out that the rate of decay depends strongly on the concentration of eigenvalues and that of the eigenfunctions of the operator $L$. We give several examples of application of our abstract result, showing in particular that for a rectangle $\Omega := (0,L_{1})\times (0,L_{2})$ the decay rate of the energy is different depending on whether the ratio $L_{1}^2/L_{2}^2$ is rational, or irrational but algebraic.
The recent results of Forshaw and Sabio Vera on small-$x$ jet rates to order $\alpha_s^3$ are extended to all orders, for any number of jets. A simple generating function is obtained.
We studied the radiative properties of small magnetic elements (active region faculae and the network) during the rising phase of solar cycle 23 from 1996 to 2001, determining their contrasts as a function of heliocentric angle, magnetogram signal, and the solar cycle phase. We combined near-simultaneous full disk images of the line-of-sight magnetic field and photospheric continuum intensity provided by the MDI instrument on board the SOHO spacecraft. Sorting the magnetogram signal into different ranges allowed us to distinguish between the contrast of different magnetic structures. We find that the contrast center-to-limb variation (CLV) of these small magnetic elements is independent of time with a 10% precision, when measured during the rising phase of solar cycle 23. A 2-dimensional empirical expression for the contrast of photospheric features as a function of both the position on the disk and the averaged magnetic field strength was determined, showing its validity through the studied time period. A study of the relationship between magnetogram signal and the peak contrasts shows that the intrinsic contrast (maximum contrast per unit of magnetic flux) of network flux tubes is higher than that of active region faculae during the solar cycle.
The semi-classical regime of standing wave solutions of a Schr\"odinger equation in presence of non-constant electric and magnetic potentials is studied in the case of non-local nonlinearities of Hartree type. It is show that there exists a family of solutions having multiple concentration regions which are located around the minimum points of the electric potential.
We present a general description of two mixed branes interactions. For this we consider two mixed branes with dimensions p_1 and p_2, in external field B_{\mu\nu} and arbitrary gauge fields A^1_{\alpha_1} and A^2_{\alpha_2} on the world volume of them, in spacetime in which some of its directions are compactified on circles with different radii. Some examples are considered to clear these general interactions. Finally contribution of the massless states on the interactions is extracted. Closed string with mixed boundary conditions and boundary state formalism, provide useful tools for calculation of these interactions.
We investigate curvature effects on geometric parameters, energetics and electronic structure of zigzag nanotubes with fully optimized geometries from first-principle calculations. The calculated curvature energies, which are inversely proportional to the square of radius, are in good agreement with the classical elasticity theory. The variation of the band gap with radius is found to differ from simple rules based on the zone folded graphene bands. Large discrepancies between tight binding and first principles calculations of the band gap values of small nanotubes are discussed in detail.
Extensive photometric and spectroscopic surveys of the Andromeda galaxy (M31) have discovered tidal debris features throughout M31's stellar halo. We present stellar kinematics and metallicities in fields with identified substructure from our on-going SPLASH survey of M31 red giant branch stars with the DEIMOS spectrograph on the Keck II 10-m telescope. Radial velocity criteria are used to isolate members of the kinematically-cold substructures. The substructures are shown to be metal-rich relative to the rest of the dynamically hot stellar population in the fields in which they are found. We calculate the mean metallicity and average surface brightness of the various kinematical components in each field, and show that, on average, higher surface brightness features tend to be more metal-rich than lower surface brightness features. Simulations of stellar halo formation via accretion in a cosmological context are used to illustrate that the observed trend can be explained as a natural consequence of the observed dwarf galaxy mass-metallicity relation. A significant spread in metallicity at a given surface brightness is seen in the data; we show that this is due to time effects, namely the variation in the time since accretion of the tidal streams' progenitor onto the host halo. We show that in this theoretical framework a relationship between the alpha-enhancement and surface brightness of tidal streams is expected, which arises from the varying times of accretion of the progenitor satellites onto the host halo. Thus, measurements of the alpha-enrichment, metallicity, and surface brightness of tidal debris can be used to reconstruct the luminosity and time of accretion onto the host halo of the progenitors of tidal streams.
Cross-section and neutron-emission data from heavy-ion fusion-fission reactions are consistent with a Kramers-modified statistical model which takes into account the collective motion of the system about the ground state; the temperature dependence of the location of fission transition points; and the orientation degree of freedom. We see no evidence to suggest that the nuclear viscosity departs from the surface-plus-window dissipation model. The strong increase in the nuclear viscosity above a temperature of ~1 MeV deduced by others is an artifact generated by an inadequate fission model.
We address the problem of a microscopic derivation of the Langevin equation for a weakly relativistic Brownian particle. A non-covariant Hamiltonian model is adopted, in which the free motion of particles is described relativistically, while their interaction is treated classically, i.e. by means of action-to-a-distance interaction potentials. Relativistic corrections to the classical Langevin equation emerge as nonlinear dissipation terms and originate from the nonlinear dependence of the relativistic velocity on momentum. On the other hand, similar nonlinear dissipation forces also appear as classical (non-relativistic) corrections to the weak-coupling approximation. It is shown that these classical corrections, which are usually ignored in phenomenological models, may be of the same order of magnitude, if not larger than relativistic ones. The interplay of relativistic corrections and classical beyond-the-weak-coupling contributions determines the sign of the leading nonlinear dissipation term in the Langevin equation, and thus is qualitatively important.