ShantanuT01/DACTYL-Pretraining huggingface dataset:
$G$-operators, a class of differential operators containing the differential operators of minimal order annihilating Siegel's $G$-functions, satisfy a condition of moderate growth called Galochkin condition, encoded by a $p$-adic quantity, the size. Previous works of Chudnovsky, Andr\'e and Dwork have provided inequalities between the size of a $G$ -operator and certain computable constants depending among others on its solutions. First, we recall Andr\'e's idea to attach a notion of size to differential modules and detail his results on the behavior of the size relatively to the standard algebraic operations on the modules. This is the corner stone to prove a quantitative version of Andr\'e's generalization of Chudnovsky's Theorem: for $f(z)=\sum_{\alpha, k,\ell} c_{\alpha, k,\ell} z^{\alpha} \log(z)^k f_{\alpha, k,\ell}(z)$, where $f_{\alpha, k,\ell}(z)$ are $G$-functions, we can determine an upper bound on the size of the minimal operator $L$ over $\overline{\mathbb{Q}}(z)$ of $f(z)$ in terms of quantities depending on the $f_{\alpha, k,\ell}(z)$, the rationals $\alpha$ and the integers $k$. We give two applications of this result: we estimate the size of a product of two $G$-operators in function of the size of each operator; we also compute a constant appearing in a Diophantine problem encountered by the author.
We report new detections of the two transient ultraluminous X-ray sources (ULXs) in NGC 5128 from an ongoing series of Chandra observations. Both sources have previously been observed Lx (2-3)E39 erg/s, at the lower end of the ULX luminosity range. The new observations allow us to study these sources in the luminosity regime frequented by the Galactic black hole X-ray binaries (BH XBs). We present the recent lightcurves of both ULXs. 1RXH J132519.8-430312 (ULX1) was observed at Lx ~ 1E38 erg/s, while CXOU J132518.2-430304 (ULX2) declined to Lx ~ 2E37 erg/s and then lingered at this luminosity for hundreds of days. We show that a reasonable upper limit for both duty cycles is 0.2, with a lower limit of 0.12 for ULX2. This duty cycle is larger than anticipated for transient ULXs in old stellar populations. By fitting simple spectral models in an observation with ~50 counts we recover properties consistent with Galactic BH XBs, but inconclusive as to the spectral state. We utilise quantile analyses to demonstrate that the spectra are generally soft, and that in one observation the spectrum of ULX2 is inconsistent with a canonical hard state at >95% confidence. This is contrary to what would be expected of an accreting IMBH primary, which we would expect to be in the hard state at these luminosities. We discuss the paucity of transient ULXs discovered in early-type galaxies and excogitate explanations. We suggest that the number of transient ULXs scales with the giant and sub-giant populations, rather than the total number of XBs.
Object detection methods have witnessed impressive improvements in the last years thanks to the design of novel neural network architectures and the availability of large scale datasets. However, current methods have a significant limitation: they are able to detect only the classes observed during training time, that are only a subset of all the classes that a detector may encounter in the real world. Furthermore, the presence of unknown classes is often not considered at training time, resulting in methods not even able to detect that an unknown object is present in the image. In this work, we address the problem of detecting unknown objects, known as open-set object detection. We propose a novel training strategy, called UNKAD, able to predict unknown objects without requiring any annotation of them, exploiting non annotated objects that are already present in the background of training images. In particular, exploiting the four-steps training strategy of Faster R-CNN, UNKAD first identifies and pseudo-labels unknown objects and then uses the pseudo-annotations to train an additional unknown class. While UNKAD can directly detect unknown objects, we further combine it with previous unknown detection techniques, showing that it improves their performance at no costs.
After simultaneous compactification of spacetime and worldvolume on $K3$, the $D=10$ heterotic fivebrane with gauge group $SO(32)$ behaves like a $D=6$ heterotic string with gauge group $SO(28) \times SU(2)$, but with Kac--Moody levels different from those of the fundamental string. Thus the string/fivebrane duality conjecture in $D=10$ gets replaced by a string/string duality conjecture in $D=6$. Since $D=6$ strings are better understood than $D=10$ fivebranes, this provides a more reliable laboratory in which to test the conjecture. According to string/string duality, the Green--Schwarz factorization of the $D=6$ spacetime anomaly polynomial $I_{8}$ into $X_4\, \tilde{X}_4$ means that just as $X_4$ is the $\sigma$-model anomaly polynomial of the fundamental string worldsheet so $\tilde{X}_4$ should be the corresponding polynomial of the dual string worldsheet. To test this idea we perform a classical dual string calculation of $\tilde{X}_4$ and find agreement with the quantum fundamental string result. This also provides an {\it a posteriori} justification for assumptions made in a previous paper on string/fivebrane duality. Finally we speculate on the relevance of string/string duality to the vacuum degeneracy problem.
The evolution with cosmic time of the star formation rate density (SFRD) and of the "Main Sequence" star formation rate-stellar mass relations are two well established observational facts. In this paper the implications of these two relations combined are analytically explored, showing that quenching of star formation must start already at very early cosmic times and the quenched fraction then dominates ever since over the star forming one. Thus, a simple picture of the cosmic evolution of the global SFRD is derived, in terms of the interplay between star formation and its quenching.
A circularly polarized light can induce a dissipationless dc current in a quantum nanoring which is responsible for a resonant helicity-driven contribution to magnetic moment. This current is not suppressed by thermal averaging despite its quantum nature. We refer to this phenomenon as the quantum resonant inverse Faraday effect. For weak electromagnetic field, when the characteristic coupling energy is small compared to the energy level spacing, we predict narrow resonances in the circulating current and, consequently, in the magnetic moment of the ring. For strong fields, the resonances merge into a wide peak with a width determined by the spectral curvature. We further demonstrate that weak short-range disorder splits the resonances and induces additional particularly sharp and high resonant peaks in dc current and magnetization. In contrast, long-range disorder leads to a chaotic behavior of the system in the vicinity of the separatrix that divides the phase space of the system into regions with dynamically localized and delocalized states.
We consider the evolution of cosmological perturbations at the QCD transition, in particular the sudden reheating from a supercooled universe to the transition temperature. Sudden reheating happens at a specific temperature, hence density, and singles out one specific hypersurface. Underdensities reach the reheating earlier than overdensities, there is a short period of huge pressure differences which leads to a jump in the fluid velocity. Density perturbations of scales far below the Hubble radius $\lambda\ll R_H $ get an amplification which grows quadratically in wavenumber. Primordial black hole formation will not be sufficiently amplified by the QCD transition unless the initial spectrum is fine tuned.
This paper aims at understanding the role of multi-scale information in the estimation of depth from monocular images. More precisely, the paper investigates four different deep CNN architectures, designed to explicitly make use of multi-scale features along the network, and compare them to a state-of-the-art single-scale approach. The paper also shows that involving multi-scale features in depth estimation not only improves the performance in terms of accuracy, but also gives qualitatively better depth maps. Experiments are done on the widely used NYU Depth dataset, on which the proposed method achieves state-of-the-art performance.
We study $q$-state clock models of regular and Villain types with $q=5,6$ using cluster-spin updates and observed double transitions in each model. We calculate the correlation ratio and size-dependent correlation length as quantities for characterizing the existence of Berezinskii-Kosterlitz-Thouless (BKT) phase and its transitions by large-scale Monte Carlo simulations. We discuss the advantage of correlation ratio in comparison to other commonly used quantities in probing BKT transition. Using finite size scaling of BKT type transition, we estimate transition temperatures and corresponding exponents. The comparison between the results from both types revealed that the existing transitions belong to BKT universality.
Monolayer transition metal dichalcogenides (TMDC) grown by chemical vapor deposition (CVD) are plagued by a significantly lower optical quality compared to exfoliated TMDC. In this work we show that the optical quality of CVD-grown MoSe$_2$ is completely recovered if the material is sandwiched in MoS$_2$/MoSe$_2$/MoS$_2$ trilayer van der Waals heterostructures. We show by means of density-functional theory that this remarkable and unexpected result is due to defect healing: S atoms of the more reactive MoS$_2$ layers are donated to heal Se vacancy defects in the middle MoSe$_2$ layer. In addition, the trilayer structure exhibits a considerable charge-transfer mediated valley polarization of MoSe$_2$ without the need for resonant excitation. Our fabrication approach, relying solely on simple flake transfer technique, paves the way for the scalable production of large-area TMDC materials with excellent optical quality.
In this work, we have considered the Friedmann-Robertson-Walker (FRW) model of the universe where bounce occurs and the universe is filled with Generalized Cosmic Chaplygin Gas (GCCG) or Variable Modified Chaplygin Gas (VMCG). We have studied the stability analysis through dynamical system for both models and found the critical points in flat, open and closed universe. In presence of scalar field, the dynamical behavior of scale factor and Hubble parameter is described in both models. Finally, we have analyzed the energy conditions for both the models in bouncing universe.
In this paper we show the equivalence of the conjectures of Giuga and Agoh in a direct way which leads to a combined conjecture. This conjecture is described by a sum of fractions from which all conditions can be derived easily.
Light meson electroproduction is analyzed on the basis of the handbag approach. Our results on the cross section and spin effects are in good agrement with experiments at HERA, COMPASS and HERMES energies. Predictions for $A_{UT}$ asymmetry for various reactions are presented.
We present a study of the X-ray emission from numerical simulations of hot bubbles in planetary nebulae (PNe). High-resolution, two-dimensional, radiation-hydrodynamical simulations of the formation and evolution of hot bubbles in PNe, with and without thermal conduction, are used to calculate the X-ray emission and study its time-dependence and relationship to the changing stellar parameters. Instabilities in the wind-wind interaction zone produce clumps and filaments in the swept-up shell of nebular material. Turbulent mixing and thermal conduction at the corrugated interface can produce quantities of intermediate temperature and density gas between the hot, shocked wind bubble and the swept-up photoionized nebular material, which can emit in soft, diffuse X-rays. We use the CHIANTI software to compute synthetic spectra for the models and calculate their luminosities. We find that models both with conduction and those without can produce the X-ray temperatures and luminosities that are in the ranges reported in observations, although the models including thermal conduction are an order of magnitude more luminous than those without. Our results show that at early times the diffuse X-ray emission should be dominated by the contribution from the hot, shocked stellar wind, whereas at later times the nebular gas will dominate the spectrum. We analyse the effect of sampling on the resultant spectra and conclude that a minimum of 200 counts is required to reliably reproduce the spectral shape. Likewise, heavily smoothed surface-brightness profiles obtained from low-count detections of PNe do not provide a reliable description of the spatial distribution of the X-ray emitting gas.
We compute the number of rhombus tilings of a hexagon with side lengths N,M,N,N,M,N, with N and M having the same parity, which contain a particular rhombus next to the center of the hexagon. The special case N=M of one of our results solves a problem posed by Propp. In the proofs, Hankel determinants featuring Bernoulli numbers play an important role.
We study the emergence of Berezinskii-Kosterlitz-Thouless (BKT) phases in (PbTiO$_3$)$_3$/(SrTiO$_3$)$_3$ superlattices by means of second-principles simulations. Beyond a threshold tensile epitaxial strain of $\epsilon = 0.25 \%$ the local dipole moments within the superlattices are confined to the film-plane, and thus the polarization can be effectively considered as two-dimensional. The analysis of the decay of the dipole-dipole correlation with the distance, together with the study of the density of defects and its distribution as function of temperature, supports the existence of a BKT phase in a range of temperature mediating the ordered ferroelectric (stable at low $T$), and the disordered paraelectric phase that appears beyond a critical temperature $T_{\rm BKT}$. This BKT phase is characterized by quasi-long-range order (whose signature is a power-law decay of the correlations with the distance), and the emergence of tightly bounded vortex-antivortex pairs whose density is determined by a thermal activation process. The proposed PbTiO$_{3}$/SrTiO$_{3}$ superlattice model and the imposed mechanical boundary conditions are both experimentally feasible, opening the door for the first experimental observation of these new topological phases in ferroelectric materials.
We show how to enhance the redshift accuracy of surveys consisting of tracers with highly uncertain positions along the line of sight. Photometric surveys with redshift uncertainty delta_z ~ 0.03 can yield final redshift uncertainties of delta_z_f ~ 0.003 in high density regions. This increased redshift precision is achieved by imposing an isotropy and 2-point correlation prior in a Bayesian analysis and is completely independent of the process that estimates the photometric redshift. As a byproduct, the method also infers the three dimensional density field, essentially super-resolving high density regions in redshift space. Our method fully takes into account the survey mask and selection function. It uses a simplified Poissonian picture of galaxy formation, relating preferred locations of galaxies to regions of higher density in the matter field. The method quantifies the remaining uncertainties in the three dimensional density field and the true radial locations of galaxies by generating samples that are constrained by the survey data. The exploration of this high dimensional, non-Gaussian joint posterior is made feasible using multiple-block Metropolis-Hastings sampling. We demonstrate the performance of our implementation on a simulation containing 2.0 x 10^7 galaxies. These results bear out the promise of Bayesian analysis for upcoming photometric large scale structure surveys with tens of millions of galaxies.
We demonstrate the first solid-state spin-wave optical quantum memory with on-demand read-out. Using the full atomic frequency comb scheme in a \PrYSO crystal, we store weak coherent pulses at the single-photon level with a signal to noise ratio $> 10$. Narrow-band spectral filtering based on spectral hole burning in a second \PrYSO crystal is used to filter out the excess noise created by control pulses to reach an unconditional noise level of $(2.0 \pm 0.3) \times10^{-3}$ photons per pulse. We also report spin-wave storage of photonic time-bin qubits with conditional fidelities higher than a measure and prepare strategy, demonstrating that the spin-wave memory operates in the quantum regime. This makes our device the first demonstration of a quantum memory for time-bin qubits, with on demand read-out of the stored quantum information. These results represent an important step for the use of solid-state quantum memories in scalable quantum networks.
We study analytically the constraints of the conformal bootstrap on the low-lying spectrum of operators in field theories with global conformal symmetry in one and two spacetime dimensions. We introduce a new class of linear functionals acting on the conformal bootstrap equation. In 1D, we use the new basis to construct extremal functionals leading to the optimal upper bound on the gap above identity in the OPE of two identical primary operators of integer or half-integer scaling dimension. We also prove an upper bound on the twist gap in 2D theories with global conformal symmetry. When the external scaling dimensions are large, our functionals provide a direct point of contact between crossing in a 1D CFT and scattering of massive particles in large $\textrm{AdS}_2$. In particular, CFT crossing can be shown to imply that appropriate OPE coefficients exhibit an exponential suppression characteristic of massive bound states, and that the 2D flat-space S-matrix should be analytic away from the real axis.
Let $X$ be a locally compact abelian group with countable base and let $\mathcal W$ be a convex cone of positive numerical functions on $X$ which is invariant under the group action and such that $(X,\mathcal W)$ is a balayage space or (equivalently, if $1\in \mathcal W$) such that $\mathcal W$ is the set of excessive functions of a Hunt process on $X$, $\mathcal W$ separates points, every function in $\mathcal W$ is the supremum of its continuous minorants in $\mathcal W$, and there exist strictly positive continuous $u,v\in \mathcal W$ such that $u/v\to 0$ at infinity.   Assuming that there is a Green function $G>0$ for $X$ which locally satisfies the triangle inequality $G(x,z)\wedge G(y,z)\le C G(x,y)$ (true for many L\'evy processes), it is shown that Hunt's hypothesis (H) holds, that is, every semipolar set is polar.
Training GANs on videos is even more sophisticated than on images because videos have a distinguished dimension: time. While recent methods designed a dedicated architecture considering time, generated videos are still far from indistinguishable from real videos. In this paper, we introduce ArrowGAN framework, where the discriminators learns to classify arrow of time as an auxiliary task and the generators tries to synthesize forward-running videos. We argue that the auxiliary task should be carefully chosen regarding the target domain. In addition, we explore categorical ArrowGAN with recent techniques in conditional image generation upon ArrowGAN framework, achieving the state-of-the-art performance on categorical video generation. Our extensive experiments validate the effectiveness of arrow of time as a self-supervisory task, and demonstrate that all our components of categorical ArrowGAN lead to the improvement regarding video inception score and Frechet video distance on three datasets: Weizmann, UCFsports, and UCF-101.
One of the most troublesome contributions to the NNLO QCD corrections to B -> X_s gamma originates from three-loop matrix elements of four-quark operators. A part of this contribution that is proportional to the QCD beta-function coefficient beta_0 was found in 2003 as an expansion in m_c/m_b. In the present paper, we evaluate the asymptotic behaviour of the complete contribution for m_c >> m_b/2. The asymptotic form of the beta_0-part matches the small-m_c expansion very well at the threshold m_c = m_b/2. For the remaining part, we perform an interpolation down to the measured value of m_c, assuming that the beta_0-part is a good approximation at m_c=0. Combining our results with other contributions to the NNLO QCD corrections, we find BR(B -> X_s gamma) = (3.15 +_ 0.23) x 10^-4 for E_gamma > 1.6 GeV in the B-meson rest frame. The indicated error has been obtained by adding in quadrature the following uncertainties: non-perturbative (5%), parametric (3%), higher-order perturbative (3%), and the interpolation ambiguity (3%).
We report the results of a time-series CCD photometric survey of variable stars in the field of the open cluster NGC 2126. In about one square degree field covering the cluster, a total number of 21 variable candidates are detected during this survey, of which 16 are newly found. The periods, classifications and spectral types of 14 newly discovered variables are discussed, which consist of six eclipsing binaries systems, three pulsating variable stars, three long period variables, one RS CVn star, and one W UMa or $\delta$ Scuti star. In addition, there are two variable candidates, the properties of which cannot be determined in this paper. By a method based on fitting spectral energy distributions(SEDs) of stars with theoretical ones, the membership probabilities and the fundamental parameters of this cluster are determined. As a result, five variables are probably members of NGC 2126. The fundamental parameters of the this cluster are determined as: the metallicity to be 0.008 $Z_\odot$, the age $\log(t)$= 8.95, the distance modulus $(m-M)_{0}$= 10.34 and the reddening value $E(B-V)$=0.55 mag.
We estimate the importance of the nonlinear terms in the Vlasov equation for the development of the unstable modes. The results allow to identify the region of wavelength where the linear evolution is justified.
We discuss various possibilities to constrain ICM turbulence in galaxy clusters using bright X-ray lines. Numerical simulations are used to find the most appropriate description of the 3D velocity field power spectrum (PDS) and to calibrate the relation of observables to this PDS. The impact of the velocity field on the surface brightness distribution and on the spectral shape of strong X-ray lines, modified by the resonant scattering (RS), is evaluated via radiative transfer calculations. We investigate the sensitivity of RS not only to amplitudes of motions, but also to anisotropy and spatial scales. We in particular show that the amplitude of radial motions is most important for RS, while tangential motions only weakly affect the scattering.
We obtain the phase diagram and thermodynamic behavior of the Kondo necklace model for arbitrary dimensions $d$ using a representation for the localized and conduction electrons in terms of local Kondo singlet and triplet operators. A decoupling scheme on the double time Green's functions yields the dispersion relation for the excitations of the system. We show that in $d\geq 3$ there is an antiferromagnetically ordered state at finite temperatures terminating at a quantum critical point (QCP). In 2-d, long range magnetic order occurs only at T=0. The line of Neel transitions for $d>2$ varies with the distance to the quantum critical point QCP $|g|$ as, $T_N \propto |g|^{\psi}$ where the shift exponent $\psi=1/(d-1)$. In the paramagnetic side of the phase diagram, the spin gap behaves as $\Delta\approx \sqrt{|g|}$ for $d \ge 3$ consistent with the value $z=1$ found for the dynamical critical exponent. We also find in this region a power law temperature dependence in the specific heat for $k_BT\gg\Delta$ and along the non-Fermi liquid trajectory. For $k_BT \ll\Delta$, in the so-called Kondo spin liquid phase, the thermodynamic behavior is dominated by an exponential temperature dependence.
In the framework of Harnack type Dirichlet forms, we prove a large deviation principle for the asymptotics of reversible Markov processes with rate function given by the energy of the paths.