ShantanuT01/DACTYL-Pretraining huggingface dataset:
This paper considers the problem of simultaneously estimating rare-event probabilities for a class of Gaussian random fields. A conventional rare-event simulation method is usually tailored to a specific rare event and consequently would lose estimation efficiency for different events of interest, which often results in additional computational cost in such simultaneous estimation problem. To overcome this issue, we propose a uniformly efficient estimator for a general family of H\"older continuous Gaussian random fields. We establish the asymptotic and uniform efficiency of the proposed method and also conduct simulation studies to illustrate its effectiveness.
One of the most important unresolved issues in gamma-ray burst physics is the origin of the prompt gamma-ray spectrum. Its general non-thermal character and the softness in the X-ray band remain unexplained. We tackle these issues by performing Monte Carlo simulations of radiation-matter interactions in a scattering dominated photon-lepton plasma. The plasma -- initially in equilibrium -- is driven to non-equilibrium conditions by a sudden energy injection in the lepton population, mimicking the effect of a shock wave or the dissipation of magnetic energy. Equilibrium restoration occurs due to energy exchange between the photons and leptons. While the initial and final equilibrium spectra are thermal, the transitional photon spectra are characterized by non-thermal features such as power-law tails, high energy bumps, and multiple components. Such non-thermal features are observed at infinity if the dissipation occurs at small to moderate optical depths, and the spectrum is released before thermalization is complete. We model the synthetic spectra with a Band function and show that the resulting spectral parameters are similar to observations for a frequency range of 2-3 orders of magnitude around the peak. In addition, our model predicts correlations between the low-frequency photon index and the peak frequency as well as between the low- and high-frequency indices. We explore baryon and pair dominated fireballs and reach the conclusion that baryonic fireballs are a better model for explaining the observed features of gamma-ray burst spectra.
In this paper, we present a novel center manifold reduction theorem for quasilinear elliptic equations posed on infinite cylinders. This is done without a phase space in the sense that we avoid explicitly reformulating the PDE as an evolution problem. Under suitable hypotheses, the resulting center manifold is finite dimensional and captures all sufficiently small bounded solutions. Compared with classical methods, the reduced ODE on the manifold is more directly related to the original physical problem and also easier to compute. The analysis is conducted directly in H\"older spaces, which is often desirable for elliptic equations.   We then use this machinery to construct small bounded solutions to a variety of systems. These include heteroclinic and homoclinic solutions of the anti-plane shear problem from nonlinear elasticity; exact slow moving invasion fronts in a two-dimensional Fisher--KPP equation; and hydrodynamic bores with vorticity in a channel. The last example is particularly interesting in that we find solutions with critical layers and distinctive "half cat's eye" streamline patterns.
We present magnetohydrodynamic (MHD) simulations of the evolution from quasi-equilibrium to eruption of a prominence-forming twisted coronal flux rope under a coronal streamer. We have compared the cases with and without the formation of prominence condensations, and the case where prominence condensations form but we artificially initiate the draining of the prominence. We find that the prominence weight has a significant effect on the stability of the flux rope, and can significantly increase the loss-of-equilibrium height. The flux rope can be made to erupt earlier by initiating draining of the prominence mass. We have also performed a simulation where large amplitude longitudinal oscillations of the prominence are excited during the quasi-static phase. We find that the gravity force along the magnetic field lines is the major restoring force for the oscillations, in accordance with the ``pendulum model'', although the oscillation periods are higher (by about 10% to 40%) than estimated from the model because of the dynamic deformation of the field line dips during the oscillations. The oscillation period is also found to be slightly smaller for the lower part of the prominence in the deeper dips compared to the upper part in the shallower dips. The oscillations are quickly damped out after about 2-3 periods and are followed by prominence draining and the eventual eruption of the prominence. However we do not find a significant enhancement of the prominence draining and earlier onset of eruption with the excitation of the prominence oscillations compared to the case without.
Video object segmentation targets at segmenting a specific object throughout a video sequence, given only an annotated first frame. Recent deep learning based approaches find it effective by fine-tuning a general-purpose segmentation model on the annotated frame using hundreds of iterations of gradient descent. Despite the high accuracy these methods achieve, the fine-tuning process is inefficient and fail to meet the requirements of real world applications. We propose a novel approach that uses a single forward pass to adapt the segmentation model to the appearance of a specific object. Specifically, a second meta neural network named modulator is learned to manipulate the intermediate layers of the segmentation network given limited visual and spatial information of the target object. The experiments show that our approach is 70times faster than fine-tuning approaches while achieving similar accuracy.
A rational Diophantine m-tuple is a set of m nonzero rationals such that the product of any two of them increased by 1 is a perfect square. The first rational Diophantine quadruple was found by Diophantus, while Euler proved that there are infinitely many rational Diophantine quintuples. In 1999, Gibbs found the first example of a rational Diophantine sextuple, and Dujella, Kazalicki, Mikic and Szikszai recently proved that there exist infinitely many rational Diophantine sextuples.   In this paper, generalizing the work of Piezas, we describe a method for generating new parametric formulas for rational Diophantine sextuples.
Hovey introduced a $k$-cordial labeling of graphs as a generalization both of harmonious and cordial labelings. He proved that all tress are $k$-cordial for $k \in \{1,...,5\}$ and he conjectured that all trees are $k$-cordial for all $k$. \indent We consider a corresponding problem for hypergraphs, namely, we show that $p$-uniform hypertrees are $k$-cordial for certain values of $k$.
We have performed ultrasonic measurements on single-crystalline URu2Si2 with pulsed magnetic fields, in order to check for possible lattice instabilities due to the hybridized state and the hidden-order state of this compound. The elastic constant (C11-C12)/2, which is associated with a response to the {\Gamma}3-type symmetry-breaking (orthorhombic) strain field, shows a three-step increase at H > 35 T for H || c at low temperatures, where successive meta-magnetic transitions are observed in the magnetization. We discovered a new fact that the absolute change of the softening of (C11-C12)/2 in the temperature dependence is quantitatively recovered at the suppression of hybridized-electronic state and the hidden order in high-magnetic field for H \perp c associated with the successive transitions. The present results suggest that the {\Gamma}3-type lattice instability, is related to both the emergence of the hybridized electronic state and the hidden-order parameter of URu2Si2. On the other hand, magnetic fields H || [100] and [110] enhance the softening of (C11-C12)/2 in the hidden order phase, while no step-like anomaly is observed up to 68.7 T. We discuss the limitation of the localized-electron picture for describing these features of URu2Si2 by examination of a crystalline electric field model in terms of mean-field theory.
The density dependent relativistic hadron field (DDRH) theory is applied to strongly asymmetric nuclear matter and finite nuclei far off stability. A new set of in-medium meson-nucleon vertices is derived from Dirac-Brueckner Hartree-Fock (DBHF) calculations in asymmetric matter, now accounting also for the density dependence of isovector coupling constants. The scalar-isovector $\delta$ meson is included. Nuclear matter calculations show that it is necessary to introduce a momentum correction in the extraction of coupling constants from the DBHF self-energies in order to reproduce the DBHF equation of state by DDRH mean-field calculations. The properties of DDRH vertices derived from the Groningen and the Bonn A nucleon-nucleon (NN) potentials are compared in nuclear matter calculations and for finite nuclei. Relativistic Hartree results for binding energies, charge radii, separation energies and shell gaps for the Ni and Sn isotopic chains are presented. Using the momentum corrected vertices an overall agreement to data on a level of a few percent is obtained. In the accessible range of asymmetries the $\delta$ meson contributions to the self-energies are found to be of minor importance but asymmetry dependent fluctuations may occur.
By analytically continuing QCD scattering amplitudes through specific complexified momenta, one can study and learn about the nature and the consequences of factorization and unitarity. In some cases, when coupled with the largest time equation and gauge invariance requirement, this approach leads to recursion relations, which greatly simplify the construction of multi-gluon scattering amplitudes. The setting for this discussion is in the space-cone gauge.
The gravitomagnetic tidal Love number of a slowly rotating body was calculated previously under the assumption that the velocity perturbation created by the tidal field consists of an induction piece proportional to the vector potential, and a rotational piece that scales with $\Omega$, the body's angular velocity. The second part of this assumption is wrong: the rotational piece of the velocity perturbation scales in fact like $\Omega^0 = 1$. The previous calculations are therefore incorrect, and the purpose of this paper is to repair the mistake. To keep the technical difficulties to a minimum, the treatment here is restricted to a post-Newtonian expansion carried out to leading order -- previous calculations of the gravitomagnetic Love number were performed in full general relativity. On the other hand, the computation presented here is not restricted to a stationary tidal field. I show that the correct scaling of the velocity perturbation with $\Omega$ leads to the promotion of the Love number to a Love tensor $k_{jk}^{\ \ pq}$, a four-index object that relates the body's current quadrupole moment $S_{jk}$ to the gravitomagnetic tidal moment ${\cal B}_{pq}$. The tensorial nature of this quantity has to do with the fact that each $e^{im\phi}$ piece of the tidal force gives rise to an $m$-specific velocity perturbation, and therefore to a Love number that depends on $m$. The collection of these $m$-specific Love numbers makes up the Love tensor $k_{jk}^{\ \ pq}$.
We present the velocity dispersion measurements of four massive $\sim10^{11}M_\odot$ quiescent galaxies at $3.2 < z < 3.7$ based on deep H and K$-$band spectra using the Keck/MOSFIRE near-infrared spectrograph. We find high velocity dispersions of order $\sigma_e\sim250$ km/s based on strong Balmer absorption lines and combine these with size measurements based on HST/WFC3 F160W imaging to infer dynamical masses. The velocity dispersion are broadly consistent with the high stellar masses and small sizes. Together with evidence for quiescent stellar populations, the spectra confirm the existence of a population of massive galaxies that formed rapidly and quenched in the early universe $z>4$. Investigating the evolution at constant velocity dispersion between $z\sim3.5$ and $z\sim2$, we find a large increase in effective radius $0.35\pm0.12$ dex and in dynamical-to-stellar mass ratio $<$log(M$_{\textrm{dyn}}$/M*)$>$ of 0.33$\pm0.08$ dex, with low expected contribution from dark matter. The dynamical masses for our $z\sim3.5$ sample are consistent with the stellar masses for a Chabrier initial mass function (IMF), with the ratio $<$log(M$_{\textrm{dyn}}$/M$^*_{\textrm{Ch}})>$ = -0.13$\pm$0.10 dex suggesting an IMF lighter than Salpeter may be common for massive quiescent galaxies at $z>3$. This is surprising in light of the Salpeter or heavier IMFs found for high velocity dispersion galaxies at $z\sim2$ and cores of present-day ellipticals, which these galaxies are thought to evolve into. Future imaging and spectroscopic observations with resolved kinematics using the upcoming James Webb Space Telescope could rule out potential systematics from rotation, and confirm these results.
We present the results of infrared 2.8-4.1 micron (L-band) spectroscopy of nearby infrared luminous galaxies with possible signatures of dust-obscured active galactic nuclei (AGNs) in data at other wavelengths. The samples are chosen to include sources with a radio excess relative to far-infrared emission, strong absorption features in mid-infrared 5-11.5 micron spectra, unusually weak [CII] 158 micron emission relative to the far-infrared continuum, and radio galaxies classified optically as narrow-line objects. Our aim is to investigate whether the signatures of possible obscured AGNs can be detected in our L-band spectra, based on the strengths of emission and absorption features. Six of nine observed sources clearly show 3.3 micron polycyclic aromatic hydrocarbon (PAH) emission features, a good starburst indicator. An absorption feature at 3.1 micron due to ice-covered dust is detected in IRAS 04154+1755 and IRAS 17208-0014. The signature of a bare carbonaceous dust absorption feature at 3.4 micron is seen in NGC 1377. Our L-band spectra reveal strong signatures of obscured AGNs in all three optical Seyfert 2 galaxies (IRAS 04154+1755, Cygnus A, and 3C 234), and two galaxies classified optically as non-Seyferts (NGC 828 and NGC 1377). Among the remaining optical non-Seyferts, IRAS 17208-0014 might also show a buried AGN signature, whereas no explicit AGN evidence is seen in the L-band spectra of the mid-infrared absorption-feature source IRAS 15250+3609, and two weak [CII] emitters IC 860 and CGCG 1510.8+0725.
We study the hydrodynamic properties of strongly coupled $SU(N)$ Yang-Mills theory of the D1-brane at finite temperature and at a non-zero density of R-charge in the framework of gauge/gravity duality. The gravity dual description involves a charged black hole solution of an Einstein-Maxwell-dilaton system in 3 dimensions which is obtained by a consistent truncation of the spinning D1-brane in 10 dimensions. We evaluate thermal and electrical conductivity as well as the bulk viscosity as a function of the chemical potential conjugate to the R-charges of the D1-brane. We show that the ratio of bulk viscosity to entropy density is independent of the chemical potential and is equal to $1/4\pi$. The thermal conductivity and bulk viscosity obey a relationship similar to the Wiedemann-Franz law. We show that at the boundary of thermodynamic stability, the charge diffusion mode becomes unstable and the transport coefficients exhibit critical behaviour. Our method for evaluating the transport coefficients relies on expressing the second order differential equations in terms of a first order equation which dictates the radial evolution of the transport coefficient. The radial evolution equations can be solved exactly for the transport coefficients of our interest. We observe that transport coefficients of the D1-brane theory are related to that of the M2-brane by an overall proportionality constant which sets the dimensions.
The elastic backward proton-deuteron scattering is analyzed within a covariant approach based on the invariant expansion of the reaction amplitude. The relativistic invariant equations for all the polarization observables are presented. Within the impulse approximation the relation of the tensor analyzing power $T_{20}$ and the polarization transfer $\kappa_0$ to $P$-wave components of the deuteron wave function is found. The comparison of the theoretical calculations with experimental data is presented. An experimental verification of the reaction mechanism is suggested by constructing some combinations of different observables.
This paper is devoted to the study of the long wave approximation for water waves under the influence of the gravity and a Coriolis forcing. We start by deriving a generalization of the Boussinesq equations in 1D (in space) and we rigorously justify them as an asymptotic model of the water waves equations. These new Boussinesq equations are not the classical Boussinesq equations. A new term due to the vorticity and the Coriolis forcing appears that can not be neglected. Then, we study the Boussinesq regime and we derive and fully justify different asymptotic models when the bottom is flat : a linear equation linked to the Klein-Gordon equation admitting the so-called Poincar{\'e} waves; the Ostrovsky equation, which is a generalization of the KdV equation in presence of a Coriolis forcing, when the rotation is weak; and finally the KdV equation when the rotation is very weak. Therefore, this work provides the first mathematical justification of the Ostrovsky equation. Finally, we derive a generalization of the Green-Naghdi equations in 1D in space for small topography variations and we show that this model is consistent with the water waves equations.
We formulate large deviations principle (LDP) for diffusion pair $(X^\epsilon,\xi^\epsilon)=(X_t^\epsilon,\xi_t^\epsilon)$, where first component has a small diffusion parameter while the second is ergodic Markovian process with fast time. More exactly, the LDP is established for $(X^\epsilon,\nu^\epsilon)$ with $\nu^\epsilon(dt,dz)$ being an occupation type measure corresponding to $\xi_t^\epsilon$. In some sense we obtain a combination of Freidlin-Wentzell's and Donsker-Varadhan's results. Our approach relies the concept of the exponential tightness and Puhalskii's theorem.
We study the Fourier-Mukai transform for holonomic D-modules on a complex abelian variety. Among other things, we show that the cohomology support loci of a holonomic complex are finite unions of translates of triple tori, the translates being by torsion points for objects of geometric origin; and that the standard t-structure on the derived category of holonomic complexes corresponds, under the Fourier-Mukai transform, to a certain perverse coherent t-structure in the sense of Kashiwara and Arinkin-Bezrukavnikov.
Self-attention based Transformer models have demonstrated impressive results for image classification and object detection, and more recently for video understanding. Inspired by this success, we investigate the application of Transformer networks for temporal action localization in videos. To this end, we present ActionFormer -- a simple yet powerful model to identify actions in time and recognize their categories in a single shot, without using action proposals or relying on pre-defined anchor windows. ActionFormer combines a multiscale feature representation with local self-attention, and uses a light-weighted decoder to classify every moment in time and estimate the corresponding action boundaries. We show that this orchestrated design results in major improvements upon prior works. Without bells and whistles, ActionFormer achieves 71.0% mAP at tIoU=0.5 on THUMOS14, outperforming the best prior model by 14.1 absolute percentage points. Further, ActionFormer demonstrates strong results on ActivityNet 1.3 (36.6% average mAP) and EPIC-Kitchens 100 (+13.5% average mAP over prior works). Our code is available at http://github.com/happyharrycn/actionformer_release.
We construct the density of states for quarks and gluons using the `Thomas - Fermi model' for atoms and the `Bethe model' for nucleons as templates. With parameters to take care of the plasma (hydrodynamical) features of the QGP with a thermal potential for the interaction, we find a window in the parametric space of the model where observable QGP droplets of $ \sim $ 5 fm radius can occur with transition temperature in the range 140 MeV to 250 MeV. By matching with the expectations of Lattice Gauge estimates of the QGP-hadron transitions, we can further narrow the window, thereby restricting the allowed values of the flow-parameters of the model.
It has been known for some time that the Green's function of a planar domain can be defined in terms of the exit time of Brownian motion, and this definition has been extended to stopping times more general than exit times. In this paper, we extend the notion of conformal invariance of Green's function to analytic functions which are not injective, and use this extension to calculate the Green's function for a stopping time defined by the winding of Brownian motion. These considerations lead to a new proof of the Riemann mapping theorem. We also show how this invariance can be used to deduce several identities, including the standard infinite product representations of several trigonometric functions.
We consider planar first-passage percolation and show that the time constant can be bounded by multiples of the first and second tertiles of the weight distribution. As a consequence we obtain a counter-example to a problem proposed by Alm and Deijfen.
The Halo Assembly in Lambda-CDM: Observations in 7 Dimensions (HALO7D) dataset consists of Keck II/DEIMOS spectroscopy and Hubble Space Telescope-measured proper motions of Milky Way halo main sequence turnoff stars in the CANDELS fields. In this paper, we present the spectroscopic component of this dataset, and discuss target selection, observing strategy, and survey properties. We present a new method of measuring line-of-sight (LOS) velocities by combining multiple spectroscopic observations of a given star, utilizing Bayesian hierarchical modeling. We present the LOS velocity distributions of the four HALO7D fields, and estimate their means and dispersions. All of the LOS distributions are dominated by the "hot halo": none of our fields are dominated by substructure that is kinematically cold in the LOS velocity component. Our estimates of the LOS velocity dispersions are consistent across the different fields, and these estimates are consistent with studies using other types of tracers. To complement our observations, we perform mock HALO7D surveys using the synthetic survey software Galaxia to "observe'" the Bullock & Johnston (2005) accreted stellar halos. Based on these simulated datasets, the consistent LOS velocity distributions across the four HALO7D fields indicates that the HALO7D sample is dominated by stars from the same massive (or few relatively massive) accretion event(s).
In this paper we give a full classification of global solutions of the obstacle problem for the fractional Laplacian (including the thin obstacle problem) with compact coincidence set and at most polynomial growth in dimension $N \geq 3$. We do this in terms of a bijection onto a set of polynomials describing the asymptotics of the solution. Furthermore we prove that coincidence sets of global solutions that are compact are also convex if the solution has at most quadratic growth.