ShantanuT01/DACTYL-Pretraining huggingface dataset:
This version improves the old version entitled "On the modularity of elliptic curves with a residually irreducible representation".   Let $E$ be an elliptic curve over an abelian totally real field $K$ unramified at 3,5, and 7. We prove that $E$ is modular.
We study the problem of stabilization for the acoustic system with a spatially distributed damping. Without imposing any hypotheses on the structural properties of the damping term, we identify logarithmic decay of solutions with growing time. Logarithmic decay rate is shown by using a frequency domain method and combines a contradiction argument with the multiplier technique and a new Carleman estimate to carry out a special analysis for the resolvent.
Simi-Supervised Recognition Challenge-FGVC7 is a challenging fine-grained recognition competition. One of the difficulties of this competition is how to use unlabeled data. We adopted pseudo-tag data mining to increase the amount of training data. The other one is how to identify similar birds with a very small difference, especially those have a relatively tiny main-body in examples. We combined generic image recognition and fine-grained image recognition method to solve the problem. All generic image recognition models were training using PaddleClas . Using the combination of two different ways of deep recognition models, we finally won the third place in the competition.
We summarize the quiescent X-ray observations of transient low-mass X-ray binaries. These observations show that, in quiescence, binaries containing black holes are fainter than those containing neutron stars. This has triggered a number of theoretical ideas about what causes the quiescent X-ray emission. For black hole binaries, the options are accretion onto the black hole or coronal emission from the rapidly rotating stellar companion. There are more possibilities for the neutron stars: accretion, thermal emission from the surface or non-thermal emission from a ``turned-on'' radio pulsar. We review recent theoretical work on these mechanisms and note where current observations can distinguish between them. We highlight the re-analysis of the quiescent neutron star emission by Rutledge and collaborators that showed thermal emission to be a predominant contributor in many of these systems. Our knowledge of these binaries is bound to dramatically improve now that the Chandra and XMM satellites are operating successfully,
We present here a relativistic theory of gravity in which the spacetime metric is derived from a single scalar field $\Phi$. The field equation, derived from a simple variational principle, is a non-linear flat-space four-dimensional wave equation which is particularly suited for numerical evolution. We demonstrate that while this theory does not generate results which are exactly identical quantitatively to those of general relativity (GR), many of the qualitative features of the full GR theory are reproduced to a reasonable approximation. The advantage of this formulation lies in the fact that 3D numerical grids can be numerically evolved in minutes or hours instead of the days and weeks required by GR, thus drastically reducing the development time of new relativistic hydrodynamical codes. Scalar gravity therefore serves as a meaningful testbed for the development of larger routines destined for use under the full theory of general relativity.
We study a relation between the concurrence of assistance and the Mermin inequality on three-qubit pure states. We find that if a given three-qubit pure state has the minimal concurrence of assistance greater than 1/2 then the state violates some Mermin inequality.
We examine the effect of the Coulomb interaction on the mobility and diffusion of spin packets in doped semiconductors. We find that the diffusion constant is reduced, relative to its non-interacting value, by the combined effect of Coulomb-enhanced spin susceptibility and spin Coulomb drag. In ferromagnetic semiconductors, the spin diffusion constant vanishes at the ferromagnetic transition temperature.
Supersymmetric extensions of Hamilton-Jacobi separable Liouville mechanical systems with two degrees of freedom are defined. It is shown that supersymmetry can be implemented in this type of systems in two independent ways. The structure of the constants of motion is unveiled and the entanglement between integrability and supersymmetry is explored.
We compare surface maps of the chemically peculiar star HD 50773 produced with a Bayesian technique and based on high quality CoRoT photometry with those derived from rotation phase resolved spectropolarimetry. The goal is to investigate the correlation of surface brightness with surface chemical abundance distribution and the stellar magnetic field.   The rotational period of the star was determined from a nearly 60 day long continuous light curve obtained during the initial run of CoRoT. Using a Bayesian approach to star-spot modelling, which in this work is applied for the first time for the photometric mapping of a CP star, we derived longitudes, latitudes and radii of four different spot areas. Additional parameters like stellar inclination and the spot's intensities were also determined. The CoRoT observations triggered an extensive ground-based spectroscopic and spectropolarimetric observing campaign and enabled us to obtain 19 different high resolution spectra in Stokes parameters I and V with NARVAL, ESPaDOnS, and SemelPol spectropolarimeters.   Doppler and Magnetic Doppler imaging techniques allowed us to derive the magnetic field geometry of the star and the surface abundance distributions of Mg, Si, Ca, Ti, Cr, Fe, Ni, Y, and Cu. We find a dominant dipolar structure of the surface magnetic field. The CoRoT light curve variations and abundances of most elements mapped are correlated with the aforementioned geometry: Cr, Fe, and Si are enhanced around the magnetic poles and coincide with the bright regions on the surface of HD 50773 as predicted by our light curve synthesis and confirmed by photometric imaging.
We consider the braid group representation which describes the non-abelian braiding statistics of the spin 1/2 particle world lines of an SU(2)$_4$ Chern-Simons theory. Up to an abelian phase, this is the same as the non-Abelian statistics of the elementary quasiparticles of the $k=4$ Read-Rezayi quantum Hall state. We show that these braiding statistics are identical to those of Z$_3$ Parafermions.
We prove a c-theorem for holographic theories.
We consider giant gravitons as probes of a class of ten-dimensional solutions of type IIB supergravity which arise as lifts of solutions of U(1)^3 gauged N=2 supergravity in five-dimensions. Surprisingly it is possible to solve exactly for minimum energy configurations of these spherical D3-brane probes in the compact directions, even in backgrounds which preserve no supersymmetry. The branes behave as massive charged particles in the five non-compact dimensions. As an example we probe geometries which are believed to represent the supergravity background of coherent states of giant gravitons. We comment on the apparently repulsive nature of the naked singularities in these geometries.
The tightening of the constraints on the standard thermal WIMP scenario has forced physicists to propose alternative dark matter (DM) models. One of the most popular alternate explanations of the origin of DM is the non-thermal production of DM via freeze-in. In this scenario the DM never attains thermal equilibrium with the thermal soup because of its feeble coupling strength ($\sim 10^{-12}$) with the other particles in the thermal bath and is generally called the Feebly Interacting Massive Particle (FIMP). In this work, we present a gauged U(1)$_{L_{\mu}-L_{\tau}}$ extension of the Standard Model (SM) which has a scalar FIMP DM candidate and can consistently explain the DM relic density bound. In addition, the spontaneous breaking of the U(1)$_{L_{\mu}-L_{\tau}}$ gauge symmetry gives an extra massive neutral gauge boson $Z_{\mu\tau}$ which can explain the muon ($g-2$) data through its additional one-loop contribution to the process. Lastly, presence of three right-handed neutrinos enable the model to successfully explain the small neutrino masses via the Type-I seesaw mechanism. The presence of the spontaneously broken U(1)$_{L_{\mu}-L_{\tau}}$ gives a particular structure to the light neutrino mass matrix which can explain the peculiar mixing pattern of the light neutrinos.
The planar solution is discussed for an N=3 Chern-Simons-matter theory constructed recently by Gaiotto and Tomasiello. The planar resolvent is obtained in terms of contour integrals. If the sum of two Chern-Simons levels k_1,k_2 is small, the expectation value of a supersymmetric Wilson loop grows exponentially with the total 't Hooft coupling, as is expected from AdS/CFT correspondence. If one of the Chern-Simons levels, say k_2, is taken to infinity, for which one of the 't Hooft coupling constants becomes zero, then the exponential behavior disappears.
Certain upper triangular matrices, termed as Parikh matrices, are often used in the combinatorial study of words. Given a word, the Parikh matrix of that word elegantly computes the number of occurrences of certain predefined subwords in that word. In this paper, we compute the Parikh matrix of any word raised to an arbitrary power. Furthermore, we propose canonical decompositions of both Parikh matrices and words into normal forms. Finally, given a Parikh matrix, the relation between its normal form and the normal forms of words in the corresponding M-equivalence class is established.
We present new millimeter observations of the ionized wind from the massive young stellar object LkHalpha101, made with the IRAM interferometer and 30m telescope. Several recombination lines, including higher order transitions, were detected for the first time at radio wavelengths in this source. From three alpha-transitions we derive an accurate value for the stellar velocity and, for the first time, an unambiguous expansion velocity of the wind which is 55 km/s, much slower than reported previously, and the mass loss rate is 1.8e-6 solar masses per year. The wide band continuum spectra and the interferometer visibilities show that the density of the wind falls off more steeply than compatible with constant-velocity expansion. We argue that these properties indicate that the wind is launched from a radially narrow region of the circumstellar disk, and we propose that slow speed and a steep density gradient are characteristic properties of the evolutionary phase where young stars of intermediate and high mass clear away the gaseous component of their accretion disks.   The recombination lines are emitted close to local thermal equilibrium, but the higher order transitions appear systematically broader and weaker than expected, probably due to impact broadening. Finally, we show that LkHalpha101 shares many properties with MWC349, the only other stellar wind source where radio recombination lines have been detected, some of them masing. We argue that LkHalpha101 evades masing at millimeter wavelengths because of the disk's smaller size and unfavorable orientation. Some amplification may however be detectable at shorter wavelengths.
In this paper we study pattern avoidance for affine permutations. In particular, we show that for a given pattern p, there are only finitely many affine permutations in $\widetilde{S}_n$ that avoid p if and only if p avoids the pattern 321. We then count the number of affine permutations that avoid a given pattern p for each p in S_3, as well as give some conjectures for the patterns in S_4.
We carry out high resolution two-dimensional radiation-hydrodynamic numerical simulations to study the formation and evolution of hot bubbles inside planetary nebulae (PNe). We take into account the evolution of the stellar parameters, wind velocity and mass-loss rate from the final thermal pulses during the asymptotic giant branch (AGB) through to the post-AGB stage for a range of initial stellar masses. The instabilities that form at the interface between the hot bubble and the swept-up AGB wind shell lead to hydrodynamical interactions, photoevaporation flows and opacity variations. We explore the effects of hydrodynamical mixing combined with thermal conduction at this interface on the dynamics, photoionization, and emissivity of our models. We find that even models without thermal conduction mix significant amounts of mass into the hot bubble. When thermal conduction is not included, hot gas can leak through the gaps between clumps and filaments in the broken swept-up AGB shell and this depressurises the bubble. The inclusion of thermal conduction evaporates and heats material from the clumpy shell, which expands to seal the gaps, preventing a loss in bubble pressure. The dynamics of bubbles without conduction is dominated by the thermal pressure of the thick photoionized shell, while for bubbles with thermal conduction it is dominated by the hot, shocked wind.
Rezzolla et al. [ApJ 531 (2000), L139; Phys. Rev. D 64 (2001), 104013; Phys. Rev. D 64 (2001), 104014] draw attention to the second order secular drift associated with r-modes and claimed that it should lead to magnetic field enhancement and suppression of r-mode instability in magnetized neutron stars. We critically revise these results. We present a particular second order r-mode solution with vanishing secular drift, thus refuting a widely believed statement that secular drift is an unavoidable feature of r-modes. This non-drifting solution is not affected by magnetic field $B$, if $B\ll B_{\mathrm{crit}}\approx 10^{17}\,(\nu/600\,\mathrm{Hz})$ G ($\nu$ is a spin frequency) and does not lead to secular evolution of magnetic field. For general second order r-mode solution the drift does not necessarily vanish, but the solution can be presented as a superposition of two solutions: one describes evolution of differential rotation in nonoscillating star (which describes secular drift; for nonmagnetized star it is arbitrary stationary rotation stratified on cylinders; for magnetized star differential rotation evolves on the Alfv\'{e}n timescale and may lead to magnetic energy enhancement), and another one is non-drifting r-mode solution mentioned above. This representation allows us to conclude that enhancement of magnetic field energy is limited by initial energy of differential rotation, which is much less (for a factor $\propto \alpha^2$, where $\alpha$ is mode amplitude) than the total energy of r-mode. Hence, magnetic field enhancement by drift cannot suppress r-mode instability. Results can be generalized for any oscillation mode in any medium, if this mode has non-drifting solution for $B=0$.
We show how phase-space simulations of Gaussian quantum states in a photonic network permit verification of measurable correlations of Gaussian boson sampling (GBS) quantum computers. Our results agree with experiments for up to 100-th order correlations, provided decoherence is included. We extend this to more than 16,000 modes, and describe how to simulate genuine multipartite entanglement.
Models of quantum-classical interactions fall into two classes: those which allow the generation of quantum entanglement via a classical mediator (such as gravity), and those which do not. Marconato and Marletto have recently sought to distinguish between these classes by claiming that known members of the first class (based on the configuration-ensemble formalism introduced by us) fail to model the mediator as a 'classical' system, and are nonlocal. We explicitly show that this claim is incorrect, and expose a large number of errors and misconceptions in their reasoning. We also point to a very simple and transparent example of the generation of entanglement between two qubits via a classical bit. It follows that there are models permitting the generation of entanglement via quantum-classical interactions that lie outside the remit of the theorem cited by Marconato and Marletto. We clarify the reasons for the limited applicability of various no-go theorems for entanglement generation.
$U(1)_X$SSM is the extension of the minimal supersymmetric standard model (MSSM) and its local gauge group is $SU(3)_C\times SU(2)_L \times U(1)_Y \times U(1)_X$. We study lepton flavor violating (LFV) decays $Z\rightarrow{{l_i}^{\pm}{l_j}^{\mp}}$($Z\rightarrow e{\mu}$, $Z\rightarrow e{\tau}$, and $Z\rightarrow {\mu}{\tau}$) and $h\rightarrow{{l_i}^{\pm}{l_j}^{\mp}}$($h\rightarrow e{\mu}$, $h\rightarrow e{\tau}$, and $h\rightarrow {\mu}{\tau}$), in this model. In the numerical results, the branching ratios of $Z\rightarrow{{l_i}^{\pm}{l_j}^{\mp}}$ are from $10^{-9}$ to $10^{-13}$ and the branching ratios of $h\rightarrow{{l_i}^{\pm}{l_j}^{\mp}}$ are from $10^{-3}$ to $10^{-9}$, which can approach the present experimental upper bounds. Based on the latest experimental data, we analyze the influence of different sensitive parameters on the branching ratio, and make reasonable predictions for future experiments. The main sensitive parameters and LFV sources are the non-diagonal elements corresponding to the initial and final generations of leptons, which can be seen from the numerical analysis.
In this paper we analyse three models of the early universe, for which the respective mechanisms for generating the curvature perturbation are considered disparate. We find that in fact the mechanisms are very similar, and hence explain why they give rise to a large non-gaussianity. We show that the mechanism for generating the primordial curvature perturbation, and hence the observable non-gaussianity, is similar in both the Curvaton and Modulated Reheating models. In both cases the model can be written in terms of an energy transfer between the constituting fluids. We then show that this is also true for the mechanism of generating the curvature perturbation by symmetry breaking the end of inflation. We then relate this to the non-gaussian contribution to the curvature perturbation and find that it is inversely proportional to the efficiency with which the curvature perturbation is transferred between the fluids. For the first time, we generalise models of modulated reheating to allow for a non-linear energy transfer rate.
We report Arecibo 21 cm absorption-emission observations to characterise the physical properties of neutral hydrogen (HI) in the proximity of five giant molecular clouds (GMCs): Taurus, California, Rosette, Mon OB1, and NGC 2264. Strong HI absorption was detected toward all 79 background continuum sources in the ~60x20 square degree region. Gaussian decompositions were performed to estimate temperatures, optical depths and column densities of the cold and warm neutral medium (CNM, WNM). The properties of individual CNM components are similar to those previously observed along random Galactic sightlines and in the vicinity of GMCs, suggesting a universality of cold HI properties. The CNM spin temperature (Ts) histogram peaks at ~50K. The turbulent Mach numbers of CNM vary widely, with a typical value of ~4, indicating that their motions are supersonic. About 60% of the total HI gas is WNM, and nearly 40% of the WNM lies in thermally unstable regime 500-5000K. The observed CNM fraction is higher around GMCs than in diffuse regions, and increases with increasing column density (NHI) to a maximum of ~75%. On average, the optically thin approximation (N*(HI)) underestimates the total N(HI) by ~21%, but we find large regional differences in the relationship between N(HI) and the required correction factor, f=N(HI)/N*(HI). We examine two different methods (linear fit of f vs log10(N*(HI)) and uniform Ts) to correct for opacity effects using emission data from the GALFA-HI survey. We prefer the uniform Ts method, since the linear relationship does not produce convincing fits for all subregions.
We present the first application of the isosceles bispectrum to MCMC parameter inference from the cosmic 21-cm signal. We extend the MCMC sampler 21cmMC to use the fast bispectrum code, BiFFT, when computing the likelihood. We create mock 1000h observations with SKA1-low, using PyObs21 to account for uv-sampling and thermal noise. Assuming the spin temperature is much higher than that of the CMB, we consider two different reionization histories for our mock observations: fiducial and late-reionization. For both models we find that bias on the inferred parameter means and 1-$\sigma$ credible intervals can be substantially reduced by using the isosceles bispectrum (calculated for a wide range of scales and triangle shapes) together with the power spectrum (as opposed to just using one of the statistics). We find that making the simplifying assumption of a Gaussian likelihood with a diagonal covariance matrix does not notably bias parameter constraints for the three-parameter reionization model and basic instrumental effects considered here. This is true even if we use extreme (unlikely) initial conditions which would be expected to amplify biases. We also find that using the cosmic variance error calculated with Monte-Carlo simulations using the fiducial model parameters whilst assuming the late-reionization model for the simulated data also does not strongly bias the inference. This implies we may be able to sparsely sample and interpolate the cosmic variance error over the parameter space, substantially reducing computational costs. All codes used in this work are publicly-available.
We report on optical measurements of the 1D Heisenberg antiferromagnet KCuF3. The crystal-field excitations of the Cu2+ ions have been observed and their temperature dependence can be understood in terms of magnetic and exchange-induced dipole mechanisms and vibronic interactions. Above T_N we observe a new temperature scale T_S characterized by the emergence of narrow absorption features that correlate with changes of the orbital ordering as observed by Paolasini et al. [Phys. Rev. Lett. 88, 106403 (2002)]. The appearance of these optical transitions provides evidence for a symmetry change above the Neel temperature that affects the orbital ordering and paves the way for the antiferromagnetic ordering.
I discuss the properties of gas-rich forming galaxies. I particularly emphasize the latest results on Lyman alpha emission that are relevant to the search of distant young galaxies. The interdependance of the Lyman alpha escape with the properties of the ISM in starburst galaxies is outlined. A new model from G. Tenorio-Tagle and his collaborators explaining Lyman alpha profiles in starburst galaxies from the hydrodynamics of superbubbles powered by massive stars is presented. I stress again that since Lyman alpha is primarely a diagnostic of the ISM, it is mandatory to understand how the ISM and Lyman alpha are related to firmly relate Lyman alpha to the cosmic star-formation rate.
We consider Koopman operator theory in the context of nonlinear infinite-dimensional systems, where the operator is defined over a space of bounded continuous functionals. The properties of the Koopman semigroup are described and a finite-dimensional projection of the semigroup is proposed, which provides a linear finite-dimensional approximation of the underlying infinite-dimensional dynamics. This approximation is used to obtain spectral properties from data, a method which can be seen as a generalization of Extended Dynamic Mode Decomposition for infinite-dimensional systems. Finally, we exploit the proposed framework to identify (a finite-dimensional approximation of) the Lie generator associated with the Koopman semigroup. This approach yields a linear method for nonlinear PDE identification, which is complemented with theoretical convergence results.
We prove that the initial value problem associated to a nonlocal perturbation of the Benjamin-Ono equation is locally and globally well-posed in Sobolev spaces $H^s(\mathbb{R})$ for any $s>-3/2$ and we establish that our result is sharp in the sense that the flow map of this equation fails to be $C^2$ in $H^s(\mathbb{R})$ for $s<-3/2$. Finally, we study persistence properties of the solution flow in the weighted Sobolev spaces $Z_{s,r}=H^s(\mathbb{R})\cap L^2(|x|^{2r}\,dx)$ for $s\geq r >0$. We also prove some unique continuation properties of the solution flow in these spaces.