ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the Abramovich--Vistoli moduli space of genus zero orbifold stable maps to [Sym^2 P^2], the stack symmetric square of P^2. This compactifies the moduli space of stable maps from hyperelliptic curves to P^2, and we show that all genus zero Gromov--Witten invariants are determined from trivial enumerative geometry of hyperelliptic curves. We also show how the genus zero Gromov--Witten invariants can be used to determine the number of hyperelliptic curves of degree d and genus g interpolating 3d + 1 generic points in P^2. Comparing our method to that of Graber for calculating the same numbers, we verify an example of the crepant resolution conjecture.
We identify SDSS J153636.22+044127.0, a QSO discovered in the Sloan Digital Sky Survey, as a promising candidate for a binary black hole system. This QSO has two broad-line emission systems separated by 3500 km/sec. The redder system at z=0.3889 also has a typical set of narrow forbidden lines. The bluer system (z=0.3727) shows only broad Balmer lines and UV Fe II emission, making it highly unusual in its lack of narrow lines. A third system, which includes only unresolved absorption lines, is seen at a redshift, z=0.3878, intermediate between the two emission-line systems. While the observational signatures of binary nuclear black holes remain unclear, J1536+0441 is unique among all QSOs known in having two broad-line regions, indicative of two separate black holes presently accreting gas. The interpretation of this as a bound binary system of two black holes having masses of 10^8.9 and 10^7.3 solar masses, yields a separation of ~ 0.1 parsec and an orbital period of ~100 years. The separation implies that the two black holes are orbiting within a single narrow-line region, consistent with the characteristics of the spectrum. This object was identified as an extreme outlier of a Karhunen-Loeve Transform of 17,500 z < 0.7 QSO spectra from the SDSS. The probability of the spectrum resulting from a chance superposition of two QSOs with similar redshifts is estimated at 2X10^-7, leading to the expectation of 0.003 such objects in the sample studied; however, even in this case, the spectrum of the lower redshift QSO remains highly unusual.
We show that in the quantum case any work distribution can be related to an equilibrium correlation function in an extended Hilbert space. As a consequence of this identification the Crooks relation is a restatement of the detailed balance principle for equilibrium correlation functions. The presented derivation serves as an alternative proof of the Crooks relation residing only on the detailed balance principle.
Context: We use the first XMM serendipitous source catalogue (1XMM) to compile a sample of normal X-ray galaxies   Aims: We seek to expand the database of X-ray selected normal galaxies at intermediate redshifts and examine the relation between X-ray emission and star formation for late-type systems   Methods: The candidates are selected based on their X-ray (soft spectra), X-ray to optical [log(fx/fo)<-2] and optical (extended sources) properties. 44 candidates are found and 35 are spectroscopically observed with the Australian National University's 2.3m telescope to examine their nature.   Results: Of the 35 sources observed, 2 are AGN, 11 emission line galaxies, 12 absorption line galaxies, 6 have featureless spectra while 4 are associated with Galactic stars. We combine our emission line sample with earlier works forming the most comprehensive X-ray selected galaxy sample for the study of the X-ray luminosity to the Halpha luminosity - a well-calibrated star-formation indicator - relation.   Conclusions: We find that the X-ray luminosity strongly correlates with the Halpha luminosity, suggesting that the X-rays efficiently trace the star-formation.
The tests of the constancy of the fundamental constants are tests of the local position invariance and thus of the equivalence principle. We summarize the various constraints that have been obtained and then describe the connection between varying constants and extensions of general relativity. To finish, we discuss the link with cosmology, and more particularly with the acceleration of the Universe. We take the opportunity to summarize various possibilities to test general relativity (but also the Copernican principle) on cosmological scales.
Given a sequence $\{Z_d\}_{d\in \mathbb{N}}$ of smooth and compact hypersurfaces in $\mathbb{R}^{n-1}$, we prove that (up to extracting subsequences) there exists a regular definable hypersurface $\Gamma\subset \mathbb{R}\mathrm{P}^n$ such that each manifold $Z_d$ appears as a component of the zero set on $\Gamma$ of some polynomial of degree $d$. (This is in sharp contrast with the case when $\Gamma$ is algebraic, where for example the homological complexity of the zero set of a polynomial $p$ on $\Gamma$ is bounded by a polynomial in $\mathrm{deg}(p)$.) We call these "pathological examples".   In particular, we show that for every $0 \leq k \leq n-2$ and every sequence of natural numbers $a=\{a_d\}_{d\in \mathbb{N}}$ there is a regular, compact and definable hypersurface $\Gamma\subset \mathbb{R}\mathrm{P}^n$, a subsequence $\{a_{d_m}\}_{m\in \mathbb{N}}$ and homogeneous polynomials $\{p_{m}\}_{m\in \mathbb{N}}$ of degree $\mathrm{deg}(p_m)=d_m$ such that: \begin{equation} \label{eq:pathintro} b_k(\Gamma\cap Z(p_m))\geq a_{d_m}.\end{equation} (Here $b_k$ denotes the $k$-th Betti number.) This generalizes a result of Gwo\'zdziewicz, Kurdyka and Parusi\'nski.   On the other hand, for a given definable $\Gamma$ we show that the Fubini-Study measure, in the gaussian space of polynomials of degree $d$, of the set $\Sigma_{d_m,a, \Gamma}$ of polynomials verifying $b_k(\Gamma\cap Z(p_m))\geq a_{d_m}$ is positive, but there exists a contant $c_\Gamma$ such that this measure can be bounded by: \begin{equation} 0<\mathbb{P}(\Sigma_{d_m, a, \Gamma})\leq \frac{c_{\Gamma} d_m^{\frac{n-1}{2}}}{a_{d_m}}. \end{equation} This shows that the set of "pathological examples" has "small" measure.
It is known that all modular forms on $SL_2(Z)$ can be expressed as a rational function in $\eta(z)$, $\eta(2z)$ and $\eta(4z)$. By using a theorem by Gordon, Hughes, and Newman, and calculating the order of vanishing, we can compute the $\eta$-quotients for a given level. Using this count, knowing how many $\eta$-quotients are linearly independent and using the dimension formula, we can figure out how the $\eta$-quotients span higher levels. In this paper, we primarily focus on the case where $N=p$ a prime, and some discussion for non-prime indicies.
Spontaneous symmetry breaking is deeply related to dimensionality of system. The Neel order going with spontaneous breaking of $U(1)$ symmetry is safely allowed at any temperature for three-dimensional systems but allowed only at zero temperature for purely two-dimensional systems. We closely investigate how smoothly the ordering process of the three-dimensional system is modulated into that of the two-dimensional one with reduction of dimensionality, considering spatially anisotropic quantum antiferromagnets. We first show that the N\'eel temperature is kept finite even in the two-dimensional limit although the N\'eel order is greatly suppressed for low-dimensionality. This feature of the N\'eel temperature is highly nontrivial, which dictates how the order parameter is squashed under the reduction of dimensionality. Next we investigate this dimensional modulation of the order parameter. We develop our argument taking as example a coupled spin-ladder system relevant for experimental studies. The ordering process is investigated multidirectionally using theoretical techniques of a mean-field method combined with analytical (exact solutions of quantum field theories) or numerial (density-matrix renormalization-group) method, a variational method, a renormalization-group study, linear spin-wave theory, and quantum Monte-Carlo simulation. We show that these methods independent of each other lead to the same conclusion about the dimensional modulation.
When the gauge groups of the two heterotic string theories are broken, over tori, to their "SO(16)x SO(16)" subgroups, the winding modes correspond to representations which are spinorial with respect to those subgroups. Globally, the two subgroups are isomorphic neither to SO(16)x SO(16) nor to each other. Any attempt to formulate the T-duality of the two theories on any manifold more complicated than the product of a circle with a Euclidean space must therefore take into account the possible non-existence of the relevant "generalised spin structure". We give here a global formulation of T-duality in this case, and discuss examples where the duality seems to be obstructed.
We consider i.i.d. last-passage percolation on $\mathbb{Z}^2$ with weights having distribution $F$ and time-constant $g_F$. We provide an explicit condition on the large deviation rate function for independent sums of $F$ that determines when some adjacent Busemann function increments are negatively correlated. As an example, we prove that $\operatorname{Bernoulli}(p)$ weights for $p > p^* \approx 0.6504$ satisfy this condition. We prove this condition by establishing a direct relationship between the negative correlations of adjacent Busemann increments and the dominance of the time-constant $g_F$ by the function describing the time-constant of last-passage percolation with exponential or geometric weights.
There is an apparent power deficit relative to the Lambda-CDM prediction of the CMB spectrum at large scales, which, though not yet statistically significant, persists from WMAP to Planck data. We first present a simple toy model corresponding to a network of frustrated topological defects of domain walls or cosmic strings that exist previous to the standard slow-roll inflationary era of the universe. Those features are phenomenologically modeled by a Chaplygin gas that can interpolate between a network of frustrated topological defects and a de Sitter-like or a power-law inflationary era. We show that these scenarios can alleviate the quadrupole anomaly of the CMB spectrum, based on the approximate initial conditions for the long-wavelength perturbations. We then go further to show that the large-scale spectrum at the end of inflation reflects the super-horizon spectrum of the initial state of the inflaton field. By studying the curvature perturbations of a scalar field in the FLRW universe parameterized by the equation of state parameter w, we find that the large-scale spectrum is suppressed if the universe begins with the adiabatic vacuum in a superinflation (w < -1) or positive-pressure (w > 0) era. In the latter case, there is however no causal mechanism to establish the initial adiabatic vacuum. To search for a more realistic initial condition of the inflationary universe, we consider the Hartle-Hawking no-boundary wave function, which is a solution to the Wheeler-DeWitt equation, as the initial condition of the universe. We find that the power suppression can be the consequence of a massive inflaton, whose initial vacuum is the Euclidean instanton in a compact manifold. We calculate the primordial power spectrum of the perturbations and show that, as long as the scalar field is moderately massive, the power spectrum is suppressed at the long-wavelength scales.
The generally adopted value for the solar abundance of indium is over six times higher than the meteoritic value. We address this discrepancy through numerical synthesis of the 451.13 nm line on which all indium abundance studies are based, both for the quiet-sun and the sunspot umbra spectrum, employing standard atmosphere models and accounting for hyperfine structure and Zeeman splitting in detail. The results, as well as a re-appraisal of indium nucleosynthesis, suggest that the solar indium abundance is close to the meteoritic value, and that some unidentified ion line causes the 451.13 nm feature in the quiet-sun spectrum.
We investigate the singular limit, as $\ep \to 0$, of the Fisher equation $\partial_t u=\ep \Delta u + \ep ^{-1}u(1-u)$ in the whole space. We consider initial data with compact support plus, possibly, perturbations very small as $\Vert x \Vert \to \infty$. By proving both generation and motion of interface properties, we show that the sharp interface limit moves by a constant speed, which is the minimal speed of some related one-dimensional travelling waves. We obtain an estimate of the thickness of the transition layers. We also exhibit initial data "not so small" at infinity which do not allow the interface phenomena.
We study a generalized quantum spin ladder with staggered long range interactions that decay as a power-law with exponent $\alpha$. Using large scale quantum Monte Carlo (QMC) and the density matrix renormalization group (DMRG) simulations, we show that this model undergoes a transition from a rung-dimer phase characterized by a non-local string order parameter, to a symmetry broken N\'eel phase. We find evidence that the transition is second order.In the magnetically ordered phase, the spectrum exhibits gapless modes, while excitations in the gapped phase are well described in terms of triplons -- bound states of spinons across the legs. We obtain the momentum resolved spin dynamic structure factor numerically and find a well defined triplon band evolves into a gapless magnon dispersion through the transition. We further discuss the possibility of deconfined criticality in this model.
Modern lane detection methods have achieved remarkable performances in complex real-world scenarios, but many have issues maintaining real-time efficiency, which is important for autonomous vehicles. In this work, we propose LaneATT: an anchor-based deep lane detection model, which, akin to other generic deep object detectors, uses the anchors for the feature pooling step. Since lanes follow a regular pattern and are highly correlated, we hypothesize that in some cases global information may be crucial to infer their positions, especially in conditions such as occlusion, missing lane markers, and others. Thus, this work proposes a novel anchor-based attention mechanism that aggregates global information. The model was evaluated extensively on three of the most widely used datasets in the literature. The results show that our method outperforms the current state-of-the-art methods showing both higher efficacy and efficiency. Moreover, an ablation study is performed along with a discussion on efficiency trade-off options that are useful in practice.
The Kuramoto model exhibits different types of synchronization transitions depending on the type of natural frequency distribution. To obtain these results, the Kuramoto self-consistency equation (SCE) approach has been used successfully. However, this approach affords only limited understanding of more detailed properties such as the stability and finite size effect. Here, we extend the SCE approach by introducing an effective potential, that is, an integral version of the SCE. We examine the landscape of this effective potential for second-order, first-order, and hybrid synchronization transitions in the thermodynamic limit. In particular, for the hybrid transition, we find that the minimum of effective potential displays a plateau across the region in which the order parameter jumps. This result suggests that the effective free energy can be used to determine a type of synchronization transition. For finite systems, the effective potential contains local minima at which the system can be trapped. Using numerical simulations, we determine the stability of the system as a function of system size and simulation time.
In this paper, we study the long-time behavior of a fluid particle immersed in a turbulent fluid driven by a diffusion with jumps, that is, a Feller process associated with a non-local operator. We derive the law of large numbers and central limit theorem for the evolution process of the tracked fluid particle in the cases when the driving process: (i) has periodic coefficients, (ii) is ergodic or (iii) is a class of L\'evy processes. The presented results generalize the classical and well-known results for fluid flows driven by elliptic diffusion processes.
A crucial building block for quantum information processing with trapped ions is a controlled-NOT quantum gate. In this paper, two different sequences of laser pulses implementing such a gate operation are analyzed using quantum process tomography. Fidelities of up to 92.6(6)% are achieved for single gate operations and up to 83.4(8)% for two concatenated gate operations. By process tomography we assess the performance of the gates for different experimental realizations and demonstrate the advantage of amplitude--shaped laser pulses over simple square pulses. We also investigate whether the performance of concatenated gates can be inferred from the analysis of the single gates.
In this paper, we establish a global Carleman estimate for an Ultrahyperbolic Schr\"odinger equation. Moreover, we prove H\"older stability for the inverse problem of determining a coefficient or a source term in the Ultrahyperbolic Schr\"odinger equation by some lateral boundary data.
We consider the possibility of a successful Affleck-Dine mechanism along the u^c d^c d^c direction in R-parity symmetric extensions of the minimal supersymmetric Standard Model (MSSM) which contain a gauge singlet superfield phi. Such gauge singlets commonly occur in extensions of the MSSM, for example in models which seek to account for neutrino masses. We consider a two scalar Affleck-Dine mechanism, with the flat direction stabilized by a non-renormalizible superpotential term of the form (lambda/M) phi udd ~ (lambda/M) phi psi^3, where psi corresponds to the gauge non-singlet flat direction. We give approximate solutions of the scalar field equations of motion which describe the evolution of the condensates and show that the final baryon asymmetry in this case is suppressed relative to that expected from the conventional single scalar Affleck-Dine mechanism, based on a superpotential term of the form (lambda/(4M)) psi^4, by a factor (m_{s}/(m_{phi}+m_{s}))^(1/2), where m_{s} is the soft supersymmetry breaking scalar mass and m_{phi} is the supersymmetric phi mass. It is possible for the model to generate a baryon asymmetry even in the limit of unbroken B-L, so long as the gauge singlet condensate doesn't decay until after anomalous electroweak B+L violation is out of equilibrium following the electroweak phase transition. This condition is generally satisfied if all Dirac neutrino masses are less than around 10keV. This class of Affleck-Dine models can, in principle,be experimentally ruled out, for example by the observation of a Dirac mass for the mu or tau neutrino significantly larger than around 10keV together with a mostly Higgsino LSP.
We determine the asymptotic behavior of the realized power variations, or more generally of sums of a given test function evaluated at the successive increments of a L\'{e}vy process. One can completely elucidate the first order behavior (convergence in probability, possibly after normalization). As for the associated CLT, one can show some versions of it, but only in a limited number of cases. In some other cases, a CLT just does not exist.
Monocular image-based 3D perception has become an active research area in recent years owing to its applications in autonomous driving. Approaches to monocular 3D perception including detection and tracking, however, often yield inferior performance when compared to LiDAR-based techniques. Through systematic analysis, we identified that per-object depth estimation accuracy is a major factor bounding the performance. Motivated by this observation, we propose a multi-level fusion method that combines different representations (RGB and pseudo-LiDAR) and temporal information across multiple frames for objects (tracklets) to enhance per-object depth estimation. Our proposed fusion method achieves the state-of-the-art performance of per-object depth estimation on the Waymo Open Dataset, the KITTI detection dataset, and the KITTI MOT dataset. We further demonstrate that by simply replacing estimated depth with fusion-enhanced depth, we can achieve significant improvements in monocular 3D perception tasks, including detection and tracking.
The vacuum expectation values for the energy-momentum tensor of a massive scalar field with general curvature coupling and obeying the Robin boundary condition on spherically symmetric boundaries in D-dimensional space are investigated. The expressions are derived for the regularized vacuum energy density, radial and azimuthal stress components (i) inside and outside a single spherical surface and (ii) in the intermediate region between two concentric spheres. Regularization procedure is carried out by making use of the generalized Abel-Plana formula for the series over zeros of cylinder functions. Asymptotic behavior of the vacuum densities near the sphere and at large distances is investigated. A decomposition of the Casimir energy into volumic and surface parts is provided for both cases (i) and (ii). We show that the mode sum energy, evaluated as a sum of the zero-point energies for each normal mode of frequency, and the volume integral of the energy density in general are different, and argue that this difference is due to the existence of an additional surface energy contribution.
Recent detection of gravitational waves from a binary-neutron star merger (GW170817) and the subsequent observations of electromagnetic counterparts provide a great opportunity to study the physics of compact binary mergers. The optical and near-infrared counterparts to GW170817 (SSS17a, also known as AT 2017gfo or DLT17ck) are found to be consistent with a kilonova/macronova scenario with red and blue components. However, in most of previous studies in which contribution from each ejecta component to the lightcurves is separately calculated and composited, the red component is too massive as dynamical ejecta and the blue component is too fast as post-merger ejecta. In this letter, we perform a 2-dimensional radiative transfer simulation for a kilonova/macronova consistently taking the interplay of multiple ejecta components into account. We show that the lightcurves and photospheric velocity of SSS17a can be reproduced naturally by a setup consistent with the prediction of the numerical-relativity simulations.
(Abridged) Differential astrometry measurements from the Palomar High-precision Astrometric Search for Exoplanet Systems (PHASES) are used to constrain the astrometric orbit of the previously known lesssim 2 day subsystem in the triple system 63 Gem A and have detected a previously unknown 2 year Keplerian wobble superimposed on the visual orbit of the much longer period (213 years) binary system HR 2896. The very small astrometric perturbation caused by the inner pair in 63 Gem A stretches the limits of current astrometric capabilities, but PHASES observations are able to constrain the orientation of the orbit. The two bright stars comprising the HR 2896 long period (213 year) system have a combined spectral type of K0III and the newly detected object's mass estimate places it in the regime of being a M dwarf. The motion of the stars are slow enough that their spectral features are always blended, preventing Doppler studies. The PHASES measurements and radial velocities (when available) have been combined with lower precision single-aperture measurements covering a much longer timeframe to improve the characterization of the long period orbits in both binaries. The visual orbits of the short and long period systems are presented for both systems, and used to calculate two possible values of the mutual inclinations between inner and outer orbits of 152 pm 12 degrees or a less likely value of 31 pm 11 degrees for 63 Gem A and 10.2 pm 2.4 degrees or 171.2 pm 2.8 degrees for HR 2896. The first is not coplanar, whereas the second is either nearly coplanar or anti-coplanar.
We use a gluing method developed in joint work with Andr\'as Vasy to show that polynomially bounded cutoff resolvent estimates at the real axis imply, up to a constant factor, the same estimates in a neighborhood of the real axis.