ShantanuT01/DACTYL-Pretraining huggingface dataset:
We generalise Wesson's procedure, whereby vacuum $(4+1)-$dimensional field equations give rise to $(3+1)-$dimensional equations with sources, to arbitrary dimensions. We then employ this generalisation to relate the usual $(3+1)-$dimensional vacuum field equations to $(2+1)-$dimensional field equations with sources and derive the analogues of the classes of solutions obtained by Ponce de Leon. This way of viewing lower dimensional gravity theories can be of importance in establishing a relationship between such theories and the usual 4-dimensional general relativity, as well as giving a way of producing exact solutions in $(2+1)$ dimensions that are naturally related to the vacuum $(3+1)-$dimensional solutions. An outcome of this correspondence, regarding the nature of lower dimensional gravity, is that the intuitions obtained in $(3+1)$ dimensions may not be automatically transportable to lower dimensions.   We also extend a number of physically motivated solutions studied by Wesson and Ponce de Leon to $(D+1)$ dimensions and employ the equivalence between the $(D+1)$ Kaluza-Klein theories with empty $D-$dimensional Brans-Dicke theories (with $\omega=0$) to throw some light on the solutions derived by these authors.
We employ our new model for the polarised emission of accreting X-ray pulsars to describe the emission from the luminous X-ray pulsar Hercules X-1. In contrast with previous works, our model predicts the polarisation parameters independently of spectral formation, and considers the structure and dynamics of the accretion column, as well as the additional effects on propagation due to general relativity and quantum electrodynamics. We find that our model can describe the observed pulse fraction and the pulse shape of the main peak, as well as the modulation of the cyclotron line with phase. We pick two geometries, assuming a single accretion column or two columns at the magnetic poles, that can describe current observations of pulse shape and cyclotron modulation with phase. Both models predict a high polarisation fraction, between 60 and 80\% in the $1-10$ keV range, that is phase- and energy-dependent, and that peaks at the same phase as the intensity. The phase and energy dependence of the polarisation fraction and of the polarisation angle can help discern between the different geometries.
In \cite{nr-1996} Nowakowski and Rall listed a series of conjectures involving several different graph products. In particular, they conjectured that $i(G\times H) \ge i(G)i(H)$ where $i(G)$ is the independent domination number of $G$ and $G\times H$ is the direct product of graphs $G$ and $H$. We show this conjecture is false, and, in fact, construct pairs of graphs for which $\min\{i(G), i(H)\} - i(G\times H)$ is arbitrarily large. We also give the exact value of $i(G\times K_n)$ when $G$ is either a path or a cycle.
Formation of primordial black holes from inflationary fluctuations is accompanied by a scalar induced gravitational wave background. We perform a Bayesian search of such background in the data from Advanced LIGO and Virgo's first, second and third observing runs, parametrizing the peak in the curvature power spectrum by a log-normal distribution. The search shows no evidence for such a background. We place 95\% confidence level upper limits on the integrated power of the curvature power spectrum peak which, for a narrow width, reaches down to $0.02$ at $10^{17}\,{\rm Mpc}^{-1}$. The resulting constraints are stronger than those arising from BBN or CMB observations. In addition, we find that LIGO and Virgo, at its design sensitivity, and the Einstein Telescope can compete with the constraints related to the abundance of the formed primordial black holes.
As the only eclipsing asynchronous polar, V1432 Aql provides an excellent laboratory to study the interaction between the accreted matter and the magnetic field. Here, we report an analysis of the X-ray data from the contemporaneous \nustar\ and \xrt\ observations. The X-ray data present a profile with a low-intensity state for almost half an orbital period, a dip at 0.6 phase, and a peak at 0.75 phase, which suggests that there was only one accretion region during the observation and the claim is supported by the spectral analysis. The comparison with the previous data indicates that the X-ray data have an orbital modulation, as the case in \sax, rather than a spin one observed in \rosat. We attribute the orbit and spin modulations to the different accretion geometries at work. The spectral analysis of the wide-band data presents a significant reflection effect, a commonly observed soft X-ray temperature, and the energy balance in V1432 Aql . Additionally, we obtained a low total accretion rate of 1.3 $\times$ 10$^{-10}$ M$_{\odot}$ yr$^{-1}$ and a high specific accretion rate of 3.8 g cm$^{-2}$ s$^{-1}$ which explains the strong reflection from the surface of the white dwarf. However, due to its complex emission, a more physical understanding of its accretion geometry is still outstanding.
A theory of the separation of a system of indirect excitons into a condensed and a gaseous phases with the formation of regular patterns of alternating phases in inhomogeneous external fields is developed. The theory is applied to the study of the non-uniform distribution of the exciton density in a double quantum well under a slot cut in a metallic electrode. It is shown that in a certain range of exciton generation rates a chain of light emitting islands periodically localized along the slot is developed. By creating a biased external potential along the slot the periodical pattern could be forced to move along the slot. Also the structures of condensed phases distribution arising at periodical external potential is considered.
We study fluctuations of the error term for the number of integer lattice points lying inside a 3-dimensional Cygan-Kor\'anyi ball of large radius. We prove that the error term, suitably normalized, has a limiting value distribution which is absolutely continuous, and we provide estimates for the decay rate of the corresponding density on the real line. In addition, we establish the existence of all moments for the normalized error term, and we prove that these are given by the moments of the corresponding density.
Based on a pure solid-state device consisting of two superconducting LC circuits coupled to a superconducting flux qubit, we propose in this paper that the maximally entangled coherent states of the two LC modes can be generated for arbitrary coherent states through flux qubit controls.
By integrating out the U(1)_B gauge field, we show that the U(n)xU(n) ABJM theory at level k is equivalent to a Z_k identification of the (SU(n)xSU(n))/Z_n Chern-Simons theory, but only when n and k are coprime. As a consequence, the k=1 ABJM model for two M2-branes in R^8 can be identified with the N=8 (SU(2)xSU(2))/Z_2 theory. We also conjecture that the U(2)xU(2) ABJM model at k=2 is equivalent to the N=8 SU(2)xSU(2)-theory.
We address the problem of the determination of the images of the Galois representations attached to genus 2 Siegel cusp forms of level 1 having multiplicity one. These representations are symplectic. We prove that the images are as large as possible for almost every prime, if the Siegel cusp form is not a Maass spezialform and verifies two easy to check conditions.
The stellar initial mass function (IMF) is a fundamental property in the measurement of stellar masses and galaxy star formation histories. In this work we focus on the most massive galaxies in the nearby universe $\log(M_{\star}/M_{\odot})>11.2$. We obtain high quality Magellan/LDSS-3 long slit spectroscopy with a wide wavelength coverage of $0.4\mu{\rm m}-1.01\mu{\rm m}$ for 41 early-type galaxies (ETGs) in the MASSIVE survey, and derive high S/N spectra within an aperture of $R_{\rm e}/8$. Using detailed stellar synthesis models, we constrain the elemental abundances and stellar IMF of each galaxy through full spectral modeling. All the ETGs in our sample have an IMF that is steeper than a Milky Way (Kroupa) IMF. The best-fit IMF mismatch parameter, $\alpha_{\rm IMF}=(M/L)/(M/L)_{\rm MW}$, ranges from 1.12 to 3.05, with an average of $\langle \alpha_{\rm IMF} \rangle=1.84$, suggesting that on average, the IMF is more bottom-heavy than Salpeter. Comparing the estimated stellar mass with the dynamical mass, we find that most galaxies have stellar masses smaller than their dynamical masses within the $1\sigma$ uncertainty. We complement our sample with lower-mass galaxies from the literature, and confirm that $\log(\alpha_{\rm IMF})$ is positively correlated with $\log(\sigma)$, $\log(M_{\star})$, and $\log(M_{\rm dyn})$. The IMF in the centers of more massive ETGs is more bottom-heavy. In addition, we find that $\log(\alpha_{\rm IMF})$ is positively correlated with both [Mg/Fe] and the estimated total metallicity [Z/H]. We find suggestive evidence that the effective stellar surface density $\Sigma_{\rm Kroupa}$ might be responsible for the variation of $\alpha_{\rm IMF}$. We conclude that $\sigma$, [Mg/Fe] and [Z/H] are the primary drivers of the global stellar IMF variation.
During the rising phase of Solar Cycle 24 tremendous activity occurred on the Sun with fast and compact emergence of magnetic flux leading to bursts of flares (C to M and even X-class). We investigate the violent events occurring in the cluster of two active regions (ARs), NOAA numbers 11121 and 11123, observed in November 2010 with instruments onboard the {\it Solar Dynamics Observatory} and from Earth. Within one day the total magnetic flux increased by $70\%$ with the emergence of new groups of bipoles in AR 11123. From all the events on 11 November, we study, in particular, the ones starting at around 07:16 UT in GOES soft X-ray data and the brightenings preceding them. A magnetic-field topological analysis indicates the presence of null points, associated separatrices and quasi-separatrix layers (QSLs) where magnetic reconnection is prone to occur. The presence of null points is confirmed by a linear and a non-linear force-free magnetic-field model. Their locations and general characteristics are similar in both modelling approaches, which supports their robustness. However, in order to explain the full extension of the analysed event brightenings, which are not restricted to the photospheric traces of the null separatrices, we compute the locations of QSLs. Based on this more complete topological analysis, we propose a scenario to explain the origin of a low-energy event preceding a filament eruption, which is accompanied by a two-ribbon flare, and a consecutive confined flare in AR 11123. The results of our topology computation can also explain the locations of flare ribbons in two other events, one preceding and one following the ones at 07:16 UT. Finally, this study provides further examples where flare-ribbon locations can be explained when compared to QSLs and only, partially, when using separatrices.
We analytically compute the flavour singlet ${\cal O}(\alpha_s^2 m_b^2/m_t^2)$ radiative corrections to the partial decay rate $\Gamma(Z\rightarrow b\bar{b})$. These corrections arise from anomalous ``double traingle'' diagrams containing a single $\gamma_5$ matrix inside each of two closed fermion loops. They represent the next-to-leading term of the asymptotic expansion in the inverse large top mass. As a byproduct of the calculcation we confirm the results of B.Kniehl and J.H.K\"uhn for the flavour singlet massless corrections \cite{KniKue90} as well as our previous ${\cal O}(\alpha_s^2 m_b^2/M_Z^2)$ result \cite{CheKwi93}.
Automorphic fundamental solutions and, more generally, solutions of automorphic differential equations, play a key role in the Diaconu-Garrett-Goldfeld prescription for spectral identities involving moments of L-functions as well as other applications, including an explicit formula relating the number of lattice points in a symmetric space to the automorphic spectrum. In this paper we discuss two cases in which the automorphic fundamental solution exhibits branching: pathwise meromorphic continuations may differ by a term involving an Eisenstein series.
Solutions of hydrodynamical equations are presented for an equation of state allowing for a first-order phase transition. The numerical analysis is supplemented by analytical treatment provided the system is close to the critical point. The processes of growth and dissolution of seeds of various sizes and shapes in meta-stable phases (like super-cooled vapor and super-heated liquid) are studied, as well as the dynamics of unstable modes in the spinodal region. We show that initially nonspherical seeds acquire spherical shape with passage of time. Applications to the description of the first-order phase transitions in nuclear systems, such as the nuclear gas-liquid transition occurring in low energy heavy-ion collisions and the hadron-quark transition in the high energy heavy-ion collisions are discussed. In both cases we point out the important role played by effects of viscosity and surface tension. It is shown that fluctuations dissolve and grow as if the fluid were effectively very viscous. Even in the spinodal region seeds may grow slowly due to viscosity and critical slowing down. This prevents the enhancement of fluctuations in the near-critical region, which is frequently considered as a signal of the critical point in heavy-ion collisions.
The friction force acting on a small neutral particle during relativistic motion relative to the blackbody radiation is calculated in the framework of fluctuation electrodynamics. It is shown that the particle acceleration is determined by the friction force in the particle rest reference frame ($K^{\prime}$-frame) which in general is not equal to the friction force in the frame of the blackbody radiation ($K$-frame). The difference between the friction forces in the different frames is connected with the change of the rest mass of a particle due to the absorption and emission of radiation. The friction force in the $K^{\prime}$-frame is determined only by the interaction of a particle with the blackbody radiation. In the $K$-frame the interaction of a particle with its own thermal radiation also contributes to the friction force. For the steady state temperature of a particle the friction forces in the $K^{\prime}$-and $K$-frames are equal. For an atom the blackbody friction is determined by the electronic linewidth broadening which is calculated considering the interaction of an atom with its own radiation. In the ultrarelativistic case ($1-\beta\rightarrow 0$) for an atom the friction force diverges as $(1-\beta)^{-3}$ and the (average) temperature of an atom $T_2\approx (1-\beta)^{-3/8}T_1$, where $T_1$ is the temperature of the blackbody radiation and $\beta=V/c$. Controversies in the theory of the blackbody friction are discussed.
We investigate dynamical generation of macroscopic nonlocal entanglements between two remote massive magnon-superconducting-circuit hybrid systems. Two fiber-coupled microwave cavities are employed to serve as an interaction channel connecting two sets of macroscopic hybrid units each containing a magnon (hosted by a Yttrium-Iron-Garnet sphere) and a superconducting-circuit qubit. Surprisingly, it is found that stronger coupling does not necessarily mean faster entanglement generation. The proposed hybrid system allows the existence of an optimal fiber coupling strength that requests the shortest amount of time to generate a systematic maximal entanglement. Our theoretical results are shown to be within the scope of specific parameters that can be achieved with current technology. The noise effects on the implementation of systems are also treated in a general environment suggesting the robustness of entanglement generation. Our discrete-variable qubit-like entanglement theory of magnons may lead to direct applications in various quantum information tasks.
Several non-local curvature flows for plane curves with a general rotation number are discussed in this work. The types of flows include the area-preserving flow and the length-preserving flow. We have a relatively good understanding of these flows for plane curves with the rotation number one. In particular, when the initial curve is strictly convex, the flow exists globally in time, and converges to a circle as time tends to infinity. Even if the initial curve is not strictly convex, a global solution, if it exists, converges to a circle. Here, we deal with curves with a general rotation number, and show, not only a similar result for global solutions, but also a blow-up criterion, upper estimates of the blow-up time, and blow-up rate from below. For this purpose, we use a geometric quantity which has never been considered before.
We address the problem of generalized zero-shot semantic segmentation (GZS3) predicting pixel-wise semantic labels for seen and unseen classes. Most GZS3 methods adopt a generative approach that synthesizes visual features of unseen classes from corresponding semantic ones (e.g., word2vec) to train novel classifiers for both seen and unseen classes. Although generative methods show decent performance, they have two limitations: (1) the visual features are biased towards seen classes; (2) the classifier should be retrained whenever novel unseen classes appear. We propose a discriminative approach to address these limitations in a unified framework. To this end, we leverage visual and semantic encoders to learn a joint embedding space, where the semantic encoder transforms semantic features to semantic prototypes that act as centers for visual features of corresponding classes. Specifically, we introduce boundary-aware regression (BAR) and semantic consistency (SC) losses to learn discriminative features. Our approach to exploiting the joint embedding space, together with BAR and SC terms, alleviates the seen bias problem. At test time, we avoid the retraining process by exploiting semantic prototypes as a nearest-neighbor (NN) classifier. To further alleviate the bias problem, we also propose an inference technique, dubbed Apollonius calibration (AC), that modulates the decision boundary of the NN classifier to the Apollonius circle adaptively. Experimental results demonstrate the effectiveness of our framework, achieving a new state of the art on standard benchmarks.
We target the problem of sparse 3D reconstruction of dynamic objects observed by multiple unsynchronized video cameras with unknown temporal overlap. To this end, we develop a framework to recover the unknown structure without sequencing information across video sequences. Our proposed compressed sensing framework poses the estimation of 3D structure as the problem of dictionary learning, where the dictionary is defined as an aggregation of the temporally varying 3D structures. Given the smooth motion of dynamic objects, we observe any element in the dictionary can be well approximated by a sparse linear combination of other elements in the same dictionary (i. e. self-expression). Moreover, the sparse coefficients describing a locally linear 3D structural interpolation reveal the local sequencing information. Our formulation optimizes a biconvex cost function that leverages a compressed sensing formulation and enforces both structural dependency coherence across video streams, as well as motion smoothness across estimates from common video sources. We further analyze the reconstructability of our approach under different capture scenarios, and its comparison and relation to existing methods. Experimental results on large amounts of synthetic data as well as real imagery demonstrate the effectiveness of our approach.
We present results from high-resolution three-dimensional simulations of the turbulent interstellar medium that study the influence of the nature of the turbulence on the formation of molecular hydrogen. We have examined both solenoidal (divergence-free) and compressive (curl-free) turbulent driving, and show that compressive driving leads to faster H2 formation, owing to the higher peak densities produced in the gas. The difference in the H2 formation rate can be as much as an order of magnitude at early times, but declines at later times as the highest density regions become fully molecular and stop contributing to the total H2 formation rate. We have also used our results to test a simple prescription suggested by Gnedin et al. (2009) for modeling the influence of unresolved density fluctuations on the H2 formation rate in large-scale simulations of the ISM. We find that this approach works well when the H2 fraction is small, but breaks down once the highest density gas becomes fully molecular.
We present photometric properties and distance measurements of 252 high redshift Type Ia supernovae (0.15 < z < 1.1) discovered during the first three years of the Supernova Legacy Survey (SNLS). These events were detected and their multi-colour light curves measured using the MegaPrime/MegaCam instrument at the Canada-France-Hawaii Telescope (CFHT), by repeatedly imaging four one-square degree fields in four bands. Follow-up spectroscopy was performed at the VLT, Gemini and Keck telescopes to confirm the nature of the supernovae and to measure their redshifts. Systematic uncertainties arising from light curve modeling are studied, making use of two techniques to derive the peak magnitude, shape and colour of the supernovae, and taking advantage of a precise calibration of the SNLS fields. A flat LambdaCDM cosmological fit to 231 SNLS high redshift Type Ia supernovae alone gives Omega_M = 0.211 +/- 0.034(stat) +/- 0.069(sys). The dominant systematic uncertainty comes from uncertainties in the photometric calibration. Systematic uncertainties from light curve fitters come next with a total contribution of +/- 0.026 on Omega_M. No clear evidence is found for a possible evolution of the slope (beta) of the colour-luminosity relation with redshift.
We prove a law of large numbers for random walks in certain kinds of i.i.d. random environments in Z^d that is an extension of a result of Bolthausen, Sznitman and Zeitouni (2003). We use this result, along with the lace expansion for self-interacting random walks, to prove a monotonicity result for the first coordinate of the speed of the random walk under some strong assumptions on the distribution of the environment.
A recently found new free field realization of the affine Sugawara operators at arbitrary level is reviewed, which involves exponentials of the well-known DDF operators in string theory.
We consider two mean-field like models which belong to the universality class of absorbing phase transitions with a conserved field. In both cases we derive analytically the order parameter as function of the control parameter and of an external field conjugated to the order parameter. This allows us to calculate the universal scaling function of the mean-field behavior. The obtained universal function is in perfect agreement with recently obtained numerical data of the corresponding five and six dimensional models, showing that four is the upper critical dimension of this particular universality class.
Any fixed cylinder is hit almost surely by a 3-dimensional Brownian motion, but is there a random cylinder that is in the complement? We answer this for cylinders, and then replacing a cylinder with a more general set.
What do you get when you cross a crystal with a quasicrystal? The surprising answer stretches from Fibonacci to Kepler, who nearly 400 years ago showed how the ancient tiles of Archimedes form periodic patterns.
We consider random reflections (according to the Lambertian distribution) of a light ray in a thin variable width (but almost circular) tube. As the width of the tube goes to zero, properly rescaled angular component of the light ray position converges in distribution to a diffusion whose parameters (diffusivity and drift) are given explicitly in terms of the tube width.