ShantanuT01/DACTYL-Pretraining huggingface dataset:
This work is devoted to provide a way of representing $4D$ spherically symmetric and static compact stellar configurations into a $5D$ space time, using the black string framework.   We write the four and five dimensional line elements and the four and five dimensional energy momentum tensor such that the four and five dimensional quantities are related by a function $A(z)$, where $z$ represents to the extra dimension. Remarkably, one consequence of our chosen form for the line element, for the energy momentum tensor and for $A(z)$, is the fact that the $5D$ equations are reduced to the usual form of the four dimensional equations of motion. Also, the five dimensional conservation equation adopts the form of the four dimensional conservation equation. It is worth mentioning that, although our methodology is simple, this form of reduction could serve to represent other types of four dimensional objects into an extra dimension in future works. Furthermore, under our assumptions the sign of the pressure along the extra dimension is given by the trace of the four dimensional energy momentum tensor.   Furthermore, our simple election for the function $A(z)$ modifies some features of the induced 4--dimensional compact stellar configuration, such as the mass--radius relation, the momentum of inertia, the central values of the thermodynamic variables, to name a few. Besides, the topology of this model is ${S}^{2}\times {S}^{1}$ and not the ${S}^{3}$ topology of the 5--dimensional structures.
Let $X$ be flat scheme over $\mathbb{Z}$ such that its base change, $X_p$, to $\bar{\mathbb{F}}_p$ is Frobenius split for all primes $p$. Let $G$ be a reductive group scheme over $\mathbb{Z}$ acting on $X$. In this paper, we prove a result on the $N_p$ property for line bundles on GIT quotients of $X_{\mathbb{C}}$ for the action of $G_{\mathbb{C}}$. We apply our result to the special cases of (1) an action of a finite group on the projective space and (2) the action of a maximal torus on the flag variety of type $A_n$.
We describe an efficient Monte Carlo algorithm for a restricted class of scattering problems in radiation transfer. This class includes many astrophysically interesting problems, including the scattering of ultraviolet and visible light by grains. The algorithm correctly accounts for multiply-scattered light. We describe the algorithm, present a number of important optimizations, and explicity show how the algorithm can be used to estimate quantities such as the emergent and mean intensity. We present two test cases, examine the importance of the optimizations, and show that this algorithm can be usefully applied to optically-thin problems, a regime sometimes considered limited to explicit single-scattering plus attenuation approximations.
We undertake a systematic study of Lipschitz Normally Embedded normal complex surface germs. We prove in particular that the topological type of such a germ determines the combinatorics of its minimal resolution which factors through the blowup of its maximal ideal and through its Nash transform, as well as the polar curve and the discriminant curve of a generic plane projection, thus generalizing results of Spivakovsky and Bondil that were known for minimal surface singularities. In an appendix, we give a new example of a Lipschitz Normally Embedded surface singularity.
Deep networks can learn to accurately recognize objects of a category by training on a large number of annotated images. However, a meta-learning challenge known as a low-shot image recognition task comes when only a few images with annotations are available for learning a recognition model for one category. The objects in testing/query and training/support images are likely to be different in size, location, style, and so on. Our method, called Cascaded Feature Matching Network (CFMN), is proposed to solve this problem. We train the meta-learner to learn a more fine-grained and adaptive deep distance metric by focusing more on the features that have high correlations between compared images by the feature matching block which can align associated features together and naturally ignore those non-discriminative features. By applying the proposed feature matching block in different layers of the few-shot recognition network, multi-scale information among the compared images can be incorporated into the final cascaded matching feature, which boosts the recognition performance further and generalizes better by learning on relationships. The experiments for few-shot learning on two standard datasets, \emph{mini}ImageNet and Omniglot, have confirmed the effectiveness of our method. Besides, the multi-label few-shot task is first studied on a new data split of COCO which further shows the superiority of the proposed feature matching network when performing few-shot learning in complex images. The code will be made publicly available.
Considering coordinates as operators whose measured values are expectations between generalized coherent states based on the group SO(N,1) leads to coordinate noncommutativity together with full $N$ dimensional rotation invariance. Through the introduction of a gauge potential this theory can additionally be made invariant under $N$ dimensional translations. Fluctuations in coordinate measurements are determined by two scales. For small distances these fluctuations are fixed at the noncommutativity parameter while for larger distances they are proportional to the distance itself divided by a {\em very} large number. Limits on this number will lbe available from LIGO measurements.
Based on SDSS DR8, we have selected a sample of 1728 red horizontal branch stars with |Z|<3 kpc by using a color-metallicity relation and stellar parameters. The sample stars clearly trace a typical thick disk population with peaks at |Z|=1.26 kpc and [Fe/H]=-0.54. The vertical metallicity gradient of the thick disk is estimated in two ways. One is a fit to the Gaussian peaks of the metallicity histograms of the thick disk by subtracting minor contributions from the thin disk and the inner halo based on the Besancon Galaxy model. The resulting gradient is -0.12+-0.01 dex/kpc for 0.5 <|Z| <3 kpc. The other method is to linearly fit the data based on stars with 1 <|Z| <3 kpc being the main component of the thick disk. Five subgroups are then selected in different directions in the X-|Z| plane to investigate the difference in the vertical metallicity gradient between the Galactocenter and anti-Galactocenter directions. We found that a vertical gradient o-0.22+-0.07 dex/kpc is detected for five directions except for one involving the pollution of stars from the bulge. The results indicate that the vertical gradient is dominant, but a radial gradient has a minor contribution for the thick disk population represented by RHB stars with 1 <|Z| <3 kpc. The present work strongly suggests the existence of a metallicity gradient in the thick disk, which is thought to be negligible in most previous works in the literature.
The Antarctic Muon And Neutrino Detector Array (AMANDA) has been taking data since 2000 and its data acquisition system was upgraded in January 2003 to read out the complete digitized waveforms from the buried Photomultipliers (PMTs) using Transient Waveform Recorders (TWR). This system currently runs in parallel with the standard AMANDA data acquisition system. Once AMANDA is incorporated into the 1 km^3 detector IceCube, only the TWR system will be kept. We report results from a first atmospheric neutrino analysis on data collected in 2003 with TWR. Good agreement in event rate and angular distribution verify the performance of the TWR system. A search of the northern hemisphere for localized event clusters shows no statistically significant excess, thus a flux limit is calculated, which is in full agreement with previous results based on the standard AMANDA data acquisition system. We also update the status of a search for diffusely distributed neutrinos with ultra high energy (UHE) using data collected by the TWR system.
We study the set of rational curves of a certain topological type in general members of certain families of Calabi-Yau threefolds. For some families we investigate to what extent it is possible to conclude that this set is finite. For other families we investigate whether this set contains at least one point representing an isolated rational curve.
We explore how the growth rate of spiral disks can be measured via analyses of the scatter in the Tully-Fisher (TF) relation of local and intermediate redshift galaxies. As an initial step, we show it is possible to construct a low-dispersion TF relation for nearly face-on, nearby spirals. We find these spiral disks are non-circular, (a mean ellipticity of 6%), which accounts for about 0.1 mag of the intrinsic scatter in the nearby TF relation of even the most ``normal'' looking spirals. If this ellipticity is induced by matter accretion, we expect to find greater disk ellipticity or disturbance in the past. We find evidence that more extreme outliers of the intermediate-redshift TF relation are more morphologically and kinematically disturbed. Whether this effect reflects a redshift trend or selection bias of local samples needs to be addressed.
We determine the baryon octet and decuplet masses as well as their wave functions in a covariant three-body Faddeev approach. We work in an approximation where irreducible three-body forces are neglected. In the two-body interactions we take into account a well explored rainbow-ladder kernel as well as flavor dependent meson-exchange terms motivated from the underlying quark-gluon interaction. Without flavor dependent forces we find agreement with the experimental spectrum on the 5-10 percent level. Including the flavor dependent terms on an exploratory level delivers a Sigma/Lambda splitting with the correct sign although the magnitude is still too small.
We show that novel low temperature properties of bulk SmB6, including the sudden growth of the de Haas-van Alphen amplitude (and heat capacity) originating from the bulk at millikelvin temperatures and a previously unreported linear-in-temperature bulk electrical conductivity at liquid helium temperatures, signal the presence of a highly asymmetric nodal semimetal. We show how the highly asymmetric nodal semimetal can be the result of a topological transformation, of the type recently considered by Shen and Fu, occurring in a Kondo lattice with dispersionless f-electron levels and Sm vacancies or other lattice defects. If supported by further data experimental, the existence of a nodal semimetal would cast considerable doubt over a neutral Fermi surface being required to explain the origin of the dHvA effect SmB6.
Let $S(n)$ be a centered random walk with finite second moment. We consider the integrated random walk $T(n) = S(0)+S(1)+\dots+S(n)$. We prove invariance principles for the meander and for the bridge of this process, under the condition that the integrated random walk remains positive. Furthermore, we prove the functional convergence of its Doob's $h$-transform to the $h$-transform of the Kolmogorov diffusion conditioned to stay positive.
Zehavi et al. (1998) have suggested that the Hubble flow within 70/h Mpc may be accelerated by the existence of a void centered on the Local Group. Its underdensity would be ~20 %, which would result in a local Hubble distortion of about 6.5 %. We have combined the peculiar velocity data of two samples of clusters of galaxies, SCI and SCII, to investigate the amplitude of Hubble distortions to 200/h Mpc. Our results are not supportive of that conclusion. The amplitude of a possible distortion in the Hubble flow within 70/h Mpc in the SCI+SCII merged data is 0.010\pm0.022. The largest, and still quite marginal, geocentric deviation from smooth Hubble flow consistent with that data set is a shell with (Delta H)/H =0.027\pm0.023, centered at hd = 101 Mpc and extending over some 30/h Mpc. Our results are thus consistent with a Hubble flow that, on distances in excess of about 50/h Mpc, is remarkably smooth.
The remarkable discovery of Quantum Error Correction (QEC), which can overcome the errors experienced by a bit of quantum information (qubit), was a critical advance that gives hope for eventually realizing practical quantum computers. In principle, a system that implements QEC can actually pass a "break-even" point and preserve quantum information for longer than the lifetime of its constituent parts. Reaching the break-even point, however, has thus far remained an outstanding and challenging goal. Several previous works have demonstrated elements of QEC in NMR, ions, nitrogen vacancy (NV) centers, photons, and superconducting transmons. However, these works primarily illustrate the signatures or scaling properties of QEC codes rather than test the capacity of the system to extend the lifetime of quantum information over time. Here we demonstrate a QEC system that reaches the break-even point by suppressing the natural errors due to energy loss for a qubit logically encoded in superpositions of coherent states, or cat states of a superconducting resonator. Moreover, the experiment implements a full QEC protocol by using real-time feedback to encode, monitor naturally occurring errors, decode, and correct. As measured by full process tomography, the enhanced lifetime of the encoded information is 320 microseconds without any post-selection. This is 20 times greater than that of the system's transmon, over twice as long as an uncorrected logical encoding, and 10% longer than the highest quality element of the system (the resonator's 0, 1 Fock states). Our results illustrate the power of novel, hardware efficient qubit encodings over traditional QEC schemes. Furthermore, they advance the field of experimental error correction from confirming the basic concepts to exploring the metrics that drive system performance and the challenges in implementing a fault-tolerant system.
We develop a general theory of a boson decomposition for both local and non-local interactions in lattice fermion models which allows us to describe fermionic degrees of freedom and collective charge and spin excitations on equal footing. An efficient perturbation theory in the interaction of the fermionic and the bosonic degrees of freedom is constructed in so-called dual variables in the path-integral formalism. This theory takes into account all local correlations of fermions and collective bosonic modes and interpolates between itinerant and localized regimes of electrons in solids. The zero-order approximation of this theory corresponds to extended dynamical mean-field theory (EDMFT), a regular way to calculate nonlocal corrections to EDMFT is provided. It is shown that dual ladder summation gives a conserving approximation beyond EDMFT. The method is especially suitable for consideration of collective magnetic and charge excitations and allows to calculate their renormalization with respect to "bare" RPA-like characteristics. General expression for the plasmonic dispersion in correlated media is obtained. As an illustration it is shown that effective superexchange interactions in the half-filled Hubbard model can be derived within the dual-ladder approximation.
Gallium chalcogenides are promising building blocks for novel van der Waals heterostructures. We report low-temperature micro-photoluminescence (PL) of GaTe and GaSe films with thickness ranging from from 200 nm to a single unit cell. In both materials, PL shows dramatic decrease by 10$^4$-10$^5$ when film thickness is reduced from 200 to 10 nm. Based on evidence from cw and time-resolved PL, we propose a model explaining the PL decrease as a result of non-radiative carrier escape via surface states.
The strongly coupled vacua of an N=1 supersymmetric gauge theory can be described by imposing quantization conditions on the periods of the gauge theory resolvent, or equivalently by imposing factorization conditions on the associated N=2 Seiberg-Witten curve (the so-called strong-coupling approach). We show that these conditions are equivalent to the existence of certain relations in the chiral ring, which themselves follow from the fact that the gauge group has a finite rank. This provides a conceptually very simple explanation of why and how the strongly coupled physics of N=1 theories, including fractional instanton effects, chiral symmetry breaking and confinement, can be derived from purely semi-classical calculations involving instantons only.
We study the quantum corrections to the Fermi energy of a two-dimensional electron system, showing that it is attracted towards the Van Hove singularity for a certain range of doping levels. The scaling of the Fermi level allows to cure the infrared singularities left in the BCS channel after renormalization of the leading logarithm near the divergent density of states. A phase of d-wave superconductivity arises beyond the point of optimal doping corresponding to the peak of the superconducting instability. For lower doping levels, the condensation of particle-hole pairs due to the nesting of the saddle points takes over, leading to the opening of a gap for quasiparticles in the neighborhood of the singular points.
Upcoming high-cadence transient survey programmes will produce a wealth of observational data for Type Ia supernovae. These data sets will contain numerous events detected very early in their evolution, shortly after explosion. Here, we present synthetic light curves, calculated with the radiation hydrodynamical approach Stella for a number of different explosion models, specifically focusing on these first few days after explosion. We show that overall the early light curve evolution is similar for most of the investigated models. Characteristic imprints are induced by radioactive material located close to the surface. However, these are very similar to the signatures expected from ejecta-CSM or ejecta-companion interaction. Apart from the pure deflagration explosion models, none of our synthetic light curves exhibit the commonly assumed power-law rise. We demonstrate that this can lead to substantial errors in the determination of the time of explosion. In summary, we illustrate with our calculations that even with very early data an identification of specific explosion scenarios is challenging, if only photometric observations are available.
We have studied the nature of the surface charge distribution in CeTe3. This is a simple, cleavable, layered material with a robust one-dimensional incommensurate charge density wave (CDW). Scanning tunneling microscopy (STM) has been applied on the exposed surface of a cleaved single crystal. At 77 K, the STM images show both the atomic lattice of surface Te atoms arranged in a square net and the CDW modulations oriented at 45 degrees with respect to the Te net. Fourier transform of the STM data shows Te square lattice peaks, and peaks related to the CDW oriented at 45 degrees to the lattice peaks. In addition, clear peaks are present, consistent with subsurface structure and wave vector mixing effects. These data are supported by electronic structure calculations, which show that the subsurface signal most likely arises from a lattice of Ce atoms situated 2.53 angstroms below the surface Te net.
Using first principles simulations we perform a detailed study of the structural, electronic and transport properties of monoatomic platinum chains, sandwiched between platinum electrodes. First we demonstrate that the most stable atomic configuration corresponds to a zigzag arrangement that gradually straightens as the chains are stretched. Secondly, we find that the conductance at equilibrium atomic spacing does not oscillate with the number of atoms $n$ in the chain, but instead decreases almost monotonically with $n$. In contrast, the conductances of chains of fixed $n$ oscillate as the end atoms are pulled apart, due to the gradual closing and opening of conductance channels as the chain straightens.
In this paper we prove a new zero-free region for the partition function of the hard-core model, that is, the independence polynomials of graphs with largest degree $\Delta$. This new domain contains the half disk $$D=\left\{ \lambda \in \mathbb{C}\ |\ \mathrm{Re}(\lambda)\geq 0, |\lambda|\leq \frac{7}{8}\tan \left( \frac{\pi}{2(\Delta-1)}\right)\right\}.$$
The critical behavior of driven lattice gas models has been studied for decades as a paradigm to explore nonequilibrium phase transitions and critical phenomena. However, there exists a long-standing controversy in the universality classes to which they belong. This is of paramount importance as it implies the question of whether or not a microscopic model and its mesoscopic field theory may possess different symmetries in nonequilibrium critical phenomena in contrast to their equilibrium counterparts. Here, we heat with finite rates two generic models of driven lattice gases across their respective nonequilibrium critical points into further nonequilibrium conditions. Employing the theory of finite-time scaling, we are able to unambiguously discriminate the universality classes between the two models. In particular, the infinitely driven lattice gas and the randomly driven lattice gas models belong to different universality classes. These results show that finite-time scaling is effective even in nonequilibrium phase transitions.
Given a compact Riemann surface $X$ with an action of a finite group $G$, the group algebra Q[G] provides an isogenous decomposition of its Jacobian variety $JX$, known as the group algebra decomposition of $JX$. We consider the set of equisymmetric Riemann surfaces $\mathcal{M}(2n-1, D_{2n}, \theta)$ for all $n\geq 2$. We study the group algebra decomposition of the Jacobian $JX$ of every curve $X\in \mathcal{M}(2n-1, D_{2n},\theta)$ for all admissible actions, and we provide affine models for them. We use the topological equivalence of actions on the curves to obtain facts regarding its Jacobians. We describe some of the factors of $JX$ as Jacobian (or Prym) varieties of intermediate coverings. Finally, we compute the dimension of the corresponding Shimura domains.
Relativistic Continuum Random Phase Approximation (CRPA) is used to investigate collective excitation phenomena in several spherical nuclei along the periodic table. We start from relativistic mean field calculations based on a covariant density functional with density dependent zero range forces. From the same functional an effective interaction is obtained as the second derivative with respect to the density. This interaction is used in relativistic continuum-RPA calculations for the investigation of isoscalar monopole, isovector dipole and isoscalar quadrupole resonances of spherical nuclei. In particular we study the low-lying E1 strength in the vicinity of the neutron evaporation threshold. The properties of the resonances, such as centroid energies and strengths distributions are compared with results of discrete RPA calculations for the same model as well as with experimental data.
An analogue of the Fourier transform will be introduced for all square integrable continuous martingale processes whose quadratic variation is deterministic. Using this transform we will formulate and prove a stochastic Heisenberg inequality.