ShantanuT01/DACTYL-Pretraining huggingface dataset:
The exchanged hypercube $EH(s,t)$, proposed by Loh {\it et al.} [The exchanged hypercube, IEEE Transactions on Parallel and Distributed Systems 16 (9) (2005) 866-874], is obtained by removing edges from a hypercube $Q_{s+t+1}$. This paper considers a kind of generalized measures $\kappa^{(h)}$ and $\lambda^{(h)}$ of fault tolerance in $EH(s,t)$ with $1\leqslant s\leqslant t$ and determines $\kappa^{(h)}(EH(s,t))=\lambda^{(h)}(EH(s,t))= 2^h(s+1-h)$ for any $h$ with $0\leqslant h\leqslant s$. The results show that at least $2^h(s+1-h)$ vertices (resp. $2^h(s+1-h)$ edges) of $EH(s,t)$ have to be removed to get a disconnected graph that contains no vertices of degree less than $h$, and generalizes some known results.
A subset of the RR Lyrae (RRL) candidates identified from the Southern Edgeworth-Kuiper Belt Object (SEKBO) survey data has been followed up photometrically (n=106) and spectroscopically (n=51). Period and light curve fitting reveals a 24 +/_ 7% contamination of SEKBO survey data by non-RRLs. This paper focuses on the region of the Virgo Stellar Stream (VSS), particularly on its extension to the South of the declination limits of the SDSS and of the QUEST RRL survey. The distribution of radial velocities in the Galactic standard of rest frame (V_GSR) for the 11 RRLs observed in the VSS region has two apparent peaks. The larger peak coincides with the four RRLs having <V_GSR>=127 +/_ 10 kms-1 and dispersion sigma=27 kms-1, marginally larger than that expected from the errors alone. The two type ab RRLs in this group have <[Fe/H]>=-1.95 +/_ 0.1. Both the radial velocities and metal abundances are consistent with membership in the VSS. The second velocity peak, which occurs at <V_GSR>=-175 +/_ 10 kms-1 may indicate the presence of stars from the Sgr leading tidal tail, which is expected to have large negative velocities in this region. We explore the extent of the VSS by constructing luminosity functions from the SEKBO data and comparing them to data synthesized with the Besancon Galactic model. Analysis of the excess over the model predictions reveals the VSS as a large (~760 deg^2) overdensity centered at roughly (RA, Dec) ~ (186deg, -4deg), spanning a length of ~15 kpc in projection, assuming a heliocentric distance of 19kpc. The data reveal for the first time the more southern regions of the stream and trace it to Dec ~ -15deg and Galactic latitudes as low as b ~ 45deg.
We give a characterization of $BMO^\alpha$-martingale spaces by using fractional Carleson measures. We get the boudedness of martingale transform and square function on $BMO^\alpha$-martingale spaces easily by using this characterization. We also proved the martingale version of Carleson's inequality related with $BMO^\alpha$-martingales.
The brightness temperature fluctuations in the 21 cm background related to neutral Hydrogen distribution provide a probe of physics related to the era of reionization when the intergalactic medium changed from a completely neutral to a partially ionized one. We formulate statistics of 21 cm brightness temperature anisotropies in terms of the angular power spectrum, the bispectrum, and the trispectrum. Using the trispectrum, we estimate the covariance related to the power spectrum measurements and show that correlations resulting from non-Gaussianities are below a percent, at most. While all-sky observations of the 21 cm background at arcminute-scale resolution can be used to measure the bispectrum with a cumulative signal-to-noise ratio of order a few ten, in the presence of foregrounds and instrumental noise related to first-generation interferometers, the measurement is unlikely to be feasible. For most purposes, non-Gaussianities in 21 cm fluctuations can be ignored and the distribution can be described with Gaussian statistics. Since 21 cm fluctuations are significantly contaminated by foregrounds, such as galactic synchrotron or low-frequency radio point sources, the lack of a significant non-Gaussianity in the signal suggests that any significant detection of a non-Gaussianity can be due to foregrounds. Similarly, in addition to frequency information that is now proposed to separate 21 cm fluctuations from foregrounds, if the non-Gaussian structure of foregrounds is a priori known, one can potentially use this additional information to further reduce the confusion.
We examine energy and particle exchange between finite-sized quantum systems and find a new form of nonequilibrium states. The exchange rate undergoes stepwise evolution in time, and its magnitude and sign dramatically change according to system size differences. The origin lies in interference effects contributed by multiply scattered waves at system boundaries. Although such characteristics are utterly different from those of true steady state for infinite systems, Onsager's reciprocal relation remains universally valid.
The generalization of the effective action [1] of the quark--antiquark system in the confining vacuum is performed for the case of arbitrary quark masses. The interaction of quarks is described by the averaged Wilson loop for which we use the minimal area law asymptotics.   The system is quantized by the path integral method and the quantum Hamiltonian is obtained. It contains not only quark degrees of freedom but also the string energy density.   As well as in the equal masses case [1] two dynamical regimes are found [2]: for large orbital excitations ($l \gg 1$) the system is represented as rotating string, which leads to asymptotically linear Regge trajectories, while at small $l$ one obtains a potential-like relativistic or nonrelativistic regime.   In the limiting cases of light-light and heavy-light mesons a unified description is developed [2]. For the Regge trajectories one obtains nearly straight-line patterns with the slope very close to $1/2 \pi \sigma$ and $1/ \pi\sigma$ correspondingly. The upper bound on the light quark(s) masses which doesn't change considerably this property of the trajectories is also found.
In this work, we propose a novel two-stage framework for the efficient 3D point cloud object detection. Instead of transforming point clouds into 2D bird eye view projections, we parse the raw point cloud data directly in the 3D space yet achieve impressive efficiency and accuracy. To achieve this goal, we propose dynamic voxelization, a method that voxellizes points at local scale on-the-fly. By doing so, we preserve the point cloud geometry with 3D voxels, and therefore waive the dependence on expensive MLPs to learn from point coordinates. On the other hand, we inherently still follow the same processing pattern as point-wise methods (e.g., PointNet) and no longer suffer from the quantization issue like conventional convolutions. For further speed optimization, we propose the grid-based downsampling and voxelization method, and provide different CUDA implementations to accommodate to the discrepant requirements during training and inference phases. We highlight our efficiency on KITTI 3D object detection dataset with 75 FPS and on Waymo Open dataset with 25 FPS inference speed with satisfactory accuracy.
In-plane thermal conductivity of the thermoelectric layered cobalt oxides has been measured using the Harman method, in which thermal conductivity is obtained from temperature gradient induced by applied current. We have found that the charge reservoir block (the block other than the CoO$_2$ block) dominates the thermal conduction, where a nano-block integration concept is effective for material design. We have further found that the thermal conductivity shows a small but finite in-plane anisotropy between $a$ and $b$ axes, which can be ascribed to the misfit structure.
In this paper, the Cauchy problem for the one-dimensional (1-D) isentropic compressible Navier-Stokes equations (\textbf{CNS}) is considered. When the viscosity $\mu(\rho)$ depends on the density $\rho$ in a sublinear power law ($ \rho^\delta$ with $0<\delta\leq 1$), based on an elaborate analysis of the intrinsic singular structure of this degenerate system, we prove the global-in-time well-posedness of regular solutions with conserved total mass, momentum, and finite total energy in some inhomogeneous Sobolev spaces. Moreover, the solutions we obtained satisfy that $\rho$ keeps positive for all point $x\in \mathbb{R}$ but decays to zero in the far field, which is consistent with the facts that the total mass of the whole space is conserved, and \textbf{CNS} is a model of non-dilute fluids where $\rho$ is bounded below away from zero. The key to the proof is the introduction of a well-designed reformulated structure by introducing some new variables and initial compatibility conditions, which, actually, can transfer the degeneracies of the time evolution and the viscosity to the possible singularity of some special source terms. Then, combined with the BD entropy estimates and transport properties of the so-called effective velocity $v=u+\varphi(\rho)_x$ ($u$ is the velocity of the fluid, and $\varphi(\rho)$ is a function of $\rho$ defined by $\varphi'(\rho)=\mu(\rho)/\rho^2$), one can obtain the required uniform a priori estimates of corresponding solutions.
We analyze the first cosmological simulations that recover the fragmentation of high-redshift galactic discs driven by cold streams. The fragmentation is recovered owing to an AMR resolution better than 70 pc with cooling below 10^4 K. We study three typical star-forming galaxies in haloes of approx. 5 10^11 Msun at z=2.3, when they were not undergoing a major merger. The steady gas supply by cold streams leads to gravitationally unstable, turbulent discs, which fragment into giant clumps and transient features on a dynamical timescale. The disc clumps are not associated with dark-matter haloes. The clumpy discs are self-regulated by gravity in a marginaly unstable state. Clump migration and angular-momentum transfer on an orbital timescale help the growth of a central bulge with a mass comparable to the disc. The continuous gas input keeps the system of clumpy disc and bulge in a near "steady state", for several Gyr. The average star-formation rate, much of which occurs in the clumps, follows the gas accretion rate of approx. 45 Msun/yr. The simulated galaxies resemble in many ways the observed star-forming galaxies at high redshift. Their properties are consistent with the simple theoretical framework presented in Dekel, Sari & Ceverino (2009). In particular, a two-component analysis reveals that the simulated discs are indeed marginally unstable, and the time evolution confirms the robustness of the clumpy configuration in a cosmological steady state. By z=1 the simulated systems are stabilized by a dominant stellar spheroid, demonstrating the process of "morphological quenching" of star formation (Martig et al. 2009) . We demonstrate that the disc fragmentation is not a numerical artifact once the Jeans length is kept larger than 7 resolution elements, i.e. beyond the standard Truelove criterion.
Let $K/F$ be a quadratic tamely ramified extension of a non-Archimedean local field $F$ of characteristic zero. In this paper, we give an explicit formula for Langlands' lambda function $\lambda_{K/F}$.
We discuss two topics related to the flavor structure of the nucleon sea. The first is on the identification of light-quark intrinsic sea from the comparison between recent data and the intrinsic sea model by Brodsky et al. Good agreement between the theory and data allows a separation of the intrinsic from the extrinsic sea components. The magnitudes of the up, down, and strange intrinsic seas have been extracted. We then discuss the flavor structure and the Bjorken-x dependence of the connected sea (CS) and disconnected sea (DS). We show that recent data together with input from lattice QCD allow a separation of the CS from the DS components of the light quark sea.
On the bases of the Papapetrou equations with various supplementary conditions and other approaches a comparative analysis of the equations of motion of rotating bodies in general relativity is made. The motion of a body with vertical spin in a circular orbit is considered. An expression for the spin-orbit force in a post-Newtonian approximation is investigated.
We study the Casimir torque between two metallic one-dimensional gratings rotated by an angle $\theta$ with respect to each other. We find that, for infinitely extended gratings, the Casimir energy is anomalously discontinuous at $\theta=0$, due to a critical zero-order geometric transition between a 2D- and a 1D-periodic system. This transition is a peculiarity of the grating geometry and does not exist for intrinsically anisotropic materials. As a remarkable practical consequence, for finite-size gratings, the torque per area can reach extremely large values, increasing without bounds with the size of the system. We show that for finite gratings with only 10 period repetitions, the maximum torque is already 60 times larger than the one predicted in the case of infinite gratings. These findings pave the way to the design of a contactless quantum vacuum torsional spring, with possible relevance to micro- and nano-mechanical devices.
Flexoelectricity is the linear response of polarization to a strain gradient. Here we address the simplest class of dielectrics, namely elemental cubic crystals, and we prove that therein there is no extrinsic (i.e. surface) contribution to flexoelectricity in the thermodynamic limit. The flexoelectric tensor is expressed as a bulk response of the solid, manifestly independent of surface configurations. Furthermore, we prove that the flexoelectric responses induced by a long-wavelength phonon and by a uniform strain gradient are identical.
We study the long-time behavior of the unique viscosity solution $u$ of the viscous Hamilton-Jacobi Equation $u_t-\Delta u + |Du|^m = f\hbox{in }\Omega\times (0,+\infty)$ with inhomogeneous Dirichlet boundary conditions, where $\Omega$ is a bounded domain of $\mathbb{R}^N$. We mainly focus on the superquadratic case ($m>2$) and consider the Dirichlet conditions in the generalized viscosity sense. Under rather natural assumptions on $f,$ the initial and boundary data, we connect the problem studied to its associated stationary generalized Dirichlet problem on one hand and to a stationary problem with a state constraint boundary condition on the other hand.
We investigate f-electron charge susceptibility in a two-impurity Anderson model on the basis of Wilson's numerical renormalization group method. The f-electron charge susceptibility diverges logarithmically at the critical point of this model when conduction-electron bands exhibit particle-hole symmetry. Although the critical point disappears without the particle-hole symmetry, the f-electron charge fluctuation is much more enhanced near the crossover regime between the Kondo-Yosida singlet and intersite spin-singlet states than that in the single-impurity case. This result shows that charge fluctuations are enhanced owing to the competition between intersite and Kondo-Yosida spin singlets. A possible scenario for the enhanced residual resistivity near the region where the Kondo temperature becomes comparable with the N\'eel temperatures under pressure in some heavy-fermion compounds is proposed.
The Langevin equation greatly simplifies the mathematical expression of the effects of thermal noise by using only two terms, a dissipation term, and a random-noise term. The Langevin description was originally applied to a system in contact with a single heat reservoir; however, many recent studies have also adopted a Langevin description for systems connected to multiple heat reservoirs. This is accomplished through the introduction of a simple summation for the dissipation and random-noise terms associated with each reservoir. However, the validity of this simple addition has been the focus of only limited discussion and has raised several criticisms. Moreover, this additive description has never been either experimentally or numerically verified, rendering its validity is still an open question. Here, we perform molecular dynamics simulations for a Brownian system in simultaneous contact with multiple heat reservoirs to check the validity of this additive approach. Our simulation results confirm that the effect of multiple heat reservoirs is additive in general.   A very small deviation in the total amount of dissipation and associated noise is found, but seems not significant within statistical errors. We find that the steady-state properties satisfy the additivity perfectly and are not affected by this deviation.
A review is presented on physical properties of the sigma-phase in Fe-Cr and Fe-V alloy systems as revealed both with experimental -- mostly with the Mossbauer spectroscopy -- and theoretical methods. In particular, the following questions relevant to the issue have been addressed: identification of sigma and determination of its structural properties, kinetics of alpha-to-sigma and sigma-to-alpha phase transformations, Debye temperature and Fe-partial phonon density of states, Curie temperature and magnetization, hyperfine fields, isomer shifts and electric field gradients.
Primordial black holes (PBHs) are black holes which may have formed very early on during the radiation dominated era in the early universe. We present here a method by which the large scale perturbations in the density of primordial black holes may be used to place tight constraints on non-gaussianity if PBHs account for dark matter (DM). The presence of local-type non-gaussianity is known to have a significant effect on the abundance of primordial black holes, and modal coupling from the observed CMB scale modes can significantly alter the number density of PBHs that form within different regions of the universe, which appear as DM isocurvature modes. Using the recent \emph{Planck} constraints on isocurvature perturbations, we show that PBHs are excluded as DM candidates for even very small local-type non-gaussianity, $|f_{NL}|\approx0.001$ and remarkably the constraint on $g_{NL}$ is almost as strong. Even small non-gaussianity is excluded if DM is composed of PBHs. If local non-Gaussianity is ever detected on CMB scales, the constraints on the fraction of the universe collapsing into PBHs (which are massive enough to have not yet evaporated) will become much tighter.
Effects of nucleon-nucleon correlations on exclusive $(e,e'p)$ reactions on closed-shell nuclei leading to single-hole states are studied using $^{16}O(e,e'p)^{15}N$ ($6.32$ MeV, $3/2^-$) as an example. The quasi-hole wave function, calculated from the overlap of translationally invariant many-body variational wave functions containing realistic spatial, spin and isospin correlations, seems to describe the initial state of the struck proton accurately inside the nucleus, however it is too large at the surface. The effect of short-range correlations on the final state is found to be largely cancelled by the increase in the transparency for the struck proton. It is estimated that the values of the spectroscopic factors obtained with the DWIA may increase by a few percent due to correlation effects in the final state.
This work presents a scenario of ultra-high energy cosmic ray source distribution where a nearby source is solely responsible for the anisotropies in arrival directions of cosmic rays while the rest of the sources contribute only isotropically. An analytical approach focused on large-scale anisotropies, which are influenced by deflections in a Kolmogorov-type turbulent magnetic field, is employed to provide more general results. When the recent Pierre Auger Observatory angular power spectrum above 8 EeV is used the restricted model gives, under the assumption of the small angle approximation, a solution where the RMS deflection with respect to the line of sight is $\alpha_{\rm rms} = \left(50^{+11}_{-10}\right)^\circ$, while the relative flux from the single source $\eta=0.03\pm 0.01$. Furthermore, the solution can be translated into constraints on the source distance, luminosity, and extra-galactic magnetic field strength. For Centaurus A and the Virgo cluster the required relation between the coherence length and the RMS magnetic field strength is obtained: a coherence length of $~\sim 100\,\mathrm{kpc}$ would imply the RMS field strength around $1\,\mathrm{nG}$ for iron dominated and above $10\,\mathrm{nG}$ for proton dominated composition. We also performed trajectory simulations with our publicly available code CRPropa to show that our analytical model can serve as a good approximation as long as the deflections in cosmic magnetic fields can be described as a random walk. The simulations showed that generally structured fields tend to suppress large-scale anisotropies, especially the dipole, compared to anisotropies at smaller scales described by higher multipoles.
Recently, Giusto and Halpern reported the open-string description of a certain basic class of untwisted open WZW strings, including their associated non-commutative geometry and open-string KZ equations. In this paper, we combine this development with results from the theory of current-algebraic orbifolds to find the open-string description of a corresponding basic class of {\it twisted} open WZW strings, which begin and end on different WZW branes. The basic class of twisted open WZW strings is in 1-to-1 correspondence with the twisted sectors of all closed-string WZW orbifolds, and moreover, the basic class can be decomposed into a large collection of open-string WZW orbifolds. At the classical level, these open-string orbifolds exhibit new {\it twisted non-commutative geometries}, and we also find the relevant {\it twisted open-string KZ equations} which describe these orbifolds at the quantum level. In a related development, we also formulate the closed-string description (in terms of twisted boundary states) of the {\it general} twisted open WZW string.
We consider Stokes systems with measurable coefficients and Lions-type boundary conditions. We show that, in contrast to the Dirichlet boundary conditions, local boundary mixed-norm $L_{s,q}$-estimates hold for the spatial second-order derivatives of solutions, assuming the smallness of the mean oscillations of the coefficients with respect to the spatial variables in small cylinders. In the un-mixed norm case with $s=q=2$, the result is still new and provides local boundary Caccioppoli-type estimates. The main challenges in the work arise from the lack of regularity of the pressure and time derivatives of the solutions and from interaction of the boundary with the nonlocal structure of the system. To overcome these difficulties, our approach relies heavily on several newly developed regularity estimates for both divergence and non-divergence form parabolic equations with coefficients that are only measurable in the time variable and in one of the spatial variables.
We carried out temperature-dependent (20 - 550 K) measurements of resonant inelastic X-ray scattering on LaCoO$_3$ to investigate the evolution of its electronic structure across the spin-state crossover. In combination with charge-transfer multiplet calculations, we accurately quantized the renormalized crystal-field excitation energies and spin-state populations. We show that the screening of the on-site Coulomb interaction of 3d electrons is orbital selective and coupled to the spin-state crossover in LaCoO$_3$. The results establish that the gradual spin-state crossover is associated with a relative change of Coulomb energy versus bandwidth, leading to a Mott-type insulator-to-metal transition.