ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let $G$ be a nontrivial connected graph of order $n$ with an edge-coloring $c:E(G)\rightarrow\{1,2,\dots,t\}$,$t\in\mathbb{N}$, where adjacent edges may be colored with the same color. A tree $T$ in $G$ is a \emph{proper tree} if no two adjacent edges of it are assigned the same color. Let $k$ be a fixed integer with $2\leq k\leq n$. For a vertex subset $S\subseteq V(G)$ with $|S|\geq 2$, a tree is called an \emph{$S$-tree} if it connects $S$ in $G$ . A \emph{$k$-proper coloring} of $G$ is an edge-coloring of $G$ having the property that for every set $S$ of $k$ vertices of $G$, there exists a proper $S$-tree $T$ in $G$. The minimum number of colors that are needed in a $k$-proper coloring of $G$ is defined as the \emph{$k$-proper index} of $G$, denoted by $px_k(G)$. In this paper, we determine the 3-proper index of all complete bipartite and complete multipartite graphs and partially determine the $k$-proper index of them for $k\geq 4$.
We provide homogeneous optical (UBVRI) and near-infrared (JHK) time series photometry for 254 cluster (omega Cen, M4) and field RR Lyrae (RRL) variables. We ended up with more than 551,000 measurements. For 94 fundamental (RRab) and 51 first overtones (RRc) we provide a complete optical/NIR characterization (mean magnitudes, luminosity amplitudes, epoch of the anchor point). The NIR light curves of these variables were adopted to provide new and accurate light-curve templates for both RRc (single period bin) and RRab (three period bins) variables. The templates for the J and the H band are newly introduced, together with the use of the pulsation period to discriminate among the different RRab templates. To overcome subtle uncertainties in the fit of secondary features of the light curves we provide two independent sets of analytical functions (Fourier series, Periodic Gaussian functions). The new templates were validated by using 26 omega Cen and Bulge RRLs covering the four period bins. We found that the difference between the measured mean magnitude along the light curve and the mean magnitude estimated by using the template on a single randomly extracted phase point is better than 0.01 mag (sigma=0.04 mag). We also validated the template on variables for which at least three phase points were available, but without information on the phase of the anchor point. The accuracy of the mean magnitudes is ~0.01 mag (sigma=0.04 mag). The new templates were applied to the Large Magellanic Cloud (LMC) globular Reticulum and by using literature data and predicted PLZ relations we found true distance moduli of 18.47+-0.10+-0.03 mag (J) and 18.49+-0.09+-0.05 mag (K). We also used literature optical and mid-infrared data and we found a mean true distance modulus of 18.47+-0.02+-0.06 mag, suggesting that Reticulum is ~1 kpc closer than the LMC.
We discuss the recently observed "loophole free" violation of Bell's inequalities in the framework of a physically realist view of quantum mechanics, which requires that physical properties are attributed jointly to a system, and to the context in which it is embedded. This approach is clearly different from classical realism, but it does define a meaningful "quantum realism" from a general philosophical point of view. Consistently with Bell test experiments, this quantum realism embeds some form of non-locality, but does not contain any action at a distance, in agreement with quantum mechanics.
Quantum mechanics stands in conflict with local realism only in its treatment of separated systems. A modification of quantum mechanics that changes the handling of separated systems is suggested that can reconcile quantum mechanics with local realism. An apparent obstacle to this program is the experimental evidence, but I argue that the experiments have been misinterpreted. By way of example, I describe a local realistic account of one important EPRB experiment that is claimed to demonstrate nonlocal entanglement. The local model can be calibrated into both quantum and classical domains via adjustment of parameters of the apparatus. Weihs incorrectly dismisses these parameters as uncritical, whereas we show that device calibration is crucial. When properly interpreted, the experiments show that nonlocal entanglement is an error. The rest of quantum mechanics remains intact, and remains highly valued as a powerful probability calculus for observables. Quantum mechanics and local realism can be reconciled, and they each can offer useful paradigms for describing systems.
A quasi-distribution function in phase space (based on Wigner functions) is used to write down the quantum version of Boltzmann equation (Wigner-Boltzmann transport equation). The relaxation time approximation is show to be a good approach when defects are homogeneously distributed and linear response to the external electric field is assumed. An expression for relaxation times based on this formalism is deduced, which consider the dependence in the quantum numbers when confinement effects are important (nanowires and nanosheets).
We propose two new realizations of the N=4, $\hat{c}=4$ superconformal system based on the compact and non-compact versions of parafermionic algebras. The target space interpretation of these systems is given in terms of four-dimensional target spaces with non-trivial metric and topology different from the previously known four-dimensional semi-wormhole realization. The proposed $\hat{c}=4$ systems can be used as a building block to construct perturbatively stable superstring solutions with covariantized target space supersymmetry around non-trivial gravitational and dilaton backgrounds.
License plate detection and recognition (LPDR) is of growing importance for enabling intelligent transportation and ensuring the security and safety of the cities. However, LPDR faces a big challenge in a practical environment. The license plates can have extremely diverse sizes, fonts and colors, and the plate images are usually of poor quality caused by skewed capturing angles, uneven lighting, occlusion, and blurring. In applications such as surveillance, it often requires fast processing. To enable real-time and accurate license plate recognition, in this work, we propose a set of techniques: 1) a contour reconstruction method along with edge-detection to quickly detect the candidate plates; 2) a simple zero-one-alternation scheme to effectively remove the fake top and bottom borders around plates to facilitate more accurate segmentation of characters on plates; 3) a set of techniques to augment the training data, incorporate SIFT features into the CNN network, and exploit transfer learning to obtain the initial parameters for more effective training; and 4) a two-phase verification procedure to determine the correct plate at low cost, a statistical filtering in the plate detection stage to quickly remove unwanted candidates, and the accurate CR results after the CR process to perform further plate verification without additional processing. We implement a complete LPDR system based on our algorithms. The experimental results demonstrate that our system can accurately recognize license plate in real-time. Additionally, it works robustly under various levels of illumination and noise, and in the presence of car movement. Compared to peer schemes, our system is not only among the most accurate ones but is also the fastest, and can be easily applied to other scenarios.
Photoelectric heating (PEH) influences the temperature and density of the interstellar medium (ISM), and potentially also affecting star formation. PEH is expected to have a stronger effect on massive galaxies, as they host larger dust reservoirs compared to dwarf systems. Accordingly, in this paper, we study PEH effects in Milky Way-like galaxies using smoothed particle hydrodynamics (SPH) code which self-consistently implements the evolution of the gas, dust, and interstellar radiation field (ISRF). Dust evolution includes dust formation by stars, destruction by SNe, and growth in dense media. We find that PEH suppresses star formation due to the excess heating that reduces the ISM density. This suppression is seen across the entire range of gas fractions, star formation recipes, dust models, and PEH efficiencies investigated by our code. The suppression ranges from negligible values to approximately a factor of five depending on the specific implementation. Galaxy models having higher gas fraction experience higher star formation suppression. The adopted dust model also alters the extent of star formation suppression. Moreover, when PEH is switched on, galaxy models show higher gas outflow rates and have higher loading factors indicative of enhanced SNe feedback. In gas-rich models (i.e. a gas fraction of 0.5), we also find that PEH suppresses the formation of disk clumps via violent disk instabilities, and thus suppresses bulge formation via clumps migration to the central regions.
We present a many-body calculation for the conductance of a conducting bridge of a simple hydrogen molecule between $Pt$ electrodes.The experimental results showed that the conductance $G=dI/dV$ has the maximum value near the quantum unit $G_{0}=2e^{2}/h$.   The $I-V$ dependence presents peak and dip and we consider that the electron-phonon interaction is responsible for this behavior. At T=0 there is a step in this dependence for the energy of phonons $\omega_{0}$ which satisfies $eV=\omega_{0}$. We calculated the conductance at finite temperature and showed that $dG(T)/dV\propto 1/4T\cosh^{2}\frac{eV-\omega_{0}}{2T}$.
We study the dc-response of the striped state under microwave irradiation. The striped state can be modeled by a two-dimensional electron system under the influence of a unidirectional periodic modulation potential, which was examined in [J. Dietel et al. Phys. Rev. B (71), 045329 (2005)]. We further extend our study of the periodically modulated system to the case of strongly overlapping Landau levels and calculate the dark and photoconductivities. The strength of the modulation potential serves as an additional parameter which allows to vary the overlap of the Landau levels independently of the filling fraction.
We show that any distribution function on $\mathbb{R}^d$ with nonnegative, nonzero and integrable marginal distributions can be characterized by a norm on $\mathbb{R}^{d+1}$, called $F$-norm. We characterize the set of $F$-norms and prove that pointwise convergence of a sequence of $F$-norms to an $F$-norm is equivalent to convergence of the pertaining distribution functions in the Wasserstein metric. On the statistical side, an $F$-norm can easily be estimated by an empirical $F$-norm, whose consistency and weak convergence we establish.   The concept of $F$-norms can be extended to arbitrary random vectors under suitable integrability conditions fulfilled by, for instance, normal distributions. The set of $F$-norms is endowed with a semigroup operation which, in this context, corresponds to ordinary convolution of the underlying distributions. Limiting results such as the central limit theorem can then be formulated in terms of pointwise convergence of products of $F$-norms.   We conclude by showing how, using the geometry of $F$-norms, we may characterize nonnegative integrable distributions in $\mathbb{R}^d$ by simple compact sets in $\mathbb{R}^{d+1}$. We then relate convergence of those distributions in the Wasserstein metric to convergence of these characteristic sets with respect to Hausdorff distances.
We have performed a spectral decomposition to search for recoiling supermassive black holes (rSMBH) in the SDSS QSOs with $z<0.25$. Out of 1271 QSOs, we have identified 26 rSMBH candidates that are recoiling toward us. The projected recoil velocities range from $-76\ \kms$ to $-307\ \kms$ with a mean of $-149\pm58\ \kms$. Most of the rSMBH candidates are hosted by gas-rich LIRGs/ULIRGs, but only 23\% of them shows signs of tidal features suggesting majority of them are advanced mergers. We find that the black hole masses $M_{BH}$ of the rSMBH candidates are on average $\sim$5 times smaller than that of their stationary counterparts and cause a scatter in $M_{BH}-\sigma_*$ relation. The Eddington ratios of all of the rSMBH candidates are larger than 0.1, with mean of 0.52$\pm$0.27, suggesting they are actively accreting mass. Velocity shifts in high-excitation coronal lines suggest that the rSMBH candidates are recoiling with an average velocity of about $-265\ \kms$. Electron density in the narrow line region of the H II rSMBH candidates is about 1/10 of that in AGN rSMBH candidates probably because AGN in the former was more spatially offset than that in the latter. The estimated spatial offsets between the rSMBH candidate and center of host galaxy range from 0.21\as \ to 1.97\as \ and need to be confirmed spatially with high-resolution adaptive optics imaging observations.
We seek to characterize how the change of global rotation rate influences the overall dynamics and large scale flows arising in the convective envelopes of stars covering stellar spectral types from early G to late K. We do so through numerical simulations with the ASH code, where we consider stellar convective envelopes coupled to a radiative interior with various global properties. As solar-like stars spin down over the course of their main sequence evolution, such change must have a direct impact on their dynamics and rotation state. We indeed find that three main states of rotation may exist for a given star: anti-solar-like (fast poles, slow equator), solar-like (fast equator, slow poles), or a cylindrical rotation profile. Under increasingly strict rotational constraints, the latter profile can further evolve into a Jupiter-like profile, with alternating prograde and retrograde zonal jets. We have further assessed how far the convection and meridional flows overshoot into the radiative zone and investigated the morphology of the established tachocline. Using simple mixing length arguments, we are able to construct a scaling of the fluid Rossby number $R_{of} = \tilde{\omega}/2\Omega_* \sim \tilde{v}/2\Omega_* R_*$, which we calibrate based on our 3-D ASH simulations. We can use this scaling to map the behavior of differential rotation versus the global parameters of stellar mass and rotation rate. Finally, we isolate a region on this map ($R_{of} \gtrsim 1.5-2$) where we posit that stars with an anti-solar differential rotation may exist in order to encourage observers to hunt for such targets.
The quantum teleportation protocol is extracted directly out of a standard classical circuit that exchanges the states of two qubits using only controlled-NOT gates. This construction of teleportation from a classically transparent circuit generalizes straightforwardly to d-state systems.
In this work, wormholes, tunnel like structures introduced by Morris \& Thorne \cite{Morris95}, are explored within the framework of $f(R)$ gravity. Using the shape function $b(r)=r_0\big(\frac{r}{r_0}\big)^\gamma$, where $0<\gamma<1$, and the equation of state $p_r=\omega\rho$, the $f(R)$ function is derived and the field equations are solved. Then null, weak, strong and dominated energy conditions are analyzed and spherical regions satisfying these energy conditions are determined. Furthermore, we calculated the range of the radius of the throat of the wormhole, where the energy conditions are satisfied.
New optical and infrared observations along the sight-line toward the quasar OI 363 (0738+313) are presented and discussed. Excluding systems which lack confirming UV spectroscopic observations of the actual Lyman alpha line, this sight-line presently contains the two lowest-redshift classical damped Lyman alpha (DLA) quasar absorption line systems known (i.e. with N(HI) \ge 2 x 10^{20} atoms cm^{-2}), one at z(abs)=0.0912 and the other at z(abs)=0.2212. The z=0.09 DLA galaxy appears to be an extended low surface brightness galaxy which is easily visible only in infrared images and shows rich morphological structure. Subtraction of the quasar nuclear and host light yields L_K \approx 0.08L_K* at z=0.09. The impact parameter between the galaxy and quasar sight-line is very small, b<3.6 kpc (<2 arcsec), which makes measurements difficult. The z=0.22 DLA galaxy is an early-type dwarf with a K-band luminosity of L_K \approx 0.1L_K* at impact parameter b=20 kpc. In general, these results serve to support mounting evidence that DLA galaxies are drawn from a wide variety of gas-rich galaxy types. (Abridged)
Interplay between the dependence of symmetry energy on density and the variation of nucleonic densities across nuclear surface is discussed. That interplay gives rise to the mass dependence of the symmetry coefficient in an energy formula. Charge symmetry of the nuclear interactions allows to introduce isoscalar and isovector densities that are approximately independent of the magnitude of neutron-proton asymmetry.
We propose a new, two-stage algorithm for inverting strong gravitational lenses. The key to the algorithm is decoupling the effects of lens magnification and intrinsic structure in the background source in the appearance of lensed arcs. First, the distribution of mass on the deflector plane and the geometry of the source-deflector-observer optical system are established. This is done by numerically simulating the lensing of light past a parametric mass model, and adjusting the handful of model parameters to match the positions and shapes of the observed and simulated lensed arcs. At the same time, this determines the magnification of the background source induced by the lensing process. The predicted magnification is then removed from the data to reveal the intrinsic, though still distorted, background distribution of light. After tracing each lensed ray back to the source plane, the data are combined to produce a surface brightness distribution of the source. This two-stage inversion scheme produces a parametric model of the deflector and a pixelized rendering of the background source which together mimic the observed gravitationally lensed features. We test the viability of scheme itself on a well-studied collection of lensed objects in the galaxy-cluster MS 2137. Confident in the algorithm, we apply it second time to predict the distribution of mass in the galaxy-cluster MS 1455 responsible for an observed triplet of lensed arcs. Our predictions about the lens in MS 1455 make it particularly interesting, for a single background source is responsible for both tangential arcs and a radial arc.
The results of paper [1] are generalized for vacuum type-III solutions with, in general, a non-vanishing cosmological constant Lambda. It is shown that all curvature invariants containing derivatives of the Weyl tensor vanish if a type-III spacetime admits a non-expanding and non-twisting null geodesic congruence.   A non-vanishing curvature invariant containing first derivatives of the Weyl tensor is found in the case of type-III spacetime with expansion or twist.
A new ground-based wide-field extensive air shower array known as the High-Altitude Water Cherenkov (HAWC) Observatory promises a new window to monitoring the $\sim$100 GeV gamma-ray sky with the potential for detecting a high energy spectral cutoff in gamma-ray bursts (GRBs). It represents a roughly 15 times sensitivity gain over the previous generation of wide-field gamma-ray air shower instruments and is able to detect the Crab Nebula at high significance ($>$5 $\sigma$) with each daily transit. Its wide field-of-view ($\sim$2 sr) and $>$95% uptime make it an ideal instrument for detecting GRB emission at $\sim$100 GeV with an expectation for observing $\sim$1 GRB per year based on existing measurements of GRB emission.   An all-sky, self-triggered search for VHE emission produced by GRBs with HAWC has been developed. We present the results of this search on three characteristic GRB emission timescales, 0.2 seconds, 1 second, and 10 seconds, in the first year of the fully-populated HAWC detector which is the most sensitive dataset to date. No significant detections were found, allowing us to place upper limits on the rate of GRBs containing appreciable emission in the $\sim$100 GeV band. These constraints exclude previously unexamined parameter space.
We study the diffusion process through an ideal polymer network, using numerical methods. Polymers are modeled by random walks on the bonds of a two-dimensional square lattice. Molecules occupy the lattice cells and may jump to the nearest-neighbor cells, with probability determined by the occupation of the bond separating the two cells. Subjected to a concentration gradient across the system, a constant average current flows in the steady state. Its behavior appears to be a non-trivial function of polymer length, mass density and temperature, for which we offer qualitative explanations.
We present an efficient and accurate algorithm for principal component analysis (PCA) of a large set of two dimensional images, and, for each image, the set of its uniform rotations in the plane and its reflection. The algorithm starts by expanding each image, originally given on a Cartesian grid, in the Fourier-Bessel basis for the disk. Because the images are bandlimited in the Fourier domain, we use a sampling criterion to truncate the Fourier-Bessel expansion such that the maximum amount of information is preserved without the effect of aliasing. The constructed covariance matrix is invariant to rotation and reflection and has a special block diagonal structure. PCA is efficiently done for each block separately. This Fourier-Bessel based PCA detects more meaningful eigenimages and has improved denoising capability compared to traditional PCA for a finite number of noisy images.
We obtain critical pair theorems for subsets S and T of an abelian group such that |S+T| < |S|+|T|+1. We generalize some results of Chowla, Vosper, Kemperman and a more recent result due to Rodseth and one of the authors.
A graph $G=(V(G), E(G))$ is supereulerian if it has a spanning Eulerian subgraph. Let $\ell(G)$ be the maximum number of edges of spanning Eulerian subgraphs of a supereulerian graph $G$. In $1996$, Catlin conjectured that if $G$ is a supereulerian graph, then $\ell(G)\ge \frac{2}{3}|E(G)|$. But in $2004$, infinitely many counterexamples were found for this conjecture and it was shown that this conjecture holds for $r$-regular graphs when $r\neq 5$. In this paper we show that Catlin's Conjecture holds for graphs having no vertex with degree $3$ and also it holds for $5$-regular graphs. Moreover, if $G$ is a graph having no vertex with degree $3$, then $\ell(G)\ge \frac{2}{3}|E(G)|+ v_2(G)$, when $v_2(G)$ is the number of vertices of degree $2$.
In this paper we study the existence phase transition of the random fractal ball model and the random fractal box model. We show that both of these are in the empty phase at the critical point of this phase transition.
Symmetries of generalized gravitational actions, yielding field equations which typically involve at most second-order derivatives of the metric, are considered. The field equations for several different higher-derivative theories in the first-order formalism are derived, and variations of a generic set of higher-order curvature terms appearing in string effective actions are studied. It is shown that there often exists a particular set of solutions to the field equations of pure gravity theories, consisting of different combinations of curvature tensors, which satisfies the vacuum equations with cosmological constant. Implications of generalized symmetries of the field equations derived from the superstring effective action for the cosmological constant problem are discussed.