ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper we study pattern-replacement equivalence relations on the set $S_n$ of permutations of length $n$. Each equivalence relation is determined by a set of patterns, and equivalent permutations are connected by pattern-replacements in a manner similar to that of the Knuth relation.   One of our main results generalizes the celebrated Erdos-Szekeres Theorem for permutation pattern-avoidance to a new result for permutation pattern-replacement. In particular, we show that under the $\{123 \cdots k, k \cdots 321\}$-equivalence, all permutations in $S_n$ are equivalent up to parity when $n \ge \Omega(k^2)$.   Additionally, we extend the work of Kuszmaul and Zhou on an infinite family of pattern-replacement equivalences known as the rotational equivalences. Kuszmaul and Zhou proved that the rotational equivalences always yield either one or two nontrivial equivalence classes in $S_n$, and conjectured that the number of nontrivial classes depended only on the patterns involved in the rotational equivalence (rather than on $n$). We present a counterexample to their conjecture, and prove a new theorem fully classifying (for large $n$) when there is one nontrivial equivalence class and when there are two nontrivial equivalence classes.   Finally, we computationally analyze the pattern-replacement equivalences given by sets of pairs of patterns of length four. We then focus on three cases, in which the number of nontrivial equivalence classes matches an OEIS sequence. For two of these we present full proofs of the enumeration and for the third we suggest a potential future method of proof.
Aims: We aim to determine the effect of converging flows on the evolution of a bipolar magnetic region (BMR), and to investigate the role of these inflows in the generation of poloidal flux. We also discuss whether the flux dispersal due to turbulent flows can be described as a diffusion process.   Methods: We developed a simple surface flux transport model based on point-like magnetic concentrations. We tracked the tilt angle, the magnetic flux and the axial dipole moment of a BMR in simulations with and without inflows and compared the results. To test the diffusion approximation, simulations of random walk dispersal of magnetic features were compared against the predictions of the diffusion treatment.   Results: We confirm the validity of the diffusion approximation to describe flux dispersal on large scales. We find that the inflows enhance flux cancellation, but at the same time affect the latitudinal separation of the polarities of the bipolar region. In most cases the latitudinal separation is limited by the inflows, resulting in a reduction of the axial dipole moment of the BMR. However, when the initial tilt angle of the BMR is small, the inflows produce an increase in latitudinal separation that leads to an increase in the axial dipole moment in spite of the enhanced flux destruction. This can give rise to a tilt of the BMR even when the BMR was originally aligned parallel to the equator.
Of late, weakly supervised object detection is with great importance in object recognition. Based on deep learning, weakly supervised detectors have achieved many promising results. However, compared with fully supervised detection, it is more challenging to train deep network based detectors in a weakly supervised manner. Here we formulate weakly supervised detection as a Multiple Instance Learning (MIL) problem, where instance classifiers (object detectors) are put into the network as hidden nodes. We propose a novel online instance classifier refinement algorithm to integrate MIL and the instance classifier refinement procedure into a single deep network, and train the network end-to-end with only image-level supervision, i.e., without object location information. More precisely, instance labels inferred from weak supervision are propagated to their spatially overlapped instances to refine instance classifier online. The iterative instance classifier refinement procedure is implemented using multiple streams in deep network, where each stream supervises its latter stream. Weakly supervised object detection experiments are carried out on the challenging PASCAL VOC 2007 and 2012 benchmarks. We obtain 47% mAP on VOC 2007 that significantly outperforms the previous state-of-the-art.
We demonstrate a method that merges the quantum filter diagonalization (QFD) approach for hybrid quantum/classical solution of the time-independent electronic Schr\"odinger equation with a low-rank double factorization (DF) approach for the representation of the electronic Hamiltonian. In particular, we explore the use of sparse "compressed" double factorization (C-DF) truncation of the Hamiltonian within the time-propagation elements of QFD, while retaining a similarly compressed but numerically converged double-factorized representation of the Hamiltonian for the operator expectation values needed in the QFD quantum matrix elements. Together with significant circuit reduction optimizations and number-preserving post-selection/echo-sequencing error mitigation strategies, the method is found to provide accurate predictions for low-lying eigenspectra in a number of representative molecular systems, while requiring reasonably short circuit depths and modest measurement costs. The method is demonstrated by experiments on noise-free simulators, decoherence- and shot-noise including simulators, and real quantum hardware.
The flavor puzzle of the Standard Model is explained in split fermion models by having the fermions localized and separated in an extra dimension. Many of these models assume a certain profile for the Higgs VEV, usually uniform, or confined to a brane, without providing a dynamical realization for it. By studying the effect of the coupling between the Higgs and the localizer fields, we obtain these scenarios as results, rather than ansaetze. Moreover, we discuss other profiles and show that they are phenomenologically viable.
We report an ultra-bright lensed submillimeter galaxy at $z_{spec}=1.4796$, identified as a result of a full-sky cross-correlation of the AllWISE and Planck compact source catalogs aimed to search for bright submillimeter galaxies at $z \sim 1.5-2.8$. APEX/LABOCA observations of the candidate galaxy reveal a source with flux (S$_{870 \mu m}= 54\pm 8$ mJy). The position of the APEX source coincides with the position of the AllWISE mid-IR source, and with the Einstein ring GAL-CLUS-022058s, observed with the HST. Archival VLT/FORS observations reveal the redshift of this Einstein ring, $z_{spec}=1.4796$, and detection of the CO(5-4) line at $z_{spec} = 1.4802$ with APEX/nFLASH230 confirms the redshift of the submillimeter emission. The lensed source appears to be gravitationally magnified by a massive foreground galaxy cluster lens at $z = 0.36$. We use Lenstool to model the gravitational lensing, which is near to a "fold arc" configuration for an elliptical mass distribution of the central halo, where four images of the lensed galaxy are seen; the mean magnification is $\mu_{\rm L} =18\pm 4$. We have determined an intrinsic rest-frame infrared luminosity of $L_{IR} \approx 10^{12} L_\odot $ and a likely star formation rate of $\sim 70-170$ $M_\odot\ yr^{-1}$. The molecular gas mass is $M_{mol} \sim 2.6 \times 10^{10} M_\odot$ and the gas fraction is $f = 0.34\pm 0.07$. We also obtain a stellar mass log$(M_\ast/M_\odot) = 10.7 \pm 0.1$ and a specific star formation rate log$(sSFR/Gyr^{-1})=0.15 \pm 0.03$. This galaxy lies on the so-called main sequence of star-forming galaxies at this redshift.
The isoscalar giant monopole resonance (ISGMR) in Cd, Sn and Pb isotopes has been studied within the self-consistent Skyrme Hartree-Fock+BCS and quasi-particle random phase approximation (QRPA). Three Skyrme parameter sets are used in the calculations, i.e., SLy5, SkM* and SkP, since they are characterized by different values of the compression modulus in symmetric nuclear matter, namely K=230, 217, and 202 MeV, respectively. We also investigate the effect of different types of pairing forces on the ISGMR in Cd, Sn and Pb isotopes. The calculated peak energies and the strength distributions of ISGMR are compared with available experimental data. We find that SkP fails completely to describe the ISGMR strength distribution for all isotopes due to its low value of the nuclear matter incompressibility, namely K=202 MeV. On the other hand, the SLy5 parameter set, supplemented by an appropriate pairing interaction, gives a reasonable description of the ISGMR in Cd and Pb isotopes. A better description of ISGMR in Sn isotopes is achieved by the SkM* interaction, that has a somewhat softer value of the nuclear incompressibility.
For one-dimensional stochastic Burgers equation driven by Brownian motion and Poisson process, we study the $\psi$-uniformly exponential ergodicity with $\psi(x)=1+\|x\|$, the moderate deviation principle and the large deviation principle for the occupation measures.
We report that a spin-1/2 tetrahedral Heisenberg chain realizes a gapless symmetry-protected topological (gSPT) phase characterized by the coexistence of the Tomonaga-Luttinger-liquid criticality due to chirality degrees of freedom and the symmetry-protected edge state due to spin degrees of freedom. This gSPT phase has an interesting feature that no symmetry forbids the trivial spin gap opening but a discrete symmetry, $\mathbb Z_3\times\mathbb Z_2^T$, forbids the unique gapped ground state. In the first part of the paper, we numerically show the coexistence of a critical entanglement entropy and a nontrivially degenerate entanglement spectrum based on the density-matrix renormalization group (DMRG) method.Next, we clarify that chirality degrees of freedom form the Tomonaga-Luttinger liquid while spin degrees of freedom form the spin-1 Haldane state based on a degenerate perturbation theory. Last but not least, we discuss the Lieb-Schultz-Mattis-type ingappability in the gSPT phase, using a local $\mathbb{Z}_3$ rotation. We can thus characterize our gSPT phase as a symmetry-protected critical phase protected by the $\mathbb{Z}_3$ on-site symmetry, the $\mathbb{Z}_2^T$ time-reversal symmetry, the lattice translation symmetry, and the U(1) spin-rotation symmetry.
In the thermodynamic limit, a many-body ground state has zero overlap with another state which is a slightly perturbed state of the original one, known as the Anderson orthogonality catastrophe (AOC). The amplitude of the overlap for two generic ground states typically exhibits exponential or power-law decay as the system size increases to infinity. In this paper, we show that for generic $(2+1)$-D topological systems at fixed points, there exists a universal topological response term in the scaling of the ground-state overlap. For Laughlin wave functions, in particular, we also find a leading term decaying faster than exponential, which is beyond AOC. Such finite-size scaling behaviors could be utilized to theoretically detect the gapless edge modes, distinguish the topology of quantum states or serve as a signature for topological phase transitions.
We study an optimal M-partition problem for the Yamabe equation on the round sphere, in the presence of some particular symmetries. We show that there is a correspondence between solutions to this problem and least-energy sign-changing symmetric solutions to the Yamabe equation on the sphere with precisely M nodal domains. The existence of an optimal partition is established through the study of the limit profiles of least-energy solutions to a weakly coupled competitive elliptic system on the sphere.
New strong non-spiralling-in gravitational wave (GW) source for LIGO/VIRGO detectors are proposed. Double O-Ne-Mg white dwarf mergers can produce strong gravitational waves with frequencies in the several hundreds Hz range. Such events can be followed by a Super Nova type Ia.
In order to constrain the bolometric luminosities, dust properties and molecular gas content of giant Lyman alpha nebulae, the so-called Lyman alpha blobs, we have carried out a study of dust continuum and CO line emission in two well-studied representatives of this population at z ~ 3: a Lya blob discovered by its strong Spitzer MIPS 24um detection (LABd05; Dey et al. 2005) and the Steidel blob 1 (SSA22-LAB01; Steidel et al. 2000). We find that the spectral energy distribution of LABd05 is well described by an AGN-starburst composite template with L(FIR) = (4.0 +/- 0.5) x 10^12 Lsun, comparable to high-z sub-millimeter galaxies and ultraluminous infrared galaxies. New APEX/LABOCA 870um measurements rule out the reported SCUBA detection of the SSA22-LAB01 (S[850um] = 16.8 mJy) at the > 4sigma level. Consistent with this, ultra-deep Plateau de Bure Interferometer (PdBI) observations with ~2arcsec spatial resolution also fail to detect any 1.2mm continuum source down to ~0.45mJy per beam (3sigma). Combined with the existing (sub)mm observations in the literature, we conclude that the FIR luminosity of SSA22-LAB01 remains uncertain. No CO line is detected in either case down to integrated flux limits of (Snu dV) < 0.25--1.0 Jy km/s, indicating a modest molecular gas reservoir, M(H_2) < 1--3 x 10^10 Msun. The non-detections exclude, with high significance (12 sigma), the previous tentative detection of a CO(4-3) line in the SSA22-LAB01. The increased sensitivity afforded by ALMA will be critical in studying molecular gas and dust in these interesting systems.
Recent realizations of single-atom trapping and tracking in cavity QED open the door for feedback schemes which actively stabilize the motion of a single atom in real time. We present feedback algorithms for cooling the radial component of motion for a single atom trapped by strong coupling to single-photon fields in an optical cavity. Performance of various algorithms is studied through simulations of single-atom trajectories, with full dynamical and measurement noise included. Closed loop feedback algorithms compare favorably to open-loop "switching" analogs, demonstrating the importance of applying actual position information in real time. The high optical information rate in current experiments enables real-time tracking that approaches the standard quantum limit for broadband position measurements, suggesting that realistic active feedback schemes may reach a regime where measurement backaction appreciably alters the motional dynamics.
A new algebraic Cayley graph is constructed using finite fields. Its connectedness and diameter bound are studied via Weil's estimate for character sums. These graphs provide a new source of expander graphs, extending classical results of Chung.
This is an improved version of the eprint previously entitled "Unexpected isomorphisms between hyperk\"ahler fourfolds."   We study smooth projective hyperk\"ahler fourfolds that are deformations of Hilbert squares of K3 surfaces and are equipped with a polarization of fixed degree and divisibility. They are parametrized by a quasi-projective irreducible 20-dimensional moduli space and Verbitksy's Torelli theorem implies that their period map is an open embedding.   Our main result is that the complement of the image of the period map is a finite union of explicit Heegner divisors that we describe. We also prove that infinitely many Heegner divisors in a given period space have the property that their general points correspond to fourfolds which are isomorphic to Hilbert squares of a K3 surfaces, or to double EPW sextics.   In two appendices, we determine the groups of biregular or birational automorphisms of various projective hyperk\"ahler fourfolds with Picard number 1 or 2.
We present magnetic and transport measurements on La5/8-yPryCa3/8MnO3 with y = 0.3, a manganite compound exhibiting intrinsic multiphase coexistence of sub-micrometric ferromagnetic and antiferromagnetic charge ordered regions. Time relaxation effects between 60 and 120K, and the obtained magnetic and resistive viscosities, unveils the dynamic nature of the phase separated state. An experimental procedure based on the derivative of the time relaxation after the application and removal of a magnetic field enables the determination of the otherwise unreachable equilibrium state of the phase separated system. With this procedure the equilibrium phase fraction for zero field as a function of temperature is obtained. The presented results allow a correlation between the distance of the system to the equilibrium state and its relaxation behavior.
We propose a new interpretation of the BFSS large N matrix quantum mechanics analogous to a novel interpretation of the IKKT matrix model where infinitely large N matrices act as differential operators in a curved space. In this picture, the Schr\"odinger equation in the BFSS model is regarded as the Wheeler-DeWitt equation which determines the wave function of universe. An explicit solution of wave function is studied in a simple two-dimensional minisuperspace model.
Image quality measurement is a critical problem for image super-resolution (SR) algorithms. Usually, they are evaluated by some well-known objective metrics, e.g., PSNR and SSIM, but these indices cannot provide suitable results in accordance with the perception of human being. Recently, a more reasonable perception measurement has been proposed in [1], which is also adopted by the PIRM-SR 2018 challenge. In this paper, motivated by [1], we aim to generate a high-quality SR result which balances between the two indices, i.e., the perception index and root-mean-square error (RMSE). To do so, we design a new deep SR framework, dubbed Bi-GANs-ST, by integrating two complementary generative adversarial networks (GAN) branches. One is memory residual SRGAN (MR-SRGAN), which emphasizes on improving the objective performance, such as reducing the RMSE. The other is weight perception SRGAN (WP-SRGAN), which obtains the result that favors better subjective perception via a two-stage adversarial training mechanism. Then, to produce final result with excellent perception scores and RMSE, we use soft-thresholding method to merge the results generated by the two GANs. Our method performs well on the perceptual image super-resolution task of the PIRM 2018 challenge. Experimental results on five benchmarks show that our proposal achieves highly competent performance compared with other state-of-the-art methods.
We analyze a (120 h^{-1} Mpc)^3 adaptive mesh refinement hydrodynamic simulation that contains a higher-resolution 31 x 31 x 35 h^{-3} Mpc subvolume centered on a ~30 Mpc diameter void. Our detailed ~1 kpc resolution allows us to identify 1300 galaxies within this void to a limiting halo mass of ~10^{10} M_sun. Nearly 1000 galaxies are found to be in underdense regions, with 300 galaxies residing in regions less than half the mean density of the simulation volume. We construct mock observations of the stellar and gas properties of these systems, and reproduce the range of colors and luminosities observed in the SDSS for nearby (z < 0.03) galaxies. We find no trends with density for the most luminous (M_r < -18) galaxies, however our dwarf void galaxies (M_r > -16), though they are less reliably resolved, typically appear bluer, with higher rates of star formation and specific star formation and lower mean stellar ages than galaxies in average density environments. We find a significant population of low luminosity (M_r ~ -14) dwarf galaxies that is preferentially located in low density regions and specifically in the void center. This population may help to reduce, but not remove, the discrepancy between the predicted and observed number of void galaxies.
We investigate the multi-wavelength emission of BzK selected star forming galaxies at z~2 in the Great Observatories Origins Deep Survey (GOODS) North region. Most (82%) of the sources are individually detected at 24um in the Spitzer MIPS imaging, and one fourth (26%) in the VLA radio data. Significant detections of the individually undetected objects are obtained through stacking in the radio, submm and X-ray domains. The typical star forming galaxy with stellar mass ~10^{11}Mo at z=2 is an Ultra-luminous Infrared Galaxy (ULIRG), with L_IR ~ 1-2x10^{12}Lo and star formation rate SFR 200-300Mo/yr, implying a comoving density of ULIRGs at z=2 at least 3 orders of magnitude above the local one. SFRs derived from the reddening corrected UV luminosities agree well, on average, with the longer wavelength estimates. The high 24um detection rate suggests a relatively large duty cycle for the BzK star forming phase, consistently with the available independent measurements of the space density of passively evolving galaxies at z>1.4. If the IMF at z=2 is similar to the local one, and in particular is not a top-heavy IMF, this suggests that a substantial fraction of the high mass tail (>10^{11}Mo) of the galaxy stellar mass function was completed by z~1.4.
We consider diagonal and non-diagonal QCD sum rules for the ground state heavy baryons to leading order in $1/m_Q$ and at next-to-leading order in $\alpha_S$. In the non-diagonal case we evaluate the eight different two-loop diagrams which determine the perturbative $\alpha_S$-corrections to the Wilson coefficient of the quark condensate in the Operator Product Expansion. The QCD corrections to the non-diagonal sum rules are moderate compared to the QCD corrections in the diagonal case. We also consider constituent type sum rules using constituent type interpolating currents. The obtained results are in reasonable agreement with the corresponding results obtained in the diagonal case. As central values for the bound state energies we find $m(\Lambda_Q)-m_Q = 760 MeV$ and $m(\Sigma_Q)-m_Q = 940 MeV$. The central values for the residues are given by $F(\Lambda_Q) = 0.030 GeV^3$ and $F(\Sigma_Q) = 0.038 GeV^3$.
Digital signature is a key technique in information security, especially for identity authentications. Compared with classical correspondence, quantum digital signatures (QDSs) provide a considerably higher level of security, i.e., information-theoretic security. At present, its performance is limited by key generation protocols (e.g., BB84 or measurement-device-independent protocols), which are fundamentally limited in terms of channel capacity. Fortunately, the recently proposed twin-field quantum key distribution can overcome this limit. This paper presents a twin-field QDS protocol and details a corresponding security analysis. In its distribution stage, a specific key generation protocol, the sending-or-not-sending twin-field protocol, has been adopted and full parameter optimization method has been implemented. Numerical simulation results show that the new protocol exhibits outstanding security and practicality compared with all other existing protocols. Therefore, the new protocol paves the way toward real-world applications of QDSs
We report on the detection of an atomic jet associated with the protostellar source SMM1 (FIRS1) in Serpens. The jet is revealed in [FeII] and [NeII] line maps observed with Spitzer/IRS, and further confirmed in HiRes IRAC and MIPS images. It is traced very close to SMM1 and peaks at ~5 arcsec" from the source at a position angle of $\sim 125 degrees. In contrast, molecular hydrogen emission becomes prominent at distances > 5" from the protostar and extends at a position angle of 160 degrees. The morphological differences suggest that the atomic emission arises from a companion source, lying in the foreground of the envelope surrounding the embedded protostar SMM1. In addition the molecular and atomic Spitzer maps disentangle the large scale CO (3-2) emission observed in the region into two distinct bipolar outflows, giving further support to a proto-binary source setup. Analysis at the peaks of the [FeII] jet show that emission arises from warm and dense gas (T ~1000 K, n(electron) 10^5 - 10^6 cm^-3). The mass flux of the jet derived independently for the [FeII] and [NeII] lines is 10^7 M(sun)/yr, pointing to a more evolved Class~I/II protostar as the driving source. All existing evidence converge to the conclusion that SMM1 is a non-coeval proto-binary source.