ShantanuT01/DACTYL-Pretraining huggingface dataset:
A key goal of digital quantum computing is the simulation of fermionic systems such as molecules or the Hubbard model. Unfortunately, for present and near-future quantum computers the use of quantum error correction schemes is still out of reach. Hence, the finite error rate limits the use of quantum computers to algorithms with a low number of gates. The variational Hamiltonian ansatz (VHA) has been shown to produce the ground state in good approximation in a manageable number of steps. Here we study explicitly the effect of gate errors on its performance. The VHA is inspired by the adiabatic quantum evolution under the influence of a time-dependent Hamiltonian, where the - ideally short - fixed Trotter time steps are replaced by variational parameters. The method profits substantially from quantum variational error suppression, e.g., unitary quasi-static errors are mitigated within the algorithm. We test the performance of the VHA when applied to the Hubbard model in the presence of unitary control errors on quantum computers with realistic gate fidelities.
Panoptic Part Segmentation (PPS) aims to unify panoptic segmentation and part segmentation into one task. Previous work mainly utilizes separated approaches to handle thing, stuff, and part predictions individually without performing any shared computation and task association. In this work, we aim to unify these tasks at the architectural level, designing the first end-to-end unified method named Panoptic-PartFormer. In particular, motivated by the recent progress in Vision Transformer, we model things, stuff, and part as object queries and directly learn to optimize the all three predictions as unified mask prediction and classification problem. We design a decoupled decoder to generate part feature and thing/stuff feature respectively. Then we propose to utilize all the queries and corresponding features to perform reasoning jointly and iteratively. The final mask can be obtained via inner product between queries and the corresponding features. The extensive ablation studies and analysis prove the effectiveness of our framework. Our Panoptic-PartFormer achieves the new state-of-the-art results on both Cityscapes PPS and Pascal Context PPS datasets with at least 70% GFlops and 50% parameters decrease. In particular, we get 3.4% relative improvements with ResNet50 backbone and 10% improvements after adopting Swin Transformer on Pascal Context PPS dataset. To the best of our knowledge, we are the first to solve the PPS problem via \textit{a unified and end-to-end transformer model. Given its effectiveness and conceptual simplicity, we hope our Panoptic-PartFormer can serve as a good baseline and aid future unified research for PPS. Our code and models are available at https://github.com/lxtGH/Panoptic-PartFormer.
We establish the large central charge behaviour of the entanglement negativity for a mixed state configuration of a single interval enclosed between two intervals in a holographic $CFT_{1+1}$. To this end we utilize the monodromy technique to elucidate the large central charge limit of a four point twist correlator which characterizes the negativity of the mixed state configuration. Subsequently we analyze the large central charge limit of the six point twist correlator which reduces to the above four point correlator in a specific limit. The results provide a strong consistency check for our recently proposed holographic entanglement negativity conjecture in the $AdS_3/CFT_2$ scenario.
We examine the correlation function \xi of the Sloan Digital Sky Survey (SDSS) Luminous Red Galaxy sample (LRG) at large scales (60<s<400 Mpc/h) using the final data release (DR7; 105,831 LRGs between 0.16<z<0.47). Using mock catalogs, we demonstrate that the observed baryonic acoustic peak and larger scale signal are consistent with LCDM at the 1.5\sigma level. The signal at 155<s<200 Mpc/h tends to be high relative to theoretical expectations; this slight deviation can be attributed to a bright subsample of the LRGs. Fitting data to a non-linear, redshift-space, template based-model, we constrain the peak position at s_p=103.6+3.6-2.4 Mpc/h when fitting the range 60<s<150 Mpc/h (1\sigma uncertainties measured from the mocks. This redshift-space distance s_p is related to the comoving sound horizon scale r_s after taking into account matter clustering non-linearities, redshift distortions and galaxy clustering bias. Mock catalogs show that the probability that a DR7-sized sample would not have an identifiable peak is at least 10%. As a consistency check of a fiducial cosmology, we use the observed s_p to obtain the distance D_V=[(1+z)^2D_A^2cz/H(z)]^(1/3) relative to the acoustic scale. We find r_s/D_V(z=0.278)=0.1394+-0.0049. This result is in excellent agreement with Percival et. al (2009), who examine roughly the same data set, but using the power spectrum. Comparison with other determinations in the literature are also in very good agreement. We have tested our results against a battery of possible systematic effects, finding all effects are smaller than our estimated sample variance.
One of the defining differences between classical and quantum systems is how measurements affect them. Here, we compare the approaches of contextuality and quantum discord in capturing quantum correlations in special classes of two-qubit states, demonstrating that although non-discordant states are non-contextual, discordant states are not always contextual.
Recent progress in the theory of hadrons containing a single heavy quark is reviewed. Particular attention is paid to those aspects that bear on the determination of the magnitudes of the Cabibbo--Kobayashi--Maskawa matrix elements $V_{cb}$ and $V_{ub}$.}
In the paper, the occurrence of zeros and ones in the binary expansion of the primes is studied. In particular the statement in the title is established. The proof is unconditional.
Well-known results of Lagrange and Jacobi prove that the every $m \in \mathbb N$ can be expressed as a sum of four integer squares, and the number $r(m)$ of such representations can be given by an explicit formula in $m$. In this paper, we prove that the only real quadratic number field for which the sum of four squares is universal is $\mathbb Q(\sqrt{5})$. We provide explicit formulas for $r(m)$ for $K= \mathbb Q (\sqrt{2})$ and $K= \mathbb Q(\sqrt{5})$. We then consider the theta series of the sum of four squares over any real quadratic number field, providing explicit upper and lower bounds for the Eisenstein coefficients. Last, we include examples of the complete theta series decomposition of the sum of four squares over $\mathbb Q (\sqrt{3})$, $\mathbb Q (\sqrt{13})$ and $\mathbb Q (\sqrt{17})$.
The interstellar medium is characterized by a rich and diverse chemistry. Many of its complex organic molecules are proposed to form through radical chemistry in icy grain mantles. Radicals form readily when interstellar ices (composed of water and other volatiles) are exposed to UV photons and other sources of dissociative radiation, and, if sufficiently mobile, the radicals can react to form larger, more complex molecules. The resulting complex organic molecules (COMs) accompany star and planet formation, and may eventually seed the origins of life on nascent planets. Experiments of increasing sophistication have demonstrated that known interstellar COMs as well as the prebiotically interesting amino acids can form through ice photochemistry. We review these experiments and discuss the qualitative and quantitative kinetic and mechanistic constraints they have provided. We finally compare the effects of UV radiation with those of three other potential sources of radical production and chemistry in interstellar ices: electrons, ions and X-rays.
The hard X-ray spectrum of magnetic cataclysmic variables can be modelled to provide a measurement of white dwarf mass. This method is complementary to radial velocity measurements, which depend on the (typically rather uncertain) binary inclination. Here we present results from a Legacy Survey of 19 magnetic cataclysmic variables with NuSTAR. We fit accretion column models to their 20-78 keV spectra and derive the white dwarf masses, finding a weighted average $\bar{M}_{\rm WD}=0.77\pm0.02$ $M_{\odot}$, with a standard deviation $\sigma=0.10$ $M_{\odot}$, when we include the masses derived from previous NuSTAR observations of seven additional magnetic cataclysmic variables. We find that the mass distribution of accreting magnetic white dwarfs is consistent with that of white dwarfs in non-magnetic cataclysmic variables. Both peak at a higher mass than the distributions of isolated white dwarfs and post-common-envelope binaries. We speculate as to why this might be the case, proposing that consequential angular momentum losses may play a role in accreting magnetic white dwarfs and/or that our knowledge of how the white dwarf mass changes over accretion-nova cycles may also be incomplete.
Motivated by the unabating interest in the spin-1/2 Heisenberg antiferromagnetic model on the Kagome lattice, we investigate the energetics of projected Schwinger boson (SB) wave functions in the $J_1$--$J_2$ model with antiferromagnetic $J_2$ coupling. Our variational Monte Carlo results show that Sachdev's $Q_1=Q_2$ SB ansatz has a lower energy than the Dirac spin liquid for $J_2\gtrsim 0.08 J_1$ and the ${\bf q=0}$ Jastrow type magnetically ordered state. This work demonstrates that the projected SB wave functions can be tested on the same footing as their fermionic counterparts.
Coquelin et al. studied biperiodic semiconductor superlattices, which consist of alternating cell types, one with wide wells and the other narrow wells, separated by equal strength barriers. If the wells were identical, it would be a simply periodic system of $N = 2n$ half-cells. When asymmetry is introduced, an allowed band splits at the Bragg point into two disjoint allowed bands. The Bragg resonance turns into a transparent state located close to the band edge of the lower(upper) band when the first(second) well is the wider. Analysis of this system gives insight into how band splitting occurs. Further we consider semi-periodic systems having $N= 2n+1$ half-cells. Surprisingly these have very different transmission properties, with an envelope of maximum transmission probability that crosses the envelope of minima at the transparent point.
The COMPTEL observations of the blazar-type quasar PKS 0528+134 in the energy range 0.75 MeV to 30 MeV carried out between April 1991 and September 1994 have been analyzed. During the first two years PKS 0528+134 was most significantly detected at energies above 3 MeV. During the last year there is only evidence for the quasar at energies below 3 MeV indicating a spectral change. The time-averaged COMPTEL energy spectrum between 0.75 MeV and 30 MeV is well represented by a power-law shape. Spectra collected from different observational periods reveal different power-law shapes: a hard state during flaring observations reported by EGRET, and a soft state otherwise. The combined simultaneous EGRET and COMPTEL spectra indicate these two spectral states as well. During low intensisty gamma-ray phases no spectral break is obvious from the combined COMPTEL and EGRET measurements. For the gamma-ray flaring phases however, the combined COMPTEL and EGRET data require a spectral bending at MeV-energies. By fitting broken power-law functions the best-fit values for the break in photon index range between 0.6 and 1.7, and for the break energy between ~5 MeV and ~20 MeV. Because the flux values measured by COMPTEL below 3 MeV in both states are roughly equal, the observations would be consistent with an additional spectral component showing up during gamma-ray flaring phases of PKS 0528+134. Such a component could be introduced by e.g. a high-energy electron-positron population with a low-energy cutoff in their bulk Lorentz factor distribution. The multiwavelength spectrum of PKS 0528+134 for gamma-ray flaring phases shows that the major energy release across the entire electro-magnetic spectrum is measured at MeV-energies.
The density matrix renormalization group method is applied to obtain the ground state phase diagram of the single impurity Anderson model on the honeycomb lattice at half filling. The calculation of local static quantities shows that the phase diagram contains two distinct phases, the local moment (LM) phase and the asymmetric strong coupling (ASC) phase. These results are supported by the local spin and charge excitation spectra, which exhibit qualitatively different behavior in these two phases and also reveal the existence of the valence fluctuating point at the phase boundary. For comparison, we also study the low-energy effective pseudogap Anderson model. Although the high-energy excitations are obviously different, we find that the ground state phase diagram and the asymptotically low-energy excitations are in good quantitative agreement with those for the single impurity Anderson model on the honeycomb lattice, thus providing the first quantitative justification for the previous studies based on low-energy approximate approaches. Furthermore, we find that the lowest entanglement level is doubly degenerate for the LM phase, whereas it is singlet for the ASC phase and is accidentally three fold degenerate at the valence fluctuating point. Our results therefore clearly demonstrate that the low-lying entanglement spectrum can be used to determine with high accuracy the phase boundary of the impurity quantum phase transition.
We consider interesting results on the kinematics of the bulge, beginning with Mould's (1983) measurement of the velocity dispersion of the late M giants in the bulge, and carrying the discussion on to the present day, to discuss the largest survey ever undertaken of luminous SiO maser AGB stars. This SiO maser population of AGB stars is too luminous to have evolved from the oldest globular cluster age stellar population, yet has a velocity dispersion consistent with the oldest populations (the red clump stars) in the bulge. We identify two groups of maser stars by their kinematics; the subgroup with kinematics similar to the bulge has the highest bolometric luminosities with some giants reaching $M_{bol}<-6$. In a new result, we find that the most luminous maser stars with bulge kinematics are concentrated to the Galactic plane with the most luminous maers being found at $b<\mid 1.5^\circ \mid$; while the disk maser population shows no such difference. This mirrors a similar concentration to the Galactic Center found for long period Miras, noted in earlier studies. We conclude that the maser population represents another facet of the growing tension between evidence supporting a bulge population dominated by old stars, and a significant fraction of intermediate age stars.
This article begins by reviewing the causal set approach in discrete quantum gravity. In our version of this approach a special role is played by covariant causal sets which we call $c$-causets. The importance of $c$-causets is that they support the concepts of a natural distance function, geodesics and curvature in a discrete setting. We then discuss curvature in more detail. By considering $c$-causets with a maximum and minimum number of paths, we are able to find $c$-causets with large and small average curvature. We then briefly discuss our previous work on the inflationary period when the curvature was essentially zero. Quantum mechanics on $c$-causets is considered next. We first introduce a free wave equation for $c$-causets. We then show how the state of a particle with a specified mass (or energy) can be derived from the wave equation. It is demonstrated for small examples that quantum mechanics predicts that particles tend to move toward vertices with larger curvature.
A positive linear recurrence sequence (PLRS) is a sequence defined by a homogeneous linear recurrence relation with positive coefficients and a particular set of initial conditions. A sequence of positive integers is \emph{complete} if every positive integer is a sum of distinct terms of the sequence. One consequence of Zeckendorf's theorem is that the sequence of Fibonacci numbers is complete. Previous work has established a generalized Zeckendorf's theorem for all PLRS's. We consider PLRS's and want to classify them as complete or not. We study how completeness is affected by modifying the recurrence coefficients of a PLRS. Then, we determine in many cases which sequences generated by coefficients of the forms $[1, \ldots, 1, 0, \ldots, 0, N]$ are complete. Further, we conjecture bounds for other maximal last coefficients in complete sequences in other families of PLRS's. Our primary method is applying Brown's criterion, which says that an increasing sequence $\{H_n\}_{n = 1}^{\infty}$ is complete if and only if $H_1 = 1$ and $H_{n + 1} \leq 1 + \sum_{i = 1}^n H_i$. This paper is an introduction to the topic that is explored further in Completeness of Positive Linear Recurrence Sequences arXiv:2010.01655.
The Cosmic Defect (CD) theory is reviewed and used to fit the data for the accelerated expansion of the universe, obtained from the apparent luminosity of 192 SnIa's. The fit from CD is compared with the one obtained by means of $\Lambda $CDM. The results from both theories are in good agreement and the fits are satisfactory. The correspondence between both approaches is discussed and interpreted.
Long gamma-ray bursts are produced during the dramatic deaths of massive stars with very short lifetimes, meaning that they explode close to the birth place of their progenitors. During a short period they become the most luminous objects observable in the Universe, being perfect beacons to study high-redshift star-forming regions. To use the afterglow of GRB 161023A at a redshift $z=2.710$ as a background source to study the environment of the explosion and the intervening systems along its line-of-sight. r the first time, we complement UV/Optical/NIR spectroscopy with millimetre spectroscopy using ALMA, which allows us to probe the molecular content of the host galaxy. The X-shooter spectrum shows a plethora of absorption features including fine-structure and metastable transitions of Fe, Ni, Si, C and O. We present photometry ranging from 43 s to over 500 days after the burst. We infer a host-galaxy metallicity of [Zn/H] $=-1.11\pm0.07$, which corrected for dust depletion results in [X/H] $=-0.94\pm0.08$. We do not detect molecular features in the ALMA data, but we derive limits on the molecular content of $log(N_{CO}/cm^{-2})<15.7$ and $log(N_{HCO+}/cm^{-2})<13.2$, which are consistent with those that we obtain from the optical spectra, $log(N_{H_2}/cm^{-2})<15.2$ and $log(N_{CO}/cm^{-2})<14.5$. Within the host galaxy we detect three velocity systems through UV/Optical/NIR absorption spectroscopy, all with levels that were excited by the GRB afterglow. We determine the distance from these systems to the GRB to be in the range between 0.7 and 1.0 kpc. The sight-line to GRB 161023A shows 9 independent intervening systems, most of them with multiple components. (Abridged)
A two-dimensional direction-length framework $(G,p)$ consists of a multigraph $G=(V;D,L)$ whose edge set is formed of "direction" edges $D$ and "length" edges $L$, and a realisation $p$ of this graph in the plane. The edges of the framework represent geometric constraints: length edges fix the distance between their endvertices, whereas direction edges specify the gradient of the line through both endvertices. A direction-length framework $(G,p)$ is globally rigid if every framework $(G,q)$ which satisfies the same direction and length constraints as $(G,p)$ can be obtained by translating $(G,p)$ in the plane, and/or rotating $(G,p)$ by $180^{\circ}$.   In this paper, we characterise global rigidity for generic direction-length frameworks whose associated rigidity matroid is connected, by showing that such frameworks are globally rigid if and only if every 2-separation of the underlying graph is direction-balanced.
We show that random walks on the infinite supercritical percolation clusters in Z^d satisfy the usual Law of the Iterated Logarithm. The proof combines Barlow's Gaussian heat kernel estimates and the ergodicity of the random walk on the environment viewed from the random walker as derived by Berger and Biskup.
We give the classification of globally generated vector bundles of rank $2$ on a smooth quadric surface with $c_1\le (2,2)$ in terms of the indices of the bundles, and extend the result to arbitrary higher rank case. We also investigate their indecomposability and give the sufficient and necessary condition on numeric data of vector bundles for indecomposability.
We present a subtraction scheme for computing jet cross sections in electron-positron annihilation at next-to-next-to-leading order accuracy in perturbative QCD. In this second part we deal with the regularization of the real-virtual contribution to the NNLO correction.
Several neutral species (MgI, SiI, CaI, FeI) have been detected in a weak MgII absorption line system (W_r(2796)~0.15 Angstroms) at z~0.45 along the sightline toward HE0001-2340. These observations require extreme physical conditions, as noted in D'Odorico (2007). We place further constraints on the properties of this system by running a wide grid of photoionization models, determining that the absorbing cloud that produces the neutral absorption is extremely dense (~100-1000/cm^3), cold (<100 K), and has significant molecular content (~72-94%). Structures of this size and temperature have been detected in Milky Way CO surveys, and have been predicted in hydrodynamic simulations of turbulent gas. In order to explain the observed line profiles in all neutral and singly ionized chemical transitions, the lines must suffer from unresolved saturation and/or the absorber must partially cover the broad emission line region of the background quasar. In addition to this highly unusual cloud, three other ordinary weak MgII clouds (within densities of ~0.005/cm^3 and temperatures of ~10000K) lie within 500 km/s along the same sightline. We suggest that the "bare molecular cloud", which appears to reside outside of a galaxy disk, may have had in situ star formation and may evolve into an ordinary weak MgII absorbing cloud.
In practice, many medical datasets have an underlying taxonomy defined over the disease label space. However, existing classification algorithms for medical diagnoses often assume semantically independent labels. In this study, we aim to leverage class hierarchy with deep learning algorithms for more accurate and reliable skin lesion recognition. We propose a hyperbolic network to learn image embeddings and class prototypes jointly. The hyperbola provably provides a space for modeling hierarchical relations better than Euclidean geometry. Meanwhile, we restrict the distribution of hyperbolic prototypes with a distance matrix that is encoded from the class hierarchy. Accordingly, the learned prototypes preserve the semantic class relations in the embedding space and we can predict the label of an image by assigning its feature to the nearest hyperbolic class prototype. We use an in-house skin lesion dataset which consists of around 230k dermoscopic images on 65 skin diseases to verify our method. Extensive experiments provide evidence that our model can achieve higher accuracy with less severe classification errors than models without considering class relations.
We consider random mappings on n = kr nodes with preimage sizes restricted to a set of the form {0,k}, where k = k(r) is greater than 1. We prove that T, the least common multiple of the cycle lengths, and B= the product of the cycle lengths, are both asymptotically lognormal. The expected values of these random variables are also also estimated and compared with numerical results. This work is motivated, in part, by the use of these mappings as heuristic models for polynomials of the form x^k + a over the integers modulo p with p congruent to 1 mod k.