ShantanuT01/DACTYL-Pretraining huggingface dataset:
We classify completely the surfaces of general type whose canonical map is 3-to-1 onto a surface of minimal degree in projective space. These surfaces fall into 5 distinct classes and we give explicit examples belonging to each of these classes. As far as we know, one of the examples thus constructed was unknown and it is a surface whose canonical system has two infinitely near base points.
Measurements of the flux and redshifts of Type Ia supernovae have provided persuasive evidence that the expansion of the universe is accelerating. If true, then in the context of standard FRW cosmology this suggests that the energy density of hte universe is dominated by "dark energy" -- a component with negative pressure of magnitude comparable to its energy density. To further investigate this phenomenon, more extensive surveys of supernovae are being planned. Given the likely timescales for completion, by the time data from these surveys are available some important cosmological parameters will be known to high precision from CMB measurements. Here we consider the impact of that foreknowledge on the design of supernova surveys. In particular we show that, despite greater opportunities to multiplex, purely from the point of view of statistical errors, a deep survey may not obviously be better than a shallow one.
The scene graph generation (SGG) task aims to detect visual relationship triplets, i.e., subject, predicate, object, in an image, providing a structural vision layout for scene understanding. However, current models are stuck in common predicates, e.g., "on" and "at", rather than informative ones, e.g., "standing on" and "looking at", resulting in the loss of precise information and overall performance. If a model only uses "stone on road" rather than "blocking" to describe an image, it is easy to misunderstand the scene. We argue that this phenomenon is caused by two key imbalances between informative predicates and common ones, i.e., semantic space level imbalance and training sample level imbalance. To tackle this problem, we propose BA-SGG, a simple yet effective SGG framework based on balance adjustment but not the conventional distribution fitting. It integrates two components: Semantic Adjustment (SA) and Balanced Predicate Learning (BPL), respectively for adjusting these imbalances. Benefited from the model-agnostic process, our method is easily applied to the state-of-the-art SGG models and significantly improves the SGG performance. Our method achieves 14.3%, 8.0%, and 6.1% higher Mean Recall (mR) than that of the Transformer model at three scene graph generation sub-tasks on Visual Genome, respectively. Codes are publicly available.
We show that there are no new consistent cosmological perfect fluid solutions when in an open neighbourhood ${\cal U}$ of an event the fluid kinematical variables and the electric and magnetic Weyl curvature are all assumed rotationally symmetric about a common spatial axis, specialising the Weyl curvature tensor to algebraic Petrov type D. The consistent solutions of this kind are either locally rotationally symmetric, or are subcases of the Szekeres dust models. Parts of our results require the assumption of a barotropic equation of state. Additionally we demonstrate that local rotational symmetry of perfect fluid cosmologies follows from rotational symmetry of the Riemann curvature tensor and of its covariant derivatives only up to second order, thus strengthening a previous result.
We prove the invariance of the Gibbs measure for the periodic Schrodinger-Benjamin-Ono system (when the coupling parameter |\gamma| \ne 0, 1) by establishing a new local well-posedness in a modified Sobolev space and constructing the Gibbs measure (which is in the sub-L^2 setting for the Benjamin-Ono part.) We also show the ill-posedness result in H^s(\mathbb{T}) \times H^{s-{1/2}}(\mathbb{T}) for s < {1/2} when |\gamma| \ne 0, 1 and for any s \in \mathbb{R} when |\gamma| =1.
Quantum phase transitions in the Hubbard model on the honeycomb lattice are investigated in the variational cluster approximation. The critical interaction for the paramagnetic to antiferromagnetic phase transition is found to be in remarkable agreement with a recent large-scale quantum Monte Carlo simulation. Calculated staggered magnetization increases continuously with $U$ and thus we find the phase transition is of a second order. We also find that the semimetal-insulator transition occurs at infinitesimally small interaction and thus a paramagnetic insulating state appears in a wide interaction range. A crossover behavior of electrons from itinerant to localized character found in the calculated single-particle excitation spectra and short-range spin correlation functions indicates that an effective spin model for the paramagnetic insulating phase is far from a simple Heisenberg model with a nearest-neighbor exchange interaction.
A simple gravitational model with torsion is studied, and it is suggested that it could explain the dark matter and dark energy in the universe. It can be reinterpreted as a model using the Einstein gravitational equations where spacetime has regions filled with a perfect fluid with negative energy (pressure) and positive mass density, other regions containing an anisotropic substance that in the rest frame (where the momentum is zero) has negative mass density and a uniaxial stress tensor, and possibly other "luminal" regions where there is no rest frame. The torsion vector field is inhomogeneous throughout spacetime, and possibly turbulent. Numerical simulations should reveal whether or not the equations are consistent with cosmological observations of dark matter and dark energy.
Uncertainty principle is one of the central concepts in quantum theory. Different forms of this particular principle have been discoursed in various foundational and information theoretic topics. In the discrete input-output scenario the limited nonlocal behavior of quantum theory has been explained by fine-grained uncertainty relation. On the other hand, in continuous variable paradigm Robertson-Schrodinger (RS) uncertainty relation has been used to detect multi-mode entanglement. Here we show that RS uncertainty relation plays an important role to discriminate between quantum and post-quantum nonlocal correlations in multi-mode continuous outcome scenario. We provide a class of m-mode post-quantum nonlocal correlations with continuous outcome spectrum. While nonlocality of the introduced class of correlations is established through Calvalcanti-Foster-Reid-Drummond (CFRD) class of Bell inequalities, RS uncertainty relation detects their post-quantum nature. Our result is a hint towards a wider role of uncertainty principle in the study of nonlocality in continuous variable multi-mode systems.
Three aspects of time series are uncertainty (dispersion at a given time scale), scaling (time-scale dependence), and intermittency (inclination to change dynamics). Simple measures of dispersion are the mean absolute deviation and the standard deviation; scaling exponents describe how dispersions change with the time scale. Intermittency has been defined as a difference between two scaling exponents. After taking a moving average, these measures give descriptive information, even for short heart rate records. For this data, dispersion and intermittency perform better than scaling exponents.
We investigate the bias and error in estimates of the cosmological parameter covariance matrix, due to sampling or modelling the data covariance matrix, for likelihood width and peak scatter estimators. We show that these estimators do not coincide unless the data covariance is exactly known. For sampled data covariances, with Gaussian distributed data and parameters, the parameter covariance matrix estimated from the width of the likelihood has a Wishart distribution, from which we derive the mean and covariance. This mean is biased and we propose an unbiased estimator of the parameter covariance matrix. Comparing our analytic results to a numerical Wishart sampler of the data covariance matrix we find excellent agreement. An accurate ansatz for the mean parameter covariance for the peak scatter estimator is found, and we fit its covariance to our numerical analysis. The mean is again biased and we propose an unbiased estimator for the peak parameter covariance. For sampled data covariances the width estimator is more accurate than the peak scatter estimator. We investigate modelling the data covariance, or equivalently data compression, and shown that the peak scatter estimator is less sensitive to biases in the model data covariance matrix than the width estimator, but requires independent realisations of the data to reduce the statistical error. If the model bias on the peak estimator is sufficiently low this is promising, otherwise the sampled width estimator is preferable.
We use the clustering results obtained by Madgwick et al. (2003) for a sample of 96,791 2dF galaxies with redshift 0.01 \lt z \lt 0.15 to study the distribution of late-type and early-type galaxies within dark matter haloes of different mass. Within the framework of our models, galaxies of both classes are found to be as spatially concentrated as the dark matter within haloes even though, while the distribution of star-forming galaxies can also allow for some steeper profiles, this is drastically ruled out in the case of early-type galaxies. We also find evidence for morphological segregation, as late-type galaxies appear to be distributed within haloes of mass scales corresponding to groups and clusters up to about two virial radii, while passive objects show a preference to reside closer to the halo centre. If we assume a broken power-law of the form <N_{gal}(m)>=(m/m_0)^{alpha_1} for m_{cut}\le m<m_0 and <N_{gal}(m)>=(m/m_0)^{alpha_2} at higher masses to describe the dependence of the average number of galaxies within haloes on the halo mass, fits to the data show that star-forming galaxies start appearing in haloes of masses m_{cut}~10^{11}m_{sun}, much smaller than what is obtained for early-type galaxies (m_{cut}~10^{12.6}m_{sun}). In the high-mass regime m\ge m_0, <N_{gal}>$ increases with halo mass more slowly (alpha_2~0.7) in the case of late-type galaxies than for passive objects which present alpha_2~1.1. We stress that there is no degeneracy in the determination of the best functional forms for rho(r) and <N_{gal}>, as they affect the behaviour of the galaxy-galaxy correlation function on different scales.
We propose a new concept for a very low background multi-ton liquid xenon Dark Matter experiment. The detector consists of two concentric spheres and a charge readout device in the centre. Xenon between the two spheres forms a self-shield and veto device. The inner surface of the central sphere is coated with CsI to form an internal photocathode with minimum of 2\pi coverage for any event in the active volume. Photoelectrons from the CsI photocathode drift toward the charge readout micro-structure in the centre of the detector. Both scintillation and ionisation are measured simultaneously for background rejection and 3-D event mapping. In addition to external shielding, the low background is achieved by eliminating PMTs and by using low radioactivity pure materials throughout the detector. We present detailed calculations of the charge readout system and design details. The detector is expected to probe the full SUSY parameter space.
The transition probability for time-dependent unitary evolution is invariant under the reversal of protocols just as in the classical Liouvillian dynamics. In this article, we generalize the expression of microscopic reversibility to externally perturbed large quantum open systems. The time-dependent external perturbation acts on the subsystem during a transient duration, and subsequently the perturbation is switched off so that the total system would thermalize. We concern with the transition probability for the subsystem between the initial and final eigenstates of the subsystem. In the course of time evolution, the energy is irreversibly exchanged between the subsystem and reservoir. The time reversed probability is given by the reversal of the protocol and the initial ensemble. Microscopic reversibility equates the time forward and reversed probabilities, and therefore appears as a thermodynamic symmetry for open quantum systems.
We derive necessary and sufficient conditions for local unitary (LU) operators to leave invariant the set of 1-qubit reduced density matrices of a multi-qubit state. LU operators with this property are tensor products of {\it cyclic local} operators, and form a subgroup, the centralizer subgroup of the set of reduced states, of the Lie group $SU(2)^{\otimes n}$. The dimension of this subgroup depends on the type of reduced density matrices. It is maximum when all reduced states are maximally mixed and it is minimum when none of them is maximally mixed. For any given multi-qubit state, pure or mixed, we compute the LU operators that fix the corresponding reduced density matrices and determine the equivalence class of the given state.
A system is non-Hermitian when it exchanges energy with its environment and non-reciprocal when it behaves differently upon the interchange of input and response. Within the field of metamaterial research on synthetic topological matter, the skin effect describes the conspiracy of non-Hermiticity and non-reciprocity to yield extensive anomalous localization of all eigenmodes in a (quasi) one-dimensional geometry. Here, we introduce the reciprocal skin effect, which occurs in non-Hermitian but reciprocal systems in two or more dimensions: Eigenmodes with opposite longitudinal momentum exhibit opposite transverse anomalous localization. We experimentally demonstrate the reciprocal skin effect in a passive RLC circuit, suggesting convenient alternative implementations in optical, acoustic, mechanical, and related platforms. Skin mode localization brings forth potential applications in directional and polarization detectors for electromagnetic waves.
The Gutzwiller technique has long been known as a method to include correlations in electronic structure calculations. Here we implement an ab-initio Gutzwiller+LDA calculation, and apply it to a classic problem, the ferromagnetism of bulk bcc Fe, whose nature has attracted recent interest. In the conventional Stoner-Wohlfarth model, the ferromagnetic ordering of iron sets in so that the electrons can reduce their mutual Coulomb repulsion at the extra cost of some increase of electron kinetic energy. Density functional theory within the spin polarized local density approximation (LDA) has long supported that picture, showing that ferromagnetic alignment causes band narrowing and a corresponding wavefunction localization, whence a kinetic energy increase. However, because of its inadequate treatment of strong intra-site correlations for localized d orbitals, LDA cannot be relied upon, particularly when it comes to separately describing fine potential and kinetic energy imbalances. With ab-initio Gutzwiller+LDA, we indeed find that the effect of correlations is to dramatically reverse the balance, the ferromagnetic ordering of Fe in fact causing a decrease of kinetic energy, at the cost of some increase of potential energy. The underlying physical mechanism, foreshadowed long ago by Goodenough and others, and more recently supported by LDA+DMFT calculations, is that correlations cause eg and t2g 3d orbitals to behave very differently. Weakly dispersive eg states are spin-polarized and almost localized, while, more than half filled, the t2g are broad band, fully delocalized states. Owing to intra-atomic Hund's rule exchange which aligns eg and t2g spins, the propagation of itinerant t2g holes is only allowed when different atomic spins are ferromagnetically aligned. We thus conclude that double exchange is at work already in the most popular ferromagnetic metal.
We investigate several hyperplane arrangements that can be viewed as deformations of Coxeter arrangements. In particular, we prove a conjecture of Linial and Stanley that the number of regions of the arrangement x_i - x_j = 1, 1 \leq i<j \leq n, is equal to the number of alternating trees on n+1 vertices. Remarkably, these numbers have several additional combinatorial interpretations in terms of binary trees, partially ordered sets, and tournaments. More generally, we give formulae for the number of regions and the Poincar'e polynomial of certain finite subarrangements of the affine Coxeter arrangement of type A_{n-1}. These formulae enable us to prove a "Riemann hypothesis" on the location of zeros of the Poincar'e polynomial. We also consider some generic deformations of Coxeter arrangements of type A_{n-1}.
Analytical solutions for the time-dependent autocorrelation function of the classical and quantum mechanical spin dimer with arbitrary spin are presented and compared. For large spin quantum numbers or high temperature the classical and the quantum dimer become more and more similar, yet with the major difference that the quantum autocorrelation function is periodic in time whereas the classical is not.
We investigated the crystal-electric field ground state of the 4$f$ manifold in the strongly correlated topological insulator SmB$_6$ using core level non-resonant inelastic x-ray scattering (NIXS). The directional dependence of the scattering function that arises from higher multipole transitions establishes unambiguously that the $\Gamma_8$ quartet state of the Sm $f^5$ $J$=$5/2$ configuration governs the ground-state symmetry and hence the topological properties of SmB$_6$. Our findings contradict the results of density functional calculations reported so far.
Fingerprint reconstruction is one of the most well-known and publicized biometrics. Because of their uniqueness and consistency over time, fingerprints have been used for identification over a century, more recently becoming automated due to advancements in computed capabilities. Fingerprint reconstruction is popular because of the inherent ease of acquisition, the numerous sources (e.g. ten fingers) available for collection, and their established use and collections by law enforcement and immigration. Fingerprints have always been the most practical and positive means of identification. Offenders, being well aware of this, have been coming up with ways to escape identification by that means. Erasing left over fingerprints, using gloves, fingerprint forgery; are certain examples of methods tried by them, over the years. Failing to prevent themselves, they moved to an extent of mutilating their finger skin pattern, to remain unidentified. This article is based upon obliteration of finger ridge patterns and discusses some known cases in relation to the same, in chronological order; highlighting the reasons why offenders go to an extent of performing such act. The paper gives an overview of different methods and performance measurement of the fingerprint reconstruction.
We point out an interesting theoretical prediction for elliptical galaxies residing inside galaxy clusters in the framework of modified Newtonian dynamics (MOND), that could be used to test this paradigm. Apart from the central brightest cluster galaxy, other galaxies close enough to the centre experience a strong gravitational influence from the other galaxies of the cluster. This influence manifests itself only as tides in standard Newtonian gravity, meaning that the systematic acceleration of the centre of mass of the galaxy has no consequence. However, in the context of MOND, a consequence of the breaking of the strong equivalence principle is that the systematic acceleration changes the own self-gravity of the galaxy. We show here that, in this framework, initially axisymmetric elliptical galaxies become lopsided along the external field's direction, and that the centroid of the galaxy, defined by the outer density contours, is shifted by a few hundreds parsecs with respect to the densest point.
Elastic scattering of electron vortex beams on magnetic materials leads to a weak magnetic contrast due to Zeeman interaction of orbital angular momentum of the beam with magnetic fields in the sample. The magnetic signal manifests itself as a redistribution of intensity in diffraction patterns due to a change of sign of the orbital angular moment. While in the atomic resolution regime the magnetic signal is most likely under the detection limits of present transmission electron microscopes, for electron probes with high orbital angular momenta, and correspondingly larger spatial extent, its detection is predicted to be feasible.
Image segmentation some of the challenging issues on brain magnetic resonance image tumor segmentation caused by the weak correlation between magnetic resonance imaging intensity and anatomical meaning.With the objective of utilizing more meaningful information to improve brain tumor segmentation,an approach which employs bilateral symmetry information as an additional feature for segmentation is proposed.This is motivated by potential performance improvement in the general automatic brain tumor segmentation systems which are important for many medical and scientific applications.Brain Magnetic Resonance Imaging segmentation is a complex problem in the field of medical imaging despite various presented methods.MR image of human brain can be divided into several sub-regions especially soft tissues such as gray matter,white matter and cerebra spinal fluid.Although edge information is the main clue in image segmentation,it cannot get a better result in analysis the content of images without combining other information.Our goal is to detect the position and boundary of tumors automatically.Experiments were conducted on real pictures,and the results show that the algorithm is flexible and convenient.
Ceramic $BiFeO_{3}$ samples were prepared by rapid sintering at $880^OC$. Two compositions were examined. A $56/44\ Bi_{2}O_{3}/Fe_{2}O_{3}\ mole\%$ composition and a $56Bi_{2}O_{3}\cdot44Fe_{2}O_{3}+6.5wt\%\,NaCl$ composition. The samples were heat treated at different times up to $8$ minutes and the phase content was examined as a function of the time using XRD measurements and analysis. It was demonstrated that using both compositions, maximum $BiFeO_{3}$ phase content is obtained after $3.5$ minutes. In the former approximately $50\%$ of the material transformed to $BiFeO_{3}$ while in the latter $98.5\%$.
We have applied the unsharp-masking technique to the 24 $\mu$m image of the Small Magellanic Cloud (SMC), obtained with the Spitzer Space Telescope, to search for high-extinction regions. This technique has been used to locate very dense and cold interstellar clouds in the Galaxy, particularly infrared dark clouds (IRDCs). Fifty five candidate regions of high-extinction, namely high-contrast regions (HCRs), have been identified from the generated decremental contrast image of the SMC. Most HCRs are located in the southern bar region and mainly distributed in the outskirts of CO clouds, but most likely contain a significant amount of H2. HCRs have a peak-contrast at 24 $\mu$m of 2 - 2.5 % and a size of 8 - 14 pc. This corresponds to the size of typical and large Galactic IRDCs, but Galactic IRDCs are 2 - 3 times darker at 24 $\mu$m than our HCRs. To constrain the physical properties of the HCRs, we have performed NH3, N2H+, HNC, HCO+, and HCN observations toward one of the HCRs, HCR LIRS36-EAST, using the Australia Telescope Compact Array and the Mopra single-dish radio telescope. We did not detect any molecular line emission, however, our upper limits to the column densities of molecular species suggest that HCRs are most likely moderately dense with n ~ 10^{3} cm-3. This volume density is in agreement with predictions for the cool atomic phase in low metallicity environments. We suggest that HCRs may be tracing clouds at the transition from atomic to molecule-dominated medium, and could be a powerful way to study early stages of gas condensation in low metallicity galaxies. Alternatively, if made up of dense molecular clumps < 0.5 pc in size, HCRs could be counterparts of Galactic IRDCs, and/or regions with highly unusual abundance of very small dust grains.