ShantanuT01/DACTYL-Pretraining huggingface dataset:
The antiferromagnetic Heisenberg model is considered for spins $s_{i}={1/2}$ located on the vertices of the dodecahedron and the icosahedron, which belong to the point symmetry group $I_{h}$. Taking into account the permutational and spin inversion symmetries of the Hamiltonian results in a drastic reduction of the dimensionality of the problem, leading to full diagonalization for both clusters. There is a strong signature of the frustration present in the systems in the low energy spectrum, where the first excited states are singlets. Frustration also results in a doubly-peaked specific heat as a function of temperature for the dodecahedron. Furthermore, there is a discontinuity in the magnetization as a function of magnetic field for the dodecahedron, where a specific total spin sector never becomes the ground state in a field. This discontinuity is accompanied by a magnetization plateau. The calculation is also extended for $s_{i}=1$ where both systems again have singlet excitations. The magnetization of the dodecahedron has now two discontinuities in an external field and also magnetization plateaux, and the specific heat of the icosahedron a two-peak structure as a function of temperature. The similarities between the two systems suggest that the antiferromagnetic Heisenberg model on a larger cluster with the same symmetry, the 60-site cluster, will have similar properties.
We present an analogue of the differential calculus in which the role of polynomials is played by certain ordered sets and trees. Our combinatorial calculus has all nice features of the usual calculus and has an advantage that the elements of the considered ordered sets might carry some additional information. In this way an analytic proof of generalized Cauchy identities from the previous work of the second author can be directly reformulated in our new language of the combinatorial calculus; furthermore the additional information carried by vertices determines uniquely the bijections presented in Part I of this series.
Change of sign of the LNRF-velocity gradient has been found for accretion discs orbiting rapidly rotating Kerr black holes with spin a > 0.9953 for Keplerian discs and a > 0.99979 for marginally stable thick discs. Aschenbach (2004) has identified the maximal rate of change of the orbital velocity within the "humpy" profile with a locally defined critical frequency of disc oscillations, but it has been done in a coordinate-dependent form. We define the critical "humpy" frequency H in general relativistic, coordinate independent form, and relate the frequency defined in the LNRF to distant observers. At radius of its definition, so-called "humpy" radius r_h, the "humpy" frequency H is compared to the radial (R) and vertical (V) epicyclic frequencies and the orbital frequency of the disc. For Keplerian thin discs, we show that the epicyclic resonance radii r_31 and r_41 (with V:R = 3:1 or 4:1) are located in vicinity of r_h where efficient triggering of oscillations with frequencies ~ H could be expected. Asymptotically (for 1-a < 10^(-4)) the ratio of the epicyclic and Keplerian frequencies and the humpy frequency is nearly constant, i.e., almost independent of spin, being for the radial epicyclic frequency R:H ~ 3:2. For thick discs the situation is more complex due to dependence on distribution of the specific angular momentum l determining the disc properties. For l = const tori and 1-a < 10^(-6) the frequency ratios of the humpy frequency and the orbital and epicyclic frequencies are again nearly constant and independent of both a and l, being for the radial epicyclic frequency R:H close to 4. In the limiting case of very slender tori (l ~ l_ms) the epicyclic resonance radius r_41 ~ r_h for spin 1-a < 2x10^(-4).
We investigate the nonlinear two- and three-point correlation functions of the cosmological density field in Fourier space and test the popular hierarchical clustering model, that the three-point amplitude Q is independent of scale. In high-resolution N-body simulations of both n=-2 scale-free and cold dark matter models, we find that Q at late times is not constant but increases with wavenumber far into the nonlinear regime. Self-similar scaling also does not hold as rigorously for the three-point function as for the two-point function in the n=-2 simulation, perhaps a manifestation of the finite simulation volume. We suggest that a better understanding of the two- and three-point correlation functions in the nonlinear regime lies in the link to the density profiles of dark matter halos. We demonstrate and quantify how the slopes of the correlation functions are affected by the slope of the halo profiles using simple halo shapes and analytic clustering models.
Template-based discriminative trackers are currently the dominant tracking paradigm due to their robustness, but are restricted to bounding box tracking and a limited range of transformation models, which reduces their localization accuracy. We propose a discriminative single-shot segmentation tracker -- D3S2, which narrows the gap between visual object tracking and video object segmentation. A single-shot network applies two target models with complementary geometric properties, one invariant to a broad range of transformations, including non-rigid deformations, the other assuming a rigid object to simultaneously achieve robust online target segmentation. The overall tracking reliability is further increased by decoupling the object and feature scale estimation. Without per-dataset finetuning, and trained only for segmentation as the primary output, D3S2 outperforms all published trackers on the recent short-term tracking benchmark VOT2020 and performs very close to the state-of-the-art trackers on the GOT-10k, TrackingNet, OTB100 and LaSoT. D3S2 outperforms the leading segmentation tracker SiamMask on video object segmentation benchmarks and performs on par with top video object segmentation algorithms.
The precision of reaction-diffusion models for mesoscopic physical systems is limited by fluctuations. To account for this uncertainty, Van Kampen derived a stochastic Langevin-like reaction-diffusion equation that incorporates spatio-temporal white noise. The resulting solutions, however, have infinite standard deviation. Ad hoc modifications that address this issue by introducing microscopic correlations are inconvenient in many physical contexts of wide interest. We instead estimate the magnitude of fluctuations by coarse-graining solutions of the Van Kampen equation at a relevant mesoscopic scale. The ensuing theory yields fluctuations of finite magnitude. Our approach is demonstrated for a specific biophysical model--the encoding of positional information. We discuss the properties of the fluctuations and the role played by the macroscopic parameters of the underlying reaction-diffusion model. The analysis and numerical methods developed here can be applied in physical problems to predict the magnitude of fluctuations. This general approach can also be extended to other classes of dynamical systems that are described by partial differential equations.
A new method for calculation of traces of Dirac $\gamma$-matrices contracted with massless vectors in Minkowski space is discussed
We demonstrate the possibility of a self-consistent characterization of the photon-number statistics of a light field by using photoemissive detectors with internal gain simply endowed with linear input/output responses. The method can be applied to both microscopic and mesoscopic photon-number regimes. The detectors must operate in the linear range without need of photon-counting capabilities.
A sample-relaxed two-dimensional color principal component analysis (SR-2DCPCA) approach is presented for face recognition and image reconstruction based on quaternion models. A relaxation vector is automatically generated according to the variances of training color face images with the same label. A sample-relaxed, low-dimensional covariance matrix is constructed based on all the training samples relaxed by a relaxation vector, and its eigenvectors corresponding to the $r$ largest eigenvalues are defined as the optimal projection. The SR-2DCPCA aims to enlarge the global variance rather than to maximize the variance of the projected training samples. The numerical results based on real face data sets validate that SR-2DCPCA has a higher recognition rate than state-of-the-art methods and is efficient in image reconstruction.
The flavor-dependent valence, sea quark and antiquark spin distributions can be determined separately from theoretical assumptions and experimental data. We have determined the valence distributions using the Bjorken sum rule and have extracted polarized sea distributions, assuming that the quarks and anti-quarks for each flavor are symmetric. Other experiments have been proposed which will allow us to completely break the SU(3) symmetry of the sea flavors. To create a physical model for the polarized gluons, we investigate the gluon spin asymmetry in a proton, $A_G(x,Q^2)={{\Delta G(x,Q^2)}\over {G(x,Q^2)}}$. By assuming that htis is is approximately $Q^2$ invariant, we can completely determine the $x$-dependence of this asymmetry, which satisfies constituent counting rules and reproduces the basic results of the Bremsstrahlung model originated by Close and Sivers. This asymmetry can be combined with the measured unpolarized gluon density, $G(x,Q^2)$ to provide a prediction for $\Delta G(x,Q^2)$. Existing and proposed experiments can test both the prediction of scale-invariance for $A_G(x,Q^2)$ and the nature of $\Delta G$ itself. These models will be discussed along with suggestions for specific experiments which can be performed at energies typical of HERA, RHIC and LHC to determine these polarized distributions.
We analyze Bose-Einstein condensates on three types of spherically symmetric and static charged black-hole spacetimes: The Reissner-Nordstr\"om spacetime, Hoffmann's Born-Infeld black-hole spacetime, and the regular Ay\'on-Beato-Garc\'ia spacetime. The Bose-Einstein condensate is modeled in terms of a massive scalar field that satisfies a Klein-Gordon equation with a self-interaction term. The scalar field is assumed to be uncharged and not self-gravitating. If the mass parameter of the scalar field is chosen sufficiently small, there are quasi-bound states of the scalar field that may be interpreted as dark matter clouds. We estimate the size and the total energy of such clouds around charged supermassive black holes and we investigate if their observable features can be used for discriminating between the different types of charged black holes.
Ground state cooling of a nanomechanical resonator coupled to a superconducting flux qubit is discussed. We show that by inducing quantum interference to cancel detrimental carrier excitations, ground state cooling becomes possible in the weak-confinement or non-resolved regime. The qubit is modelled as a three-level system in lambda configuration, and the driving fluxes are applied such that the qubit absorption spectrum exhibits electromagnetically induced transparency, thereby cancelling the unwanted carrier excitation. As our interference-based scheme allows to apply strong cooling fields, fast and efficient cooling can be achieved.
Heartbeat stars are eccentric binary stars in short period orbits whose light curves are shaped by tidal distortion, reflection, and Doppler beaming. Some heartbeat stars exhibit tidally excited oscillations and present new opportunities for understanding the physics of tidal dissipation within stars. We present detailed methods to compute the forced amplitudes, frequencies, and phases of tidally excited oscillations in eccentric binary systems. Our methods i) factor out the equilibrium tide for easier comparison with observations, ii) account for rotation using the traditional approximation, iii) incorporate non-adiabatic effects to reliably compute surface luminosity perturbations, iv) allow for spin-orbit misalignment, and v) correctly sum over contributions from many oscillation modes. We also discuss why tidally excited oscillations are more visible in hot stars with surface temperatures $T \! \gtrsim \! 6500 \, {\rm K}$, and we derive some basic probability theory that can be used to compare models with data in a statistical manner. Application of this theory to heartbeat systems can be used to determine whether observed tidally excited oscillations can be explained by chance resonances with stellar oscillation modes, or whether a resonance locking process is operating.
Following the RG flow of an N=1 quiver gauge theory and applying Seiberg duality whenever necessary defines a duality cascade, that in simple cases has been understood holographically. It has been argued that in certain cases, the dualities will pile up at a certain energy scale called the duality wall, accompanied by a dramatic rise in the number of degrees of freedom. In string theory, this phenomenon is expected to occur for branes at a generic threefold singularity, for which the associated quiver has Lorentzian signature. We here study sequences of Seiberg dualities on branes at the C_3/Z_3 orbifold singularity. We use the naive beta functions to define an (unphysical) scale along the cascade. We determine, as a function of initial conditions, the scale of the wall as well as the critical exponent governing the approach to it. The position of the wall is piecewise linear, while the exponent appears to be constant. We comment on the possible implications of these results for physical walls.
Most publicly available image quality databases have been created under highly controlled conditions by introducing graded simulated distortions onto high-quality photographs. However, images captured using typical real-world mobile camera devices are usually afflicted by complex mixtures of multiple distortions, which are not necessarily well-modeled by the synthetic distortions found in existing databases. The originators of existing legacy databases usually conducted human psychometric studies to obtain statistically meaningful sets of human opinion scores on images in a stringently controlled visual environment, resulting in small data collections relative to other kinds of image analysis databases. Towards overcoming these limitations, we designed and created a new database that we call the LIVE In the Wild Image Quality Challenge Database, which contains widely diverse authentic image distortions on a large number of images captured using a representative variety of modern mobile devices. We also designed and implemented a new online crowdsourcing system, which we have used to conduct a very large-scale, multi-month image quality assessment subjective study. Our database consists of over 350000 opinion scores on 1162 images evaluated by over 7000 unique human observers. Despite the lack of control over the experimental environments of the numerous study participants, we demonstrate excellent internal consistency of the subjective dataset. We also evaluate several top-performing blind Image Quality Assessment algorithms on it and present insights on how mixtures of distortions challenge both end users as well as automatic perceptual quality prediction models.
We study deuterium fractionation in two massive starless/early-stage cores C1-N and C1-S in Infrared Dark Cloud (IRDC) G028.37+00.07, first identified by Tan et al. (2013) with ALMA. Line emission from multiple transitions of $\rm N_2H^+$ and $\rm N_2D^+$ were observed with the ALMA, CARMA, SMA, JCMT, NRO 45m and IRAM 30m telescopes. By simultaneously fitting the spectra, we estimate the excitation conditions and deuterium fraction, $D_{\rm frac}^{\rm N_2H^+} \equiv [\rm N_2D^+]/[N_2H^+]$, with values of $D_{\rm frac}^{\rm N_2H^+} \simeq 0.2$--$0.7$, several orders of magnitude above the cosmic [D]/[H] ratio. Additional observations of o-H$_2$D$^+$ are also presented that help constrain the ortho-to-para ratio of $\rm H_2$, which is a key quantity affecting the degree of deuteration. We then present chemodynamical modeling of the two cores, exploring especially the implications for the collapse rate relative to free-fall, $\alpha_{\rm ff}$. In order to reach the high level of observed deuteration of $\rm N_2H^+$, we find that the most likely evolutionary history of the cores involves collapse at a relatively slow rate, $\lesssim1/10$th of free-fall.
The magnetic moment of the $\tau$ lepton is an interesting quantity that is potentially sensitive to physics beyond the Standard Model. Electroweak gauge invariance implies that a heavy new physics contribution to it takes the form of an operator which involves the Higgs boson, implying that rare Higgs decays are able to probe the same physics as $a_\tau$. We examine the prospects for rare Higgs decays at future high energy lepton (electron or muon) colliders, and find that such a project collecting a few ab$^{-1}$ would be able to advance our understanding of this physics by roughly a factor of 10 compared to the expected reach of the high luminosity LHC.
The effective version of Chebotarev's density theorem under the Generalized Riemann Hypothesis and the Artin conjecture (cf. Iwaniec and Kowalski's Analytic Number Theory, 5.13) involves a numerical invariant of a subset $D$ of a finite group $G$ that we call the Littlewood Complexity of $D$. We study this invariant in detail. Using this study, and a new application of the large sieve, we give improved versions of two standard questions related to Chebotarev: the bound on the first prime in a Frobenian set, and the asymptotic of the set of primes with given Frobenius in an infinite Galois extension. We then give concrete applications to various problems in number theory, such as the first primitive root modulo a prime $\ell$, the factorization of an integral polynomial modulo primes, the Lang-Trotter conjecture and its generalizations, and Serre's uniformity conjecture.
Using all the observations from Rossi X-ray Timing Explorer for Z source GX 349+2, we systematically carry out cross-correlation analysis between its soft and hard X-ray light curves. During the observations from January 9 to January 29, 1998, GX 349+2 traced out the most extensive Z track on its hardness-intensity diagram, making a comprehensive study of cross-correlation on the track. The positive correlations and positively correlated time lags are detected throughout the Z track. Outside the Z track, anti-correlations and anti-correlated time lags are found, but the anti-correlated time lags are much longer than the positively correlated time lags, which might indicate different mechanisms for producing the two types of time lags. We argue that neither the short-term time lag models nor the truncated accretion disk model can account for the long-term time lags in neutron star low mass X-ray binaries (NS-LMXBs). We suggest that the extended accretion disk corona model could be an alternative model to explain the long-term time lags detected in NS-LMXBs.
We devise a simple modification that essentially doubles the efficiency of the BB84 quantum key distribution scheme proposed by Bennett and Brassard. We also prove the security of our modified scheme against the most general eavesdropping attack that is allowed by the laws of physics. The first major ingredient of our scheme is the assignment of significantly different probabilities to the different polarization bases during both transmission and reception, thus reducing the fraction of discarded data.   A second major ingredient of our scheme is a refined analysis of accepted data: We divide the accepted data into various subsets according to the basis employed and estimate an error rate for each subset *separately*.   We then show that such a refined data analysis guarantees the security of our scheme against the most general eavesdropping strategy, thus generalizing   Shor and Preskill's proof of security of BB84 to our new scheme. Up till now, most proposed proofs of security of single-particle type quantum key distribution schemes have relied heavily upon the fact that the bases are chosen uniformly, randomly and independently. Our proof removes this symmetry requirement.
This paper derives exact expressions for the Laplace-Stieltjes transform of the order picking time in single- and 2-block warehouses. We consider manual warehouses that deploy return routing and assume that order sizes follow a Poisson distribution. The results in this paper apply to a wide range of storage policies, including but not restricted to class-based and random storage. Furthermore, we compare the performance of the storage policies and warehouse lay-outs by using numerical inversion of the Laplace-Stieltjes transforms.
Using a generalization of the Schensted insertion algorithm to rc-graphs, we provide a Littlewood-Richardson rule for multiplying certain Schubert polynomials by Schur polynomials.
We study a class of semilinear elliptic equations with constraints in higher dimension. It is known that several mathematical structures of the problem are closed to those of the Liouville equation in dimension two. In this paper, we establish a classification of entire solutions, the $\sup + \inf$ type inequality and the quantized blowup mechanism.
We prove the existence of infinitely many radial solutions for elliptic systems in Rn with power weights. A key tool for the proof will be a weighted imbedding theorem for fractional-order Sobolev spaces, that could be of independent interest.
We have applied the optimal estimator for f_{NL}^{local} to the 5 year WMAP data. Marginalizing over the amplitude of foreground templates we get -4 < f_{NL}^{local} < 80 at 95% CL. Error bars of previous (sub-optimal) analyses are roughly 40% larger than these. The probability that a Gaussian simulation, analyzed using our estimator, gives a result larger in magnitude than the one we find is 7%. Our pipeline gives consistent results when applied to the three and five year WMAP data releases and agrees well with the results from our own sub-optimal pipeline. We find no evidence of any residual foreground contamination.
Phase separation in the Hubbard model is investigated with the dynamical cluster approximation. We find that it is present in the paramagnetic solution for values of filling smaller than one and at finite temperature when a positive next-nearest neighbor hopping is considered. The phase separated region is characterized by a mixture of a strongly correlated metallic and Mott insulating phases. Our results indicate that phase separation is driven by the formation of doped regions with strong antiferromagnetic correlations and low kinetic energy
We classify the order parameters on the honeycomb lattice using the SO(4) symmetry of the Hubbard model. We will focus on the topologically nontrivial quantum spin Hall order and spin triplet superconductor, which together belong to the (3, 3) representation of the SO(4). Depending on the microscopic parameters, this (3, 3) order parameter has two types of ground states with different symmetries: type A, the ground state manifold is [S^2xS^2]/Z_2; and type B, with ground state manifold SO(3)xZ_2. We demonstrate that phase A is adjacent to a Z_2xZ_2 topological phase with mutual semion statistics between spin and charge excitations, while phase B is adjacent to a nonabelian phase described by SU(2) Chern-Simons theory. Connections of our study to the recent quantum Monte Carlo simulation on the Hubbard model on the honeycomb lattice will also be discussed.
Using a recently proposed duality for $U(N)$ supersymmetric QCD (SQCD) in three dimensions with monopole superpotential, in this paper we derive the mirror dual description of $\mathcal{N}=2$ SQCD with unitary gauge group, generalizing the known mirror dual description of abelian gauge theories. We match the chiral ring of the dual theories and their partition functions on the squashed sphere. We also conjecture a generalization for SQCD with orthogonal and symplectic gauge groups.