ShantanuT01/DACTYL-Pretraining huggingface dataset:
We analyze the relation between rigid and local supersymmetric N=2 field theories, when half of the supersymmetries are spontaneously broken. In particular, we show that the recently found partial supersymmety breaking induced by electric and magnetic Fayet-Iliopoulos terms in rigid theories can be obtained by a suitable flat limit of previously constructed N=2 supergravity models with partial super-Higgs in the observable sector.
In this appendix, we observe that our March preprint on Serre's conjecture was indeed correct: the only "missing argument" follows automatically from a result of Bockle and Ramakrishna. Thus, we get a proof of the level 1 weight 2 case of Serre's conjecture (a result that has been also proved independently by Khare and Wintenberger).
We show that general triple planes with p_g=q=0 belong to at most 12 families, that we call surfaces of type I,..., XII, and we prove that the corresponding Tschirnhausen bundle is direct sum of two line bundles in cases I, II, III, whereas is a rank 2 Steiner bundle in the remaining cases.   We also provide existence results and explicit constructions for surfaces of type I,..., VII, recovering all classical examples and discovering several new ones. In particular, triple planes of type VII provide counterexamples to a wrong claim made in 1942 by Bronowski.
The paper is devoted to the problem of the determination of regular and thermal forces acting on microscopic and smaller objects in fluids. One of the methods how regular forces are determined is the measurement of the drift velocity of Brownian particles. We have obtained an exact expression for this velocity within the hydrodynamic theory of the Brownian motion. It is shown that the influence of the inertial and memory effects can be significant in the force determination when the experimental times are sufficiently short. In the second part of the work, within the same theory, we study the properties of the thermal force driving the particles in incompressible fluids. We show that the usual assumption for the Kubo's generalized Langevin equation (called the "fundamental hypothesis") that the thermal force at a time t and the velocity of the particle in preceding times are uncorrelated, leads to an unexpected super-diffusion of the particle. To obtain the Einstein diffusion at long times, the mentioned hypothesis must be abandoned, which however does not contradict to causality. Finally, we consider the "color" of thermal noise, recently measured experimentally [Th. Franosch et al., Nature 478, 85 (2011)], and correct the interpretation of these experiments.
We briefly review the significance of quantum corrections in the total energy of systems with voids: bubble nuclei, atomic clusters and the inhomogeneous phase of neutron stars.
We study the (analytic) finite-size corrections in the Ising model on the strip with fixed ($+ -$) boundary conditions. We find that subdominant finite-size corrections to scaling should be to the form $a_k/N^{2k-1}$ for the free energy $f_N$ and $b_k^{(n)}/N^{2k-1}$ for inverse correlation length $\xi_n^{-1}$, with integer value of $k$. We investigate the set $\{a_k, b_k^{(n)}\}$ by exact evaluation and their changes upon varying anisotropy of coupling. We find that the amplitude ratios $b_k^{(n)}/a_k$ remain constant upon varying coupling anisotropy. Such universal behavior are correctly reproduced by the conformal perturbative approach.
For a projective curve $C\subset\mathbf{P}^n$ defined over $\mathbf{F}_q$ we study the statistics of the $\mathbf{F}_q$-structure of a section of $C$ by a random hyperplane defined over $\mathbf{F}_q$ in the $q\to\infty$ limit. We obtain a very general equidistribution result for this problem. We deduce many old and new results about decomposition statistics over finite fields in this limit. Our main tool will be the calculation of the monodromy of transversal hyperplane sections of a projective curve.
Adiabatic nucleon-nucleon potentials are calculated in a six-quark nonrelativistic chiral constituent quark model where the Hamiltonian contains a linear confinement and a pseudoscalar meson (Goldstone boson) exchange interaction between quarks. Calculations are performed both in a cluster model and a molecular orbital basis, through coupled channels. In both cases the potentials present an important hard core at short distances, explained through the dominance of the [51]_{FS} configuration, but do not exhibit an attractive pocket. We add a scalar meson exchange interaction and show how it can account for some middle-range attraction.
Recently a hard X-ray transient event, Sw J1644+57, was discovered by the Swift satellite. It likely marks the onset of a relativistic jet from a supermassive black hole, possibly triggered by a tidal disruption event. Another candidate in the same category, Sw J2058+05, was also reported. The low event rate suggests that only a small fraction of TDEs launch relativistic jets. A common speculation is that these rare events are related to rapidly spinning black holes. We attribute jet launching to the Blandford-Znajek mechanism, and use the available data to constrain the black hole spin parameter for the two events. It is found that the two black holes indeed carry a moderate to high spin, suggesting that black hole spin is likely the crucial factor behind the Sw J1644+57 - like events.
In this paper, we examined the viability bounds of a higher derivative $f(R,\Box R, T)$ theory through analyzing energy conditions (where $R$ and $T$ are the Ricci scalar and trace of energy momentum tensor, respectively). We take flat Friedmann-Lema\^{i}tre-Robertson-Walker spacetime coupled with ideal configurations of matter content. We consider three different realistic models of this gravity, that could be utilized to understand the stability of cosmological solutions. After constructing certain bounds mediated by energy conditions, more specifically weak energy condition, we discuss viable zones of the under considered modified models in an environment of recent estimated numerical choices of the cosmic parameters.
We provide an exact formula for the complex exponents in the modular product expansion of the modular units, and deduce a characterization of the modular units in terms of the growth of these exponents, answering a question of W. Kohnen.
We provide dramatic evidence that `Mellin space' is the natural home for correlation functions in CFTs with weakly coupled bulk duals. In Mellin space, CFT correlators have poles corresponding to an OPE decomposition into `left' and `right' sub-correlators, in direct analogy with the factorization channels of scattering amplitudes. In the regime where these correlators can be computed by tree level Witten diagrams in AdS, we derive an explicit formula for the residues of Mellin amplitudes at the corresponding factorization poles, and we use the conformal Casimir to show that these amplitudes obey algebraic finite difference equations. By analyzing the recursive structure of our factorization formula we obtain simple diagrammatic rules for the construction of Mellin amplitudes corresponding to tree-level Witten diagrams in any bulk scalar theory. We prove the diagrammatic rules using our finite difference equations. Finally, we show that our factorization formula and our diagrammatic rules morph into the flat space S-Matrix of the bulk theory, reproducing the usual Feynman rules, when we take the flat space limit of AdS/CFT. Throughout we emphasize a deep analogy with the properties of flat space scattering amplitudes in momentum space, which suggests that the Mellin amplitude may provide a holographic definition of the flat space S-Matrix.
After reviewing the ideal Bose-Einstein gas in a box and in a harmonic trap, I discuss the effect of interactions on the formation of a Bose-Einstein condensate (BEC), along with the dynamics of small-amplitude perturbations (the Bogoliubov equations). When the condensate rotates with angular velocity Omega, one or several vortices nucleate, with many observable consequences. With more rapid rotation, the vortices form a dense triangular array, and the collective behavior of these vortices has additional experimental implications. For Omega near the radial trap frequency omega_perp, the lowest-Landau-level approximation becomes applicable, providing a simple picture of such rapidly rotating condensates. Eventually, as Omega approaches omega_perp, the rotating dilute gas is expected to undergo a quantum phase transition from a superfluid to various highly correlated (nonsuperfluid) states analogous to those familiar from the fractional quantum Hall effect for electrons in a strong perpendicular magnetic field.
The interplay between quarter-filled and half-filled umklapp scattering has been examined by applying the renormalization group method to a one-dimensional quarter-filled electron system with dimerization, on-site (U) and nearest-neighbor (V) repulsive interactions. The phase diagram on the U-V plane is obtained at absolute zero temperature where the Mott insulator (the charge ordered insulator) is found for smaller (larger) V. By choosing the moderate parameter in the region of Mott insulator, it is shown that the resistivity exhibits a crossover from behavior of quarter-filling to that of half-filling with decreasing temperature.
We have studied the electronic structure of the interface between 6H-SiC{0001} and graphite. On n-type and p-type 6H-SiC(0001) we observe Schottky barriers of Phi_b,n^Si= 0.3+-0.1eV and Phi_b,p^Si=2.7+-0.1eV, respectively. The observed barrier is face specific: on n-type 6H-SiC(000-1) we find Phi_b,n^C=1.3+-0.1eV. The impact of these barriers on the electrical properties of metal/SiC contacts is discussed.
This paper presents a systematic literature review of image datasets for document image analysis, focusing on historical documents, such as handwritten manuscripts and early prints. Finding appropriate datasets for historical document analysis is a crucial prerequisite to facilitate research using different machine learning algorithms. However, because of the very large variety of the actual data (e.g., scripts, tasks, dates, support systems, and amount of deterioration), the different formats for data and label representation, and the different evaluation processes and benchmarks, finding appropriate datasets is a difficult task. This work fills this gap, presenting a meta-study on existing datasets. After a systematic selection process (according to PRISMA guidelines), we select 65 studies that are chosen based on different factors, such as the year of publication, number of methods implemented in the article, reliability of the chosen algorithms, dataset size, and journal outlet. We summarize each study by assigning it to one of three pre-defined tasks: document classification, layout structure, or content analysis. We present the statistics, document type, language, tasks, input visual aspects, and ground truth information for every dataset. In addition, we provide the benchmark tasks and results from these papers or recent competitions. We further discuss gaps and challenges in this domain. We advocate for providing conversion tools to common formats (e.g., COCO format for computer vision tasks) and always providing a set of evaluation metrics, instead of just one, to make results comparable across studies.
Standard methods of the theory of permanent state reduction are shown to offer an alternative realization of Omn\`es' project. Our proposal, as simple as Omn\`es' one, possesses closed master equation for the ensemble density operator, assuring causality.
We present analytic models for the local structure of self-regulated self-gravit ating accretion discs that are subject to realistic cooling. Such an approach can be used to predict the secular evolution of self-gravitating discs (which can usefully be compared with future radiation hydrodynamical simulations) and to define various physical regimes as a function of radius and equivalent steady state accretion rate. We show that fragmentation is inevitable, given realistic rates of infall into the disc, once the disc extends to radii $> 70$ A.U. (in the case of a solar mass central object). Owing to the outward redistribution of disc material by gravitational torques, we also predict fragmentation at $> 70$ A.U. even in the case of low angular momentum cores which initially collapse to a much smaller radius. We point out that 70 A.U. is close to the median binary separation and propose that such delayed fragmentation, at the point that the disc expands to $> 70$ A.U., ensures the creation of low mass ratio companions that can avoid substantial further growth and consequent evolution towards unit mass ratio. We thus propose this as a promising mechanism for producing low mass ratio binaries, which, while abundant observationally, are severely underproduced in hydrodynamical models.
We show that the locus of stable rank four vector bundles without theta divisor over a smooth projective curve of genus two is in canonical bijection with the set of theta-characteristics. We give several descriptions of these bundles and compute the degree of the rational theta map.
Human interaction recognition is a challenging problem in computer vision and has been researched over the years due to its important applications. With the development of deep models for the human pose estimation problem, this work aims to verify the effectiveness of using the human pose in order to recognize the human interaction in monocular videos. This paper developed a method based on 5 steps: detect each person in the scene, track them, retrieve the human pose, extract features based on the pose and finally recognize the interaction using a classifier. The Two-Person interaction dataset was used for the development of this methodology. Using a whole sequence evaluation approach it achieved 87.56% of average accuracy of all interaction. Yun, et at achieved 91.10% using the same dataset, however their methodology used the depth sensor to recognize the interaction. The methodology developed in this paper shows that an RGB camera can be as effective as depth cameras to recognize the interaction between two persons using the recent development of deep models to estimate the human pose.
We present a timing analysis of the 2009 outburst of the accreting millisecond X-ray pulsar Swift J1756.9-2508, and a re-analysis of the 2007 outburst. The source shows a short recurrence time of only ~2 years between outbursts. Thanks to the approximately 2 year long baseline of data, we can constrain the magnetic field of the neutron star to be 0.4x10^8 G < B < 9x10^8 G, which is within the range of typical accreting millisecond pulsars. The 2009 timing analysis allows us to put constraints on the accretion torque: the spin frequency derivative within the outburst has an upper limit of $|\dot{\nu}| < 3x10^-13 Hz/s at the 95% confidence level. A study of pulse profiles and their evolution during the outburst is analyzed, suggesting a systematic change of shape that depends on the outburst phase.
Weak measurement of a subset of noncommuting observables of a quantum system can be modeled by the open-system evolution, governed by the master equation in the Lindblad form. The open-system density operator can be represented as statistical mixture over non unitarily evolving pure states, driven by the stochastic Nonlinear Schrodinger equation (sNLSE). The globally stable solution of the sNLSE is obtained in the case where the measured subset of observables comprises the spectrum-generating algebra of the system. This solution is a generalized coherent state (GCS), associated with the algebra. The result is based on proving that GCS minimize the trace-norm of the covariance matrix, associated with the spectrum-generating algebra.
In an effort to further the study of amplitudes in the celestial CFT (CCFT), we construct conformal primary wavefunctions for massive fermions. Upon explicitly calculating the wavefunctions for Dirac fermions, we deduce the corresponding transformation of momentum space amplitudes to celestial amplitudes. The shadow wavefunctions are shown to have opposite spin and conformal dimension $2-\Delta$. The Dirac conformal primary wavefunctions are delta function normalizable with respect to the Dirac inner product provided they lie on the principal series with conformal dimension $\Delta = 1+i\lambda$ for $\lambda\in\mathbb{R}$. It is shown that there are two choices of a complete basis: single spin $J=\frac{1}{2}$ or $J=-\frac{1}{2}$ and $\lambda\in\mathbb{R}$ or multiple spin $J=\pm\frac{1}{2}$ and $\lambda\in\mathbb{R}_{+\cup 0}$. The massless limit of the Dirac conformal primary wavefunctions is shown to agree with previous literature. The momentum generators on the celestial sphere are derived and, along with the Lorentz generators, form a representation of the Poincare algebra. Finally, we show that the massive spin-$1$ conformal primary wavefunctions can be constructed from the Dirac conformal primary wavefunctions using the standard Clebsch-Gordan coefficients. We use this procedure to write the massive spin-$\frac{3}{2}$, Rarita-Schwinger, conformal primary wavefunctions. This provides a prescription for constructing all massive fermionic and bosonic conformal primary wavefunctions starting from spin-$\frac{1}{2}$.
The addition of non-renormalizable terms involving the Higgs fields to the MSSM ameliorates the little hierarchy problem of the MSSM. For neutralino dark matter, new regions for which the relic abundance of the LSP is consistent with WMAP (as the bulk region and the stop coannihilation region) are now permitted. In this framework, we analyze in detail first the direct dark matter detection prospects in a XENON-like experiment; then we study the capability of detecting gamma-rays produced in the annihilation of neutralino LSPs in the FERMI satellite.
Nonlinear response of a Mott insulator to external electric field, corresponding to dielectric breakdown phenomenon, is studied within of a one-dimensional half-filled Hubbard model. It is shown that in the limit of nearly spin polarized insulator the decay rate of the ground state into excited holon-doublon pairs can be evaluated numerically as well to high accuracy analytically. Results show that the threshold field depends on the charge gap as $F_{th} \propto \Delta^{3/2}$. Numerical results on small systems indicate on the persistence of a similar mechanism for the breakdown for decreasing magnetization down to unpolarised system.
In this paper we prove, if $u\in\mathcal C([0,\infty),{\bf {\mathcal X}^{-1}}(\mathbb R^3))$ is global solution of 3D Navier-Stokes equations, then $\|u(t)\|_{{\bf {\mathcal X}^{-1}}}$ decays to zero as time goes to infinity. Fourier analysis and standard techniques are used.
An abelian square is a string of length 2n where the last n symbols form a permutation of the first n symbols. In this note we count the number of abelian squares and give an asymptotic estimate of this quantity.
MAXI J1421-613 is an X-ray burster discovered by Monitor of All-sky X-ray Image (MAXI) on 9 January 2014 and is considered to be a low-mass X-ray binary. A previous study analyzing follow-up observation data obtained by Suzaku on 31 January to 3 February 2014 reported that an annular emission of ~3'-9' radius was found around the transient source. The most plausible origin of the annular emission is a dust scattering echo by the outburst of MAXI J1421-613. In this paper, we confirm the annular emission by analyzing the data of the Swift follow-up observation which was conducted by the photon counting mode on 18 January 2014. In a radial profile, we found an annular emission at ~2'.5-4'.5. Its spectrum was well explained by an absorbed power law, and the photon index was higher than that of MAXI J1421-613 itself by delta Gamma~2. The flux and radius of the annular emission observed by Swift are explained by dust scattering of the same outburst as is responsible for the annular emission observed by Suzaku. Assuming that the dust layer causing the annular emission found by Swift is located at the same position as the CO cloud in front of MAXI J1421-613, the distance to the transient source was estimated to be ~3 kpc, which is consistent with the value estimated by the previous study of Suzaku.
We present a new algorithm to rapidly and optimally compute power spectra. This new algorithm is based on a generalization of iterative multigrid, and has computational cost O(N log N), compared to the standard brute force approach which costs O(N^3). The procedure retains this speed on the full sky and for ill-conditioned matrices. It is applicable to galaxy power spectra, CMB, polarization and weak lensing data. We present a mathematical convergence analysis, and performance results.
We present the visible entangled states of 4-qubit system which can be observed easily in physical laboratories. This was motivated from the fact that the entangled state of 2-qubit system comes from singlet and triplet states which are constructed through the angular momentum addition formalism. We show that 4-qubit system has the new entangled states different from GHZ or W types entangled states
In this paper, we propose a \textbf{Tr}ansformer-based RGB-D \textbf{e}gocentric \textbf{a}ction \textbf{r}ecognition framework, called Trear. It consists of two modules, inter-frame attention encoder and mutual-attentional fusion block. Instead of using optical flow or recurrent units, we adopt self-attention mechanism to model the temporal structure of the data from different modalities. Input frames are cropped randomly to mitigate the effect of the data redundancy. Features from each modality are interacted through the proposed fusion block and combined through a simple yet effective fusion operation to produce a joint RGB-D representation. Empirical experiments on two large egocentric RGB-D datasets, THU-READ and FPHA, and one small dataset, WCVS, have shown that the proposed method outperforms the state-of-the-art results by a large margin.
In the present paper, we generalize the celebrated classical lemma of Birch and Heegner on quadratic twists of elliptic curves over $\mathbb{Q}$. We prove the existence of explicit infinite families of quadratic twists with analytic ranks $0$ and $1$ for a large class of elliptic curves, and use Heegner points to explicitly construct rational points of infinite order on the twists of rank $1$. In addition, we show that these families of quadratic twists satisfy the $2$-part of the Birch and Swinnerton-Dyer conjecture when the original curve does. We also prove a new result in the direction of the Goldfeld conjecture.