ShantanuT01/DACTYL-Pretraining huggingface dataset:
We introduce orbifold Euler numbers for normal surfaces with Q-divisors. These numbers behave multiplicatively under finite maps and in the log canonical case we prove that they satisfy the Bogomolov-Miyaoka-Yau type inequality. As a corollary we prove effective versions of Bogomolov's result on boundedness of rational curves in some surfaces of general type. Finally, we give some applications to singularities of plane curves.
In the 1950's, English painter Anthony Hill described drawings of complete graphs $K_n$ in the plane having precisely $$H(n) = \tfrac{1}{4}\lfloor \tfrac{n}{2}\rfloor \, \lfloor \tfrac{n-1}{2}\rfloor \, \lfloor \tfrac{n-2}{2}\rfloor \,\lfloor \tfrac{n-3}{2}\rfloor$$ crossings. It became a conjecture that this number is minimum possible and, despite serious efforts, the conjecture is still widely open. Another way of drawing $K_n$ with the same number of crossings was found by Bla\v{z}ek and Koman in 1963. In this note we provide, for the first time, a very general construction of drawings attaining the same bound. Surprisingly, the proof is extremely short and may as well qualify as a "book proof". In particular, it gives a very simple explanation of the phenomenon discovered by Moon in 1968 that a random set of $n$ points on the unit sphere $\SS^2$ in $\RR^3$ joined by geodesics gives rise to a drawing whose number of crossings asymptotically approaches the Hill value $H(n)$.
We consider the hypodissipative Navier-Stokes equations on $[0,T]\times\mathbb{T}^{d}$ and seek to construct non-unique, H\"older-continuous solutions with epochs of regularity (smooth almost everywhere outside a small singular set in time), using convex integration techniques. In particular, we give quantitative relationships between the power of the fractional Laplacian, the dimension of the singular set, and the regularity of the solution. In addition, we also generalize the usual vector calculus arguments to higher dimensions with Lagrangian coordinates.
Deep hashing has shown promising results in image retrieval and recognition. Despite its success, most existing deep hashing approaches are rather similar: either multi-layer perceptron or CNN is applied to extract image feature, followed by different binarization activation functions such as sigmoid, tanh or autoencoder to generate binary code. In this work, we introduce a novel decision-making approach for deep supervised hashing. We formulate the hashing problem as travelling across the vertices in the binary code space, and learn a deep Q-network with a novel label embedding reward defined by Bose-Chaudhuri-Hocquenghem (BCH) codes to explore the best path. Extensive experiments and analysis on the CIFAR-10 and NUS-WIDE dataset show that our approach outperforms state-of-the-art supervised hashing methods under various code lengths.
This paper presents three results on dependent site percolation on the square lattice. First, there exists no positively associated probability measure on {0,1}^{Z^2} with the following properties: a) a single infinite 0cluster exists almost surely, b) at most one infinite 1*cluster exists almost surely, c) some probabilities regarding 1*clusters are bounded away from zero. Second, we show that coexistence of an infinite 1*cluster and an infinite 0cluster is almost surely impossible when the underlying probability measure is ergodic with respect to translations, positively associated, and satisfies the finite energy condition. The third result analyses the typical structure of infinite clusters of both types in the absence of positive association. Namely, under a slightly sharpened finite energy condition, the existence of infinitely many disjoint infinite self-avoiding 1*paths follows from the existence of an infinite 1*cluster. The same holds with respect to 0paths and 0clusters.
Symmetry protected topological (SPT) states are short-range entangled states with symmetry. Nontrivial SPT states have symmetry protected gapless edge excitations. In 2-dimension (2D), there are infinite number of nontrivial SPT phases with SU(2) or SO(3) symmetry. These phases can be described by SU(2)/SO(3) nonlinear-sigma models with a quantized topological \theta-term. At open boundary, the \theta-term becomes the Wess-Zumino-Witten term and consequently the boundary excitations are decoupled gapless left movers and right movers. Only the left movers (if \theta>0) carry the SU(2)/SO(3) quantum numbers. As a result, the SU(2) SPT phases have a half-integer quantized spin Hall conductance and the SO(3) SPT phases an even-integer quantized spin Hall conductance. Both the SU(2)/SO(3) SPT phases are symmetric under their U(1) subgroup and can be viewed as U(1) SPT phases with even-integer quantized Hall conductance.
In this note, we establish a new closed formula for the solution of homogeneous second-order linear difference equations with constant coefficients by using matrix theory. This, in turn, gives new closed formulas concerning all sequences of this type such as the Fibonacci and Lucas sequences. As applications; we show that Binet's formula, in this case, is valid for negative integers as well. Finally, we find new summation formulas relating the elements of such sequences.
The global regularity for the incompressible magnetohydrodynamic equations (MHD) in three dimensions is a long standing open problem of fluid dynamics and PDE theory. The Navier-Stokes equations can be viewed as a special case of MHD with a constant magnetic field, whose global regularity problem is known as a Clay Millennium Prize Problem. In this article, we prove the global regularity of axially symmetric solutions to the ideal MHD in three dimensions for a family of non-trivial magnetic fields. The proofs are based on the special structures of MHD and can of course also applied to the resistive MHD. Our result might indicate that there are richer fantastic research topics in MHD than Navier-Stokes equations.
SN 2005kd is among the most luminous supernovae (SNe) to be discovered at X-ray wavelengths. We have re-analysed all good angular resolution (better than $20"$ FWHM PSF) archival X-ray data for SN 2005kd. The data reveal an X-ray light curve that decreases as t$^{-1.62 \pm 0.06}$. Our modelling of the data suggests that the early evolution is dominated by emission from the forward shock in a high-density medium. Emission from the radiative reverse shock is absorbed by the cold dense shell formed behind the reverse shock. Our results suggest a progenitor with a mass-loss rate towards the end of its evolution of $\ge$ 4.3 $\times$ 10$^{-4} M_{\odot} \,{\rm yr}^{-1}$, for a wind velocity of 10 km s$^{-1}$, at 4.0 $\times$ 10$^{16}$ cm. This mass-loss rate is too high for most known stars, except perhaps hypergiant stars. A higher wind velocity would lead to a correspondingly higher mass-loss rate. A Luminous Blue Variable star undergoing a giant eruption could potentially fulfill this requirement, but would need a high mass-loss rate lasting for several hundred years, and need to explain the plateau observed in the optical light curve. The latter could perhaps be due to the ejecta expanding in the dense circumstellar material at relatively small radii. These observations are consistent with the fact that Type IIn SNe appear to expand into high density and high mass-loss rate environments, and also suggest rapid variability in the wind mass-loss parameters within at least the last 5000 years of stellar evolution prior to core-collapse.
The mixing process of discrete-time quantum walks on one-dimensional lattices is revisited in a setting where the walker is coupled to an environment, and the time evolution of the walker and the environment is unitary. The mixing process is found to be incomplete, in the sense that the walker does not approach the maximally mixed state indefinitely, but the distance to the maximally mixed state saturates to some finite value depending on the size of the environment. The quantum speedup of mixing time is investigated numerically as the size of the environment decreases from infinity to a finite value. The mixing process in this unitary setting can be explained by interpreting it as an equilibration process in a closed quantum system, where subsystems can exhibit equilibration even when the entropy of the total system remains zero.
Certain towers of function fields with complete splitting of rational places at each stage are constructed. Also, families oof towers with positive N/g ratios are described.
A numerical study of static, spherically symmetric sphaleron solutions in the standard model coupled to the dilaton field is presented. We show that sphaleron is surrounded by strong dilaton cloud which vanishes inside the sphaleron.
We say that a graph G is Class 0 if its pebbling number is exactly equal to its number of vertices. For a positive integer d, let k(d) denote the least positive integer so that every graph G with diameter at most d and connectivity at least k(d) is Class 0. The existence of the function k was conjectured by Clarke, Hochberg and Hurlbert, who showed that if the function k exists, then it must satisfy k(d)=\Omega(2^d/d). In this note, we show that k exists and satisfies k(d)=O(2^{2d}). We also apply this result to improve the upper bound on the random graph threshold of the Class 0 property.
Scene text erasing, which replaces text regions with reasonable content in natural images, has drawn significant attention in the computer vision community in recent years. There are two potential subtasks in scene text erasing: text detection and image inpainting. Both subtasks require considerable data to achieve better performance; however, the lack of a large-scale real-world scene-text removal dataset does not allow existing methods to realize their potential. To compensate for the lack of pairwise real-world data, we made considerable use of synthetic text after additional enhancement and subsequently trained our model only on the dataset generated by the improved synthetic text engine. Our proposed network contains a stroke mask prediction module and background inpainting module that can extract the text stroke as a relatively small hole from the cropped text image to maintain more background content for better inpainting results. This model can partially erase text instances in a scene image with a bounding box or work with an existing scene-text detector for automatic scene text erasing. The experimental results from the qualitative and quantitative evaluation on the SCUT-Syn, ICDAR2013, and SCUT-EnsText datasets demonstrate that our method significantly outperforms existing state-of-the-art methods even when they are trained on real-world data.
Different from traditional action recognition based on video segments, online action recognition aims to recognize actions from unsegmented streams of data in a continuous manner. One way for online recognition is based on the evidence accumulation over time to make predictions from stream videos. This paper presents a fast yet effective method to recognize actions from stream of noisy skeleton data, and a novel weighted covariance descriptor is adopted to accumulate evidence. In particular, a fast incremental updating method for the weighted covariance descriptor is developed for accumulation of temporal information and online prediction. The weighted covariance descriptor takes the following principles into consideration: past frames have less contribution for recognition and recent and informative frames such as key frames contribute more to the recognition. The online recognition is achieved using a simple nearest neighbor search against a set of offline trained action models. Experimental results on MSC-12 Kinect Gesture dataset and our newly constructed online action recognition dataset have demonstrated the efficacy of the proposed method.
We survey recent results concerning ground states and bound states $u\colon\mathbb{R}^3\to\mathbb{R}^3$ to the curl-curl problem $$\nabla\times(\nabla\times u)+V(x)u= f(x,u) \quad\hbox{ in } \mathbb{R}^3,$$ which originates from the nonlinear Maxwell equations. The energy functional associated with this problem is strongly indefinite due to the infinite dimensional kernel of $\nabla\times(\nabla\times \cdot)$. The growth of the nonlinearity $f$ is superlinear and subcritical at infinity or purely critical and we demonstrate a variational approach to the problem involving the generalized Nehari manifold. We also present some refinements of known results.
Asymptotic behaviour of gravitational and electromagnetic fields of exact type D solutions from the large Plebanski-Demianski family of black hole spacetimes is analyzed. The amplitude and directional structure of radiation is evaluated in cases when the cosmological constant is non-vanishing, so that the conformal infinities have either de Sitter-like or anti-de Sitter-like character. In particular, explicit relations between the parameters that characterize the sources (that is their mass, electric and magnetic charges, NUT parameter, rotational parameter, and acceleration) and properties of the radiation generated by them are presented. The results further elucidate the physical interpretation of these solutions and may help to understand radiative characteristics of more general spacetimes than those that are asymptotically flat.
In the colour string model the impact of string percolation on multiplicities, their long-range correlations and average transverse momentum is studied. The multiplicities are shown to be damped by a simple factor which follows from the percolation theory. A clear signature of the phase transition is found to be a behaviour of the correlations for intensive observables, such as average transverse momentum, which can be detected in the high-energy heavy ion collisions.
We investigate the topological theory obtained by twisting the N=(2,2) supersymmetric nonlinear sigma model with target a bihermitian space with torsion. For the special case in which the two complex structures commute, we show that the action is a Q-exact term plus a quasi-topological term. The quasi-topological term is locally given by a closed two-form which corresponds to a flat gerbe-connection and generalises the usual topological term of the A-model. Exponentiating it gives a Wilson surface, which can be regarded as a generalization of a Wilson line. This makes the quantum theory globally well-defined.
While the dynamical origin of the variability observed in Galactic Black hole systems, such as quasi-periodic oscillations (QPOs), are still a matter of debate, insight into the radiative components responsible for such behaviour can be obtained by studying their energy dependent temporal behaviour. In particular, one needs to ascertain which variations of the parameters of the best fit time-averaged spectral components reproduce the observed energy dependent fractional r.m.s and time-lags. However, to obtain meaningful interpretation, the standard spectral component parameters have to be recast to physically relevant ones. Then, the energy dependent temporal variations that their fluctuations will cause, needs to be predicted and compared with observations. In this work, we describe a generic method to do this and apply the technique to the ~ 3-4 Hz QPOs observed in the black hole system GRS 1915+105 as observed by AstroSat where the time-averaged spectra can be represented by emission from a truncated disk and a hot thermal Comptonizing coronae in the inner regions. We find that the QPOs and their harmonic can be explained in terms of correlated local accretion rate variations in the disk, the truncated disk radius, the optical depth and the heating rate of the coronae with time-delays between them. We highlight the potential of such techniques to unravel the radiative process responsible for variability using high quality spectral and temporal data from AstroSat and NICER.
Event rates for dark matter detectors in neutralino--nucleus scattering are studied for supergravity unified models, including the constraint arising from the $b\rightarrow s\gamma$ experiment. The recent experimental measurement of this decay by the CLEO Collaboration leads to strong constraints on the SUSY particle spectrum,and also significantly affects the event rates in dark matter detectors. The analysis given here uses the accurate method for the computation of the relic density and leads to a dip in the event rate when the neutralino mass is $\sim M_Z/2$ due to the $Z$-pole, and similar results hold when the neutralino mass is $\sim m_h/2$ due to the Higgs pole . Implication of these results for dark matter detectors are discussed.
We consider the effect of lensing magnification on high redshift sources in the case that magnification varies on the sky, as expected in wide fields of view or within observed galaxy clusters. We give expressions for number counts, flux and flux variance as integrals over the probability distribution of the magnification. We obtain these through a simple mapping between averages over the observed sky and over the magnification probability distribution in the source plane. Our results clarify conflicting expressions in the literature and can be used to calculate a variety of magnification effects. We highlight two applications: 1. Lensing of high-z galaxies by galaxy clusters can provide the dominant source of scatter in SZ observations at frequencies larger than the SZ null. 2. The number counts of high-z galaxies with a Schechter-like luminosity function will be changed at high luminosities to a power law, with significant enhancement of the observed counts at L > 10 L*.
Spitzer IRS spectroscopy supports the interpretation that BP Piscium, a gas and dust enshrouded star residing at high Galactic latitude, is a first-ascent giant rather than a classical T Tauri star. Our analysis suggests that BP Piscium's spectral energy distribution can be modeled as a disk with a gap that is opened by a giant planet. Modeling the rich mid-infrared emission line spectrum indicates that the solid-state emitting grains orbiting BP Piscium are primarily composed of ~75 K crystalline, magnesium-rich olivine; ~75 K crystalline, magnesium-rich pyroxene; ~200 K amorphous, magnesium-rich pyroxene; and ~200 K annealed silica ('cristobalite'). These dust grains are all sub-micron sized. The giant planet and gap model also naturally explains the location and mineralogy of the small dust grains in the disk. Disk shocks that result from disk-planet interaction generate the highly crystalline dust which is subsequently blown out of the disk mid-plane and into the disk atmosphere.
Macroscopic dark matter (macros) refers to a broad class of alternative candidates to particle dark matter with still unprobed regions of parameter space. Prior work on macros has considered elastic scattering to be the dominant energy transfer mechanism in deriving constraints on the abundance of macros for some range of masses $M_x$ and (geometric) cross-sections $\sigma_x$ However, macros with a significant amount of electric charge would, through Coulomb interactions, interact strongly enough to have produced observable signals on terrestrial, galactic and cosmological scales. We determine the expected signals and constrain the corresponding regions of parameter space, based on the lack of these signals in observations.
The Galactic source G2.4$+$1.4 is an optical and radio nebula containing an extreme Wolf--Rayet star. At one time this source was regarded as a supernova remnant, because of its apparent non-thermal radio spectrum, although this was based on limited observations. Subsequent observations instead supported a flat, optically thin thermal radio spectrum for G2.4$+$1.4, and it was identified as a photoionized, mass-loss bubble, not a supernova remnant. Recently, however, it has been claimed that this source has a non-thermal integrated radio spectrum. I discuss the integrated radio flux densities available for G2.4$+$1.4 from a variety of surveys, and show that it has a flat spectrum at gigahertz frequencies (with a spectral index $\alpha$ of $0.02 \pm 0.08$, where flux density $S$ scales with frequency $\nu$ as $S \propto \nu^{-\alpha}$).
The magnetic fields of the quiet Sun cover at any time more than 90\% of its surface and their magnetic energy budget is crucial to explain the thermal structure of the solar atmosphere. One of the possible origins of these fields is due to the action of local dynamo in the upper convection zone of the Sun. Existing simulations of the local solar dynamo require an initial seed field, and sufficiently high spatial resolution, in order to achieve the amplification of the seed field to the observed values in the quiet Sun. Here we report an alternative model of seeding based on the action of the Bierman battery effect. This effect generates a magnetic field due to the local imbalances in electron pressure in the partially ionized solar plasma. We show that the battery effect self-consistently creates from zero an initial seed field of a strength of the order of micro G, and together with dynamo amplification, allows the generation of quiet Sun magnetic fields of a similar strength to those from solar observations.
We demonstrate a vertical field-effect transistor based on a graphene/MoSe2 van der Waals (vdW) heterostructure. The vdW interface between the graphene and MoSe2 exhibits a Schottky barrier with an ideality factor of around 1.3, suggesting a high-quality interface. Owing to the low density of states in graphene, the position of the Fermi level in the graphene can be strongly modulated by an external electric field. Therefore, the Schottky barrier height at the graphene/MoSe2 vdW interface is also modulated. We demonstrate a large current ON-OFF ratio of 10^5. These results point to the potential high performance of the graphene/MoSe2 vdW heterostructure for electronics applications.
This note provides a deeper understanding of the main results obtained in the author's 2007 DPDE paper \cite{Xiao}.
Adiabatic processes in the quantum Ising model and the anisotropic Heisenberg model are discussed. The adiabatic processes are assumed to consist in the slow variation of the strength of the magnetic field that environs the spin-systems. These processes are of current interest in the treatment of cold atoms in optical lattices and in Adiabatic Quantum Computation. We determine the probability that, during an adiabatic passage starting from the ground state, states with higher energy are excited.
It is shown that the matter content of F-theory compactifications on elliptic Calabi-Yau threefolds is encoded in the Gromov-Witten invariants.
We consider the spreading dynamics of two nested invasion clusters on an infinite tree. This model was defined as the chase-escape model by Kordzakhia and it admits a limit process, the birth-and-assassination process, previously introduced by Aldous and Krebs. On both models, we prove an asymptotic equivalent of the extinction probability near criticality. In the subcritical regime, we give a tail bound on the total progeny of the preys before extinction.
Compactifying N=(1,0) theories on a torus, with additional fluxes for global symmetries, we obtain N=1 supersymmetric theories in four dimensions. It is shown that for many choices of flux these models are toric quiver gauge theories with singlet fields. In particular we compare the anomalies deduced from the description of the six-dimensional theory and the anomalies of the quiver gauge theories. We also give predictions for anomalies of four-dimensional theories corresponding to general compactifications of M5-branes probing C_2/Z_k singularities.
We consider the Type IIB string theory in the presence of various extra $7/\bar 7$-brane pairs compactified on a warped Calabi-Yau threefold that admits a conifold singularity. We demonstrate that the volume modulus can be stabilized perturbatively at a non-supersymmetric $AdS_4/dS_4$ vacuum by the effective potential that includes the stringy $(\alpha^\prime)^3$ correction obtained by Becker {\it et al.} together with a combination of positive tension and anomalous negative tension terms generated by the additional 7-brane-antibrane pairs.