ShantanuT01/DACTYL-Pretraining huggingface dataset:
We prove a rainbow version of the blow-up lemma of Koml\'os, S\'ark\"ozy and Szemer\'edi for $\mu n$-bounded edge colourings. This enables the systematic study of rainbow embeddings of bounded degree spanning subgraphs. As one application, we show how our blow-up lemma can be used to transfer the bandwidth theorem of B\"ottcher, Schacht and Taraz to the rainbow setting. It can also be employed as a tool beyond the setting of $\mu n$-bounded edge colourings. Kim, K\"uhn, Kupavskii and Osthus exploit this to prove several rainbow decomposition results. Our proof methods include the strategy of an alternative proof of the blow-up lemma given by R\"odl and Ruci\'nski, the switching method, and the partial resampling algorithm developed by Harris and Srinivasan.
In this paper, we investigate the properties of a random walk on the alternating group $A_n$ generated by $3$-cycles of the form $(i,n-1,n)$ and $(i,n,n-1)$. We call this the transpose top-$2$ with random shuffle. We find the spectrum of the transition matrix of this shuffle. We show that the mixing time is of order $\left(n-\frac{3}{2}\right)\log n$ and prove that there is a total variation cutoff for this shuffle.
This paper deals with a model of sympatric speciation, that is, speciation in the absence of geographical separation, originally proposed by U. Dieckmann and M. Doebeli in 1999. We modify their original model to obtain a Fleming--Viot type model and study its stationary distribution. We show that speciation may occur, that is, the stationary distribution puts most of the mass on a configuration that does not concentrate on the phenotype with maximum carrying capacity, if competition between phenotypes is intense enough. Conversely, if competition between phenotypes is not intense, then speciation will not occur and most of the population will have the phenotype with the highest carrying capacity. The length of time it takes speciation to occur also has a delicate dependence on the mutation parameter, and the exact shape of the carrying capacity function and the competition kernel.
A selection of 17 stars in the Sloan Digital Sky Survey, previously identified as DC class white dwarfs (WDs), has been reported to show spectra very close to blackbody radiation in the wavelength range from ultraviolet to infrared. Due to the absence of lines and other details in their spectra, the surface gravity of these objects has not been previously well constrained and their effective temperatures have been determined by fits to the continuum spectrum using pure helium atmosphere models. We compute model atmospheres with pure helium and H/He mixtures and use Gaia DR2 parallaxes available for 16 out of the 17 selected stars to analyze their physical properties. We find that the atmospheres of the selected stars are very probably contaminated with a trace amount of hydrogen as $-6 \leq \log{N_H/N_{He}} \leq -5.4$. For the 16 stars with Gaia parallaxes, we calculate a mean stellar mass $0.606\pm 0.076\,M_\odot$, which represents typical mass values and surface gravities ($7.8<\log g<8.3$) for WDs.
We study the $(\gamma,p)$ reaction on $^{208}Pb$ leading to $^{207}Pb$ with a bound pion attached to it in the lowest 1s or 2p pionic levels. The reaction can be made recoilless to optimize the production cross section but we must choose a bit higher photon energy to overcome the Coulomb barrier in the proton emission. The cross sections obtained are easily measurable and can be larger than 50 per cent of the background from inclusive ($\gamma$,p). This makes it a clear case for the detection of the pionic atom signals, converting this reaction into a practical tool to produce deeply bound pionic atoms.
A systematic experimental and theoretical study about substrate induced molecular conformation in rubrene thin films by varying film thickness from sub-monolayer to multilayer, which currently attracts substantial attention with regard to its application in organic electronics, is performed. The clean polycrystalline Au and Ag were used as noble-metals, whereas, H passivated and SiO2 terminated Si (100) were used as dielectric substrates. Angle dependent near edge x-ray absorption fine structure spectroscopy (NEXAFS) was employed to understand the molecular conformation whereas atomic force microscopy (AFM) was used to investigate the surface morphologies of the films. X-ray absorption spectra (XAS) of rubrene molecules with flat and twisted conformations were calculated using density functional theory (DFT). All the observed NEXAFS spectra of rubrene thin films at various thicknesses and onto different substrates were explained in terms of different combination of the spectral intensity from the twisted and the flat molecules. In contrast to general findings, comparatively rough polycrystalline Ag surface is found to support growth of better quality rubrene films. The results have important implications for the understanding of the substrate induced molecular conformations in rubrene thin films with its thickness and are beneficial for the improvement of the device performance.
If V(R) is the vertex set of a symmetric cycle R in the tope graph of a simple oriented matroid M, then for any tope T of M there exists a unique inclusion-minimal subset Q(T,R) of V(R) such that T is the sum of the topes of Q(T,R).   If for decompositions Q(T',R') and Q(T",R") with respect to symmetric cycles R' and R" in the tope graphs of two simple oriented matroids, whose ground sets have the cardinalities of opposite parity, we have |Q(T',R')|>3 and |Q(T",R")|>3, then these decompositions satisfy a certain orthogonality relation.
Non-equilibrium quantum rings emit circular polarized subterahertz radiation with a polarization degree controllable on nano- to picosecond time scales. This we conclude using a theory developed here for the time-dependent detection of the circular polarization of polychromatic radiations, valid for time scales comparable to the reciprocal of characteristic emission frequencies. The theory is applied to driven quantum rings whereby the influence of radiative and non-radiative processes on the properties of the emitted light is incorporated.
We compute the force between a stack of smeared antibranes at the bottom of a warped throat and a stack of smeared branes at some distance up the throat, both for anti-D3 branes and for anti-M2 branes. We perform this calculation in two ways: first, by treating the antibranes as probes in the background sourced by the branes and second, by treating the branes as probes in the candidate background sourced by the antibranes. These two very different calculations yield exactly the same expression for the force, for all values of the brane-antibrane separation. This indicates that the force between a brane and an antibrane is not screened in backgrounds where there is positive charge dissolved in flux, and gives a way to precisely compute the inflaton potential in certain string cosmology scenarios.
In this paper, we consider the Cauchy problem to the planar non-resistive magnetohydrodynamic equations without heat conductivity, and establish the global well-posedness of strong solutions with large initial data. The key ingredient of the proof is to establish the a priori estimates on the effective viscous flux and a newly introduced "transverse effective viscous flux" vector field inducted by the transverse magnetic field. The initial density is assumed only to be uniformly bounded and of finite mass and, in particular, the vacuum and discontinuities of the density are allowed.
The purpose of this study is to successfully train our vehicle detector using R-CNN, Faster R-CNN deep learning methods on a sample vehicle data sets and to optimize the success rate of the trained detector by providing efficient results for vehicle detection by testing the trained vehicle detector on the test data. The working method consists of six main stages. These are respectively; loading the data set, the design of the convolutional neural network, configuration of training options, training of the Faster R-CNN object detector and evaluation of trained detector. In addition, in the scope of the study, Faster R-CNN, R-CNN deep learning methods were mentioned and experimental analysis comparisons were made with the results obtained from vehicle detection.
We present three maps of the millimeter-wave sky created by combining data from the South Pole Telescope (SPT) and the Planck satellite. We use data from the SPT-SZ survey, a survey of 2540 deg$^2$ of the the sky with arcminute resolution in three bands centered at 95, 150, and 220 GHz, and the full-mission Planck temperature data in the 100, 143, and 217 GHz bands. A linear combination of the SPT-SZ and Planck data is computed in spherical harmonic space, with weights derived from the noise of both instruments. This weighting scheme results in Planck data providing most of the large-angular-scale information in the combined maps, with the smaller-scale information coming from SPT-SZ data. A number of tests have been done on the maps. We find their angular power spectra to agree very well with theoretically predicted spectra and previously published results.
We construct uniform gauge D1-brane action in general background. We also discuss how this action transforms under double Wick rotation and determine transformation properties of background fields.
Catalytic equations appear in several combinatorial applications, most notably in the numeration of lattice path and in the enumeration of planar maps. The main purpose of this paper is to show that the asymptotic estimate for the coefficients of the solutions of (so-called) positive catalytic equations has a universal asymptotic behavior. In particular, this provides a rationale why the number of maps of size $n$ in various planar map classes grows asymptotically like $c\cdot n^{-5/2} \gamma^n$, for suitable positive constants $c$ and $\gamma$. Essentially we have to distinguish between linear catalytic equations (where the subexponential growth is $n^{-3/2}$) and non-linear catalytic equations (where we have $n^{-5/2}$ as in planar maps). Furthermore we provide a quite general central limit theorem for parameters that can be encoded by catalytic functional equations, even when they are not positive.
This paper is devoted to the study of the Cauchy problem for the Boussinesq system with partial viscosity in dimension $N\geq3.$ First we prove a global existence result for data in Lorentz spaces satisfying a smallness condition which is at the scaling of the equations. Second, we get a uniqueness result in Besov spaces with {\it negative} indices of regularity (despite the fact that there is no smoothing effect on the temperature). The proof relies on a priori estimates with loss of regularity for the nonstationary Stokes system with convection. As a corollary, we obtain a global existence and uniqueness result for small data in Lorentz spaces.
A well-known theorem of Kulikov, Persson and Pinkham states that a degeneration of a family of K3-surfaces with trivial monodromy can be completed to a smooth family. We give a simple example that an analogous statement does not hold for Calabi-Yau threefolds.
In the Standard Model (SM) the photon in radiative $\bar B^0$ and $\bar B_s$ decays is predominantly left-handed. Thus, mixing induced CP asymmetries in $b\to s\gamma$ and $b\to d\gamma$ are suppressed by $m_s/m_b$ and $m_d/m_b$, respectively, and are very small. In many extensions of the SM, such as the left-right symmetric model (LRSM), SU(2)xU(1) models with exotic fermions and SUSY, the amplitude of right-handed photons grows proportional to the virtual heavy fermion mass, which can lead to large asymmetries. As an example, in the LRSM, asymmetries larger than 50% are possible even when radiative decay rate measurements agree with SM predictions.
We study the existence and uniqueness of new classes of solutions of the superlinear equation $-\Delta u+u^q=0$ (q>1) in a domain of R^N or in a finely open set for the topology associated to the Bessel capacity C_{2,q'}. Condition of existence or uniqueness of solutions with boundary blow-up are obtained generalizing the results of Dhersin-Le Gall and of Labutin.
An extensive non-LTE abundance analysis based on Na I 5890/5896 doublet lines was carried out for a large unbiased sample of ~120 A-type main-sequence stars (including 23 Hyades stars) covering a wide v_e sin i range of ~10--300 km/s, with an aim to examine whether the Na abundances in such A dwarfs can be reliably established from these strong Na I D lines. The resulting abundances ([Na/H]_{58}), which were obtained by applying the T_eff-dependent microturbulent velocities of \xi ~2--4 km/s with a peak at T_eff ~ 8000 K (typical for A stars), turned out generally negative with a large diversity (from ~-1 to ~0), while showing a sign of v_e sin i-dependence (decreasing toward higher rotation). However, the reality of this apparently subsolar trend is very questionable, since these [Na/H]_{58} are systematically lower by ~0.3--0.6 dex than more reliable [Na/H]_{61} (derived from weak Na I 6154/6161 lines for sharp-line stars). Considering the large \xi-sensitivity of the abundances derived from these saturated Na I D lines, we regard that [Na/H]_{58} must have been erroneously underestimated, suspecting that the conventional \xi values are improperly too large at least for such strong high-forming Na I 5890/5896 lines, presumably due to the depth-dependence of \xi decreasing with height. The nature of atmospheric turbulent velocity field in mid-to-late A stars would have to be more investigated before we can determine reliable sodium abundances from these strong resonance D lines.
A general canonical transformation of mechanical operators of position and momentum is considered. It is shown that it automatically generates a parameter s which leads to a generalized (or s-parameterized) Wigner function. This allows one to derive a generalized (s-parameterized) Moyal brackets for any dimensions. In the classical limit the s-parameterized Wigner averages of the momentum and its square yield the respective classical values. Interestingly enough,in the latter case the classical Hamilton-Jacobi equation emerges as a consequence of such a transition only if there is a non-zero parameter s.
The dynamics of electrons in the presence of a positive ion is considered for conditions of weak electron-electron couping but strong electron-ion coupling. The equilibrium electron density and electric field time correlation functions are evaluated for semi-classical conditions using a classical statistical mechanics with a regularized electron-ion interaction for MD simulation. The theoretical analysis for the equilibrium state is obtained from the corresponding nonlinear Vlasov equation. Time correlation functions for the electrons are determined from the linearized Vlasov equation. The resulting electron dynamics is described in terms of a distribution of single electron-ion trajectories screened by an inhomogeneous electron gas dielectric function. The results are applied to calculation of the autocorrelation function for the electron electric field at the ion for $ 0\leq Z\leq 40$, including conditions of strong electron-ion coupling. The electron stopping power and self-diffusion coefficient are determined from these results, and all properties calculated are compared with those obtained from semi-classical molecular dynamics simulation. The agreement with semi-classical MD simulation is found to be reasonable. The theoretical description provides an instructive interpretation for the strong electron-ion results.
The spin dynamics of the layered square-lattice vanadate Pb2VO(PO4)2 is investigated by electron spin resonance at various magnetic fields and at temperatures above magnetic ordering. The linewidth divergence towards low temperatures seems to agree with isotropic Heisenberg-type spin exchange suggesting that the spin relaxation in this quasi-two dimensional compound is governed by low-dimensional quantum fluctuations. However, a weak easy- plane anisotropy of the g factor points to the presence of a planar XY type of exchange. Indeed, we found that the linewidth divergence is described best by XY-like spin fluctuations which requires a single parameter only. Therefore, ESR-probed spin dynamics could establish Pb2VO(PO4)2 as the first frustrated square lattice system with XY-inherent spin topological fluctuations.
Here we examine the evolution of irradiated clouds using the Smoothed Particle Hydrodynamics ({\small SPH}) algorithm coupled with a ray-tracing scheme that calculates the position of the ionisation-front at each timestep. We present results from simulations performed for three choices of {\small IR}-flux spanning the range of fluxes emitted by a typical {\small B}-type star to a cluster of {\small OB}-type stars. The extent of photo-ablation, of course, depends on the strength of the incident flux and a strong flux of {\small IR} severely ablates a {\small MC}. Consequently, the first star-formation sites appear in the dense shocked layer along the edges of the irradiated cloud. Radiation-induced turbulence readily generates dense filamentary structure within the photo-ablated cloud although several new star-forming sites also appear in some of the densest regions at the junctions of these filaments. Prevalent physical conditions within a {\small MC} play a crucial role in determining the mode, i.e., filamentary as compared to isolated pockets, of star-formation, the timescale on which stars form and the distribution of stellar masses. The probability density functions ({\small PDF}s) derived for irradiated clouds in this study are intriguing due to their resemblance with those presented in a recent census of irradiated {\small MC}s. Furthermore, irrespective of the nature of turbulence, the protostellar mass-functions({\small MF}s) derived in this study follow a power-law distribution. When turbulence within the cloud is driven by a relatively strong flux of {\small IR} such as that emitted by a massive {\small O}-type star or a cluster of such stars, the {\small MF} approaches the canonical form due to Salpeter, and even turns-over for protostellar masses smaller than $\sim$0.2 M$_{\odot}$.
The purpose of this paper is to investigate the Cahn-Hillard approximation for entire minimal hypersurfaces in the hyperbolic space. Combining comparison principles with minimization and blow-up arguments, we prove existence results for entire local minimizers with prescribed behaviour at infinity. Then, we study the limit as the length scale tends to zero through a $\Gamma$-convergence analysis, obtaining existence of entire minimal hypersurfaces with prescribed boundary at infinity. In particular, we recover some existence results proved in M. Anderson and U. Lang using geometric measure theory.
We have studied the magnetic torque in uranium monosulfide (US) single crystals to explore the magnetic anisotropy in this material. Uranium monosulfide crystallizes in cubic, NaCl-type of crystal structure and exhibits the largest magneto-crystalline anisotropy observed in cubic systems. By performing detailed torque measurements we observe a strongly anisotropic behavior in the paramagnetic phase due to crystal defects and quadrupolar pair interactions. Our studies also confirm the presence of a large anisotropy in the ferromagnetic state of the US system with the <100>, <111>, and <110> directions being hard, easy, and intermediate axis, respectively. Furthermore, the anisotropy in the paramagnetic phase shows similar characteristics to the anisotropy observed in the ferromagnetic phase, as characterized by second and fourth rank susceptibility terms. The similarity of the anisotropic behaviors in paramagnetic and ferromagnetic phases is the consequence of strong magneto-elastic properties in this system, which possibly lead to the rhombohedral structural distortion, not only in the ferromagnetic phase but also in the paramagnetic phase (induced by applied magnetic fiield).
We present a catalog of 5324 massive stars in the Small Magellanic Cloud (SMC), with accurate spectral types compiled from the literature, and a photometric catalog for a subset of 3654 of these stars, with the goal of exploring their infrared properties. The photometric catalog consists of stars with infrared counterparts in the Spitzer, SAGE-SMC survey database, for which we present uniform photometry from 0.3-24 um in the UBVIJHKs+IRAC+MIPS24 bands. We compare the color magnitude diagrams and color-color diagrams to those of the Large Magellanic Cloud (LMC), finding that the brightest infrared sources in the SMC are also the red supergiants, supergiant B[e] (sgB[e]) stars, luminous blue variables, and Wolf-Rayet stars, with the latter exhibiting less infrared excess, the red supergiants being less dusty and the sgB[e] stars being on average less luminous. Among the objects detected at 24 um are a few very luminous hypergiants, 4 B-type stars with peculiar, flat spectral energy distributions, and all 3 known luminous blue variables. We detect a distinct Be star sequence, displaced to the red, and suggest a novel method of confirming Be star candidates photometrically. We find a higher fraction of Oe and Be stars among O and early-B stars in the SMC, respectively, when compared to the LMC, and that the SMC Be stars occur at higher luminosities. We estimate mass-loss rates for the red supergiants, confirming the correlation with luminosity even at the metallicity of the SMC. Finally, we confirm the new class of stars displaying composite A & F type spectra, the sgB[e] nature of 2dFS1804 and find the F0 supergiant 2dFS3528 to be a candidate luminous blue variable with cold dust.
We extend some methods of bounding exponential sums of the type $\displaystyle\sum_{n\le N}e^{2\pi iag^n/p}$ to deal with the case when $g$ is not necessarily a primitive root. We also show some recent results of Shkredov concerning additive properties of multiplicative subgroups imply new bounds for the sums under consideration.
In Weyl materials the valence and conduction electron bands touch at an even number of isolated points in the Brillouin zone. In the vicinity of these points the electron dispersion is linear and may be described by the massless Dirac equation. This results in nontrivial topology of Berry connection curvature. One of its consequences is the existence of peculiar surface electron states whose Fermi surfaces form arcs connecting projections of the Weyl points onto the surface plane. Band bending near the boundary of the crystal also produces surface states. We show that in Weyl materials band bending near the crystal surface gives rise to spiral structure of energy surfaces of arc states. The corresponding Fermi surface has the shape of a spiral that winds about the projection of the Weyl point onto the surface plane. The direction of the winding is determined by the helicity of the Weyl point and the sign of the band bending potential. For close valleys arc state morphology may be understood in terms of avoided crossing of oppositely winding spirals.
New B, V, I photometry was obtained for a sample of 152 variables (125 RR Lyrae's, 4 anomalous Cepheids, 11 classical Cepheids, 11 eclipsing binaries and a delta Scuti star) in two regions near the bar of the Large Magellanic Cloud (LMC). We derived complete and well sampled B and V light curves, very accurate periods, epochs of maximum light, amplitudes, intensity- and magnitude-averaged apparent luminosities for about 95% of the RR Lyrae stars. All these informations are contained in the photometric catalogue. Metallicities from the Fourier decomposition of the V light curves were derived for 29 of the ab type RR Lyrae's and are compared with the DeltaS metal abundances from low resolution spectra obtained with the Very Large Telescope (VLT).