ShantanuT01/DACTYL-Pretraining huggingface dataset:
We give further support to Smirnov's conjecture on the exact kink S-matrix for the massive Quantum Field Theory describing the integrable perturbation of the c=0.7 minimal Conformal Field theory (known to describe the tri-critical Ising model) by the operator $\phi_{2,1}$. This operator has conformal dimensions $(7/16,7/16)$ and is identified with the subleading magnetic operator of the tri-critical Ising model. In this paper we apply the Thermodynamic Bethe Ansatz (TBA) approach to the kink scattering theory by explicitly utilising its relationship with the solvable lattice hard hexagon model. Analytically examining the ultraviolet scaling limit we recover the expected central charge c=0.7 of the tri-critical Ising model. We also compare numerical values for the ground state energy of the finite size system obtained from the TBA equations with the results obtained by the Truncated Conformal Space Approach and Conformal Perturbation Theory.
We present strong approximations with rate of convergence for the solution of a stochastic differential equation of the form $$ dX_t=b(X_t)dt+\sigma(X_t)dB^H_t, $$ where $b\in C^1_b$, $\sigma \in C^2_b$, $B^H$ is fractional Brownian motion with Hurst index $H$, and we assume existence of a unique solution with Doss-Sussmann representation. The results are based on a strong approximation of $B^H$ by means of transport processes of Garz\'on et al (2009). If $\sigma$ is bounded away from 0, an approximation is obtained by a general Lipschitz dependence result of R\"omisch and Wakolbinger (1985). Without that assumption on $\sigma$, that method does not work, and we proceed by means of Euler schemes on the Doss-Sussmann representation to obtain another approximation, whose proof is the bulk of the paper.
In a companion paper by Koposov et al., RR Lyrae from \textit{Gaia} Data Release 2 are used to demonstrate that stars in the Orphan stream have velocity vectors significantly misaligned with the stream track, suggesting that it has received a large gravitational perturbation from a satellite of the Milky Way. We argue that such a mismatch cannot arise due to any realistic static Milky Way potential and then explore the perturbative effects of the Large Magellanic Cloud (LMC). We find that the LMC can produce precisely the observed motion-track mismatch and we therefore use the Orphan stream to measure the mass of the Cloud. We simultaneously fit the Milky Way and LMC potentials and infer that a total LMC mass of $1.38^{+0.27}_{-0.24} \times10^{11}\,\rm{M_\odot}$ is required to bend the Orphan Stream, showing for the first time that the LMC has a large and measurable effect on structures orbiting the Milky Way. This has far-reaching consequences for any technique which assumes that tracers are orbiting a static Milky Way. Furthermore, we measure the Milky Way mass within 50 kpc to be $3.80^{+0.14}_{-0.11}\times10^{11} M_\odot$. Finally, we use these results to predict that, due to the reflex motion of the Milky Way in response to the LMC, the outskirts of the Milky Way's stellar halo should exhibit a bulk, upwards motion.
Gravitational waves from inspiraling compact binaries are known to be an excellent absolute distance indicator, yet it is unclear whether electromagnetic counterparts of these events are securely identified for measuring their redshifts, especially in the case of black hole-black hole mergers such as the one recently observed with the Advanced LIGO. We propose to use the cross-correlation between spatial distributions of gravitational wave sources and galaxies with known redshifts as an alternative means of constraining the distance-redshift relation from gravitational waves. In our analysis, we explicitly include the modulation of the distribution of gravitational wave sources due to weak gravitational lensing. We show that the cross-correlation analysis in next-generation observations will be able to tightly constrain the relation between the absolute distance and the redshift, and therefore constrain the Hubble constant as well as dark energy parameters.
Dense atomic jets from young stars copiously emit in [FeII] IR lines, which can, therefore, be used to trace the immediate environments of embedded protostars. We want to investigate the morphology of the bright [FeII] 1.64um line in the jet of the source HH34 IRS and compare it with the most commonly used optical tracer [SII]. We analyse a 1.64um narrow-band filter image obtained with the Large Binocular Telescope (LBT) LUCI instrument, which covers the HH34 jet and counterjet. A Point Spread Function (PSF) deconvolution algorithm was applied to enhance spatial resolution and make the IR image directly comparable to a [SII] HST image of the same source. The [FeII] emission is detected from both the jet, the (weak) counter-jet, and from the HH34-S and HH34-N bow shocks. The deconvolved image allows us to resolve jet knots close to about 1\arcsec from the central source. The morphology of the [FeII] emission is remarkably similar to that of the [SII] emission, and the relative positions of [FeII] and [SII] peaks are shifted according to proper motion measurements, which were previously derived from HST images. An analysis of the [FeII]/[SII] emission ratio shows that Fe gas abundance is much lower than the solar value with up to 90% of Fe depletion in the inner jet knots. This confirms previous findings on dusty jets, where shocks are not efficient enough to remove refractory species from grains.
New shell model Hamiltonians are derived for the T=1 part of the residual interaction in the f5/2 p3/2 p1/2 g9/2 model space based on the analysis and fit of the available experimental data for 57Ni-78Ni isotopes and 77Cu-100Sn isotones. The fit procedure, properties of the determined effective interaction as well as new results for valence-mirror symmetry and seniority isomers for nuclei near 78Ni and 100Sn are discussed.
Using physical models, we study the sensitivity of polycyclic aromatic hydrocarbon (PAH) emission spectra to the character of the illuminating starlight, to the PAH size distribution, and to the PAH charge distribution. Starlight models considered range from the emission from a 3 Myr-old starburst, rich in far-ultraviolet (FUV) radiation, to the FUV-poor spectrum of the very old population of the M31 bulge. A wide range of starlight intensities is considered. The effects of reddening in dusty clouds are investigated for different starlight spectra. For a fixed PAH abundance parameter $q_{\rm PAH}$ (the fraction of the total dust mass in PAHs with $<10^3$ C atoms), the fraction of the IR power appearing in the PAH emission features can vary by a factor of two as the starlight spectrum varies from FUV-poor (M31 bulge) to FUV-rich (young starburst). We show how $q_{\rm PAH}$ can be measured from the strength of the 7.7$\mu$m emission. The fractional power in the 17$\mu$m feature can be suppressed by high starlight intensities.
We present new spectropolarimetry of a sample of nearby Compton-thin Seyfert 2 galaxies (ie those with N_H<10^23 cm^-2). We show that the detection rate of scattered broad Halpha in this sample is considerably higher than in Seyfert 2 galaxies as a whole. Our results also show that in this low obscuration set it is possible to find scattered broad Halpha even when the global properties of the galaxy are largely dominated by the host galaxy and not the active galactic nucleus. These results argue against the existence of a population of `pure' Seyfert 2 galaxies.
This paper studies the loss of the semimartingale property of the process $g(Y)$ at the time a one-dimensional diffusion $Y$ hits a level, where $g$ is a difference of two convex functions. We show that the process $g(Y)$ can fail to be a semimartingale in two ways only, which leads to a natural definition of non-semimartingales of the \textit{first} and \textit{second kind}. We give a deterministic if and only if condition (in terms of $g$ and the coefficients of $Y$) for $g(Y)$ to fall into one of the two classes of processes, which yields a characterisation for the loss of the semimartingale property. A number of applications of the results in the theory of stochastic processes and real analysis are given: e.g. we construct an adapted diffusion $Y$ on $[0,\infty)$ and a \emph{predictable} finite stopping time $\zeta$, such that $Y$ is a semimartingale on the stochastic interval $[0,\zeta)$, continuous at $\zeta$ and constant after $\zeta$, but is \emph{not} a semimartingale on $[0,\infty)$.
We theoretically studied the effect of the perpendicular electric field on the thermoelectric properties of the intrinsic, n-type and p-type bismuth telluride nanowires with the growth direction [110]. The electronic structure and the wave functions were calculated by solving self-consistently the system of the Schrodinger and Poisson equations using the spectral method. The Poisson equation was solved in terms of the Newton - Raphson method within the predictor-corrector approach. The electron - electron exchange - correlation interactions were taken into account in our analysis. In the temperature range from 77 to 500 K, the dependences of the Seebeck coefficient, thermal conductivity, electron (hole) concentration, and thermoelectric figure of merit on the nanowire thickness, gate voltage, and excess hole (electron) concentration were investigated in the constant relaxation-time approximation. The results of our calculations indicate that the external perpendicular electric field can increase the Seebeck coefficient of the bismuth telluride nanowires with thicknesses of 7 - 15 nm by nearly a factor of 2 and enhance ZT by an order of magnitude. At room temperature, ZT can reach a value as high as 3.4 under the action of the external perpendicular electric field for realistic widths of the nanowires. The obtain results may open up a completely new way for a drastic enhancement of the thermoelectric figure of merit in a wide temperature range.
We prove that, for any real $\lambda$, the system $-\Delta u +\lambda u = u^3-\beta uv^2$, $ -\Delta v+\lambda v =v^3-\beta vu^2$, $ u,v\in H^1_0(\Omega),$ where $\Omega$ is a bounded smooth domain of $R^3$, admits a bounded family of positive solutions $(u_{\beta}, v_{\beta})$ as $\beta \to +\infty$. An upper bound on the number of nodal sets of the weak limits of difference $u_{\beta}-v_{\beta}$ is also provided. Moreover, for any sufficiently large fixed value of $\beta >0$ the system admits infinitely many positive solutions.
Goulden and Jackson (1996) introduced, using Jack symmetric functions, some multivariate generating series $\psi(x, y, z; 1, 1+\beta)$ with an additional parameter $\beta$ that may be interpreted as a continuous deformation of the rooted bipartite maps generating series. Indeed, it has the property that for $\beta \in \{0,1\}$, it specializes to the rooted, orientable (general, i.e. orientable or not, respectively) bipartite maps generating series. They made the following conjecture: coefficients of $\psi$ are polynomials in $\beta$ with positive integer coefficients that can be written as a multivariate generating series of rooted, general bipartite maps, where the exponent of $\beta$ is an integer-valued statistic that in some sense "measures the non-orientability" of the corresponding bipartite map.   We show that except for two special values of $\beta = 0,1$ for which the combinatorial interpretation of the coefficients of $\psi$ is known, there exists a third special value $\beta = -1$ for which the coefficients of $\psi$ indexed by two partitions $\mu,\nu$, and one partition with only one part are given by rooted, orientable bipartite maps with arbitrary face degrees and black/white vertex degrees given by $\mu$/$\nu$, respectively. We show that this evaluation corresponds, up to a sign, to a top-degree part of the coefficients of $\psi$. As a consequence, we introduce a collection of integer-valued statistics of maps $(\eta)$ such that the top-degree of the multivariate generating series of rooted bipartite maps with only one face (called unicellular) with respect to $\eta$ gives the top-degree of the appropriate coefficients of $\psi$. Finally, we show that the $b$-conjecture holds true for all rooted, unicellular bipartite maps of genus at most $2$.
Through Bayesian optimization and the least absolute shrinkage and selection operator (LASSO) technique combined with first-principles calculations, we investigated the tunnel magnetoresistance (TMR) effect of Fe/disordered-MgAl2O4(MAO)/Fe(001) magnetic tunnel junctions (MTJs) to determine structures of disordered-MAO that give large TMR ratios. The optimal structure with the largest TMR ratio was obtained by Bayesian optimization with 1728 structural candidates, where the convergence was reached within 300 structure calculations. Characterization of the obtained structures suggested that the in-plane distance between two Al atoms plays an important role in determining the TMR ratio. Since the Al-Al distance of disordered MAO significantly affects the imaginary part of complex band structures, the majority-spin conductance of the {\Delta}1 state in Fe/disordered-MAO/Fe MTJs increases with increasing in-plane Al-Al distance, leading to larger TMR ratios. Furthermore, we found that the TMR ratio tended to be large when the ratio of the number of Al, Mg, and vacancies in the [001] plane was 2:1:1, indicating that the control of Al atomic positions is essential to enhancing the TMR ratio in MTJs with disordered MAO. The present work reveals the effectiveness and advantage of material informatics combined with first-principles transport calculations in designing high-performance spintronic devices based on MTJs.
The eigenvalues of Frobenius acting on $\ell$-adic cohomology of a complete intersection over a finite field have the divisibility predicted by the theorem of Ax and Katz. We have corrected some unforgivable typos.
The goal of this work is to to investigate different numerical approaches and to introduce a new, physically-based sub-grid model for the ISM physics, including a treatment of star formation and Type II supernovae energy feedback (MUPPI, MUlti-Phase Particle Integrator). Our model follows the ISM physics using a system of ordinary differential equations, describing mass and energy flows among the different gas phases in the ISM inside each gas particle. The model also includes the treatment of SNe energy transfer from star-forming particles to their neighbours. We will show in this Thesis how this model is able to reproduce observed ISM properties, while also providing an effective thermal energy feedback and responding to variations in the local hydrodynamical properties of the gas, e.g. crossing of a spiral density wave in a galaxy disk. We believe the model we presented here will be particularly useful in cosmological simulations of formation and evolution of isolated galaxies and galaxy clusters. For this reason, the first application of the present Ph.D. work will therefore be to apply MUPPI to cosmological simulations, with the aim of determine how an improved treatment of star formation and feedback astrophysical processes impacts on many open issues, from the properties of simulated disk galaxies to the properties of cold baryons (galaxies and diffuse stellar component) in galaxy clusters, to the properties of the Intra-Cluster Medium in presence of an effective supernovae thermal feedback.
Natural interaction with virtual objects in AR/VR environments makes for a smooth user experience. Gestures are a natural extension from real world to augmented space to achieve these interactions. Finding discriminating spatio-temporal features relevant to gestures and hands in ego-view is the primary challenge for recognising egocentric gestures. In this work we propose a data driven end-to-end deep learning approach to address the problem of egocentric gesture recognition, which combines an ego-hand encoder network to find ego-hand features, and a recurrent neural network to discern temporally discriminating features. Since deep learning networks are data intensive, we propose a novel data augmentation technique using green screen capture to alleviate the problem of ground truth annotation. In addition we publish a dataset of 10 gestures performed in a natural fashion in front of a green screen for training and the same 10 gestures performed in different natural scenes without green screen for validation. We also present the results of our network's performance in comparison to the state-of-the-art using the AirGest dataset
Multiple Instance Learning is a form of weakly supervised learning in which the data is arranged in sets of instances called bags with one label assigned per bag. The bag level class prediction is derived from the multiple instances through application of a permutation invariant pooling operator on instance predictions or embeddings. We present a novel pooling operator called \textbf{Certainty Pooling} which incorporates the model certainty into bag predictions resulting in a more robust and explainable model. We compare our proposed method with other pooling operators in controlled experiments with low evidence ratio bags based on MNIST, as well as on a real life histopathology dataset - Camelyon16. Our method outperforms other methods in both bag level and instance level prediction, especially when only small training sets are available. We discuss the rationale behind our approach and the reasons for its superiority for these types of datasets.
Velocity profiles of a line of H$_3^+$ at 3.7 $\mu$m produced in warm diffuse gas have been observed toward 18 stars in the Central Molecular Zone (CMZ) of the Galaxy. Their longitude-velocity diagram indicates that the gas is radially expanding within the CMZ at speeds up to a maximum of $\sim$150 km s$^{-1}$. The current momentum and energy in the gas are $\sim 5 \times 10^8 M_\odot$ km s$^{-1}$ and $\sim 5\times 10^{53}$ erg. The motion is similar to that of the Expanding Molecular Ring (EMR) discovered in 1972 by Kaifu et al. and by Scoville. We propose that the expanding gas seen in H$_3^+$ is part of the same phenomenon, in spite of differences in estimates of density, morphology, and degree of rotation. The outward motion suggests that one or more ejection events occurred near the center of the CMZ (0.5$-$1) $\times$ 10$^6$ years ago, which may be related to creation of the recently observed microwave bubble. These observations revive the circular face-on view of the CMZ proposed in 1972, which fell out of favor after 1991 when Binney et al. proposed that a face-on view of the CMZ would show it to have an elliptical shape, with high eccentricity. While that model may apply on kiloparsec scales, we argue that it is incorrect to apply it to the much smaller CMZ. We discuss the fate of the expanding gas, which appears to be eventual infall into the center, leading to episodes of star formation and violent events associated with accretion onto Sgr~A$^\ast$.
A model for the solar dynamo, consistent in global flow and numerical method employed with the differential rotation model, is developed. The magnetic turbulent diffusivity is expressed in terms of the entropy gradient, which is controlled by the model equations. The magnetic Prandtl number and latitudinal profile of the alpha-effect are specified by fitting the computed period of the activity cycle and the equatorial symmetry of magnetic fields to observations. Then, the instants of polar field reversals and time-latitude diagrams of the fields also come into agreement with observations. The poloidal field has a maximum amplitude of about 10 Gs in the polar regions. The toroidal field of several thousand Gauss concentrates near the base of the convection zone and is transported towards the equator by the meridional flow. The model predicts a value of about 10^37 erg for the total magnetic energy of large-scale fields in the solar convection zone.
In the current article, we study anisotropic spherically symmetric strange star under the background of $f(R,T)$ gravity using the metric potentials of Tolman-Kuchowicz type~\cite{Tolman1939,Kuchowicz1968} as $\lambda(r)=\ln(1+ar^2+br^4)$ and $\nu(r)=Br^2+2\ln C$ which are free from singularity, satisfy stability criteria and also well behaved. We calculate the value of constants $a$, $b$, $B$ and $C$ using matching conditions and the observed values of the masses and radii of known samples. To describe the strange quark matter (SQM) distribution, here we have used the phenomenological MIT bag model equation of state (EOS) where the density profile ($\rho$) is related to the radial pressure ($p_r$) as $p_r(r)=\frac{1}{3}(\rho-4B_g)$. Here quark pressure is responsible for generation of bag constant $B_g$. Motivation behind this study lies in finding out a non-singular physically acceptable solution having various properties of strange stars. The model shows consistency with various energy conditions, TOV equation, Herrera's cracking condition and also with Harrison-Zel$'$dovich-Novikov's static stability criteria. Numerical values of EOS parameter and the adiabatic index also enhance the acceptability of our model.
Many different physical processes have been suggested to explain the prompt gamma-ray emission in gamma-ray bursts (GRBs). Although there are examples of both bursts with photospheric and synchrotron emission origins, these distinct spectral appearances have not been generalized to large samples of GRBs. Here, we search for signatures of the different emission mechanisms in the full Fermi Gamma-ray Space Telescope GBM catalogue. We use Gaussian Mixture Models to cluster bursts according to their parameters from the Band function ($\alpha$, $\beta$, and $E_{pk}$) as well as their fluence and $T_{90}$. We find five distinct clusters. We further argue that these clusters can be divided into bursts of photospheric origin (2/3 of all bursts, divided into 3 clusters) and bursts of synchrotron origin (1/3 of all bursts, divided into 2 clusters). For instance, the cluster that contains predominantly short bursts is consistent of photospheric emission origin. We discuss several reasons that can determine which cluster a burst belongs to: jet dissipation pattern and/or the jet content, or viewing angle.
The time and size distribution of the waves of topplings in the Abelian sandpile model are expressed as the first arrival at the origin distribution for a scale invariant, time inhomogeneous Fokker-Planck equation. Assuming a linear conjecture for the the time inhomogeneity exponent as function of loop erased random walk (LERW) critical exponent, suggested by numerical results, this approach allows to estimate the lower critical dimension of the model and the exact value of the critical exponent for LERW in three dimension. The avalanche size distribution in two dimensions is found to be the difference between two closed power laws.
We use semiclassical propagation of singularities to give a general method for gluing together resolvent estimates. As an application we prove estimates for the analytic continuation of the resolvent of a Schr\"odinger operator for certain asymptotically hyperbolic manifolds in the presence of trapping which is sufficiently mild in one of several senses. As a corollary we obtain local exponential decay for the wave propagator and local smoothing for the Schr\"odinger propagator.
Uniformly for small $q$ and $(a,q)=1$, we obtain an estimate for the weighted number of ways a sufficiently large integer can be represented as the sum of a prime congruent to $a$ modulo $q$ and a square-free integer. Our method is based on the notion of local model developed by Ramar\'e and may be viewed as an abstract circle method.