ShantanuT01/DACTYL-Pretraining huggingface dataset:
This is basically a summary of [Mu]. The focus of the paper is the explicit computation of Hecke operators for period functions. In particular we compute the matrix representations of the 2nd Hecke operator on period functions for the full modular group $SL(2,Z)$ and the congruence subgroup $\Gamma_0(2)$.   [Mu] Tobias M\"uhlenbruch. Hecke operators on period functions for $\Gamma_0(N)$. Journal of Number Theory. http://dx.doi.org/10.1016/j.jnt.2005.09.003
Unsupervised domain adaptation challenges the problem of transferring knowledge from a well-labelled source domain to an unlabelled target domain. Recently,adversarial learning with bi-classifier has been proven effective in pushing cross-domain distributions close. Prior approaches typically leverage the disagreement between bi-classifier to learn transferable representations, however, they often neglect the classifier determinacy in the target domain, which could result in a lack of feature discriminability. In this paper, we present a simple yet effective method, namely Bi-Classifier Determinacy Maximization(BCDM), to tackle this problem. Motivated by the observation that target samples cannot always be separated distinctly by the decision boundary, here in the proposed BCDM, we design a novel classifier determinacy disparity (CDD) metric, which formulates classifier discrepancy as the class relevance of distinct target predictions and implicitly introduces constraint on the target feature discriminability. To this end, the BCDM can generate discriminative representations by encouraging target predictive outputs to be consistent and determined, meanwhile, preserve the diversity of predictions in an adversarial manner. Furthermore, the properties of CDD as well as the theoretical guarantees of BCDM's generalization bound are both elaborated. Extensive experiments show that BCDM compares favorably against the existing state-of-the-art domain adaptation methods.
We observe that three context-free grammars of Dumont can be brought to a common ground, via the idea of transformations of grammars, proposed by Ma-Ma-Yeh. Then we develop a unified perspective to investigate several combinatorial objects in connection with the bivariate Eulerian polynomials. We call this approach the Dumont ansatz.   As applications, we provide grammatical treatments, in the spirit of the symbolic method, of relations on the Springer numbers, the Euler numbers, the three kinds of peak polynomials, an identity of Petersen, and the two kinds of derivative polynomials, introduced by Knuth-Buckholtz and Carlitz-Scoville, and later by Hoffman in a broader context. We obtain a convolution formula on the left peak polynomials, leading to the Gessel formula. In this framework, we are led to the combinatorial interpretations of the derivative polynomials due to Josuat-Verg\`es.
We present the first published maps of magnetic fields in pre-stellar cores, to test theoretical ideas about the way in which the magnetic field geometry affects the star formation process. The observations are JCMT-SCUBA maps of 850 micron thermal emission from dust. Linear polarizations at typically ten or more independent positions in each of three objects, L1544, L183 and L43 were measured, and the geometries of the magnetic fields in the plane of the sky were mapped from the polarization directions. The observed polarizations in all three objects appear smooth and fairly uniform. In L1544 and L183 the mean magnetic fields are at an angle of around 30 degrees to the minor axes of the cores. The L43 B-field appears to have been influenced in its southern half, such that it is parallel to the wall of a cavity produced by a CO outflow from a nearby T Tauri star, whilst in the northern half the field appears less disturbed and has an angle of 44 degrees to the core minor axis. We briefly compare our results with published models of magnetized cloud cores and conclude that no current model can explain these observations simultaneously with previous ISOCAM data.
We study entanglement distillability of bipartite mixed spin states under Wigner rotations induced by Lorentz transformations. We define weak and strong criteria for relativistic isoentangled and isodistillable states to characterize relative and invariant behavior of entanglement and distillability. We exemplify these criteria in the context of Werner states, where fully analytical methods can be achieved and all relevant cases presented.
In our recent paper (hep-ph/9501348) we argued that the Bjorken variable $x$ in deep inelastic scattering cannot be interpreted as the light cone momentum fraction $\xi$ even in the Bjorken limit and in zero order of the perturbation theory. The purpose of the present paper is to qualitatively explain this fact using only a few simplest kinematical relations.
In this work we present the results of a search for continuous gravitational waves from the Galactic Center using LIGO O2 data. The search uses the Band-Sampled-Data directed search pipeline, which performs a semi-coherent wide-parameter-space search, exploiting the robustness of the FrequencyHough transform algorithm. The search targets signals emitted by isolated asymmetric spinning neutron stars, located within 25-150 parsecs from the Galactic Center. The frequencies covered in this search range between 10 and 710 Hz with a spin-down range from $-1.8\times10^{-9}$ to $3.7\times10^{-11}$ Hz/s. No continuous wave signal has been detected and upper limits on the gravitational wave amplitude are presented. The most stringent upper limit at $95\%$ confidence level, for the Livingston detector, is $\sim 1.4 \times 10^{-25}$ at frequencies near 160 Hz. To date, this is the most sensitive directed search for continuous gravitational-wave signals from the Galactic Center and the first search of this kind using the LIGO second observing run.
We consider the domain dependence of the best constant in the subcritical fractional Sobolev constant,   $$   \lambda_{s,p}(\Omega):=\inf \left\{ [u]_{H^s(\mathbb{R}^N)}^2,\,\, u\in C^\infty_c(\Omega),\,\, \|u\|_{L^p(\Omega)}=1 \right\},   $$ where $s\in (0,1)$, $\Omega$ is bounded of class $C^{1,1}$ and $p\in [1, \frac{2N}{N-2s})$ if $2s<N$, $p\in [1, \infty)$ if $2s\geq N=1$. Explicitly, we derive formula for the one-sided shape derivative of the mapping $\Omega\mapsto \lambda_{s,p}(\Omega)$ under domain perturbations. In the case where $ \lambda_{s,p}(\Omega)$ admits a unique positive minimizer (e.g. $p=1$ or $p=2$), our result implies a nonlocal version of the classical variational Hadamard formula for the first eigenvalue of the Dirichlet Laplacian on $\Omega$. Thanks to the formula for our one-sided shape derivative, we characterize smooth local minimizers of $\lambda_{s,p}(\Omega)$ under volume-preserving deformations, and we find that they are balls if $p\in \{1\}\cup [2,\infty)$. Finally, we consider the maximization problem for $\lambda_{s,p}(\Omega)$ among annular-shaped domains of fixed volume of the type $B\setminus \overline B'$, where $B$ is a fixed ball and $B'$ is ball whose position is varied within $B$. We prove that, for $p\in \{1,2\}$, the value $\lambda_{s,p}(B\setminus \overline B')$ is maximal when the two balls are concentric.
This paper proposes a deep learning based method for colored transparent object matting from a single image. Existing approaches for transparent object matting often require multiple images and long processing times, which greatly hinder their applications on real-world transparent objects. The recently proposed TOM-Net can produce a matte for a colorless transparent object from a single image in a single fast feed-forward pass. In this paper, we extend TOM-Net to handle colored transparent object by modeling the intrinsic color of a transparent object with a color filter. We formulate the problem of colored transparent object matting as simultaneously estimating an object mask, a color filter, and a refractive flow field from a single image, and present a deep learning framework for learning this task. We create a large-scale synthetic dataset for training our network. We also capture a real dataset for evaluation. Experiments on both synthetic and real datasets show promising results, which demonstrate the effectiveness of our method.
The nearby spiral galaxy NGC 6946 was observed with ISO-CAM in the mid-infrared, achieving 7 arcsec resolution and sub-MJy/steradian sensitivity. Images taken with CAM filters LW2 (7 microns) and LW3 (15 microns) are analysed to determine the morphology of this galaxy and understand better the emission mechanisms. The mid-infrared emission follows an exponential disk with a scale length 75 arcsec. This is 60% of the scale length in the optical R-band and radio continuum. The nuclear starburst region is too bright for reliable measurement in these images. Its surface brightness exceeds the inner disk by at least a factor of 12. The arms and interarm regions are clearly detected, with each of these components contributing about equally to the disk emission. The arm-interarm contrast is 2-4 in the mid-IR, close to that measured in the visible R band light and lower than the contrast in $H\alpha$, suggesting that non-ionizing radiation contributes significantly to dust heating.
Let $R$ be a commutative ring with identity. A unit $u$ of $R$ is called exceptional if $1-u$ is also a unit. When $R$ is a finite commutative ring, we determine the additive and multiplicative structures of its exceptional units; and then as an application we find a necessary and sufficient condition under which $R$ is generated by its exceptional units.
Extended X-ray Absorption Fine Structure (EXAFS) studies on Ni$_{50}$Mn$_{25+x}$In$_{25-x}$ have been carried out at Ni and Mn K edge as a function of temperature. Thermal evolution of nearest neighbor Ni-Mn and Mn-Mn bond distances in the martensitic phase give a clear evidence of a close relation between structural and magnetic degrees of freedom in these alloys. In particular, the study highlights the role of Ni 3d - Mn 3d hybridization in the magnetism of martensitic phase of these alloys.
We present an exact derivation for non-commuting coordinates induced by the SU(2) transformation used to diagonalize the spin-orbit hamiltonian in two dimension.As a result an exact non-dissipative Hall current less sensitive to disorder and complementary to the dissipative conductivity is found.   We compute the non-dissipative charge and spin-Hall conductance for the spin-orbit problem.We find that the spin-Hall conductance is quantized in units of $\frac{eg\mu_{B}}{h}$ .In the presence of a Zeeman interaction the charge-Hall conductivity is proportional to the magnetic field. We propose an experiment to test our theory.
For an integer $k \ge 1$, a (distance) $k$-dominating set of a connected graph $G$ is a set $S$ of vertices of $G$ such that every vertex of $V(G) \setminus S$ is at distance at most~$k$ from some vertex of $S$. The $k$-domination number, $\gamma_k(G)$, of $G$ is the minimum cardinality of a $k$-dominating set of $G$. In this paper, we establish lower bounds on the $k$-domination number of a graph in terms of its diameter, radius and girth. We prove that for connected graphs $G$ and $H$, $\gamma_k(G \times H) \ge \gamma_k(G) + \gamma_k(H) -1$, where $G \times H$ denotes the direct product of $G$ and $H$.
We present Galactic mean metallicity maps derived from the first year of the SDSS-III APOGEE experiment. Mean abundances in different zones of Galactocentric radius (0 < R < 15 kpc) at a range of heights above the plane (0 < |z| < 3 kpc), are derived from a sample of nearly 20,000 stars with unprecedented coverage, including stars in the Galactic mid-plane at large distances. We also split the sample into subsamples of stars with low and high-[{\alpha}/M] abundance ratios. We assess possible biases in deriving the mean abundances, and find they are likely to be small except in the inner regions of the Galaxy. A negative radial gradient exists over much of the Galaxy; however, the gradient appears to flatten for R < 6 kpc, in particular near the Galactic mid-plane and for low-[{\alpha}/M] stars. At R > 6 kpc, the gradient flattens as one moves off of the plane, and is flatter at all heights for high-[{\alpha}/M] stars than for low-[{\alpha}/M] stars. Alternatively, these gradients can be described as vertical gradients that flatten at larger Galactocentric radius; these vertical gradients are similar for both low and high-[{\alpha}/M] populations. Stars with higher [{\alpha}/M] appear to have a flatter radial gradient than stars with lower [{\alpha}/M]. This could suggest that the metallicity gradient has grown steeper with time or, alternatively, that gradients are washed out over time by migration of stars.
Can magnetic interactions between single-molecule magnets (SMMs) in a crystal establish long-range magnetic order at low temperatures deep in the quantum regime, where the only electron spin-fluctuations are due to incoherent magnetic quantum tunneling (MQT)? Put inversely: can MQT provide the temperature dependent fluctuations needed to destroy the ordered state above some finite Tc, although it should basically itself be a T-independent process? Our experiments on two novel Mn4 SMMs provide a positive answer to the above, showing at the same time that MQT in the SMMs has to involve spin-lattice coupling at a relaxation rate equaling that predicted and observed recently for nuclear spin-mediated quantum relaxation.
Evidence for the existence of van der Waals loops in pressure p versus volume v plots has for some time supported the belief that melting in two dimensions is a first order phase transition. We report rather accurate equilibrium p(v) curves for systems of hard disks obtained from long Monte Carlo simulations. These curves, obtained in the constant volume ensemble, using periodic boundary conditions, exhibit well defined van der Waals loops. We illustrate their existence for finite systems that are known to undergo a continuous transition in the thermodynamic limit. To this end, we obtain magnetization m versus applied field curves from Monte Carlo simulations of the 2D Ising model, in the constant m ensemble, at the critical point. Whether van der Waals loops for disk systems behave in the thermodynamic limit as they do for the 2D Ising model at the critical point cannot be ruled out. Thus, the often made claim that melting in 2D is a first order phase transition, based on the evidence that van der Waals loops exist, is not sound.
Gaussianity and statistical isotropy of the Universe are modern cosmology's minimal set of hypotheses. In this work we introduce a new statistical test to detect observational deviations from this minimal set. By defining the temperature correlation function over the whole celestial sphere, we are able to independently quantify both angular and planar dependence (modulations) of the CMB temperature power spectrum over different slices of this sphere. Given that planar dependence leads to further modulations of the usual angular power spectrum $C_l$, this test can potentially reveal richer structures in the morphology of the primordial temperature field. We have also constructed an unbiased estimator for this angular-planar power spectrum which naturally generalizes the estimator for the usual $C_l$'s. With the help of a chi-square analysis, we have used this estimator to search for observational deviations of statistical isotropy in WMAP's 5 year release data set (ILC5), where we found only slight anomalies on the angular scales $l=7$ and $l=8$. Since this angular-planar statistic is model-independent, it is ideal to employ in searches of statistical anisotropy (e.g., contaminations from the galactic plane) and to characterize non-Gaussianities.
We present the single-epoch black hole mass estimators based on the CIV (1549 A) broad emission line, using the updated sample of the reverberation-mapped AGNs and high-quality UV spectra. By performing multi-component spectral fitting analysis, we measure the CIV line widths (FWHM_CIV) and line dispersion (sigma_CIV) and the continuum luminosity at 1350 A (L_1350) to calibrate the CIV-based mass estimators. By comparing with the Hbeta reverberation-based masses, we provide new mass estimators with the best-fit relationships, i.e., M_BH \propto L_1350 ^ (0.50+-0.07) sigma_CIV ^2 and M_BH \propto L_1350 ^ (0.52+-0.09) FWHM_CIV ^ (0.56+-0.48). The new CIV-based mass estimators show significant mass-dependent systematic difference compared to the estimators commonly used in the literature. Using the published Sloan Digital Sky Survey QSO catalog, we show that the black hole mass of high-redshift QSOs decreases on average by ~0.25 dex if our recipe is adopted.
We prove a formula which allows us to recursively compute planar tropical gravitational descendants which involve psi-classes of arbitrary power at marked ends fixed by points and additionally a psi-class of power one at exactly one marked end fixed by a line. Up to now almost exclusively tropical gravitational descendants with psi-classes at marked ends restricted by points had been considered.
ESO 381-47 is an early type galaxy with an extended HI disk. GALEX and very deep optical images reveal a distinct stellar ring far outside the optical body with a diameter of ~30 kpc, which has undergone recent star formation at 1.8 x 10^-4 Msun/yr/kpc^-2, consistent with other new results which detect low level star formation below the traditional Kennicutt relation in the outer parts of spiral galaxies. The morphology of this galaxy resembles the recently identified class of ultraviolet objects called extended ultraviolet disks, or XUV-disks. New HI observations of this galaxy taken at the ATCA and in the CnB array at the VLA show that the cold gas lies in an extended (diameter ~90 kpc) ring around the central S0 galaxy. The HI data cube can be well modeled by a warped ring. The faint ionized gas in the inner parts of the galaxy is kinematically decoupled from the stars and instead appears to exhibit velocities consistent with the rotation of the HI ring at larger radius. The peak of the stellar ring, as seen in the optical and UV, is slightly displaced to the inside relative to the peak of the HI ring. We discuss the manner in which this offset could be caused by the propagation of a radial density wave through an existing stellar disk, perhaps triggered by a galaxy collision at the center of the disk, or possibly due to a spiral density wave set up at early times in a disk too hot to form a stellar bar. Gas accretion and resonance effects due to a bar which has since dissolved are also considered to explain the presence of the star forming ring seen in the GALEX and deep optical data.
Here we first discuss briefly the quantum annealing technique. We then study the quantum annealing of Sherrington-Kirkpatrick spin glass model with the tuning of both transverse and longitudinal fields. Both the fields are time-dependent and vanish adiabatically at the same time, starting from high values. We solve, for rather small systems, the time-dependent Schrodinger equation of the total Hamiltonian by employing a numerical technique. At the end of annealing we obtain the final state having high overlap with the exact ground state(s) of classical spin glass system (obtained independently).
The channeling of the ion recoiling after a collision with a WIMP changes the ionization signal in direct detection experiments, producing a larger scintillation or ionization signal than otherwise expected. We give estimates of the fraction of channeled recoiling ions in solid Xe, Ar and Ne crystals using analytic models produced since the 1960's and 70's to describe channeling and blocking effects.
We report an exhaustive numerical analysis of violations of local realism by two qutrits in all possible pure entangled states. In Bell type experiments we allow any pairs of local unitary U(3) transformations to define the measurement bases. Surprisingly, Schmidt rank-2 states, resembling pairs of maximally entangled qubits, lead to the most noise-robust violations of local realism. The phenomenon seems to be even more pronounced for four and five dimensional systems, for which we tested a few interesting examples.
The momentum and density dependence of mean fields in symmetric and asymmetric nuclear matter are analysed using the simple density dependent finite range effective interaction containing a single Gaussian term alongwith the zero-range terms. Within the formalism developed, it is possible to reproduce the various diverging predictions on the momentum and density dependence of isovector part of the mean field in asymmetric matter. The finite nucleus calculation is formulated for the simple Gaussian interaction in the framework of quasilocal density functional theory. The prediction of energies and charge radii of the interaction for the spherical nuclei compares well with the results of other effective theories.
We present an extended analysis of deep Chandra HETG observations of the WR+OB binary system WR 147 that was resolved into a double X-ray source (Zhekov & Park, 2010, ApJ, 709, L119). Our analysis of the profiles of strong emission lines shows that their centroids are blue-shifted in the spectrum of the northern X-ray source. We find no suppressed forbidden line in the He-like triplets which indicates that the X-ray emitting region is not located near enough to the stars in the binary system to be significantly affected by their UV radiation. The most likely physical picture that emerges from the entire set of HETG data suggests that the northern X-ray source can be associated with the colliding stellar wind region in the wide WR+OB binary system, while the X-rays of its southern counterpart, the WN8 star, are result from stellar wind shocking onto a close companion (a hypothesized third star in the system).
Consider a generic random element $F_\infty= \sum_{\text{finite}} \lambda_k (N^2_k -1)$ in the second Wiener chaos with a finite number of non-zero coefficients in the spectral representation where $(N_k)_{k \ge 1}$ is a sequence of i.i.d $\mathscr{N}(0,1)$. Using the recently discovered (see Arras et al. \cite{a-a-p-s-stein}) stein operator $\RR_\infty$ associated to $F_\infty$, we introduce a new class of polynomials $$\PP_\infty:= \{ P_n = \RR^n_\infty \textbf{1} \, : \, n \ge 1 \}.$$ We analysis in details the case where $F_\infty$ is distributed as the normal product distribution $N_1 \times N_2$, and relate the associated polynomials class to Rota's {\it Umbral calculus} by showing that it is a \textit{Sheffer family} and enjoys many interesting properties. Lastly, we study the connection between the polynomial class $\PP_\infty$ and the non-central probabilistic limit theorems within the second Wiener chaos.
The pressure-induced transformation of diatomic nitrogen into non-molecular polymeric phases may produce potentially useful high-energy-density materials. We combine first-principles calculations with structure searching to predict a new class of nitrogen-rich boron nitrides with a stoichiometry of B3N5 that are stable or metastable relative to solid N2 and h-BN at ambient pressure. The most stable phase at ambient pressure has a layered structure (h-B3N5) containing hexagonal B3N3 layers sandwiched with intercalated freely rotating N2 molecules. At 15 GPa, a three-dimensional C2221 structure with single N-N bonds becomes the most stable. This pressure is much lower than that required for triple-to-single bond transformation in pure solid nitrogen (110 GPa). More importantly, C2221-B3N5 is metastable, and can be recovered under ambient conditions. Its energy density of 3.44 kJ/g makes it a potential high-energy-density material. In addition, stress-strain calculations estimate a Vickers hardness of 44 GPa. Structure searching reveals a new clathrate sodalite-like BN structure that is metastable under ambient conditions.