ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper we generalize permutations to plane permutations. We employ this framework to derive a combinatorial proof of a result of Zagier and Stanley, that enumerates the number of $n$-cycles $\omega$, for which $\omega(12\cdots n)$ has exactly $k$ cycles. This quantity is $0$, if $n-k$ is odd and $\frac{2C(n+1,k)}{n(n+1)}$, otherwise, where $C(n,k)$ is the unsigned Stirling number of the first kind. The proof is facilitated by a natural transposition action on plane permutations which gives rise to various recurrences. Furthermore we study several distance problems of permutations. It turns out that plane permutations allow to study transposition and block-interchange distance of permutations as well as the reversal distance of signed permutations. Novel connections between these different distance problems are established via plane permutations.
We study the isospin singlet pairing in asymmetric nuclear matter with nonzero total momentum of the condensate Cooper pairs. The quasiparticle excitation spectrum is fourfold split compared to the usual BCS spectrum of the symmetric, homogeneous matter. A twofold splitting of the spectrum into separate branches is due to the finite momentum of the condensate, the isospin asymmetry, or the finite quasiparticle lifetime. The coupling of the isospin singlet and triplet paired states leads to further twofold splitting of each of these branches. We solve the gap equation numerically in the isospin singlet channel in the case where the pairing in the isospin triplet channel is neglected and find nontrivial solutions with finite total momentum of the pairs. The corresponding phase assumes a periodic spatial structure which carries a isospin density wave at constant total number of particles. The phase transition from the BCS to the inhomogeneous superconducting phase is found to be first order and occurs when the density asymmetry is increased above 0.25. The transition from the inhomogeneous superconducting to the unpaired normal state is second order. The maximal values of the critical total momentum (in units of the Fermi momentum) and the critical density asymmetry at which condensate disappears are $P_c/p_F = 0.3$ and $\alpha_c = 0.41$. The possible spatial forms of the ground state of the inhomogeneous superconducting phase are briefly discussed.
The four-point correlation function of two 1/2 BPS primaries of conformal weight $\Delta=2$ and two 1/2-BPS primaries of conformal weight $\Delta=n$ is calculated in the large 't Hooft, large $N$ limit. These operators are dual to Kaluza-Klein supergravity fields $s_k$ with masses $m^2=-4$ and $m^2=n(n-4)$. Given that the existing formalism for evaluating sums of products of SO(6) tensors that determine the effective couplings is only suitable for primaries with small conformal dimensions, we make us of an alternative formalism based on harmonic polynomials introduced by Dolan and Osborn.   We then show that the supergravity lagrangian relevant to the computation is of sigma-model type (i.e., the four-derivative couplings vanish) and that the final result for the connected amplitude splits into a free and an interacting part, as expected on general grounds.
We study the local symplectic algebra of curves with semigroups $(4,5,6,7)$, $(4,5,6)$ and $(4,5,7)$. We use the method of algebraic restrictions to parameterized curves as in \cite{D1}. A new discrete invariant for algebraic restrictions to parameterized quasi-homogeneous curves is introduced. This invariant together with the method of algebraic restriction can distinguish different symplectic orbits of quasi-homogeneous curves.
We present the results of 3D hydrodynamic simulations of gamma-ray burst (GRB) jet emanating from a massive star with a particular focus on the formation of high-velocity quasi-spherical ejecta and the jet-induced chemical mixing. Recent early-time optical observations of supernovae associated with GRBs (e.g., GRB 171205A/SN 2017iuk) indicate a considerable amount of heavy metals in the high-velocity outer layers of the ejecta. Using our jet simulations, we show that the density and chemical structure of the outer ejecta implied by observations can be naturally reproduced by a powerful jet penetrating the progenitor star. We consider three representative jet models with a stripped massive star, a standard jet, a weak jet, and a jet choked by an extended circumstellar medium, to clarify the differences in the dynamical evolution and the chemical properties of the ejected materials. The standard jet successfully penetrates the progenitor star and creates a quasi-spherical ejecta component (cocoon). The jet-induced mixing significantly contaminates the cocoon with heavy elements that have been otherwise embedded in the inner layer of the ejecta. The weak and choked jet models fail to produce an ultra-relativistic jet but produce a quasi-spherical cocoon with different chemical properties. We discuss the impact of the different jet-star interactions on the expected early-time electromagnetic signatures of long GRBs and how to probe the jet dynamics from observations.
Context-dependence in human cognition process is a well-established fact. Following this, we introduced the image segmentation method that can use context to classify a pixel on the basis of its membership to a particular object-class of the concerned image. In the broad methodological steps, each pixel was defined by its context window (CW) surrounding it the size of which was fixed heuristically. CW texture defined by the intensities of its pixels was convoluted with weights optimized through a non-parametric function supported by a backpropagation network. Result of convolution was used to classify them. The training data points (i.e., pixels) were carefully chosen to include all variety of contexts of types, i) points within the object, ii) points near the edge but inside the objects, iii) points at the border of the objects, iv) points near the edge but outside the objects, v) points near or at the edge of the image frame. Moreover the training data points were selected from all the images within image-dataset. CW texture information for 1000 pixels from face area and background area of images were captured, out of which 700 CWs were used as training input data, and remaining 300 for testing. Our work gives the first time foundation of quantitative enumeration of efficiency of image-segmentation which is extendable to segment out more than 2 objects within an image.
We have used the Very Long Baseline Array (VLBA) and the Very Large Array (VLA) to image Galactic neutral hydrogen in absorption towards four compact extragalactic radio sources with 10 milliarcsecond resolution. Previous VLBA data by Faison et al (1998) have shown the existence of prominent structures in the direction of the extragalactic source 3C~138 with scale sizes of 10-20 AU with changes in HI optical depth in excess of 0.8 $\pm$ 0.1. In this paper we confirm the small scale \hi optical depth variations toward 3C~147 suggested earlier at a level up to 20 % $\pm$ 5% . The sources 3C~119, 2352+495 and 0831+557 show no significant change in \hi optical depth across the sources with one sigma limits of 30%, 50%, and 100%. Of the seven sources recently investigated with the VLBA and VLA, only 3C~138 and 3C~147 show statistically significant variations in HI opacities.   Deshpande (2000) have attempted to explain the observed small-scale structure as an extension of the observed power spectrum of structure on parsec size scales. The predictions of Deshpande (2000) are consistent with the VLBA HI data observed in the directions of a number of sources, including 3C~147, but are not consistent with our previous observations of the HI opacity structure toward 3C~138.
Non-mesonic transition of Lambda(1405) N to YN is investigated as one of the essential processes for the non-mesonic absorption of Kbar in nuclei. Using one-meson exchange model in the calculation of the transition, we find that the non-mesonic transition ratio Gamma_{Lambda N} / Gamma_{Sigma N} depends strongly on the ratio of the Lambda(1405) (Lambda^*) couplings to Kbar N and pi Sigma. Especially a larger Lambda^*-Kbar N coupling leads to enhancement of the transition to Lambda N. Using the chiral unitary model for the description of the Lambda^*, we obtain Gamma_{Lambda N} / Gamma_{Sigma^{0} N} is approximately 1.2 which is almost independent of the nucleon density, and find the total non-mesonic decay width of the Lambda^* in uniform nuclear matter to be 22 MeV at the normal density.
Facial pose estimation refers to the task of predicting face orientation from a single RGB image. It is an important research topic with a wide range of applications in computer vision. Label distribution learning (LDL) based methods have been recently proposed for facial pose estimation, which achieve promising results. However, there are two major issues in existing LDL methods. First, the expectations of label distributions are biased, leading to a biased pose estimation. Second, fixed distribution parameters are applied for all learning samples, severely limiting the model capability. In this paper, we propose an Anisotropic Spherical Gaussian (ASG)-based LDL approach for facial pose estimation. In particular, our approach adopts the spherical Gaussian distribution on a unit sphere which constantly generates unbiased expectation. Meanwhile, we introduce a new loss function that allows the network to learn the distribution parameter for each learning sample flexibly. Extensive experimental results show that our method sets new state-of-the-art records on AFLW2000 and BIWI datasets.
The central star of the planetary nebula (CSPN) M 2-29 shows an extraordinary R Coronae Borealis-like fading event in its optical lightcurve. The only other CSPN to show these events are CPD-568032 (Hen 3-1333) and V651 Mon (NGC 2346). Dust cloud formation in the line of sight appears responsible but the exact triggering mechanism is not well understood. Understanding how planetary nebulae (PNe) trigger dust obscuration events may help understand the same process in a wide range of objects including Population-I WC9 stars, symbiotic stars and perhaps Asymptotic Giant Branch (AGB) stars with long secondary periods (LSPs). A binary scenario involving an eccentric, wide companion that triggers dust formation via interaction at periastron is a potential explanation that has been suggested for LSP variables. Model fits to the lightcurves of CPD-568032 and M 2-29 show the dust forms in excess of 70 AU at the inner edge of a dust disk. In the case of CPD-568032 this radius is far too large to coincide with a binary companion trigger, although a binary may have been responsible for the formation of the dust disk. We find no direct evidence to support previous claims of binarity in M 2-29 either from the OGLE lightcurve or deep medium-resolution VLT FLAMES spectroscopy of the CSPN. We classify the CSPN as Of(H) with T_eff=50+-10 kK and log g=4.0+-0.3. We find a mean distance of 7.4+-1.8 kpc to M 2-29 at which the M_V=-0.9 mag CSPN could potentially hide a subgiant luminosity or fainter companion. A companion would help explain the multiple similarities with D'-type symbiotic stars whose outer nebulae are thought to be bona-fide PNe. The 7.4 kpc distance, oxygen abundance of 8.3 dex and Galactic coordinates (l=4.0, b=-3.0) prove that M 2-29 is a Galactic Bulge PN and not a Halo PN as commonly misconceived.
We prove a universal coefficients theorem for the overconvergent cohomology modules introduced by Ash and Stevens, and give several applications. In particular, we sketch a very simple construction of eigenvarieties using overconvergent cohomology and prove many instances of a conjecture of Urban on the dimensions of these spaces. For example, when the underlying reductive group is an inner form of GL(2) over a quadratic imaginary extension of the rationals, the cuspidal component of the eigenvariety is a rigid analytic curve.
The aim of this paper is to propose for the first time a reconstruction scheme and a stability result for recovering from acoustic-optic data absorption distributions with bounded variation. The paper extends earlier results on smooth absorption distributions. It opens a door for a mathematical and numerical framework for imaging, from internal data, parameter distributions with high contrast in biological tissues.
In the solar corona, magnetic reconnection usually takes place at the singular configuration of magnetic field, in particular near a magnetic null owing to its high susceptibility to perturbations. In this Letter, we report a rare X-shaped structure, encompassing a magnetic null, above a trans-equatorial quadrupole active region group that is well observed by the Atmospheric Imaging Assembly (AIA). The observations show that this X-shaped structure is visible in all AIA EUV passbands and stably exists for days. However, possibly induced by flare activities at the northern part of the quadrupole active region group, the X-shaped structure starts to destabilize and meanwhile a jet erupted near its center at 15:05 UT on 2013 October 7. Through the non-linear force-free field modeling, we identify a magnetic null, which is above the quadrupole polarities and well corresponds to the X-shaped structure. After the jet eruption, the temperature and emission measure of the plasma near the X-shaped structure rise from 2.3 MK and 1.2x10^27 cm-5 at 15:01 UT to 5.4 MK and 3.7x10^27 cm-5 at 15:36 UT, respectively, revealed by the differential emission measure analysis, indicating that magnetic reconnection most likely takes place there to heat the plasma. Moreover, the height of the null has an increase of 10 Mm, which is most likely due to the partial opening of the field lines near the fan surface that makes the null underneath rise to seek for a new equilibrium.
Video super-resolution, which attempts to reconstruct high-resolution video frames from their corresponding low-resolution versions, has received increasingly more attention in recent years. Most existing approaches opt to use deformable convolution to temporally align neighboring frames and apply traditional spatial attention mechanism (convolution based) to enhance reconstructed features. However, such spatial-only strategies cannot fully utilize temporal dependency among video frames. In this paper, we propose a novel deep learning based VSR algorithm, named Deformable Kernel Spatial Attention Network (DKSAN). Thanks to newly designed Deformable Kernel Convolution Alignment (DKC_Align) and Deformable Kernel Spatial Attention (DKSA) modules, DKSAN can better exploit both spatial and temporal redundancies to facilitate the information propagation across different layers. We have tested DKSAN on AIM2020 Video Extreme Super-Resolution Challenge to super-resolve videos with a scale factor as large as 16. Experimental results demonstrate that our proposed DKSAN can achieve both better subjective and objective performance compared with the existing state-of-the-art EDVR on Vid3oC and IntVID datasets.
A fundamental aspect of the quantum-to-classical limit is the transition from a non-commutative algebra of observables to commutative one. However, this transition is not possible if we only consider unitary evolutions. One way to describe this transition is to consider the Gamow vectors, which introduce exponential decays in the evolution. In this paper, we give two mathematical models in which this transition happens in the infite time limit. In the first one, we consider operators acting on the space of the Gamow vectors, which represent quantum resonances. In the second one, we use an algebraic formalism from scattering theory. We construct a non-commuting algebra which commutes in the infinite time limit.
We say that the order of an algebraic number $A$ is the minimum of positive integers $k$ such that $A^k$ is rational. In this paper, we show that the number of algebraic numbers $A$ with order $k$ such that \[ A,\ A^A,\ A^{A^A},\ \ldots   \] converges to an algebraic number is approximated by $(e-1/e)\varphi (k)$. Here $\varphi(k)$ denotes Euler's totient function.
Multiple photon subtraction applied to a displaced phase-averaged coherent state, which is a non-Gaussian classical state, produces conditional states with a non trivial (positive) Glauber-Sudarshan $P$-representation. We theoretically and experimentally demonstrate that, despite its simplicity, this class of conditional states cannot be fully characterized by direct detection of photon numbers. In particular, the non-Gaussianity of the state is a characteristics that must be assessed by phase-sensitive measurements. We also show that the non-Gaussianity of conditional states can be manipulated by choosing suitable conditioning values and composition of phase-averaged states.
We search for host galaxy candidates of nearby fast radio bursts (FRBs), FRB 180729.J1316+55, FRB 171020, FRB 171213, FRB 180810.J1159+83, and FRB 180814.J0422+73 (the second repeating FRB). We compare the absolute magnitudes and the expected host dispersion measure $\rm DM_{host}$ of these candidates with that of the first repeating FRB, FRB 121102, as well as those of long gamma ray bursts (LGRBs) and superluminous supernovae (SLSNe), the proposed progenitor systems of FRB 121102. We find that while the FRB 121102 host is consistent with those of LGRBs and SLSNe, the nearby FRB host candidates, at least for FRB 180729.J1316+55, FRB 171020, and FRB180814.J0422+73, either have a smaller $\rm DM_{host}$ or are fainter than FRB121102 host, as well as the hosts of LGRBs and SLSNe. In order to avoid the uncertainty in estimating $\rm DM_{host}$ due to the line-of-sight effect, we propose a galaxy-group-based method to estimate the electron density in the inter-galactic regions, and hence, $\rm DM_{IGM}$. The result strengthens our conclusion. We conclude that the host galaxy of FRB 121102 is atypical, and LGRBs and SLSNe are likely not the progenitor systems of at least most nearby FRB sources. {The recently reported two FRB hosts differ from the host of FRB 121102 and also the host candidates suggested in this paper. This is consistent with the conclusion of our paper and suggests that the FRB hosts are very diverse. }
In this paper we derive a full expression for the propagation of weak lensing shape measurement biases into cosmic shear power spectra including the effect of missing data. We show using simulations that terms higher than first order in bias parameters can be ignored and the impact of biases can be captured by terms dependent only on the mean of the multiplicative bias field. We identify that the B-mode power contains information on the multiplicative bias. We find that without priors on the residual multiplicative bias $\delta m$ and stochastic ellipticity variance $\sigma_e$ that constraints on the amplitude of the cosmic shear power spectrum are completely degenerate, and that when applying priors the constrained amplitude $A$ is slightly biased low via a classic marginalisation paradox. Using all-sky Gaussian random field simulations we find that the combination of $(1+2\delta m)A$ is unbiased for a joint EE and BB power spectrum likelihood if the error and mean (precision and accuracy) of the stochastic ellipticity variance is known to better than $\sigma(\sigma_e)\leq 0.05$ and $\Delta\sigma_e\leq 0.01$, or the multiplicative bias is known to better than $\sigma(m)\leq 0.07$ and $\Delta m\leq 0.01$.
The recent synthesis and characterization of bilayers of vitreous silica has produced valuable new information on ring sizes and distributions. In this paper, we compare the ring statistics of experimental samples with computer generated samples. The average ring size is fixed at six by topology, but the width, skewness and other moments of the distribution of ring edges are characteristics of particular samples. We examine the Aboav-Weaire law that quantifies the propensity of smaller rings to be adjacent to larger rings, and find similar results for available experimental samples which however differ somewhat from computer-generated bilayers currently. We introduce a new law for the areas of rings of various sizes.
We give an elementary probabilistic proof of Veraverbeke's Theorem for the asymptotic distribution of the maximum of a random walk with negative drift and heavy-tailed increments. The proof gives insight into the principle that the maximum is in general attained through a single large jump.
We study the phenomenology of a hypercharge-zero SU(2) triplet scalar whose existence is motivated by two-step electroweak symmetry-breaking. We consider both the possibility that the triplets are stable and contribute to the dark matter density, or that they decay via mixing with the standard model Higgs boson. The former is constrained by disappearing charged track searches at the LHC and by dark matter direct detection experiments, while the latter is constrained by existing multilepton collider searches. We find that a two-step electroweak phase transition involving a stable triplet with a negative quadratic term is ruled out by direct detection searches, while an unstable triplet with a mass less than $230\ \mathrm{GeV}$ is excluded at $95\%$ confidence level.
This work aims at transferring a Generative Adversarial Network (GAN) pre-trained on one image domain to a new domain referring to as few as just one target image. The main challenge is that, under limited supervision, it is extremely difficult to synthesize photo-realistic and highly diverse images, while acquiring representative characters of the target. Different from existing approaches that adopt the vanilla fine-tuning strategy, we import two lightweight modules to the generator and the discriminator respectively. Concretely, we introduce an attribute adaptor into the generator yet freeze its original parameters, through which it can reuse the prior knowledge to the most extent and hence maintain the synthesis quality and diversity. We then equip the well-learned discriminator backbone with an attribute classifier to ensure that the generator captures the appropriate characters from the reference. Furthermore, considering the poor diversity of the training data (i.e., as few as only one image), we propose to also constrain the diversity of the generative domain in the training process, alleviating the optimization difficulty. Our approach brings appealing results under various settings, substantially surpassing state-of-the-art alternatives, especially in terms of synthesis diversity. Noticeably, our method works well even with large domain gaps, and robustly converges within a few minutes for each experiment.
This paper is motivated by the study of a version of the so-called Schrodinger-Poisson-Slater problem: $$ - \Delta u + \omega u + \lambda (u^2 \star \frac{1}{|x|}) u=|u|^{p-2}u,$$ where $u \in H^1(\R^3)$. We are concerned mostly with $p \in (2,3)$. The behavior of radial minimizers motivates the study of the static case $\omega=0$. Among other things, we obtain a general lower bound for the Coulomb energy, that could be useful in other frameworks. The radial and nonradial cases turn out to yield essentially different situations.
The critical behavior of a model describing phase transitions in 3D antiferromagnets with 2N-component real order parameters is studied within the renormalization-group (RG) approach. The RG functions are calculated in the three-loop order and resummed by the generalized Pade-Borel procedure preserving the specific symmetry properties of the model. An anisotropic stable fixed point is found to exist in the RG flow diagram for N > 1 and lies near the Bose fixed point; corresponding critical exponents are close to those of the XY model. The accuracy of the results obtained is discussed and estimated.