ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present a new module of the parallel N-Body code P-GADGET3 for cosmological simulations of light bosonic non-thermal dark matter, often referred as Fuzzy Dark Matter (FDM). The dynamics of the FDM features a highly non-linear Quantum Potential (QP) that suppresses the growth of structures at small scales. Most of the previous attempts of FDM simulations either evolved suppressed initial conditions, completely neglecting the dynamical effects of QP throughout cosmic evolution, or resorted to numerically challenging full-wave solvers. The code provides an interesting alternative, following the FDM evolution without impairing the overall performance. This is done by computing the QP acceleration through the Smoothed Particle Hydrodynamics (SPH) routines, with improved schemes to ensure precise and stable derivatives. As an extension of the P-GADGET3 code, it inherits all the additional physics modules implemented up to date, opening a wide range of possibilities to constrain FDM models and explore its degeneracies with other physical phenomena. Simulations are compared with analytical predictions and results of other codes, validating the QP as a crucial player in structure formation at small scales.
In this paper, we study the following fractional nonlinear Schr\"odinger system $$ \left\{% \begin{array}{ll} (-\Delta)^s u +u=\mu_1 |u|^{2p-2}u+\beta |v|^p|u|^{p-2}u,~~x\in \R^N,\vspace{2mm}\\ (-\Delta)^s v +v=\mu_2 |v|^{2p-2}v+\beta |u|^p|v|^{p-2}v,~~x\in \R^N, \end{array}% \right. $$ where $0<s<1, \mu_1 >0, \mu_2>0, 1<p<2_s^*/2, 2_s^*=+\infty$ for $N\le 2s$ and $2_s^*=2N/(N-2s)$ for $N>2s$, and $\beta \in \R$ is a coupling constant. We investigate the existence and non-degeneracy of proportional positive vector solutions for the above system in some ranges of $\mu_1,\mu_2, p, \beta$. We also prove that the least energy vector solutions must be proportional and unique under some additional assumptions.
Let ${\cal P}(t)\in {\Bbb K}(t)^{n}$ be a rational parametrization of an algebraic space curve $\cal C$. In this paper, we introduce the notion of limit point, $P_L$, of the given parametrization $\mathcal{P}(t)$, and some remarkable properties of $P_L$ are obtained. In addition, we generalize the results in \cite{MyB-2017} concerning the T--function, $T(s)$, which is defined by means of a univariate resultant. More precisely, independently on whether the limit point is regular or not, we show that $T(s)=\prod_{i=1}^n H_{P_i}(s)^{m_i-1}$. The polynomials $H_{P_i}(s),\,i=1,\ldots,n$ are the fibre functions, and its roots are the fibre of the ordinary singularities $P_i\in {\cal C}$ of multiplicity $m_i,\,i=1,\ldots,n$. Thus, a complete classification of the singularities of a given space curve, via the factorization of a resultant, is obtained.
We present high resolution X-ray spectroscopy of two recent GRB afterglows observed with the Low Energy Transmission Gratings on Chandra. The afterglows to GRBs 030328 and 041006 are detected beginning 15.33 and 16.8 hours after each burst, respectively, and are observed to fade in time during each ~90 ksec observation. We fit for the continuum emission in each full data set and for the data sliced into half and quarter time sections. For both afterglows, the continuum emission is well described by an absorbed power-law model, and the model parameters describing the absorption and spectral slope do not appear to evolve in time. We perform a careful search for deviations from the model continua for the full and time-sliced data and find no evidence for significant (>~3sigma) narrow emission/absorption lines or edges. The lack of detections implies that line emission--if it is a general feature in GRB X-ray afterglows--occurs early (t~0.3 days in the source frame) and/or is short-lived (dt<~10 ksec). We also comment on synchrotron fireball models for the X-ray and optical data.
Despite a great success of the Skyrme mean-field approach in exploration of nuclear dynamics, it seems to fail in description of the spin-flip M1 giant resonance. The results for different Skyrme parameterizations are contradictory and poorly agree with experiment. In particular, there is no parameterization which simultaneously describes the one-peak gross structure of M1 strength in doubly magic nuclei and two-peak structure in heavy deformed nuclei. The reason of this mismatch could lie in an unsatisfactory treatment of spin correlations and spin-orbit interaction. We discuss the present status of the problem and possible ways of its solution. In particular, we inspect i) the interplay of the collective shift and spin-orbit splitting, ii) the isovector M1 response versus isospin-mixed responses, and iii) the role of tensor and isovector spin-orbit interaction.
The Galactic Centre has been studied with the High Energy Stereoscopic System (H.E.S.S.) for over 10 years, revealing a bright, complex gamma-ray morphology. Besides a strong point-like very-high-energy gamma-ray source coincident with the supermassive black hole Sgr A*, pre- vious analyses also revealed a diffuse ridge of gamma-ray emission, indicative of a powerful cosmic-ray accelerator in this region. The addition of a fifth telescope with 600 m 2 mirror area to the centre of the H.E.S.S. array has increased the energy range accessible, allowing observations to take place down to 100 GeV and potentially below. This wider energy range allows an important overlap in observations with satellite instruments such as the Fermi-LAT gamma-ray telescope. We will present the results of new H.E.S.S observations of the Galactic Centre region and show a detailed analysis of the central source, including comparisons to results at other wavelengths.
We present results from our analysis of the finite-temperature properties of the spin 1/2 $J_{1}$-$J_{2}$ Heisenberg model on a square lattice. The analysis is based on the exact diagonalization of small clusters with 16 and 20 sites utilizing the finite-temperature Lanczos method. In particular, we focus on the temperature dependence of the third-order magnetic susceptibility as a method to resolve the ambiguity of exchange constants. We discuss the entire range of the frustration angle $\phi=\tan^{-1}(J_{2}/J_{1})$ parameterizing the different possible phases of the model, including the large region in the phase diagram with at least one ferromagnetic exchange constant.
We report the analysis results of far ultraviolet (FUV) observations, made for a broad region around $\alpha$ Vir (Spica) including the interaction zone of Loop I and the Local Bubble. The whole region was optically thin and a general correlation was seen between the FUV continuum intensity and the dust extinction, except in the neighborhood of the bright central star, indicating the dust scattering nature of the FUV continuum. We performed Monte-Carlo radiative transfer simulations to obtain the optical parameters related to the dust scattering as well as the geometrical structure of the region. The albedo and asymmetry factor were found to be 0.38$\pm$0.06 and 0.46$\pm$0.06, respectively, in good agreement with the Milky Way dust grain models. The distance to and the thickness of the interaction zone were estimated to be 70$^{+4}_{-8}$ pc and 40$^{+8}_{-10}$ pc, respectively. The diffuse FUV continuum in the northern region above Spica was mostly the result of scattering of the starlight from Spica, while that in the southern region was mainly due to the background stars. The \ion{C}{4} $\lambda\lambda$1548, 1551 emission was found throughout the whole region, in contrast to the \ion{Si}{2}* $\lambda$1532 emission which was bright only within the \ion{H}{2} region. This indicates that the \ion{C}{4} line arises mostly at the shell boundaries of the bubbles, with a larger portion likely from the Loop I than from the Local Bubble side, whereas the \ion{Si}{2}* line is from the photoionized Spica nebula.
We present 4D-Net, a 3D object detection approach, which utilizes 3D Point Cloud and RGB sensing information, both in time. We are able to incorporate the 4D information by performing a novel dynamic connection learning across various feature representations and levels of abstraction, as well as by observing geometric constraints. Our approach outperforms the state-of-the-art and strong baselines on the Waymo Open Dataset. 4D-Net is better able to use motion cues and dense image information to detect distant objects more successfully.
The asymptotic behavior of solutions of the three-dimensional Navier-Stokes equations is considered on bounded smooth domains with no-slip boundary conditions or on periodic domains. Asymptotic regularity conditions are presented to ensure that the convergence of a Leray-Hopf weak solution to its weak omega-limit set (weak in the sense of the weak topology of the space H of square-integrable divergence-free velocity fields) are achieved also in the strong topology of H. In particular, if a weak omega-limit set is bounded in the space V of velocity fields with square-integrable vorticity then the attraction to the set holds also in the strong topology of H. Corresponding results for the strong convergence towards the weak global attractor of Foias and Temam are also presented.
We prove limit theorems and variance estimates for quantities related to ponds and outlets for 2D invasion percolation. We first exhibit several properties of a sequence $({\mathbf{O}}(n))$ of outlet variables, the $n$th of which gives the number of outlets in the box centered at the origin of side length $2^n$. The most important of these properties describes the sequence's renewal structure and exponentially fast mixing behavior. We use these to prove a central limit theorem and strong law of large numbers for $({\mathbf{O}}(n))$. We then show consequences of these limit theorems for the pond radii and outlet weights.
In this article, we investigate mean field effects for a bosonic gas harmonically trapped above the transition temperature in the collisionless regime. We point out that those effects can play also a role in low dimensional system. Our treatment relies on the Boltzmann equation with the inclusion of the mean field term.   The equilibrium state is first discussed. The dispersion relation for collective oscillations (monopole, quadrupole, dipole modes) is then derived. In particular, our treatment gives the frequency of the monopole mode in an isotropic and harmonic trap in the presence of mean field in all dimensions.
In the framework of the chiral quark-soliton model of the nucleon we investigate the properties of the polarized quark distribution. In particular we analyse the so called anomalous difference between the representations of the quark distribution functions in terms of occupied and non-occupied quark states. By an explicit analytical calculation it is shown that this anomaly is absent in the polarized isoscalar distribution \Delta u + \Delta d, which is ultaviolet finite. In the case of the polarized isovector quark distribution \Delta u - \Delta d the anomaly can be cancelled by a Pauli-Villars subtraction which is also needed for the regularization of the ultraviolet divergence.
Let $G$ be a connected reductive algebraic group. We develop a Gr\"obner theory for multiplicity-free $G$-algebras, as well as a tropical geometry for subschemes in a spherical homogeneous space $G/H$. We define the notion of a spherical tropical variety and prove a fundamental theorem of tropical geometry in this context. We also propose a definition for a spherical amoeba in $G/H$. Our work partly builds on the previous work of Vogiannou on spherical tropicalization and in some ways is complementary.
We theoretically study the inverse Faraday effect, i.e., the optical induction of spin polarization with circularly polarized light, by particularly focusing on effects of band dispersions and Fermi surfaces in crystal systems with the spin-orbit interaction (SOI). By numerically solving the time-dependent Schr\"odinger equation of a tight-binding model with the Rashba-type SOI, we reproduce the light-induced spin polarization proportional to $E_0^2/\omega^3$ where $E_0$ and $\omega$ are the electric-field amplitude and the angular frequency of light, respectively. This optical spin induction is attributed to dynamical magnetoelectric coupling between the light electric field and the electron spins mediated by the SOI. We elucidate that the magnitude and sign of the induced spin polarization sensitively depend on the electron filling. To understand these results, we construct an analytical theory based on the Floquet theorem. The theory successfully explains the dependencies on $E_0$ and $\omega$ and ascribes the electron-filling dependence to a momentum-dependent effective magnetic field governed by the Fermi-surface geometry. Several candidate materials and experimental conditions relevant to our theory and model parameters are also discussed. Our findings will enable us to engineer the magneto-optical responses of matters via tuning the material parameters.
We present the results of a search for new circumstellar disks around low-mass stars and brown dwarfs with spectral types >K5 that are confirmed or candidate members of nearby young moving groups. Our search input sample was drawn from the BANYAN surveys of Malo et al. and Gagn\'e et al. Two-Micron All-Sky Survey and Wide-field Infrared Survey Explorer data were used to detect near- to mid-infrared excesses that would reveal the presence of circumstellar disks. A total of 13 targets with convincing excesses were identified: four are new and nine were already known in the literature. The new candidates are 2MASS J05010082$-$4337102 (M4.5), J08561384$-$1342242 (M8$\,\gamma$), J12474428$-$3816464 (M9$\,\gamma$) and J02265658$-$5327032 (L0$\,\delta$), and are candidate members of the TW Hya ($\sim10\pm 3\,$Myr), Columba ($\sim 42^{+6}_{-4}\,$Myr) and Tucana-Horologium ($\sim 45\pm 4\,$Myr) associations, with masses of $120$ and $13-18\,M_{\mathrm{Jup}}$. The M8$-$L0 objects in Columba and Tucana-Horologium are potentially among the first substellar disk systems aged $\sim 40\,$Myr. Estimates of the new candidates' mean disk temperatures and fractional luminosities are in the ranges $\sim 135-520\,$K and $0.021-0.15$, respectively. New optical spectroscopy of J0501$-$4337 reveals strong H$\alpha$ emission, possibly indicating ongoing accretion, provides a detection of lithium absorption and a radial velocity measurement that is consistent with a membership to Columba. We also present a near-infrared spectrum of J0226$-$5327 that reveals Paschen $\beta$ emission and shows signs of low surface gravity, consistent with accretion from a disk and a young age.
Let $G_n$ be a graph obtained by the strong product of $P_2$ and $C_n$, where $n\geqslant3$. In this paper, explicit expressions for the Kirchhoff index, multiplicative degree-Kirchhoff index and number of spanning trees of $G_n$ are determined, respectively. It is surprising to find that the Kirchhoff (resp. multiplicative degree-Kirchhoff) index of $G_n$ is almost one-sixth of its Wiener (resp. Gutman) index. Moreover, let $\mathcal{G}^r_n$ be the set of subgraphs obtained from $G_n$ by deleting any $r$ vertical edges of $G_n$, where $0\leqslant r\leqslant n$. Explicit formulas for the Kirchhoff index and the number of spanning trees for any graph $G^r_n\in \mathcal{G}^r_{n}$ are completely established, respectively. Finally, it is interesting to see that the Kirchhoff index of $G^r_n$ is almost one-sixth of its Wiener index.
We study the Severi variety $V_{d,g}$ of plane curves of degree $d$ and geometric genus $g$. Corresponding to every such variety, there is a one-parameter family of genus $g$ stable curves whose numerical invariants we compute. Building on the work of Caporaso and Harris, we derive a recursive formula for the degrees of the Hodge bundle on the families in question. For $d$ large enough, these families induce moving curves in $\bar{M}_g$. We use this to derive lower bounds for the slopes of effective divisors on $\bar{M}_g$. Another application of our results is to various enumerative problems on $V_{d,g}$.
The over-segmentation into superpixels is an important preprocessing step to smartly compress the input size and speed up higher level tasks. A superpixel was traditionally considered as a small cluster of square-based pixels that have similar color intensities and are closely located to each other. In this discrete model the boundaries of superpixels often have irregular zigzags consisting of horizontal or vertical edges from a given pixel grid. However digital images represent a continuous world, hence the following continuous model in the resolution-independent formulation can be more suitable for the reconstruction problem.   Instead of uniting squares in a grid, a resolution-independent superpixel is defined as a polygon that has straight edges with any possible slope at subpixel resolution. The harder continuous version of the over-segmentation problem is to split an image into polygons and find a best (say, constant) color of each polygon so that the resulting colored mesh well approximates the given image. Such a mesh of polygons can be rendered at any higher resolution with all edges kept straight.   We propose a fast conversion of any traditional superpixels into polygons and guarantees that their straight edges do not intersect. The meshes based on the superpixels SEEDS (Superpixels Extracted via Energy-Driven Sampling) and SLIC (Simple Linear Iterative Clustering) are compared with past meshes based on the Line Segment Detector. The experiments on the Berkeley Segmentation Database confirm that the new superpixels have more compact shapes than pixel-based superpixels.
The discovery of the integer quantum Hall effect in the early eighties of the last century, with highly precise quantization values for the Hall conductance in multiples of $e^2/h$, has been the first fascinating manifestation of the topological state of matter driven by magnetic field and disorder, and related to the formation of non-dissipative current flow. In 2005, several new phenomena such as the spin Hall effect and the quantum spin Hall effect were predicted in the presence of strong spin-orbit coupling and vanishing external magnetic field. More recently, the Zeeman spin Hall effect and the formation of valley Hall topological currents have been introduced for graphene-based systems, under time-reversal or inversion symmetry-breaking conditions, respectively. This review presents a comprehensive coverage of all these Hall effects in disordered graphene from the perspective of numerical simulations of quantum transport in two-dimensional bulk systems (by means of the Kubo formalism) and multiterminal nanostructures (by means of the Landauer-B\"{u}ttiker scattering and nonequilibrium Green function approaches). In contrast to usual two-dimensional electron gases, the presence of defects in graphene generates more complex electronic features such as electron-hole asymmetry, defect resonances or percolation effect between localized impurity states, which, together with extra degrees of freedom (sublattice pseudospin, valley isospin), bring a higher degree of complexity and enlarge the transport phase diagram.
Traditionally, object tracking and segmentation are treated as two separate problems and solved independently. However, in this paper, we argue that tracking and segmentation are actually closely related and solving one should help the other. On one hand, the object track, which is a set of bounding boxes with one bounding box in every frame, would provide strong high-level guidance for the target/background segmentation task. On the other hand, the object segmentation would separate object from other objects and background, which will be useful for determining track locations in every frame. We propose a novel framework which combines online multiple target tracking and segmentation in a video. In our approach, the tracking and segmentation problems are coupled by Lagrange dual decomposition, which leads to more accurate segmentation results and also \emph{helps resolve typical difficulties in multiple target tracking, such as occlusion handling, ID-switch and track drifting}. To track targets, an individual appearance model is learned for each target via structured learning and network flow is employed to generate tracks from densely sampled candidates. For segmentation, multi-label Conditional Random Field (CRF) is applied to a superpixel based spatio-temporal graph in a segment of video to assign background or target labels to every superpixel. The experiments on diverse sequences show that our method outperforms state-of-the-art approaches for multiple target tracking as well as segmentation.
We present the results of the quest for ring-type structures on the maps observed by the Planck satellite. The results show that the vicinity of one radius ({\gamma} = 0.14 radians) of the rings is distinguished. Twisting the circles into deformed ellipses gives a pronounced drop of significance with the increase of twisting.
The three dimensional Total Routhian Surface (TRS) calculations are carried out for 64 nuclei between $70\leq A\leq 90$ to find triaxial superdeformed nuclei. Total of 12 nuclei were predicted to have triaxial superdeformation in which the neutron rotational energy plays a key role and the neutron shell energy plays additional role in the formation of triaxial superdeformed nuclei.
In this paper we fully describe all tropical linear mappings in the tropical projective plane, that is, maps from the tropical plane to itself given by tropical multiplication by an order 3 matrix. An erratum has been added fixing two mistakes in the main paper.
Reported are UBV and uvbybeta observations of 15 candidates for Kepler primary astero- seismic targets and 14 other stars in the Kepler field, carried out at the M.G. Fracastoro station of the Catania Astrophysical Observatory. These data serve to plot the 29 stars in two-parameter diagrams with the photometric indices (such as B-V or delta m1 and the atmospheric parameters (such as the MK type or [Fe/H]) as coordinates. The two-parameter diagrams show no evidence of interstellar reddening. The photometric indices B-V and beta are then used to derive photometric effective temperatures, Teff(B-V) and Teff(beta). For Teff(B-V) > 6400 K, the photometric effective temperatures turn out to be systematically higher than spectroscopic effective temperatures by 311 +/- 34 K and 346 +/- 91 K for Teff(B-V) and Teff(beta), respectively. For T_eff(B-V) < 6250 K, the agreement between Teff(B-V) and the spectroscopic effective temperatures is very good. The photometric surface gravities, derived from c_1 and beta, show a range of about a factor of two greater than their spectroscopic counterparts do.
Electronic spin systems with S>1/2 provide an efficient method for DC vector magnetometry, since the conventional electron spin resonance spectra at a given magnetic field reflect not only the field strength but also orientation in the presence of strong spin-spin interactions. S=1 spins, e.g. the nitrogen-vacancy centers in diamond, have been intensively investigated for such a purpose. In this report, we compare S=1 and S=3/2 spins, and discuss how one can apply general principles for the use of high spin systems as a vector magnetometer to the S=3/2 spin systems. We find analytical solutions which allow a reconstruction of the magnetic field strength and polar angle using the observed resonance transitions if an uniaxial symmetry exists for the spin-spin interaction as in S=1 systems. We also find that an ambiguity of determining the field parameters may arise due to the unique properties of S=3/2 systems, and present solutions for it utilizing additional transitions in the low-field region. The electronic spins of the silicon vacancy in silicon carbide will be introduced as a model for the S=3/2 DC vector magnetometer and the practical usage of it, including the magic-angle spinning type method, will be presented too.