ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present a dynamical model describing how halo particles can receive a significant energy kick from the merger between their own host halo and a target halo. This is highly relevant for understanding the growth of cosmological halos, and could especially provide an explanation for some high velocity objects. The model we present includes a \emph{double scattering mechanism}, where a halo particle is given a significant energy kick by undergoing two subsequent gravitational deflections during the merger. The first deflection is by the potential of the target halo, whereas the second is by the potential of the particle's original host halo. The resultant energy kick arises because the two halos move relative to each other during the two deflections. To our knowledge, this mechanism has never been characterized in this context before. We derive analytically a halo particle's total kick energy, which is composed of energy from the double scattering mechanism and energy release from tidal fields, as a function of its position in its original host halo. In the case of a $1:10$ merger between two Hernquist halos, we estimate that the presented mechanisms can generate particles with a velocity $\sim 2$ times the virial velocity of the target halo measured at its virial sphere. This motivates us to suggest that the high velocity of the recently discovered globular cluster HVCG-1 \citep{2014ApJ...787L..11C} can be explained by a head-on halo merger. Finally, we illustrate the orbital evolution of particles outside the virial sphere of the target halo, by solving the equation of motion in an expanding universe. We find a 'sweet spot' around a scale factor of $0.3-0.5$ for ejecting particles into large orbits, which easily can reach beyond $\sim 5$ virial radii.
A linear defect, viz. an elastic string, diffusing on a planar substrate traversed by a travelling wave experiences a drag known as Stokes' drift. In the limit of an infinitely long string, such a mechanism is shown to be characterized by a sharp threshold that depends on the wave parameters, the string damping constant and the substrate temperature. Moreover, the onset of the Stokes' drift is signaled by an excess diffusion of the string center of mass, while the dispersion of the drifting string around its center of mass may grow anomalous.
We study the symmetry properties of the single-band Hubbard model with general spin-orbit coupling (SOC) on the Kagome lattice. We show that the global U(1) spin-rotational symmetry is present in the Hubbard Hamiltonian owing to the inversion symmetry centered at sites. The corresponding spin Hamiltonian has, therefore, the SO(2) spin-rotational symmetry, which can be captured by including SOC non-perturbatively. The exact classical groundstates, which we obtain for arbitrary SOC, are governed by the SU(2) fluxes associated with SOC threading the constituent triangles. The groundstates break the SO(2) symmetry, and the associated Berezinsky-Kosterlitz-Thouless transition temperature is determined by the SU(2) fluxes through the triangles, which we confirm by finite temperature classical Monte Carlo simulation.
In this paper, we fix some errors made by Jitman [1] and by Prugsapitak and Jitman [3] while characterizing good integers and $2^{\beta}$-good integers.
The Kashiwara $B(\infty)$ crystal pertains to a Verma module for a Kac- Moody Lie algebra. Ostensibly it provides only a parametrisation of the global/canonical basis for the latter. Yet it is much more having a rich combinatorial structure from which one may read of a parametrisation of the corresponding basis for any integrable highest weight module, describe the decomposition of the tensor products of highest weight modules, the Demazure submodules of integrable highest weight modules and Demazure flags for translates of Demazure modules. $B(\infty)$ has in general infinitely many presentations as subsets of countably many copies of the natural numbers each given by successive reduced decompositions of Weyl group elements. In each presentation there is an action of Kashiwara operators determined by Kashiwara functions. These functions are linear in the entries. Thus a natural question is to show that in each presentation the subset $B(\infty)$ is polyhedral. Here a new approach to this question is initiated based on constructing dual Kashiwara functions and in this it is enough to show that the latter are also linear in the entries.   The present work resolves one of the two very difficult obstacles in a step-wise construction, namely that the resulting functions must satisfy a sum, or simply S, condition. It depends very subtly on inequalities between the coefficients occurring in functions obtained from the previous step. The only remaining obstacle, that sufficiently many functions are obtained, can at least be verified in many families of cases, though this is to be postponed to a subsequent paper.   This theory has some intriguing numerology which involves the Catalan numbers in two different ways.
NGC 4258 is an SABbc Seyfert galaxy, located at a distance of $7.2 \pm 0.3$ Mpc. This object is well known by its nearly edge-on molecular nuclear disc, located between 0.16 and 0.28 pc from the nucleus, whose H$_2$O maser emission allows a very precise measurement of the central supermassive black hole mass ($M_{\bullet}(maser) = 3.78 \pm 0.01 \times 10^7$ Mo). We analyse the emission line properties and the stellar kinematics in a data cube of the central region of NGC 4258, obtained, in the K band, with the Near-Infrared Integral Field Spectrograph, at the Gemini-north telescope. The nuclear spectrum, after the starlight subtraction, shows only the H$_2 \lambda 2.1218$ $\mu$m and Br$\gamma$ emission lines, the latter having a broad component with FWHM$_{Br\gamma}(broad) = 1600 \pm 29$ km s$^{-1}$. The spatial morphology and kinematics of the H$_2 \lambda 2.1218$ $\mu$m line are consistent with a rotating molecular disc around the supermassive black hole, with an upper limit for its diameter of 15.7 pc. The inner radio jet in this object is, in projection, almost perpendicular to the H$_2$ emitting disc detected in this work, and also to the H$_2$O maser emitting disc. The main features of the maps of the stellar kinematic parameters are well reproduced by a model of a thin rotating stellar circular disc. The supermassive black hole mass provided by this dynamical modelling ($M_{\bullet}(disc) = 2.8 \pm 1.0 \times 10^7$ Mo) is compatible, at 1$\sigma$ level, with the precise measurement resulting from the H$_2$O maser emission.
The Central Molecular Zone (CMZ) at the center of our Galaxy is the best template to study star formation processes under extreme conditions, similar to those in high-redshift galaxies. We observed on-the-fly maps of para-H$_{2}$CO transitions at 218 GHz and 291 GHz towards seven Galactic Center clouds. From the temperature-sensitive integrated intensity line ratios of H$_{2}$CO(3$_{2,1}-$2$_{2,0}$)/H$_{2}$CO(3$_{0,3}-$2$_{0,2}$) and H$_{2}$CO(4$_{2,2}-$3$_{2,1}$)/H$_{2}$CO(4$_{0,4}-$3$_{0,3}$) in combination with radiative transfer models, we produce gas temperature maps of our targets. These transitions are sensitive to gas with densities of $\sim$10$^{5}$ cm$^{-3}$ and temperatures <150 K. The measured gas temperatures in our sources are all higher (>40 K) than their dust temperatures ($\sim$25 K). Our targets have a complex velocity structure that requires a careful disentanglement of the different components. We produce temperature maps for each of the velocity components and show that the temperatures of the components differ, revealing temperature gradients in the clouds. Combining the temperature measurements with the integrated intensity line ratio of H$_{2}$CO(4$_{0,4}-$3$_{0,3}$)/H$_{2}$CO(3$_{0,3}-$2$_{0,2}$), we constrain the density of this warm gas to 10$^{4}-$10$^{6}$ cm$^{-3}$. We find a positive correlation of the line width of the main H$_{2}$CO lines with the temperature of the gas, direct evidence for gas heating via turbulence. Our data is consistent with a turbulence heating model with a density of n = 10$^5$ cm$^{-3}$.
The melting process of the orbital order in   Pr0.5Ca0.5MnO3 single crystal has been studied in detail as a function of temperature by neutron diffraction. It is demonstrated that a commensurate-incommensurate (C-IC) transition of the orbital ordering takes place in a bulk sample, being consistent with the electron diffraction studies. The lattice structure and the transport properties go through drastic changes in the IC orbital ordering phase below the charge/orbital ordering temperature   Tco/oo, indicating that the anomalies are intimately related to the partial disordering of the orbital order, unlike the consensus that it is related to the charge disordering process. For the same T range, partial disorder of the orbital ordering turns on the ferromagnetic spin fluctuations which were observed in a previous neutron scattering study.
Generating images from word descriptions is a challenging task. Generative adversarial networks(GANs) are shown to be able to generate realistic images of real-life objects. In this paper, we propose a new neural network architecture of LSTM Conditional Generative Adversarial Networks to generate images of real-life objects. Our proposed model is trained on the Oxford-102 Flowers and Caltech-UCSD Birds-200-2011 datasets. We demonstrate that our proposed model produces the better results surpassing other state-of-art approaches.
Number the cells of a (possibly infinite) chessboard in some way with the numbers 0, 1, 2, ... Consider the cells in order, placing a queen in a cell if and only if it would not attack any earlier queen. The problem is to determine the positions of the queens. We study the problem for a doubly-infinite chessboard of size Z x Z numbered along a square spiral, and an infinite single-quadrant chessboard (of size N x N) numbered along antidiagonals. We give a fairly complete solution in the first case, based on the Tribonacci word. There are connections with combinatorial games.
We provide q-generalizations of Spivey's Bell number formula in various settings by considering statistics on different combinatorial structures. This leads to new identities involving q-Stirling numbers of both kinds and q-Lah numbers. As corollaries, we obtain identities for both binomial and q-binomial coefficients. Our results at the same time also generalize recent r-Stirling number formulas of Mezo. Finally, we provide a combinatorial proof and refinement of Xu's extension of Spivey's formula to the generalized Stirling numbers of Hsu and Shiue. To do so, we develop a combinatorial interpretation for these numbers in terms of extended Lah distributions.
Most extrasolar planets are observed to have eccentricities much larger than those in the solar system. Some of these planets have sibling planets, with comparable masses, orbiting around the same host stars. In these multiple planetary systems, eccentricity is modulated by the planets' mutual secular interaction as a consequence of angular momentum exchange between them. For mature planets, the eigenfrequencies of this modulation are determined by their mass and semi-major axis ratios. But, prior to the disk depletion, self gravity of the planets' nascent disks dominates the precession eigenfrequencies. We examine here the initial evolution of young planets' eccentricity due to the apsidal libration or circulation induced by both the secular interaction between them and the self gravity of their nascent disks. We show that as the latter effect declines adiabatically with disk depletion, the modulation amplitude of the planets' relative phase of periapse is approximately invariant despite the time-asymmetrical exchange of angular momentum between planets. However, as the young planets' orbits pass through a state of secular resonance, their mean eccentricities undergo systematic quantitative changes. For applications, we analyze the eccentricity evolution of planets around Upsilon Andromedae and HD168443 during the epoch of protostellar disk depletion. We find that the disk depletion can change the planets' eccentricity ratio. However, the relatively large amplitude of the planets' eccentricity cannot be excited if all the planets had small initial eccentricities.
Single image super-resolution aims to generate a high-resolution image from a single low-resolution image, which is of great significance in extensive applications. As an ill-posed problem, numerous methods have been proposed to reconstruct the missing image details based on exemplars or priors. In this paper, we propose a fast and simple single image super-resolution strategy utilizing patch-wise sigmoid transformation as an imposed sharpening regularization term in the reconstruction, which realizes amazing reconstruction performance. Extensive experiments compared with other state-of-the-art approaches demonstrate the superior effectiveness and efficiency of the proposed algorithm.
We introduce a sufficient and necessary condition for the separability of a specific class of $N$ $d$-dimensional system (qudits) states, namely special generalized Werner state (SGWS): $W^{[d^N]}(v)=(1-v)\frac{I^{(N)}}{d^N}+v|\psi _d^N><\psi_d^N|$, where $ |\psi_d^N>=\sum_{i=0}^{d-1}\alpha_i|i... i>$ is an entangled pure state of $N$ qudits system and $\alpha_i$ satisfys two restrictions: (i) $\sum_{i=0}^{d-1}\alpha_i\alpha_i^*=1$; (ii) Matrix $\frac{1}{d}(I^{(1)}+\mathcal{T}\sum_{i\neq j}\alpha_i|i>< j|\alpha_j^*)$, where $\mathcal{T}=\texttt{Min}_{i\neq j}\{1/|\alpha_i\alpha_j|\}$, is a density matrix. Our condition gives quite a simple and efficiently computable way to judge whether a given SGWS is separable or not and previously known separable conditions are shown to be special cases of our approach.
Using numerical hydrodynamics code, we perform various idealized galaxy merger simulations to study the star formation (SF) of two merging disk galaxies. Our simulations include gas accretion onto supermassive black holes and active galactic nucleus (AGN) feedback. By comparing AGN simulations with those without AGNs, we attempt to understand when the AGN feedback effect is significant. With ~70 simulations, we investigated the SF with the AGN effect in mergers with variety of mass ratios, inclinations, orbits, galaxy structures and morphologies. Using these merger simulations with AGN feedback, we measure merger-driven SF using the burst efficiency parameter introduced by Cox et al. We confirm the previous studies that, in galaxy mergers, AGN suppresses SF more efficiently than in isolated galaxies. However, we additionally find that the effect of AGNs on SF is larger in major mergers than in minor mergers. In minor merger simulations with different primary bulge-to-total ratios, the effect of bulge fraction on the merger-driven SF decreases due to AGN feedback. We create models of Sa, Sb and Sc type galaxies and compare their SF properties while undergoing mergers. With the current AGN prescriptions, the difference in merger-driven SF is not as pronounced as that in the recent observational study of Kaviraj. We discuss the implications of this discrepancy.
In this paper, we embed metric space endowed with a convex combination operation, named convex combination space, into a Banach space and the embedding preserves the structures of metric and convex combination. For random element taking values in this kind of space, applications of embedding are also established. On the one hand, some nice properties of expectation such as representation of expected value through continuous affine mappings, the linearity of expectation will be given. On the other hand, the notion of conditional expectation will be also introduced and discussed. Thanks to embedding theorem, we establish some basic properties of conditional expectation, Jensen's inequality, convergences of martingales and ergodic theorem.
We construct 1/4 BPS configurations, `M-ribbons', in M-theory on T^2, which give the supertubes and supercurves in type IIA theory upon dimensional reduction. These M-ribbons are generalized so as to be consistent with the SL(2,Z) modular transformation on T^2. In terms of the type IIB theory, the generalized M-ribbons are interpreted as an SL(2,Z) duality family of super D-helix. It is also shown that the BPS M-ribbons must be straight in one direction.
The formulae needed to parametrise sigma, kappa, a0(980) and f0(980) are reviewed. For sigma and kappa, the Adler zero due to Chiral Symmetry Breaking plays a crucial role. The f0(980) and a0(980) are locked to the KK threshold by a cusp mechanism which leads to a sharp peak in attraction at the threshold. This mechanism may play a wider role. A novel suggestion is that the confinement potential involves a cooperative effect between QCD effects (coloured quarks and gluons) and conventional meson exchanges.
The statistical mechanics of a one-dimensional Ising model in thermal equilibrium is well-established, textbook material. Yet, when driven far from equilibrium by coupling two sectors to two baths at different temperatures, it exhibits remarkable phenomena, including an unexpected 'freezing by heating.' These phenomena are explored through systematic numerical simulations. Our study reveals complicated relaxation processes as well as a crossover between two very different steady-state regimes.
In this talk I review modern theories of dynamical electroweak symmetry breaking and some of their signatures at Run II of the Tevatron collider.
The trace of the stress tensor characterizes the transformation of a theory under rescaling. In quantum chromodynamics (QCD), this trace contains contributions from the bare masses of the quarks and also from a purely quantum effect, called the QCD trace anomaly. It affects all masses in the theory. We present an estimation of the QCD trace anomaly from the near-threshold J/${\rm \Psi}$ photo-production data of the GlueX experiment, at JLab. We apply a vector meson dominance model to describe the photo-production of J/${\rm \Psi}$ and a running strong coupling which includes the nonperturbative effects in the low $\mu^2$ region. Despite the large uncertainty, we find that the experimental data favors a small value of the trace anomaly parameter $b=0.07\pm 0.17$. We report the resulting proton mass decompositions at $\mu^2=0.41$ GeV$^2$ and $\mu^2=4$ GeV$^2$.
We study degenerations of Grassmannians constructed using convex lattice configurations in Bruhat-Tits buildings. Using techniques from quiver representations, we analyze their special fibers, which are explicitly described as quiver Grassmannians. For a class of lattice configurations, called the locally linearly independent configurations, we show that our construction coincide with Mustafin degenerations, thus generalizing a result of Faltings. In such cases, our analysis of special fibers also generalizes results of Cartwright et al. As an application, we prove a smoothing criterion for limit linear series on arbitrary reducible nodal curves.
An exact expression of the transmission probability through a finite graphene superlattice with an arbitrary number of potential barriers $n$ is derived in two cases of the periodic potential: rectangular electric potential and $\delta$-function magnetic potential. Obtained transmission probabilities show two types of resonance energy: barrier-induced resonance energies unchanged as $n$ varies and well-induced resonance energies undergone the $(n - 1)$-fold splitting as $n$ increases. Supported by numerical calculations for various types of graphene superlattices, these analytical findings are assumed to be in equal applied to all of finite graphene superlattices regardless of potential natures [electric or magnetic] as well as potential barrier shapes.
A (positive definite integral) quadratic form is called almost 2-universal if it represents all (positive definite integral) binary quadratic forms except those in only finitely many equivalence classes. Oh [7] determined all almost 2-universal quinary diagonal quadratic forms remaining three as candidates. In this article, we prove that those three candidates are indeed almost 2-universal.
The spin-1/2 J1-J2 antiferromagnet is a prototypical model for frustrated magnetism and one possible candidate for a realization of a spin liquid phase. The generalization of this system on the anisotropic square lattice is given by the J1-J2-J1'-J2' Heisenberg model, which can be treated by a renormalization group (RG) analysis of coupled frustrated chains. The J1-J2-J1'-J2'-model shows an interesting interplay of N\'eel order, dimerization, and spin liquid behavior. The analytical findings supported by numerical results indicate that for the isotropic model the phase at intermediate coupling strength 0.4 J1 < J2 < 0.6 J1 is not a spin liquid, but has instead a spontaneously staggered dimer order.
A general form for the surface roughness effects on the capacitance of a capacitor is proposed. We state that a capacitor with two uncoupled rough surfaces could be treated as two capacitors in series which have been divided from the mother capacitor by a slit. This is in contrast to the case where the two rough surfaces are coupled. When the rough surfaces are coupled, the type of coupling decides the modification of the capacitance in comparison to the uncoupled case. It is shown that if the coupling between the two surfaces of the capacitor is positive (negative), the capacitance is less (higher) than the case of two uncoupled rough plates. Also, we state that when the correlation length and the roughness exponent are small, the coupling effect is not negligible.
Let $m$ be a square-free integer ($m\neq 0,\pm 1$). We show that the structure of the integral bases of the fields $K=Q(\sqrt[n]{m})$ are periodic in $m$. For $3\leq n\leq 9$ we show that the period length is $n^2$. We explicitly describe the integral bases, and for $n=3,4,5,6,8$ we explicitly calculate the index forms of $K$. This enables us in many cases to characterize the monogenity of these fields. Using the explicit form of the index forms yields a new technic that enables us to derive new results on monogenity and to get several former results as easy consequences. For $n=4,6,8$ we give an almost complete characterization of the monogenity of pure fields.
In this minireview we present the main results regarding the transport properties of stochastic movement with relocations to known positions. To do so, we formulate the problem in a general manner to see several cases extensively studied during the last years as particular situations within a framework of random walks with memory. We focus on (i) stochastic motion with resets to its initial position followed by a waiting period, and (ii) diffusive motion with memory-driven relocations to previously visited positions. For both of them we show how the overall transport regime may be actively modified by the details of the relocation mechanism.
In this paper, we address the open research problem of surgical gesture recognition using motion cues from video data only. We adapt Optical flow ConvNets initially proposed by Simonyan et al.. While Simonyan uses both RGB frames and dense optical flow, we use only dense optical flow representations as input to emphasize the role of motion in surgical gesture recognition, and present it as a robust alternative to kinematic data. We also overcome one of the limitations of Optical flow ConvNets by initializing our model with cross modality pre-training. A large number of promising studies that address surgical gesture recognition highly rely on kinematic data which requires additional recording devices. To our knowledge, this is the first paper that addresses surgical gesture recognition using dense optical flow information only. We achieve competitive results on JIGSAWS dataset, moreover, our model achieves more robust results with less standard deviation, which suggests optical flow information can be used as an alternative to kinematic data for the recognition of surgical gestures.