ShantanuT01/DACTYL-Pretraining huggingface dataset:
Effective dynamics using conditional expectation was proposed in [F. Legoll and T. Leli\`evre, Nonlinearity, 2010] to approximate the essential dynamics of high-dimensional diffusion processes along a given reaction coordinate. The approximation error of the effective dynamics when it is used to approximate the behavior of the original dynamics has been considered in recent years. As a continuation of the previous work [F. Legoll, T. Leli\`evre, and S. Olla, Stoch. Process. Appl, 2017], in this paper we obtain pathwise estimates for effective dynamics when the reaction coordinate function is either nonlinear or vector-valued.
In the present article we are interested in further investigations for the barotropic compressible Navier-Stokes system endowed with a non-local capillarity we studied in [7]. Thanks to an accurate study of the associated linear system using a Lagrangian change of coordinates, we provide more precise energy estimates in terms of hybrid Besov spaces naturally depending on a threshold frequency (which is determined in function of the physical parameter) distinguishing the low and the high regimes. It allows us in particular to prove the convergence of the solutions from the non-local to the local Korteweg system. Another mathematical interest of this article is the study of the effect of the Lagrangian change on the non-local capillary term.
Using methods developed for hard exclusive QCD processes, we calculate the asymptotic behaviour of heavy-meson form factors at large recoil. It is determined by the leading- and subleading-twist meson wave functions. For $1\ll |v\cdot v'|\ll m_Q/\Lambda$, the form factors are dominated by the Isgur--Wise function, which is determined by the interference between the wave functions of leading and subleading twist. At $|v\cdot v'|\gg m_Q/\Lambda$, they are dominated by two functions arising at order $1/m_Q$ in the heavy-quark expansion, which are determined by the leading-twist wave function alone. The sum of these contributions describes the form factors in the whole region $|v\cdot v'|\gg 1$. As a consequence, there is an exact zero in the form factor for the scattering of longitudinally polarized $B^*$ mesons at some value $v\cdot v'\sim m_b/\Lambda$, and an approximate zero in the form factor of $B$ mesons in the timelike region ($v\cdot v'\sim -m_b/\Lambda$). We obtain the evolution equations and sum rules for the wave functions of leading and subleading twist as well as for their moments. We briefly discuss applications to heavy-meson pair production in $e^+ e^-$ collisions.
We analyse the antiferromagnetic spin-$1/2$ XXZ model on the kagome lattice at finite external magnetic field with the help of a nonperturbative zero-temperature renormalization group (RG) technique. Following the work of Kumar \emph{et al} (Phys. Rev. B {\bf 90}, 174409 (2014)), we use a Jordan-Wigner transformation to map the spin problem into one of spinless fermions (spinons) in the presence of a statistical gauge field, and with nearest-neighbour interactions. While the work of Kumar \emph{et al} was confined mostly to the plateau at $1/3$-filling (magnetisation per site) in the XY regime, we analyse the role of inter-spinon interactions in shaping the phases around this plateau in the entire XXZ model. The RG phase diagram obtained contains three spin liquid phases whose position is determined as a function of the exchange anisotropy and the energy scale for fluctuations arising from spinon scattering. Two of these spins liquids are topologically ordered states of matter with gapped, degenerate states on the torus. The gap for one of these phases corresponds to the one-spinon band gap of the Azbel-Hofstadter spectrum for the XY part of the Hamiltonian, while the other arises from two-spinon interactions. The Heisenberg point of this problem is found to lie within the interaction gapped spin liquid phase, in broad agreement with a recent experimental finding. The third phase is an algebraic spin liquid with a gapless Dirac spectrum for spinon excitations, and possess properties that show departures from the Fermi liquid paradigm. The three phase boundaries correspond to critical theories, and meet at a $SU(2)$-symmetric multicritical point. This special critical point agrees well with the gap-closing transition point predicted by Kumar \emph{et al}. We discuss the relevance of our findings to various recent experiments, as well as results obtained from other theoretical analyses.
Massive stars have been associated with the production of high-energy neutrinos since the early claims of detection of very high-energy gamma rays from Cygnus X-3 in the 1970s and early 1980s. Although such claims are now discredited, many thoretical models were developed predicting significant neutrino fluxes from binary systems with massive stars. With the discovery of microquasars, new, improved models appeared. The large neutrino telescopes currently under construction (IceCube, Antares) and the detection of gamma-ray sources of likely hadronic origin associated with massive binaries and star-forming regions make the prospects for high-energy neutrino astronomy quite promising. In this paper I will review the basic features of neutrino production in stellar systems and I will discuss the physical implications of a positive neutrino detection from such systems for our view of the stellar evolution and comsic ray origin.
Observationally, the mysterious fast radio bursts (FRBs) are classified as repeating ones and apparently non-repeating ones. While repeating FRBs cannot be classified into the non-repeating group, it is unknown whether the apparently non-repeating FRBs are actually repeating FRBs whose repetitions are yet to be discovered, or whether they belong to another physically distinct type from the repeating ones. In a series of two papers, we attempt to disentangle this mystery with machine learning methods. In this first paper, we focus on an array of supervised machine learning methods. We train the machine learning algorithms with a fraction of the observed FRBs in the first CHIME/FRB catalog, telling them which ones are apparently non-repeating and which ones are repeating. We then let the trained models predict the repetitiveness of the rest of the FRB data with the observed parameters, and we compare the predictions with the observed repetitiveness. We find that the models can predict most FRBs correctly, hinting towards distinct mechanisms behind repeating and non-repeating FRBs. We also find that the two most important distinguishing factors between non-repeating and repeating FRBs are brightness temperature and rest-frame frequency bandwidth. By applying the trained models back to the entire first CHIME catalog, we further identify some potentially repeating FRBs currently reported as non-repeating. We recommend a list of these bursts as targets for future observing campaigns to search for repeated bursts in a combination with the results presented in Paper II using unsupervised machine learning methods.
Background subtraction (BGS) is a fundamental video processing task which is a key component of many applications. Deep learning-based supervised algorithms achieve very good perforamnce in BGS, however, most of these algorithms are optimized for either a specific video or a group of videos, and their performance decreases dramatically when applied to unseen videos. Recently, several papers addressed this problem and proposed video-agnostic supervised BGS algorithms. However, nearly all of the data augmentations used in these algorithms are limited to the spatial domain and do not account for temporal variations that naturally occur in video data. In this work, we introduce spatio-temporal data augmentations and apply them to one of the leading video-agnostic BGS algorithms, BSUV-Net. We also introduce a new cross-validation training and evaluation strategy for the CDNet-2014 dataset that makes it possible to fairly and easily compare the performance of various video-agnostic supervised BGS algorithms. Our new model trained using the proposed data augmentations, named BSUV-Net 2.0, significantly outperforms state-of-the-art algorithms evaluated on unseen videos of CDNet-2014. We also evaluate the cross-dataset generalization capacity of BSUV-Net 2.0 by training it solely on CDNet-2014 videos and evaluating its performance on LASIESTA dataset. Overall, BSUV-Net 2.0 provides a ~5% improvement in the F-score over state-of-the-art methods on unseen videos of CDNet-2014 and LASIESTA datasets. Furthermore, we develop a real-time variant of our model, that we call Fast BSUV-Net 2.0, whose performance is close to the state of the art.
We study the electronic and magnetic structure of carbon and nitrogen impurities and interstitials in rutile TiO${_2}$. To this end we perform \textit{ab-initio} calculations of a 48-atom supercell employing the VASP code. In order to obtain a realistic description of the electronic and magnetic structure, exchange and correlation are treated with the HSE06 hybrid functional. Both, atomic positions and cell dimensions are fully relaxed. Substitutional carbon and nitrogen are found to have a magnetic moment of 2 and 1$\mu{_B}$, respectively, with a tendency for anti-ferromagnetic long range order. For C/N on interstitial sites we find that carbon is non-magnetic while nitrogen always possesses a magnetic moment of 1$\mu{_B}$. We find that these interstitial positions are on a saddle point of the total energy. The stable configuration is reached when both carbon and nitrogen form a C-O and N-O dimer with a bond length close to the double bond for CO and NO. This result is in agreement with earlier experimental investigations detecting such N-O entities from XPS measurements. The frequencies of the symmetric stretching mode are calculated for these dimers, which could provide a means for experimental verification. For all configurations investigated both C and N states are found inside the TiO${_2}$ gap. These new electronic states are discussed with respect to tuning doped TiO${_2}$ for the application in photocatalysis
Motivated by a recent paper of Adin, Bagno and Roichman, we present an involution on Dyck paths that preserves the rise composition and interchanges the number of returns and the position of the first double fall.
A technique is presented that automates the direction characterization of curvilinear features in multidimensional solar imaging data sets. It is an extension of the Rolling Hough Transform (RHT) technique presented by Clark, Peek, and Putman (Astrophys. J. 789, 82, 2014), and it excels at rapid quantification of spatial and spatiotemporal feature orientation even for low signal to noise applications. It operates on a pixel-by-pixel basis within a data set and reliably quantifies orientation even for locations not centered on a feature ridge, which is used here to derive a quasi-continuous map of the chromospheric fine structure projection angle. For time-series analysis, a procedure is developed that uses a hierarchical application of the RHT to automatically derive apparent motion of coronal rain observed off-limb. Essential to the success of this technique is this paper's formulation for the RHT error analysis as it provides a means to properly filter results.
We study the problem of specifying algebraic conditions on the coefficients of a binary form, so that it may have roots with preassigned multiplicities.
Context. Although a variety of techniques have been employed for determining the Milky Way dark matter halo mass distribution, the range of allowed masses spans both light and heavy values. Knowing the precise mass of our Galaxy is important for placing the Milky Way in a cosmological $\Lambda$CDM context. Aims. We show that hypervelocity stars (HVSs) ejected from the center of the Milky Way galaxy can be used to constrain the mass of its dark matter halo. Methods. We use the asymmetry in the radial velocity distribution of halo stars due to escaping HVSs, which depends on the halo potential (escape speed) as long as the round trip orbital time is shorter than the stellar lifetime, to discriminate between different models for the Milky Way gravitational potential. Results. Adopting a characteristic HVS travel time of $330$ Myr, which corresponds to the average mass of main sequence HVSs, we find that current data favors a mass for the Milky Way in the range $(1.2$-$1.9)\times 10^{12} \mathrm{M}_\odot$.
Three possible scenarios of the statistical hadronization model are reexamined with the use of the $p_{T}$ spectra of the PHENIX and very low $p_{T}$ PHOBOS measurements at $\sqrt{s_{NN}}=200$ GeV. These scenarios are: (\textit{a}) full chemical non-equilibrium, (\textit{b}) strangeness chemical non-equilibrium and (\textit{c}) chemical equilibrium. Fits to the spectra are done within the Cracow single-freeze-out model, which takes into account both the expansion and resonance decays. Predictions for spectra of $\phi$, $K(892)^{\ast 0}$ and $\pi^{0}$ are also given. The global variables like the transverse energy at midrapidity, the charged particle multiplicity at midrapidity and the total multiplicity of charged particles are evaluated and their predicted values agree qualitatively well with the experimental data. The thorough analysis within this model suggests that the chemical full non-equilibrium case is the least likely and both other cases are of the similar likelihood. It is also shown that if the full chemical non-equilibrium freeze-out took place it could manifest itself in the enhancement of the $\pi^{0}$-production at very low transverse momenta.
(Some Latex problems should be removed in this version) Fermi coordinates (FC) are supposed to be the natural extension of Cartesian coordinates for an arbitrary moving observer in curved space-time. Since their construction cannot be done on the whole space and even not in the whole past of the observer we examine which construction principles are responsible for this effect and how they may be modified. One proposal for a modification is made and applied to the observer with constant acceleration in the two and four dimensional Minkowski space. The two dimensional case has some surprising similarities to Kruskal space which generalize those found by Rindler for the outer region of Kruskal space and the Rindler wedge. In perturbational approaches the modification leads also to different predictions for certain physical systems. As an example we consider atomic interferometry and derive the deviation of the acceleration-induced phase shift from the standard result in Fermi coordinates.
Deriving relationships between images and tracing back their history of modifications are at the core of Multimedia Phylogeny solutions, which aim to combat misinformation through doctored visual media. Nonetheless, most recent image phylogeny solutions cannot properly address cases of forged composite images with multiple donors, an area known as multiple parenting phylogeny (MPP). This paper presents a preliminary undirected graph construction solution for MPP, without any strict assumptions. The algorithm is underpinned by robust image representative keypoints and different geometric consistency checks among matching regions in both images to provide regions of interest for direct comparison. The paper introduces a novel technique to geometrically filter the most promising matches as well as to aid in the shared region localization task. The strength of the approach is corroborated by experiments with real-world cases, with and without image distractors (unrelated cases).
The temperature dependences of spin-lattice relaxation time $T_1$ of $^{133}$Cs in CsFeCl$_3$ and $^{87}$Rb in RbFeCl$_3$ were measured in the temperature range between 1.5 K and 22 K, at various fields up to 7 T applied parallel (or perpendicular) to the c-axis, and the analysis was made on the basis of the DCEFA. The mechanism of the nuclear magnetic relaxation is interpreted in terms of the magnetic fluctuations which are characterized by the singlet ground state system. In the field region where the phase transition occurs, $T_1^{-1}$ exhibited the tendency of divergence near $T_{\rm N}$, and this feature was ascribed to the transverse spin fluctuation associated with the mode softening at the $K$-point. It was found that the damping constant of the soft mode is remarkably affected by the occurrence of the magnetic ordering at lower temperature, and increases largely in the field region where the phase transition occurs.
The text of lectures to the 2011 Tenerife Winter School. The School's theme was "Secular Evolution of Galaxies" and my task was to present the underlying stellar-dynamical theory. Other lecturers were speaking on the role of bars and chemical evolution, so these topics are avoided here. We start with an account of the connections between isolating integrals, quasiperiodicity and angle-action variables - these variables played a unifying role throughout the lectures. This leads on to the phenomenon of resonant trapping and how this can lead to chaos in cuspy potentials and phase-space mixing in slowly evolving potentials. Surfaces of section and frequency analysis are introduced as diagnostics of phase-space structure. Real galactic potentials include a fluctuating part that drives the system towards unattainable thermal equilibrium. Two-body encounters are only one source of fluctuations, and all fluctuations will drive similar evolution. We derive the orbit-averaged Fokker-Planck equation and relations that hold between the second-order diffusion coefficients and both the power spectrum of the fluctuations and the first-order diffusion coefficients. From the observed heating of the solar neighbourhood we show that the second-order diffusion coefficients must scale as J^{1/2}. We show that periodic spiral structure shifts angular momentum outwards, heating at the Lindblad resonances and mixing at corotation. The equation that would yield the normal modes of a stellar disc is first derived and then used to discuss the propagation of tightly-wound spiral waves. The winding up of such waves is explains why cool stellar discs are responsive systems that amplify ambient noise. An explanation is offered of why the Lin-Shu-Kalnajs dispersion relation and even global normal-mode calculations provide a very incomplete understanding of the dynamics of stellar discs.
In this paper we demonstrate for the first time that it is possible to solve numerically the Cauchy problem for the linearisation of the general conformal field equations near spacelike infinity, which is only well-defined in Friedrich's cylinder picture. We have restricted ourselves here to the "core" of the equations - the spin-2 system - propagating on Minkowski space. We compute the numerical solutions for various classes of initial data, do convergence tests and also compare to exact solutions. We also choose initial data which intentionally violate the smoothness conditions and then check the analytical predictions about singularities. This paper is the first step in a long-term investigation of the use of conformal methods in numerical relativity.
We present a new measurement of the Ly$\alpha$ luminosity function at redshift $z=6.9$, finding moderate evolution from $z=5.7$ that is consistent with a fully or largely ionized $z\sim7$ intergalactic medium. Our result is based on four fields of the LAGER (Lyman Alpha Galaxies in the Epoch of Reionization) project. Our survey volume of $6.1\times10^{6}$ Mpc$^{3}$ is double that of the next largest $z\sim 7$ survey. We combine two new LAGER fields (WIDE12 and GAMA15A) with two previously reported LAGER fields (COSMOS and CDFS). In the new fields, we identify $N=95$ new $z=6.9$ Ly$\alpha$ emitters (LAEs); characterize our survey's completeness and reliability; and compute Ly$\alpha$ luminosity functions. The best-fit Schechter luminosity function parameters for all four LAGER fields are in good general agreement. Two fields (COSMOS and WIDE12) show evidence for a bright-end excess above the Schechter function fit. We find that the Ly$\alpha$ luminosity density declines at the same rate as the UV continuum LF from $z=5.7$ to $z=6.9$. This is consistent with an intergalactic medium that was fully ionized as early as redshift $z\sim 7$, or with a volume-averaged neutral hydrogen fraction of $x_{HI} < 0.33$ at $1\sigma$.
No-scale structure of the Kahler potential is obtained in many types of supersymmetric models. In this paper, phenomenological aspects of these models are investigated with special attention to the current Higgs mass bound at LEP and b \to s \gamma result at the CLEO. When the boundary condition is given at the GUT scale and gaugino masses are universal at this scale, very narrow parameter region is allowed only for positive Higgsino mass region if R-parity is conserved. The negative Higgsino mass case is entirely excluded. On the other hand, relatively large parameter region is allowed when the boundary condition is given above the GUT scale, and Tevatron can discover SUSY signals for the positive Higgs mass case. The no-scale models with Wino, Higgsino or sneutrino LSP are also considered. We show that the Higgs mass constraint is important for the Higgsino LSP case, which requires the LSP mass to be larger than about 245 GeV.
We study ground states of two-dimensional Bose-Einstein condensates with attractive interactions in a trap $V(x)$ rotating at the velocity $\Omega $. It is known that there exist a critical rotational velocity $0<\Omega ^*:=\Omega^*(V)\leq \infty$ and a critical number $0<a^*<\infty$ such that for any rotational velocity $0\le \Omega <\Omega ^*$, ground states exist if and only if the coupling constant $a$ satisfies $a<a^*$. For a general class of traps $V(x)$, which may not be symmetric, we prove in this paper that up to a constant phase, there exists a unique ground state as $a\nearrow a^*$, where $\Omega\in(0,\Omega^*)$ is fixed. This result extends essentially our recent uniqueness result, where only the radially symmetric traps $V(x)$ could be handled with.
We have produced an atlas of Spitzer Infrared Spectrograph (IRS) spectra of mass-losing, evolved stars in the Large Magellanic Cloud. These stars were selected to have high mass-loss rates and so contribute significantly to the return of processed materials to the ISM. Our high-quality spectra enable the determination of the chemistry of the circumstellar envelope from the mid-IR spectral features and continuum. We have classified the spectral types of the stars and show that the spectral types separate clearly in infrared color-color diagrams constructed from 2MASS data and synthetic IRAC/MIPS fluxes derived from our IRS spectra. We present diagnostics to identify and classify evolved stars in nearby galaxies with high confidence levels using Spitzer and 2MASS photometry. Comparison of the spectral classes determined using IRS data with the IR types assigned based on NIR colors also revealed a significant number of misclassifications and enabled us to refine the NIR color criteria resulting in more accurate NIR color classifications of dust-enshrouded objects.