ShantanuT01/DACTYL-Pretraining huggingface dataset:
Matrix hierarchies are: multi-component KP, general Zakharov-Shabat (ZS) and its special cases, e.g., AKNS. The ZS comprises all integrable systems having a form of zero-curvature equations with rational dependence of matrices on a spectral parameter. The notion of a $\tau$-function is introduced here in the most general case along with formulas linking $\tau$-functions with wave Baker functions. The method originally invented by Sato et al. for the KP hierarchy is used. This method goes immediately from definitions and does not require any assumption about the character of a solution, being the most general. Applied to the matrix hierarchies, it involves considerable sophistication. The paper is self-contained and does not expect any special prerequisite from a reader.
Magnetic fields are fundamental to the dynamics of both accretion disks and the jets that they often drive. We review the basic physics of these phenomena, the past and current efforts to model them numerically with an emphasis on the jet-disk connection, and the observational constraints on the role of magnetic fields in the jets of active galaxies on all scales.
In this work we show how the criterion of asymptotic Hamiltonian diagonalization originated in hybrid quantum cosmology serves to pick out a unique vacuum for the Dirac field in de Sitter, in the context of quantum field theory in curved spacetimes. This criterion is based on the dynamical definition of annihilation and creationlike variables for the fermionic field, which obey the linearized dynamics of a Hamiltonian that has been diagonalized in a way that is adapted to its local spatial structure. This leads to fermionic variables that possess a precise asymptotic expansion in the ultraviolet limit of large wavenumbers. We explicitly show that, when the cosmological background is fixed as a de Sitter solution, this expansion uniquely selects the choice of fermionic annihilation and creationlike variables for all spatial scales, and thus picks out a unique privileged Fock representation and vacuum state for the Dirac field in de Sitter. The explicit form of the basis of solutions to the Dirac equation associated with this vacuum is then computed.
We apply the regularized theory of light-cone gauge memberbranes to find the matrix model in the Kaluza-Klein Melvin background. In the static system the Melvin matrix model becomes the BFSS model with two extra mass terms and another term. We solve the equation of motion for simplest N=2 D0 branes system and find that there is a nontrivial configuration. Especially, we also make an ansatz to find the nonstatic solution. The new solution shows that $D_0$ propagating in the magnetic tube field background may expand into a rotating noncommutative ring.
We show that the delay between GRB170817A and GW170817 is incompatible with de-beamed emission from an off-axis relativistic jet. The prompt emission and the subsequent radio and X-ray observations can instead be interpreted within a giant-flare-like scenario, being the result of a relativistic outflow driven by the ultra-strong magnetic field produced by magnetohydrodynamic amplification during the merger of the progenitor double neutron-star binary. Within such picture, the data indicate that the outflow must be endowed with a steep velocity profile, with a relatively fast tail extending to Gamma~8. Since the conditions for the launch of such an outflow are quite general, and the presence of a velocity profile is a natural expectation of the acceleration process, most neutron star binary mergers should feature this quasi-isotropic, hard X-ray emission component, that can be a powerful guide to the discovery of additional kilonovae associated to relatively nearby gravitational wave events.
For any flag simplicial complex $\Theta$ obtained by stellar subdividing the boundary of the cross polytope in edges, we define a flag simplicial complex $\Gamma(\Theta)$ (dependent on the sequence of subdivisions) whose $f$-vector is the $\gamma$-vector of $\Theta$. This proves that the $\gamma$-vector of any such simplicial complex satisfies the Frankl-F\"{u}redi-Kalai inequalities, partially solving a conjecture by Nevo and Petersen \cite{np}. We show that when $\Theta$ is the dual simplicial complex to a nestohedron, and the sequence of subdivisions corresponds to a flag ordering as defined in \cite{ai}, that $\Gamma(\Theta)$ is equal to the flag simplical complex defined there.
The presence of a circumnuclear stellar disk around Sgr A* and megamaser systems near other black holes indicates that dense neutral disks can be found in galactic nuclei. We show that depending on their inclination angle, optical depth, and spin temperature, these disks could be observed spectroscopically through 21 cm absorption. Related spectroscopic observations of Sgr A* can determine its HI disk parameters and the possible presence of gaps in the disk. Clumps of dense gas similar to the G2 could could also be detected in 21 cm absorption against Sgr A* radio emission.
Based on a less-known result, we prove a recent conjecture concerning the determinant of a certain Sylvester-Kac type matrix and consider an extension of it.
Inversion codes for the polarized radiative transfer equation can be used to infer the temperature $T$, line-of-sight velocity $v_{\rm los}$, and magnetic field $\rm{\bf B}$ as a function of the continuum optical-depth $\tau_{\rm c}$. However, they do not directly provide the gas pressure $P_{\rm g}$ or density $\rho$. In order to obtain these latter parameters, inversion codes rely instead on the assumption of hydrostatic equilibrium (HE) in addition to the equation of state (EOS). Unfortunately, the assumption of HE is rather unrealistic across magnetic field lines. This is because the role of the Lorentz force, among other factors, is neglected. This translates into an inaccurate conversion from optical depth $\tau_{\rm c}$ to geometrical height $z$. We aim at improving this conversion via the application of magneto-hydrostatic (MHS) equilibrium instead of HE. We develop a method to solve the momentum equation under MHS equilibrium (i.e., taking the Lorentz force into account) in three dimensions. The method is based on the solution of a Poisson-like equation. Considering the gas pressure $P_{\rm g}$ and density $\rho$ from three-dimensional magneto-hydrodynamic (MHD) simulations of sunspots as a benchmark, we compare the results from the application of HE and MHS equilibrium. We find that HE retrieves the gas pressure and density within an order of magnitude of the MHD values in only about 47 \% of the domain. This translates into an error of about $160-200$ km in the determination of the $z-\tau_{\rm c}$ conversion. On the other hand, the application of MHS equilibrium allows determination of $P_{\rm g}$ and $\rho$ within an order of magnitude in 84 \% of the domain. In this latter case, the $z-\tau_{\rm c}$ conversion is obtained with an accuracy of $30-70$ km.
We describe an iterative scheme which allows us to calculate any multi-loop correlator for the complex matrix model to any genus using only the first in the chain of loop equations. The method works for a completely general potential and the results contain no explicit reference to the couplings. The genus $g$ contribution to the $m$--loop correlator depends on a finite number of parameters, namely at most $4g-2+m$. We find the generating functional explicitly up to genus three. We show as well that the model is equivalent to an external field problem for the complex matrix model with a logarithmic potential.
We investigate the characteristics of magneto-acoustic surface waves propagating at a single density interface, in the presence of an inclined magnetic field. For linear wave propagation, dispersion relation is obtained and analytical solutions are derived for small inclination angle. The inclination of the field renders the frequency of waves to be complex, where the imaginary part describes wave attenuation, due to lateral energy leakage.
In ophthalmological imaging, multiple imaging systems, such as color fundus, infrared, fluorescein angiography, optical coherence tomography (OCT) or OCT angiography, are often involved to make a diagnosis of retinal disease. Multi-modal retinal registration techniques can assist ophthalmologists by providing a pixel-based comparison of aligned vessel structures in images from different modalities or acquisition times. To this end, we propose an end-to-end trainable deep learning method for multi-modal retinal image registration. Our method extracts convolutional features from the vessel structure for keypoint detection and description and uses a graph neural network for feature matching. The keypoint detection and description network and graph neural network are jointly trained in a self-supervised manner using synthetic multi-modal image pairs and are guided by synthetically sampled ground truth homographies. Our method demonstrates higher registration accuracy as competing methods for our synthetic retinal dataset and generalizes well for our real macula dataset and a public fundus dataset.
A Ryser design $\mathcal{D}$ on $v$ points is a collection of $v$ proper subsets (called blocks) of a point-set with $v$ points satisfying (i) every two blocks intersect each other in $\lambda$ points for a fixed $\lambda < v$ (ii) there are at least two block sizes. A design $\mathcal{D}$ is called a symmetric design, if all the blocks of $\mathcal{D}$ have the same size   (or equivalently, every point has the same replication number) and every two blocks intersect each other in $\lambda$ points. The only known construction of a Ryser design is via block complementation of a symmetric design also known as the Ryser-Woodall complementation method. Such a Ryser design is called a Ryser design of Type-1. The Ryser-Woodall conjecture states: "every Ryser design is of Type-1".   Main results of the present article are the following. An expression for the inverse of the incidence matrix $\mathsf{A}$ of a Ryser design is obtained. A necessary condition for the design to be of Type-1 is obtained. A well known conjecture states that, for a Ryser design on \textit{v} points $\mbox{ }4\lambda-1\leq v\leq\lambda^2+\lambda+1$.   A partial support for this conjecture is obtained. Finally a special case of Ryser designs with two block sizes is shown to be of Type-1.
We investigate the effects of (2+1)d event-by-event fluctuating hydrodynamic backgrounds on the nuclear modification factor and momentum anisotropies of heavy-flavor mesons. Using the state-of-the-art D and B mesons modular simulation code (the so-called DAB-mod), updated recently with heavy-light quark coalescence, we perform a systematic comparison of different transport equations, including two energy loss models and a relativistic Langevin model with two drag parametrizations. We present the resulting D$^0$ meson $R_{AA}$, $v_2$ and $v_3$, using the multiparticle cumulant method, in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV and compare them to the latest experimental data. We investigate the $v_2\{4\}/v_2\{2\}$ ratio as a function of centrality for different initial conditions (MCKLN vs. Trento) and different system geometries and sizes (coming from Pb-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV, spherical and prolate Xe-Xe collisions at $\sqrt{s_{\rm NN}}=5.44$ TeV).
Narrow-band Lya line and broad-band continuum have played important roles in the discovery of high-redshift galaxies in recent years. Hence, it is crucial to study the radiative transfer of both Lya and continuum photons in the context of galaxy formation and evolution in order to understand the nature of distant galaxies. Here, we present a three-dimensional Monte Carlo radiative transfer code, All-wavelength Radiative Transfer with Adaptive Refinement Tree (ART^2), which couples Lya line and multi-wavelength continuum, for the study of panchromatic properties of galaxies and interstellar medium. This code is based on the original version of Li et al., and features three essential modules: continuum emission from X-ray to radio, Lya emission from both recombination and collisional excitation, and ionization of neutral hydrogen. The coupling of these three modules, together with an adaptive refinement grid, enables a self-consistent and accurate calculation of the Lya properties. As an example, we apply ART^2 to a cosmological simulation that includes both star formation and black hole growth, and study in detail a sample of massive galaxies at redshifts z=3.1 - 10.2. We find that these galaxies are Lya emitters (LAEs), whose Lya emission traces the dense gas region, and that their Lya lines show a shape characteristic of gas inflow. Furthermore, the Lya properties, including photon escape fraction, emergent luminosity, and equivalent width, change with time and environment. Our results suggest that LAEs evolve with redshift, and that early LAEs such as the most distant one detected at z ~ 8.6 may be dwarf galaxies with a high star formation rate fueled by infall of cold gas, and a low Lya escape fraction.
We study exact results concerning the non-affine displacement fields observed by Tanguy et al [Europhys. Lett. {\bf 57}, 423 (2002), Phys. Rev. B {\bf 66}, 174205 (2002)] and their contributions to elasticity. A normal mode analysis permits us to estimate the dominant contributions to the non-affine corrections to elasticity, and relate these corrections to the correlator of a fluctuating force field. We extend this analysis to the visco-elastic dynamical response of the system.
Switching identities have a long history in potential theory and stochastic analysis. In recent work of Cox and Wang, a switching identity was used to connect an optimal stopping problem and the Skorokhod embedding problem (SEP). Typically switching identies of this form are derived using deep analytic connections. In this paper, we prove the switching identities using a simple probabilistic argument, which furthermore highlights a previously unexplored symmetry between the Root and Rost solutions to the SEP.
We propose Deep Feature Interpolation (DFI), a new data-driven baseline for automatic high-resolution image transformation. As the name suggests, it relies only on simple linear interpolation of deep convolutional features from pre-trained convnets. We show that despite its simplicity, DFI can perform high-level semantic transformations like "make older/younger", "make bespectacled", "add smile", among others, surprisingly well - sometimes even matching or outperforming the state-of-the-art. This is particularly unexpected as DFI requires no specialized network architecture or even any deep network to be trained for these tasks. DFI therefore can be used as a new baseline to evaluate more complex algorithms and provides a practical answer to the question of which image transformation tasks are still challenging in the rise of deep learning.
The central idea of contrastive learning is to discriminate between different instances and force different views from the same instance to share the same representation. To avoid trivial solutions, augmentation plays an important role in generating different views, among which random cropping is shown to be effective for the model to learn a generalized and robust representation. Commonly used random crop operation keeps the distribution of the difference between two views unchanged along the training process. In this work, we show that adaptively controlling the disparity between two augmented views along the training process enhances the quality of the learned representation. Specifically, we present a parametric cubic cropping operation, ParamCrop, for video contrastive learning, which automatically crops a 3D cubic by differentiable 3D affine transformations. ParamCrop is trained simultaneously with the video backbone using an adversarial objective and learns an optimal cropping strategy from the data. The visualizations show that ParamCrop adaptively controls the center distance and the IoU between two augmented views, and the learned change in the disparity along the training process is beneficial to learning a strong representation. Extensive ablation studies demonstrate the effectiveness of the proposed ParamCrop on multiple contrastive learning frameworks and video backbones. Codes and models will be available.
The bandstructure of pentacene is calculated using first-principles density functional theory. A large anisotropy of the hole and electron effective masses within the molecular planes is found. The band dispersion of the HOMO and the LUMO is analyzed with the help of a tight-binding fit. The anisotropy is shown to be intimately related to the herringbone structure.
Magnetic skyrmion is a topologically stable particle-like swirling spin texture potentially suitable for high-density information bit, which was first observed in noncentrosymmetric magnets with Dzyaloshinskii-Moriya interaction. Recently, nanometric skyrmion has also been discovered in centrosymmetric rare-earth compounds, and the identification of their skyrmion formation mechanism and further search of nontrivial spin textures are highly demanded. Here, we have exhaustively studied magnetic structures in a prototypical skyrmion-hosting centrosymmetric tetragonal magnet GdRu2Si2, by performing the resonant X-ray scattering experiments. We identified a rich variety of double-Q magnetic structures, including the antiferroic order of meron(half-skyrmion)/anti-meronlike textures with fractional local topological charges. The observed intricate magnetic phase diagram has been successfully reproduced by the theoretical framework considering the four-spin interaction mediated by itinerant electrons and magnetic anisotropy. The present results will contribute to the better understanding of the novel skyrmion formation mechanism in this centrosymmetric rare-earth compound, and suggest that itinerant electrons can ubiquitously host a variety of unique multiple-Q spin orders in a simple crystal lattice system.
Spin-1 resonances are naturally present in composite Higgs frameworks. We first review a model independent approach to parametrize a single additional heavy triplet and then we consider more realistic models arising in composite Higgs scenarios where a larger number of spin-1 resonances is expected. In these cases, finite width and interference effects can heavily affect the bounds extracted from the data.
Using large-scale dynamical cluster quantum Monte Carlo simulations, we study the Lifshitz transition of the two dimensional Hubbard model with next-nearest-neighbor hopping ($t'$), chemical potential and temperature as control parameters. At $t'\le0$, we identify a line of Lifshitz transition points associated with a change of the Fermi surface topology at zero temperature. In the overdoped region, the Fermi surface is complete and electron-like; across the Lifshitz transition, the Fermi surface becomes hole-like and develops a pseudogap. At (or very close to) the Lifshitz transition points, a van Hove singularity in the density of states crosses the Fermi level. The van Hove singularity occurs at finite doping due to correlation effects, and becomes more singular when $t'$ becomes more negative. The resulting temperature dependence on the bare d-wave pairing susceptibility close to the Lifshitz points is significantly different from that found in the traditional van Hove scenarios. Such unambiguous numerical observation of the Lifshitz transition at $t'\le0$ extends our understanding of the quantum critical region in the phase diagram, and shines lights on future investigations of the nature of the quantum critical point in the two dimensional Hubbard model.
We study fully nonlinear second-order (forward) stochastic partial differential equations (SPDEs). They can also be viewed as forward path-dependent PDEs (PPDEs) and will be treated as rough PDEs (RPDEs) under a unified framework. We develop first a local theory of classical solutions and define then viscosity solutions through smooth test functions. Our notion of viscosity solutions is equivalent to the alternative one using semi-jets. Next, we prove basic properties such as consistency, stability, and a partial comparison principle in the general setting. When the diffusion coefficient is semi-linear (but the drift can be fully nonlinear), we establish a complete theory, including global existence and comparison principle. Our methodology relies heavily on the method of characteristics.
Neutrino reaction cross-sections, $(\nu_\mu,\mu^-)$, $(\nu_e,e^-)$, $\mu$-capture and photoabsorption rates on $^{12}$C are computed within a large-basis shell-model framework, which included excitations up to $4\hbar\omega$. When ground-state correlations are included with an open $p$-shell the predictions of the calculations are in reasonable agreement with most of the experimental results for these reactions. Woods-Saxon radial wave functions are used, with their asymptotic forms matched to the experimental separation energies for bound states, and matched to a binding energy of 0.01 MeV for unbound states. For comparison purposes, some results are given for harmonic oscillator radial functions. Closest agreement between theory and experiment is achieved with unrestricted shell-model configurations and Woods-Saxon radial functions. We obtain for the neutrino-absorption inclusive cross sections: $\bar{\sigma} = 13.8 \times 10^{-40}$ cm$^2$ for the $(\nu_{\mu},\mu^{-})$ decay-in-flight flux in agreement with the LSND datum of $(12.4 \pm 1.8) \times 10^{-40}$ cm$^2$; and $\bar{\sigma} = 12.5 \times 10^{-42}$ cm$^2$ for the $(\nu_{e},e^{-})$ decay-at-rest flux, less than the experimental result of $(14.4 \pm 1.2) \times 10^{-42}$ cm$^2$.
We present the results of the gluino and scalar quarks contribution to the flavour changing top quark decay into a charm quark and a photon, gluon or a $Z^0$\ boson within the minimal supersymmetric standard model. We include the mixing of the scalar partners of the left and right handed top quark. This mixing has several effects, the most important of which are to greatly enhance the c Z decay mode for large values of the soft SUSY breaking scalar mass $m_S$\ and to give rise to a GIM--like suppresion in the c $\gamma$\ mode for certain combinations of parameters.
We describe preliminary results of a detailed numerical analysis of the volume operator as formulated by Ashtekar and Lewandowski. Due to a simplified explicit expression for its matrix elements, it is possible for the first time to treat generic vertices of valence greater than four. It is found that the vertex geometry characterizes the volume spectrum.
Generative based strategy has shown great potential in the Generalized Zero-Shot Learning task. However, it suffers severe generalization problem due to lacking of feature diversity for unseen classes to train a good classifier. In this paper, we propose to enhance the generalizability of GZSL models via improving feature diversity of unseen classes. For this purpose, we present a novel Diverse Feature Synthesis (DFS) model. Different from prior works that solely utilize semantic knowledge in the generation process, DFS leverages visual knowledge with semantic one in a unified way, thus deriving class-specific diverse feature samples and leading to robust classifier for recognizing both seen and unseen classes in the testing phase. To simplify the learning, DFS represents visual and semantic knowledge in the aligned space, making it able to produce good feature samples with a low-complexity implementation. Accordingly, DFS is composed of two consecutive generators: an aligned feature generator, transferring semantic and visual representations into aligned features; a synthesized feature generator, producing diverse feature samples of unseen classes in the aligned space. We conduct comprehensive experiments to verify the efficacy of DFS. Results demonstrate its effectiveness to generate diverse features for unseen classes, leading to superior performance on multiple benchmarks. Code will be released upon acceptance.