ShantanuT01/DACTYL-Pretraining huggingface dataset:
The goal of this work is to study positivity of subvarieties with nef normal bundle in the sense of intersection theory. After Ottem's work on ample subschemes, we introduce the notion of a nef subscheme, which generalizes the notion of a subvariety with nef normal bundle. We show that restriction of a pseudoeffective (resp. big) divisor to a nef subvariety is pseudoeffective (resp. big). We also show that ampleness and nefness are transitive properties. We define the weakly movable cone as the cone generated by the pushforward of cycle classes of nef subvarieties via proper surjective maps. This cone contains the movable cone and shares similar intersection-theoretic properties with it, thanks to the aforementioned properties of nef subvarieties. On the other hand, we prove that if $Y\subset X$ is an ample subscheme of codimension $r$ and $D|_Y$ is $q$-ample, then $D$ is $(q+r)$-ample. This is analogous to a result proved by Demailly-Peternell-Schneider. We use the theory of $q$-ample divisors, as developed by Totaro, throughout the paper.
We analyse features of the patterns formed from a simple model for a martensitic phase transition. This is a fragmentation model that can be encoded by a general branching random walk. An important quantity is the distribution of the lengths of the interfaces in the pattern and we establish limit theorems for some of the asymptotics of the interface profile. We are also able to use a general branching process to show almost sure power law decay of the number of interfaces of at least a certain size. We discuss the numerical aspects of determining the behaviour of the density profile and power laws from simulations of the model.
We investigate the dynamics of single microparticles immersed in water that are driven out of equilibrium in the presence of an additional external colored noise. As a case study, we trap a single polystyrene particle in water with optical tweezers and apply an external electric field with flat spectrum but a finite bandwidth of the order of kHz. The intensity of the external noise controls the amplitude of the fluctuations of the position of the particle, and therefore of its effective temperature. Here we show, in two different nonequilibrium experiments, that the fluctuations of the work done on the particle obey Crooks fluctuation theorem at the equilibrium effective temperature, given that the sampling frequency and the noise cutoff frequency are properly chosen. Our experimental setup can be therefore used to improve the design of microscopic motors towards fast and efficient devices, thus extending the frontiers of nano machinery.
The Gamma Ray Burst (GRB) 180720B is one of the brightest events detected by the Fermi satellite and the first GRB detected by the H.E.S.S. telescope above 100 GeV. We analyse the Fermi (GBM and LAT) and Swift (XRT and BAT) data and describe the evolution of the burst spectral energy distribution in the 0.5 keV - 10 GeV energy range over the first 500 seconds of emission. We reveal a smooth transition from the prompt phase, dominated by synchrotron emission in a moderately fast cooling regime, to the afterglow phase whose emission has been observed from the radio to the GeV energy range. The LAT (0.1 - 100 GeV) light curve initially rises ($F_{\rm LAT}\propto t^{2.4}$), peaks at $\sim$78 s, and falls steeply ($F_{\rm LAT}\propto t^{-2.2}$) afterwards. The peak, which we interpret as the onset of the fireball deceleration, allows us to estimate the bulk Lorentz factor $\Gamma_{0}\sim 150 \ (300)$ under the assumption of a wind-like (homogeneous) circum-burst medium density. We derive a flux upper limit in the LAT energy range at the time of H.E.S.S. detection, but this does not allow us to unveil the nature of the high energy component observed by H.E.S.S. We fit the prompt spectrum with a physical model of synchrotron emission from a non-thermal population of electrons. The 0 - 35 s spectrum after its $E F(E)$ peak (at 1 - 2 MeV) is a steep power law extending to hundreds of MeV. We derive a steep slope of the injected electron energy distribution $N(\gamma)\propto \gamma^{-5}$. Our fit parameters point towards a very low magnetic field ($B'\sim 1 $ G) in the emission region.
We study the possibility of performing quantum state reconstruction from a measurement record that is obtained as a sequence of expectation values of a Hermitian operator evolving under repeated application of a single random unitary map, U_0. We show that while this single-parameter orbit in operator space is not informationally complete, it can be used to yield surprisingly high-fidelity reconstruction. For a d-dimensional Hilbert space with the initial observable in su(d), the measurement record lacks information about a matrix subspace of dimension > d-2 out of the total dimension d^2-1. We determine the conditions on U_0 such that the bound is saturated, and show they are achieved by almost all pseudorandom unitary matrices. When we further impose the constraint that the physical density matrix must be positive, we obtain even higher fidelity than that predicted from the missing subspace. With prior knowledge that the state is pure, the reconstruction will be perfect (in the limit of vanishing noise) and for arbitrary mixed states, the fidelity is over 0.96, even for small d, and reaching F > 0.99 for d > 9. We also study the implementation of this protocol based on the relationship between random matrices and quantum chaos. We show that the Floquet operator of the quantum kicked top provides a means of generating the required type of measurement record, with implications on the relationship between quantum chaos and information gain.
We investigate the electronic structure of the transition-metal oxide YVO3 by a hybrid first-principles scheme. The density-functional theory with the local-density-approximation by using the local muffin-tin orbital basis is applied to derive the whole band structure. The electron degrees of freedom far from the Fermi level are eliminated by a downfolding procedure leaving only the V 3d t2g Wannier band as the low-energy degrees of freedom, for which a low-energy effective model is constructed. This low-energy effective Hamiltonian is solved exactly by the path-integral renormalization group method. It is shown that the ground state has the G-type spin and the C-type orbital ordering in agreement with experimental indications. The indirect charge gap is estimated to be around 0.7 eV, which prominently improves the previous estimates by other conventional methods.
The first detection of gravitational waves from a neutron star - neutron star (NS-NS) merger, GW170817, and the increasing number of observations of short gamma-ray bursts (SGRBs) have greatly motivated studies of the origins of NS-NS and neutron star - black hole (NS-BH) binaries. We calculate the merger rates of NS-NS and NS-BH binaries from globular clusters (GCs) using realistic GC simulations with the \texttt{CMC} cluster catalog. We use a large sample of models with a range of initial numbers of stars, metallicities, virial radii and galactocentric distances, representative of the present-day Milky Way GCs, to quantify the inspiral times and volumetric merger rates as a function of redshift, both inside and ejected from clusters. We find that over the complete lifetime of most GCs, stellar BHs dominate the cluster cores and prevent the mass segregation of NSs, thereby reducing the dynamical interaction rates of NSs so that at most a few NS binary mergers are ever produced. We estimate the merger rate in the local universe to be $\sim\rm{0.02\,Gpc^{-3}\,yr^{-1}}$ for both NS-NS and NS-BH binaries, or a total of $\sim 0.04$~Gpc$^{-3}$~yr$^{-1}$ for both populations. These rates are about 5 orders of magnitude below the current empirical merger rate from LIGO/Virgo. We conclude that dynamical interactions in GCs do not play a significant role in enhancing the NS-NS and NS-BH merger rates.
The magnetic field created in proton-proton and nucleus-nucleus collisions at ultra high energies are studied with models of point-like charges and hard sphere for distribution of the constituents for vacuum conditions. The various beam ions are considered from light to heavy nuclei at energies corresponded to the nominal energies of proton beam within the projects of further accelerator facilities high-energy Large Hadron Collider (HE-LHC) and Future Circular Collider (FCC). The magnetic field strength immediately after collisions reaches the value tens of GeV$^{2}$ while the approach with point-like charges some overestimate the amplitude of the field in comparison with more realistic hard sphere model. The absolute value of magnetic field rapidly decrease with time and increases with growth of atomic number. The amplitude for $eB$ is estimated at level $100$ GeV$^{2}$ in order to magnitude for quark-quark collisions at energies corresponded to the nominal energies of proton beams. These estimations are close to the range for onset of $W$ boson condensation.
In $2016-17$, the Galactic transient black hole candidate GRS 1716-249 exhibited an outburst event after a long period of quiescence of almost 23 years. The source remained in the outbursting phase for $\sim 9$ months. We study the spectral and temporal properties of the source during this outburst using archival data from four astronomy satellites, namely MAXI, Swift, NuSTAR and AstroSat. Initial spectral analysis is done using combined disk black body and power-law models. For a better understanding of the accretion flow properties, we studied spectra with the physical two component advective flow (TCAF) model. Accretion flow parameters are extracted directly from the spectral fits with the TCAF model. Low frequency quasi-periodic oscillations are also observed in the Swift/XRT and AstroSat/LAXPC data. From the nature of the variation of the spectral and temporal properties, we find the source remains in hard state during the entire outburst. It never had a transition to other states which makes this event a `failed' outburst. An absence of the softer spectral states is consistent with the class of short orbital period objects, where the source belongs to. From the spectral fit, we also estimate the probable mass of GRS~1716-249 to be in the range of $4.50-5.93 M_\odot$ or $5.02^{+0.91}_{-0.52} M_\odot$.
We study the inner structure of a positronium confined to a void by treating it as a two-particle quantum system where the electron is captured by an infinite potential well and the positron feels only the Coulomb attraction of the electron. We calculate the ground state and the related quantities that govern the annihilation rate, and discuss implications of the results.
We study the canonical quantization of a bosonic string in presence of N twist fields. This generalizes the quantization of the twisted string in two ways: the in and out states are not necessarily twisted and the number of twist fields N can be bigger than 2.   In order to quantize the theory we need to find the normal modes. Then we need to define a product between two modes which is conserved. Because of this we need to use the Klein-Gordon product and to separate the string coordinate into the classical and the quantum part. The quantum part has different boundary conditions than the original string coordinates but these boundary conditions are precisely those which make the operator describing the equation of motion self adjoint.   The splitting of the string coordinates into a classical and quantum part allows the formulation of an improved overlap principle. Using this approach we then proceed in computing the generating function for the generic correlator with L untwisted operators and N (excited) twist fields for branes at angles. We recover as expected the results previously obtained using the path integral. This construction explains why these correlators
We have constructed a set of supercluster catalogues for the galaxies from the SDSS survey main and luminous red galaxy (LRG) flux-limited samples. To delineate superclusters, we calculated luminosity density fields using the B3-spline kernel of the radius of 8 Mpc/h for the main sample and 16 Mpc/h for the LRG sample and define regions with densities over a selected threshold as superclusters, while utilising almost the whole volume of both samples. We created two types of catalogues, one with an adaptive local threshold and a set of catalogues with different global thresholds. We describe the supercluster catalogues and their general properties. Using smoothed bootstrap, we find uncertainty estimates for the density field and use these to attribute confidence levels to the catalogue objects. We have also created a test catalogue for the galaxies from the Millennium simulation to compare the simulated and observed superclusters and to clarify the methods we use. We find that the superclusters are well-defined systems, and the properties of the superclusters of the main and LRG samples are similar. We also show that with adaptive local thresholds we get a sample of superclusters, the properties of which do not depend on their distance from the observer. The Millennium galaxy catalogue superclusters are similar to those observed.
We study the correlators of the 2d W_N minimal model in the semiclassical regime with large central charge from bulk viewpoint by utilizing open Wilson lines in sl(N) Chern-Simons gauge theory. We extend previous works for the tree level of bulk theory to incorporate loop corrections in this paper. We offer a way to regularize divergences associated with loop diagrams such that three point functions with two scalars and a higher spin current agree with the values fixed by the boundary W_N symmetry. With the prescription, we reproduce the conformal weight of the operator corresponding to a bulk scalar up to the two loop order for explicit examples with N=2,3.
We have surveyed an optical/IR selected sample of nearby E/S0 galaxies with and without nuclear dust structures with the VLA at 3.6 cm to a sensitivity of 100 $\mu$Jy. We can construct a Radio Luminosity Function (RLF) of these galaxies to ~10^19 W/Hz and find that ~50% of these galaxies have AGNs at this level. The space density of these AGNs equals that of starburst galaxies at this luminosity. Several dust-free galaxies have low luminosity radio cores, and their RLF is not significantly less than that of the dusty galaxies.
We present photometric and spectroscopic data of the interacting starburst galaxy NGC 6052 obtained with the Spitzer Space Telescope. The mid-infrared (MIR) spectra of the three brightest spatially resolved regions in the galaxy are remarkably similar and are consistent with dust emission from young nearly coeval stellar populations. Analysis of the brightest infrared region of the system, which contributes ~18.5 % of the total 16\micron flux, indicates that unlike similar off-nuclear infrared-bright regions found in Arp 299 or NGC 4038/9, its MIR spectrum is inconsistent with an enshrouded hot dust (T > 300K) component. Instead, the three brightest MIR regions all display dust continua of temperatures less than ~ 200K. These low dust temperatures indicate the dust is likely in the form of a patchy screen of relatively cold material situated along the line of sight. We also find that emission from polycyclic aromatic hydrocarbons (PAHs) and the forbidden atomic lines is very similar for each region. We conclude that the ionization regions are self-similar and come from young (about 6 Myr) stellar populations. A fourth region, for which we have no MIR spectra, exhibits MIR emission similar to tidal tail features in other interacting galaxies.
The formation and evolution of tidal tails like those observed around some globular clusters and dwarf satellite galaxies is examined with an N-body simulation. In particular, we analyse in detail the evolving tidal features of a one-component satellite that is moving on a highly eccentric orbit in the external field of a host galaxy potential like our own. The results show that every time the satellite approaches apogalacticon, a fresh pair of tidal tails becomes notably prominent, and that eventually, the satellite possesses multiple tidal tails via repeating apocentre passages. Accordingly, the number of observed tidal arms can be used as a tracer of the number of orbital periods that such a system has completed around the centre of its host galaxy. By identifying the arm particles included in each of the first three consecutively formed pairs of tidal tails, we find that each pair of tidal tails is practically identical to one another regarding the energy and angular-momentum distributions. In addition, we demonstrate that the density profiles of these three pairs of tidal tails at their first apogalacticons after formation agree well with one another. It therefore follows that the multiplicity in tidal features originates from the repeated episode of tidal-arm formation in the course of the precessing motion of a satellite.
Aims. We aim to improve the understanding of the physical mechanisms behind the slower than free-fall motion and the two-stage evolution (an initial phase of acceleration followed by an almost constant velocity phase) detected in coronal rain events.   Methods. Using the Mancha3D code, we solve the 2D ideal MHD equations. We represent the solar corona as an isothermal vertically stratified atmosphere with a uniform vertical magnetic field and the plasma condensation as a density enhancement described by a 2D Gaussian profile. We analyse the temporal evolution of the descending plasma and study its dependence on parameters such as density and magnetic field strength.   Results. We confirm previous findings that the pressure gradient is the main force that opposes the action of gravity and slows down the blob descent and that larger densities require larger pressure gradients to reach the constant speed phase. We find that the shape of a condensation with a horizontal variation of density is distorted as it falls, due to the denser parts of the blob falling faster than the lighter ones. This is explained by the fact that the duration of the initial acceleration phase, and therefore the maximum falling speed attained by the plasma, increases with the ratio of blob to coronal density. We also find that the magnetic field plays a fundamental role in the evolution of the descending condensations. A strong enough magnetic field (greater than 10 G in our simulations) forces each plasma element to follow the path given by a particular field line, which allows to describe the evolution of each vertical slice of the blob in terms of 1D dynamics, without influence of the adjacent slices. In addition, under the typical conditions of the coronal rain events, the magnetic field prevents the development of the Kelvin-Helmholtz instability.
Basic idea presented in Parts (I) and (II) for the deformed boson scheme is applied to the case of the su(2,1)-algebra for describing many-body systems consisting of three kinds of boson operators. A possible form of the coherent state for the su(2,1)-algebra is generalized and the deformed su(2,1)-algebra is presented. As an application, the time-evolution of the statistically mixed state in a certain boson system, which has been already investigated by the present authors, is reinvestigated.
We present an entirely new sample of 388 low-mass galaxies ($M_\star \leq 10^{10} M_\odot$) that have spectroscopic signatures indicating the presence of massive black holes (BHs) in the form of active galactic nuclei (AGNs) or tidal disruption events (TDEs). Of these, 70 have stellar masses in the dwarf galaxy regime with $10^8 \lesssim M_\star/M_\odot \lesssim 10^{9.5}$. We identify the active galaxies by analyzing optical spectra of a parent sample of $\sim$23,000 low-mass emission-line galaxies in the Galaxy and Mass Assembly (GAMA) Survey Data Release 4, and employing four different diagnostics based on narrow emission line ratios and the detection of high-ionization coronal lines. We find that 47 of the 388 low-mass active galaxies exhibit broad H$\alpha$ in their spectra, corresponding to virial BH masses in the range $M_{\rm BH} \sim 10^{5.0-7.7} M_\odot$ with a median BH mass of $\langle M_{\rm BH}\rangle \sim 10^{6.2} M_\odot$. Our sample extends to higher redshifts ($z \le 0.3; \langle z \rangle=0.13$) than previous samples of AGNs in low-mass/dwarf galaxies based on Sloan Digital Sky Survey spectroscopy, which can be attributed to the spectroscopic limit of GAMA being $\sim 2$ magnitudes deeper. Moreover, our multi-diagnostic approach has revealed low-mass active galaxies spanning a wide range of properties, from blue star-forming dwarfs to luminous "miniquasars" powered by low-mass BHs. As such, this work has implications for BH seeding and AGN feedback at low masses.
If quark stars exist, they may be enveloped in thin electron layers (electron seas), which uniformly surround the entire star. These layers will be affected by the magnetic fields of quark stars in such a way that the electron seas would transmit hydromagnetic cyclotron waves, as studied in this paper. Particular attention is devoted to vortex hydrodynamical oscillations of the electron sea. The frequency spectrum of these oscillations is derived in analytic form. If the thermal X-ray spectra of quark stars are modulated by vortex hydrodynamical vibrations, the thermal spectra of compact stars, foremost central compact objects (CCOs) and X-ray dim isolated neutron stars (XDINSs), could be used to verify the existence of these vibrational modes observationally. The central compact object 1E 1207.4-5209 appears particularly interesting in this context, since its absorption features at 0.7 keV and 1.4 keV can be comfortably explained in the framework of the hydro-cyclotron oscillation model.
Compressive sensing is a method to recover the original image from undersampled measurements. In order to overcome the ill-posedness of this inverse problem, image priors are used such as sparsity in the wavelet domain, minimum total-variation, or self-similarity. Recently, deep learning based compressive image recovery methods have been proposed and have yielded state-of-the-art performances. They used deep learning based data-driven approaches instead of hand-crafted image priors to solve the ill-posed inverse problem with undersampled data. Ironically, training deep neural networks for them requires "clean" ground truth images, but obtaining the best quality images from undersampled data requires well-trained deep neural networks. To resolve this dilemma, we propose novel methods based on two well-grounded theories: denoiser-approximate message passing and Stein's unbiased risk estimator. Our proposed methods were able to train deep learning based image denoisers from undersampled measurements without ground truth images and without image priors, and to recover images with state-of-the-art qualities from undersampled data. We evaluated our methods for various compressive sensing recovery problems with Gaussian random, coded diffraction pattern, and compressive sensing MRI measurement matrices. Our methods yielded state-of-the-art performances for all cases without ground truth images and without image priors. They also yielded comparable performances to the methods with ground truth data.
We prove an existence result for a class of Dirichlet boundary value problems with discontinuous nonlinearity and involving a Leray-Lions operator. The proof combines monotonicity methods for elliptic problems, variational inequality techniques and basic tools related to monotone operators.
According to the AdS/CFT correspondence conjecture, the Randall-Sundrum infinite braneworld is equivalent to four dimensional Einstein gravity with ${\cal N}=4$ super Yang-Mills fields at low energies. Here we derive a four dimensional effective equation of motion for tensor-type perturbations in two different pictures, and demonstrate their equivalence.