ShantanuT01/DACTYL-Pretraining huggingface dataset:
Consider a family of Fano varieties $\pi: X \longrightarrow B\ni o$ over a curve germ with a smooth total space $X$. Assume that the generic fiber is smooth and the special fiber $F=\pi^{-1}(o)$ has simple normal crossings. Then $F$ is called a semistable degeneration of Fano varieties. We show that the dual complex of $F$ is a simplex of dimension $\leq \mathrm{dim}\ F$. Simplices of any admissible dimension can be realized for any dimension of the fiber. Using this result and the Minimal Model Program in dimension $3$ we reproduce the classification of the semistable degenerations of del Pezzo surfaces obtained by Fujita. We also show that the maximal degeneration is unique and has trivial monodromy in dimension $\leq3$.
Using a $d_{x^2 - y^2}$ superconductor in 2+1 dimensions we show that the Nambu Goldstone fluctuations are replaced by dissipative excitations. We find that the nodal quasi-particles damping is caused by the strong dissipative excitations near the nodal points. As a result we find that the scattering rates are linear in frequency and not cubic as predicted in the literature for the ``d'' wave superconductors. Our results explain the recent angle resolved photoemission spectroscopy and optical conductivity in the BSCCO high $T_c$ compounds.
Combining the recently available experimental evidence of D-Dbar mixing, we extract model-independent information on the mixing amplitude and on its CP-violating phase. Using this information, we present new constraints on the flavour structure of up-type squark mass matrices in supersymmetric extensions of the Standard Model.
We give a brief overview of the string landscape and techniques used to construct string compactifications. We then explain how this motivates the notion of the swampland and review a number of conjectures that attempt to characterize theories in the swampland. We also compare holography in the context of superstrings with the similar, but much simpler case of topological string theory. For topological strings, there is a direct definition of topological gravity based on a sum over a "quantum gravitational foam." In this context, holography is the statement of an identification between a gravity and gauge theory, both of which are defined independently of one another. This points to a missing corner in string dualities which suggests the search for a direct definition of quantum theory of gravity rather than relying on its strongly coupled holographic dual as an adequate substitute (Based on TASI 2017 lectures given by C. Vafa).
We consider functions $u\in L^\infty(L^2)\cap L^p(W^{1,p})$ with $1<p<\infty$ on a time space domain. Solutions to non-linear evolutionary PDE's typically belong to these spaces. Many applications require a Lipschitz approximation $u_\lambda$ of $u$ which coincides with $u$ on a large set. For problems arising in fluid mechanics one needs to work with solenoidal (divergence-free) functions. Thus, we construct a Lipschitz approximation, which is also solenoidal. As an application we revise the existence proof for non-stationary generalized Newtonian fluids in [DRW10]. Since ${\rm div} u_\lambda=0$, we are able to work in the pressure free formulation, which heavily simplifies the proof. We also provide a simplified approach to the stationary solenoidal Lipschitz truncation of [BDF12].
We present a detailed spectral and timing analysis of X-ray observations of the brightest eclipsing systems Alpha Coronae Borealis taken by XMM-Newton. We got from the thermal plasma model metal the abundances of some elements (O, Mg, Si, and Fe) and an emission line at 1.3 Kev from the simple Gaussian line profile. From the light curves, there is a strong active region at the lower left in the maps, near the limb of the G component, and increasing in some parts which means a band diagonally running across the G star disk from lower left to upper right, close to the projected center.
The LOw Frequency ARray, LOFAR, will have the sensitivity, bandwidth, frequency range and processing power to revolutionise low-frequency pulsar studies. We present results of simulations that indicate that a LOFAR survey will find approximately 1500 new pulsars. These new pulsars will give us a much better understanding of the low end of the luminosity function and thus allow for a much more precise estimate of the true total local pulsar population. The survey will also be very sensitive to the ultra-steep spectrum pulsars, RRATs, and the pulsed radio emission from objects like Geminga and AXPs. We will also show that by enabling us to observe single pulses from hundreds of pulsars, including many millisecond pulsars, LOFAR opens up new possibilities for the study of emission physics.
The structure and the dielectric properties of Pb(Zn1/3Nb2/3)O3 (PZN) crystal have been investigated by means of high-resolution synchrotron x-ray diffraction (with an x-ray energy of 32 keV) and dielectric spectroscopy (in the frequency range of 100 Hz - 1 MHz). At high temperatures, the PZN crystal exhibits a cubic symmetry and polar nanoregions inherent to relaxor ferroelectrics are present, as evidenced by the single (222) Bragg peak and by the noticeable tails at the basis of the peak. At low temperatures, in addition to the well-known rhombohedral phase, another low-symmetry, probably ferroelectric, phase is found. The two phases coexist in the form of mesoscopic domains. The para- to ferroelectric phase transition is diffused and observed between 325 and 390 K, where the concentration of the low-temperature phases gradually increases and the cubic phase disappears upon cooling. However, no dielectric anomalies can be detected in the temperature range of diffuse phase transition. The temperature dependence of the dielectric constant show the maximum at higher temperature (Tm = 417 - 429 K, depending on frequency) with the typical relaxor dispersion at T < Tm and the frequency dependence of Tm fitted to the Vogel-Fulcher relation. Application of an electric field upon cooling from the cubic phase or poling the crystal in the ferroelectric phase gives rise to a sharp anomaly of the dielectric constant at T 390 K and diminishes greatly the dispersion at lower temperatures, but the dielectric relaxation process around Tm remains qualitatively unchanged. The results are discussed in the framework of the present models of relaxors and in comparison with the prototypical relaxor ferroelectric Pb(Mg1/3Nb2/3)O3.
We discuss QCD sum rule constraints based on moments of vector meson spectral distributions in the vacuum and in a nuclear medium. Sum rules for the two lowest moments of these spectral distributions do not suffer from uncertainties related to QCD condensates of dimension higher than four. We exemplify these relations for the case of the omega meson and discuss the issue of in-medium mass shifts from this viewpoint.
The arithmetic motivic Poincar\'e series of a variety $V$ defined over a field of characteristic zero, is an invariant of singularities which was introduced by Denef and Loeser by analogy with the Serre-Oesterl\'e series in arithmetic geometry. They proved that this motivic series has a rational form which specializes to the Serre-Oesterl\'e series when $V$ is defined over the integers. This invariant, which is known explicitly for a few classes of singularities, remains quite mysterious. In this paper we study this motivic series when $V$ is an affine toric variety. We obtain a formula for the rational form of this series in terms of the Newton polyhedra of the ideals of sums of combinations associated to the minimal system of generators of the semigroup of the toric variety. In particular, we deduce explicitly a finite set of candidate poles for this invariant.
We give an extension of Sister Celine's method of proving hypergeometric sum identities that allows it to handle a larger variety of input summands. We then apply this to several problems. Some give new results, and some reprove already known results in an automated way.
A new type of approximate scaling compatible with the Balitsky-Kovchegov equation with running coupling is found, which is different from the previously known running coupling geometric scaling. The corresponding asymptotic traveling wave solution is derived. Although featuring different scaling behaviors, the two solutions are complementary approximations of the same universal solution, and they become equivalent in the high energy limit. The new type of scaling is observed in the small-x DIS data.
Inspired by the Solovay-Kitaev decomposition for approximating unitary operations as a sequence of operations selected from a universal quantum computing gate set, we introduce a method for approximating any single-qubit channel using single-qubit gates and the controlled-NOT (CNOT). Our approach uses the decomposition of the single-qubit channel into a convex combination of "quasiextreme" channels. Previous techniques for simulating general single-qubit channels would require as many as 20 CNOT gates, whereas ours only needs one, bringing it within the range of current experiments.
Using Green Bank Telescope radio recombination line (RRL) data, we analyze the role of leaking radiation from HII regions in maintaining the ionization of the interstellar medium. We observed a sample of eight Galactic HII regions of various sizes, morphologies, and luminosities. For each region the hydrogen RRL intensity decreases roughly as a power-law with distance from the center of the region. This suggests that radiation leaking from the HII region is responsible for the majority of surrounding ionized gas producing RRL emission. Our results further indicate that the hydrogen RRL intensity appears to be fundamentally related to the HII region sizes traced by their photodissociation regions, such that physically smaller HII regions show a steeper decrease in intensity with increasing distance from the region centers. As a result, giant HII regions may have a much larger effect in maintaining the ionization of the interstellar medium. For six of the eight observed HII regions we find a decrease in the 4He+/H+ abundance ratio with increasing distance, indicating that He-ionizing photons are being absorbed within the ionization front of the HII region. There is enhanced carbon RRL emission toward directions with strong continuum background, suggesting that the carbon emission is amplified by stimulated emission.
One-dimensional directed driven stochastic flow with competing nonlocal and local hopping events has an instability threshold from a populated phase into an empty-road (ER) phase. We implement this in the context of the asymmetric exclusion process. The nonlocal skids promote strong clustering in the stationary populated phase. Such clusters drive the dynamic phase transition and determine its scaling properties. We numerically establish that the instability transition into the ER phase is second order in the regime where the entry point reservoir controls the current and first order in the regime where the bulk is in control. The first order transition originates from a turn-about of the cluster drift velocity. At the critical line, the current remains analytic, the road density vanishes linearly, and fluctuations scale as uncorrelated noise. A self-consistent cluster dynamics analysis explains why these scaling properties remain that simple.
We present K-band echelle spectra of the cataclysmic variable SS Cyg and the pre-cataclysmic variable V471 Tau in order to measure the strengths of the 12CO and 13CO bands at 2.3525 and 2.3448 microns, respectively, and so perform the observational test of the common-envelope model of close binary star evolution proposed by Sarna et al. (1995). Although we find evidence of an absorption feature coincident with the expected wavelength of 13CO in both objects, we attribute it instead to a cluster of neutral atomic absorption features (primarily due to TiI) possibly arising from star-spots on the surfaces of the rapidly rotating secondary stars in these systems, thereby rendering the test inconclusive. We present a modified observational test of common-envelope evolution, based on the observation of the 13CO bands at 2.3739 and 2.4037 microns, which is insensitive to spectral contamination by star-spots.
Very high energy (VHE $>$100 GeV) gamma rays coming from blazars can produce pairs when interacting with the Extragalactic Background Light (EBL) and the Cosmic Microwave Background, generating an electromagnetic cascade. Depending on the Intergalactic Magnetic Field (IGMF) intensity, this cascade may result in an extended isotropic emission of photons around the source (halo), or in a broadening of the emission beam. The detection of these effects might lead to important constrains both on the IGMF intensity and the EBL density, quantities of great relevance in cosmological models. Using a Monte Carlo program, we simulate electromagnetic cascades for different values of the IGMF intensities and coming from a source similar to 1ES0229+200, a blazar with hard intrinsic spectrum at redshift $z=0.14$, which is an ideal distance for potentially observing the effect. We study the possible response of a generic future Cherenkov telescope using a simplified model for the sensitivity, effective area and angular resolution. Finally, combining these instrument properties, we calculate the angular distribution of photons and develop a method to test the statistical feasibility of detecting the effect in the near future.
A large fraction of accreting black hole and neutron stars systems present clear evidence of the reprocessing of X-rays in the atmosphere of an optically-thick accretion disk. The main hallmarks of X-ray reflection include fluorescent K-shell emission lines from iron ($\sim 6.4-6.9$ keV), the absorption iron K-edge ($\sim 7-9$ keV), and a broad featureless component known as the Compton hump ($\sim 20-40$ keV). This Compton hump is produced as the result of the scattering of high-energy photons ($E \gtrsim 10$ keV) of the relatively colder electrons ($T_e \sim 10^5-10^7$ K) in the accretion disk, in combination with photoelectric absorption from iron. The treatment of this process in most current models of ionized X-ray reflection has been done using an approximated Gaussian redistribution kernel. This approach works sufficiently well up to $\sim100$ keV, but it becomes largely inaccurate at higher energies and at relativistic temperatures ($T_e\sim10^9$ K). We present new calculations of X-ray reflection using a modified version of our code XILLVER, including an accurate solution for Compton scattering of the reflected unpolarized photons in the disk atmosphere. This solution takes into account quantum electrodynamic and relativistic effects allowing the correct treatment of high photon energies and electron temperatures. We show new reflection spectra computed with this model, and discuss the improvements achieved in the reproducing the correct shape of the Compton hump, the discrepancies with previous calculations, and the expected impact of these new models in the interpretation of observational data.
The analysis of vessel morphology and connectivity has an impact on a number of cardiovascular and neurovascular applications by providing patient-specific high-level quantitative features such as spatial location, direction and scale. In this paper we present an end-to-end approach to extract an acyclic vascular tree from angiographic data by solving a connectivity-enforcing anisotropic fast marching over a voxel-wise tensor field representing the orientation of the underlying vascular tree. The method is validated using synthetic and real vascular images. We compare VTrails against classical and state-of-the-art ridge detectors for tubular structures by assessing the connectedness of the vesselness map and inspecting the synthesized tensor field as proof of concept. VTrails performance is evaluated on images with different levels of degradation: we verify that the extracted vascular network is an acyclic graph (i.e. a tree), and we report the extraction accuracy, precision and recall.
We describe the Gevrey series solutions at singular points of the irregular hypergeometric system (GKZ system) associated with an affine plane monomial curve. We also describe the irregularity complex of such a system with respect to its singular support.
Elliptic stochastic differential equations (SDE) make sense when the coefficients are only continuous. We study the corresponding linearized SDE whose coefficients are not assumed to be locally bounded. This leads to existence of $W_{\loc}^{1,p}$ solution flows for elliptic SDEs with H\"older continuous and $\cap_{p} W_{\loc}^{1,p}$ coefficients. Furthermore an approximation scheme is studied from which we obtain a representation for the derivative of the Markov semigroup, and an integration by parts formula.
The goal of this survey paper is to present, in chronological order, certain research works on continued fractions in power series fields over a finite field, all of them being derivated from some examples introduced thirty years ago by Mills and Robbins.
Using computational algebraic geometry techniques and Hilbert bases of polyhedral cones we derive explicit formulas and generating functions for the number of magic squares and magic cubes.
We have performed a statistical analysis using broad band IRAS data on about 500 planetary nebulae with the aim of characterizing their dust content. Our approach is different from previous studies in that it uses an extensive grid of photoionization models to test the methods for deriving the dust temperature, the dust-to-gas mass ratio and the average grain size. In addition, we use only distance independent diagrams. With our models, we show the effect of contamination by atomic lines in the broad band IRAS fluxes during planetary nebula evolution. We find that planetary nebulae with very different dust-to-gas mass ratios exist, so that the dust content is a primordial parameter for the interpretation of far infrared data of planetary nebulae. In contrast with previous studies, we find no evidence for a decrease in the dust-to-gas mass ratio as the planetary nebulae evolve. We also show that the decrease in grain size advocated by Natta and Panagia (1981, ApJ 248,189) and Lenzuni et al. (1989, ApJ 345, 306) is an artefact of their method of analysis. Our results suggest that the timescale for destruction of dust grains in planetary nebulae is larger than their lifetime.   Footnote: Table 1 is also accessible in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/Abstract.html
We present a 1.4 GHz Karl G. Jansky Very Large Array (VLA) study of a sample of early-type galaxies (ETGs) from the volume- and magnitude-limited ATLAS-3D survey. The radio morphologies of these ETGs at a resolution of 5" are diverse and include sources that are compact on sub-kpc scales, resolved structures similar to those seen in star-forming spiral galaxies, and kpc-scale radio jets/lobes associated with active nuclei. We compare the 1.4 GHz, molecular gas, and infrared (IR) properties of these ETGs. The most CO-rich ATLAS-3D ETGs have radio luminosities consistent with extrapolations from H_2-mass-derived star formation rates from studies of late-type galaxies. These ETGs also follow the radio-IR correlation. However, ETGs with lower molecular gas masses tend to have less radio emission relative to their CO and IR emission compared to spirals. The fraction of galaxies in our sample with high IR-radio ratios is much higher than in previous studies, and cannot be explained by a systematic underestimation of the radio luminosity due to the presence extended, low-surface-brightness emission that was resolved-out in our VLA observations. In addition, we find that the high IR-radio ratios tend to occur at low IR luminosities, but are not associated with low dynamical mass or metallicity. Thus, we have identified a population of ETGs that have a genuine shortfall of radio emission relative to both their IR and molecular gas emission. A number of mechanisms may conspire to cause this radio deficiency, including a bottom-heavy stellar initial mass function, weak magnetic fields, a higher prevalence of environmental effects compared to spirals and enhanced cosmic ray losses.
The Lazarus project was designed to make the most of limited 3D binary black-hole simulations, through the identification of perturbations at late times, and subsequent evolution of the Weyl scalar $\Psi_4$ via the Teukolsky formulation. Here we report on new developments, employing the concept of the ``quasi-Kinnersley'' (transverse) frame, valid in the full nonlinear regime, to analyze late-time numerical spacetimes that should differ only slightly from Kerr. This allows us to extract the essential information about the background Kerr solution, and through this, to identify the radiation present. We explicitly test this procedure with full numerical evolutions of Bowen-York data for single spinning black holes, head-on and orbiting black holes near the ISCO regime. These techniques can be compared with previous Lazarus results, providing a measure of the numerical-tetrad errors intrinsic to the method, and give as a by-product a more robust wave extraction method for numerical relativity.
We discuss a scheme for reconstructing experimentally the diagonal elements of the density matrix of quantum optical states. Applications to PDC heralded photons, multi-thermal and attenuated coherent states are illustrated and discussed in some details.
Inspired by the striking similarities between the metal-insulator transitions in graphite and Si-MOSFET's and the recent attention to charge doping in carbon-based materials, we have made attempts to fabricate a field-effect transistor based on graphite. A relatively thick layer of boron nitride turned out to be able to serve as a gate dielectric. This, however, limits the achievable electric gate field, which might be the reason for our observation of no charge-doping effect.
Recent observation of 850 micron sub-mm polarization from T Tauri disks opens up the possibility of studying magnetic field structure within protostellar disks. The degree of polarization is around 3 % and the direction of polarization is perpendicular to the disk. Since thermal emission from dust grains dominates the spectral energy distribution at the sub-mm/FIR regime, dust grains are thought to be the cause of the polarization. We discuss grain alignment by radiation and we explore the efficiency of dust alignment in T Tauri disks. Calculations show that dust grains located far away from the Central proto-star are more efficiently aligned. In the presence of a regular magnetic field, the aligned grains produce polarized emission in sub-mm/FIR wavelengths. The direction of polarization is perpendicular to the local magnetic field direction. When we use a recent T Tauri disk model and take a Mathis-Rumpl-Nordsieck-type distribution with maximum grain size of 500-1000 $\mu$m, the degree of polarization is around 2-3 % level at wavelengths larger than $\sim100\mu$m. Our study indicates that multifrequency infrared polarimetric studies of protostellar disks can provide good insights into the details of their magnetic structure. We also provide predictions for polarized emission for disks viewed at different wavelengths and viewing angles.
We give a few explicit examples which answer an open minded question of Professor Igor Dolgachev on complex dynamics of the inertia group of a smooth rational curve on a projective K3 surface and its variants for a rational surface and a non-projective K3 surface.
We describe the search for delta Scuti stars in the MACHO database of bulge fields. Concentrating on a sample of high amplitude delta Scutis, we examine the light curves and pulsation modes. We also discuss their spatial distribution and evolutionary status using mean colors and absolute magnitudes.