ShantanuT01/DACTYL-Pretraining huggingface dataset:
A very general surface of degree at least four in projective space of dimension three contains no curves other than intersections with surfaces. We find a formula for the degree of the locus of surfaces of degree at least five which contain some elliptic quartic curve. We also compute the degree of the locus of quartic surfaces containing an elliptic quartic curve, a case not covered by that formula.
Optical and radio observations of shock-ionised bubble nebulae surrounding ultraluminous X-ray sources (ULXs) suggest that they are powered by jets or super-critical outflows presumably launched from the ULX accretion disc. Recent simulations of these systems have shown that the shocked wind can emit thermal X-rays with estimated luminosities $\sim 10^{36}$ erg s$^{-1}$. In this work, we investigated whether it is possible to detect and spatially resolve the X-ray emission from these systems using archival Chandra observations of the ULX Holmberg IX X-1. This source is an ideal target to study for two reasons: it is surrounded by an optical bubble nebula with a large spatial extent ($\sim$ 400 pc) that can easily be resolved with Chandra. Further, it has a hard X-ray continuum that is easily distinguishable from the expected soft thermal emission from the nebula. However, a spectral and photometric analysis on stacked Chandra observations of the source reveals that there is no strong evidence for an X-ray bubble associated with it, to a limiting luminosity of $\sim 2 \times 10^{36}$ erg s$^{-1}$. The detection of such X-ray nebulae may be possible with future X-ray missions such as Athena, which would provide useful constraints on the kinematics of the outflow. Finally, our observations also emphasise that the nebular emission does not contribute significantly to the residuals in the X-ray spectrum of the source, which are more likely to be linked to processes localised to the ULX.
Stellar abundances of beryllium are useful in different areas of astrophysics, including studies of the Galactic chemical evolution, of stellar evolution, and of the formation of globular clusters. Determining Be abundances in stars is, however, a challenging endeavor. The two Be II resonance lines useful for abundance analyses are in the near UV, a region strongly affected by atmospheric extinction. CUBES is a new spectrograph planned for the VLT that will be more sensitive than current instruments in the near UV spectral region. It will allow the observation of fainter stars, expanding the number of targets where Be abundances can be determined. Here, a brief review of stellar abundances of Be is presented together with a discussion of science cases for CUBES. In particular, preliminary simulations of CUBES spectra are presented, highlighting its possible impact in investigations of Be abundances of extremely metal-poor stars and of stars in globular clusters.
We study the asymptotic volume dependence of the heavy-heavy-light three-point functions in the $\mathcal{N}=4$ Super-Yang-Mills theory using the hexagon bootstrap approach, where the volume is the length of the heavy operator. We extend the analysis of our previous short letter 1511.06199 to the general case where the heavy operators can be in any rank one sector and the light operator being a generic non-BPS operator. We prove the conjecture of Bajnok, Janik and Wereszczynski 1404.4556 up to leading finite size corrections.
In ``Ramified G-bundles as parabolic bundles'' (J. Ramanujan Math. Soc. (2003) Vol. 18) with Balaji and Nagaraj we introduced the ramified principal bundles. The aim here is to define the Higgs bundles in the ramified context.
The dark matter candidates we are searching for, e.g. neutralinos, may be one of many components of the cold dark matter (CDM). We point out here that very subdominant components, constituting even 1% of the CDM for indirect detection and much less for direct detection, remain observable in current and future searches. So if a CDM signal is confirmed in CDM search experiments (except for a signal from annihilations in the dark halo) we will need to find out the halo fraction accounted for the CDM component we detected.
The equivalence principle is treated on a mathematically rigorous base on sufficiently general subsets of a differentiable manifold. This is carried out using the basis of derivations of the tensor algebra over that manifold. Necessary and/or sufficient conditions of existence, uniqueness, and holonomicity of these bases in which the components of the derivations of the tensor algebra over it vanish on these subsets, are studied. The linear connections are considered in this context. It is shown that the equivalence principle is identically valid at any point, and along any path, in every gravitational theory based on linear connections. On higher dimensional submanifolds it may be valid only in certain exceptional cases.
We study the diagonalizability of the Atkin $U_t$-operator acting on Drinfeld cusp forms for $\Gamma_1(t)$ and $\Gamma(t)$ using Teitelbaum's interpretation as harmonic cocycles. For small weights $k\leqslant 2q$, we prove $U_t$ is diagonalizable in odd characteristic and we point out that non diagonalizability in even characteristic depends on antidiagonal blocks.
The Planck CMB experiment has delivered the best constraints so far on primordial non-Gaussianity, ruling out early-Universe models of inflation that generate large non-Gaussianity. Although small improvements in the CMB constraints are expected, the next frontier of precision will come from future large-scale surveys of the galaxy distribution. The advantage of such surveys is that they can measure many more modes than the CMB -- in particular, forthcoming radio surveys with the SKA will cover huge volumes. Radio continuum surveys deliver the largest volumes, but with the disadvantage of no redshift information. In order to mitigate this, we use two additional observables. First, the integrated Sachs-Wolfe effect -- the cross-correlation of the radio number counts with the CMB temperature anisotropies -- helps to reduce systematics on the large scales that are sensitive to non-Gaussianity. Second, optical data allows for cross-identification in order to gain some redshift information. We show that, while the single redshift bin case can provide a sigma(fNL) ~ 20, and is therefore not competitive with current and future constraints on non-Gaussianity, a tomographic analysis could improve the constraints by an order of magnitude, even with only two redshift bins. A huge improvement is provided by the addition of high-redshift sources, so having cross-ID for high-z galaxies and an even higher-z radio tail is key to enabling very precise measurements of fNL. Our results show that SKA continuum surveys could provide constraints competitive with CMB and forthcoming optical surveys, potentially allowing a measurement of sigma(fNL) ~ 1 to be made. Moreover, these measurements would act as a useful check of results obtained with other probes at other redshift ranges with other methods.
We discuss solutions of Vlasov-Einstein equation for collisionless dark matter particles in the context of a flat Friedmann universe. We show that, after decoupling from the primordial plasma, the dark matter phase-space density indicator Q remains constant during the expansion of the universe, prior to structure formation. This well known result is valid for non-relativistic particles and is not "observer dependent" as in solutions derived from the Vlasov-Poisson system. In the linear regime, the inclusion of velocity dispersion effects permits to define a physical Jeans length for collisionless matter as function of the primordial phase-space density indicator: \lambda_J = (5\pi/G)^(1/2)Q^(-1/3)\rho_dm^(-1/6). The comoving Jeans wavenumber at matter-radiation equality is smaller by a factor of 2-3 than the comoving wavenumber due to free-streaming, contributing to the cut-off of the density fluctuation power spectrum at the lowest scales. We discuss the physical differences between these two scales. For dark matter particles of mass equal to 200 GeV, the derived Jeans mass is 4.3 x 10^(-6) solar masses.
We consider three different families of Vafa-Witten invariants of $K3$ surfaces. In each case, the partition function that encodes the Vafa-Witten invariants is given by combinations of twisted Dedekind $\eta$-functions. By utilising known properties of these $\eta$-functions, we obtain exact formulae for each of the invariants and prove that they asymptotically satisfy all higher-order Tur\'{a}n inequalities.
The least number of products of linear forms that may be added together to obtain a given form is the Chow rank of this form. The Chow rank of a generic form corresponds to the smallest s for which the sth secant variety of the Chow variety fills the ambient space. We show that, except for certain known exceptions, this secant variety has the expected dimension for low values of s.
We obtain Gr\"onwall type estimates for the gradient of the harmonic functions for a L\'evy operator with order strictly larger than 1 and minimal assumptions of its L\'evy measure.
We present optical spectra for a representative sample of 27 nearby (z < 0.2) 2MASS-selected AGN with red near-IR colours (J-K 2.0). The spectra were taken with the ISIS spectrograph on the WHT with the aim of determining the nature of the red 2MASS AGN, in particular whether they are young quasars obscured by their natal cocoon of gas and dust. We compare our findings with those obtained for comparison samples of PG quasars and unobscured type 1 AGN.   The spectra show a remarkable variety, including moderately reddened type 1 objects (45%), type 1 objects that appear similar to traditional UV/optical selected AGN (11%), narrow-line Seyfert 1 AGN (15%), type 2 AGN (22%) and HII/composite objects (7%). The high Balmer decrements that we measure in many of the type 1 objects are consistent with their red J-KS colours being due to moderate levels of dust extinction (0.2 < E(B-V) < 1.2). However, we measure only modest velocity shifts and widths for the broader [OIII]{\lambda}5007 emission line components that are similar to those measured in the comparison samples. This suggests that the outflows in the red 2MASS objects are not unusual compared with those of optical/UV selected AGN of similar luminosity. In addition, the Eddington ratios for the 2MASS sample are relatively modest.   Overall, based on their optical spectra, we find no clear evidence that the population of red, 2MASS selected AGN at low redshifts represents young quasars. Most plausibly, these objects are normal type 1 AGN that are moderately obscured by material in the outer layers of the circum-nuclear tori or in the disks of the host galaxies.
Active authentication refers to the process in which users are unobtrusively monitored and authenticated continuously throughout their interactions with mobile devices. Generally, an active authentication problem is modelled as a one class classification problem due to the unavailability of data from the impostor users. Normally, the enrolled user is considered as the target class (genuine) and the unauthorized users are considered as unknown classes (impostor). We propose a convolutional neural network (CNN) based approach for one class classification in which a zero centered Gaussian noise and an autoencoder are used to model the pseudo-negative class and to regularize the network to learn meaningful feature representations for one class data, respectively. The overall network is trained using a combination of the cross-entropy and the reconstruction error losses. A key feature of the proposed approach is that any pre-trained CNN can be used as the base network for one class classification. Effectiveness of the proposed framework is demonstrated using three publically available face-based active authentication datasets and it is shown that the proposed method achieves superior performance compared to the traditional one class classification methods. The source code is available at: github.com/otkupjnoz/oc-acnn.
Topic of this article are tomographic measurements of the integrated Sachs-Wolfe effect with specifically designed, orthogonal polynomials which project out statistically independent modes of the galaxy distribution. The polynomials are contructed using the Gram-Schmidt orthogonalisation method. To quantify the power of the iSW-effect in contraining cosmological parameters we perfom a combined Fisher matrix analysis for the iSW-, galaxy- and cross-spectra for wCDM cosmologies using the survey characteristics of PLANCK and EUCLID. The signal to noise ratio has also been studied for other contemporary galaxy surveys, such as SDSS, NVSS and 2MASS. For the cross-spectra our tomographic method provides a 16% increase in the signal to noise ratio and an improvement of up to 30% in conditional errors on parameters. Including all spectra, the marginalised errors approach an inverse square-root dependence with increasing cumulative polynomial order which underlines the statistical independence of the weighted signal spectra.
Collective modes of exotic quantum fluids reveal underlying physical mechanisms responsible for emergent complex quantum ground states. We observe unexpected new collective modes in the fractional quantum Hall (FQH) regime: intra-Landau-level plasmons in the second Landau level measured by resonant inelastic light scattering. The plasmons herald rotational-symmetry-breaking phases in tilted magnetic fields and reveal long-range translational invariance in these phases. The fascinating dependence of plasmon features on filling factor provide new insights on interplays between topological quantum Hall order and nematic electronic liquid crystal phases. A marked intensity minimum in the plasmon spectrum at Landau level filling factor v = 5/2 strongly suggests that this paired state, which could support non-Abelian excitations, overwhelms competing nematic phases, unveiling the robustness of the 5/2 superfluid state for small tilt angles. At v = 7/3, a sharp and strong plasmon peak that links to emerging macroscopic coherence supports the proposed model of a FQH nematic state at this filling factor.
We predict a fast relaxation of photo-excited carriers in monolayer transition metal dichalcogenides (TMDCs), which is mediated by the emission of longitudinal optical (LO) phonons. By evaluating Born effective charges for ${\rm MoS_2, MoSe_2,WS_2}$, and ${\rm WSe_2}$, we find that, due to the polar coupling of electrons with LO phonons, the relaxation times for hot electrons and holes are of the order of a few ps.
Charge and spin transport in spintronics devices can be described by a spin diffusion equation suitable for modelling scales much larger than the scattering and atomic scales. This work concerns the coarse graining procedure used to compute the coefficients of the diffusion equation, which are sensitive the details of individual atoms and impurities. We show with two simple examples that in spintronics devices which have both a spin-orbit interaction and magnetization, standard coarse graining can easily obtain diffusion equations which fail to conserve electronic charge. The same failure can occur in systems with both a spin-orbit interaction and orbital polarization. We show that linear response theory, coupled with the self-consistent Born approximation and ladder diagrams, offers an improved way of calculating diffusion equations. We show that the resulting equations satisfy a Ward-Takahashi identity that guarantees charge conservation.
We present simultaneous, multiband monitoring of 19 field M dwarfs (spectral types M2-M9). Significant variability was found in seven objects in at least one out of the three channels I, R and G. Two objects, LHS370 (M5V) and 2M1707+64 (M9V), show periods of 5.9+-2.0 and 3.65+-0.1 hours respectively. On account of the agreement with the typical values of v*sin(i) published for M dwarfs (Mohanty & Basri 2003), we claim these to be the objects' rotation periods. In the case of 2M1707+64 we furthermore find evidence for the presence of magnetically-induced cool spots as the reason for the observed variability (at a temperature contrast of 4-8 percent, with a projected surface coverage factor of less than 0.075) and can rule out the scenario of dust clouds (as represented by the COND or DUSTY models). Comparing the frequency of occurrence of variability in this and various L dwarf samples published over the past few years, we find that variability is more common in field L dwarfs than in field M dwarfs. This implies a change in the physical nature and/or extent of surface features when moving from M to L dwarfs.
New applications of the formula $A |\psi\rangle = \langle A \rangle |\psi\rangle + \Delta A |\psi_{\perp} \rangle$ are discussed. Simple derivations of the Heisenberg uncertainty principle and of related inequalities are presented. In addition, the formula is used in an instructive paradox which clarifies a fundamental notion in quantum mechanics.
We investigate the electrical conductivity of spin-polarized graphene in the presence of short-ranged magnetic scatterers within the relaxation time approximation and the semi-classical Boltzmann approach. Spin-flip scattering of the itinerant electrons from the majority spin sub-band into the minority one results in a minimum in the electrical resistivity at a finite temperature. While this behavior is reminiscent of the renowned Kondo effect, it has an entirely different origin and differs from the Kondo effect in several aspects. In particular, unlike the Kondo effect, this is a single particle phenomena, and it does not require antiferromagnetic coupling between the magnetic moments of impurities and spins of the itinerant electrons.
In this work we describe an interesting application of a simple derivative-free optimization method to extract the quasinormal modes (QNM's) of a massive scalar field propagating in a 4-dimensional Schwarzschild anti-de Sitter black hole (Sch-AdS$_4$). In this approach, the problem to find the QNM's is reduced to minimize a real valued function of two variables and does not require any information about derivatives. In fact, our strategy requires only evaluations of the objective function to search global minimizers of the optimization problem. Firstly, numerical experiments were performed to find the QNM's of a massless scalar field propagating in intermediate and large Sch-AdS$_4$ black holes. The performance of this optimization algorithm was compared with other numerical methods used in previous works. Our results showed to be in good agreement with those obtained previously. Finally, the massive scalar field case and its QNM's were also obtained and discussed.
This paper presents a novel method for 3D human pose and shape estimation from images with sparse views, using joint points and silhouettes, based on a parametric model. Firstly, the parametric model is fitted to the joint points estimated by deep learning-based human pose estimation. Then, we extract the correspondence between the parametric model of pose fitting and silhouettes on 2D and 3D space. A novel energy function based on the correspondence is built and minimized to fit parametric model to the silhouettes. Our approach uses sufficient shape information because the energy function of silhouettes is built from both 2D and 3D space. This also means that our method only needs images from sparse views, which balances data used and the required prior information. Results on synthetic data and real data demonstrate the competitive performance of our approach on pose and shape estimation of the human body.
We present a catalog of Galactic star clusters, associations and candidates with 10978 entries. This multi-band catalog was constructed over 20 years, starting with visual inspections on the Digital Sky Survey and incremented with the 2MASS, WISE, VVV, Spitzer and Herschel surveys. Large and small catalogs, as well as papers on individual objects have been systematically cross-identified. The catalog provides Galactic and equatorial coordinates, angular diameters, and chronologically ordered designations, making it simple to assign discoveries, and verify how often the objects were cataloged by different authors, search methods and/or surveys. Detection in a single band is the minimum constraint to validate an entry. About 3200 objects have measured parameters in the literature. A fundamental contribution of the present study is to present additional $\approx7700$ objects for first analyses of nature, photometry, spectroscopy and structure. The present focus is not to compile or determine fundamental parameters, but to provide a catalog characterizing uniformly the entries. A major result is that now 4060 embedded clusters are catologed, a factor of $\approx2$ larger than open clusters. Besides cross-identifications in different references and wavelength domains, we also communicate the discovery of 638 star clusters and alike objects. The present general catalog provides previously studied objects and thousands of additional entries in a homogeneous way, a timely contribution to {\em Gaia} related works.
We propose an on-chip optical waveguide for Bose-Einstein condensates based on the evanescent light fields created by surface states of a photonic crystal. It is shown that the modal properties of these surface states can be tailored to confine the condensate at distances from the chip surface significantly longer that those that can be reached by using conventional index-contrast guidance. We numerically demonstrate that by index-guiding the surface states through two parallel waveguides, the atomic cloud can be confined in a two-dimensional trap at about 1$\mu$m above the structure using a power of 0.1mW.
Inspired by symplectic geometry and a microlocal characterizations of perverse (constructible) sheaves we consider an alternative definition of perverse coherent sheaves. We show that a coherent sheaf is perverse if and only if $R\Gamma_Z(\mathcal{F})$ is concentrated in degree 0 for special subvarieties Z of X. These subvarieties Z are analogs of Lagrangians in the symplectic case.
We revisit the regularity theory of Escauriaza, Seregin, and \v{S}ver\'ak for solutions to the three-dimensional Navier-Stokes equations which are uniformly bounded in the critical $L^3_x(\mathbf{R}^3)$ norm. By replacing all invocations of compactness methods in these arguments with quantitative substitutes, and similarly replacing unique continuation and backwards uniqueness estimates by their corresponding Carleman inequalities, we obtain quantitative bounds for higher regularity norms of these solutions in terms of the critical $L^3_x$ bound (with a dependence that is triple exponential in nature). In particular, we show that as one approaches a finite blowup time $T_*$, the critical $L^3_x$ norm must blow up at a rate $(\log\log\log \frac{1}{T_*-t})^c$ or faster for an infinite sequence of times approaching $T_*$ and some absolute constant $c>0$.
We study small points for the Arakelov height on the projective line. First, we identify the smallest positive value taken by the Arakelov height, and we characterize all cases of equality. Next we solve several archimedean energy minimization problems with respect to the chordal metric on the projective line, and as an application, we obtain lower bounds on the Arakelov height in fields of totally real and totally p-adic numbers.