ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let $f:X\rightarrow Z$ be a separable fibration of relative dimension 1 between smooth projective varieties over an algebraically closed field $k$ of positive characteristic. We prove the subadditivity of Kodaira dimension $\kappa(X)\geq\kappa(Z)+\kappa(F)$, where $F$ is the generic geometric fiber of $f$, and $\kappa(F)$ is the Kodaira dimension of the normalization of $F$. Moreover, if $\dim X=2$ and $\dim Z=1$, we have a stronger inequality $\kappa(X)\geq \kappa(Z)+\kappa_1(F)$ where $\kappa_1(F)=\kappa(F,\omega^o_F)$ is the Kodaira dimension of the dualizing sheaf $\omega_F^o$.
We develop a statistical estimator to infer the redshift probability distribution of a photometric sample of galaxies from its angular cross-correlation in redshift bins with an overlapping spectroscopic sample. This estimator is a minimum variance weighted quadratic function of the data: a quadratic estimator. This extends and modifies the methodology presented by McQuinn & White (2013). The derived source redshift distribution is degenerate with the source galaxy bias, which must be constrained via additional assumptions. We apply this estimator to constrain source galaxy redshift distributions in the Kilo-Degree imaging survey through cross-correlation with the spectroscopic 2-degree Field Lensing Survey, presenting results first as a binned step-wise distribution in the range z < 0.8, and then building a continuous distribution using a Gaussian process model. We demonstrate the robustness of our methodology using mock catalogues constructed from N-body simulations, and comparisons with other techniques for inferring the redshift distribution.
The scalar field can behave like a fluid with equation of state $p_{\phi}=w\rho_{\phi}$, where $w \in [-1,1]$. In this Letter we derive a class of the scalar field potentials for which $w=$ const. Scalar field with such a potential can mimic ordinary matter, radiation, cosmic strings, etc. We perform our calculations in the framework of the loop cosmology with holonomy corrections. We solve the model analytically for the whole parameter space. Subsequently, we perform similar consideration for the model with a phantom field ($w<-1$). We show that scalar field is monotonic function in both cases. This indicates that it can be treated as a well-defined internal time for these models. Moreover we perform preliminary studies of the scalar field perturbations with this potential. We indicate that non-Gaussian features are present admitting for the possible observational constraints of the model.
We investigate the nonequilibrium transport properties of a silicene armchair nanoribbon with a random distribution of adsorbed atoms in apex positions. A ferromagnetic insulator grown below the nanoribbon splits spin-up and spin-down electron bands and gives rise to a spin polarization of the conductance. The conductance vanishes when the Fermi energy matches the adatom levels due to the coupling of adatom localized states with the continuum spectra of the nanoribbon. This is the well-known Fano effect, resulting in a spin-dependent antiresonance in the conductance. The different antiresonance energies of spin-up and spin-down electrons give rise to a full spin polarization of the conductance in a broad energy window. This spin-dependent Fano effect opens the possibility to using it in spintronics as a tuneable source of polarized electrons.
Asteroseismology using space-based telescopes is vital to our understanding of stellar structure and evolution. {\textit{CoRoT}}, {\textit{Kepler}}, and {\textit{TESS}} space telescopes have detected large numbers of solar-like oscillating evolved stars. %(kaynaklar, Kallinger, vb ). Solar-like oscillation frequencies have an important role in the determination of fundamental stellar parameters; in the literature, the relations between the two is established by the so-called scaling relations. % These scaling relations are in better agreement with mass and radius of main-sequence stars with large separation ($\Delta\nu$) and frequency of maximum amplitude (${\nu_{\rm max}}$). In this study, we analyse data obtained from the observation of 15 evolved solar-like oscillating stars using the {\textit{Kepler}} and ground-based %\textit{CoRoT} telescopes.   The main purpose of the study is to determine very precisely the fundamental parameters of evolved stars by constructing interior models using asteroseismic parameters. We also fit the reference frequencies of models to the observational reference frequencies caused by the He {\scriptsize II} ionization zone.   The 15 evolved stars are found to have masses and radii within ranges of $0.79$-$1.47$ $M_{\rm sun}$ and $1.60$-$3.15$ $R_{\rm sun}$, respectively. Their model ages range from $2.19$ to $12.75$ Gyr. %Using a number of methods based on conventional and modified scaling relations and evolutionary models constructed with using the {\small {MESA}} code, we determine stellar radii, masses and ages. It is revealed that fitting reference frequencies typically increase the accuracy of asteroseismic radius, mass, and age. The typical uncertainties of mass and radius are $\sim$ 3-6 and $\sim$ 1-2 per cent, respectively. Accordingly, the differences between the model and literature ages are generally only a few Gyr.
There are three families of bivariate polynomial maps associated with the rank-$2$ simple complex Lie algebras $A_2, B_2 \cong C_2$ and $G_2$. It is known that the bivariate polynomial map associated with $A_2$ induces a permutation of $\mathbf{F}_q^2$ if and only if $\gcd(k,q^s-1)=1$ for $s=1, 2, 3$. In this paper, we give similar criteria for the other two families. As an application, a counterexample is given to a conjecture posed by Lidl and Wells about the generalized Schur's problem.
We introduce the concept of functions of locally bounded variation on abstract Wiener spaces and study their properties. Some nontrivial examples and applications to stochastic analysis are also discussed.
We present a detailed analysis of a confined filament eruption and jet associated with a C1.5 class solar flare. Multi-wavelength observations from GONG and SDO reveal the filament forming over several days following the emergence and then partial cancellation of a minority polarity spot within a decaying bipolar active region. The emergence is also associated with the formation of a 3D null point separatrix that surrounds the minority polarity. The filament eruption occurs concurrent with brightenings adjacent to and below the filament, suggestive of breakout and flare reconnection, respectively. The erupting filament material becomes partially transferred into a strong outflow jet (~ 60 km/s) along coronal loops, becoming guided back towards the surface. Utilising high resolution H$\alpha$ observations from SST/CRISP, we construct velocity maps of the outflows demonstrating their highly structured but broadly helical nature. We contrast the observations with a 3D MHD simulation of a breakout jet in a closed-field background and find close qualitative agreement. We conclude that the suggested model provides an intuitive mechanism for transferring twist/helicity in confined filament eruptions, thus validating the applicability of the breakout model not only to jets and coronal mass ejections but also to confined eruptions and flares.
This paper proposes a concept of computer vision-based guidance assistance for agricultural vehicles to increase the accuracy in plowing and reduce driver's cognitive burden in long-lasting tillage operations. Plowing is a common agricultural practice to prepare the soil for planting in many countries and it can take place both in the spring and the fall. Since plowing operation requires high traction forces, it causes increased energy consumption. Moreover, longer operation time due to unnecessary maneuvers leads to higher fuel consumption. To provide necessary information for the driver and the control unit of the tractor, a first concept of furrow detection system based on an RGB-D camera was developed.
The relatively intense X-ray emission from large scale (tens to hundreds kpc) jets discovered with Chandra likely implies that jets (at least in powerful quasars) are still relativistic at that distances from the active nucleus. In this case the emission is due to Compton scattering off seed photons provided by the Cosmic Microwave Background, and this on one hand permits to have magnetic fields close to equipartition with the emitting particles, and on the other hand minimizes the requirements about the total power carried by the jet. The emission comes from compact (kpc scale) knots, and we here investigate what we can predict about the possible emission between the bright knots. This is motivated by the fact that bulk relativistic motion makes Compton scattering off the CMB photons efficient even when electrons are cold or mildly relativistic in the comoving frame. This implies relatively long cooling times, dominated by adiabatic losses. Therefore the relativistically moving plasma can emit, by Compton scattering the microwave seed photons, for a long time. We discuss how the existing radio--to--X-ray observations of large scale jets already pose strong constraints on the structure and dynamics of knots and we present a scenario that can satisfactorily reproduce the observed phenomenology of the jet in 3C273. In this scenario the kiloparsec-scale knots visible with HST, Chandra and VLA are composed of several smaller sub--units, accounting for the fast decrease of the flux outside the large knot. Substructure in the X-ray- emitting knots can also explain the month--year variability timescale reported for the large scale jet in M87.
We study the duality between string theory on AdS_3 X S^3 X S^3 and two-dimensional conformal theories with large N=4 superconformal algebra A_gamma. We discuss configurations of intersecting branes which give rise to such near-horizon geometries. We compute the Kaluza-Klein spectrum and propose that the boundary superconformal theory can be described by a sigma model on a suitable symmetric product space with a particular choice of anti-symmetric two-form.
We present the results of a search for extended X-ray sources and their corresponding galaxy groups from 800-ks Chandra coverage of the All-wavelength Extended Groth Strip International Survey (AEGIS). This yields one of the largest X-ray selected galaxy group catalogs from a blind survey to date. The red-sequence technique and spectroscopic redshifts allow us to identify 100$%$ of reliable sources, leading to a catalog of 52 galaxy groups. The groups span the redshift range $z\sim0.066-1.544$ and virial mass range $M_{200}\sim1.34\times 10^{13}-1.33\times 10^{14}M_\odot$. For the 49 extended sources which lie within DEEP2 and DEEP3 Galaxy Redshift Survey coverage, we identify spectroscopic counterparts and determine velocity dispersions. We select member galaxies by applying different cuts along the line of sight or in projected spatial coordinates. A constant cut along the line of sight can cause a large scatter in scaling relations in low-mass or high-mass systems depending on the size of cut. A velocity dispersion based virial radius can more overestimate velocity dispersion in comparison to X-ray based virial radius for low mass systems. There is no significant difference between these two radial cuts for more massive systems. Independent of radial cut, overestimation of velocity dispersion can be created in case of existence of significant substructure and also compactness in X-ray emission which mostly occur in low mass systems. We also present a comparison between X-ray galaxy groups and optical galaxy groups detected using the Voronoi-Delaunay method (VDM) for DEEP2 data in this field.
In the past decade, room temperature ferromagnetism was often observed in transition metal doped semiconductors, which were claimed as diluted magnetic semiconductors (DMS). Nowadays intensive activities are devoted to clarify wether the observed ferromagnetism stems from carrier mediated magnetic impurities, ferromagnetic precipitates, or spinodal decomposition. In this paper, we have correlated the structural and magnetic properties of transition metal doped ZnO, TiO2, and Si, prepared by ion implantation. Crystalline precipitates, i.e., transition metal (Co, Ni) and Mn-silicide nanocrystals, are responsible for the magnetism. Additionally due to their orientation nature with respect to the host, these nanocrystals in some cases are not detectable by conventional x-ray diffraction (XRD). This nature results in the pitfall of using XRD to exclude magnetic precipitates in DMS materials.
We conducted a Green Bank Telescope search for the ground state 6.8 GHz hyperfine transition of rubidium ($^{87}$Rb) toward giant stars detected in Rb I optical resonance lines. The spin-flip transition of $^{87}$Rb is one of the principal transitions used in atomic clocks, in addition to the hydrogen 21 cm maser and the $^{133}$Cs hyperfine transition (which defines the second). The optical lines of $^{87}$Rb and $^{85}$Rb can together pump the 6.8 GHz transition to form a maser, and the same optical pumping used in atomic clocks may occur in the atmospheres of evolved stars. No 6.8 GHz $^{87}$Rb lines were detected above 3.8$\sigma$.
RX J1131-1231 is a gravitationally lensed system which includes four images of a quasar lensed by an elliptical galaxy. The flux in the individual images is known to be affected by microlensing effect in the visible and X-ray bands. We study the multi-wavelength properties of RX J1131-1231 over a broad energy range, from optical to hard X-ray, during the periods of the microlensing caustic crossings. We aim to constrain the spatial extent of the X-ray emission region at different energies. We combine the data of the source monitoring in the visible band with the X-ray data of the Burst Alert Telescope (BAT) on board of SWIFT satellite and Chandra X-ray observatory. Inspecting the broad band spectrum and lightcurves of the source we identify several microlensing caustic crossing events, and study the details of variability of the source during these events. The caustic crossings of image A on MJD 55150 and 55500 produce strong variations of the overall X-ray flux from the source. In the soft X-ray band, the caustic crossing events are characterised by the exponential growth / decay of the flux ratio between the source images with the exponentiating time scale T_d~60 d, which corresponds to the caustic transit time of the source of the size ~10^{14} cm. Variability induced by the microlensing dominates the overall variability of the sum of the fluxes of four images of the source which should also be detectable in the hard X-ray lightcurve, if the hard X-ray source is comparably compact. Non-detection of the caustic crossing events in the SWIFT/BAT lightcurve of the source indicates that geometry of the region of emission of X-rays with energies above 15 keV is different from that of the lower energy X-rays, with the hard X-ray emission an order of magnitude larger in size.
In this paper, we study the asymptotic behavior of the outliers of the sum a Hermitian random matrix and a finite rank matrix which is not necessarily Hermitian. We observe several possible convergence rates and outliers locating around their limits at the vertices of regular polygons as in a previous work by Benaych-Georges and Rochet, as well as possible correlations between outliers at macroscopic distance as in works by Knowles, Yin, Benaych-Georges and Rochet. We also observe that a single spike can generate several outliers in the spectrum of the deformed model, as already noticed in several previous works. In the particular case where the perturbation matrix is Hermitian, our results complete a previous work of Benaych-Georges, Guionnet and Ma\"ida, as we consider fluctuations of outliers lying in "holes" of the limit support, which happen to exhibit surprising correlations.
We investigate bounds for the multiplicities $m(\beta+i\gamma)$, where $\beta+i\gamma\,$ ($\beta\ge \1/2, \gamma>0)$ denotes complex zeros of $\zeta(s)$. It is seen that the problem can be reduced to the estimation of the integrals of the zeta-function over "very short" intervals. A new, explicit bound for $m(\beta+i\gamma)$ is also derived, which is relevant when $\beta$ is close to unity. The related Karatsuba conjectures are also discussed.
The repeating FRB 20190520B is localized to a galaxy at $z=0.241$, much closer than expected given its dispersion measure $\rm DM=1205\pm4\ pc\ cm^{-3}$. Here we assess implications of the large DM and scattering observed from FRB 20190520B for the host galaxy's plasma properties. A sample of 75 bursts detected with the Five-hundred-meter Aperture Spherical radio Telescope shows scattering on two scales: a mean temporal delay $\tau(1.41\ {\rm GHz})=10.9\pm1.5$ ms, which is attributed to the host galaxy, and a mean scintillation bandwidth $\nu_{\rm d}(1.41\ {\rm GHz})=0.21\pm0.01$ MHz, which is attributed to the Milky Way. Balmer line measurements for the host imply an H$\alpha$ emission measure (galaxy frame) $\rm EM_s=620$ pc cm$^{-6} \times (T/10^4 {\rm K})^{0.9}$, implying $\rm DM_{\rm H\alpha}$ of order the value inferred from the FRB DM budget, $\rm DM_h=1121^{+89}_{-138}$ pc cm$^{-3}$ for plasma temperatures greater than the typical value $10^4$ K. Combining $\tau$ and $\rm DM_h$ yields a nominal constraint on the scattering amplification from the host galaxy $\tilde{F} G=1.5^{+0.8}_{-0.3}$ (pc$^2$ km)$^{-1/3}$, where $\tilde{F}$ describes turbulent density fluctuations and $G$ represents the geometric leverage to scattering that depends on the location of the scattering material. For a two-screen scattering geometry where $\tau$ arises from the host galaxy and $\Delta \nu_{\rm d}$ from the Milky Way, the implied distance between the FRB source and dominant scattering material is $\lesssim100$ pc. The host galaxy scattering and DM contributions support a novel technique for estimating FRB redshifts using the $\tau-\rm DM$ relation, and are consistent with previous findings that scattering of localized FRBs is largely dominated by plasma within host galaxies and the Milky Way.
In this study we have compared magnetic, magnetostrictive and piezomagnetic properties of isotropic and anisotropic cobalt ferrite pellets. The isotropic sample was prepared by the ceramic method while the sample exhibiting uniaxial anisotropy was made by reactive sintering using Spark Plasma Sintering (SPS). This technique permits to induce a magnetic anisotropy in cobalt ferrite in the direction of the applied pressure during SPS process. Sample with uniaxial anisotropy revealed a higher longitudinal magnetostriction and piezomagnetism compared to the isotropic sample, but the transversal magnetostriction and piezomagnetism were dramatically reduced. In the case of magnetoelectric layered composite, the magnetoelectric coefficient is directly related to the sum of the longitudinal and transversal piezomagnetic coefficients. These two coefficients being opposite in sign, the use of material exhibiting high longitudinal and low transversal piezomagnetic coefficient (or vice versa) in ME devices is expected to improve the ME effect. Hence, ME bilayer devices were made using isotropic and anisotropic cobalt ferrite stuck with a PZT layer. ME measurements at low frequencies revealed that bilayer with anisotropic cobalt ferrite exhibits a ME coefficient three times higher than a bilayer with isotropic cobalt ferrite. We also investigated the behavior of such composites when excited at resonant frequency.
A concept is presented serving to guide in the search for new materials with high spin polarization. It is shown that the magnetic moment of half-metallic ferromagnets can be calculated from the generalized Slater-Pauling rule. Further, it was found empirically that the Curie temperature of Co$_2$ based Heusler compounds can be estimated from a seemingly linear dependence on the magnetic moment. As a successful application of these simple rules, it was found that Co$_2$FeSi is, actually, the half-metallic ferromagnet exhibiting the highest magnetic moment and the highest Curie temperature measured for a Heusler compound.
The aim of this paper is to prove energy conservation for the incompressible Euler equations in a domain with boundary. We work in the domain $\mathbb{T}^2\times\mathbb{R}_+$, where the boundary is both flat and has finite measure.   However, first we study the equations on domains without boundary (the whole space $\mathbb{R}^3$, the torus $\mathbb{T}^3$, and the hybrid space $\mathbb{T}^2\times\mathbb{R}$). We make use of some of the arguments of Duchon \& Robert ({\it Nonlinearity} {\bf 13} (2000) 249--255) to prove energy conservation under the assumption that $u\in L^3(0,T;L^3(\mathbb{R}^3))$ and one of the two integral conditions \begin{equation*} \lim_{|y|\to 0}\frac{1}{|y|}\int^T_0\int_{\mathbb{R}^3} |u(x+y)-u(x)|^3\,d x\,d t=0 \end{equation*} or \begin{equation*}   \int_0^T\int_{\mathbb{R}^3}\int_{\mathbb{R}^3}\frac{|u(x)-u(y)|^3}{|x-y|^{4+\delta}}\,d x\,d y<\infty,\qquad\delta>0, \end{equation*} the second of which is equivalent to requiring $u\in L^3(0,T;W^{\alpha,3}(\mathbb{R}^3))$ for some $\alpha>1/3$.   We then use the first of these two conditions to prove energy conservation for a weak solution $u$ on $D_+:=\mathbb{T}^2\times \mathbb{R}_+$: we extend $u$ a solution defined on the whole of $\mathbb{T}^2\times\mathbb{R}$ and then use the condition on this domain to prove energy conservation for a weak solution $u\in L^3(0,T;L^3(D_+))$ that satisfies \begin{equation*} \lim_{|y|\to 0} \frac{1}{|y|}\int^{T}_{0}\iint_{\mathbb{T}^2}\int^\infty_{|y|}|u(t,x+y)-u(t,x)|^3 \,d x_3 \,d x_1 \,d x_2 \,d t=0, \end{equation*} and certain continuity conditions near the boundary $\partial D_+=\{x_3=0\}$.
In many computer vision tasks, for example saliency prediction or semantic segmentation, the desired output is a foreground map that predicts pixels where some criteria is satisfied. Despite the inherently spatial nature of this task commonly used learning objectives do not incorporate the spatial relationships between misclassified pixels and the underlying ground truth. The Weighted F-measure, a recently proposed evaluation metric, does reweight errors spatially, and has been shown to closely correlate with human evaluation of quality, and stably rank predictions with respect to noisy ground truths (such as a sloppy human annotator might generate). However it suffers from computational complexity which makes it intractable as an optimization objective for gradient descent, which must be evaluated thousands or millions of times while learning a model's parameters. We propose a differentiable and efficient approximation of this metric. By incorporating spatial information into the objective we can use a simpler model than competing methods without sacrificing accuracy, resulting in faster inference speeds and alleviating the need for pre/post-processing. We match (or improve) performance on several tasks compared to prior state of the art by traditional metrics, and in many cases significantly improve performance by the weighted F-measure.