ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let G be a reductive group over an algebraically closed field k. Consider the moduli space of stable principal G-bundles on a smooth projective curve C over k. We give necessary and sufficient conditions for the existence of Poincar\'e bundles over open subsets of this moduli space, and compute the orders of the corresponding obstruction classes. This generalizes the previous results of Newstead, Ramanan and Balaji-Biswas-Nagaraj-Newstead to all reductive groups, to all topological types of bundles, and also to all characteristics.
Starspots are important manifestations of stellar magnetic activity. By studying their behaviour in young solar analogues, we can unravel the properties of their magnetic cycles. This gives crucial information of the underlying dynamo process. Comparisons with the solar cycle enable us to infer knowledge about how the solar dynamo has evolved during the Sun's lifetime. Here we study the correlation between photometric brightness variations, spottedness and mean temperature in V889 Her, a young solar analogue. Our data covers 18 years of spectroscopic and 25 years of photometric observations. We use Doppler imaging to derive temperature maps from high-resolution spectra. We use the Continuous Period Search method to retrieve mean V-magnitudes from photometric data. Our Doppler imaging maps show a persistent polar spot structure varying in strength. This structure is centered slightly off the rotational pole. The mean temperature derived from the maps shows an overall decreasing trend, as does the photometric mean brightness, until it reaches its minimum around 2017. The filling factor of cool spots, however, shows only a weak tendency to anti-correlate with the decreasing mean brightness. We interpret V889 Her to have entered into a grand maximum in its activity. The clear relation between the mean temperature of the Doppler imaging surface maps and the mean magnitude supports the reliability of the Doppler images. The lack of correlation between the mean magnitude and the spottedness may indicate that bright features in the Doppler images are real.
For a multigraph G, the integer round-up phi(G) of the fractional chromatic index yields a good general lower bound for the chromatic index . For an upper bound, Kahn showed that for any real c > 0 there exists a positive integer N so that the chromatic index is less than (1+c)*phi(G) whenever the fractional index > N. We show the amount by which the chromatic index can surpass phi(G) is in fact logarithmic, by showing that for any multigraph G with order n > 3 and at least one edge, the chromatic index is less than phi(G) + log (min {(n+1)/3, phi(G)}) .
Clusters of galaxies as the largest clearly defined objects in our Universe are ideal laboratories to study the distribution of the most abundant chemical elements heavier than hydrogen and helium and the history of their production. The cluster environment allows us to study the element abundances not only inside the galaxies, but also in the intergalactic space, the intracluster medium. Since the intracluster medium is heated to temperatures of several ten Million degrees, we can study the chemical composition of this medium through X-ray spectroscopy. Up to 13 heavy elements have been detected by X-ray spectroscopy so far. The element most easily detected in the X-ray spectra is iron. In massive galaxy clusters we find a larger mass of heavy elements in the intracluster medium than in the galaxies. The consideration of the intracluster medium is therefore vital for an understanding of the complete history of nucleosynthesis of the heavy elements. The observed abundances for all elements heavier than nitrogen can roughly be modeled by using two types of sources: core collapse supernovae and supernovae type Ia. So called cool-core galaxy clusters show a larger heavy element abundance in the cluster center which seems to be enriched primarily by products of supernovae of type Ia. The evidence for observations of an evolution of the heavy element abundance with redshift has still a moderate significance.
We explicitly bound T-singularities on normal projective surfaces $W$ with one singularity, and $K_W$ ample. This bound depends only on $K_W^2$, and it is optimal when $W$ is not rational. We classify and realize surfaces attaining the bound for each Kodaira dimension of the minimal resolution of $W$. This answers effectiveness of bounds (see [Alexeev94], [Alexeev-Mori04], [Lee99]) for those surfaces.
Rapidly rotating stars show short-period oscillations in magnetic activity and polar appearance of starspots. The aim of this paper is to study large-scale shallow water waves in the tachoclines of rapidly rotating stars and their connection to the periodicity and the formation of starspots at high latitudes. Shallow-water magnetohydrodynamic equations were used to study the dynamics of large-scale waves at the rapidly rotating stellar tachoclines in the presence of toroidal magnetic field. Dispersion relations and latitudinal distribution of wave modes were derived. We found that low-frequency magnetic Rossby waves tend to be located at poles, but high-frequency magnetic Poincare waves are concentrated near the equator in rapidly rotating stars. These results have important implications for the evolution of the stellar wind in young Sun-like stars. Unstable magnetic Rossby waves may lead to the local enhancement of magnetic flux at high latitudes of tachoclines in rapidly rotating stars. The enhanced magnetic flux may rise upwards owing to the magnetic buoyancy in the form of tubes and appear as starspots at polar regions. Magnetic Rossby waves may also cause observed short-term periodicity in the stellar magnetic activity.
We define a primitive index of an integer in a sequence to be the index of the term with the integer as a primitive divisor. For the sequences $k^u+h^u$ and $k^u-h^u$, we discern a formula to find the primitive indexes of any composite number given the primitive indexes of its prime factors. We show how this formula reduces to a formula relating the multiplicative order of $k$ modulo $N$ to that of its prime factors. We then introduce immediate consequences of the formula: certain sequences which yield the same primitive indexes for numbers with the same unique prime factors, an expansion of the lifting the exponent lemma for $v_2(k^n+h^n)$, a simple formula to find any Zsigmondy number, a note on a certain class of pseudoprimes titled overpseudoprime, and a proof that numbers such as Wagstaff numbers are either overpseudoprime or prime.
Tunneling field-effect transistors (FETs) have been intensely explored recently due to its potential to address power concerns in nanoelectronics. The recently discovered graphene nanoribbon (GNR) is ideal for tunneling FETs due to its symmetric bandstructure, light effective mass, and monolayer-thin body. In this work, we examine the device physics of p-i-n GNR tunneling FETs using atomistic quantum transport simulations. The important role of the edge bond relaxation in the device characteristics is identified. The device, however, has ambipolar I-V characteristics, which are not preferred for digital electronics applications. We suggest that using either an asymmetric source-drain doping or a properly designed gate underlap can effectively suppress the ambipolar I-V. A subthreshold slope of 14mV/dec and a significantly improved on-off ratio can be obtained by the p-i-n GNR tunneling FETs.
Nagell proved that for each prime $p\equiv 1\pmod{3}$, $p > 7$, there is a prime $q<2p^{1/2}$ that is a cubic residue modulo $p$. Here we show that for each fixed $\epsilon > 0$, and each prime $p\equiv 1\pmod{3}$ with $p > p_0(\epsilon)$, the number of prime cubic residues $q < p^{1/2+\epsilon}$ exceeds $p^{\epsilon/30}$. Our argument, like Nagell's, is rooted in the law of cubic reciprocity; somewhat surprisingly, character sum estimates play no role. We use the same method to establish related results about prime quadratic and biquadratic residues. For example, for all large primes $p$, there are more than $p^{1/9}$ prime quadratic residues $q<p$.
Let $G$ denote a finite group and $\pi: Z \to Y$ a Galois covering of smooth projective curves with Galois group $G$. For every subgroup $H$ of $G$ there is a canonical action of the corresponding Hecke algebra $\mathbb{Q}[H \backslash G/H]$ on the Jacobian of the curve $X = Z/H$. To each rational irreducible representation $\mathcal{W}$ of $G$ we associate an idempotent in the Hecke algebra, which induces a correspondence of the curve $X$ and thus an abelian subvariety $P$ of the Jacobian $JX$. We give sufficient conditions on $\mathcal{W}$, $H$, and the action of $G$ on $Z$, which imply $P$ to be a Prym-Tyurin variety. We obtain many new families of Prym-Tyurin varieties of arbitrary exponent in this way.
We calculate the strong lensing probability as a function of the image-separation $\Delta\theta$ in TeVeS (tensor-vector-scalar) cosmology, which is a relativistic version of MOND (MOdified Newtonian Dynamics). The lens, often an elliptical galaxy, is modeled by the Hernquist profile. We assume a flat cosmology with $\Omega_b=1-\Omega_\Lambda=0.04$ and the simplest interpolating function $\mu(x)={\rm min}(1,x)$. For comparison, we recalculated the probabilities for lenses by Singular Isothermal Sphere (SIS) galaxy halos in LCDM with Schechter-fit velocity function. The amplification bias is calculated based on the magnification of the second bright image rather than the total of the two brighter images. Our calculations show that the Hernquist model predicts insufficient but acceptable probabilities in flat TeVeS cosmology compared with the results of the well defined combined sample of Cosmic Lens All-Sky Survey (CLASS) and Jodrell Bank/Very Large Array Astrometric Survey (JVAS); at the same time, it predicts higher probabilities than SIS model in LCDM at small image separations.
The structural, elastic, electronic and optical (x = 0) properties of doped Sn1-xBixO2 and Sn1-xTaxO2 (0 \leq x \leq 0.75) are studied by using the first-principles pseudopotential plane-wave method within the local density approximation. The independent elastic constants Cij and other elastic parameters of these compounds have been calculated for the first time. The mechanical stability of the compounds with different doping concentrations has also been studied. The electronic band structure and density of states are calculated and the effect of doping on these properties is also analyzed. It is seen that the band gap of the undoped compound narrowed with dopant concentration which disappeared for x = 0.26 for Bi doping and 0.36 for Ta doping. The materials thus become conductive oxides through the change in the electronic properties of the compound for x \leq 0.75 which may be useful for potential application. The calculated optical properties, e.g. dielectric function, refractive index, absorption spectrum, loss-function, reflectivity and conductivity of the undoped SnO2 in two polarization directions are compared with both previous calculations and measurements.   Keywords: Doped SnO2; First-principles; Mechanical properties; Electronic band structure; Optical properties.
Let $H$ be a Krull monoid with class group $G$ such that every class contains a prime divisor (for example, rings of integers in algebraic number fields or holomorphy rings in algebraic function fields). For $k \in \mathbb N$, let $\mathcal U_k (H)$ denote the set of all $m \in \mathbb N$ with the following property: There exist atoms $u_1, ..., u_k, v_1, ..., v_m \in H$ such that $u_1 \cdot ... \cdot u_k = v_1 \cdot ...\cdot v_m$. Furthermore, let $\lambda_k (H) = \min \mathcal U_k (H)$ and $\rho_k (H) = \sup \mathcal U_k (H)$. The sets $\mathcal U_k (H) \subset \mathbb N$ are intervals which are finite if and only if $G$ is finite. Their minima $\lambda_k (H)$ can be expressed in terms of $\rho_k (H)$. The invariants $\rho_k (H)$ depend only on the class group $G$, and in the present paper they are studied with new methods from Additive Combinatorics.
A statistical analysis of stacked Compton$-y$ maps of quasar hosts with a median redshift of $1.5$ using Millennium Simulation is performed to address two issues, one on the feedback energy from quasars and the other on testing dark matter halo models for quasar hosts. On the first, we find that, at the resolution of FWHM=$10$ arcmin obtained by Planck data, the observed thermal Sunyaev-Zeldovich (tSZ) effect can be entirely accounted for and explained by the thermal energy of halos sourced by gravitational collapse of halos, without a need to invoke additional, large energy sources, such as quasar or stellar feedback. Allowing for uncertainties of dust temperature in the calibration of observed Comton$-y$ maps, the maximum additional feedback energy is $\sim 25\%$ of that previously suggested. Second, we show that, with FWHM=$1$ arcmin beam, tSZ measurements will provide a potentially powerful test of quasar-hosting dark matter halo models, limited only by possible observational systematic uncertainties, not by statistical ones, even in the presence of possible quasar feedback.
The principle of boundary bootstrap plays a significant role in the algebraic study of the purely elastic boundary reflection matrix $K_a(\theta)$ for integrable quantum field theory defined on a space-time with a boundary. However, general structure of that principle in the form as was originally introduced by Fring and K\"oberle has remained unclear. In terms of a new matrix $J_a(\theta)=\sqrt{K_a(\theta)/K_{\bar{a}}(i\pi +\theta)}$, the boundary bootstrap takes a simple form. Incidentally, a hypothesised expression of the boundary reflection matrix for simply-laced $ADE$ affine Toda field theory defined on a half line with the Neumann boundary condition is obtained in terms of geometrical quantities of root systems \`a la Dorey.
An edge-colored graph $G$ is rainbow connected, if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph $G$, denoted $rc(G)$, is the smallest number of colors that are needed in order to make $G$ rainbow connected. In this paper we show that $rc(G)\leq 3$, if $|E(G)|\geq {{n-2}\choose 2}+2$, and $rc(G)\leq 4$, if $|E(G)|\geq {{n-3}\choose 2}+3$. These bounds are sharp.
Entanglement is an invaluable resource for fundamental tests of physics and the implementation of quantum information protocols such as device-independent secure communications. In particular, time-bin entanglement is widely exploited to reach these purposes both in free-space and optical fiber propagation, due to the robustness and simplicity of its implementation. However, all existing realizations of time-bin entanglement suffer from an intrinsic postselection loophole, which undermines their usefulness. Here, we report the first experimental violation of Bell's inequality with "genuine" time-bin entanglement, free of the postselection loophole. We introduced a novel function of the interferometers at the two measurement stations, that operate as fast synchronized optical switches. This scheme allowed to obtain a postselection-loophole-free Bell violation of more than nine standard deviations. Since our scheme is fully implementable using standard fiber-based components and is compatible with modern integrated photonics, our results pave the way for the distribution of genuine time-bin entanglement over long distances.
In the solar limb, linear polarisation is due to anisotropy of the radiation field induced by limb darkening. It is maximal when it is seen parallel to the limb and it vanishes when it is integrated over the spherically-symmetric solar disk. Therefore for distant stars, that present spherical symmetry, linear polarisation signatures are very difficult to observe. However strong linear polarisation features have been reported in the prototypical red supergiant star alpha Ori (Betelgeuse). With an analytical model we propose to explain them.
In recent years, research on image generation methods has been developing fast. The auto-encoding variational Bayes method (VAEs) was proposed in 2013, which uses variational inference to learn a latent space from the image database and then generates images using the decoder. The generative adversarial networks (GANs) came out as a promising framework, which uses adversarial training to improve the generative ability of the generator. However, the generated pictures by GANs are generally blurry. The deep convolutional generative adversarial networks (DCGANs) were then proposed to leverage the quality of generated images. Since the input noise vectors are randomly sampled from a Gaussian distribution, the generator has to map from a whole normal distribution to the images. This makes DCGANs unable to reflect the inherent structure of the training data. In this paper, we propose a novel deep model, called generative adversarial networks with decoder-encoder output noise (DE-GANs), which takes advantage of both the adversarial training and the variational Bayesain inference to improve the performance of image generation. DE-GANs use a pre-trained decoder-encoder architecture to map the random Gaussian noise vectors to informative ones and pass them to the generator of the adversarial networks. Since the decoder-encoder architecture is trained by the same images as the generators, the output vectors could carry the intrinsic distribution information of the original images. Moreover, the loss function of DE-GANs is different from GANs and DCGANs. A hidden-space loss function is added to the adversarial loss function to enhance the robustness of the model. Extensive empirical results show that DE-GANs can accelerate the convergence of the adversarial training process and improve the quality of the generated images.
A coarsened model for a binary system with limited miscibility of components is proposed; the system is described in terms of structural states in small parts of the material. The material is assumed to have two alternative types of crystalline local arrangements associated with two components of the alloy. Fluctuating characteristics of a cluster are the type and the space orientation of its crystalline arrangement. There are two different phase transitions in the model system, an orientation order-disorder transition representing melting, and a phase transition between phases differing in concentration of components. Depending on the parameters characterizing the interaction in the system, this last transition may take place both in the crystalline and in the amorphous (molten) phase. A special approximation is used to study the thermodynamics of the system. The calculated phase diagram describes, at least qualitatively, the most important features of a binary system.
In this paper we deal with Diophantine equations involving products of consecutive integers, inspired by a question of Erd\H{o}s and Graham.
We present a new measurement, 0.85-3.5 Z_solar, of the metallicity of high velocity cloud (HVC) Complex M by analyzing ultraviolet spectroscopic observations of the blazar Mrk 421 taken with the Cosmic Origins Spectrograph on the Hubble Space Telescope and the Far Ultraviolet Spectroscopic Explorer. Although an HVC at V_LSR = -131 km/s is not visible in 21 cm emission (logN_HI<18.38; 3sigma), it is detected in ultraviolet absorption lines of C II, N I, O I, O VI, Si II, Si III, Si IV, Fe II, and HI. By referencing velocities to the intermediate velocity cloud at -60 km/s and jointly analyzing HI absorption from high-order HI Lyman lines, we measure logN_HI=16.84(0.13,+0.34) (1sigma) in the HVC. Comparing HI, and O I, we find an HVC metallicity [O/H]=0.32(-0.39, +0.22). Because the sight line passes 4 degrees from the HVCs in Complex M, the detected HVC may represent the highest velocity component of the Complex, and our measurements provide a lower limit to its metallicity. The high, possibly super-solar metallicity, together with the low distance, z<3.5 kpc, above the Galactic plane suggest that Complex M is condensed returning gas from a Galactic fountain.
We consider the following degenerate half wave equation on the one dimensional torus $$\quad i\partial_t u-|D|u=|u|^2u, \; u(0,\cdot)=u_0. $$ We show that, on a large time interval, the solution may be approximated by the solution of a completely integrable system-- the cubic Szeg\"o equation. As a consequence, we prove an instability result for large $H^s$ norms of solutions of this wave equation.
One of the most promising frameworks for understanding the anomalies of cold and especially supercooled water is that of two-structure thermodynamics, in which water is viewed as a non-ideal mixture of two interconvertible local structures. The non-ideality of this mixture may give rise, at very low temperatures, to a liquid-liquid phase transition (LLPT) and a liquid-liquid critical point (LLCP), at which thermodynamic response functions diverge. Various versions of the "two-structure equation of state" (TSEOS) based on this concept have shown remarkable agreement with both experimental data in real water and simulation results. However, recent experiments probing supercooled water at negative pressures reveal the inadequacy of extrapolations of equations of state developed for positive pressures, and have begun to shed additional light on the source of the anomalies of supercooled water. We have analyzed simulation results for the TIP4P/2005 model over a broad range of positive and negative pressures from ambient temperature to deep supercooling. We find that by explicitly incorporating a liquid-vapor spinodal into a two-structure equation of state, we are able to match the simulation data in TIP4P/2005 with striking accuracy. In particular, our equation of state reproduces the observed lines of minima and maxima in the density, isothermal compressibility, and isobaric heat capacity. Contrary to scenarios in which a retracing spinodal accounts for the thermodynamic anomalies of water, we find that the liquid-vapor spinodal in this model continues monotonically to lower pressures as temperature is decreased, influencing but not giving rise to the locus of density maxima and other thermodynamic anomalies. We explain the behavior of TIP4P/2005 in terms of two phenomena: the competition between two local structures and a monotonic liquid-vapor spinodal.
The interdependence of luminosity distance, $D_L$ and angular diameter distance, $D_A$ given by the distance duality relation (DDR) is very significant in observational cosmology. It is very closely tied with the temperature- redshift relation of Cosmic Microwave Background (CMB) radiation. Any deviation from $\eta(z)\equiv \frac{D_L}{D_A (1+z)^2} =1$ indicates a possible emergence of new physics. Our aim in this work is to check the consistency of these relations using a non-parametric regression method namely, LOESS with SIMEX. This technique avoids dependency on the cosmological model and works with a minimal set of assumptions. Further, to analyze the efficiency of the methodology, we simulate a dataset of $200$ points of $\eta (z)$ data based on a phenomenological model $\eta(z)= (1+z)^\epsilon$. The error on the simulated data points is obtained by using the temperature of CMB radiation at various redshifts. For testing the distance duality relation, we use the JLA SNe Ia data for luminosity distances, while the angular diameter distances are obtained from radio galaxies datasets. Since the DDR is linked with CMB temperature - redshift relation, therefore we also use the CMB temperature data to reconstruct $\eta (z)$. It is important to note that with CMB data, we are able to study the evolution of DDR up to a very high redshift $ z = 2.418$. In this analysis, we find no evidence of deviation from $\eta=1$ within a $1\sigma$ region in the entire redshift range used in this analysis ($0 < z \leq 2.418$).