ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let $A$ be an abelian variety over $\mathbb{F}_q$. Let $h_A(t)$ be the characteristic polynomial of $A$. Rybakov showed that if $h_A(t)$ is squarefree and $G$ is any finite group with $|G| = h_A(1)$, then $G = A'(\mathbb{F}_q)$ for some $A'$ isogenous to $A$ if and only if the $\ell^{th}$ Hodge polygon of $G$ is under the $\ell^{th}$ Newton polygon of $h_A(1-t)$ for all primes $\ell$. In this paper, we will extend this result to get a classification theorem for the group structure of all abelian varieties.
Galactic bars are the most important driver of secular evolution in galaxies. They can efficiently drive gas into the central kiloparsec of galaxies, thus feed circumnuclear starbursts, and possibly help to fuel AGN. The connection between bars and AGN activities has been actively debated in the past two decades. Previous work used fairly small samples and often lacked a proper control sample. They reported conflicting results on the correlation between bars and AGN activity. Here we revisit the bar-AGN and bar-starburst connections using the analysis of bars in a large sample of about 2000 SDSS disk galaxies (Barazza, Jogee, & Marinova 2008). We find that AGN and star-forming galaxies have similar optical bar fractions, 47% and 50%, respectively. Both bar fractions are higher than that in inactive galaxies (29%). We discuss the implications of the study on the relationship between host galaxies and their central activities.
Neutron powder diffraction (NPD) study of \textit{Ln}MnSbO (\textit{Ln }$=$ La or Ce) reveals differences between the magnetic ground state of the two compounds due to the strong Ce-Mn coupling compared to La-Mn. The two compounds adopt the \textit{P4/nmm} space group down to 2 K and whereas magnetization measurements do not show obvious anomaly at high temperatures, NPD reveals a C-type antiferromagnetic (AFM) order below $T_{\mathrm{N}} = 255 $ K for LaMnSbO and 240 K for CeMnSbO. While the magnetic structure of LaMnSbO is preserved to base temperature, a sharp transition at $T_{\mathrm{SR}} = 4.5 $K is observed in CeMnSbO due to a spin-reorientation (SR) transition of the Mn$^{\mathrm{2+}}$ magnetic moments from pointing along the $c$-axis to the \textit{ab}-plane. The SR transition in CeMnSbO is accompanied by a simultaneous long-range AFM ordering of the Ce moments which indicates that the Mn SR transition is driven by the Ce-Mn coupling. The ordered moments are found to be somewhat smaller than those expected for Mn$^{\mathrm{2+}}$ ($S = 5/2$) in insulators, but large enough to suggest that these compounds belong to the class of local-moment antiferromagnets. The lower $T_{\mathrm{N\thinspace }}$ found in these two compounds compared to the As-based counterparts ($T_{\mathrm{N}} = 317$ for LaMnAsO, $T_{\mathrm{N}} = 347$ K for CeMnAsO) indicates that the Mn-$Pn$ ($Pn=$ As or Sb) hybridization that mediates the superexchange Mn-$Pn$-Mn coupling is weaker for the Sb-based compounds.
During the recent years the Konkoly Blazhko Group (PIs Johanna Jurcsik and B\'ela Szeidl, co-workers \'Ad\'am S\'odor, Zsombor Hurta and several undergraduate, graduate students) published new important results of Blazhko variables in 15 reviewed Journal articles. These results utilize multicolor CCD observations obtained with an automatic 60 cm telescope, and also previously unpublished Konkoly archive photometric data. Our light curves are the most extended multicolor data-sets ever obtained for a Blazhko variable, the observations cover each phase of the pulsation and the modulation as well. We have detected many previously unknown features of the light curve modulation, and based on the different band's observations we also revealed the underlying variations of the mean physical parameters during the Blazhko cycle. In my contribution the main achievements of the Konkoly Blazhko Group are summarised.
The detection of the first electromagnetic counterpart to the binary neutron star (BNS) merger remnant GW170817 established the connection between short $\gamma$-ray bursts and BNS mergers. It also confirmed the forging of heavy elements in the ejecta (a so-called kilonova) via the r-process nucleosynthesis. The appearance of non-thermal radio and X-ray emission, as well as the brightening, which lasted more than 100 days, were somewhat unexpected. Current theoretical models attempt to explain this temporal behavior as either originating from a relativistic off-axis jet or a kilonova-like outflow. In either scenario, there is some ambiguity regarding how much energy is transported in the non-thermal electrons versus the magnetic field of the emission region. Combining the VLA (radio) and Chandra (X-ray) measurements with observations in the GeV-TeV domain can help break this ambiguity, almost independently of the assumed origin of the emission. Here we report for the first time on deep H.E.S.S. observations of GW170817 / GRB 170817A between 124 and 272 days after the BNS merger with the full H.E.S.S. array of telescopes, as well as on an updated analysis of the prompt (<5 days) observations with the upgraded H.E.S.S. phase-I telescopes. We discuss implications of the H.E.S.S. measurement for the magnetic field in the context of different source scenarios.
In connection with the weak null condition, Alinhac introduced a sufficient condition for global existence of small amplitude solutions to systems of semilinear wave equations in three space dimensions. We introduce a slightly weaker sufficient condition for the small data global existence, and we investigate the asymptotic pointwise behavior of global solutions for systems satisfying this condition. As an application, the asymptotic behavior of global solutions under the Alinhac condition is also derived.
Understanding the physical process responsible for the transport of energy in the core of $\alpha$ Centauri A is of the utmost importance if this star is to be used in the calibration of stellar model physics. Adoption of different parallax measurements available in the literature results in differences in the interferometric radius constraints used in stellar modelling. Further, this is at the origin of the different dynamical mass measurements reported for this star. With the goal of reproducing the revised dynamical mass derived by Pourbaix & Boffin, we modelled the star using two stellar grids varying in the adopted nuclear reaction rates. Asteroseismic and spectroscopic observables were complemented with different interferometric radius constraints during the optimisation procedure. Our findings show that best-fit models reproducing the revised dynamical mass favour the existence of a convective core ($\gtrsim$ 70% of best-fit models), a result that is robust against changes to the model physics. If this mass is accurate, then $\alpha$ Centauri A may be used to calibrate stellar model parameters in the presence of a convective core.
In this work an extremal principle driving the far from equilibrium evolution of a system of structureless particles is derived by using the stochastic quantum hydrodynamic analogy. For a classical phase (i.e., the quantum correlations decay on a distance smaller than the mean inter-molecular distance) the far from equilibrium kinetic equation can be cast in the form of a Fokker-Plank equation whose phase space velocity vector maximizes the dissipation of the energy-type function, named here, stochastic free energy. Near equilibrium the maximum stochastic free energy dissipation is shown to be compatible with the Prigogine s principle of minimum entropy production. Moreover, in the case of elastic molecular collisions and in absence of chemical reactions, in quasi-isothermal far from equilibrium states, the theory shows that the maximum stochastic free energy dissipation reduces to the maximum free energy dissipation. Following the tendency to reach the highest rate of stochastic free energy dissipation, the system transition to states with higher free energy can happen. Given that in incompressible ordinary fluids such an increase of free energy is almost given by a decrease of entropy, the matter self-organization becomes possible. When chemical reactions or relevant thermal gradients are present, the theory highlights that the Sawada enunciation of maximum free energy dissipation can be violated. The proposed model depicts the Prigogine s principle of minimum entropy production near-equilibrium and the far from equilibrium Sawada s principle of maximum energy dissipation as two complementary principia of a unique theory where the latter one is a particular case of the more general one of maximum stochastic free energy dissipation.
We study a class of corner growth models in which the weights are either all exponentially or all geometrically distributed. The parameter of the distribution at site $(i, j)$ is $a_i+b_j$ in the exponential case and $a_ib_j$ in the geometric case, where $(a_i)_{i \ge 1}$ and $(b_j)_{j \ge 1}$ are themselves drawn randomly at the outset from ergodic distributions. These models are inhomogeneous generalizations of the much studied exactly solvable models in which the parameters are the same for all sites. Our motivation is to understand how inhomogeneity influences the limit shape and the corresponding limit fluctuations. We obtain a simple variational formula for the shape function and prove that it is strictly concave inside a cone (possibly the entire quadrant) but is linear outside. This is in contrast with the situation in the models with i.i.d. weights in which the shape function is expected to be strictly concave under mild assumptions. For the directions inside the cone, we show that the limit fluctuations are governed by the Tracy-Widom GUE distribution and derive bounds for the deviations of the last-passage times above the shape function. To obtain the shape result, we couple the model with an explicit family of stationary versions of it. For the fluctuation and large deviation results, we perform steepest-descent analysis on an available Fredholm determinant formula for the one-point distribution of the last-passage time. We also develop a detailed appendix on the steepest-descent curves of harmonic functions of two real variables and approximate the contour integral of an arbitrary meromorphic function along such curves.
(abridged) We present measurements of the pairwise velocity dispersion (PVD) for different classes of galaxies in the Sloan Digital Sky Survey. For a sample of about 200,000 galaxies, we study the dependence of the PVD on galaxy properties such as luminosity, stellar mass (M_*), colour (g-r), 4000A break strength (D4000), concentration index (C), and stellar surface mass density (\mu_*). The luminosity dependence of the PVD is in good agreement with the results of Jing & B\"orner (2004) for the 2dFGRS catalog. The value of \sigma_{12} measured at k=1 h/Mpc decreases as a function of increasing galaxy luminosity for galaxies fainter than L*, before increasing again for the most luminous galaxies in our sample. Each of the galaxy subsamples selected according to luminosity or stellar mass is divided into two further subsamples according to colour, D4000, C and \mu_*. We find that galaxies with redder colours and higher D4000, C, and \mu_* values have larger PVDs on all scales and at all luminosities/stellar masses. The dependence of the PVD on parameters related to recent star formation(colour, D4000) is stronger than on parameters related to galaxy structure (C, \mu_*), especially on small scales and for faint galaxies. The reddest galaxies and galaxies with high surface mass densities and intermediate concentrations have the highest pairwise peculiar velocities, i.e. these move in the strongest gravitational fields. We conclude that the faint red population located in rich clusters is responsible for the high PVD values that are measured for low-luminosity galaxies on small scales.
Dense 3D shape acquisition of swimming human or live fish is an important research topic for sports, biological science and so on. For this purpose, active stereo sensor is usually used in the air, however it cannot be applied to the underwater environment because of refraction, strong light attenuation and severe interference of bubbles. Passive stereo is a simple solution for capturing dynamic scenes at underwater environment, however the shape with textureless surfaces or irregular reflections cannot be recovered. Recently, the stereo camera pair with a pattern projector for adding artificial textures on the objects is proposed. However, to use the system for underwater environment, several problems should be compensated, i.e., disturbance by fluctuation and bubbles. Simple solution is to use convolutional neural network for stereo to cancel the effects of bubbles and/or water fluctuation. Since it is not easy to train CNN with small size of database with large variation, we develop a special bubble generation device to efficiently create real bubble database of multiple size and density. In addition, we propose a transfer learning technique for multi-scale CNN to effectively remove bubbles and projected-patterns on the object. Further, we develop a real system and actually captured live swimming human, which has not been done before. Experiments are conducted to show the effectiveness of our method compared with the state of the art techniques.
For a smooth vector field in a neighborhood of a critical point with all positive eigenvalues of the linearization, we consider the associated dynamics perturbed by white noise. Using Malliavin calculus tools, we obtain polynomial asymptotics for probabilities of atypically long exit times in the vanishing noise limit.
We present a more accurate numerical scheme for the calculation of diffusive shock acceleration of cosmic rays using Stochastic Differential Equations. The accuracy of this scheme is demonstrated using a simple analytical flow profile that contains a shock of finite width and a varying diffusivity of the cosmic rays, where the diffusivity decreases across the shock. We compare the results for the slope of the momentum distribution with those obtained from a perturbation analysis valid for finite but small shock width. These calculations show that this scheme, although computationally more expensive, provides a significantly better performance than the Cauchy-Euler type schemes that were proposed earlier in the case where steep gradients in the cosmic ray diffusivity occur. For constant diffusivity the proposed scheme gives similar results as the Cauchy-Euler scheme.
The hydrodynamic description of transversally thermalized matter, possibly formed at the early stages of ultra-relativistic heavy-ion collisions, is developed. The formalism is based on the thermodynamically consistent approach with all thermodynamic variables referring to two-dimensional objects, the so-called transverse clusters, which are identified with the particles having the same rapidity. The resulting hydrodynamic equations for a single cluster have the form of the two-dimensional hydrodynamic equations of the perfect fluid. Since the clusters do not perform any work in the longitudinal direction, their energy is completely transformed and used to generate strong radial and elliptic flows that turn out to be compatible with the experimental data.
Triple-gluon elastic scatterings are briefly reviewed since the scatterings explain the early thermalization puzzle in Au-Au collisions at RHIC energies. A numerical solution of the transport equation with the triple-gluon elastic scatterings demonstrates gluon momentum isotropy achieved at a time of the order of 0.65 fm/c. Triple-gluon scatterings lead to a short thermalization time of gluon matter.
I review current results from searching for galaxies giving rise to damped Lya absorbers (DLAs) at z<1. Using 14 confirmed DLA galaxies, I further show that intermediate-redshift galaxies possess large HI envelope out to 24-30 h^{-1} kpc radius. The photometric and spectral properties of these galaxies confirm that DLA galaxies are drawn from the typical field population, and not from a separate population of low surface brightness or dwarf galaxies. Comparisons of the ISM abundances of the DLA galaxies and the metallicities of the absorbers at large galactic radii suggest that some DLAs originate in the relatively unevolved outskirts of galactic disks.
It is known that a single quantum harmonic oscillator is characterized by a hidden spectrum generating superconformal symmetry, but its origin has remained rather obscure. We show how this hidden superconformal symmetry can be derived by applying a nonlocal Foldy-Wouthuysen transformation to three extended systems with fermion degrees of freedom. The associated systems have essentially different nature from the point of view of conventional supersymmetric quantum mechanics, and generate the desired hidden symmetry in three different ways. We also trace out how the hidden superconformal symmetry of the quantum free particle system is produced in the limit of zero frequency.
Mechanical active galactic nucleus (AGN) feedback plays a key role in massive galaxies, galaxy groups and clusters. However, the energy content of AGN jets that mediate this feedback process is still far from clear. Here we present a preliminary study of radial elongations $\tau$ of a large sample of X-ray cavities, which are apparently produced by mechanical AGN feedback. All the cavities in our sample are elongated along the angular (type-I) or jet directions (type-II), or nearly circular (type-III). The observed value of $\tau$ roughly decreases as the cavities rise buoyantly, confirming the same trend found in hydrodynamic simulations. For young cavities, both type-I and II cavities exist, and the latter dominates. Assuming a spheroidal cavity shape, we derive an analytical relation between the intrinsic radial elongation $\bar{\tau}$ and the inclination-angle-dependent value of $\tau$, showing that projection effect makes cavities appear more circular, but does not change type-I cavities into type-II ones, or vice versa. We summarize radial elongations of young cavities in simulations, finding that $\bar{\tau}$ increases with the kinetic fraction of AGN jets. While mild jets always produce type-II cavities, thermal-energy-dominated strong jets produce type-I cavities, and kinetic-energy-dominated strong jets produce type-II cavities. Our results suggest that some AGN jets are strong and dominated by thermal energy (or cosmic rays). However, these jets do not dominate in AGN feedback. If most jets are dominated by non-kinetic energies, they should be mainly mild jets. If most jets are strong, they must be mainly dominated by the kinetic energy.
We provide formulas and algorithms for computing the excess numbers of certain ideals. The solution for monomial ideals is given by the mixed volumes of certain polytopes. These results enable us to design specific homotopies for numerical algebraic geometry.
In this paper, we give an alternative proof of the fact that, when compounding a nonnegative probability distribution, convex ordering between the distributions of the number of summands implies convex ordering between the resulting compound distributions. Although this is a classical textbook result in risk theory, our proof exhibits a concrete coupling between the compound distributions being compared, using the representation of one-period discrete martingale laws as a mixture of the corresponding extremal measures.
We study the mean field equation derived by Neri in the context of the statistical mechanics description of 2D-turbulence, under a "stochastic" assumption on the vortex circulations. The corresponding mathematical problem is a nonlocal semilinear elliptic equation with exponential type nonlinearity, containing a probability measure $\mathcal P\in\mathcal M([-1,1])$ which describes the distribution of the vortex circulations. Unlike the more investigated "deterministic" version, we prove that Neri's equation may be viewed as a perturbation of the widely analyzed standard mean field equation, obtained by taking $\mathcal P=\delta_1$. In particular, in the physically relevant case where $\mathcal P$ is non-negatively supported and $\mathcal P(\{1\})>0$, we prove the mass quantization for blow-up sequences. We apply this result to construct minimax type solutions on bounded domains in $\mathbb R^2$ and on compact 2-manifolds without boundary.
Unconventional symmetry breaking without spin order,such as the rotational symmetry breaking (=nematic or smectic) orders as well as the spontaneous loop-current orders, have been recently reported in cuprate superconductors and their related materials.They are theoretically represented by non-$A_{1g}$ symmetry breaking in self-energy, which we call the form factor $f_{k,q}$.In this paper, we analyze typical Hubbard models by applying the renormalization-group (RG) method, and find that various unconventional ordering emerges due to the quantum interference among spin fluctuations. Due to this mechanism,nematic ($q=0$) and smectic ($q \ne 0$)bond orders with $d$-wave form factor appear $f_{k,q}\propto \cos k_x - \cos k_y$ in both cuprates and $\kappa$-(BEDT-TTF)$_2$X. The derived bond orders naturally explain the pseudogap behaviors in these compounds. The quantum interference also induces various current orders with odd-parity form factor. For example, we find the emergence of the charge and spin loop-current orders with $p$-wave form factor in geometrically frustrated Hubbard models. Thus, rich quantum phase transitions with $d$- and $p$-wave form factors are driven by the paramagnon interference in many low-dimensional Hubbard models.
Let $\Bbbk$ be a field of characteristic 0. Let $X$ be a smooth complete intersection over $k$ of dimension $n-k$ in the projective space $\mathbf{P}^n_{k}$, for given positive integers $n$ and $k$. When $k=\mathbb{C}$, Terasoma (\cite{Ter90}) and Konno (\cite{Ko91}) provided an explicit representative (in terms of differential forms) of a basis for the primitive middle-dimensional algebraic de Rham cohomology $H_{dR,\operatorname{prim}}^{n-k}(X;\mathbb{C})$. Later Dimca constructed another explicit representative of a basis of $H_{dR,\operatorname{prim}}^{n-k}(X;\mathbb{C})$ in \cite{Dim95}. Moreover, he proved that his representative gives the same cohomology class as the previous representative of Terasoma and Konno. The goal of this article is to examine the above two different approaches without assuming that $k=\mathbb{C}$ and provide a similar comparison result for any field $k$. Dimca's argument depends heavily on the condition $k=\mathbb{C}$ and our idea is to find appropriate Cech-de Rham complexes and spectral sequences corresponding to those two approaches, which work without restrictions on $k$.
We present a mesoscopic model for thermoelectric phenomena in terms of an interacting particle system, a lattice electron gas dynamics that is a suitable extension of the standard simple exclusion process. We concentrate on electronic heat and charge transport in different but connected metallic substances. The electrons hop between energy-cells located alongside the spatial extension of the metal wire. When changing energy level, the system exchanges energy with the environment. At equilibrium the distribution satisfies the Fermi-Dirac occupation-law. Installing different temperatures at two connections induces an electromotive force (Seebeck effect) and upon forcing an electric current, an additional heat flow is produced at the junctions (Peltier heat). We derive the linear response behavior relating the Seebeck and Peltier coefficients as an application of Onsager reciprocity. We also indicate the higher order corrections. The entropy production is characterized as the anti-symmetric part under time-reversal of the space-time Lagrangian.