ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present an analysis of selection biases in the M-sigma relation using Monte- Carlo simulations including the sphere of influence resolution selection bias and a selection bias in the velocity dispersion distribution. We find that the sphere of influence selection bias has a significant effect on the measured slope of the M-sigma relation, modeled as \beta_intrinsic = -4.69 + 2.22\beta_measured, where the measured slope is shallower than the model slope in the parameter range of \beta > 4, with larger corrections for steeper model slopes. Therefore, when the sphere of influence is used as a criterion to exclude unreliable measurements, it also in- troduces a selection bias that needs to be modeled to restore the intrinsic slope of the relation. We find that the selection effect due to the velocity dispersion distribution of the sample, which might not follow the overall distribution of the population, is not important for slopes of \beta ~ 4-6 of a logarithmically linear M-sigma relation, which could impact some studies that measure low (e.g., \beta < 4) slopes. Combining the selection biases in velocity dispersions and the sphere of influence cut, we find the uncertainty of the slope is larger than the value without modeling these effects, and estimate an intrinsic slope of \beta = 5.28^{+0.84}_{-0.55}.
Kinetics of spatially uniform distribution of 2D electrons in crossed electric and magnetic fields in the presence of microwave radiation has been studied. In the present model the contribution from the microwave radiation and the effects of Landau quantization are considered exactly, while scattering is treated perturbatively. Here Landau--Floquet states interact with the impurity potential that causes transitions between them. The linear response of a non-equilibrium system to a weak measurement field has been considered for the case when the non-equilibrium state of the carriers can be described by the average values of the total energy and the number of particles.
We give a detailed proof that locally Noetherian moduli stacks of sections carry canonical obstruction theories. As part of the argument we construct a dualizing sheaf and trace map, in the lisse-etale topology, for families of tame twisted curves, when the base stack is locally Noetherian.
Finding a sample of the most massive clusters with redshifts $z>0.6$ can provide an interesting consistency check of the $\Lambda$ cold dark matter ($\Lambda$CDM) model. Here we present results from our search for clusters with $0.6\lesssim z\lesssim1.0$ where the initial candidates were selected by cross-correlating the RASS faint and bright source catalogues with red galaxies from the Sloan Digital Sky Survey DR8. Our survey thus covers $\approx10,000\,\rm{deg^2}$, much larger than previous studies of this kind. Deeper follow-up observations in three bands using the William Herschel Telescope and the Large Binocular Telescope were performed to confirm the candidates, resulting in a sample of 44 clusters for which we present richnesses and red sequence redshifts, as well as spectroscopic redshifts for a subset. At least two of the clusters in our sample are comparable in richness to RCS2-$J$232727.7$-$020437, one of the richest systems discovered to date. We also obtained new observations with the Combined Array for Research in Millimeter Astronomy for a subsample of 21 clusters. For 11 of those we detect the Sunyaev-Zel'dovich effect signature. The Sunyaev-Zel'dovich signal allows us to estimate $M_{200}$ and check for tension with the cosmological standard model. We find no tension between our cluster masses and the $\Lambda$CDM model.
This thesis is concerned with the mixed Tate property of reductive algebraic groups $G$, which in particular guarantees a Chow Kunneth property for the classifying space $BG$. Toward this goal, we first refine the construction of the compactly supported motive of a quotient stack.   In the first section, we construct the compactly supported motive $M^c(X)$ of an algebraic space $X$ and demonstrate that it satisfies expected properties, following closely Voevodsky's work in the case of schemes.   In the second section, we construct a functorial version of Totaro's definition of the compactly supported motive $M^c([X/G])$ for any quotient stack $[X/G]$ where $X$ is an algebraic space and $G$ is an affine group scheme acting on it. A consequence of functoriality is a localization triangle for these motives.   In the third section, we study the mixed Tate property for the classical groups as well as the exceptional group $G_2$. For these groups, we demonstrate that all split forms satisfy the mixed Tate property, while exhibiting non-split forms that do not. Finally, we prove that for any affine group scheme $G$ and normal split unipotent subgroup $J$ of $G$, the motives $M^c(BG)$ and $M^c(B(G/J))$ are isomorphic.
We present a method for the real-time estimation of the full 3D pose of one or more human hands using a single commodity RGB camera. Recent work in the area has displayed impressive progress using RGBD input. However, since the introduction of RGBD sensors, there has been little progress for the case of monocular color input. We capitalize on the latest advancements of deep learning, combining them with the power of generative hand pose estimation techniques to achieve real-time monocular 3D hand pose estimation in unrestricted scenarios. More specifically, given an RGB image and the relevant camera calibration information, we employ a state-of-the-art detector to localize hands. Given a crop of a hand in the image, we run the pretrained network of OpenPose for hands to estimate the 2D location of hand joints. Finally, non-linear least-squares minimization fits a 3D model of the hand to the estimated 2D joint positions, recovering the 3D hand pose. Extensive experimental results provide comparison to the state of the art as well as qualitative assessment of the method in the wild.
Class of spherically symmetric Stephani cosmological models is examined in the context of evolution type. It is assumed that the equation of state at the symmetry center of the models is barotropic. Classification of cosmological models is performed depending on different values and signs of two free parameters. It is shown that for (hyperbolic geometry) dust-like cosmological model exhibits accelerated expansion at later stages of evolution. The Hubble and deceleration parameters are defined in the model and it is shown that the deceleration parameter decreases with the distance becoming negative for sufficiently distant galaxies. Redshift-magnitude relation is calculated and discussed in the context of SnIa observational data. It is noticed that the most distant supernovae of type Ia fit quite well to the redshift-magnitude relation calculated in the considered model without introducing the cosmological constant. It is also shown that the age of the universe in the model is longer than in the Friedmann model corresponding to the same Hubble and energy density parameters.
A primordial cosmological magnetic field induces Faraday rotation of the cosmic microwave background polarization. This rotation produces a curl-type polarization component even when the unrotated polarization possesses only gradient-type polarization, as expected from scalar density perturbations. We compute the angular power spectrum of curl-type polarization arising from small Faraday rotation due to a weak stochastic primordial magnetic field with a power-law power spectrum. The induced polarization power spectrum peaks at arcminute angular scales. Faraday rotation is one of the few cosmological sources of curl-type polarization, along with primordial tensor perturbations, gravitational lensing, and the vector and tensor perturbations induced by magnetic fields; the Faraday rotation signal peaks on significantly smaller angular scales than any of these, with a power spectrum amplitude which can be comparable to that from gravitational lensing. Prospects for detection are briefly discussed.
We develop a theory of pseudodifferential operators of infinite order for the global classes $\mathcal{S}_{\omega}$ of ultradifferentiable functions in the sense of Bj\"orck, following the previous ideas given by Prangoski for ultradifferentiable classes in the sense of Komatsu. We study the composition and the transpose of such operators with symbolic calculus and provide several examples.
We consider correlation decay in the hard-core model with fugacity $\lambda$ on a rooted tree $T$ in which the arity of each vertex is independently Poisson distributed with mean $d$. Specifically, we investigate the question of which parameter settings $(d, \lambda)$ result in strong spatial mixing, weak spatial mixing, or neither. (In our context, weak spatial mixing is equivalent to Gibbs uniqueness.) For finite fugacity, a zero-one law implies that these spatial mixing properties hold either almost surely or almost never, once we have conditioned on whether $T$ is finite or infinite.   We provide a partial answer to this question, which implies in particular that   1. As $d \to \infty$, weak spatial mixing on the Poisson tree occurs whenever $\lambda < f(d) - o(1)$ but not when $\lambda$ is slightly above $f(d)$, where $f(d)$ is the threshold for WSM (and SSM) on the $d$-regular tree. This suggests that, in most cases, Poisson trees have similar spatial mixing behavior to regular trees.   2. When $1 < d \le 1.179$, there is weak spatial mixing on the Poisson($d$) tree for all values of $\lambda$. However, strong spatial mixing does not hold for sufficiently large $\lambda$. This is in contrast to regular trees, for which strong spatial mixing and weak spatial mixing always coincide.   For infinite fugacity SSM holds only when the tree is finite, and hence almost surely fails on the Poisson($d$) tree when $d>1$. We show that WSM almost surely holds on the Poisson($d$) tree for $d < \mathbf{e}^{1/\sqrt{2}}/\sqrt{2} =1.434...$, but that it fails with positive probability if $d>\mathbf{e}$.
Non-equilibrium dynamics for relativistic fluid or quark gluon plasma (QGP) have already been calculated earlier upto third order using both kinetic and thermodynamic approaches. Calculations presented in this manuscript are based on thermodynamics principles. The expressions for third order dissipative fluxes have been derived from equation for entropy 4-current developed earlier by A. Muronga. The relaxation equations in the present work have been developed in a simple Bjorken (1+1)D scenario and Eckart frame. The relaxation equations are found to have slightly different values for the coupling coefficients as compared to calculations from earlier models. The solutions to the differential equations have been found to be sensitive to values of these coefficients. The shear relaxation equations derived in third order theory are discussed term by term. Effects of third order theory on shear relaxation time has been discussed. Thermodynamic quantities related to hot and dense matter have been calculated as functions of proper time. Moreover, various initial conditions for the relaxation equations have been assumed to study their effects on above mentioned observables. A LHC QGP formation time of $\tau_0$ = 0.4 fm/c and temperature of T$_0$ = 500 MeV have been assumed.
We consider the following game, played on a $k$-uniform hypergraph $H$. There are $q$ colors available and two players take it in turns to color vertices. A partial coloring is proper if no edge is mono-chromatic. One player, A, wishes to color all the vertices and the other player, B, wishes to prevent this. The {\em game chromatic number} $\chi_g(H)$ is the minimum number of colors for which A has a winning strategy. We consider this in the context of a random $k$-uniform hypergraph and prove upper and lower bounds that hold w.h.p.
Fiber bursts are a type of fine structure that is often superposed on type IV radio continuum emission during solar flares. Although studied for many decades, its physical exciter, emission mechanism, and association with the flare energy release remain unclear, partly due to the lack of simultaneous imaging observations. We report the first dynamic spectroscopic imaging observations of decimetric fiber bursts, which occurred during the rise phase of a long-duration eruptive flare on 2012 March 3, as obtained by the Karl G. Jansky Very Large Array in 1--2 GHz. Our results show that the fiber sources are located near and above one footpoint of the flare loops. The fiber source and the background continuum source are found to be cospatial and share the same morphology. It is likely that they are associated with nonthermal electrons trapped in the converging magnetic fields near the footpoint, as supported by a persistent coronal hard X-ray source present during the flare rise phase. We analyze three groups of fiber bursts in detail with dynamic imaging spectroscopy and obtain their mean frequency-dependent centroid trajectories in projection. By using a barometric density model and magnetic field based on a potential-field extrapolation, we further reconstruct the 3-D source trajectories of fiber bursts, for comparison with expectations from the whistler wave model and two MHD-based models. We conclude that the observed fiber burst properties are consistent with an exciter moving at the propagation velocity expected for whistler waves, or models that posit similar exciter velocities.
In this letter we establish that the supersymmetric R^2 effective action for the heterotic string, obtained from the supersymmetrisation of the Lorentz Chern-Simons term, is to order $\alpha'$ equivalent modulo field redefinitions to heterotic string effective actions computed by different methods.
Imagine two parties, Alice and Bob who share an entangled quantum state. A well-established result that if Alice performs two-outcome measurement on the portion of the state in her possession and Bob does likewise, they are able to produce correlations that cannot be reproduced by any classical theory. The allowed classical correlations can be expressed quantitatively by the Bell inequalities. Here we propose new families of Bell inequalities, as a generalization of the Clauser-Horne-Shimony-Holt (CHSH) inequality and show that the maximum violation of these Bell inequalities allowed by quantum theory can not be attained by a bipartite quantum system having support on a qubit at each site.
Context. The Galactic Center (GC) region has been studied in gamma rays in the past decades - the GC excess detected by Fermi is still not fully understood and the first detection of a PeVatron by H.E.S.S. indicates the existence of sources that can accelerate cosmic rays up to a PeV or higher.   Aims. In this paper, we are investigating the origin of the PeVatron emission detected by H.E.S.S. by, for the first time, simulating cosmic rays in the GC in a realistic three-dimensional gas and photon field distribution and large-scale magnetic field.   Methods. We solve the 3D transport equation with an anisotropic diffusion tensor using the approach of stochastic differential equations as implemented in the propagation software CRPropa 3.1 (Merten et al. 2017). We test five different source distributions for four different configurations of the diffusion tensor, i.e. with ratios of the perpendicular to parallel components $\epsilon = 0.001,\ 0.01,\ 0.1,\ 0.3$.   Results. We find that the two-dimensional distribution of gamma rays as measured by H.E.S.S. is best fit by a model that considers three cosmic-ray sources, i.e. a central source, the SNR G0.9+0.1 and the source HESS J1746-285. The fit indicates that propagation is dominated by parallel diffusion with $ \espilon = 0.001 $.   Conclusions. We find that the 3D propagation in the 3D gas and B-field configurations taken from Guenduez et al. (2020) can explain the general features of the data well. We predict that CTA should be able to identify emission from SgrB2 and the six dust ridge clouds that are included in our simulations and that should be detectable with a the expected resolution of CTA of 0.033$^\circ$.
We investigate the effects of a top-heavy stellar initial mass function on the reionisation history of the intergalactic medium (IGM). We use cosmological simulations that include self-consistently the feedback from ionising radiation, H_2 dissociating radiation and supernova (SN) explosions. We find that it is difficult to reionise the IGM at z_rei>10 with stellar sources even after making extreme assumptions. If star formation in 10^9 M_\odot galaxies is not suppressed by SN explosions, the optical depth to Thomson scattering is tau_e< 0.13. If we allow for the normal energy input from SNe or if pair-instability SNe are dominant, we find taue<0.09. Assuming normal yields for the first stars (popIII), the mean metallicity of the IGM is already Z/Z_\odot=2x10^-3 (10^-3<Z/Z_\odot<1 in overdense regions) when the IGM mean ionisation fraction is less than 10%. For these reasons popIII stars cannot contribute significantly to reionisation unless the mechanical energy input from SNe is greatly reduced and either the metal yield or the mixing efficiency is reduced by a factor of 1000. Both problems have a solution if popIII stars collapse to black holes. This can happen if, having masses M_*< 130 M_\odot, they are characterised by heavy element fall-back or if, having masses M_*>260 M_\odot, they collapse directly onto black holes without exploding as SNe.If metal-poor stars are initially important and collapse to black holes is the typical outcome, then the secondary emission of ionising radiation from accretion on SN induced seed black holes, might be more important than the primary emission. Surprisingly, including feedback effects, we estimate that a warm dark matter scenario (with particle mass of 1.25 keV) reduces tau_e by only approximately 10%.[abridged]
In an early work the Rossby Wave Instability (RWI) has been proposed to explain variability thought to originate in the close vicinity of black-holes but this was done in the pseudo-Newtonian approach. Here we present the first general relativistic hydrodynamics simulations of this instability not only proving its theorized existence in a full general relativistic (GR) environment but also studying the effect of the strong gravity on the instability. To that end we performed a set of simulations increasingly closer to the black hole with our new GR version of the MPI-AMRVAC code.This allows us to study the minute changes in the behaviour of the instability.We found that the pseudo-Newtonian approach gives adequate results provided that time shifting induced by the black hole gravity is taken into account. Hence, to view the disc as a distant observer would a full GR ray-tracing post treatment of the simulations is a must.
We study the Lepton Flavor Violating (LFV) $e(\mu)-\tau$ conversion in Deep Inelastic Scattering (DIS) of electron (muon) on fixed-target nuclei. Our model-independent analysis is based on the set of the low-energy effective four-fermion LFV operators composed of leptons and quarks with the corresponding mass scales $\Lambda_{k}$ for each operator. Using the estimated sensitivity of the search for this LFV process in events with large missing energy in the NA64 experiment at the CERN SPS, we derive lower limits for $\Lambda_{k}$ and compared them with the corresponding limits existing in the literature. We show that the DIS $e(\mu)-\tau$ conversion is able to provide a plenty of new limits as yet non-existing in the literature. We also analyzed the energy spectrum of the final-state $\tau$ and discussed viability of the observation of this process in the NA64 experiment and ones akin to it. The case of polarized beams and targets is also discussed.
Our goal is to analyse singularities of integral models of Shimura varieties. One approach is to construct local models, which model the singularities of the corresponding integral model using linear algebra dada and find resolutions with mild singularities thereof. More precisely we will attack the question of existence of semi-stable resolutions. We will discuss an approach developed by Genestier. In this approach a candidate for a semi-stable resolution was given as the blow-up of a Grassmannian variety in Schubert varieties of its special fiber. Explicit calculations show that this approach does not work in general. Using the flatness of the local models, we describe these local models as Mustafin varieties for Grassmannian varieties. We combine several results on the structure of Mustafin varieties for projective spaces with the Pl\"ucker embedding to construct a candidate for a semi-stable resolution of local models. Under some additional assumptions this candidate generalises the approach suggested by Genestier. Furthermore under the same assumptions the new candidate agrees with the semi-stable resolution constructed by G\"ortz for small dimensions.
Historically, it has been assumed that globular and open clusters never interact. However, recent evidence suggests that: globular clusters passing through the disk may be able to perturb giant molecular clouds (GMCs) triggering formation of open clusters and some old open clusters may be linked to accreted globulars. Here, we further explore the existence of possible dynamical connections between globular and open clusters, and realize that the most obvious link must be in the form of gravitational interactions. If open clusters are born out of GMCs, they have to move in similar orbits. If we accept that globulars can interact with GMCs, triggering star formation, it follows that globular and open clusters must also interact. Consistently, theoretical arguments as well as observational evidence, show that globular and open clusters certainly are interacting populations and their interactions are far more common than usually thought, especially for objects part of the bulge/disk. Monte Carlo calculations confirm that conclusion. Globular clusters seem capable of not only inducing formation of open clusters but, more often, their demise. Relatively frequent high speed cluster encounters or cluster harassment may also cause, on the long-term, slow erosion and tidal truncation on the globulars involved. The disputed object FSR 1767 (2MASS-GC04) may be, statistically speaking, the best example of an ongoing interaction.
We analytically investigate the condition for a particle accelerator to be active in the outer magnetosphere of a rotation-powered pulsar. Within the accelerator (or the gap), magnetic-field-aligned electric field accelerates electrons and positrons, which emit copious gamma-rays via curvature process. If one of the gamma-rays emitted by a single pair materializes as a new pair on average, the gap is self-sustained. However, if the neutron-star spin-down rate decreases below a certain limit, the gap becomes no longer self-sustained and the gamma-ray emission ceases. We explicitly compute the multiplicity of cascading pairs and find that the obtained limit corresponds to a modification of previously derived outer-gap death line. In addition to this traditional death line, we find another death line, which becomes important for millisecond pulsars, by separately considering the threshold of photon-photon pair production. Combining these traditional and new death lines, we give predictions on the detectability of gamma-ray pulsars with Fermi and AGILE. An implication on the X-ray observations of heated polar-cap emission is also discussed.