ShantanuT01/DACTYL-Pretraining huggingface dataset:
The Beauville-Voisin conjecture predicts the existence of a filtration on projective hyper-K\"ahler manifolds opposite to the conjecture Bloch-Beilinson filtration, called the Beauivlle-Voisin filtration. Voisin has introduced a filtration on zero cycles of an arbitrary projective hyper-K\"ahler manifold. On moduli space of stable objects of a projective K3 surface, there are other candidates constructed by Shen-Yin-Zhao, Barros-Flapan-Marian-Silversmith and more recently by Vial from different point of views. According to the work of Vial, all of them are proved to be equivalent except Voisin's filtration. In this paper, we show that Voisin's filtration is the same as the other filtrations. As an application, we prove a conjecture in Barros-Flapan-Marian-Silversmith's paper.
A modification of the Press-Schechter theory allowing for presence of a background large-scale structure (LSS) - a supercluster or a void, is proposed. The LSS is accounted as the statistical constraints in form of linear functionals of the random overdensity field. The deviation of the background density within the LSS is interpreted in a pseudo-cosmological sense. Using the constraints formalism may help us to probe non-trivial spatial statistics of haloes, e.g. edge and shape effects on boundaries of the superclusters and voids. Parameters of the constraints are connected to features of the LSS: its mean overdensity, a spatial scale and a shape, and spatial momenta of higher orders. It is shown that presence of a non-virialized LSS can lead to an observable deviation of the mass function. This effect is exploited to build a procedure to recover parameters of the background perturbation from the observationally estimated mass function.
Baryonic physical processes could leave non-negligible imprint on cosmic matter distribution pattern. Series of high precision simulation data sets with identical initial condition are employed for count-in-cell (CIC) analysis, including one N-body dark matter run, one with adiabatic gas only and one with dissipative processes. Variances and higher order correlation functions of dark matter and gas are estimated. It is found that baryon physical processes mainly affected dark matter distribution at scales less than $1h^{-1}$Mpc. In comparison with the pure dark matter run, adiabatic process alone strengthens variance of dark matter by \sim 10% at scale $0.1h^{-1}$Mpc, while $S_n$s of dark matter deviate from pure dark matter case only mildly at a few percentages. Dissipative gas run does not differ much to the adiabatic run in dark matter variance, but renders significantly different $S_n$ parameters of dark matter, bringing about more than 10% enhancement to $S_3$ at $0.1h^{-1}$Mpc and $z=0$. Distribution patterns of gas in two hydrodynamical simulations are prominently different. Variance of gas at $z=0$ decreases by $\sim 30%$ in adiabatic simulation while by $\sim 60%$ in non-adiabatic simulation at $0.1h^{-1}$Mpc, the attenuation is weaker at larger scales but still obvious at $\sim 10h^{-1}$Mpc. $S_n$ parameters of gas are biased upward at scales $< \sim 4h^{-1}$Mpc, dissipative processes give $\sim 84%$ promotion at $z=0$ to $S_3$ at $0.1h^{-1}$Mpc against the moderate $\sim 7%$ in adiabatic simulation. The clustering segregation we observed between gas and dark matter could have intricate implication on modeling galaxy distribution and relevant cosmological application demanding fine details of matter distribution in strongly nonlinear regime.
In this paper we consider the Prym variety $P(\widetilde{C}/C)$ associated to a Galois coverings of curves $f:\widetilde{C}\to C$ branched at $r$ points. We discuss some properties and equivalent definitions and then consider the Prym map $\mathcal{P}=\mathcal{P}(G,g,r):R(G,g,r)\to A_{p,\delta}$ with $\delta$ the type of the polarization. For Galois coverings whose Galois group is abelian and metabelian (non-abelian) we show that the differential of this map at certain points is injective. We also consider the Abel-Prym map $u:\widetilde{C}\to P(\widetilde{C}/C)$ and prove some results for its injectivity. In particular we show that in contrast to the classical and cyclic case, the behavior of this map here is more complicated. The theories of abelian and metabelian Galois coverings play a substantial role in our analysis and have been used extensively throughout the paper.
We have studied in detail the 0.15-15 GHz radio spectrum of the gamma-ray binary LS 5039 to look for a possible turnover and absorption mechanisms at low frequencies, and to constrain the physical properties of its emission. We have analysed two archival VLA monitorings, all the available archival GMRT data and a coordinated quasi-simultaneous observational campaign conducted in 2013 with GMRT and WSRT. The data show that the radio emission of LS 5039 is persistent on day, week and year timescales, with a variability $\lesssim 25~\%$ at all frequencies, and no signature of orbital modulation. The obtained spectra reveal a power-law shape with a curvature below 5 GHz and a turnover at $\sim0.5$ GHz, which can be reproduced by a one-zone model with synchrotron self-absorption plus Razin effect. We obtain a coherent picture for a size of the emitting region of $\sim0.85~\mathrm{mas}$, setting a magnetic field of $B\sim20~\mathrm{mG}$, an electron density of $n_{\rm e}\sim4\times10^5~{\rm cm^{-3}}$ and a mass-loss rate of $\dot M\sim5\times10^{-8}~{\rm M_{\odot} yr^{-1}}$. These values imply a significant mixing of the stellar wind with the relativistic plasma outflow from the compact companion. At particular epochs the Razin effect is negligible, implying changes in the injection and the electron density or magnetic field. The Razin effect is reported for first time in a gamma-ray binary, giving further support to the young non-accreting pulsar scenario.
We prove that the complex cobordism class of any hyper-K\"{a}hler manifold of dimension $2n$ is a unique combination with rational coefficients of classes of products of punctual Hilbert schemes of $K3$ surfaces. We also prove a similar result using the generalized Kummer varieties instead of punctual Hilbert schemes. As a key step, we establish a closed formula for the top Chern character of their tangent bundles.
A wide variety of complex phases in quantum materials are driven by electron-electron interactions, which are enhanced through density of states peaks. A well known example occurs at van Hove singularities where the Fermi surface undergoes a topological transition. Here we show that higher order singularities, where multiple disconnected leaves of Fermi surface touch all at once, naturally occur at points of high symmetry in the Brillouin zone. Such multicritical singularities can lead to stronger divergences in the density of states than canonical van Hove singularities, and critically boost the formation of complex quantum phases via interactions. As a concrete example of the power of these Fermi surface topological transitions, we demonstrate how they can be used in the analysis of experimental data on Sr$_3$Ru$_2$O$_7$. Understanding the related mechanisms opens up new avenues in material design of complex quantum phases.
Torsion gravitational effects in the quantum interference of charged particles are investigated. The influence of axial torsion in the Schiff-Banhill effect (SB) inside a metallic shell is given. The effect of torsion on the surface of the earth on (SB) experiment is estimated. Torsion gravity effects on the Sagnac phase-shift of neutron interferometry are also computed.
The Schroedinger equation with one and two dimensional potentials are solved in the frame work of the sl(2) Lie algebra. Eigenfunctions of the Schroedinger equation for various asymmetric double-well potentials have been determined and the eigenstates are expressed in terms of the orthogonal polynomials. The solution of the double-well potential in two dimension have been analyzed.
Characterizing the dynamics of open systems usually starts with a perturbative theory and involves various approximations, such as the Born, Markov and rotating-wave approximation (RWA). However, the approximation approaches could introduce more or less incompleteness in describing the bath behaviors. Here, we consider a quantum channel, which is modeled by a qubit (a two-level system) interacting with a bosonic bath. Unlike the traditional works, we experimentally simulate the system-bath interaction without applying the Born, Markov, and rotating-wave approximations. To our knowledge, this is the first experimental simulation of the quantum channels without any approximations mentioned above, by using linear optical devices. The results are quite useful and interesting, which not only reveal the effect of the counter-rotating terms but also present a more accurate picture of the quantum channel dynamics. Besides, we experimentally investigate the dynamics of the quantum temporal steering (TS), i.e., a temporal analogue of Einstein-Podolsky-Rosen steering. The experimental and theoretical results are in good agreement and show that the counter-rotating terms significantly influence the TS dynamics. When one monogamously associates TS with the security of the cryptographic protocols (e.g., BB84), our experimental tests reveal that the channels based on RWA will provide exaggerated security durations, while they are actually insecure in non-RWA channel cases. This implies that doing RWA may result in a risk for the security of quantum key distribution. Our findings are expected to have useful applications in secure quantum communications and future interesting TS studies.
We present a broad-band analysis of deep Suzaku observations of nearby Seyfert 1 AGN: Fairall 9, MCG--6-30-15, NGC 3516, NGC 3783 and NGC 4051. The use of deep observations (exposures >200 ks) with high S/N allows the complex spectra of these objects to be examined in full, taking into account features such as the soft excess, reflection continuum and complex absorption components. After a self-consistent modelling of the broad-band data (0.6-100.0 keV, also making use of BAT data from Swift), the subtle curvature which may be introduced as a consequence of warm absorbers has a measured affect upon the spectrum at energies >3 keV and the Fe K region. Forming a model (including absorption) of these AGN allows the true extent to which broadened diskline emission is present to be examined and as a result the measurement of accretion disc and black hole parameters which are consistent over the full 0.6-100.0 keV energy range.   Fitting relativistic line emission models appear to rule out the presence of maximally spinning black holes in all objects at the 90% confidence level, in particular MCG--6-30-15 at >99.5% confidence. Relativistic Fe K line emission is only marginally required in NGC 3516 and not required in NGC 4051, over the full energy bandpass. Nonetheless, statistically significant broadened 6.4 keV Fe K alpha emission is detected in Fairall 9, MCG--6-30-15 and NGC 3783 yielding black hole spin estimates of a=0.67(+0.10,-0.11), a=0.4(+0.20,-0.12) and a<-0.04 respectively, when fitted with disc emission models.
This article studies the stability of solutions of equilibrium equations arising in so-called resource dependent branching processes. We argue that these new models, building on the model already presented by Bruss (1984 a), refined and elaborated in Bruss and Duerinckx (2015) and now extended to allow immigration, are suitable to cope with specific properties of human populations. Our main interest is here to understand under which conditions immigration may lead to an equilibrium. At the same time, we would like to advertize resource dependent branching processes as possibly the best models to study such questions.   The equilibrium equations for the new models we obtain are clear and informative for several important stability questions. The goal of the study of the specific examples we provide is to see where the impact of immigration is most visible, and in how far increased efforts of integration can cope with dangers of instability. Moreover we discuss the advantages and a weaker point of our model, and also include a brief look at continuous-state, continuous-time branching processes as an alternative.
We study capability of $f(R)$ gravity models to allow crossing the phantom boundary in both Jordan and Einstein conformal frames. In Einstein frame, these models are equivalent to Einstein gravity together with a scalar field minimally coupled to gravity. This scalar degree of freedom appears as a quintessence field with a coupling with the matter sector. We investigate evolution of the equation of sate parameter for some cosmologically viable $f(R)$ gravity models in both conformal frames. This investigation (beyond mere theoretical arguments) acts as an operational tool to distinguish physical status of the two conformal frames. It shows that the two conformal frames have not the same physical status.
Additional high-frequency components of the pulsar radiation in Crab Nebula are considered as a result of the resonance with the surface electromagnetic wave at nonlinear reflection from of the neutron star surface.This stimulated scattering consists in generation of a surface periodic relief by an incident field and diffraction on that relief the radiation of relativistic positrons, which fly from the magnetosphere to the star in the accelerating electric field of a polar gap.
Mott insulators can be portrayed as "unsuccessful metals": systems in which a strong Coulomb repulsion prevents charge conduction notwithstanding the metal-like density of conduction electrons. The possibility to unlock such large density of frozen carriers with an electric field offers a tantalizing opportunity to realize new Mott-based microelectronic devices. Here we explicitly unveil how such unlocking happens by solving a simple, yet generic, model for correlated insulators using dynamical mean-field theory. Specifically, we show that the electric breakdown of a Mott insulator can occur via a first-order insulator-to-metal transition, characterized by an abrupt gap-collapse in sharp contrast to the Zener tunneling mechanism. The switch-on of charge conduction is due to the energetic stabilization of a metallic phase that preexists as metastable state in equilibrium and is disconnected from the stable insulator. Our findings rationalize recent experimental observations and offer a guideline for future technological research.
We present a set of predictions for weak lensing correlation functions in the context of modified gravity models, including a prescription for the impact of the nonlinear power spectrum regime in these models. We consider the DGP and f(R) models, together with dark energy models with the same expansion history. We use the requirement that gravity is close to GR on small scales to estimate the non-linear power for these models. We then calculate weak lensing statistics, showing their behaviour as a function of scale and redshift, and present predictions for measurement accuracy with future lensing surveys, taking into account cosmic variance and galaxy shape noise. We demonstrate the improved discriminatory power of weak lensing for testing modified gravities once the nonlinear power spectrum contribution has been included. We also examine the ability of future lensing surveys to constrain a parameterisation of the non-linear power spectrum, including sensitivity to the growth factor.
We discuss 6 GHz JVLA observations covering a volume-limited sample of 178 low redshift ($0.2 < z < 0.3$) optically selected QSOs. Our 176 radio detections fall into two clear categories: (1) About $20$\% are radio-loud QSOs (RLQs) having spectral luminosities $L_6 \gtrsim 10^{\,23.2} \mathrm{~W~Hz}^{-1}$ primarily generated in the active galactic nucleus (AGN) responsible for the excess optical luminosity that defines a \emph{bona fide} QSO. (2) The radio-quiet QSOs (RQQs) have $10^{\,21} \lesssim L_6 \lesssim 10^{\,23.2} \mathrm{~W~Hz}^{-1}$ and radio sizes $\lesssim 10 \mathrm{~kpc}$, and we suggest that the bulk of their radio emission is powered by star formation in their host galaxies. "Radio silent" QSOs ($L_6 \lesssim 10^{\,21} \mathrm{~W~Hz}^{-1}$) are rare, so most RQQ host galaxies form stars faster than the Milky Way; they are not "red and dead" ellipticals. Earlier radio observations did not have the luminosity sensitivity $L_6 \lesssim 10^{\,21} \mathrm{~W~Hz}^{-1}$ needed to distinguish between such RLQs and RQQs. Strong, generally double-sided, radio emission spanning $\gg 10 \mathrm{~kpc}$ was found associated with 13 of the 18 RLQ cores having peak flux densities $S_\mathrm{p} > 5 \mathrm{~mJy~beam}^{-1}$ ($log(L) \gtrsim 24$). The radio luminosity function of optically selected QSOs and the extended radio emission associated with RLQs are both inconsistent with simple "unified" models that invoke relativistic beaming from randomly oriented QSOs to explain the difference between RLQs and RQQs. Some intrinsic property of the AGNs or their host galaxies must also determine whether or not a QSO appears radio loud.
The recovery of images from the observations that are degraded by a linear operator and further corrupted by Poisson noise is an important task in modern imaging applications such as astronomical and biomedical ones. Gradient-based regularizers involve the popular total variation semi-norm have become standard techniques for Poisson image restoration due to its edge-preserving ability. Various efficient algorithms have been developed for solving the corresponding minimization problem with non-smooth regularization terms. In this paper, motivated by the idea of the alternating direction minimization algorithm and the Newton's method with upper convergent rate, we further propose inexact alternating direction methods utilizing the proximal Hessian matrix information of the objective function, in a way reminiscent of Newton descent methods. Besides, we also investigate the global convergence of the proposed algorithms under certain conditions. Finally, we illustrate that the proposed algorithms outperform the current state-of-the-art algorithms through numerical experiments on Poisson image deblurring.
Vacuum decay in de Sitter space is a process of great physical interest, as it allows to rule out cosmological models in the early and current Universe. Its rate may be described in terms of an instanton in Euclidean space called bounce and it is usually interpreted as thermally assisted quantum tunneling. According to analytical and numerical evidence in the literature, a bounce exists only for certain values of the Hubble parameter in single scalar field theories with Einstein-Hilbert gravity. In the present paper, we rely on a novel approach to provide more stringent bounds, which may be easily extended to theories with non-minimally coupled and quadratic gravity. An additional restriction is also derived, which specifically applies to the latter.
Observations of molecular clouds in the gamma ray domain provide us with a tool to study the distribution of cosmic rays in the Galaxy. This is because cosmic rays can penetrate molecular clouds, undergo hadronic interactions in the dense gas, and produce neutral pions that in turn decay into gamma rays. The detection of this radiation allows us to estimate the spectrum and intensity of cosmic rays at the cloud's position. Remarkably, this fact can be used to constrain the cosmic ray diffusion coefficient at specific locations in the Galaxy.
We present the generalization of the minimal model for surface flows of granular mixtures, proposed by Boutreux and de Gennes [J. Phys. I France 6, 1295 (1996)]. The minimal model was valid for grains differing only in their surface properties. The present model also takes into account differences in the size of the grains. We apply the model to study segregation in two-dimensional silos of mixtures of grains differing in size and/or surface properties. When the difference in size is small, the model predicts that a continuous segregation appears in the static phase during the filling of a silo. When the difference in size is wide, we take into account the segregation of the grains in the rolling phase, and the model predicts complete segregation and stratification in agreement with experimental observations.
The light gluino (12 - 16 GeV) and light sbottom (2 - 6 GeV) scenario has been used to explain the apparent overproduction of b-quarks at the Tevatron. This scenario also predicts the decay Z -> b b-bar ~g ~g where the gluinos subsequently decay into b-quarks and sbottoms. We show that this can contribute to the width Gamma_4b = Gamma(Z -> b b-bar b b-bar) since most of the sbottoms and b-quarks arising from gluino decay have a small angular separation. We find that while no excess in Gamma_4b is observable due to large uncertainties in experimental measurements, the ratio Gamma(Z -> b b-bar ~g ~g)/Gamma(Z -> b b-bar b b-bar) can be large due to sensitivity to b-quark mass, the sbottom mixing angle and the gluino mass. We calculate it to be in the range 0.05 - 0.41 inclusive of the entire parameter space.
An algorithm to construct analytic approximations to two-loop diagrams describing their behaviour at small non-zero thresholds is discussed. For some special cases (involving two different-scale mass parameters), several terms of the expansion are obtained.
Cosmic Birefringence (CB) is the in-vacuo rotation of the linear polarization direction of photons during propagation, caused by parity-violating extensions of Maxwell electromagnetism. We build low resolution CB angle maps using Planck Legacy and NPIPE products and provide for the first time estimates of the cross-correlation spectra $C_L^{\alpha E}$ and $C_L^{\alpha B}$ between the CB and the CMB polarization fields. We also provide updated CB auto-correlation spectra $C_L^{\alpha\alpha}$ as well as the cross-correlation $C_L^{\alpha T}$ with the CMB temperature field. We report constraints by defining the scale-invariant amplitudes $A^{\alpha X} \equiv L(L + 1)C_L^{\alpha X}/2\pi$, where $X = \alpha, T, E, B$, finding no evidence of CB. In particular, we find $A^{\alpha E} = (-7.8 \pm 5.6)$ nK deg and $A^{\alpha B} = (0.3 \pm 4.0)$ nK deg at 68% C.L..
Measuring the volume-weighted peculiar velocity statistics from inhomogeneously and sparsely distributed galaxies/halos, by existing velocity assignment methods, suffers from a significant sampling artifact. As an alternative, the Kriging interpolation based on Gaussian processes was introduced and evaluated [Y. Yu, J. Zhang, Y. Jing, and P. Zhang, Phys. Rev. D 92, 083527 (2015)]. Unfortunately, the most straightforward application of Kriging does not perform better than the existing methods in the literature. In this work, we investigate two physically motivated extensions. The first takes into account of the anisotropic velocity correlations. The second introduces the nugget effect, on account of multi-streaming of the velocity field. We find that the performance is indeed improved. For sparsely sampled data [$n_P\lesssim 6\times 10^{-3}(h^{-1} {\rm Mpc})^{-3}$] where the sampling artifact is the most severe, the improvement is significant and is two-fold: 1) The scale of reliable measurement of the velocity power spectrum is extended by a factor $\sim 1.6$, and 2) the dependence on the velocity correlation prior is weakened by a factor of $\sim 2$. We conclude that such extensions are desirable for accurate velocity assignment by Kriging.
The main goal of this paper is to generalize Serre-Tate theory of "ordinary" local moduli to Shimura varieties of PEL type. To this end we develop a generalized notion of ordinariness, we prove a number of basic results about this, and we study the formal deformations of ordinary objects. In general, the formal deformation spaces get a new "group-like" structure that we call a "cascade". Further the paper contains some results on the Ekedahl-Oort stratification of PEL moduli spaces, and an application of our results to the study of congruence relations.