ShantanuT01/DACTYL-Pretraining huggingface dataset:
The stability of the de Sitter era of cosmic expansion in spatially curved homogeneous isotropic universes is studied. The source of the gravitational field is an imperfect fluid such that the parameters that characterize it may change with time. In this way we extend our previous analysis for spatially-flat spaces as well as the work of Barrow.
Arthur Cohn's irreducibility criterion for polynomials with integer coefficients and its generalization connect primes to irreducibles, and integral bases to the variable $x$. As we follow this link, we find that these polynomials are ready to spill two of their secrets: (i) There exists a unique "base-$x$" representation of such polynomials that makes the ring $\mathbb{Z}[x]$ into an ordered domain; and (ii) There is a 1-1 correspondence between positive rational primes $p$ and certain infinite sets of irreducible polynomials $f(x)$ that attain the value $p$ at sufficiently large $x$, each generated in finitely many steps from the $p$th cyclotomic polynomial. The base-$x$ representation provides practical conversion methods among numeric bases (not to mention a polynomial factorization algorithm), while the prime-irreducible correspondence puts a new angle on the Bouniakowsky Conjecture, a generalization of Dirichlet's Theorem on Primes in Arithmetic Progressions.
In this paper, by using Girsanov's transformation and the property of the corresponding reference stochastic differential equations, we investigate weak existence and uniqueness of solutions and weak convergence of Euler-Maruyama scheme to stochastic functional differential equations with H\"older continuous drift driven by fractional Brownian motion with Hurst index $H\in (1/2,1)$.
The maximum magnetic moment to angular momentum conjecture, recently posed by Barrow \& Gibbons, is in tension with the generally accepted parameters of magnetars. According to the conjecture the dimensionless Schuster-Wilson-Blacket number, $c\mu/J\sqrt{G}$ where $\mu$ is the magnetic moment and $J$ is the angular momentum, should be of order unity. A resolution is to assume that not only the low-magnetic field magnetars, but all magnetars have their super-critical fields in the higher multipoles. This requires the presence of external torques other than the magnetic dipole torque, such as from fallback disks or winds, on these systems to yield the measured high spin-down rates.
Based on the result on derived categories on K3 surfaces due to Mukai and Orlov and the result concerning almost-prime numbers due to Iwaniec, we remark the following fact: For any given positive integer N, there are N (mutually non-isomorphic) projective complex K3 surfaces such that their Picard lattices are not isomorphic but their transcendental lattices are Hodge isometric, or equivalently, their derived categories are mutually equivalent. After reviewing some finiteness result, we also give an explicit formula for the cardinality of the isomorphism classes of projective K3 surfaces having derived categories equivalent to the one of X with Picard number 1 in terms of the degree of X.
We consider a stochastic differential equation and its Euler-Maruyama (EM) scheme, under some appropriate conditions, they both admit a unique invariant measure, denoted by $\pi$ and $\pi_\eta$ respectively ($\eta$ is the step size of the EM scheme). We construct an empirical measure $\Pi_\eta$ of the EM scheme as a statistic of $\pi_\eta$, and use Stein's method developed in \citet{FSX19} to prove a central limit theorem of $\Pi_\eta$. The proof of the self-normalized Cram\'er-type moderate deviation (SNCMD) is based on a standard decomposition on Markov chain, splitting $\eta^{-1/2}(\Pi_\eta(.)-\pi(.))$ into a martingale difference series sum $\mcl H_\eta$ and a negligible remainder $\mcl R_\eta$. We handle $\mcl H_\eta$ by the time-change technique for martingale, while prove that $\mcl R_\eta$ is exponentially negligible by concentration inequalities, which have their independent interest. Moreover, we show that SNCMD holds for $x = o(\eta^{-1/6})$, which has the same order as that of the classical result in \citet{shao1999cramer,JSW03}.
We consider the Skorokhod problem in a time-varying interval. We prove existence and uniqueness for the solution. We also express the solution in terms of an explicit formula. Moving boundaries may generate singularities when they touch. We establish two sets of sufficient conditions on the moving boundaries that guarantee that the variation of the local time of the associated reflected Brownian motion is, respectively, finite and infinite. We also apply these results to study the semimartingale property of a class of two-dimensional reflected Brownian motions.
High-frequency sampled multivariate continuous time autoregressive moving average processes are investigated. We obtain asymptotic expansion for the spectral density of the sampled MCARMA process $(Y_{n\Delta})_{n \in \mathbb{Z}}$ as $\Delta \downarrow 0$, where $(Y_t)_{t \in \mathbb{R}}$ is an MCARMA process. We show that the properly filtered process is a vector moving average process, and determine the asymptotic moving average representation of it, thus generalizing the results by Brockwell et al. in the univariate case to the multivariate model. The determination of the moving average representation of the filtered process, important for the analysis of high-frequency data, is difficult for any fixed positive $\Delta$. However, the results established here provide a useful and insightful approximation when $\Delta$ is very small.
We aim at proving existence of weak solutions to the stationary compressible Navier-Stokes system coupled with the Allen-Cahn equation. The model is studied in a bounded three dimensional domain with slip boundary conditions for the momentum equations and the Neumann condition for the Allen-Cahn model. The main result establishes existence of weak solutions with bounded densities. The construction is possible assuming sufficiently large value of the heat capacity ratio $\gamma$ ($p \sim \rho^\gamma$). As a corollary we obtain weak solutions for a less restrictive case losing point-wise boundedness of the density.
After providing an overview of $\theta$-expansions introduced by Chakraborty and Rao, we focus on the Gauss-Kuzmin problem for this new transformation. Actually, we complete our study on these expansions by proving a two-dimensional Gauss-Kuzmin theorem. More exactly, we obtain such a theorem related to the natural extension of the associated measure-dynamical system. Finally, we derive explicit lower and upper bounds of the error term which provide interesting numerical calculations for the convergence rate involved.
Hydrodynamic simulations have been used to study accretion disks consisting of counterrotating components with an intervening shear layer(s). Configurations of this type can arise from the accretion of newly supplied counterrotating matter onto an existing corotating disk. The grid-dependent numerical viscosity of our hydro code is used to simulate the influence of a turbulent viscosity of the disk. Firstly, we consider the case where the gas well above the disk midplane rotates with angular rate +\Omega(r) and that well below has the same properties but rotates with rate -\Omega(r). We find that there is angular momentum annihilation in a narrow equatorial boundary layer in which matter accretes supersonically with a velocity which approaches the free-fall velocity and the average accretion speed of the disk can be enormously larger than that for a conventional \alpha-disk rotating in one direction. Secondly, we consider the case of a corotating accretion disk for r<r_t and a counterrotating disk for r>r_t. In this case we observed, that matter from the annihilation layer lost its stability and propagated inward pushing matter of inner regions of the disk to accrete. Thirdly, we investigated the case where counterrotating matter inflowing from large radial distances encounters an existing corotating disk. Friction between the inflowing matter and the existing disk is found to lead to fast boundary layer accretion along the disk surfaces and to enhanced accretion in the main disk. These models are pertinent to the formation of counterrotating disks in galaxies and possibly in Active Galactic Nuclei and in X-ray pulsars in binary systems.
EuB6 is a low carrier density ferromagnet which exhibits large magnetoresistance, positive or negative depending on temperature. The formation of magnetic polarons just above the magnetic critical temperature has been suggested by spin-flip Raman scattering experiments. We find that the fact that EuB6 is a semimetal has to be taken into account to explain its electronic properties, including magnetic polarons and magnetoresistance.
Nominally 45 nm GaN:Mg/ 5 nm (Ga,Mn)N / 45 nm GaN:Mg trilayers structures prepared by molecular beam epitaxy on GaN-buffered Al2O3 substrates are investigated to verify whether the indirect co-doping by holes from the cladding layers can alter the spin-spin interaction in (Ga,Mn)N. The four investigated structures, differing with the Mg doping level, are carefully characterized at the nanoscale by HRTEM, EDX, and by SIMS. HRTEM decisively excluded a presence of foreign Mn-rich phases. The structures, up to medium Mg doping, show no Mg over-doping effects. Magnetic studies of these structures are aided by the employment of a dedicated experimental approach of the in situ compensation of the magnetic contribution from the substrate, allowing up to about fifty-fold reduction of this contribution. This technique, dedicated to these structures, simultaneously provides a tenfold reduction of temporal instabilities of the magnetometric unit and lowers the experimental jitter to merely $5 \times 10^{-7}$~emu at 70~kOe, vastly increasing the precision and the credibility of the results of the standard integral SQUID magnetometry in high magnetic fields. The magnetic characteristics of the trilayers structures established here prove identical with the already known properties of the thick (Ga,Mn)N single layers, namely (i) the low temperature ferromagnetism among Mn$^{3+}$ ions driven by superexchange and (ii) purely paramagnetic response at higher temperatures. The possible cause of the lack of any effects brought about by the adjacent Mg-doping is a presence of residual Mn in the cladding layers, resulting in the deactivation of the p-type doping intended there. This finding points out that a more intensive technological effort has to be exerted to promote the co-doping-driven carrier-mediated ferromagnetic coupling in Mn-enriched GaN, especially at elevated temperatures.
The core-level electronic structures of the exfoliated graphene sheets on a Au-coated SiOx substrate have been studied by synchrotron radiation photoelectron spectroscopy (SR-PES) on a micron-scale. The graphene was firstly demonstrated its visibility on the Au-coated SiOx substrate by micro-optical characterization, and then conducted into SR-PES study. Because of the elimination of charging effect, precise C 1s core-level characterization clearly shows graphitic and contaminated carbon states of graphene. Different levels of Au-coating-induced p-type doping on single- and double-layer graphene sheets were also examined in the C 1s core-level shift. The Au-coated SiOx substrate can be treated as a simple but high-throughput platform for in situ studying graphene under further hybridization by PES.
We present precise Sunyaev-Zeldovich (SZ) effect measurements in the direction of 62 nearby galaxy clusters (z <0.5) detected at high signal-to-noise in the first Planck all-sky dataset. The sample spans approximately a decade in total mass, 10^14 < M_500 < 10^15, where M_500 is the mass corresponding to a total density contrast of 500. Combining these high quality Planck measurements with deep XMM-Newton X-ray data, we investigate the relations between D_A^2 Y_500, the integrated Compton parameter due to the SZ effect, and the X-ray-derived gas mass M_g,500, temperature T_X, luminosity L_X, SZ signal analogue Y_X,500 = M_g,500 * T_X, and total mass M_500. After correction for the effect of selection bias on the scaling relations, we find results that are in excellent agreement with both X-ray predictions and recently-published ground-based data derived from smaller samples. The present data yield an exceptionally robust, high-quality local reference, and illustrate Planck's unique capabilities for all-sky statistical studies of galaxy clusters.
We propose a novel task of joint few-shot recognition and novel-view synthesis: given only one or few images of a novel object from arbitrary views with only category annotation, we aim to simultaneously learn an object classifier and generate images of that type of object from new viewpoints. While existing work copes with two or more tasks mainly by multi-task learning of shareable feature representations, we take a different perspective. We focus on the interaction and cooperation between a generative model and a discriminative model, in a way that facilitates knowledge to flow across tasks in complementary directions. To this end, we propose bowtie networks that jointly learn 3D geometric and semantic representations with a feedback loop. Experimental evaluation on challenging fine-grained recognition datasets demonstrates that our synthesized images are realistic from multiple viewpoints and significantly improve recognition performance as ways of data augmentation, especially in the low-data regime. Code and pre-trained models are released at https://github.com/zpbao/bowtie_networks.
In this paper we study pseudo-processes related to odd-order heat-type equations composed with L\'evy stable subordinators. The aim of the article is twofold. We first show that the pseudo-density of the subordinated pseudo-process can be represented as an expectation of damped oscillations with generalized gamma distributed parameters. This stochastic representation also arises as the solution to a fractional diffusion equation, involving a higher-order Riesz-Feller operator, which generalizes the odd-order heat-type equation. We then prove that, if the stable subordinator has a suitable exponent, the time-changed pseudo-process becomes a genuine L\'evy stable process. This result permits us to obtain a power series representation for the probability density function of an arbitrary asymmetric stable process of exponent $\nu>1$ and skewness parameter $\beta$, with $0<\lvert\beta\lvert<1$. The methods we use in order to carry out our analysis are based on the study of a fractional Airy function which emerges in the investigation of the higher-order Riesz-Feller operator.
From our sample of spotted late-type stars showing surface differential rotation we find that the relationship between the rotation period and the surface shear coefficient $\alpha=\Delta\Omega/\Omega_{\rm eq}$ is significantly different for single stars compared to members in close binaries. Single stars follow a general trend that $\alpha$ increases with the rotation period. However, differential rotation of stars in close binary systems shows much weaker dependence on the rotation, if any, suggesting that in such systems tidal forces operate as a controlling mechanism of differential rotation.
We investigate the multiple use of a ferromagnetic spin chain for quantum and classical communications without resetting. We find that the memory of the state transmitted during the first use makes the spin chain a qualitatively different quantum channel during the second transmission, for which we find the relevant Kraus operators. We propose a parameter to quantify the amount of memory in the channel and find that it influences the quality of the channel, as reflected through fidelity and entanglement transmissible during the second use. For certain evolution times, the memory allows the channel to exceed the memoryless classical capacity (achieved by separable inputs) and in some cases it can also enhance the quantum capacity.
The prediction of small neutrino masses through the Seesaw Mechanism and their subsequent measurement suggests that the natural cut-off of the Standard Model is very high indeed. The recent neutrino data must be interpreted as a reflection of physics at very high energy. We examine their implications in terms of ideas of Grand Unification and Supersymmetry, and as possible hints for a unified theory of flavor.
We use multiwavelength data from space and ground based instruments to study the solar flares and coronal mass ejections (CMEs) on January 23, 2012 that were responsible for one of the largest solar energetic particle (SEP) events of solar cycle 24. The eruptions consisting of two fast CMEs (1400 km/s and 2000 km/s) and M-class flares that occurred in active region 11402 located at N28 W36. The two CMEs occurred in quick successions, so they interacted very close to the Sun. The second CME caught up with the first one at a distance of 11-12 Rsun. The CME interaction may be responsible for the elevated SEP flux and significant changes in the intensity profile of the SEP event. The compound CME resulted in a double-dip moderate geomagnetic storm (Dst = -73 nT). The two dips are due to the southward component of the interplanetary magnetic field in the shock sheath and the ICME intervals. One possible reason for the lack of a stronger geomagnetic storm may be that the ICME delivered a glancing blow to Earth.
The problem of how to compute accurately and efficiently the sign of the overlap between two general HFB wave functions is addressed. The results obtained can easily be extrapolated to the evaluation of the sign of the trace of a density operator exponential of one body operators.
We present a detailed study of AGN feedback in the narrow-line region (NLR) of the Seyfert 1 galaxy NGC 4151. We illustrate the data and techniques needed to determine the mass outflow rate and kinetic luminosity of the outflowing ionized gas as a function of position in the NLR. We find that the mass outflow rate peaks at a value of 3 solar masses per year at a distance of 70 pc from the central supermassive black hole (SMBH), which is about 10 times the outflow rate coming from inside 13 pc, and 230 times the mass accretion rate inferred from the bolometric luminosity of NGC 4151. Thus, most of the outflow must arise from "in situ" acceleration of ambient gas throughout the NLR. The kinetic luminosity peaks at 90 pc and drops rapidly thereafter, indicating that most of the kinetic energy is deposited within about 100 pc from the SMBH. Both values exceed the mass outflow rate and kinetic luminosity determined for the UV/X-ray absorber outflows in NGC 4151, indicating the importance of NLR outflows in providing feedback on scales where circumnuclear star formation and bulge growth occur.
Assuming a two-qubit system in Werner state which evolves in Heisenberg XY model with Dzyaloshinskii-Moriya (DM) interaction under the effect of different environments. We evaluate and compare quantum entanglement, quantum and classical correlation measures. It is shown that in the absence of decoherence effects, there is a critical value of DM interaction for which entanglement may vanish while quantum and classical correlations do not. In the presence of environment the behavior of correlations depends on the kind of system-environment interaction. Correlations can be sustained by manipulating Hamiltonian anisotropic-parameter in a dissipative environment. Quantum and classical correlations are more stable than entanglement generally.
In many applications, it is often necessary to sample the mean value of certain quantity with respect to a probability measure {\mu} on the level set of a smooth function $\xi: \mathbb{R}^d\rightarrow \mathbb{R}^k$, $1\le k < d$. A specially interesting case is the so-called conditional probability measure, which is useful in the study of free energy calculation and model reduction of diffusion processes. By Birkhoff's ergodic theorem, one approach to estimate the mean value is to compute the time average along an infinitely long trajectory of an ergodic diffusion process on the level set whose invariant measure is {\mu}. Motivated by the previous work of Ciccotti, Leli\`evre, and Vanden-Eijnden [11], as well as the work of Leli\`evre, Rousset, and Stoltz [33], in this paper we construct a family of ergodic diffusion processes on the level set of $\xi$ whose invariant measures coincide with the given one. For the conditional measure, in particular, we show that the corresponding SDEs of the constructed ergodic processes have relatively simple forms, and, moreover, we propose a consistent numerical scheme which samples the conditional measure asymptotically. The numerical scheme doesn't require computing the second derivatives of $\xi$ and the error estimates of its long time sampling efficiency are obtained.
The lattice strain and domain switching behaviour was investigated as a function of cyclic field and grain orientation for a pseudorhombohedral composition of the high Curie point piezoelectric system xBiScO3 - (1-x)PbTiO3 (x = 0.40) by in-situ electric field diffraction technique with high energy synchrotron x-rays. Along the field direction, the system exhibts five time large strain along 100 as compared to the 111 direction. A one-to-one correspondence between the 200 lattice strain and the 111 domain switching suggests a strong correlation between the two phenomena.
Particle acceleration in massive star forming regions can proceed via a large variety of possible emission scenarios, including high-energy gamma-ray production in the colliding wind zone of the massive Wolf-Rayet binary (here WR 20a and WR 121a), collective wind scenarios, diffusive shock acceleration at the boundaries of wind-blown bubbles in the stellar cluster, and outbreak phenomena from hot stellar winds into the interstellar medium. In view of the recent Fermi-LAT detection of HESS J1023-575 (in the vicinity of Westerlund 2), we examine another very high energy (VHE) gamma-ray source, HESS J1848-0145 (in the vicinity of W43), possibly associated with a massive star cluster. Considering multi-wavelength data, in particular TeV gamma-rays, we examine the available evidence that the gamma-ray emission coincident with Westerlund 2 and W43 could originate in particles accelerated by the above-mentioned mechanisms in massive star clusters.
We propose a new scaling law for anomalous Hall effect in ferromagnetic thin films by distinguishing three scattering sources, namely, bulk impurity, phonon, and more importantly a rough surface. This new scaling law fits the recent experimental data excellently with constant coefficients that are independent of temperature and film thickness. This is in stark constrast with previous scaling laws that use temperature/thickness dependent fitting coefficients, and is a strong indicator that this law captures the essential physics. By intepretating the experiments for Fe, Co, and Ni with this new law, we conclude that (i) the phonon-induced skew scattering is unimportant as expected; (ii) contribution from the impurity-induced skew scattering is negative; (iii) the intrinsic (extrinsic) mechanism dominates in Fe (Co), and both the extrinsic and the intrinsic contribution are important in Ni.
We propose a controllable way of tuning Fano resonances in open quantum dots in the absence of magnetic field. A quantum dot can be modified by changing the gate voltages that define the dot itself. An extra degree of freedom can be introduced by means of a controllable repulsive perturbation, such as the one induced by scanning a Atomic Force Microscope tip on a real sample. We numerically investigate the coupling between localized states in the dot and the continuum in the leads. The advantage of such position controllable perturbation is the selective manipulation of the quantum dot states. We show that this could be a feasible alternative to quantum dots in Aharonov-Bohm interferometers as a Fano resonance tuning device.