ShantanuT01/DACTYL-Pretraining huggingface dataset:
For graphs $H$ and $F$, let $\operatorname{ex}(n, H, F)$ be the maximum possible number of copies of $H$ in an $F$-free graph on $n$ vertices. The study of this function, which generalises the well-studied Tur\'an numbers of graphs, was initiated recently by Alon and Shikhelman. We show that if $F$ is a tree then $\operatorname{ex}(n, H, F) = \Theta(n^r)$ for some integer $r = r(H, F)$, thus answering one of their questions.
We study the Kronecker symbol $\left(\frac st\right)$ for the sequence of the convergents $s/t$ of a purely periodic continued fraction expansion. Whereas the corresponding sequence of Jacobi symbols is always periodic, it turns out that the sequence of Kronecker symbols may be aperiodic. Our main result describes the period length in the periodic case in terms of the period length of the sequence of Jacobi symbols and gives a necessary and sufficient condition for the occurrence of the aperiodic case.
The work examines the effect of multiple photon emission on the quantum mechanical state of an electron emitting synchrotron radiation and on the intensity of that radiation. Calculations are done with the variant of perturbation theory based on the use of extended coherent states. A general formula is derived for the number of emitted photons, which allows for taking into account their mutual interaction. A model problem is used to demonstrate the absence of the infrared catastrophe in the modified perturbation theory. Finally, the electron density matrix is calculated, and the analysis of this matrix makes it possible to conclude that the degree of the elecron's spatial localization increases with the passage of time if the electron is being accelerated.
We review, in a historical perspective, some results about black hole spacetimes with a regular center. We then see how their properties are realized in a specific solution that recently appeared; in particular we analyze in detail the (necessary) violation of the strong energy condition.
The unexpected rising flux of early-type galaxies at decreasing ultraviolet (UV) wavelengths is a long-standing mystery. One important observational constraint is the correlation between UV-optical colours and Mg2 line strengths found by Burstein et al. (1988). The simplest interpretation of this phenomenon is that the UV strength is related to the Mg line strength. Under this assumption, we expect galaxies with larger Mg gradients to have larger UV colour gradients. By combining UV imaging from GALEX, optical imaging from MDM and SAURON integral-field spectroscopy, we investigate the spatially-resolved relationships between UV colours and stellar population properties of 34 early-type galaxies from the SAURON survey sample. We find that galaxies with old stellar populations show tight correlations between the FUV colours (FUV-V and FUV-NUV) and the Mgb index, H{\beta} index and metallicity [Z/H]. The equivalent correlations for the Fe5015 index, {\alpha}-enhancement [{\alpha}/Fe] and age are present but weaker. We have also derived logarithmic internal radial colour, measured line strength and derived stellar population gradients for each galaxy and again found a strong dependence of the FUV-V and FUV-NUV colour gradients on both the Mg b line strength and the metallicity gradients for galaxies with old stellar populations. In particular, global gradients of Mg b and [Z/H] with respect to the UV colour across galaxies are consistent with their local gradients within galaxies, suggesting that the global correlations also hold locally. From a simple model based on multi-band colour fits of UV upturn and UV-weak galaxies, we have identified a plausible range of parameters that reproduces the observed radial colour profiles. In these models, the centers of elliptical galaxies, where the UV flux is strong, are enhanced in metals by roughly 60% compared to UV-weak regions.
We study the local well-posedness of the Einstein-Yang-Mills equations in constant mean extrinsic curvature spatial harmonic generalized Coulomb gauge (CMCSHGC). In this choice of gauge, the complete Einstein-Yang-Mills equations reduce to a coupled elliptic-hyperbolic system. Utilizing the method developed by Andersson and Moncrief \cite{andersson2003elliptic}, we establish the existence of a unique, local, continuous-in-time solution of this coupled system. This yields an `in time' continuation criteria of the solutions which is to be used in the potential future proof of an improved continuation criteria for this coupled system utilizing Moncrief's light cone estimate technique.
We study InAs nanowire resonators fabricated on sapphire substrate with a local gate configuration. The key advantage of using an insulating sapphire substrate is that it results in a reduced parasitic capacitance thus allowing both wide bandwidth actuation and detection using a network analyzer as well as signal detection at room temperature. Both in-plane and out-of-plane vibrational modes of the nanowire can be driven and the non-linear response of the resonators studied. In addition this technique enables the study of variation of thermal strains due to heating in nanostructures
The color-magnitude relation of early-type galaxies differs slightly but significantly from a pure power-law, curving downwards at low and upwards at large luminosities (Mr>-20.5 and Mr<-22.5). This remains true of the color-size relation, and is even more apparent with stellar mass (M* < 3x10^10 Msun and M* > 2x10^11 Msun). The upwards curvature at the massive end does not appear to be due to stellar population effects. In contrast, the color-sigma relation is well-described by a single power law. Since major dry mergers change neither the colors nor sigma, but they do change masses and sizes, the clear features observed in the scaling relations with M*, but not with sigma > 150 km/s, suggest that M* > 2x10^11 Msun is the scale above which major dry mergers dominate the assembly history. We discuss three models of the merger histories since z ~ 1 which are compatible with our measurements. In all three models, dry mergers are responsible for the flattening of the color-M* relation at M* > 3x10^10 Msun - wet mergers only matter at smaller masses. At M* > 2 x 10^11 Msun, the merger histories in one model are dominated by major rather than minor dry mergers, as suggested by the axis ratio and color gradient trends. In another, although both major and minor mergers occur at the high mass end, the minor mergers contribute primarily to the formation of the ICL, rather than to the mass growth of the central massive galaxy. A final model assumes that the reddest objects were assembled by a mix of major and minor dry mergers.
In this work, a study of the magnetic behavior of the spinel ZnFe2O4 is presented by using the Monte Carlo simulations (MCS). The iron atoms provide the magnetism in this material. In fact, the magnetic spin of moment of the Fe3+ ions is S=5/2. In this context, we propose a Hamiltonian describing and modeling this compound. Firstly, at zero temperature we have studied the ground state phase diagrams of the system in order to find the more stable configurations. On the other hand, for a non-null temperature values, we obtained the results of the Monte Carlo simulations, namely: the magnetizations and the susceptibilities as a function of temperature. The behavior of those physical parameters shows an anti-ferromagnetic behavior with a Neel-temperature of about TN=12 K. This value is found to be in good agreement with the literature. Moreover, the effect of varying the crystal field, the exchange coupling interactions and the external magnetic field is studied and discussed on the behavior of the magnetizations. To complete this study, we presented the magnetic hysteresis loops deducing the antiferromagnetic behavior of the ZnFe2O4 compound.
The main purpose of this survey is to provide an introduction, algebro-topological in nature, to Hirzebuch-type inequalities for plane curve arrangements in the complex projective plane. These inequalities gain more and more interest due to their utility in many combinatorial problems related to point or line arrangements in the plane. We would like to present a summary of the technicalities and also some recent applications, for instance in the context of the Weak Dirac Conjecture. We also advertise some open problems and questions.
We study correlations functions of magnetic vortices $V$ and Polyakov loop $P$ operators in the 2+1 dimensional Georgi-Glashow model in the vicinity of the deconfining phase transition. In this regime the (dimensionally reduced) model is mapped onto a free theory of two massive Majorana fermions. We utilize this fermionic representation to explicitly calculate the expectation values of $V$ and $P$ as well as their correlators. In particular we show that the $VV$ correlator is large, and thus the anomalous breaking of the magnetic $U(1)$ symmetry is order one effect in the near critical region. We also calculate the contribution of magnetic vortices to the entropy and the free energy of the system.
Current approaches for fine-grained recognition do the following: First, recruit experts to annotate a dataset of images, optionally also collecting more structured data in the form of part annotations and bounding boxes. Second, train a model utilizing this data. Toward the goal of solving fine-grained recognition, we introduce an alternative approach, leveraging free, noisy data from the web and simple, generic methods of recognition. This approach has benefits in both performance and scalability. We demonstrate its efficacy on four fine-grained datasets, greatly exceeding existing state of the art without the manual collection of even a single label, and furthermore show first results at scaling to more than 10,000 fine-grained categories. Quantitatively, we achieve top-1 accuracies of 92.3% on CUB-200-2011, 85.4% on Birdsnap, 93.4% on FGVC-Aircraft, and 80.8% on Stanford Dogs without using their annotated training sets. We compare our approach to an active learning approach for expanding fine-grained datasets.
In this study, the direct pair production of the pseudoscalar Higgs boson at a photon-photon collision is analyzed in the context of two Higgs doublet model, taking account the complete one-loop contributions. In order to illustrate the effect of the new physics, four benchmark points scenarios, which are consistent with theoretical and current experimental constraints, are chosen in the type-I of THDM with an exact alignment limit. In these benchmark points, the CP even lightest Higgs boson ($h^0$) have the Standard Model like couplings to the gauge bosons. The effect of individual contributions from each type of one-loop diagrams on the total cross section are examined in detail. The dependence of total cross section on the center-of-mass energy is also presented at the various polarization configurations of the incoming photons. Moreover, the regions $m_{12}^2-\tan\beta$ and $m_A-\tan\beta$ in the parameter space of the THDM are scanned for some fixed values of other parameters. The box-type diagrams make a much larger contribution to the total cross section than the others at high energies. Total cross section can be enhanced by a two factor thanks to opposite polarized photons as well as threshold effects.
The characterization of the stationary states in the spin-Hall effect is discussed within the framework of the phenomenological two spin-channel model. It is shown that two different definitions of the stationary states can be applied in the spin-Hall effect, leading to two different types of state in the bulk: zero transverse spin-current or non-zero pure spin-current. This difference is due to the treatment of the region near the edges, in which electric charge accumulation occurs. The screening equations that describe the accumulation of electric charges due to spin-orbit coupling are derived. The spin-accumulation associated to spin-flip scattering and the spin-Hall accumulation due to spin-orbit coupling are two independent effects if we assume that the screening length is small with respect to the spin-diffusion length. The corresponding transport equations are discussed in terms of the Dyakonov-Perel equations.
Although the spectral lines of hydrogen contain valuable information on the physical properties of a variety of astrophysical plasmas, including the upper solar chromosphere, relatively little is known about their scattering polarization signals whose modification via the Hanle effect may be exploited for magnetic field diagnostics. Here we report on a basic theoretical investigation of the linear polarization produced by scattering processes and the Hanle effect in Ly-a, Ly-b and H-a taking into account multilevel radiative transfer effects in an isothermal stellar atmosphere model, the fine-structure of the hydrogen levels, as well as the impact of collisions with electrons and protons. The main aim of this first paper is to elucidate the physical mechanisms that control the linear polarization in the three lines, as well as its sensitivity to the perturbers density and to the strength and structure of micro-structured and deterministic magnetic fields. To this end, we apply an efficient radiative transfer code we have developed for performing numerical simulations of the Hanle effect in multilevel systems with overlapping line transitions. For low density plasmas such as that of the upper solar chromosphere collisional depolarization is caused mainly by collisional transitions between the fine-structure levels of n=3, so that it is virtually insignificant for Ly-a but important for Ly-b and H-a. We show the impact of the Hanle effect on the three lines taking into account the radiative transfer coupling between the different hydrogen line transitions. For example, we demonstrate that the linear polarization profile of the H-a line is sensitive to the presence of magnetic field gradients in the line core formation region and that in solar-like chromospheres selective absorption of polarization components does not play any significant role on the emergent scattering polarization.
We consider the problem of image-to-video translation, where an input image is translated into an output video containing motions of a single object. Recent methods for such problems typically train transformation networks to generate future frames conditioned on the structure sequence. Parallel work has shown that short high-quality motions can be generated by spatiotemporal generative networks that leverage temporal knowledge from the training data. We combine the benefits of both approaches and propose a two-stage generation framework where videos are generated from structures and then refined by temporal signals. To model motions more efficiently, we train networks to learn residual motion between the current and future frames, which avoids learning motion-irrelevant details. We conduct extensive experiments on two image-to-video translation tasks: facial expression retargeting and human pose forecasting. Superior results over the state-of-the-art methods on both tasks demonstrate the effectiveness of our approach.
Randomness is a fundamental feature in nature and a valuable resource for applications ranging from cryptography and gambling to numerical simulation of physical and biological systems. Random numbers, however, are difficult to characterize mathematically, and their generation must rely on an unpredictable physical process. Inaccuracies in the theoretical modelling of such processes or failures of the devices, possibly due to adversarial attacks, limit the reliability of random number generators in ways that are difficult to control and detect. Here, inspired by earlier work on nonlocality based and device independent quantum information processing, we show that the nonlocal correlations of entangled quantum particles can be used to certify the presence of genuine randomness. It is thereby possible to design of a new type of cryptographically secure random number generator which does not require any assumption on the internal working of the devices. This strong form of randomness generation is impossible classically and possible in quantum systems only if certified by a Bell inequality violation. We carry out a proof-of-concept demonstration of this proposal in a system of two entangled atoms separated by approximately 1 meter. The observed Bell inequality violation, featuring near-perfect detection efficiency, guarantees that 42 new random numbers are generated with 99% confidence. Our results lay the groundwork for future device-independent quantum information experiments and for addressing fundamental issues raised by the intrinsic randomness of quantum theory.
In this paper, we prove that there is no number with the Lehmer property in the sequence of Pell numbers.
We study the space geometry of a rotating disk both from a theoretical and operational approach, in particular we give a precise definition of the space of the disk, which is not clearly defined in the literature. To this end we define an extended 3-space, which we call relative space: it is recognized as the only space having an actual physical meaning from an operational point of view, and it is identified as the 'physical space of the rotating platform'. Then, the geometry of the space of the disk turns out to be non Euclidean, according to the early Einstein's intuition; in particular the Born metric is recovered, in a clear and self consistent context. Furthermore, the relativistic kinematics reveals to be self consistent, and able to solve the Ehrenfest's paradox without any need of dynamical considerations or ad hoc assumptions.
The microscopic theory of interaction between the heavy fermions and the crystal field excitations in Kondo lattices is presented. It is shown that the heavy-fermion spectrum scaled by the Kondo temperature $T_K$ can be modified by the crystal field excitations with the energy $\Delta_{CF}$ provided the inequality $\Delta_{CF}<T_K$ is realized. On the base of general description of excitation spectrum the detailed qualitative and quantitative explanation of anisotropic inelastic neutron scattering spectra and low-temperature specific heat of orthorhombic CeNiSn is given. The theory resolves the apparent contradiction between the metallic conductivity and the gap-wise behavior of thermodynamic properties and spin response of CeNiSn at low temperatures.
The absorption of light by a metal disturbs the electron distribution around the Fermi surface. Here, we calculate the phonon dispersion relations of free-electron-like metal, bcc sodium, with a stepwise electron distribution function by using a model pseudo-potential method. The step can behave as a pseudo-Fermi surface, which produces the singularities at specific wavenumbers in the response function. The singularity gives rise to long-range oscillations in the interatomic potential and results in imaginary phonon frequencies around the N point.
The use of a band offset between the two leads of an electron pump driven by a local oscillating voltage is shown to increase the pump current dramatically. The structure of the electron transmission suggests the existence of dominant inelastic channels which we call pipelines. This permits the formulation of a simple model that gives a physical account of the numerical results for a realistic device. A spectral analysis reveals the pump current to be carried by scattering states with initial energy deep within the Fermi sea and not at its surface, thereby rendering the effect insensitive to temperature. We show this is compatible with the current flowing near the Fermi surface in the leads.
The theory of relativistic {\em location systems} is sketched. An interesting class of these systems is that of relativistic {\em positioning systems,} which consists in sets of four clocks broadcasting their proper time. Among them, the more important ones are the {\em auto-located positioning systems,} in which every clock broadcasts not only its proper time but the proper times that it receives from the other three. At this level, no reference to any exterior system (the Earth surface, for example) and no synchronization are needed. Some properties are presented. In the SYPOR project, such a structure is proposed, eventually anchored to a classical reference system on the Earth surface, as the best relativistic structure for Global Navigation Satellite Systems.
We present spectroscopic observations of the host galaxy and explosion site of the long-duration gamma-ray burst GRB 020819. We determine a metallicity for this host environment of log(O/H) + 12 = 9.0 +/- 0.1, by far the highest metallicity determined for a long-duration GRB to date. We compare the metallicity and other properties of the GRB 020819 host environment to existing observations of long-duration GRB host galaxies, and consider the implications that this metallicity has for our understanding of long-duration GRB progenitor scenarios. We also consider how this unusually high metallicity may relate to the status of GRB 020819 as a "dark" burst, with no detected optical afterglow.
We propose a scheme for preparation of large-scale entangled $GHZ$ states and $W$ states with neutral Rydberg atoms. The scheme mainly depends on Rydberg antiblockade effect, i.e., as the Rydberg-Rydberg-interaction (RRI) strength and the detuning between the atom transition frequency and the classical laser frequency satisfies some certain conditions, the effective Rabi oscillation between the two ground states and the two excitation Rydberg states would be generated. The prominent advantage is that both two-multiparticle $GHZ$ states and two-multiparticle $W$ states can be fused in this model, especially the success probability for fusion of $GHZ$ states can reach unit. In addition, the imperfections induced by the spontaneous emission is also discussed through numerical simulation.
A notion of admissible probability measures $\mu$ on a locally compact Abelian group (LCA-group) $G$ with connected dual group $\hat G=\R^d\times \T^n$ is defined. To such a measure $\mu$, a closed semigroup $\Lambda(\mu)\subseteq (0,\infty)$ can be associated, such that, for $t\in \Lambda(\mu)$, the Fourier transform to the power $t$, $(\hat \mu)^t$, is a characteristic function. We prove that the existence of roots for non admissible probability measures underlies some restrictions, which do not hold in the admissible case. As we show for the example $\Z_2$, in the case of LCA-groups with non connected dual group, there is no canonical definition of the set $\Lambda(\mu)$.
We demonstrate the sensitivity of magnetic energy and helicity computations regarding the quality of the underlying coronal magnetic field model. We apply the method of Wiegelmann & Inhester (2010) to a series of SDO/HMI vector magnetograms, and discuss nonlinear force-free (NLFF) solutions based on two different sets of the free model parameters. The two time series differ from each other concerning their force-free and solenoidal quality. Both force- and divergence-freeness are required for a consistent NLFF solution. Full satisfaction of the solenoidal property is inherent in the definition of relative magnetic helicity in order to insure gauge-independence. We apply two different magnetic helicity computation methods (Thalmann et al. 2011; Valori et al. 2012) to both NLFF time series and find that the output is highly dependent on the level to which the NLFF magnetic fields satisfy the divergence-free condition, with the computed magnetic energy being less sensitive than the relative helicity. Proxies for the non-potentiality and eruptivity derived from both quantities are also shown to depend strongly on the solenoidal property of the NLFF fields. As a reference for future applications, we provide quantitative thresholds for the force- and divergence-freeness, for the assurance of reliable computation of magnetic energy and helicity, and of their related eruptivity proxies.