ShantanuT01/DACTYL-Pretraining huggingface dataset:
Deep inelastic scattering data on F2 structure function from various fixed-target experiments were analyzed in the non-singlet approximation with a next-to-next-to-leading-order accuracy. The study of high statistics deep inelastic scattering data provided by BCDMS, SLAC, NMC and BFP collaborations was carried out separately for the first one and the rest, followed by a combined analysis done as well. For the coupling constant the following value \alpha_s(M_Z^2) = 0.1167 +/- 0.0021 (total exp.error) +0.0056/-0.0036(theor) was found, which in this approximation turns out to be slightly less than that obtained at the next-to-leading-order, as was generally anticipated. Ditto the theoretical uncertainties reduced with respect to those obtained in the case of the next-to-leading-order analysis thus confirming earlier observations.
We address a question posed by Ono, prove a general result for powers of an arbitrary prime, and provide an explanation for the appearance of higher congruence moduli for certain small primes. One of our results coincides with a recent result of Edixhoven, and we hope that the comparison of the methods, which are entirely different, may reveal a connection between the p-adic geometry and the arithmetic of half-integral weight Hecke operators.
The rhodium doping in the LaCo$_{1-x}$Rh$_{x}$O$_3$ perovskite series ($x=0.02-0.5$) has been studied by X-ray diffraction, electric transport and magnetization measurements, complemented by electronic structure GGA+U calculations in supercell for different concentration regimes. No charge transfer between Co$^{3+}$ and Rh$^{3+}$ is evidenced. The diamagnetic ground state of LaCoO$_3$, based on Co$^{3+}$ in low-spin (LS) state, is disturbed even by a small doping of Rh. The driving force is the elastic energy connected with incorporation of a large Rh$^{3+}$ cation into the matrix of small LS Co$^{3+}$ cations, which is relaxed by formation of large Co$^{3+}$ in high-spin (HS) state in the next-nearest sites to the inserted Rh atom. With increasing temperature, the population of Co$^{3+}$ in HS state increases through thermal excitation, and a saturated phase is obtained close to room temperature, consisting of a nearest-neighbor correlation of small (LS Co$^{3+}$) and large (HS Co$^{3+}$ and LS Rh$^{3+}$) cations in a kind of double perovskite structure. The stabilizing role of elastic and electronic energy contributions is demonstrated in supercell calculations for dilute Rh concentration compared to other dopants with various trivalent ionic radius.
The revolution of helio- and asteroseismology provides access to the detailed properties of stellar interiors by studying the star's oscillation modes. Among them, gravity (g) modes are formed by constructive interferences between progressive internal gravity waves (IGWs), propagating in stellar radiative zones. Our new 3D nonlinear simulations of the interior of a solar-like star allows us to study the excitation, propagation, and dissipation of these waves. The aim of this article is to clarify our understanding of the behavior of IGWs in a 3D radiative zone and to provide a clear overview of their properties. We use a method of frequency filtering that reveals the path of {individual} gravity waves of different frequencies in the radiative zone. We are able to identify the region of propagation of different waves in 2D and 3D, to compare them to the linear raytracing theory and to distinguish between propagative and standing waves (g modes). We also show that the energy carried by waves is distributed in different planes in the sphere, depending on their azimuthal wave number. We are able to isolate individual IGWs from a complex spectrum and to study their propagation in space and time. In particular, we highlight in this paper the necessity of studying the propagation of waves in 3D spherical geometry, since the distribution of their energy is not equipartitioned in the sphere.
Quantum entanglement and coherence are two fundamental resources for quantum information processing. Recent results clearly demonstrate their relevance in quantum technological tasks, including quantum communication and quantum algorithms. In this Letter we study the role of quantum coherence for quantum state redistribution, a fundamental task where two parties aim to relocate a quantum particle by using a limited amount of quantum communication and shared entanglement. We provide general bounds for the resource rates required for this process, and show that these bounds are tight under additional reasonable constraints, including the situation where the receiving party cannot use local coherence. While entanglement cannot be directly converted into local coherence in our setting, we show that entanglement is still useful for local coherence creation if an additional quantum channel is provided, and the optimal protocol for local coherence creation for any given amount of quantum communication and shared entanglement is presented. We also discuss possible extensions of our methods to other scenarios where the receiving party is limited by local constraints, including theories of thermodynamics and asymmetry.
In view of persisting misunderstanding about the determination of the pion-nucleon coupling constants in the Nijmegen multienergy partial-wave analyses of pp, np, and pbar-p scattering data, we present additional information which may clarify several points of discussion. We comment on several recent papers addressing the issue of the pion-nucleon coupling constant and criticizing the Nijmegen analyses.
We present a novel class of models for Type Ia supernova time-evolving spectral energy distributions (SED) and absolute magnitudes: they are each modeled as stochastic functions described by Gaussian processes. The values of the SED and absolute magnitudes are defined through well-defined regression prescriptions, so that data directly inform the models. As a proof of concept, we implement a model for synthetic photometry built from the spectrophotometric time series from the Nearby Supernova Factory. Absolute magnitudes at peak $B$ brightness are calibrated to 0.13 mag in the $g$-band and to as low as 0.09 mag in the $z=0.25$ blueshifted $i$-band, where the dispersion includes contributions from measurement uncertainties and peculiar velocities. The methodology can be applied to spectrophotometric time series of supernovae that span a range of redshifts to simultaneously standardize supernovae together with fitting cosmological parameters.
Spiral arms are common features in low-redshift disc galaxies, and are prominent sites of star-formation and dust obscuration. However, spiral structure can take many forms: from galaxies displaying two strong `grand design' arms, to those with many `flocculent' arms. We investigate how these different arm types are related to a galaxy's star-formation and gas properties by making use of visual spiral arm number measurements from Galaxy Zoo 2. We combine UV and mid-IR photometry from GALEX and WISE to measure the rates and relative fractions of obscured and unobscured star formation in a sample of low-redshift SDSS spirals. Total star formation rate has little dependence on spiral arm multiplicity, but two-armed spirals convert their gas to stars more efficiently. We find significant differences in the fraction of obscured star-formation: an additional $\sim 10$ per cent of star-formation in two-armed galaxies is identified via mid-IR dust emission, compared to that in many-armed galaxies. The latter are also significantly offset below the IRX-$\beta$ relation for low-redshift star-forming galaxies. We present several explanations for these differences versus arm number: variations in the spatial distribution, sizes or clearing timescales of star-forming regions (i.e., molecular clouds), or contrasting recent star-formation histories.
We present new molecular gas maps of NGC5195 (alternatively known as M51b) from the Combined Array for Research in Millimeter Astronomy (CARMA), including 12CO(1-0), 13CO(1-0), CN(1-0), and CS(2-1). NGC5195 has also been detected in 3mm continuum. NGC5195 has a 12CO/13CO ratio consistent with normal star-forming galaxies. The CN(1-0) intensity is higher than is seen in an average star-forming galaxy, possibly enhanced in the diffuse photo-dissociation regions. Stellar template fitting of the nuclear spectrum of NGC5195 shows two stellar populations: an 80% mass fraction of old (>10Gyr) and a 20% mass fraction of intermediate-aged (~1Gyr) stellar populations, providing a constraint on the timescale over which NGC5195 experienced enhanced star formation during its interaction with M51a. The average molecular gas depletion timescale in NGC5195 is: tdep=3.08Gyr, a factor of ~2 larger than the depletion timescales in nearby star-forming galaxies, but consistent with the depletion seen in CO-detected early-type galaxies. While the radio continuum emission at centimeter and millimeter wavelengths is present in the vicinity of the nucleus of NGC5195, we find it is most likely associated with nuclear star formation rather than a radio-loud AGN. Thus, despite having a substantial interaction with M51a ~1/2Gyr ago, the molecular gas in NGC5195 has resettled and is forming stars at an efficiency consistent with settled early-type galaxies at the present time.
We report on the discovery of a coherent periodicity in the B light curve of the symbiotic star BF Cyg. The signal was detected in some sections of the light curve of the star recorded in the year 2003 as double hump periodic variations with an amplitude of ~7 mmag.   In the year 2004 the signal was also present in only a subsection of the light curve. In that year, the system was about twice as bright and the amplitude of the oscillations was about half of what it was in 2003. In 2004 the cycle structure was of a single hump, the phase of which coincided with the phase of one of the humps in the 2003 cycle. No periodic signal was detected in a third, short series of observations performed in the year 2007, when the star was three magnitudes brighter than in 2003.   We interpret the periodicity as the spin period of the white dwarf component of this interacting binary system. We suggest that the signal in 2003 originated in two hot spots on or near the surface of the white dwarf, most likely around the two antipodes of an oblique dipole magnetic field of this star. Magnetic field lines funneled accreted matter from the wind of the cool component to the pole areas, where the falling material created the hot spots. This process is apparently intermittent in its nature. In 2004, the activity near only one pole was enhanced enough to raise the signal above the threshold of our detection ability.
We present an empirical-yet-rigorous approach for solving a wide class of functional equations, thereby automating many results that previously required considerable human ingenuity and human labor.
So far magnetic domain walls in one-dimensional structures have been described theoretically only in the cases of flat strips, or cylindrical structures with a compact cross-section, either square or disk. Here we describe an extended phase diagram unifying the two pictures, extensively covering the (width,thickness) space. It is derived on the basis of symmetry and phase-transition arguments, and micromagnetic simulations. A simple classification of all domain walls in two varieties is proposed on the basis of their topology: either with a combined transverse/vortex character, or of the Bloch-point type. The exact arrangement of magnetization within each variety results mostly from the need to decrease dipolar energy, giving rise to asymmetric and curling structures. Numerical evaluators are introduced to quantify curling, and scaling laws are derived analytically for some of the iso-energy lines of the phase diagram.
The 'Internal Linear Combination' (ILC) component separation method has been extensively used to extract a single component, the CMB, from the WMAP multifrequency data. We generalise the ILC approach for separating other millimetre astrophysical emissions. We construct in particular a multidimensional ILC filter, which can be used, for instance, to estimate the diffuse emission of a complex component originating from multiple correlated emissions, such as the total emission of the Galactic interstellar medium. The performance of such generalised ILC methods, implemented on a needlet frame, is tested on simulations of Planck mission observations, for which we successfully reconstruct a low noise estimate of emission from astrophysical foregrounds with vanishing CMB and SZ contamination.
The Keck Interferometer Nuller (KIN) was used to survey 25 nearby main sequence stars in the mid-infrared, in order to assess the prevalence of warm circumstellar (exozodiacal) dust around nearby solar-type stars. The KIN measures circumstellar emission by spatially blocking the star but transmitting the circumstellar flux in a region typically 0.1 - 4 AU from the star. We find one significant detection (eta Crv), two marginal detections (gamma Oph and alpha Aql), and 22 clear non-detections. Using a model of our own Solar System's zodiacal cloud, scaled to the luminosity of each target star, we estimate the equivalent number of target zodis needed to match our observations. Our three zodi detections are eta Crv (1250 +/- 260), gamma Oph (200 +/- 80) and alpha Aql (600 +/- 200), where the uncertainties are 1-sigma. The 22 non-detected targets have an ensemble weighted average consistent with zero, with an average individual uncertainty of 160 zodis (1-sigma). These measurements represent the best limits to date on exozodi levels for a sample of nearby main sequence stars. A statistical analysis of the population of 23 stars not previously known to contain circumstellar dust (excluding eta Crv and gamma Oph) suggests that, if the measurement errors are uncorrelated (for which we provide evidence) and if these 23 stars are representative of a single class with respect to the level of exozodi brightness, the mean exozodi level for the class is <150 zodis (3-sigma upper-limit, corresponding to 99% confidence under the additional assumption that the measurement errors are Gaussian). We also demonstrate that this conclusion is largely independent of the shape and mean level of the (unknown) true underlying exozodi distribution.
Spekkens' toy theory is a non-contextual hidden variable model with an epistemic restriction, a constraint on what the observer can know about the reality. It has been shown in [3] that for qudits of odd dimensions it is operationally equivalent to stabiliser quantum mechanics by making use of Gross' theory of discrete Wigner functions. This result does not hold in the case of qubits, because of the unavoidable negativity of any Wigner function representation of qubit stabiliser quantum mechanics. In this work we define and characterise the subtheories of Spekkens' theory that are operationally equivalent to subtheories of stabiliser quantum mechanics. We use these Spekkens' subtheories as a unifying framework for the known examples of state-injection schemes where contextuality is an injected resource to reach universal quantum computation. In addition, we prove that, in the case of qubits, stabiliser quantum mechanics can be reduced to a Spekkens' subtheory in the sense that all its objects that do not belong to the Spekkens' subtheory, namely non-covariant Clifford gates, can be injected. This shows that within Spekkens' subtheories we possess the toolbox to perform state-injection of every object outside of them and it suggests that there is no need to use bigger subtheories to reach universal quantum computation via state-injection. We conclude with a novel scheme of computation suggested by our approach which is based on the injection of CCZ states and we also relate different proofs of contextuality to different state injections of non-covariant gates.
New results towards the Duffin-Schaeffer conjecture, which is a fundamental unsolved problem in metric number theory, have been established recently assuming extra divergence. Given a non-negative function $\psi: \mathbb{N}\to\mathbb{R}$ we denote by $W(\psi)$ the set of all $x\in\mathbb{R}$ such that $|nx-a|<\psi(n)$ for infinitely many $a,n$. Analogously, denote $W'(\psi)$ if we additionally require $a,n$ to be coprime. Aistleitner et al. [1] proved that $W'(\psi)$ is of full Lebesgue measure if there exist an $\varepsilon>0$ such that $\sum_{n=2}^\infty\psi(n)\varphi(n)/(n(\log n)^\varepsilon)=\infty$. This result seems to be the best one can expect from the method used. Assuming the extra divergence $\sum_{n=2}^\infty\psi(n)/(\log n)^\varepsilon=\infty$ we prove that $W(\psi)$ is of full measure. This could also be deduced from the result in [1], but we believe that our proof is of independent interest, since its method is totally different from the one in [1]. As a further application of our method, we prove that a variant of Khintchine's theorem is true without monotonicity, subject to an additional condition on the set of divisors of the support of $\psi$.
Let X be a quasiprojective smooth surface defined over an algebraically closed field of positive characteristic. We show that if X is Frobenius split then so is the Hilbert scheme Hilb^n(X) of n points in X. In particular, we get the higher cohomology vanishing for ample line bundles on Hilb^n(X) when X is projective and Frobenius split.
The major challenges to fabricate quantum processors and future nano solid state devices are material modification techniques with nanometre resolution and suppression of statistical fluctuations of dopants or qubit carriers. Based on a segmented ion trap with mK laser cooled ions we have realized a deterministic single ion source which could operate with a huge range of sympathetically cooled ion species, isotopes or ionic molecules. We have deterministically extracted a predetermined number of ions on demand and have measured a longitudinal velocity uncertainty of 6.3m/s and a spatial beam divergence of 0.6 mrad. We show in numerical simulations that if the ions are cooled to the motional ground state (Heisenberg limit) nanometre spatial resolution can be achieved.
It is shown that the models recently proposed by Meyer, Kent and Clifton (MKC) exhibit a novel kind of contextuality, which we term existential contextuality. In this phenomenon it is not simply the pre-existing value but the actual existence of an observable which is context dependent. This result confirms the point made elsewhere, that the MKC models do not, as the authors claim, ``nullify'' the Kochen-Specker theorem. It may also be of some independent interest.
In order to test the Vibration-Transit (V-T) theory of liquid dynamics, ab initio density functional theory (DFT) calculations of thermodynamic properties of Na and Cu are performed and compared with experimental data. The calculations are done for the crystal at T = 0 and T_m, and for the liquid at T_m. The key theoretical quantities for crystal and liquid are the structural potential and the dynamical matrix, both as function of volume. The theoretical equations are presented, as well as details of the DFT computations. The properties compared with experiment are the equilibrium volume, the isothermal bulk modulus, the internal energy and the entropy. The agreement of theory with experiment is uniformly good. Our primary conclusion is that the application of DFT to V-T theory is feasible, and the resulting liquid calculations achieve the same level of accuracy as does ab initio lattice dynamics for crystals. Moreover, given the well established reliability of DFT, the present results provide a significant confirmation of V-T theory itself.
Coalescence of two massive black holes is the strongest and most promising source for LISA. In fact, gravitational signal from the end of inspiral and merger will be detectable throughout the Universe. In this article we describe the first step in the two-step hierarchical search for gravitational wave signal from the inspiraling massive BH binaries. It is based on the routinely used in the ground base gravitational wave astronomy method of filtering the data through the bank of templates. However we use a novel Monte-Carlo based (stochastic) method to lay a grid in the parameter space, and we use the likelihood maximized analytically over some parameters, known as F-statistic, as a detection statistic. We build a coarse template bank to detect gravitational wave signals and to make preliminary parameter estimation. The best candidates will be followed up using Metropolis-Hasting stochastic search to refine the parameter estimation. We demonstrate the performance of the method by applying it to the Mock LISA data challenge 1B (training data set).
We comment on Tabesh Qureshi, "Understanding Popper's Experiment," AJP 73, 541 (June 2005), in particular on the implications of its section IV. We show, in the situation envisaged by Popper, that analysis solely with conventional non-relativistic quantum mechanics suffices to exclude the possibility of superluminal communication.
We consider a thin elastic sheet in the shape of a disk that is clamped at its boundary such that the displacement and the deformation gradient coincide with a conical deformation with no stretching there. We define the free elastic energy as a variation of the von K\'arm\'an energy, that penalizes bending energy in $L^p$ with $p\in (2,\frac83)$ (instead of, as usual, $p=2$). We prove ansatz free upper and lower bounds for the elastic energy that scale like $h^{p/(p-1)}$, where $h$ is the thickness of the sheet.
In this paper, we study the implications of the modular $A^{}_4$ flavor symmetry in constructing a supersymmetric minimal type-(I+II) seesaw model, in which only one right-handed neutrino and two Higgs triplets are introduced to account for the tiny neutrino masses, flavor mixing and CP violation. The right-handed neutrino as well as the Higgs triplets in this model are assigned into the trivial one-dimensional irreducible representation of the modular group $A^{}_{4}$. We show that the individual contributions to the neutrino masses from the right-handed neutrino and the Higgs triplet are comparable. We also find that the neutrino mass matrix can possess an approximate $\mu-\tau$ reflection symmetry for some specific values of free model parameters. Moreover, our model predicts relatively large masses of three light neutrinos, thus can be easily tested in future neutrino experiments.
Let $(\varepsilon_{t})_{t>0}$ be a sequence of independent real random vectors of $p$-dimension and let $X_T=\sum_{t=s+1}^{s+T}\varepsilon_t\varepsilon^T_{t-s}/T$ be the lag-$s$ ($s$ is a fixed positive integer) auto-covariance matrix of $\varepsilon_t$. This paper investigates the limiting behavior of the singular values of $X_T$ under the so-called {\em ultra-dimensional regime} where $p\to\infty$ and $T\to\infty$ in a related way such that $p/T\to 0$. First, we show that the singular value distribution of $X_T$ after a suitable normalization converges to a nonrandom limit $G$ (quarter law) under the forth-moment condition. Second, we establish the convergence of its largest singular value to the right edge of $G$. Both results are derived using the moment method.
We provide a fractional counterpart of the classical results by Schwarz and Malmheden on harmonic functions. From that we obtain a representation formula for $s$-harmonic functions as a linear superposition of weighted classical harmonic functions which also entails a new proof of the fractional Harnack inequality. This proof also leads to optimal constants for the fractional Harnack inequality in the ball.