ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let $k$ be a number field. We study how well can finite sets of $\mathcal O_k$ equidistribute modulo powers of prime ideals, for all prime ideals at the same time. Our main result states that the optimal rate of equidistribution in $\mathcal O_k$ predicted by the local contstraints cannot be achieved unless $k=\mathcal Q$. We deduce that $\mathcal Q$ is the only number field where the ring of integers $\mathcal O_k$ admits a simultaneous $\frak p$-ordering, answering a question of Bhargava. Along the way we establish a non-trivial upper bound on the number of solutions $x\in \mathcal O_k$ of the inequality $|N_{k/\mathcal Q}(x(a-x))|\leq X^2$ where $X$ is a positive real parameter and $a\in\mathcal O_k$ is of norm at least $e^{-B}X$ for a fixed real number $B$. The latter can be translated as an upper bound on the average number of solutions of certain unit equations in $\mathcal O_k$.
The present work is devoted to the investigation of the interaction between vortices (topological defects) and site-impurities (structural defects) in the 2D XY model and its influence on the well-known properties of the pure system. The main goal is a theoretical description of the Berezinskii-Kosterlitz-Thouless (BKT) temperature reduction by quenched non-magnetic impurities, based on the vacancy-vortex interactions and the vortex-pair dissociation mechanism of the transition. The non-magnetic impurity interaction with a system of vortices can be found either from the phenomenological theory of topological defects or from the Villain model. We take both paths and compare the results obtained. Our prediction for the BKT temperature reduction is confirmed by the available Monte Carlo data.
We investigate the environment and line of sight of the H0LiCOW lens B1608+656 using Subaru Suprime-Cam and the Hubble Space Telescope (HST) to perform a weak lensing analysis. We compare three different methods to reconstruct the mass map of the field, i.e. the standard Kaiser-Squires inversion coupled with inpainting and Gaussian or wavelet filtering, and $\tt{Glimpse}$ a method based on sparse regularization of the shear field. We find no substantial difference between the 2D mass reconstructions, but we find that the ground-based data is less sensitive to small-scale structures than the space-based observations. Marginalising over the results obtained with all the reconstruction techniques applied to the two available HST filters F606W and F814W, we estimate the external convergence, $\kappa_{\rm ext}$ at the position of B1608+656 is $\kappa_{\rm ext} = 0.11^{+0.06}_{-0.04}$, where the error bars corresponds respectively to the 16th and 84th quartiles. This result is compatible with previous estimates using the number-counts technique, suggesting that B1608+656 resides in an over-dense line of sight, but with a completely different technique. Using our mass reconstructions, we also compare the convergence at the position of several groups of galaxies in the field of B1608+656 with the mass measurements using various analytical mass profiles, and find that the weak lensing results favor truncated halo models.
In order to elucidate the emission properties of ultraluminous X-ray sources (ULXs) during their power-law (PL) state, we examined long-term X-ray spectral data of IC342 X-1 during its PL state by using our own Suzaku data and the archival data by XMM-Newton, Chandra, and Swift observations. The PL state of this source seems to be classified into two sub-states in terms of the X-ray luminosities in 0.5-10 keV: the low luminosity PL state with 4-6*10^{39} erg/s and the high luminosity one with 1.1-1.4*10^{40} erg/s. During the Suzaku observations which were made in 2010 August and 2011 March, X-1 stayed in the low luminosity PL state. The observed X-ray luminosity (4.9-5.6*10^{39} erg/s) and the spectral shape (photon index = 1.67-1.83) slightly changed between the two observations. Using the Suzaku PIN detector, we for the first time confirmed a PL tail extending up to at least 20 keV with no signatures of a high-energy turnover in both of the Suzaku observations. In contrast, a turnover at about 6 keV was observed during the high luminosity PL state in 2004 and 2005 with XMM-Newton. Importantly, photon indices are similar between the two PL states and so is the Compton y-parameters of y ~ 1, which indicates a similar energy balance (between the corona and the accretion disk) holding in the two PL states despite different electron temperatures. From spectral similarities with recent studies about other ULXs and the Galactic black hole binary GRS1915+105, IC342 X-1 is also likely to be in a state with a supercritical accretion rate, although more sensitive higher energy observations would be necessary to conclude.
The aim of this work is to achieve a formulation of the bosonic string theory in which T-duality appears as a manifest symmetry. Two models exhibiting this property are discussed. The first is based on the stringy extension of the Floreanini-Jackiw Lagrangians for chiral fields and is characterized by the loss of manifest covariance on the world-sheet, recovered on mass-shell. The second model exhibits two-dimensional covariance while doubling a priori the string coordinates in the target space. They are shown to be equivalent.
We search Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) and Wide Field Camera 3 (WFC3) broadband imaging data from the Panchromatic Hubble Andromeda Treasury (PHAT) survey to identify detections of cataloged planetary nebulae (PNe). Of the 711 PNe currently in the literature within the PHAT footprint, we find 467 detected in the broadband. For these 467 we are able to refine their astrometric accuracy from ~0."3 to 0."05. Using the resolution of HST, we are able to show that 152 objects currently in the catalogs are definitively not PNe, and we show that 32 objects thought to be extended in ground-based images are actually point-like and therefore good PN candidates. We also find one PN candidate that is marginally resolved. If this is a PN, it is up to 0.7 pc in diameter. With our new photometric data, we develop a method of measuring the level of excitation in individual PNe by comparing broadband and narrowband imaging and describe the effects of excitation on a PN's photometric signature. Using the photometric properties of the known PNe in the PHAT catalogs, we search for more PN, but do not find any new candidates, suggesting that ground-based emission-line surveys are complete in the PHAT footprint to F475W $\simeq$ 24.
We propose a protocol for measurement of the phonon number distribution of a harmonic oscillator based on selective mapping to a discrete spin-1/2 degree of freedom. We consider a system of a harmonically trapped ion, where a transition between two long lived states can be driven with resolved motional sidebands. The required unitary transforms are generated by amplitude-modulated polychromatic radiation fields, where the time-domain ramps are obtained from numerical optimization by application of the Chopped RAndom Basis (CRAB) algorithm. We provide a detailed analysis of the scaling behavior of the attainable fidelities and required times for the mapping transform with respect to the size of the Hilbert space. As one application we show how the mapping can be employed as a building block for experiments which require measurement of the work distribution of a quantum process.
We investigated the optical properties of epitaxial \textit{n}- and \textit{p}-type ZnO films grown on lattice-matched ScAlMgO$_4$ substrates. Chemical doping yielded a severe inhomogeneity in a statistical distribution of involved charged impurities. Two approaches are adopted to treat the inhomogeneity effects; Monte Carlo simulation technique for the \textit{n}-doped films, and the fluctuation theory for the \textit{p}-ZnO. The broadening of PL band of \textit{n}-ZnO was significantly larger than predicted by theoretical results in which the linewidths of each individual emissions have been determined mainly from the concentration fluctuation of donor-type dopants by the simulation. Moreover, the rather asymmetrical line shape was observed. To explain these features, a vibronic model was developed accounting for contributions from a series of phonon replicas. In case of \textit{p}-type ZnO:N, analysis of excitation-intensity dependence of the peak shift of donor-acceptor luminescence with a fluctuation model has also proven the importance of the inhomogeneity effect of charged impurity distribution, as in the case of ZnO:Ga. We extracted the inhomogeneity in the sample and acceptor activation energy prepared under the various growth conditions. It is shown that the theoretical results are in good agreement with the experimental 5-K time-resolved luminescence for the systems in a fluctuation field. Finally, localized-state distributions have been studied in N-doped ZnO thin films by means of transient photocurrent measurement.
In computational relativity, critical behaviour near the black hole threshold has been studied numerically for several models in the last decade. In this paper we present a spatial Galerkin method, suitable for finding numerical solutions of the Einstein-Dirac equations in spherically symmetric spacetime (in polar/areal coordinates). The method features exact conservation of the total electric charge and allows for a spatial mesh adaption based on physical arclength. Numerical experiments confirm excellent robustness and convergence properties of our approach. Hence, this new algorithm is well suited for studying critical behaviour.
We justify the Villani conjecture on the smoothing effect for measure value solutions to the space homogeneous Boltzmann equation of Maxwellian type cross sections. This is the first rigorous proof of the smoothing effect for any measure value initial data except the single Dirac mass, which gives the optimal description on the regularity of solutions for positive time, caused by the singularity in the cross section. The main new ingredient in the proof is the introduction of a time degenerate coercivity estimate by using the microlocal analysis.
We present the new basis functions to investigate the 't Hooft equation, the lowest order mesonic Light-Front Tamm-Dancoff equation for $\rm SU(N_C)$ gauge theories. We find the wave function can be well approximated by new basis functions and obtain an analytic formula for the mass of the lightest bound state. Its value is consistent with the precedent results.
We discuss the apparent widespread presence of Weak-Line T-Tauri stars (WTTS) among stellar coronal sources detected in the ROSAT All-Sky Survey (RASS), and their relative number with respect to young main-sequence stars in the same samples. The approach taken in most of the current literature for identifying and classifying WTT stars among RASS X-ray sources is based on the usage of low-resolution optical spectra only and on simple, mass-independent thresholds on the equivalent width of the LiI 6707.8 A doublet. We show that this approach is likely to lead to putative WTTS samples which contain a large number of normal, young main-sequence stars masquerading as WTTS sources. Young main-sequence stars are known to be the dominant contributor in stellar X-ray selected samples at the limiting flux levels of the RASS, yet they appear to be very rare in the RASS samples discussed here. We argue that many of the putative WTTS sources are actually mis-classified young main-sequence stars, and that thus there is likely not a true ``WTTS question'' in the RASS samples.
The goal of Science is to understand phenomena and systems in order to predict their development and gain control over them. In the scientific process of knowledge elaboration, a crucial role is played by models which, in the language of quantitative sciences, mean abstract mathematical or algorithmical representations. This short review discusses a few key examples from Physics, taken from dynamical systems theory, biophysics, and statistical mechanics, representing three paradigmatic procedures to build models and predictions from available data. In the case of dynamical systems we show how predictions can be obtained in a virtually model-free framework using the methods of analogues, and we briefly discuss other approaches based on machine learning methods. In cases where the complexity of systems is challenging, like in biophysics, we stress the necessity to include part of the empirical knowledge in the models to gain the minimal amount of realism. Finally, we consider many body systems where many (temporal or spatial) scales are at play and show how to derive from data a dimensional reduction in terms of a Langevin dynamics for their slow components.
Matched filtering is used to search for gravitational waves emitted by inspiralling compact binaries in data from ground-based interferometers. One of the key aspects of the detection process is the deployment of a set of templates, also called a template bank, to cover the astrophysically interesting region of the parameter space. In a companion paper, we described the template-bank algorithm used in the analysis of LIGO data to search for signals from non-spinning binaries made of neutron star and/or stellar-mass black holes; this template bank is based upon physical template families. In this paper, we describe the phenomenological template bank that was used to search for gravitational waves from non-spinning black hole binaries (from stellar mass formation) in the second, third and fourth LIGO science runs. We briefly explain the design of the bank, whose templates are based on a phenomenological detection template family. We show that this template bank gives matches greater than 95% with the physical template families that are expected to be captured by the phenomenological templates.
The Balmer emission originated in the broad line region (BLR) of active galactic nuclei (AGNs) could be either weak and difficult to detect, or even absent, for low luminosity AGNs, as LINERs. Our goals in this paper are threefold. First, we want to explore the AGN-nature of nearby type-1 LINERs. Second, we aim at deriving a reliable interpretation for the different components of emission lines by studying their kinematics and ionization mechanism. Third, we intend to probe the neutral gas in the nuclei of these LINERs. We study the 22 local (z<0.025) type-1 LINERs from the Palomar Survey, on the basis of optical ground- and space-based long-slit spectroscopic observations taken with TWIN/CAHA and ALFOSC/NOT. Kinematics and fluxes of a set of emission lines, from H{\beta} to [S II], and the NaD doublet in absorption have been modelled and measured, after the subtraction of the underlying starlight. We also use ancillary spectroscopic data from HST/STIS. We found that the broad H{\alpha} component is sometimes elusive in our ground-based spectroscopy whereas it is ubiquitous for space-based data. By combining optical diagnostic diagrams, theoretical models (for AGNs, pAGB-stars and shocks) and the weak/strong-[O I] classification, we exclude the pAGBs-stars scenario in favor of the AGN as the dominant mechanism of ionisation in these LINERs, being shocks however relevant. The kinematical properties of the emission lines may indicate the presence of ionized outflows, preferentially seen in [O I]. However, the neutral gas outflows, diagnosed by NaD, would appear to be less frequent.
In this paper, we investigate the local universality of the number of zeros of a random periodic signal of the form $S_n(t)=\sum_{k=1}^n a_k f(k t)$, where $f$ is a $2\pi-$periodic function satisfying weak regularity conditions and where the coefficients $a_k$ are i.i.d. random variables, that are centered with unit variance. In particular, our results hold for continuous piecewise linear functions. We prove that the number of zeros of $S_n(t)$ in a shrinking interval of size $1/n$ converges in law as $n$ goes to infinity to the number of zeros of a Gaussian process whose explicit covariance only depends on the function $f$ and not on the common law of the random coefficients $(a_k)$. As a byproduct, this entails that the point measure of the zeros of $S_n(t)$ converges in law to an explicit limit on the space of locally finite point measures on $\mathbb R$ endowed with the vague topology. The standard tools involving the regularity or even the analyticity of $f$ to establish such kind of universality results are here replaced by some high-dimensional Berry-Esseen bounds recently obtained in [CCK17]. The latter allow us to prove functional CLT's in $C^1$ topology in situations where usual criteria can not be applied due to the lack of regularity.
In this paper, we establish space like strong unique continuation property (sucp) for uniformly parabolic sublinear equations under appropriate structural assumptions. Our main result Theorem 1.1 constitutes the parabolic counterpart of the strong unique continuation result recently established by Ruland in [Ru] for analogous elliptic sublinear equations. Similar to that in [Ru], this is accomplished via a new $L^{2}-L^{2}$ type Carleman estimate for a class of sublinear parabolic operators.
Consumption of magic states promotes the stabilizer model of computation to universal quantum computation. Here, we propose three different classical algorithms for simulating such universal quantum circuits, and characterize them by establishing precise connections with a family of magic monotones. Our first simulator introduces a new class of quasiprobability distributions and connects its runtime to a generalized notion of negativity. We prove that this algorithm has significantly improved exponential scaling compared to all prior quasiprobability simulators for qubits. Our second simulator is a new variant of the stabilizer-rank simulation algorithm, extended to work with mixed states and with significantly improved runtime bounds. Our third simulator trades precision for speed by discarding negative quasiprobabilities. We connect each algorithm's performance to a corresponding magic monotone and, by comprehensively characterizing the monotones, we obtain a precise understanding of the simulation runtime and error bounds. Our analysis reveals a deep connection between all three seemingly unrelated simulation techniques and their associated monotones. For tensor products of single-qubit states, we prove that our monotones are all equal to each other, multiplicative and efficiently computable, allowing us to make clear-cut comparisons of the simulators' performance scaling. Furthermore, our monotones establish several asymptotic and non-asymptotic bounds on state interconversion and distillation rates. Beyond the theory of magic states, our classical simulators can be adapted to other resource theories under certain axioms, which we demonstrate through an explicit application to the theory of quantum coherence.
The new multi-epoch near-infrared VVV survey (VISTA Variables in the Via Lactea) is sampling 562 sq. deg of the Galactic bulge and adjacent regions of the disk. Accurate astrometry established for the region surveyed allows the VVV data to be merged with overlapping surveys (e.g., GLIMPSE, WISE, 2MASS, etc.), thereby enabling the construction of longer baseline spectral energy distributions for astronomical targets. However, in order to maximize use of the VVV data, a set of transformation equations are required to place the VVV JHKs photometry onto the 2MASS system. The impetus for this work is to develop those transformations via a comparison of 2MASS targets in 152 VVV fields sampling the Galactic disk. The transformation coefficients derived exhibit a reliance on variables such as extinction. The transformed data were subsequently employed to establish a mean reddening law of E_{J-H}/E_{H-Ks}=2.13 +/- 0.04, which is the most precise determination to date and merely emphasizes the pertinence of the VVV data for determining such important parameters.
The nature of dark energy remains a profound mystery 20 years after the discovery of cosmic acceleration. A very high number density galaxy redshift survey over a wide area (HD GRS Wide) spanning the redshift range of 0.5<z<4 using the same tracer, carried out using massively parallel wide field multi-object slit spectroscopy from space, will provide definitive dark energy measurements with minimal observational systematics by design. The HD GRS Wide will illuminate the nature of dark energy, and lead to revolutionary advances in particle physics and cosmology. It will also trace the cosmic web of dark matter and provide key insight into large-scale structure in the Universe. The required observational facility can be established as part of the probe portfolio by NASA within the next decade.
The discovery of group IV and V elemental Xene's which exhibit topologically non-trivial characters natively in their honeycomb lattice structure (HLS) has led to extensive efforts in realising analogous behaviour in group VI elemental monolayers. Although; it was theoretically concluded that group VI elemental monolayers cannot exist as HLS but recent experimental evidence suggests otherwise. In this letter we report that, HLS of group VI elemental monolayer (such as, Tellurene) can be realised to be dynamically stable when functionzalised with Oxygen. The functionalization leads to, peculiar orbital filtering effects (OFE) and broken spatial inversion symmetry which gives rise to the non-trivial topological character. The exotic quantum behaviour of this system is characterized by, spin-orbit coupling induced large-gap $\approx$ 0.36 eV with isolated Dirac cone along the edges indicating perspective room temperature spin-transport applications. Further investigations of spin Hall conductivity and the Berry curvatures unravel high conductivity as compared to previously explored Xene's. The non-trivial topological character is quantified in terms of the $\mathbb{Z}_2$ invaraint as $\nu =$ 1 and Chern number $\mathit{C} =$ 1. Also, for practical purposes, we report that, \textit{h}BN/TeO/\textit{h}BN quantum-wells can be strain engineered to realize a sizable non-trivial gap ($\approx$ 0.11 eV). We finally conclude that, functionalization of group VI elemental monolayer with Oxygen gives rise to, exotic quantum properties which are robust against surface oxidation and degradations while providing viable electronic degrees of freedom for spintronic applications.
The orientation, chirality, and dynamics of solar eruptive filaments is a key to understanding the magnetic field of coronal mass ejections (CMEs) and therefore to predicting the geoeffectiveness of CMEs arriving at Earth. However, confusion and contention remain over the relationship between the filament chirality, magnetic helicity, and sense of rotation during eruption. To resolve the ambiguity in observations, in this paper, we used stereoscopic observations to determine the rotation direction of filament apex and the method proposed by Chen et al. (2014) to determine the filament chirality. Our sample of 12 eruptive active-region filaments establishes a strong one-to-one relationship, i.e., during the eruption, sinistral/dextral filaments (located in the southern/northern hemisphere) rotate clockwise/counterclockwise when viewed from above, and corroborates a weak hemispheric preference, i.e., a filament and related sigmoid both exhibit a forward (reverse) S shape in the southern (northern) hemisphere, which suggests that the sigmoidal filament is associated with a low-lying magnetic flux rope with its axis dipped in the middle. As a result of rotation, the projected S shape of a filament is anticipated to be reversed during eruption.