ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the discrete logarithm problem for the multiplicative group and for elliptic curves over a finite field by using a lifting of the corresponding object to an algebraic number field and global duality. We introduce the \textit{signature} of a Dirichlet character (in the multiplicative group case) or principal homogeneous space (in the elliptic curve case), which is a measure of the ramification at certain places. We then develop \textit{signature calculus}, which generalizes and refines the index calculus method. Finally, we show the random polynomial time equivalence for these two cases between the problem of computing signatures and the discrete logarithm problem.
We develop analytical tools and numerical methods for time evolving the total density matrix of the finite-size Anderson model. The model is composed of two finite metal grains, each prepared in canonical states of differing chemical potential and connected through a single electronic level (quantum dot or impurity). Coulomb interactions are either excluded all together, or allowed on the dot only. We extend this basic model to emulate decoherring and inelastic scattering processes for the dot electrons with the probe technique. Three methods, originally developed to treat impurity dynamics, are augmented to yield global system dynamics: the quantum Langevin equation method, the well known fermionic trace formula, and an iterative path integral approach. The latter accommodates interactions on the dot in a numerically exact fashion. We apply the developed techniques to two open topics in nonequilibrium many-body physics: (i) We explore the role of many-body electron-electron repulsion effects on the dynamics of the system. Results, obtained using exact path integral simulations, are compared to mean-field quantum Langevin equation predictions. (ii) We analyze aspects of quantum equilibration and thermalization in large quantum systems using the probe technique, mimicking elastic-dephasing effects and inelastic interactions on the dot. Here, unitary simulations based on the fermionic trace formula are accompanied by quantum Langevin equation calculations.
Inhomogeneous fluids exhibit physical properties that are neither uniform nor isotropic. The pressure tensor is a case in point, key to the mechanical description of the interfacial region. Kirkwood and Buff, and later Irving and Kirkwood, obtained a formal treatment based on the analysis of the pressure across a planar surface [J.G. Kirkwood and F.P. Buff, J. Chem. Phys., 17(3), (1949), J.H. Irving and J.G. Kirkwood, J. Chem. Phys. 18, 817 (1950)]. We propose a generalisation of Irving and Kirkwood's argument to fluctuating, non-planar surfaces and obtain an expression for the pressure tensor that is not smeared by thermal fluctuations at the molecular scale and corresponding capillary waves [F.P. Buff, R.A. Lovett, and F.H. Stillinger, Jr., Phys. Rev. Lett. 15, 621 (1965)]. We observe the emergence of surface tension, defined as an excess tangential stress, acting exactly across the dividing surface at the sharpest molecular resolution. The new statistical mechanical expressions extend current treatments to fluctuating inhomogeneous systems far from equilibrium.
The bulge represents the best compromise between old and massive Galactic component, and as such its study is a valuable opportunity to understand how the bulk of the Milky Way formed and evolved. In addition, being the only bulge in which we can individually resolve stars in all evolutionary sequences, the properties of its stellar content provide crucial insights on the formation of bulges at large. We aim at providing a detailed and comprehensive census of the Milky Way bulge stellar populations by producing deep and accurate photometric catalogs of the inner ~300 sqdeg of the Galaxy. We perform DAOPHOT/ALLFRAME PSF-fitting photometry of multi-epochs J and Ks images provided by the VVV survey to obtain deep photometric catalogs. Artificial star experiments have been conducted on all images to properly assess the completeness and the accuracy of the photometric measurements. We present a photometric database containing nearly 600 million stars across the bulge area surveyed by the VVV. Through the comparison of derived color-magnitude diagrams of selected fields representative of different levels of extinction and crowding, we show the quality, completeness and depth of the new catalogs. With the exception of the fields located along the plane, this new photometry samples stars down to ~1-2 mag below the MS-TO with unprecedented accuracy. To demonstrate the tremendous potential inherent to this new dataset, we give few examples of possible applications such as: i) star counts studies through the dataset completeness map; ii) surface brightness map; and iii) cross-correlation with Gaia DR2. The database presented here represents an invaluable collection for the whole community, and we encourage its exploitation. The photometric catalogs including completeness information are publicly available through the ESO Science Archive.
Systematic properties of the first excited state are presented for various ring sizes and spin quantum numbers which are only partly covered by the theorem of Lieb, Schultz and Mattis. For odd ring sizes the first excited energy eigenvalue shows unexpected degeneracy and related shift quantum numbers. As a byproduct the ground state energy as well as the energy of the first excited state of infinite chains are calculated by extrapolating the properties of only a few, finite, antiferromagnetically coupled Heisenberg rings using the powerful Levin sequence acceleration method.
The elastic leptoproduction of $\phi$ measured by the H1 collaboration at HERA is described by a perturbative QCD model, based on open $s\bar{s}$ production and parton hadron duality, proposed by Martin et al. We observe that both the total cross section and the ratio of the longitudinal and transverse cross sections are well reproduced with an effective strange-quark mass $m_s \sim 320- 380 $ MeV for various gluon distribution functions. Possible connection of the effective mass and the momentum dependent dynamical mass associated with dynamical breaking of chiral symmetry is also discussed.
We present a high quality CMD for a 36'x 36' field located 8 degrees (7 kpc) from the LMC center, as well as a precise determination of the LMC surface brightness derived from the resolved stellar population out to this large galactocentric radius. This deep CMD shows for the first time the detailed age distribution at this position, where the surface brightness is V=26.5 mag/sq". At a radius R=474' the main sequence is well populated from the oldest turnoff at I=21.5 to the 2.5 Gyr turnoff at I=19.5. Beyond this radius, a relatively strong gradient in the density of stars with ages in the 2.5-4 Gyr range is apparent. There are some stars brighter and bluer than the main population, quite uniformly distributed over the whole area surveyed, which are well matched by a 1.5 Gyr isochrone and may be indicative of a relatively recent star formation, or merger, event. The surface brightness profile of the LMC remains exponential to this large galactocentric radius and shows no evidence of disk truncation. Combining the information on surface brightness and stellar population we conclude that the LMC disk extends (and dominates over a possible stellar halo) out to a distance of at least 7 kpc. These results confirm that the absence of blue stars in the relatively shallow off-center CMDs of dIrr galaxies is not necessarily evidence for an exclusively old stellar population resembling the halo of the Milky Way.
The time behaviour of the radial abundance gradients in the galactic disk is investigated on the basis of four different samples of planetary nebulae, comprising both smaller, homogeneous sets of data, and larger, albeit non-homogeneous samples. Four different chemical elements are considered, namely, oxygen, sulphur, argon and neon. Our analysis support our earlier conclusions that, on the average, the radial abundance gradients have flattened out in the last 6 to 8 Gyr.
We study the reconstruction of the source function in space-time directly from the measured HBT correlation function using the Maximum Entropy Principle. We find that the problem is ill-defined without at least one additional theoretical constraint as input. Using the requirement of a finite source lifetime for the latter we find a new Gaussian parametrization of the source function directly in terms of the measured HBT radius parameters and its lifetime, where the latter is a free parameter which is not directly measurable by HBT. We discuss the implications of our results for the remaining freedom in building source models consistent with a given set of measured HBT radius parameters.
The Euler buckling theorem states that the buckling critical strain is an inverse square function of the length for a thin plate in the static compression process. However, the suitability of this theorem in the dynamical process is unclear, so we perform molecular dynamics simulations to examine the applicability of the Euler buckling theorem in case of a fast compression of the single-layer MoS2. We find that the Euler buckling theorem is not applicable in such dynamical process, as the buckling critical strain becomes a length-independent constant in the buckled system with many ripples. However, the Euler buckling theorem can be resumed in this dynamical process after restricting the theorem to an individual ripple in the buckled structure.
The room temperature structure of aluminum, copper and gold infinite nanowires is studied. The molecular dynamics simulation method and the same type of the embedded atom potentials made by Voter and coworkers are used. It was found that multi-shelled and various filled metallic nanowires exist depending on the metal and the initial configuration. The results were compared with previous simulations for gold nanowires using different type of the potential.
We consider an arbitrary continuous-variable three-party Gaussian quantum state which is used to perform quantum teleportation of a pure Gaussian state between two of the parties (Alice and Bob). In turn, the third party (Charlie) can condition the process by means of local operations and classical communication. We find the best measurement that Charlie can implement on his own mode that preserves the Gaussian character of the three-mode state and optimizes the teleportation fidelity between Alice and Bob.
We report the detection of H2 in a zabs= 0.0963 Damped Lyman-{\alpha} (DLA) system towards zem = 0.4716 QSO J1619+3342. This DLA has log N(H I) = 20.55 (0.10), 18.13 < log N(H2) < 18.40, [S/H] = -0.62 (0.13), [Fe/S] = -1.00 (0.17) and the molecular fraction -2.11 < log f(H2) < -1.85. The inferred gas kinetic temperature using the rotational level population is in the range 95 - 132 K. We do not detect C I or C II* absorption from this system. Using R- and V-band deep images we identify a sub-L* galaxy at an impact parameter of 14 kpc from the line of sight, having consistent photometric redshift, as a possible host for the absorber. We use the photoionization code CLOUDY to get the physical conditions in the H2 component using the observational constrains from H2, C I, C II* and Mg I. All the observations can be consistently explained if one or more of the following is true: (i) Carbon is underabundant by more than 0.6 dex as seen in halo stars with Z ~ 0.1 Z_sun, (ii) H I associated with H2 component is less than 50% of the H I measured along the line of sight and (iii) the H2 formation rate on the dust grains is at least a factor two higher than what is typically used in analytic calculations for Milky Way interstellar medium. Even when these are satisfied, the gas kinetic temperature in the models are much lower than what is inferred from the ortho-to-para ratio of the molecular hydrogen. Alternatively the high kinetic temperature could be a consequence of contribution to the gas heating from non-radiative heating processes seen in hydrodynamical simulations.
The power of quantum computers relies on the capability of their components to maintain faithfully and process accurately quantum information. Since this property eludes classical certification methods, fundamentally new protocols are required to guarantee that elementary components are suitable for quantum computation. These protocols must be device-independent, that is, they cannot rely on a particular physical description of the actual implementation if one is to qualify a block for all possible usages. Bell's theorem has been proposed to certify, in a device-independent way, blocks either producing or measuring quantum states. In this manuscript, we provide the missing piece: a method based on Bell's theorem to certify coherent operations such as storage, processing and transfer of quantum information. This completes the set of tools needed to certify all building blocks of a quantum computer. Our method is robust to experimental imperfections, and so can be readily used to certify that today's quantum devices are qualified for usage in future quantum computers.
We examine the gas and stellar metallicities in a sample of HII galaxies from the Sloan Digital Sky Survey, which possibly contains the largest homogeneous sample of HII galaxy spectra to date. We eliminated all spectra with an insufficient signal-to-noise ratio, without strong emission lines, and without the [OII] lambda3727 {\AA} line, which is necessary for the determination of the gas metallicity. This excludes galaxies with redshift <~ 0.033. Our final sample contains ~700 spectra of HII galaxies. Through emission line strength calibrations and a detailed stellar population analysis employing evolutionary stellar synthesis methods, which we already used in previous works, we determined the metallicities of both the gas and the stellar content of these galaxies. We find that in HII galaxies up to stellar masses of 5\cdot10^9 M_sol, enrichment mechanisms do not vary with galactic mass, being the same for low- and high-mass galaxies on average. They do seem to present a greater variety at the high-mass end, though, indicating a more complex assembly history for high-mass galaxies. In around 23 per cent of our HII galaxies we find a metallicity decrease over the last few Gyr. Our results favour galaxy evolution models featuring constantly infalling low-metallicity clouds that retain part of the galactic winds. Above 5\cdot10^9 M_sol stellar mass, the retention of high metallicity gas by the galaxies' gravitational potential dominates.
We investigate, using density functional theory, how the interaction between the ferroelectric polarization and the chemical structure of the (001) surfaces of bismuth ferrite influences the surface properties and reactivity of this material. A precise understanding ofthe surface behavior of ferroelectrics is necessary for their use in surface science applications such as catalysis as well as for their incorporation in microelectronic devices. Using the (001) surface of bismuth ferrite as a model system we show that the most energetically favoured surface geometries are combinations of surface termination and polarization direction that lead to uncharged, stable surfaces. On the unfavorable charged surfaces, we explore the compensation mechanisms of surface charges provided by the introduction of point defects and adsorbates, such as water. Finally, we propose that the special surface properties of bismuth ferrite (001) could be used to produce an effective water splitting cycle through cyclic polarization switching.
Scaling laws that describe the structure of river networks are shown to follow from three simple assumptions. These assumptions are: (1) river networks are structurally self-similar, (2) single channels are self-affine, and (3) overland flow into channels occurs over a characteristic distance (drainage density is uniform). We obtain a complete set of scaling relations connecting the exponents of these scaling laws and find that only two of these exponents are independent. We further demonstrate that the two predominant descriptions of network structure (Tokunaga's law and Horton's laws) are equivalent in the case of landscapes with uniform drainage density. The results are tested with data from both real landscapes and a special class of random networks.
We construct supersymmetric (SUSY) generalized MIC-Kepler system and show that the systems with half integral Dirac quantization condition \mu= \pm{1/2}, \pm{3/2}, \pm{5/2},..... belong to a SUSY family (hierarchy of Hamiltonian) with same spectrum between the respective partner Hamiltonians except for the ground state. Similarly, the systems with integral Dirac quantization condition \mu =\pm 1,\pm 2, \pm 3,...... belong to another family. We show that, it is necessary to introduce additional potential to MIC-Kepler system in order to unify the two families into one. We also reproduce the results of the (super-symmetric) Hydrogenic problem in our study.
The SINFONI survey for Unveiling the Physics and Effect of Radiative feedback (SUPER) was designed to conduct a blind search for AGN-driven outflows on X-ray selected AGN at redshift z$\sim$2 with high ($\sim$2 kpc) spatial resolution, and correlate them to the properties of the host galaxy and central black hole. The main aims of this paper are: a) to derive reliable estimates for the BH mass and accretion rates for the Type-1 AGN in this survey; b) to characterize the properties of the AGN driven winds in the BLR. We analyzed rest-frame optical and UV spectra of 21 Type-1 AGN. We found that the BH masses estimated from H$\alpha$ and H$\beta$ lines are in agreement. We estimate BH masses in the range Log(M$\rm_{BH}/M_{\odot}$)=8.4-10.8 and Eddington ratios $\rm\lambda_{Edd}$ =0.04-1.3. We confirm that the CIV line width does not correlate with the Balmer lines and the peak of the line profile is blue-shifted with respect to the [OIII]-based systemic redshift. These findings support the idea that the CIV line is tracing outflowing gas in the BLR, with velocities up to $\sim$4700 km/s. We confirm the strong dependence of the BLR wind velocity with the UV-to-Xray continuum slope, L$\rm_{Bol}$ and $\rm\lambda_{Edd}$. We inferred BLR mass outflow rates in the range 0.005-3 M$_{\odot}$/yr, showing a correlation with the bolometric luminosity consistent with that observed for ionized winds in the NLR and X-ray winds detected in local AGN, and kinetic power $\sim$10$^{[-7:-4]}\times$ L$\rm_{Bol}$. Finally, we found an anti-correlation between the equivalent width of the [OIII] line with respect to the CIV shift, and a positive correlation with [OIII] outflow velocity. These findings, for the first time in an unbiased sample of AGN at z$\sim$2, support a scenario where BLR winds are connected to galaxy scale detected outflows, and are capable of affecting the gas in the NLR located at kpc scale.
Semantic image segmentation, which becomes one of the key applications in image processing and computer vision domain, has been used in multiple domains such as medical area and intelligent transportation. Lots of benchmark datasets are released for researchers to verify their algorithms. Semantic segmentation has been studied for many years. Since the emergence of Deep Neural Network (DNN), segmentation has made a tremendous progress. In this paper, we divide semantic image segmentation methods into two categories: traditional and recent DNN method. Firstly, we briefly summarize the traditional method as well as datasets released for segmentation, then we comprehensively investigate recent methods based on DNN which are described in the eight aspects: fully convolutional network, upsample ways, FCN joint with CRF methods, dilated convolution approaches, progresses in backbone network, pyramid methods, Multi-level feature and multi-stage method, supervised, weakly-supervised and unsupervised methods. Finally, a conclusion in this area is drawn.
We discuss the difficulties that arise when one tries to calculate $\delta\rho$ using dispersion relations.
We investigate which bipartite quantum states admit a symmetric extension and apply the results in the analysis of noise thresholds in quantum key distribution protocols with two-way postprocessing.   We find that states that admit a symmetric extension can be decomposed into a convex combination of states that admit a_pure_ symmetric extension. For a state to have a pure symmetric extension, its nonzero eigenvalues must be equal to the nonzero eigenvalues of one of the subsystems. While this does not fully characterize the set of states with a pure symmetric extension in all dimensions, it is a full characterization for two qubits. A conjectured formula characterizing two-qubit states with a (mixed or pure) symmetric extension is presented. Proofs are given for some special classes. For multi-qubit Bell-diagonal states, the symmetric extension is simplified using the symmetries of the states and formulated as a semidefinite program.   Quantum key distribution with two-way advantage distillation steps is then analyzed. For the commonly used repetition code advantage distillation, the failure to distill a secret key beyond the currently known noise thresholds is explained by a failure to break a symmetric extension. More general linear advantage distillation schemes are analyzed, but for those schemes analyzed, we find that they tolerate strictly less noise than repetition code advantage distillation before they fail to break a symmetric extension. The results suggest that no other linear advantage distillation scheme can reach the noise threshold of 27.6 % for the six-state protocol which is achieved by repetition code advantage distillation.
A zero-one law of Engelbert--Schmidt type is proven for the norm process of a transient random walk. An invariance principle for random walk local times and a limit version of Jeulin's lemma play key roles.
We present a recent ALMA observation of the CO(1-0) line emission in the central galaxy of the Zw 3146 galaxy cluster ($z=0.2906$). We also present updated X-ray cavity measurements from archival Chandra observations. The $5\times 10^{10}\,M_{\odot}$ supply of molecular gas, which is confined to the central 4 kpc, is marginally resolved into three extensions that are reminiscent of the filaments observed in similar systems. No velocity structure that would be indicative of ordered motion is observed. The three molecular extensions all trail X-ray cavities, and are potentially formed from the condensation of intracluster gas lifted in the wakes of the rising bubbles. Many cycles of feedback would be require to account for the entire molecular gas reservoir. The molecular gas and continuum source are mutually offset by 2.6 kpc, with no detected line emission coincident with the continuum source. It is the molecular gas, not the continuum source, that lies at the gravitational center of the brightest cluster galaxy. As the brightest cluster galaxy contains possible tidal features, the displaced continuum source may correspond to the nucleus of a merging galaxy. We also discuss the possibility that a gravitational wave recoil following a black hole merger may account for the displacement.