ShantanuT01/DACTYL-Pretraining huggingface dataset:
We investigate how entanglement entropy behaves in a non-conformal scalar field system with a quantum phase transition, by the replica method. We study the $\sigma$-model in 3+1 dimensions which is $O(N)$ symmetric as the mass squared parameter $\mu^{2}$ is positive, and undergoes spontaneous symmetry breaking while $\mu^{2}$ becomes negative. The area law leading divergence of the entanglement entropy is preserved in both of the symmetric and the broken phases. The spontaneous symmetry breaking changes the subleading divergence from log to log squared, due to the cubic interaction on the cone. At the leading order of the coupling constant expansion, the entanglement entropy reaches a cusped maximum at the quantum phase transition point $\mu^{2}=0$, and decreases while $\mu^{2}$ is tuned away from 0 into either phase.
The role of the sea quarks to ground state nucleon properties with electroweak probes is discussed. A relativistic Green's function approach to parity violating electron scattering and a distorted-wave impulse-approximation applied to charged- and neutral-current neutrino-nucleus quasi-elastic scattering are presented in view of the possible determination of the strangeness content of the nucleon.
For inversion-symmetric topological insulators and superconductors characterized by ${\mathbb Z}_{2}$ topological invariants, two scaling schemes are proposed to judge topological phase transitions driven by an energy parameter. The scaling schemes renormalize either the phase gradient or the second derivative of the Pfaffian of the time-reversal operator, through which the renormalization group flow of the driving energy parameter can be obtained. The Pfaffian near the time-reversal invariant momentum is revealed to display a universal critical behavior for a great variety of models examined.
In this paper we derived oxygen abundance gradients from HII regions located in eleven galaxies in eight systems of close pairs. Long-slit spectra in the range 4400-7300A were obtained with the Gemini Multi-Object Spec- trograph at Gemini South (GMOS). Spatial profiles of oxygen abundance in the gaseous phase along galaxy disks were obtained using calibrations based on strong emission-lines (N2 and O3N2). We found oxygen gradients signifi- cantly flatter for all the studied galaxies than those in typical isolated spiral galaxies. Four objects in our sample, AM1219A, AM1256B, AM 2030A and AM2030B, show a clear break in the oxygen abundance at galactocentric radius R/R25 between 0.2 and 0.5. For AM1219A and AM1256B we found negative slopes for the inner gradients, and for AM2030B we found a positive one. In all these three cases they show a flatter behaviour to the outskirts of the galaxies. For AM2030A, we found a positive-slope outer gradient while the inner one is almost compatible with a flat behaviour. A decrease of star forma- tion efficiency in the zone that corresponds to the oxygen abundance gradient break for AM1219A and AM2030B was found. For the former, a minimum in the estimated metallicities was found very close to the break zone that could be associated with a corotation radius. On the other hand, AM1256B and AM2030A, present a SFR maximum but not an extreme oxygen abundance value. All the four interacting systems that show oxygen gradient breakes the extreme SFR values are located very close to break zones. Hii regions lo- cated in close pairs of galaxies follow the same relation between the ionization parameter and the oxygen abundance as those regions in isolated galaxies.
We investigate the rapidity dependence of the elliptical flow in heavy ion collisions at 200 GeV (cms), by employing a three-dimensional hydrodynamic evolution, based on different initial conditions, and different freeze-out scenarios. It will be shown that the form of pseudo-rapidity ($\eta$) dependence of the elliptical flow is almost identical to space-time-rapidity ($\eta_{s}$) dependence of the initial energy distribution, independent of the freeze-out prescriptions.
Due to recent advances in laboratory spectroscopy, the first optical detection of a very large molecule has been claimed in the diffuse interstellar medium (ISM): C60+ (ionized Buckminsterfullerene). Confirming the presence of this molecule would have significant implications regarding the carbon budget and chemical complexity of the ISM. Here we present results from a new method for ultra-high signal-to-noise (S/N) spectroscopy of background stars in the near infrared (at wavelengths 0.9-1 micron), using the Hubble Space Telescope Imaging Spectrograph (STIS) in a previously untested `STIS scan' mode. The use of HST provides the crucial benefit of eliminating the need for error-prone telluric correction methods in the part of the spectrum where the C60+ bands lie, and terrestrial water vapor contamination is severe. Our STIS spectrum of the heavily-reddened B0 star BD63\,1964 reaches an unprecedented S/N for this instrument ($\sim600-800$), allowing the detection of the diffuse interstellar band (DIB) at 9577 \AA\ attributed to C60+ as well as new DIBs in the near-IR. Unfortunately, the presence of overlapping stellar lines, and the unexpected weakness of the C60+ bands in this sightline, prevents conclusive detection of the weaker C60+ bands. A probable correlation between the 9577 \AA\ DIB strength and interstellar radiation field is identified, which suggests that more strongly-irradiated interstellar sightlines will provide the optimal targets for future C60+ searches.
P\'olya's enumeration theorem is concerned with counting labeled sets up to symmetry. Given a finite group acting on a finite set of labeled elements it states that the number of labeled sets up to symmetry is given by a polynomial in the number of labels. We give a new perspective on this theorem by generalizing it to partially ordered sets and order preserving maps. Further we prove a reciprocity statement in terms of strictly order preserving maps generalizing a classical result by Stanley (1970). We apply our results to counting graph colorings up to symmetry.
We will use overlays and templates derived from two-dimensional recurrence relations to build the arrays, and we will study the structure of the overlays, including initial conditions and basis arrays.
We study galaxy formation in sterile neutrino dark matter models that differ signifi- cantly from both cold and from `warm thermal relic' models. We use the EAGLE code to carry out hydrodynamic simulations of the evolution of pairs of galaxies chosen to resemble the Local Group, as part of the APOSTLE simulations project. We compare cold dark matter (CDM) with two sterile neutrino models with 7 keV mass: one, the warmest among all models of this mass (LA120) and the other, a relatively cold case (LA10). We show that the lower concentration of sterile neutrino subhalos compared to their CDM counterparts makes the inferred inner dark matter content of galaxies like Fornax (or Magellanic Clouds) less of an outlier in the sterile neutrino cosmologies. In terms of the galaxy number counts the LA10 simulations are indistinguishable from CDM when one takes into account halo-to-halo (or `simulation-to-simulation') scatter. In order for the LA120 model to match the number of Local Group dwarf galaxies, a higher fraction of low mass haloes is required to form galaxies than is predicted by the EAGLE simulations. As the census of the Local Group galaxies nears completion, this population may provide a strong discriminant between cold and warm dark matter models.
The NASA Kepler mission -in flight since March 2009- is producing an enormous number of high-quality continuous light curves. Now, and for the first time ever, we are able to do ensemble asteroseismology, i.e., to do an asteroseismic analysis with a statistically significant sub-sample of solar-like stars covering a wide range of stellar characteristics. In the present work, I highlight some of the most recent studies carried out using these data.
We study the effects of quantum fluctuations on the dynamical generation of a gap and on the evolution of the spin-wave spectra of a frustrated magnet on a triangular lattice with bond-dependent Ising couplings, analog of the Kitaev honeycomb model. The quantum fluctuations lift the subextensive degeneracy of the classical ground-state manifold by a quantum order-by-disorder mechanism. Nearest-neighbor chains remain decoupled and the surviving discrete degeneracy of the ground state is protected by a hidden model symmetry. We show how the four-spin interaction, emergent from the fluctuations, generates a spin gap shifting the nodal lines of the linear spin-wave spectrum to finite energies.
Triple donor devices have the potential to exhibit adiabatic tunneling via the CTAP (Coherent Tunneling Adiabatic Passage) protocol which is a candidate transport mechanism for scalable quantum computing. We examine theoretically the statistics of dopant placement using counted ion implantation by employing an analytical treatment of CTAP transport properties under hydrogenic assumptions. We determine theoretical device yields for proof of concept devices for different implant energies. In particular, we determine a significant theoretical device yield (~80%) for 14keV phosphorus in silicon with nominal 20nm spacing.
We investigate the production of $e^+e^-$ pairs from $p + Be$ and nucleus-nucleus collisions from 2 GeV/A to 200 GeV/A within a covariant transport approach and focus on the dilepton angular anisotropies as a function of the dilepton invariant mass. Whereas the low mass regime yields information about the Dalitz decays of the $\Delta, \eta$ and $\omega$, above M $\approx $0.5 GeV the angular anisotropies provide additional information about the $\pi^+\pi^- \to \rho^0 \to e^+e^-$ channel in the medium. The anisotropy coefficient is found to change its sign for M $>$ 0.5 GeV in case of nucleus-nucleus reactions when increasing the bombarding energy from 2 GeV/A to 200 GeV/A which sheds some light on the $\pi \pi \to \rho$ dynamics.
A simple graph $G$ is said to admit an antimagic orientation if there exist an orientation on the edges of $G$ and a bijection from $E(G)$ to $\{1,2,\ldots,|E(G)|\}$ such that the vertex sums of vertices are pairwise distinct, where the vertex sum of a vertex is defined to be the sum of the labels of the in-edges minus that of the out-edges incident to the vertex. It was conjectured by Hefetz, M\"{u}tze, and Schwartz~\cite{HMS10} in 2010 that every connected simple graph admits an antimagic orientation.   In this paper, we prove that the Mycielski construction and the corona product for graphs with some conditions yield graphs satisfying the above conjecture.
A resonant inelastic x-ray scattering study of the electronic structure of the semiconductor cuprous oxide, $\rm Cu_2O$, is reported. When the incident x-ray energy is tuned to the Cu K-absorption edge, large enhancements of the spectral features corresponding to the electronic transitions between the valence band and the conduction band are observed. A feature at 6.5 eV can be well described by an interband transition from occupied states of mostly Cu 3d charactor to unoccupied states with mixed 3d, 4s and 2p character. In addition, an insulating band gap is observed, and the momentum dependence of the lower bound is measured along the $\Gamma-R$ direction. This is found to be in good agreement with the valence band dispersion measured with angle-resolved photoemission spectroscopy.
We show that the cosmic ray (CR) knee can be entirely explained by energy-dependent CR leakage from the Milky Way, with an excellent fit to all existing data. We test this hypothesis calculating the trajectories of individual CRs in the Galactic magnetic field. We find that the CR escape time $\tau_{\rm esc}(E)$ exhibits a knee-like structure around $E/Z={\rm few}\times 10^{15}$ eV for small coherence lengths and strengths of the turbulent magnetic field. The resulting intensities for different groups of nuclei are consistent with the ones determined by KASCADE and KASCADE-Grande, using simple power-laws as injection spectra. The transition from Galactic to extragalactic CRs is terminated at $\approx 2\times 10^{18}$ eV, while extragalactic CRs contribute sizeable to the subdominant proton flux already for $\gtrsim 2\times 10^{16}$ eV. The natural source of extragalactic CRs in the intermediate energy region up to the ankle are in this model normal and starburst galaxies. The escape model provides a good fit to $\ln(A)$ data; it predicts that the phase of the CR dipole varies strongly in the energy range between $1\times 10^{17}$ and $3\times 10^{18}$ eV, while our estimate for the dipole magnitude is consistent with observations.
The evolution of galaxy cluster counts is a powerful probe of several fundamental cosmological parameters. A number of recent studies using this probe have claimed tension with the cosmology preferred by the analysis of the Planck primary CMB data, in the sense that there are fewer clusters observed than predicted based on the primary CMB cosmology. One possible resolution to this problem is systematic errors in the absolute halo mass calibration in cluster studies, which is required to convert the standard theoretical prediction (the halo mass function) into counts as a function of the observable (e.g., X-ray luminosity, Sunyaev-Zel'dovich flux, optical richness). Here we propose an alternative strategy, which is to directly compare predicted and observed cluster counts as a function of the one-dimensional velocity dispersion of the cluster galaxies. We argue that the velocity dispersion of groups/clusters can be theoretically predicted as robustly as mass but, unlike mass, it can also be directly observed, thus circumventing the main systematic bias in traditional cluster counts studies. With the aid of the BAHAMAS suite of cosmological hydrodynamical simulations, we demonstrate the potential of the velocity dispersion counts for discriminating even similar $\Lambda$CDM models. These predictions can be compared with the results from existing redshift surveys such as the highly-complete Galaxy And Mass Assembly (GAMA) survey, and upcoming wide-field spectroscopic surveys such as the Wide Area Vista Extragalactic Survey (WAVES) and the Dark Energy Survey Instrument (DESI).
We produce a short and elementary algorithm to compute an upper bound for the canonical dimension of a spit semisimple linear algebraic group. Using this algorithm we confirm previously known bounds by Karpenko and Devyatov as well as we produce new bounds (e.g. for groups of types $F_4$, adjoint $E_6$, for some semisimple groups).
We use the redshift Hubble parameter $H(z)$ data derived from relative galaxy ages, distant type Ia supernovae (SNe Ia), the Baryonic Acoustic Oscillation (BAO) peak, and the Cosmic Microwave Background (CMB) shift parameter data, to constrain cosmological parameters in the Undulant Universe. We marginalize the likelihood functions over $h$ by integrating the probability density $P\propto e^{-\chi^2/2}$. By using the Markov Chain Monte Carlo (MCMC) technique, we obtain the best fitting results and give the confidence regions on the $b-\Omega_{\rm m0}$ plane. Then we compare their constraints. Our results show that the $H(z)$ data play a similar role with the SNe Ia data in cosmological study. By presenting the independent and joint constraints, we find that the BAO and CMB data play very important roles in breaking the degeneracy compared with the $H(z)$ and SNe Ia data alone. Combined with the BAO or CMB data, one can improve the constraints remarkably. The SNe Ia data sets constrain $\Omega_{\rm m0}$ much tighter than the $H(z)$ data sets, but the $H(z)$ data sets constrain $b$ much tighter than the SNe Ia data sets. All these results show that the Undulant Universe approaches the $\Lambda \rm$CDM model. We expect more $H(z)$ data to constrain cosmological parameters in future.
The class of Archimax copulas is generalized to hierarchical Archimax copulas in two ways. First, a hierarchical construction of $d$-norm generators is introduced to construct hierarchical stable tail dependence functions which induce a hierarchical structure on Archimax copulas. Second, by itself or additionally, hierarchical frailties are introduced to extend Archimax copulas to hierarchical Archimax copulas in a similar way as nested Archimedean copulas extend Archimedean copulas. Possible extensions to nested Archimax copulas are discussed. Additionally, a general formula for the density and its evaluation of Archimax copulas is introduced.
We introduce the Scalable ZX-calculus (SZX-calculus for short), a formal and compact graphical language for the design and verification of quantum computations. The SZX-calculus is an extension of the ZX-calculus, a powerful framework that captures graphically the fundamental properties of quantum mechanics through its complete set of rewrite rules. The ZX-calculus is, however, a low level language, with each wire representing a single qubit. This limits its ability to handle large and elaborate quantum evolutions. We extend the ZX-calculus to registers of qubits and allow compact representation of sub-diagrams via binary matrices. We show soundness and completeness of the SZX-calculus and provide two examples of applications, for graph states and error correcting codes.
Deeper insight leads to better practice. We show how the study of the foundations of quantum mechanics has led to new pictures of open systems and to a method of computation which is practical and can be used where others cannot. We illustrate the power of the new method by a series of pictures that show the emergence of classical features in a quantum world. We compare the development of quantum mechanics and of the theory of (biological) evolution.
Experimentally it has been known for a long time that the electric charges of the observed particles appear to be quantized. An approach to understanding electric charge quantization that can be used for gauge theories with explicit $U(1)$ factors -- such as the standard model and its variants -- is pedagogically reviewed and discussed in this article. This approach uses the allowed invariances of the Lagrangian and their associated anomaly cancellation equations. We demonstrate that charge may be de-quantized in the three-generation standard model with massless neutrinos, because differences in family-lepton--numbers are anomaly-free. We also review the relevant experimental limits. Our approach to charge quantization suggests that the minimal standard model should be extended so that family-lepton--number differences are explicitly broken. We briefly discuss some candidate extensions (e.g. the minimal standard model augmented by Majorana right-handed neutrinos).
We prove sharp radial estimates using Besov spaces. We also prove the propagation of singularities in Besov spaces.
In this article we construct a Koszul-type resolution of the p-th exterior power of the sheaf of holomorphic differential forms on smooth toric varieties and use this to prove a Nadel-type vanishing theorem for Hodge ideals associated to effective \mathbb{Q}-divisors on smooth projective toric varieties. This extends earlier results of Musta\c{t}\u{a} and Popa.
We demonstrate how gauge singlets can be used to find new examples of Kutasov duality (i.e. where the matching of the dual theories relies on a non-zero superpotential) in N}=1 SU(N) SQCD with F_Q flavours of quark and multiple generations of adjoints, or antisymmetrics, or symmetrics. The role of the singlets is to simplify greatly the truncation of the chiral ring whilst maintaining an R-symmetry, and at the same time allowing an unambiguous identification of the elementary mesons of the magnetic theory. The dual theories satisfy all the usual tests, including the highly non-trivial 't Hooft anomaly matching conditions.
In this paper, inspired by the seminal work by Caffarelli-Kohn-Nirenberg \cite{CKN} on the incompressible Navier-Stokes equation, we establish the existence of a suitable weak solution to the Navier-Stokes-Planck-Nernst-Poisson equation in dimension three, which is shown to be smooth away from a closed set whose $1$-dimensional parabolic Hausdorff measure is zero.
We prove effective joint equidistribution of several natural parameters associated to primitive vectors in $\mathbb{Z}^{n}$, as the norm of these vectors tends to infinity. These parameters include the direction, the orthogonal lattice, and the length of the shortest solution to the associated $\gcd$ equation. We show that the first two parameters equidistribute w.r.t. the Haar measure on the corresponding spaces, which are the unit sphere and the space of unimodular rank $n-1$ lattices in $\mathbb{R}^{n}$ respectively. The main novelty is the equidistribution of the shortest solutions to the $\gcd$ equations: we show that, when normalized by the covering radius of the orthogonal lattice, the lengths of these solutions equidistribute in the interval $\left[0,1\right]$ w.r.t. a measure that is Lebesgue only when $n=2$, and non-Lebesgue otherwise. These equidistribution results are deduced from effectively counting lattice points in domains which are defined w.r.t. a generalization of the Iwasawa decomposition in simple algebraic Lie groups, where we apply a method due to A. Gorodnik and A. Nevo.
Excitation energies of light-emitting organic conjugated polymers have been investigated with time-dependent density functional theory (TDDFT) within the adiabatic approximation for the dynamical exchange-correlation potential. Our calculations show that the accuracy of the calculated TDDFT excitation energies largely depends upon the accuracy of the dihedral angle obtained by the geometry optimization on ground-state DFT methods. We find that, when the DFT torsional dihedral angles between two adjacent phenyl rings are close to the experimental dihedral angles, the TDDFT excitation energies agree fairly well with experimental values. Further study shows that, while hybrid density functionals can correctly respect the thumb rule between singlet-singlet and singlet-triplet excitation energies, semilocal functionals do not, suggesting inadequacy of the semilocal functionals in predicting triplet excitation energies of conjugated polymers.
Visual question answering is a vision-and-language multimodal task, that aims at predicting answers given samples from the question and image modalities. Most recent methods focus on learning a good joint embedding space of images and questions, either by improving the interaction between these two modalities, or by making it a more discriminant space. However, how informative this joint space is, has not been well explored. In this paper, we propose a novel regularization for VQA models, Constrained Optimization using Barlow's theory (COB), that improves the information content of the joint space by minimizing the redundancy. It reduces the correlation between the learned feature components and thereby disentangles semantic concepts. Our model also aligns the joint space with the answer embedding space, where we consider the answer and image+question as two different `views' of what in essence is the same semantic information. We propose a constrained optimization policy to balance the categorical and redundancy minimization forces. When built on the state-of-the-art GGE model, the resulting model improves VQA accuracy by 1.4% and 4% on the VQA-CP v2 and VQA v2 datasets respectively. The model also exhibits better interpretability.