ShantanuT01/DACTYL-Pretraining huggingface dataset:
For a totally real number field $F$ and its ad\`ele ring $\mathbb{A}_F$, let $\pi$ vary in the set of irreducible cuspidal automorphic representations of ${\rm PGL}_2(\mathbb{A}_F)$ corresponding to primitive Hilbert modular forms of a fixed weight. Then, we determine the symmetry type of the one-level density of low-lying zeros of the symmetric power $L$-functions $L(s,{\rm Sym}^r(\pi))$ weighted by special values of symmetric square $L$-functions $L(\frac{z+1}{2},{\rm Sym}^2(\pi))$ at $z \in [0, 1]$ in the level aspect. If $0 < z \le 1$, our weighted density in the level aspect has the same symmetry type as Ricotta and Royer's density of low-lying zeros of symmetric power $L$-functions for $F=\mathbb{Q}$ with harmonic weight. Hence our result is regarded as a $z$-interpolation of Ricotta and Royer's result. If $z=0$, density of low-lying zeros weighted by central values is a different type only when $r=2$, and it does not appear in random matrix theory as Katz and Sarnak predicted. Moreover, we propose a conjecture on weighted density of low-lying zeros of $L$-functions by special $L$-values.   In the latter part, Appendices A, B and C are dedicated to the comparison among several generalizations of Zagier's parameterized trace formula. We prove that the explicit Jacquet-Zagier type trace formula (the ST trace formula) by Tsuzuki and the author recovers all of Zagier's, Takase's and Mizumoto's formulas by specializing several data. Such comparison is not so straightforward and includes non-trivial analytic evaluations.
For distant extragalactic sources of gamma-rays in the PeV energy range, interactions of the gamma rays with intergalactic diffuse radiation fields will initiate a pair cascade. Depending on the magnetic fields in the vicinity of the source, the cascade can either result in an isotropic halo around an initially beamed source, or remain more or less collimated. Data recorded by the HEGRA system of imaging atmospheric Cherenkov telescopes are used to derive limits on the halo flux from the AGN Mrk 501. This is achieved by comparing the angular distribution of TeV gamma-rays during the 1997 burst phase -- where direct photons should dominate -- with the distribution during the 1998/99 quiescent state, where a steady-state halo contribution should be most pronounced. The results depend on the assumptions concerning the angular distribution of the halo; limits on the halo flux within 0.5 to 1 degr. from the source range between 0.1% and 1% of the peak burst flux.
Consider an asymptotically Euclidean initial data set with a smooth marginally trapped surface (possibly a union of future and past multi-connected components) as inner boundary. By a further development of the spinorial framework underlying the positive energy theorem, a refined Witten identity is worked out and in the maximal slicing case, a close connection of the identity with a conformal invariant of Yamabe type is revealed. A Kato-Yau inequality for the Sen-Witten operator is also proven from a conformal geometry perspective. Guided by the Hamiltonian picture underlying the spinorial framework, a Penrose type inequality is then proven to the effect that given the dominant energy condition, the ADM energy-momentum is, up to a non-zero constant less than unity, bounded by the areal radius of the marginally trapped surface. To establish the Penrose inequality in full generality, it is then sufficient to show that the norm of the Sen-Witten spinor, subject to the APS boundary condition imposed on a suitably defined outermost marginally trapped surface, is bounded below by that attained in the Schwarzschild metric.
We study the dependence of satellite galaxy properties on the distance to the host galaxy and the orbital motion using the SDSS data. From SDSS DR7 we find 3515 isolated satellite systems of galaxies at z<0.03 that contain 8904 satellite galaxies. Using this sample we construct a catalog of 635 satellites associated with 215 host galaxies whose spin directions are determined by our inspection of the SDSS color images and/or by spectroscopic observations in the literature. We divide satellite galaxies into prograde and retrograde orbit subsamples depending on their orbital motion respect to the spin direction of the host. We find that the number of galaxies in prograde orbit is nearly equal to that of retrograde orbit galaxies: the fraction of satellites in prograde orbit is 50+/-2%. The velocity distribution of satellites with respect to their hosts is found almost symmetric: the median bulk rotation of satellites is -1+/- 8 km/s. It is found that the radial distribution of early-type satellites in prograde orbit is strongly concentrated toward the host while that of retrograde ones shows much less concentration. We also find the orbital speed of late-type satellites in prograde orbit increases as the projected distance to the host (R) decreases while the speed decreases for those in retrograde orbit. At R less than 0.1 times the host virial radius the orbital speed decreases in both prograde and retrograde orbit cases. Prograde satellites are on average fainter than retrograde satellites for both early and late morphological types. The u-r color becomes redder as R decreases for both prograde and retrograde orbit late-type satellites. The differences between prograde and retrograde orbit satellites may be attributed to their different origin or the different strength of physical processes that they have experienced through hydrodynamic interactions with their host galaxies.
Vaidman's analysis of the photon's past is based on incorrect interpretation of quantum probability amplitudes. The confusion stems from his original work [{\it Phys. Rev. Lett.} \textbf{60}, 1351 (1988)], which missed the connection between the amplitudes and the "weak values" introduced therein.
We present high-time resolution optical spectroscopy and imaging of the black hole transient Swift J1357.2-0933 during its 2017 outburst. The light curves show recurrent dips resembling those discovered during the 2011 outburst. The dip properties (e.g duration and depth) as well as the evolution of their recurrence time are similar to those seen in 2011. Spectra obtained during the dips are characterised by broad and blue-shifted absorptions in Balmer and He ii. The absorptions show core velocities of $\sim$ -800 km/s and terminal velocities approaching $\sim$ 3000 km/s i.e. in the upper-end of wind velocities measured in other black hole transients (both at optical and X-ray wavelengths). Our observations suggest that the dips are formed in a dense and clumpy outflow, produced near the disc equatorial plane and seen at high inclination. We also study the colour evolution and observe that, as it has been previously reported, the source turns bluer during dips. We show that this is due to a gradual change in the slope of the optical continuum and discuss possible implications of this behaviour.
These notes present a pedagogical introduction to magnetic monopoles and exact electromagnetic duality in supersymmetric gauge theories. They are based on lectures given at the 1995 Trieste Summer School in High Energy Physics and Cosmology and at the 1995 Busstepp Summer School at Cosener's House.
By using an average heavy nuclei model, the effects of the electron screening on electron capture (EC) in core-collapse supernovae are investigated. A one-dimension code based on the Ws15$M_{\sun}$ progenitor model is utilized to test the effects of electron screening during the collapsing process. The results show that, at high densities, the effects of EC on electron capture becomes significant. During the collapsing stage, the EC rate is decreased, the collapse timescale is prolonged and the leakage of the neutrino energy is increased. These effects lead to an appreciable decrease in the initial energy of the bounce shock wave. The effects of electron screeening in the other progenitor models are also discussed.
White dwarfs in globular clusters offer additional possibilities to determine distances and ages of globular clusters, provided their spectral types and masses are known. We therefore started a project to obtain spectra of white dwarfs in the globular clusters NGC 6397 and NGC 6752. All observed white dwarfs show hydrogen-rich spectra and are therefore classified as DA. Analysing the multi-colour photometry of the white dwarfs in NGC 6752 yields an average gravity of log g = 7.84 and 0.53 Msolar as the most probable average mass for globular cluster white dwarfs. Using this average gravity we try to determine independent temperatures by fitting the white dwarf spectra. While the stellar parameters determined from spectroscopy and photometry usually agree within the mutual error bars, the low resolution and S/N of the spectra prevent us from setting constraints stronger than the ones derived from the photometry alone. For the same reasons the white dwarf spectra obtained for NGC 6397 unfortunately do not provide an independent distance estimate of sufficient accuracy to distinguish between the long and short distance scale for globular clusters.
Let $A$ be an absolutely simple abelian variety without (potential) complex multiplication, defined over the number field $K$. Suppose that either $\dim A=2$ or $A$ is of $\operatorname{GL}_2$-type: we give an explicit bound $\ell_0(A,K)$ such that, for every prime $\ell>\ell_0(A,K)$, the image of the absolute Galois group of $K$ in $\operatorname{Aut}(T_\ell(A))$ is as large as it is allowed to be by endomorphisms and polarizations.
Baryon Acoustic Oscillations are considered to be a very robust standard ruler against various systematics. This premise has been tested against observational systematics, but not to the level required for the next generation of galaxy surveys such as the Dark Energy Spectroscopic Instrument (DESI) and Euclid. In this paper, we investigate the effect of observational systematics on the BAO measurement of the final sample of quasars from the extended Baryon Oscillation Spectroscopic Survey Data Release 16 in order to prepare and hone a similar analysis for upcoming surveys. We employ catalogues with various treatments of imaging systematic effects using linear and neural network-based nonlinear approaches and consider how the BAO measurement changes. We also test how the variations to the BAO fitting model respond to the observational systematics. As expected, we confirm that the BAO measurements obtained from the DR16 quasar sample are robust against imaging systematics well within the statistical error, while reporting slightly modified constraints that shift the line-of-sight BAO signal by less than 1.1% . We use realistic simulations with similar redshift and angular distributions as the DR16 sample to conduct statistical tests for validating the pipeline, quantifying the significance of differences, and estimating the expected bias on the BAO scale in future high-precision data sets. Although we find a marginal impact for the eBOSS QSO data, the work presented here is of vital importance for constraining the nature of dark energy with the BAO feature in the new era of big data cosmology with DESI and Euclid.
We discuss a specific model of elliptic flow fluctuations due to Gaussian fluctuations in the initial spatial $x$ and $y$ eccentricity components $\left\{\mean{(\sigma_y^2-\sigma_x^2)/(\sigma_x^2+\sigma_y^2)}, \mean{2\sigma_{xy}/(\sigma_x^2+\sigma_y^2)} \right\}$. We find that in this model $\vfour$, elliptic flow determined from 4-particle cumulants, exactly equals the average flow value in the reaction plane coordinate system, $\mean{v_{RP}}$, the relation which, in an approximate form, was found earlier by Bhalerao and Ollitrault in a more general analysis, but under the same assumption that $v_2$ is proportional to the initial system eccentricity. We further show that in the Gaussian model all higher order cumulants are equal to $\vfour$. Analysis of the distribution in the magnitude of the flow vector, the $Q-$distribution, reveals that it is totally defined by two parameters, $\vtwo$, the flow from 2-particle cumulants, and $\vfour$, thus providing equivalent information compared to the method of cumulants. The flow obtained from the $Q-$distribution is again $\vfour=\mean{v_{RP}}$.
We consider some energy integrals under slow growth and we prove that the local minimizers are locally Lipschitz continuous. Many examples are given, either with subquadratic $p,q-$growth and/or anisotropic growth.
We construct a family of rotating vortex patches with fixed angular velocity for the two-dimensional Euler equations in a disk. As the vorticity strength goes to infinity, the limit of these rotating vortex patches is a rotating point vortex whose motion is described by the Kirchhoff-Routh equation. The construction is performed by solving a variational problem for the vorticity which is based on an adaption of Arnold's variational principle. We also prove nonlinear orbital stability of the set of maximizers in the variational problem under $L^p$ perturbation when $p\in[{3}/{2},+\infty)$.
We provide the integral representation formula for the relaxation in $BV(\Omega; \mathbb{R}^M)$ with respect to strong convergence in $L^1(\Omega; \mathbb{R}^M)$ of a functional with a boundary contact energy term. This characterization is valid for a large class of surface energy densities, and for domains satisfying mild regularity assumptions. Motivated by some classical examples where lower semicontinuity fails, we analyze the extent to which the geometry of the set enters the relaxation procedure.
Based on a simple approximation scheme we have computed the local density of states (LDOS) of the antiferromagnetic and ferromagnetic Kondo models for the full range of band occupations and coupling strengths. For both models the LDOS with its full energy dependence has not been calculated before. Arguments are given for the results to be qualitatively trustworthy despite the simplicity of the approximation scheme.
Cross-correlation signals are recorded from fluorescence photons scattered in free space off a trapped ion structure. The analysis of the signal allows for unambiguously revealing the spatial frequency, thus the distance, as well as the spatial alignment of the ions. For the case of two ions we obtain from the cross-correlations a spatial frequency $f_\text{spatial}=1490 \pm 2_{stat.}\pm 8_{syst.}\,\text{rad}^{-1}$, where the statistical uncertainty improves with the integrated number of correlation events as $N^{-0.51\pm0.06}$. We independently determine the spatial frequency to be $1494\pm 11\,\text{rad}^{-1}$, proving excellent agreement. Expanding our method to the case of three ions, we demonstrate its functionality for two-dimensional arrays of emitters of indistinguishable photons, serving as a model system to yield structural information where direct imaging techniques fail.
The microwave response of a two-dimensional electron system (2DES) covered by a conducting top gate is investigated in the relativistic regime for which the 2D conductivity $\sigma_{2 \rm{D}} > c/2\pi$. Weakly damped plasma waves are excited in the gated region of the 2DES. The frequency and amplitude of the resulting plasma excitations show a very unusual dependence on the magnetic field, conductivity, gate geometry and separation from the 2DES. We show that such relativistic plasmons survive for temperatures up to 300 K, allowing for new room-temperature microwave and terahertz applications.
The usual procedures to extract effective refractive indices for negative-index metamaterials are complicated by branching ambiguities in the inverse cosine function. The existing methods to eliminate ambiguities either involve calculations with varying geometries which are inherently flawed, as metamaterial properties depend strongly on geometry, or are more subjective as one must inspect and select branches to yield effec- tive parameters as a continuous function of frequency. We propose that the Kramers-Kronig relations, which hold for negative-index materials, naturally guide the selection of the proper branches, and in fact predict negative refractive index where other extraction procedures alone might not. The experimental realization of high quality negative-index materials requires a robust and reliable index retrieval procedure; the combined extraction/Kramers-Kronig retrieval can be used to design optimal metama- terials in a simple, systemmatic, and general manner.
We apply the empirical method built for z=0 in the previous work of Wang et al. to a higher redshift, to link galaxy stellar mass directly with its hosting dark matter halo mass at z~0.8. The relation of the galaxy stellar mass and the host halo mass M_infall is constrained by fitting both the stellar mass function and the correlation functions at different stellar mass intervals of the VVDS observation, where M_infall is the mass of the hosting halo at the time when the galaxy was last the central galaxy. We find that for low mass haloes, their residing central galaxies are less massive at high redshift than those at low redshift. For high mass haloes, central galaxies in these haloes at high redshift are a bit more massive than the galaxies at low redshift. Satellite galaxies are less massive at earlier times, for any given mass of hosting haloes. Fitting both the SDSS and VVDS observations simultaneously, we also propose a unified model of the M_stars-M_infall relation, which describes the evolution of central galaxy mass as a function of time. The stellar mass of a satellite galaxy is determined by the same M_stars-M_infall relation of central galaxies at the time when the galaxy is accreted. With these models, we study the amount of galaxy stellar mass increased from z~0.8 to the present day through galaxy mergers and star formation. Low mass galaxies gain their stellar masses from z~0.8 to z=0 mainly through star formation. For galaxies of higher mass, the increase of stellar mass solely through mergers from z=0.8 can make the massive galaxies a factor ~2 larger than observed at z=0. We can also predict stellar mass functions of redshifts up to z~3, and the results are consistent with the latest observations.
In 1935 Carlitz introduced Bernoulli-Carlitz numbers as analogues of Bernoulli numbers for the rational function field $\mathbb F_r(T)$. In this paper, we introduce Cauchy-Carlitz numbers as analogues of Cauchy numbers. By using Stirling-Carlitz numbers, we give their arithmetical and combinatorial properties and relations with Bernoulli-Carlitz numbers for $\mathbb F_r(T)$. Several new identities are also obtained by using Hasse-Teichim\"uller derivatives.
Coherent Compton scattering on light nuclei in the delta resonance region is studied in the impulse approximation and is shown to be a sensitive probe of the in-medium properties of the delta resonance. The elementary amplitude on a single nucleon is calculated from the unitary K-matrix approach developed previously. Modifications of the properties of the delta resonance due to the nuclear medium are accounted for through the self-energy operator of the delta, calculated from the one-pion loop. The dominant medium effects such as the Pauli blocking, mean-field modification of the nucleon and delta masses, and particle-hole excitations in the pion propagator are consistently included in nuclear matter.
We report the magnetic properties strongly varying with the rare-earth elements in the newly found ternary compounds $R$Al$_{0.9}$Si$_{1.1}$, which crystallize in the tetragonal $\alpha$-ThSi$_2$-type structure. For $R$ = Ce the alloy has a weak ferromagnetism below 11 K and for $R$ = Pr it orders ferromagnetically at 17 K, while for $R$ = Gd it is antiferromagnetic with $T_{\rm N}$ = 30.5 K. In addition, we find no field effect on $T_{\rm N}$ of $R$ = Gd because of the large internal mean field, but significant changes in the magnetic properties of $R$ = Ce and Pr.
In this paper, power-law cosmology whose scale factor is a power of time, $a \propto t^{\a}$, is investigated. Considering late universe with canonical scalar field and dust domination, we use observational data from Cosmic Microwave Background (WMAP7), Baryon Acoustic Oscillations (BAO) and observational Hubble data to find power exponent $\a$ of the power-law and other cosmological variables. The power $\a$ is found to be $0.99 \pm 0.02$ (WMAP7+BAO+$H_0$) and $0.99 \pm 0.04$ (WMAP7). These values do not exclude possibility of acceleration at 1$\sigma$ hence giving viability to power-law cosmology in general. When considering scenario of canonical scalar field dark energy with power-law expansion, we derive scalar field potential, exact solution, equation of state parameter and plots their evolutions using observational data. We confirm that the scenario of power-law cosmology containing dynamical canonical scalar field is ruled out by WMAP7 data since its present value of equation of state parameter does not match the WMAP7 result, i.e. the scalar-field power-law cosmology using WMAP7 gives $w_{\phi, 0} = -0.4493 \pm 0.0300 $ while the $w_{\phi}$CDM with WMAP7 data allows a maximum (+1$\sigma$) value of the equation of state parameter at $w_{\phi, 0} = -0.69$.
Thermodynamic properties of Ne, Ar, Kr, and Xe adsorbed on an Al-Ni-Co quasicrystalline surface (QC) are studied with Grand Canonical Monte Carlo by employing Lennard-Jones interactions with parameter values derived from experiments and traditional combining rules. In all the gas/QC systems, a layer-by-layer film growth is observed at low temperature. The monolayers have regular epitaxial fivefold arrangements which evolve toward sixfold close-packed structures as the pressure is increased. The final states can contain either considerable or negligible amounts of defects. In the latter case, there occurs a structural transition from five to sixfold symmetry which can be described by introducing an order parameter, whose evolution characterizes the transition to be continuous or discontinuous as in the case of Xe/QC (first-order transition with associated latent heat). By simulating fictitious noble gases, we find that the existence of the transition is correlated with the size mismatch between adsorbate and substrate's characteristic lengths. A simple rule is proposed to predict the phenomenon.
The quantum approximate optimization algorithm (QAOA) has become a cornerstone of contemporary quantum applications development. In QAOA, a quantum circuit is trained -- by repeatedly adjusting circuit parameters -- to solve a problem. Several recent findings have reported parameter concentration effects in QAOA and their presence has become one of folklore: while empirically observed, the concentrations have not been defined and analytical approaches remain scarce, focusing on limiting system and not considering parameter scaling as system size increases. We found that optimal QAOA circuit parameters concentrate as an inverse polynomial in the problem size, providing an optimistic result for improving circuit training. Our results are analytically demonstrated for variational state preparations at $p=1,2$ (corresponding to 2 and 4 tunable parameters respectively). The technique is also applicable for higher depths and the concentration effect is cross verified numerically. Parameter concentrations allow for training on a fraction $w < n$ of qubits to assert that these parameters are nearly optimal on $n$ qubits. Clearly this effect has significant practical importance.
Let $n\geq 3$ be an integer and $d$ an odd square-free integer. We shall compute the rank of the $2$-class group of $L_{n,d}:=\mathbb{Q}(\zeta_{2^n},\sqrt{d})$, when all the prime divisors of $d$ are congruent to $\pm 3\pmod 8$ or $9\pmod{16}$.
We present a general classification of all four fermion final states in $\gamma\gamma$~collisions and a calculation of cross sections below the $W^+W^-$-threshold.