ShantanuT01/DACTYL-Pretraining huggingface dataset:
We report on measurements of the polarization of extragalactic sources at 148 GHz made during the first two seasons of the Atacama Cosmology Telescope Polarization (ACTPol) survey. The survey covered 680 deg$^{2}$ of the sky on the celestial equator. Polarization measurements of 169 intensity-selected sources brighter than 30 mJy, that are predominantly Active Galactic Nuclei, are presented. Above a total flux of 215 mJy where the noise bias removal in the polarization measurement is reliable, we detect 26 sources, 14 of which have a detection of linear polarization at greater than 3$\sigma_{p}$ significance. The distribution of the fractional polarization as a function of total source intensity is analyzed. Our result is consistent with the scenario that the fractional polarization of our measured radio source population is independent of total intensity down to the limits of our measurements and well described by a Gaussian distribution with a mean fractional polarization $p=0.028\pm$0.005 and standard deviation $\sigma_{\mathrm{p}}=0.054$, truncated at $p=0$. Extrapolating this model for the distribution of source polarization below the ACTPol detection threshold, we predict that one could get a clean measure of the E-mode polarization power spectrum of the microwave background out to $\ell=6000$ with 1 $\mu$K-arcminute maps over 10$\%$ of the sky from a future survey. We also study the spectral energy distribution of the total and polarized source flux densities by cross-matching with low radio frequency catalogs. We do not find any correlation between the spectral indices for total flux and polarized flux.
We present a new class of hydrodynamical models for the formation of bulges (either massive elliptical galaxies or classical bulges in spirals) in which we implement detailed prescriptions for the chemical evolution of H, He, O and Fe. Our results hint toward an outside-in formation in the context of the supernovae-driven wind scenario. The build-up of the chemical properties of the stellar populations inhabiting the galactic core is very fast. Therefore we predict a non significant evolution of both the mass-metallicity and the mass-[alpha/Fe] relations after the first 0.5 - 1 Gyr. In this framework we explain how the observed slopes, either positive or negative, in the radial gradient of the mean stellar [alpha/Fe], and their apparent lack of any correlation with all the other observables, can arise as a consequence of the interplay between star formation and metal-enhanced internal gas flows.
We study $N$ interacting massless Dirac fermions confined in a two-dimensional quantum dot. Physical realizations of this problem include a graphene monolayer and the surface state of a strong topological insulator. We consider both a magnetic confinement and an infinite mass confinement. The ground state energy is computed as a function of the effective interaction parameter $\alpha$ from the Hartree-Fock approximation and, alternatively, by employing the M\"uller exchange functional. For N=2, we compare those approximations to exact diagonalization results. The Hartree-Fock energies are highly accurate for the most relevant interaction range $\alpha\alt 2$, but the M\"uller functional leads to an unphysical instability when $\alpha\agt 0.756$. Up to 20 particles were studied using Hartree-Fock calculations. Wigner molecule formation was observed for strong but realistic interactions, accompanied by a rich peak structure in the addition energy spectrum.
Recent studies of early-type galaxies have suggested that the initial mass function (IMF) slope is bottom-heavy, i.e. they contain a larger fraction of low-mass stars than the Milky Way. However, measurements of the IMF remain challenging in unresolved galaxies because features in their observed spectra are sensitive to a number of factors including the stellar age, metallicity, and elemental abundances, in addition to the IMF. In this paper, we use new high signal-to-noise IMACS (Magellan) spectra to study the elliptical shell galaxy NGC 3923 at optical (3700-6600 Angstrom), and near-infrared (7900-8500 Angstrom) wavelengths, as a function of radius. We have undertaken a number of independent approaches to better understand the uncertainties in our results. 1) We compare two different stellar population model libraries; 2) we undertake spectral index fitting as well as full spectral fitting; 3) we have performed simulations for which we a priori know the input IMF, and which closely match our data; 4) we also investigate the effects of including a two-component, rather than a single stellar population. We show that our results are sensitive to the assumptions we make and to the methods we use. In addition, we evaluate the accuracy and precision of our results based on simulated mock data. We find some indication (although assumption-dependent) for a bottom-heavy IMF in the mass-range 0.5-1.0 M_sun, while the IMF in the mass-range 0.08-0.5 M_sun appears to be Milky-Way like and constant. Including near-infrared data to our analysis gives consistent results, and improves the precision.
We introduce transition operators that in a given basis of the single-site states of a many-body system have a single non-vanishing matrix element and introduce their correlation functions. We show that they fall into groups that decay with the same rate. The mutual information defined in terms of the von Neumann entropy between two sites is given in terms of these so-called generalized correlation functions. We confirm numerically that the long-distance decay of the mutual information follows the square of that of the most slowly decaying generalized correlation function. The main advantage of our procedure is that, in order to identify the most relevant physical processes, there is no need to know a priori the nature of the ordering in the system, i.e., no need to explicitly construct particular physical correlation functions. We explore the behavior of the mutual information and the generalized correlation functions for conformally invariant models and for the SU($n$) Hubbard model with $n=2,3,4$, and 5, which are, in general, not conformally invariant. In this latter case, we show that for filling $f=1/q$ and $q<n$, the ground state consists of highly entangled $q$-site units that are further entangled by single bonds. In addition, we extend the picture of the two-site mutual information and the corresponding generalized correlation functions to the $n$-site case.
We describe the foundation of the log minimal model program for log canonical pairs according to Ambro's idea. We generalize Koll\'ar's vanishing and torsion-free theorems for embedded simple normal crossing pairs. Then we prove the cone and contraction theorems for quasi-log varieties, especially, for log canonical pairs.
Magnetic exchange in Kondo lattice systems is of the Ruderman-Kittel-Kasuya-Yosida type, whose sign depends on the Fermi wave vector, $k_F$ . In the simplest setting, for small $k_F$ , the interaction is predominately ferromagnetic, whereas it turns more antiferromagnetic with growing $k_F$. It is remarkable that even though $k_F$ varies vastly among the rare-earth systems, an overwhelming majority of lanthanide magnets are in fact antiferromagnets. To address this puzzle, we investigate the effects of a p-wave form factor for the Kondo coupling pertinent to nearly all rare-earth intermetallics. We show that this leads to interference effects which for small kF are destructive, greatly reducing the size of the RKKY interaction in the cases where ferromagnetism would otherwise be strongest. By contrast, for large $k_F$, constructive interference can enhance antiferromagnetic exchange. Based on this, we propose a new route for designing ferromagnetic rare-earth magnets.
Let $\boldsymbol{\alpha}\in \mathbb{R}^N$ and $Q\geq 1$. We consider the sum $\sum_{\boldsymbol{q}\in [-Q,Q]^N\cap\mathbb{Z}^N\backslash\{\boldsymbol{0}\}}\|\boldsymbol{\alpha}\cdot\boldsymbol{q}\|^{-1}$. Sharp upper bounds are known when $N=1$, using continued fractions or the three distance theorem. However, these techniques do not seem to apply in higher dimension. We introduce a different approach, based on a general counting result of Widmer for weakly admissible lattices, to establish sharp upper bounds for arbitrary $N$. Our result also sheds light on a question raised by L\^{e} and Vaaler in 2013 on the sharpness of their lower bound $\gg Q^N\log Q$.
Neutron spectroscopic measurements of the magnetic excitations in PrO$_2$ reveal (1) sharp peaks characteristic of transitions between levels of the $4f^1$ configuration of Pr$^{4+}$ split by the cubic crystal field, and (2) broad bands of scattering centred near 30 meV and 160 meV. We present a simple model based on a vibronic Hamiltonian that accounts for the main features of the data. The analysis shows that $90\pm10$% of the Pr ions have a localized $4f^1$ configuration and provides strong evidence for a dynamic Jahn-Teller effect in the $\Gamma_8$ electronic ground state.
We establish $C^2$ a priori estimate for convex hypersurfaces whose principal curvatures $\kappa=(\kappa_1,..., \kappa_n)$ satisfying Weingarten curvature equation $\sigma_k(\kappa(X))=f(X,\nu(X))$. We also obtain such estimate for admissible 2-convex hypersurfaces in the case $k=2$. Our estimates resolve a longstanding problem in geometric fully nonlinear elliptic equations.
In a flat, k=0 cosmology with galaxies that approximate singular isothermal spheres, gravitational lens image separations should be uncorrelated with source redshift. But in an open k=-1 cosmology such gravitational lens image separations become smaller with increasing source redshift. The observed separations do become smaller with increasing source redshift but the effect is even stronger than that expected in an Omega=0 cosmology. The observations are thus not compatible with the "standard" gravitational lensing statistics model in a flat universe. We try various open and flat cosmologies, galaxy mass profiles, galaxy merging and evolution models, and lensing aided by clusters to explain the correlation. We find the data is not compatible with any of these possibilities within the 95% confidence limit, leaving us with a puzzle. If we regard the observed result as a statistical fluke, it is worth noting that we are about twice as likely to observe it in an open universe (with 0<Omega<0.4) as we are to observe it in a flat one. Finally, the existence of an observed multiple image lens system with a source at z=4.5 places a lower limit on the deceleration parameter: q_0 > -2.0.
A network of driven nonlinear oscillators without dissipation has recently been proposed for solving combinatorial optimization problems via quantum adiabatic evolution through its bifurcation point. Here we investigate the behavior of the quantum bifurcation machine in the presence of dissipation. Our numerical study suggests that the output probability distribution of the dissipative quantum bifurcation machine is Boltzmann-like, where the energy in the Boltzmann distribution corresponds to the cost function of the optimization problem. We explain the Boltzmann distribution by generalizing the concept of quantum heating in a single oscillator to the case of multiple coupled oscillators. The present result also suggests that such driven dissipative nonlinear oscillator networks can be applied to Boltzmann sampling, which is used, e.g., for Boltzmann machine learning in the field of artificial intelligence.
The mean field equation involving the $N$-Laplace operator and an exponential nonlinearity is considered in dimension $N\geq2$ on bounded domains with homogenoeus Dirichlet boundary condition. By a detailed asymptotic analysis we derive a quantization property in the non-compact case, yielding to the compactness of the solutions set in the so-called non-resonant regime. In such a regime, an existence result is then provided by a variational approach.
We analyze empirical relationships between the optical, near infrared, and HI characteristics of isolated galaxies from the 2MIG Catalog covering the entire sky. Data on morphological types, K_S-, and B-magnitudes, linear diameters, HI masses, and rotational velocities are examined. The regression parameters, dispersions, and correlation coefficients are calculated for pairs of these characteristics. The resulting relationships can be used to test the hierarchical theory of galaxy formation through numerous mergers of cold dark matter.
We study p-divisibility of discriminants of Hecke algebras associated to spaces of cusp forms of prime level. We make a precise conjecture about the indexes of Hecke algebras in their normalisation which implies (if true) the conjecture that there are no mod p congruences between non-conjugate newforms of weight 2 and level Gamma_0(p).
[Abridged] We present a critical analysis of the rich optical recombination spectrum of NGC 7009, in the context of the bi-abundance nebular model proposed by Liu et al. (2000). The observed relative intensities are compared with the theoretical predictions based on high quality effective recombination coefficients, now available for the recombination line spectrum of a number of heavy element ions. The possibility of plasma diagnostics using the optical recombination lines (ORLs) of heavy element ions is discussed in detail. Plasma diagnostics based on the N II and O II recombination spectra both yield electron temperatures close to 1000 K, which is lower than those derived from the collisionally excited line (CEL) ratios by nearly one order of magnitude. The very low temperatures yielded by the O II and N II ORLs indicate that they originate from very cold regions. The C^{2+}/H^+, N^{2+}/H^+, O^{2+}/H^+ and Ne^{2+}/H^+ ionic abundance ratios derived from ORLs are consistently higher, by about a factor of 5, than the corresponding values derived from CELs. In calculating the ORL ionic abundance ratios, we have used the newly available high quality effective recombination coefficients, and adopted an electron temperature of 1000 K, as given by the ORL diagnostics and as a consequence presumably representing the physical conditions prevailing in the regions where the heavy element ORLs arise. A comparison of the results of plasma diagnostics and abundance determinations for NGC 7009 points to the existence of "cold", metal-rich (i.e. H-deficient) inclusions embedded in the hot, diffuse ionized gas, first postulated by Liu et al. (2000).
A Yang-Mills solution is constructed on T^6 which corresponds to a brane configuration composed purely of 0-branes and 6-branes. This configuration breaks all supersymmetries and has an energy greater than the sum of the energies of its components; nonetheless, the configuration is stable classically, at least to quadratic order. An analogous construction is also given for a system of 0-branes and 8-branes on T^8. These constructions may prove to be useful for describing 6-branes and 8-branes in M(atrix) theory.
Damage spreading for 2D Ising cluster dynamics is investigated numerically by using random numbers in a way that conforms with the notion of submitting the two evolving replicas to the same thermal noise. Two damage spreading transitions are found; damage does not spread either at low or high temperatures. We determine the critical exponents at the high-temperature transition point, which seem consistent with directed percolation.
We derive light-cone cubic interaction vertices involving fermions and bosons of arbitrary spin by demanding closure of the Poincar\'e algebra. We derive the three-point scattering amplitude corresponding to these interaction vertices and find that they possess interesting factorization properties, identical to the case of three boson scattering.
The post-Newtonian expansion appears to be a relevant tool for predicting the gravitational waveforms generated by some astrophysical systems such as binaries. In particular, inspiralling compact binaries are well-modelled by a system of two point-particles moving on a quasi-circular orbit whose decay by emission of gravitational radiation is described by a post-Newtonian expansion. In this paper we summarize the basics of the computation by means of a series of multipole moments of the exterior field generated by an isolated source in the post-Newtonian approximation. This computation relies on an ansatz of matching the exterior multipolar field to the inner field of a slowly-moving source. The formalism can be applied to point-particles at the price of a further ansatz, that the infinite self-field of point-particles can be regularized in a certain way. As it turns out, the concept of point-particle requires a precise definition in high post-Newtonian approximations of general relativity.
Using a density functional approach based on a Skyrme interaction, thermodynamic properties of finite nuclei are investigated at non-zero temperture. The role of a momentum dependent isovector term is now studied besides volume, symmetry, surface and Coulomb effects. Various features associated with both mechanical and chemical instability and the liquid-gas coexistence curve are sensitive to the Skyrme interaction. The separated effects of the isoscalar term and the isovector term of momentum dependent interaction are studied for a modified SKM($m^*=m$) interaction. The frequently used Skyrme interaction SLy4 is one of the cases considered and is shown to have better features for neutron star studies due to a larger symmetry energy.
Medical image segmentation, the task of partitioning an image into meaningful parts, is an important step toward automating medical image analysis and is at the crux of a variety of medical imaging applications, such as computer aided diagnosis, therapy planning and delivery, and computer aided interventions. However, the existence of noise, low contrast and objects' complexity in medical images are critical obstacles that stand in the way of achieving an ideal segmentation system. Incorporating prior knowledge into image segmentation algorithms has proven useful for obtaining more accurate and plausible results. This paper surveys the different types of prior knowledge that have been utilized in different segmentation frameworks. We focus our survey on optimization-based methods that incorporate prior information into their frameworks. We review and compare these methods in terms of the types of prior employed, the domain of formulation (continuous vs. discrete), and the optimization techniques (global vs. local). We also created an interactive online database of existing works and categorized them based on the type of prior knowledge they use. Our website is interactive so that researchers can contribute to keep the database up to date. We conclude the survey by discussing different aspects of designing an energy functional for image segmentation, open problems, and future perspectives.
We have investigated a polymer growth process on the triangular lattice where the configurations produced are self-avoiding trails. We show that the scaling behaviour of this process is similar to the analogous process on the square lattice. However, while the square lattice process maps to the collapse transition of the canonical interacting self-avoiding trail model (ISAT) on that lattice, the process on the triangular lattice model does not map to the canonical equilibrium model. On the other hand, we show that the collapse transition of the canonical ISAT model on the triangular lattice behaves in a way reminiscent of the $\theta$-point of the interacting self-avoiding walk model (ISAW), which is the standard model of polymer collapse. This implies an unusual lattice dependency of the ISAT collapse transition in two dimensions.   By studying an extended ISAT model, we demonstrate that the growth process maps to a multi-critical point in a larger parameter space. In this extended parameter space the collapse phase transition may be either $\theta$-point-like (second-order) or first-order, and these two are separated by a multi-critical point. It is this multi-critical point to which the growth process maps. Furthermore, we provide evidence that in addition to the high-temperature gas-like swollen polymer phase (coil) and the low-temperature liquid drop-like collapse phase (globule) there is also a maximally dense crystal-like phase (crystal) at low temperatures dependent on the parameter values. The multi-critical point is the meeting point of these three phases. Our hypothesised phase diagram resolves the mystery of the seemingly differing behaviours of the ISAW and ISAT models in two dimensions as well as the behaviour of the trail growth process.
In this manuscript, the behavior of the Wigner function of accelerated and non-accelerated two qubit system passing through different noisy channels is discussed. The decoherence of the initial quantum correlation due to the noisy channels and the acceleration process is investigated by means of Wigner function. The negative (positive) behavior of the Wigner function predicts the gain of the quantum (classical) correlations. Based on the upper and lower bounds of the Wigner function, the entangled initial state loses its quantum correlation due the acceleration process and the strengths of the noisy channels. However, by controlling the distribution angles, the decoherence of these quantum correlation may be suppressed. For accelerated state, the robustness of the quantum correlations contained in the initial state appears in different ranges of the distribution angles depending on the noisy type. For the bit phase flip and the phase flip channels, the robustness of the quantum correlations is shown at any acceleration and large range of distribution angles. However, the fragility of the quantum correlation is depicted for large values for strength of the bit flip channel. Different profiles of the Wigner function are exhibited for the quantum and classical correlations, cup, lune, hemisphere.
We present a detailed analysis of the far-IR properties of the bright, lensed, z = 2.3, SMG, SMM J2135-0102, using new observations with Herschel, SCUBA-2 and the VLA. These data allow us to constrain the galaxy's SED and show that it has an intrinsic rest-frame 8-1000um luminosity, L(bol), of (2.3 +/- 0.2) x 10^12 L(sun) and a likely SFR of ~400 M(sun)/yr. The galaxy sits on the far-IR/radio correlation for far-IR-selected galaxies. At ~>70um, the SED can be described adequately by dust components with T(d) ~ 30 and 60K. Using SPIRE's Fourier Transform Spectrometer we report a detection of the [CII] 158um cooling line. If the [CII], CO and far-IR continuum arise in photo-dissociation regions, we derive a characteristic gas density, n ~ 10^3 cm^-3, and a far-UV radiation field, G_0, 10^3x stronger than the Milky Way. L([CII])/L(bol) is significantly higher than in local ULIRGs but similar to the values found in local star-forming galaxies and starburst nuclei. This is consistent with SMM J2135-0102 being powered by starburst clumps distributed across ~2 kpc, evidence that SMGs are not simply scaled-up ULIRGs. Our results show that SPIRE's FTS has the ability to measure the redshifts of distant, obscured galaxies via the blind detection of atomic cooling lines, but it will not be competitive with ground-based CO-line searches. It will, however, allow detailed study of the integrated properties of high-redshift galaxies, as well as the chemistry of their ISM, once more suitably bright candidates have been found.
Let $\rho(G)$ denote the number of convex cycles of a simple graph G of order n, size m, and girth 3 <= g <=n. It is proved that $\rho(G) \leq \frac{n}{g}(m-n+1)$ and that equality holds if and only if G is an even cycle or a Moore graph. The equality also holds for a possible Moore graph of diameter 2 and degree 57 thus giving a new characterization of Moore graphs.