ShantanuT01/DACTYL-Pretraining huggingface dataset:
It takes $n^2/4$ cliques to cover all the edges of a complete bipartite graph $K_{n/2,n/2}$, but how many cliques does it take to cover all the edges of a graph $G$ if $G$ has no $K_{t,t}$ induced subgraph? We prove that $O(|G|^{2-1/(2t)})$ cliques suffice; and also prove that, even for graphs with no stable set of size four, we may need more than linearly many cliques. This settles two questions discussed at a recent conference in Lyon.
We establish inversion formulas of the so called filtered back-projection type to recover a function supported in the ball in even dimensions from its spherical means over spheres centered on the boundary of the ball. We also find several formulas to recover initial data of the form (f,0) (or (0,g)) for the free space wave equation in even dimensions from the trace of the solution on the boundary of the ball, provided the initial data has support in the ball.
We analyze the stability of a dilute plasma with thermal and composition gradients in the limit where conduction is slow compared to the dynamical timescale. We find necessary and sufficient conditions for stability when the background magnetic field is either parallel or perpendicular to the thermal and composition gradients that are parallel to the gravitational field. We provide approximate solutions for all the relevant modes involved, which are driven by gravity, conduction, and diffusion. We discuss the astrophysical implications of our findings for a representative galaxy cluster where helium has sedimented.
We address open quantum systems out-of-equilibrium as effective quantum probes for the characterisation of their environment. We discuss estimation schemes for parameters driving a de-phasing evolution of the probe and then focus on qubits, establishing a relationship between the quantum Fisher information and the residual coherence of the probe. Finally, we apply our results to the characterisation of the ohmicity parameter of a bosonic environment.
We present a general model, based on a Hamiltonian approach, for the joint quantum state of photon pairs generated through pulsed spontaneous four-wave mixing, including nonlinear phase-modulation and a finite material response time. For the case of a silica fiber, it is found that the pair-production rate depends weakly on the waveguide temperature, due to higher-order Raman scattering events, and more strongly on pump-pair frequency detuning. From the analytical model, a numerical scheme is derived, based on the well-known split-step method. This scheme allows computation of joint states where nontrivial effects are included, such as group-velocity dispersion and Raman scattering. In this work, the numerical model is used to study the impact of the non-instantaneous response on the pre-filtering purity of heralded single photons. We find that for pump pulses shorter than 1 ps, a significant detuning-dependent change in quantum-mechanical purity may be observed in silica.
For a toric log variety with standard coefficients, we show that the minimal log discrepancy at a closed invariant point bounds the Cartier index of a neighbourhood.
We use the Science Demonstration Phase data of the Herschel Virgo Cluster Survey to search for dust emission of early-type dwarf galaxies in the central regions of the Virgo Cluster as an alternative way of identifying the interstellar medium.We present the first possible far-infrared detection of cluster early-type dwarf galaxies: VCC781 and VCC951 are detected at the 10 sigma level in the SPIRE 250 micron image. Both detected galaxies have dust masses of the order of 10^5 Msun and average dust temperatures ~20K. The detection rate (less than 1%) is quite high compared to the 1.7% detection rate for Hi emission, considering that dwarfs in the central regions are more Hi deficient. We conclude that the removal of interstellar dust from dwarf galaxies resulting from ram pressure stripping, harassment, or tidal effects must be as efficient as the removal of interstellar gas.
The localization behavior of noninteracting two-dimensional electrons in a random potential and strong magnetic field is of fundamental interest for the physics of the quantum Hall effect. In order to understand the emergence of power-law delocalization near the discrete extended-state energies $E_n = \hbar \omega_c (n+{1/2})$, we study a generalization of the disorder-averaged Liouvillian framework for the lowest Landau level to $N$ flavors of electron densities (N=1 for the physical case). We find analytically the large-N limit and 1/N corrections for all disorder strengths: at $N = \infty$ this gives an estimate of the critical conductivity, and at order 1/N an estimate of the localization exponent $\nu$. The localization properties of the analytically tractable $N \gg 1$ theory seem to be continuously connected to those of the exact quantum Hall plateau transition at $N = 1$.
GaN based high electron mobility transistors show promise in numerous device applications which elicits the need for accurate models of bulk, surface, and interface electronic properties. We detail here a hybrid density functional theory study of zinc blende (zb) GaN and diamond bulk and surface properties, and zb GaN on diamond interfaces using slab supercell models. Details are provided on the dependence of electronic properties with respect to supercell size, the use of pseudo-hydrogen to passivate the bottom GaN layer, and dipole corrections. The large bulk modulus of diamond provides a templating structure for GaN to grow upon, where a large lattice mismatch is accounted for through the inclusion of a cationic Ga adlayer. Looking at both type I and II surfaces and interfaces of GaN shows the instability of zb GaN without an adlayer (type II), where increased size, pseudo-hydrogen passivation and dipole corrections do not remove the spurious interaction between the top and bottom layers in type II GaN. Layer dependent density of states, local potential differences, and charge density differences show that the type I interface (with a Ga adlayer) is stable with an adhesion energy of 0.704 eV/{\AA}2 (4.346 J/m2); interestingly, the diamond charge density intercalates into the first layer of GaN, which was seen experimentally for wurtzite GaN grown over diamond. The type II interface is shown to be unstable which implies that, to form a stable, thin-film zb interface between GaN and diamond, the partial pressure of trimethylgallium must be controlled to ensure a Ga layer exists both on the top and bottom layer of the GaN thin film atop the diamond. We believe our results can shed light towards a better understanding of the GaN/diamond multifaceted interface present in the GaN overgrowth on diamond samples.
We consider elliptic equations and systems in divergence form with the conormal or the Robin boundary conditions, with small BMO (bounded mean oscillation) or variably partially small BMO coefficients. We propose a new class of domains which are locally close to a half space (or convex domains) with respect to the Lebesgue measure in the system (or scalar, respectively) case, and obtain the $W^1_p$ estimate for the conormal problem with the homogeneous boundary condition. Such condition is weaker than the Reifenberg flatness condition, for which the closeness is measured in terms of the Hausdorff distance, and the semi-convexity condition. For the conormal problem with inhomogeneous boundary conditions, we also assume that the domain is Lipschitz. By using these results, we obtain the $W^1_p$ and weighted $W^1_p$ estimates for the Robin problem in these domains.
Recently, Andrews, Chan, Kim and Osburn introduced the even strings and the odd strings in the overpartitions. We show that their conjecture $A_k (n) \geq B_k (n)$ holds for large enough positive integers n, where A_k(n) (resp. B_k(n)) is the number of odd (resp. even) strings along the overpartitions of n. We introduce m-strings and show that how this new combinatorial object is related with another positivity conjecture of Andrews, Chan, Kim, and Osburn. Finally, we confirm that the positivity conjecture is also true for large enough integers.
The quark mass dependence of the energy spectrum in the Nambu--Goto string with point--like masses (quarks) at its ends is analyzed. To this end, linearized equations of motion and boundary conditions in this model are considered. It is shown that for sufficiently large quark masses, the first excited state in string spectrum may be arbitrary close to the ground state. Obviously this points to infrared instability in the system under consideration. Possible modifications of string model which could remove this drawback are discussed.
The interactions between a group of components are commonly studied in several areas of science (social science, biology, material science, complex dynamical systems, among others) using the methods of thermodynamics and statistical mechanics. In this work we study the properties of the recently proposed off-lattice, two-dimensional Potts model [Eur. Phys. J. B 87, 78 (2014)], originally motivated by the dynamics of agent opinions, and which is described by a Hamiltonian obtained by a maximum entropy inference procedure. We performed microcanonical and canonical Monte Carlo simulations of the first-order phase transition in the model, revealing a caloric curve with metastable regions. Furthermore, we report a "switching" behavior between multiple metastable states. We also note that the thermodynamics of the model has striking similarities with systems having long-range interactions, even though the interactions are short-ranged.
We probe the star formation properties of the gas in AzTEC-1 in the COSMOS field, one of the best resolved and brightest starburst galaxies at $z \approx 4.3$, forming stars at a rate > 1000 $\mathrm{M_{\odot}}\,\mathrm{yr^{-1}}$. Using recent ALMA observations, we study star formation in the galaxy nucleus and an off-center star-forming clump and measure a median star formation rate (SFR) surface density of $\Sigma^{\mathrm{nucleus}}_{\mathrm{SFR}} = 270\pm54$ and $\Sigma^{\mathrm{sfclump}}_{\mathrm{SFR}} = 170\pm38\,\mathrm{M_{\odot}}\,\mathrm{yr}^{-1}\,\mathrm{kpc}^{-2}$, respectively. Following the analysis by Sharda et al. (2018), we estimate the molecular gas mass, freefall time and turbulent Mach number in these regions to predict $\Sigma_{\mathrm{SFR}}$ from three star formation relations in the literature. The Kennicutt-Schmidt (Kennicutt 1998, KS) relation, which is based on the gas surface density, underestimates the $\Sigma_{\mathrm{SFR}}$ in these regions by a factor 2-3. The $\Sigma_{\mathrm{SFR}}$ we calculate from the single-freefall model of Krumholz et al. 2012 (KDM) is consistent with the measured $\Sigma_{\mathrm{SFR}}$ in the nucleus and the star-forming clump within the uncertainties. The turbulence-regulated star formation relation by Salim et al. 2015 (SFK) agrees slightly better with the observations than the KDM relation. Our analysis reveals that an interplay between turbulence and gravity can help sustain high SFRs in high-redshift starbursts. It can also be extended to other high- and low-redshift galaxies thanks to the high angular resolution and sensitivity of ALMA observations.
The theory of quantum propagator and time--dependent integrals of motion in quantum optics is reviewed as well as the properties of Wigner function, Q--function, and coherent state representation. Propagators and wave functions of a free particle, harmonic oscillator, and the oscillator with varying frequency are studied using time--dependent linear in position and momentum integrals of motion. Such nonclassical states of light (of quantum systems) as squeezed states, correlated states, even and odd coherent states (Schr\"odinger cat states) are considered. Photon distribution functions of Schr\"odinger cat male and female states are given, and the photon distribution function of squeezed vacuum is derived using the theory of the oscillator with varying parameters. Properties of multivariable Hermite polynomials used for the description of the multimode squeezed and correlated light and polymode Schr\"odinger cats are studied.
We consider a model of non-Markovian Quantum Brownian motion that consists of an harmonic oscillator bilinearly coupled to a thermal bath, both via its position and momentum operators. We derive the master equation for such a model and we solve the equations of motion for a generic Gaussian system state. We then investigate the resulting evolution of the first and second moments for both an Ohmic and a super-Ohmic spectral density. In particular, we show that, irrespective of the specific form of the spectral density, the coupling with the momentum enhances the dissipation experienced by the system, accelerating its relaxation to the equilibrium, as well as modifying the asymptotic state of the dynamics. Eventually, we characterize explicitly the non-Markovianity of the evolution, using a general criterion which relies on the positivity of the master equation coefficients.
We propose a novel estimator of the polarization amplitude from a single measurement of its normally distributed $(Q,U)$ Stokes components. Based on the properties of the Rice distribution and dubbed 'MAS' (Modified ASymptotic), it meets several desirable criteria:(i) its values lie in the whole positive region; (ii) its distribution is continuous; (iii) it transforms smoothly with the signal-to-noise ratio (SNR) from a Rayleigh-like shape to a Gaussian one; (iv) it is unbiased and reaches its components' variance as soon as the SNR exceeds 2; (v) it is analytic and can therefore be used on large data-sets. We also revisit the construction of its associated confidence intervals and show how the Feldman-Cousins prescription efficiently solves the issue of classical intervals lying entirely in the unphysical negative domain. Such intervals can be used to identify statistically significant polarized regions and conversely build masks for polarization data. We then consider the case of a general $[Q,U]$ covariance matrix and perform a generalization of the estimator that preserves its asymptotic properties. We show that its bias does not depend on the true polarization angle, and provide an analytic estimate of its variance. The estimator value, together with its variance, provide a powerful point-estimate of the true polarization amplitude that follows an unbiased Gaussian distribution for a SNR as low as 2. These results can be applied to the much more general case of transforming any normally distributed random variable from Cartesian to polar coordinates.
We generalize the classical lifting and recombination scheme for rational and absolute factorization of bivariate polynomials to the case of a critical fiber. We explore different strategies for recombinations of the analytic factors, depending on the complexity of the ramification. We show that working along a critical fiber leads in some cases to a good theoretical complexity, due to the smaller number of analytic factors to recombine. We pay a particular attention to the case of polynomials that are non degenerate with respect to their P-adic Newton polytopes.
We demonstrate that, according to a recently suggested Lorentz-force approach to the Casimir effect, the vacuum force on an atom embedded in a material cavity differs substantially from the force on an atom of the cavity medium. The force on an embedded atom is of the familiar (van der Waals and Casimir-Polder) type, however, more strongly modified by the cavity medium than usually considered. The force on an atom of the cavity medium is of the medium-assisted force type with rather unusual properties, as demonstrated very recently [M. S. Tomas, Phys. Rev. A 71, 060101(R) (2005)]. This implies similar properties of the vacuum force between two atoms in a medium.
Chandra obtained two High Energy Transmission Grating (HETG) spectra of the stellar-mass black hole GRO J1655-40 during its 2005 outburst, revealing a rich and complex disk wind. Soon after its launch, the Neil Gehrels Swift Observatory began monitoring the same outburst. Some X-ray Telescope (XRT) observations were obtained in a mode that makes it impossible to remove strong Mn calibration lines, so the Fe K-alpha line region in the spectra was previously neglected. However, these lines enable a precise calibration of the energy scale, facilitating studies of the absorption-dominated disk wind and its velocity shifts. Here, we present fits to 15 Swift/XRT spectra, revealing variability and evolution in the outflow. The data strongly point to a magnetically driven disk wind: both the higher velocity (e.g., v ~ 10^4 km/s) and lower velocity (e.g., v ~ 10^3 km/s) wind components are typically much faster than is possible for thermally driven outflows (v < 200 km/s), and photoionization modeling yields absorption radii that are two orders of magnitude below the Compton radius that defines the typical inner extent of thermal winds. Moreover, correlations between key wind parameters yield an average absorption measure distribution (AMD) that is consistent with magnetohydrodynamic wind models. We discuss our results in terms of recent observational and theoretical studies of black hole accretion disks and outflows, and future prospects.
We present IRAC 3.6, 4.5, 5.8 and 8 micron photometry for the 17 A, K and M type members of the Eta Chameleontis association. These data show infrared excesses toward six of the 15 K and M stars, indicating the presence of circumstellar disks around 40% of the stars with masses of 0.1-1 solar mass. The two A-stars show no infrared excesses. The excess emission around one of the stars is comparable to the median excess for classical T Tauri stars in the Taurus association; the remaining five show comparatively weak excess emission. Taking into account published Halpha spectroscopy that shows that five of the six stars are accreting, we argue that the disks with weak mid-infrared excesses are disks in which the inner disks have been largely depleted of small grains by grain growth, or, in one case, the small grains have settled to the midplane. This suggests that Eta Cha has a much higher fraction of disks caught in the act of transitioning into optically thin disks than that measured in younger clusters and associations.
A sequence of nonnegative integers $\pi$ is {\it graphic} if it is the degree sequence of some graph $G$. In this case we say that $G$ is a \textit{realization} of $\pi$, and we write $\pi=\pi(G)$. A graphic sequence $\pi$ is {\it potentially $H$-graphic} if there is a realization of $\pi$ that contains $H$ as a subgraph.   Given nonincreasing graphic sequences $\pi_1=(d_1,\ldots,d_n)$ and $\pi_2 = (s_1,\ldots,s_n)$, we say that $\pi_1$ {\it majorizes} $\pi_2$ if $d_i \geq s_i$ for all $i$, $1 \leq i \leq n$. In 1970, Erd\H{o}s showed that for any $K_{r+1}$-free graph $H$, there exists an $r$-partite graph $G$ such that $\pi(G)$ majorizes $\pi(H)$. In 2005, Pikhurko and Taraz generalized this notion and showed that for any graph $F$ with chromatic number $r+1$, the degree sequence of an $F$-free graph is, in an appropriate sense, nearly majorized by the degree sequence of an $r$-partite graph.   In this paper, we give similar results for degree sequences that are not potentially $H$-graphic. In particular, there is a graphic sequence $\pi^*(H)$ such that if $\pi$ is a graphic sequence that is not potentially $H$-graphic, then $\pi$ is close to being majorized by $\pi^*(H)$. Similar to the role played by complete multipartite graphs in the traditional extremal setting, the sequence $\pi^*(H)$ asymptotically gives the maximum possible sum of a graphic sequence $\pi$ that is not potentially $H$-graphic.
We introduce a holomorphic representation for the Lorentzian EPRL spinfoam on arbitrary 2-complexes. The representation is obtained via the Ashtekar-Lewandowski-Marolf-Mour\~ao-Thiemann heat kernel coherent state transform. The new variables are classical holonomy-flux phase space variables $(h,X)\simeq \mathcal T^*SU(2)$ of Hamiltonian loop quantum gravity prescribing the holonomies of the Ashtekar connection $A=\Gamma + \gamma K$, and their conjugate gravitational fluxes. For small heat kernel `time' the spinfoam amplitude is peaked on classical space-time geometries, where at most countably many curvatures are allowed for non-zero Barbero-Immirzi parameter. We briefly comment on the possibility to use the alternative flipped classical limit.
Theoretical foundations of a new algorithm for determining the p-capitulation type kappa(K) of a number field K with p-class rank rho=2 are presented. Since kappa(K) alone is insufficient for identifying the second p-class group G=Gal(F(p,2,K) | K) of K, complementary techniques are developed for finding the nilpotency class and coclass of G. An implementation of the complete algorithm in the computational algebra system Magma is employed for calculating the Artin pattern AP(K)=(tau(K),kappa(K)) of all 34631 real quadratic fields K=Q(squareroot(d)) with discriminants 0<d<100000000 and 3-class group of type (3,3). The results admit extensive statistics of the second 3-class groups G=Gal(F(3,2,K) | K) and the 3-class field tower groups H=Gal(F(3,K) | K).
We present a fully quantum theory describing the cooling of a cantilever coupled via radiation pressure to an illuminated optical cavity. Applying the quantum noise approach to the fluctuations of the radiation pressure force, we derive the opto-mechanical cooling rate and the minimum achievable phonon number. We find that reaching the quantum limit of arbitrarily small phonon numbers requires going into the good cavity (resolved phonon sideband) regime where the cavity linewidth is much smaller than the mechanical frequency and the corresponding cavity detuning. This is in contrast to the common assumption that the mechanical frequency and the cavity detuning should be comparable to the cavity damping.
We address the Cauchy problem for a nonlinear Schr{\"o}dinger equation where the dispersion is modulated by a deterministic noise. The noise is understood as the derivative of a self-affine function of order H $\in$ (0, 1). Due to the self-similarity of the noise, we obtain modified Strichartz estimates which enables us to prove the global well-posedness of the equation for L2-supercritical nonlinearities. This is an occurence of regularization by noise in a purely deterministic context.
A theoretical analysis of the partial inclusive B-->X_s gamma decay rate with a cut E_gamma>E_0 on photon energy must deal with short-distance contributions associated with three different mass scales: the hard scale m_b, an intermediate scale \sqrt{m_b Delta}, and a soft scale Delta, where Delta=m_b-2E_0=1GeV for E_0=1.8GeV. The cut-dependent effects are described in terms of two perturbative objects called the jet function and the soft function, which for a next-to-next-to-leading order analysis of the decay rate are required with two-loop accuracy. The two-loop calculation of the soft function is presented here, while that of the jet function will be described in a subsequent paper. As a by-product, we rederive the two-loop anomalous-dimension kernel of the B-meson shape function.
A well known observation of Lov\'asz is that if a hypergraph is not $2$-colorable, then at least one pair of its edges intersect at a single vertex. %This very simple criterion turned out to be extremly useful . In this short paper we consider the quantitative version of Lov\'asz's criterion. That is, we ask how many pairs of edges intersecting at a single vertex, should belong to a non $2$-colorable $n$-uniform hypergraph? Our main result is an {\em exact} answer to this question, which further characterizes all the extremal hypergraphs. The proof combines Bollob\'as's two families theorem with Pluhar's randomized coloring algorithm.