ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present a Chandra monitoring campaign of the highly variable Seyfert galaxy UGC 4203 (the "Phoenix Galaxy") which revealed variations in the X-ray absorbing column density on time scales of two weeks. This is the third, clear case, after NGC 1365 and NGC 7582, of dramatic N_H variability on short time scales observed in a "changing look" source, i.e. an AGN observed in the past in both a reflection-dominated and a Compton-thin state. The inferred limits on the distance of the X-ray absorber from the center suggest that the X-ray "torus" could be one and the same with the broad emission line region. This scenario, first proposed for an "ad-hoc" picture for NGC 1365, may be the common structure of the circumnuclear medium in AGN.
Let $K$ be a global field of positive characteristic. We give an asymptotic formula for the number of $K$-points of bounded height on the Hilbert scheme $\text{Hilb}^2\mathbb{P}^2$ and show that by eliminating an exceptional thin set, the constant in front of the main term agrees with the prediction of Peyre in the function field setting. Moreover, we extend the analogy between the integers and $0$-cycles on a variety $V$ over a finite field to $0$-cycles on a variety $V$ over $K$ and establish a version of the prime number theorem in the case when $V = \mathbb{P}^2$.
We present near-IR photometry and spectroscopy of 30 extremely luminous radio and mid-IR selected galaxies. With bolometric luminosities exceeding $\sim10^{13}$ $\rm{L_{\odot}}$ and redshifts ranging from $z = 0.880-2.853$, we use VLT instruments X-shooter and ISAAC to investigate this unique population of galaxies. Broad multi-component emission lines are detected in 18 galaxies and we measure the near-IR lines $\rm{H\rm{\beta}}$, $\text{[OIII]}\rm{\lambda}\rm{\lambda}4959,5007$ and $\rm{H\rm{\alpha}}$ in six, 15 and 13 galaxies respectively, with 10 $\rm{Ly\alpha}$ and five CIV lines additionally detected in the UVB arm. We use the broad $\text{[OIII]}\rm{\lambda}5007$ emission lines as a proxy for the bolometric AGN luminosity, and derive lower limits to supermassive black hole masses of $10^{7.9}$-$10^{9.4}$ $\text{M}_{\odot}$ with expectations of corresponding host masses of $10^{10.4}$-$10^{12.0}$ $\text{M}_{\odot}$. We measure $\rm{\lambda}_{Edd}$ > 1 for eight of these sources at a $2\sigma$ significance. Near-IR photometry and SED fitting are used to compare stellar masses directly. We detect both Balmer lines in five galaxies and use these to infer a mean visual extinction of $A_{V}$ = 2.68 mag. Due to non-detections and uncertainties in our $\rm{H\rm{\beta}}$ emission line measurements, we simulate a broad $\rm{H\rm{\beta}}$ line of FWHM = 1480 $\rm{kms^{-1}}$ to estimate extinction for all sources with measured $\rm{H\rm{\alpha}}$ emission. We then use this to infer a mean $A_{V}=3.62$ mag, demonstrating the highly-obscured nature of these galaxies, with the consequence of increasing our estimates of black-hole masses by an 0.5 orders of magnitude in the most extreme and obscured cases.
We explore the regular or chaotic nature of orbits of stars moving in the meridional (R,z) plane of an axially symmetric time-dependent disk galaxy model with a central, spherically symmetric nucleus. In particular, mass is linearly transported from the disk to the galactic nucleus, in order to mimic, in a way, the case of self-consistent interactions of an actual N-body simulation. We thus try to unveil the influence of this mass transportation on the different families of orbits of stars by monitoring how the percentage of chaotic orbits, as well as the percentages of orbits of the main regular resonant families, evolve as the galaxy develops a dense and massive nucleus in its core. The SALI method is applied to samples of orbits in order to distinguish safely between ordered and chaotic motion. In addition, a method based on the concept of spectral dynamics is used for identifying the various families of regular orbits and also for recognizing the secondary resonances that bifurcate from them. Our computations strongly suggest that the amount of the observed chaos is substantially increased as the nucleus becomes more massive. Furthermore, extensive numerical calculations indicate that there are orbits which change their nature from regular to chaotic and vice versa and also orbits which maintain their orbital character during the galactic evolution. The present outcomes are compared to earlier related work.
This paper deals with iteration stable (STIT) tessellations, and, more generally, with a certain class of tessellations that are infinitely divisible with respect to iteration. They form a new, rich and flexible class of spatio-temporal models considered in stochastic geometry. The martingale tools developed in \cite{STP1} are used to study second-order properties of STIT tessellations. Firstly, a general formula for the variance of the total surface area of cell boundaries inside a convex observation window is shown. This general expression is combined with tools from integral geometry to derive explicit exact and asymptotic second-order formulae in the stationary and isotropic set-up, where a family of chord-power integrals plays an important role. Also a general formula for the pair-correlation function of the surface measure is found.
In recent works, \v{C}aslav Brukner and Jacques Pienaar have raised interesting objections to the relational interpretation of quantum mechanics. We answer these objections in detail and show that, far from questioning the viability of the interpretation, they sharpen and clarify it.
We present a new derivation of the CORS Baade-Wesselink method in the Walraven photometric system. We solved the complete Baade-Wesselink equation by calibrating the surface brightness function with a recent grid of atmosphere models. The new approach was adopted to estimate the mean radii of a sample of Galactic Cepheids for which are available precise light curves in the Walraven bands. Current radii agree, within the errors, quite well with Cepheid radii based on recent optical and near-infrared interferometric measurements. We also tested the impact of the projection factor on the Period-Radius relation using two different values (p=1.36, p=1.27) that bracket the estimates available in the literature. We found that the agreement of our Period-Radius relation with similar empirical and theoretical Period-Radius relations in the recent literature, improves by changing the projection factor from p=1.36 to p=1.27. Our Period-Radius relation is log(R)=(0.75\pm 0.03)log(P)+(1.10 \pm 0.03), with a rms=0.03 dex. Thanks to accurate estimates of the effective temperature of the selected Cepheids, we also derived the Period-Luminosity relation in the V band and we found Mv=(-2.78 \pm 0.11)log(P)+(-1.42 \pm 0.11) with rms=0.13 mag, for p=1.27. It agrees quite well with recent results in the literature, while the relation for p=1.36 deviates by more than 2sigma. We conclude that, even taking into account the intrinsic dispersion of the obtained Period-Luminosity relations, that is roughly of the same order of magnitude as the effect of the projection factor, the results of this paper seem to favour the value p = 1.27.
We conjecture a formula for the symmetric function $\frac{[n-k]_t}{[n]_t}\Delta_{h_m}\Delta_{e_{n-k}}\omega(p_n)$ in terms of decorated partially labelled square paths. This can be seen as a generalization of the square conjecture of Loehr and Warrington (Loehr, Warrington 2007), recently proved by Sergel (Sergel 2017) after the breakthrough of Carlsson and Mellit (Carlsson, Mellit 2018). Moreover, it extends to the square case the combinatorics of the generalized Delta conjecture of Haglund, Remmel and Wilson (Haglund, Remmel, Wilson 2015), answering one of their questions. We support our conjecture by proving the specialization $m=q=0$, reducing it to the same case of the Delta conjecture, and the Schr\"{o}der case, i.e. the case $\langle \cdot ,e_{n-d}h_d\rangle$. The latter provides a broad generalization of the $q,t$-square theorem of Can and Loehr (Can, Loehr 2006). We give also a combinatorial involution, which allows to establish a linear relation among our conjectures (as well as the generalized Delta conjectures) with fixed $m$ and $n$. Finally, in the appendix, we give a new proof of the Delta conjecture at $q=0$.
Scaling exponents are the central quantitative prediction of theories of turbulence and in-situ satellite observations of the high Reynolds number solar wind flow have provided an extensive testbed of these. We propose a general, instrument independent method to estimate the uncertainty of velocity field fluctuations. We obtain the systematic shift that this uncertainty introduces into the observed spectral exponent. This shift is essential for the correct interpretation of observed scaling exponents. It is sufficient to explain the contradiction between spectral features of the Elsasser fields observed in the solar wind with both theoretical models and numerical simulations of Magnetohydrodynamic turbulence.
We study the enumeration problem for different kind of tree parking functions introduced recently, called tree parking functions, tree parking distributions, prime tree parking functions, and prime tree parking distributions, for rooted labelled trees of important combinatorial tree families including labelled ordered, unordered and binary trees. Using combinatorial decompositions of the underlying structures yields, after solving the resulting equations, implicit characterizations of suitable generating functions of the total number of such tree parking functions for trees of size $n$ and $n$ successful drivers, from which we obtain exact and asymptotic enumeration results. The approach can be extended to the general situation of tree parking functions for trees of size $n$ and $m<n$ drivers for which we are also able to characterize the generating functions solutions, which allow, by applying analytic combinatorics techniques, a study of the asymptotic behaviour of the total number of tree parking functions and distributions for $n \to \infty$ depending on the load factor $0 < \alpha = \frac{m}{n} < 1$.
Spanning trees are relevant to various aspects of networks. Generally, the number of spanning trees in a network can be obtained by computing a related determinant of the Laplacian matrix of the network. However, for a large generic network, evaluating the relevant determinant is computationally intractable. In this paper, we develop a fairly generic technique for computing determinants corresponding to self-similar networks, thereby providing a method to determine the numbers of spanning trees in networks exhibiting self-similarity. We describe the computation process with a family of networks, called $(x,y)$-flowers, which display rich behavior as observed in a large variety of real systems. The enumeration of spanning trees is based on the relationship between the determinants of submatrices of the Laplacian matrix corresponding to the $(x,y)$-flowers at different generations and is devoid of the direct laborious computation of determinants. Using the proposed method, we derive analytically the exact number of spanning trees in the $(x,y)$-flowers, on the basis of which we also obtain the entropies of the spanning trees in these networks. Moreover, to illustrate the universality of our technique, we apply it to some other self-similar networks with distinct degree distributions, and obtain explicit solutions to the numbers of spanning trees and their entropies. Finally, we compare our results for networks with the same average degree but different structural properties, such as degree distribution and fractal dimension, and uncover the effect of these topological features on the number of spanning trees.
We consider the problem of extremizing the tension for BPS strings in D=6 supergravities with different number of supersymmetries. General formulae for fixed scalars and a discussion of degenerate directions is given. Quantized moduli, according to recent analysis, are supposed to be related to conformal field theories which are the boundary of three dimensional anti-de Sitter space time.
We study a thermal engine model for which Newton's cooling law is obeyed during heat transfer processes. The thermal efficiency and its bounds at maximum output power are derived and discussed. This model, though quite simple, can be applied not only to Carnot engines but also to four other types of engines. For the long thermal contact time limit, new bounds, tighter than what were known before, are obtained. In this case,this model can simulate Otto, Joule Brayton, Diesel, and Atkinson engines. While in the short contact time limit, which corresponds to the Carnot cycle, the same efficiency bounds as Esposito et al's are derived. In both cases, the thermal efficiency decreases as the ratio between the heat capacities of the working medium during heating and cooling stages increases. This might provide instructions for designing real engines.
In the paper [Phys. Rev. A \textbf{69}, 052319 (2004)], a quantum direct communication protocol is proposed which is claimed to be unconditionally secure even for the case of a noisy channel. We show that this is not the case by giving an undetectable attack scheme.
The rigidity theorem for homotopy invariant presheaves with Witt-transfers on the category of smooth affine varieties over a field $k$ with characteristic not equal to 2 is proved. Namely for such a presheaf $\mathcal F$ the isomorphism $\mathcal F(U)\simeq \mathcal F(x)$ where $U$ is henseliation of a variety at smooth closed point with separable residue field (over $k$) is proved. The rigidity for presheaves $W^i(X\times -)$ where $X$ is smooth variety and $W^i(-)$ are derived Witt-groups ($i\in \mathbb Z/4\mathbb Z$) follows as corollary.
We compute the Small Quantum Cohomology of Hilb^2(P^1xP^1) and determine recursively most of the Big Quantum Cohomology. We prove a relationship between the invariants so obtained and the enumerative geometry of hyperelliptic curves in P^1xP^1. This extends the results obtained by Graber for Hilb^2(P^2) and hyperelliptic curves in P^2.
Extending investigations of Barker, Humpherys, Lafitte, Rudd, and Zumbrun for compressible gas dynamics and Freist\"uhler and Trakhinin for compressible magnetohydrodynamics, we study by a combination of asymptotic ODE estimates and numerical Evans function computations the one-dimensional stability of parallel isentropic magnetohydrodynamic shock layers over the full range of physical parameters (shock amplitude, strength of imposed magnetic field, viscosity, magnetic permeability, and electrical resistivity) for a $\gamma$-law gas with $\gamma\in [1,3]$. Other $\gamma$-values may be treated similarly, but were not checked numerically. Depending on magnetic field strength, these shocks may be of fast Lax, intermediate (overcompressive), or slow Lax type; however, the shock layer is independent of magnetic field, consisting of a purely gas-dynamical profile. In each case, our results indicate stability. Interesting features of the analysis are the need to renormalize the Evans function in order to pass continuously across parameter values where the shock changes type or toward the large-amplitude limit at frequency $\lambda=0$ and the systematic use of winding number computations on Riemann surfaces.
We investigate stochastic particle acceleration in accretion flows. It is believed that the magnetorotational instability (MRI) generates turbulence inside accretion flows and that cosmic rays (CRs) are accelerated by the turbulence. We calculate equations of motion for CRs in the turbulent fields generated by MRI with the shearing box approximation without back reaction to the field. The results show that the CRs randomly gain or lose their energies through the interaction with the turbulent fields. The CRs diffuse in the configuration space anisotropically: The diffusion coefficient in direction of the unperturbed flow is about twenty times higher than the Bohm coefficient, while those in the other directions are only a few times higher than the Bohm. The momentum distribution is isotropic, and its evolution can be described by the diffusion equation in momentum space where the diffusion coefficient is a power-law function of the CR momentum. We show that the shear acceleration efficiently works for energetic particles. We also cautiously note that in the shearing box approximation, particles that cross the simulation box many times along the radial direction suffer unphysical runaway acceleration by the Lorentz transformation, which needs to be taken with special care.
Fine-grained object recognition concerns the identification of the type of an object among a large number of closely related sub-categories. Multisource data analysis, that aims to leverage the complementary spectral, spatial, and structural information embedded in different sources, is a promising direction towards solving the fine-grained recognition problem that involves low between-class variance, small training set sizes for rare classes, and class imbalance. However, the common assumption of co-registered sources may not hold at the pixel level for small objects of interest. We present a novel methodology that aims to simultaneously learn the alignment of multisource data and the classification model in a unified framework. The proposed method involves a multisource region attention network that computes per-source feature representations, assigns attention scores to candidate regions sampled around the expected object locations by using these representations, and classifies the objects by using an attention-driven multisource representation that combines the feature representations and the attention scores from all sources. All components of the model are realized using deep neural networks and are learned in an end-to-end fashion. Experiments using RGB, multispectral, and LiDAR elevation data for classification of street trees showed that our approach achieved 64.2% and 47.3% accuracies for the 18-class and 40-class settings, respectively, which correspond to 13% and 14.3% improvement relative to the commonly used feature concatenation approach from multiple sources.
Lattice model of directed self avoiding walk is used to investigate adsorption properties of a semiflexible sequential copolymer chain on an impenetrable curved surface on a hexagonal lattice in two dimensions. Walks of the copolymer chains are directed in a direction away from the surface at a suitable value of monomer surface attraction, the copolymer chain gets adsorbed on the surface. To calculate exact value of monomer surface attraction, the directed walk model have been solved analytically using generating function method to discuss results when one type monomer of the copolymer chain has attractive, repulsive or no interaction with the surface. Results obtained show that adsorption transition point is independent of bending energy of the copolymer chain.
The family of MAX phases and their derivative MXenes are continuously growing in terms of both crystalline and composition varieties. In the last couple of years, several breakthroughs have been achieved that boosted the synthesis of novel MAX phases with ordered double transition metals and, consequently, the synthesis of novel MXenes with a higher chemical diversity and structural complexity, rarely seen in other families of two-dimensional (2D) materials. Considering the various elemental composition possibilities, surface functional tunability, various magnetic orders, and large spin$-$orbit coupling, MXenes can truly be considered as multifunctional materials that can be used to realize highly correlated phenomena. In addition, owing to their large surface area, hydrophilicity, adsorption ability, and high surface reactivity, MXenes have attracted attention for many applications, e.g., catalysts, ion batteries, gas storage media, and sensors. Given the fast progress of MXene-based science and technology, it is timely to update our current knowledge on various properties and possible applications. Since many theoretical predictions remain to be experimentally proven, here we mainly emphasize the physics and chemistry that can be observed in MXenes and discuss how these properties can be tuned or used for different applications.
As pointed out by the authors of the comment quant-ph/9712046, in our paper quant-ph/9712030 we studied in detail the metastability of a Bose-Einstein Condensate (BEC) confined in an harmonic trap with zero-range interaction. As well known, the BEC with attractive zero-range interaction is not stable but can be metastable. In our paper we analyzed the role of dimensionality for the metastability of the BEC with attractive and repulsive interaction.
We explore the effect of magnetic fields on the vertical distribution and multiphase structure of the supernova-driven interstellar medium (ISM) in simulations that admit dynamo action. As the magnetic field is amplified to become dynamically significant, gas becomes cooler and its distribution in the disc becomes more homogeneous. We attribute this to magnetic quenching of vertical velocity, which leads to a decrease in the cooling length of hot gas. A non-monotonic vertical distribution of the large-scale magnetic field strength, with the maximum at |z| $\approx$ 300 pc causes a downward pressure gradient below the maximum which acts against outflow driven by SN explosions, while it provides pressure support above the maximum.
We describe a general setting where the monodromy action on the first cohomology group of the Milnor fiber of a hyperplane arrangement is the identity.
We investigate a competition of tendencies towards ferromagnetic and incommensurate order in two-dimensional fermionic systems within functional renormalization group technique using temperature as a scale parameter. We assume that the Fermi surface (FS) is substantially curved, lies in the vicinity of van Hove singularity points and perform an account of the self-energy corrections. It is shown that the character of magnetic fluctuations is strongly asymmetric with respect to the Fermi level position relatively to van Hove singularity (VHS). For the Fermi level above VHS we find at low temperatures dominant incommensurate magnetic fluctuations, while below VHS level we find indications for ferromagnetic ground state. In agreement with the Mermin-Wagner theorem, at finite temperatures and in small magnetic fields we obtain rather small magnetization, which appears to be a power-law function of magnetic field. It is found that the FS curvature is slightly increased by correlation effects, and the renormalized bandwidth decreases at sufficiently low temperatures.
The noise driven motion in a bistable potential acts as the archetypal model of various physical phenomena. Here, we contrast the overdamped dynamics with the full (underdamped) dynamics. For the overdamped particle driven by a non-equilibrium, $\alpha$-stable noise the ratio of forward and backward transition rates depends only on the width of a potential barrier separating both minima. Using analytical and numerical methods, we show that in the regime of full dynamics, contrary to the overdamped case, the ratio of transition rates depends both on widths and heights of the potential barrier. The analytical formula for the ratio of transition rates is corroborated by extensive numerical simulations.