ShantanuT01/DACTYL-Pretraining huggingface dataset:
Many results in the theory of Gaussian processes rely on the eigenstructure of the covariance operator. However, eigenproblems are notoriously hard to solve explicitly and closed form solutions are known only in a limited number of cases. In this paper we set up a framework for the spectral analysis of the fractional type covariance operators, corresponding to an important family of processes, which includes the fractional Brownian motion and its noise. We obtain accurate asymptotic approximations for the eigenvalues and the eigenfunctions. Our results provide a key to several problems, whose solution is long known in the standard Brownian case, but was missing in the more general fractional setting. This includes computation of the exact limits of $L^2$-small ball probabilities and asymptotic analysis of singularly perturbed integral equations, arising in mathematical physics and applied probability.
Using the simultaneous Infra-Red (IR) and X-ray light curves obtained by Kalamkar et al. (2016), we perform a Fourier analysis of the IR/X-ray timing correlations of the black hole X-ray binary (BHB) GX 339-4. The resulting IR vs X-ray Fourier coherence and lag spectra are similar to those obtained in previous studies of GX 339-4 using optical light curves. In particular, above 1 Hz, the lag spectrum features an approximately constant IR lag of about 100 ms. We model simultaneously the radio to IR Spectral Energy Distribution (SED), the IR Power Spectral Density (PSD), and the coherence and lag spectra using the jet internal shock model ISHEM assuming that the fluctuations of the jet Lorentz factor are driven by the accretion flow. It turns out that most of the spectral and timing features, including the 100 ms lag, are remarkably well reproduced by this model. The 100 ms time-scale is then associated with the travel time from the accretion flow to the IR emitting zone. Our exploration of the parameter space favours a jet which is at most mildly relativistic ($\bar{\Gamma}< 3$), and a linear and positive relation between the jet Lorentz factor and X-ray light curve i.e. $\Gamma(t)-1\propto L_{X}(t)$. The presence of a strong Low Frequency Quasi Periodic Oscillation (LFQPO) in the IR light curve could be caused by jet precession driven by Lense-Thirring precession of the jet-emitting accretion flow. Our simulations confirm that this mechanism can produce an IR LFQPO similar to that observed in GX 339-4.
The HIDEEP survey (Minchin et al. 2003) was done in an attempt to find objects having low inferred neutral hydrogen column densities, yet they found a distribution which was strongly peaked at 10^20.65 cm^-2. In an attempt to understand this distribution and similar survey results, we model HI profiles of gas discs and use simple simulations of objects having a wide range of HI properties in the presence of an ionizing background. We find that inferred column density (N_HI^o) values, which are found by averaging total HI masses over some disc area, do not vary strongly with central column density (N_max) for detectable objects, so that even a population having a wide range of N_max values will give rise to a strongly peaked distribution of N_HI^o values. We find that populations of objects, having a wide range of model parameters, give rise to inferred column density distributions around 10^20.6+/-0.3 cm^-2. However, populations of fairly massive objects having a wide range of central column densities work best in reproducing the HIDEEP data, and these populations are also consistent with observed Lyman limit absorber counts. It may be necessary to look two orders of magnitude fainter than HIDEEP limits to detect ionized objects having central column densities <10^20 cm^-2, but the inferred column densities of already detected objects might be lower if their radii could be estimated more accurately.
We report on an atomic-scale X-ray Photon Correlation Spectroscopy study on Fe-rich FeAl in the B2-ordered regime revealing effective <111>-exchanges of atoms on the Al-sublattice. The diffusion mechanism responsible for these exchanges is the dominating process for chemical diffusion and therefore controls long-range material transport in the system. Comparison with previous atomistic results shows that the dominance of further exchanges can be characteristic at moderate temperatures where the system is highly ordered.
We have undertaken a survey for HI 21-cm absorption within the host galaxies of z ~ 1.2 - 1.5 radio sources, in the search of the cool neutral gas currently "missing" at z > 1. This deficit is believed to be due to the optical selection of high redshift objects biasing surveys towards sources of sufficient ultra-violet luminosity to ionise all of the gas in the surrounding galaxy. In order to avoid this bias, we have selected objects above blue magnitudes of B~20, indicating ultra-violet luminosities below the critical value above which 21-cm has never been detected. As a secondary requirement to the radio flux and faint optical magnitude, we shortlist targets with radio spectra suggestive of compact sources, in order to maximise the coverage of background emission. From this, we obtain one detection out of ten sources searched, which at z=1.278 is the third highest redshift detection of associated 21-cm absorption to date. Accounting for the spectra compromised by radio frequency interference, as well as various other possible pitfalls (reliable optical redshifts and turnover frequencies indicative of compact emission), we estimate a detection rate of ~30%, close to that expected for L_UV < 1e23 W/Hz sources.
The aim of this paper is to model the propagation of slow magnetohydrodynamic (MHD) sausage waves in a thick expanding magnetic flux tube in the context of the quiescent (VAL C) solar atmosphere. The propagation of these waves is found to be described by the Klein-Gordon equation. Using the governing MHD equations and the VAL C atmosphere model we study the variation of the cut-off frequency along and across the magnetic tube guiding the waves. Due to the radial variation of the cut-off frequency the flux tubes act as low frequency filters for waves.
We present a new, semi-analytic formalism to model the acceleration and collimation of relativistic jets in a gravitational potential. The gravitational energy density includes the kinetic, thermal, and electromagnetic mass contributions. The solutions are close to self-similar throughout the integration, from very close to the black hole to the region where gravity is unimportant. The field lines are tied to the conditions very close to the central object and eventually overcollimate, possibly leading to a collimation shock. This collimation shock could provide the conditions for diffusive shock acceleration, leading to the observed electron populations with a power-law energy distribution in jets.   We provide the derivation, a detailed analysis of a solution, and describe the effects the parameters have on the properties of the solutions, such as the Lorentz factor and location of the collimation shock. We also discuss the deviations from self-similarity.   By comparing the new gravity term with the gravity term obtained from a non-relativistic formalism in a previous work, we show they are equivalent in the non-relativistic limit. This equivalence shows the approach taken in that work is valid and allows us to comment on its limitations.
In 1993 A. Ori \cite{Ori93} presented spacetimes violating the chronology condition in order to answer the question whether a time machine construction has to violate the weak energy condition or not. Later, in 2005 \cite{Ori05}, he constructed a class of time machine solutions with compact vacuum core. Both classes include an interesting global structure and it is possible to obtain closed timelike curves. Besides we focus on the geometric structure, in particular symmetries and geodesics, if feasible, and visualize several aspects.
We present detailed, analytical models for the formation of disc galaxies to investigate the impact that cooling and feedback have on their structural properties. In particular, we investigate which observables extracted directly from the models are best suited as virial mass estimators, and to what extent they allow the recovery of the model input parameters regarding the feedback and cooling efficiencies. Contrary to naive expectations, the luminosities and circular velocities of disc galaxies are extremely poor indicators of total virial mass. Instead, we show that the product of disc scale length and rotation velocity squared yields a much more robust estimate. We show that feedback can cause a narrow correlation between galaxy mass fraction and halo spin parameter, similar to that found recently by van den Bosch, Burkert and Swaters from an analysis of dwarf galaxy rotation curves. Finally we investigate the impact that cooling and feedback have on the colors, metallicities, star formation histories and Tully-Fisher relation of disc galaxies.
Trinucleon longitudinal response functions R_L(q,omega) are calculated for q values up to 500 MeV/c. These are the first calculations beyond the threshold region in which both three-nucleon (3N) and Coulomb forces are fully included. We employ two realistic NN potentials (configuration space BonnA, AV18) and two 3N potentials (UrbanaIX, Tucson-Melbourne). Complete final state interactions are taken into account via the Lorentz integral transform technique. We study relativistic corrections arising from first order corrections to the nuclear charge operator. In addition the reference frame dependence due to our non-relativistic framework is investigated. For q less equal 350 MeV/c we find a 3N force effect between 5 and 15 %, while the dependence on other theoretical ingredients is small. At q greater equal 400 MeV/c relativistic corrections to the charge operator and effects of frame dependence, especially for large omega, become more important. In comparison with experimental data there is generally a rather good agreement. Exceptions are the responses at excitation energies close to threshold, where there exists a large discrepancy with experiment at higher q. Concerning the effect of 3N forces there are a few cases, in particular for the R_L of 3He, where one finds a much improved agreement with experiment if 3N forces are included.
Despite its potential in the fields of optoelectronics and topological insulators, experimental electronic band structure studies of Bi-doped GaAs are scarce. The reason is the complexity of growth which tends to leave bulk and in particular surface properties in an undefined state. Here we present an in depth investigation of structural and electronic properties of GaAsBi epilayers grown by molecular beam epitaxy with high (001) crystalline order and well-defined surface structures evident from low-energy electron diffraction. X-ray and ultraviolet photoemission spectrocopy as well as angle-resolved photoemission data at variable photon energies allows to disentangle a Bi-rich surface layer with $(1\times3)$ symmetry from the effects of Bi atoms incorporated in the GaAs bulk matrix. The influence of Bi concentrations up to $\approx 1$\% integrated in the GaAs bulk are visible in angle-resolved photoemission spectra after mild ion bombardment and subsequent annealing steps. Interpretation of our results is obtained via density functional theory simulations of bulk and $\beta 2(2\times 4)$ reconstructed slab geometries with and without Bi. Bi-induced energy shifts in the dispersion of GaAs heavy and light hole bulk bands are evident both in experiment and theory, which are relevant for modulations in the optical band gap and thus optoelectronic applications.
The well-known light minima of stars with the R Coronae Borealis variability are caused by the formation of an additional circumstellar dust shell, the screening shell, inside the permanent shell. Under the assumption of uniform distribution of matter in the circumstellar environment we estimated the optical thickness of the permanent gas-and-dust shell at 0.2-0.7, and its geometrical thickness is no less than 0.4 of its own radius. The wavelength dependence of extinction is close to neutral. From spectral observations of R CrB itself in the 1985 minimum we traced the transformation of the stellar linear and molecular absorption spectrum to the emission spectrum and established that the fast variation of the U-B colour index by -0.6 in the light decline was caused purely by a change of the spectrum type. The spectrum transformation causes an increase of star brightness in the U, B, and V bands by about 1.4, 0.75, and 0.75 mags, correspondingly. It is suggested that a high-velocity (>200 km/s) matter stream through the circumstellar environment is the cause of the excitation of the emissions observed during light minima when the photospheric flux is weakening.
In the early 1980s, Mills, Robbins and Rumsey conjectured, and in 1996 Zeilberger proved a simple product formula for the number of $n \times n$ alternating sign matrices with a 1 at the top of the $i$-th column. We give an alternative proof of this formula using our operator formula for the number of monotone triangles with prescribed bottom row. In addition, we provide the enumeration of certain 0-1-(-1) matrices generalizing alternating sign matrices.
Let $a>1$. Denote by $l_a(p)$ the multiplicative order of $a$ modulo $p$. We look for an estimate of sum of $\frac{l_a(p)}{p-1}$ over primes $p\leq x$ on average. When we average over $a\leq N$, we observe a statistic of $C\mathrm{Li}(x)$. P. J. Stephens ~\cite[Theorem 1]{S} proved this statistic for $N>\exp(c_1\sqrt{\log x})$ for some positive constant $c_1$. Upon this result, we give an explicit value of $c_1$. In fact, ~\cite[Theorem 1, 3]{S} hold with $N>\exp(3.42\sqrt{\log x})$, and ~\cite[Theorem 2, 4]{S} hold with $N>\exp(4.8365\sqrt{\log x})$. Also, we improve the range of $y$, from $y\geq \exp((2+\epsilon)\sqrt{\log x\log\log x})$ in ~\cite[Theorem 1]{LP}, to $y > \exp(3.42\sqrt{\log x})$.
There is mounting evidence that the ejection of magnetic helicity from the solar surface is important for the solar dynamo. Observations suggest that in the northern hemisphere the magnetic helicity flux is negative. We propose that this magnetic helicity flux is mostly due to small scale magnetic fields; in contrast to the more systematic large scale field of the 11 year cycle, whose helicity flux may be of opposite sign, and may be excluded from the observational interpretation. Using idealized simulations of MHD turbulence as well as a simple two-scale model, we show that shedding small scale (helical) field has two important effects. (i) The strength of the large scale field reaches the observed levels. (ii) The evolution of the large scale field proceeds on time scales shorter than the resistive time scale, as would otherwise be enforced by magnetic helicity conservation. In other words, the losses ensure that the solar dynamo is always in the near-kinematic regime. This requires, however, that the ratio of small scale to large scale losses cannot be too small, for otherwise the large scale field in the near-kinematic regime will not reach the observed values.
Using supersymmetric localization, we study the sector of chiral primary operators $({\rm Tr} \, \phi^2 )^n$ with large $R$-charge $4n$ in $\mathcal{N}=2$ four-dimensional superconformal theories in the weak coupling regime $g\rightarrow 0$, where $\lambda\equiv g^2n$ is kept fixed as $n\to\infty $, $g$ representing the gauge theory coupling(s). In this limit, correlation functions $G_{2n}$ of these operators behave in a simple way, with an asymptotic behavior of the form $G_{2n}\approx F_{\infty}(\lambda) \left(\frac{\lambda}{2\pi e}\right)^{2n}\ n^\alpha $, modulo $O(1/n)$ corrections, with $\alpha=\frac{1}{2} \mathrm{dim}(\mathfrak{g})$ for a gauge algebra $\mathfrak{g}$ and a universal function $F_{\infty}(\lambda)$. As a by-product we find several new formulas both for the partition function as well as for perturbative correlators in ${\cal N}=2$ $\mathfrak{su}(N)$ gauge theory with $2N$ fundamental hypermultiplets.
This paper is devoted to study the Bianchi type III model in the presence of anisotropic fluid in f(R) gravity. Exponential and power-law volumetric expansions are used to obtain exact solutions of the field equations. We discuss the physical behavior of the solutions and anisotropy behavior of the fluid, the expansion parameter and the model in future evolution of the universe.
Rewriting for semigroups is a special case of Groebner basis theory for noncommutative polynomial algebras. The fact is a kind of folklore but is not fully recognised. The aim of this paper is to elucidate this relationship, showing that the noncommutative Buchberger algorithm corresponds step-by-step to the Knuth-Bendix completion procedure.
We respond to a comment on our high-speed technique for the implementation of free-space quantum key distribution (QKD). The model used in the comment assigns inappropriately high link losses to the technique in question. We show that the use of reasonable loss parameters in the model invalidates the comment's main conclusion and highlights the benefits of increased transmission rates.
We prove a simple theorem on the overlap of the wavefunctions of a manybody system with and without a single impurity and show how, and under which conditions, this leads to the ``Orthogonality Catastrophe'' (OC) described by Anderson. A compact new derivation of the known result for the OC exponent in a free electron gas, $\alpha=2 \sum_l(2l+1) (\delta_l(\epsilon_f)/\pi)^2 $ %$\alpha = 2\sum_l [2l+1] (\delta_l(\epsilon_f)/\pi)^2$, is given. We also introduce a simple way of calculating core level photoemission (XPS) lineshapes from the finite size scaling of groundstate energies, reproducing and extending results previously derived using boundary conformal field theory. Different conditions under which the OC fails are discussed, and simple physical predictions for XPS lineshapes made in each case.
Given a connected graph $G=(V(G), E(G))$, the length of a shortest path from a vertex $u$ to a vertex $v$ is denoted by $d(u,v)$. For a proper subset $W$ of $V(G)$, let $m(W)$ be the maximum value of $d(u,v)$ as $u$ ranging over $W$ and $v$ ranging over $V(G)\setminus W$. The proper subset $W=\{w_1,\ldots,w_{|W|}\}$ is a {\em completeness-resolving set} of $G$ if   $$   \Psi_W: V(G)\setminus W \longrightarrow [m(W)]^{|W|},\qquad u\longmapsto (d(w_1,u),\ldots,d(w_{|W|},u))   $$ is a bijection, where   $$   [m(W)]^{|W|}=\{(a_{(1)},\ldots,a_{(|W|)})\mid 1\leq a_{(i)}\leq m(W)\text{ for each }i=1,\ldots,|W|\}.   $$ A graph is {\em completeness-resolvable} if it admits a completeness-resolving set.   In this paper, we first construct the set of all completeness-resolvable graphs by using the edge coverings of some vertices in given bipartite graphs, and then establish posets on some subsets of this set by the spanning subgraph relationship. Based on each poset, we find the maximum graph and give the lower and upper bounds for the number of edges in a minimal graph. Furthermore, minimal graphs satisfying the lower or upper bound are characterized.
We apply a (Moyal) deformation quantization to a bicomplex associated with the classical nonlinear Schrodinger equation. This induces a deformation of the latter equation to noncommutative space-time while preserving the existence of an infinite set of conserved quantities.
Knowledge of the geometry of pulsational modes is a prerequisite for seismic modelling of stars. In the case of slowly pulsating B-type (SPB) pulsators, the simple zero-rotation approach so far used for mode identification is usually not valid because pulsational frequencies are often of the order of the rotational frequency. Moreover, this approach allows us to determine only the spherical harmonic degree, $\ell$, while the azimuthal order, $m$, is beyond its reach. On the other hand, because of the density of oscillation spectra of SPB stars, knowledge of $m$ is indispensable if one wants to assign the radial order, $n$, to the observed frequency peaks. Including the effects of rotation via the traditional approximation, we perform identification of the mode angular numbers ($\ell,~m$) for 31 SPB stars with available multicolour time series photometry. Simultaneously, constraints on the rotational velocity, $V_{\rm rot}$, and the inclination angle, $i$, are determined assuming uniform rotation and a constant value of $V_{\rm rot}\sin i$. Dependence of the results on the adopted model is tested using HD\,21071 as an example. Despite some model uncertainties and limitations of the method, our studies show the correct approach to identifying the low-frequency oscillation modes.
We report the observation of efficient and low-noise frequency conversion between two microwave modes, mediated by the motion of a mechanical resonator subjected to radiation pressure. We achieve coherent conversion of more than $10^{12}~\mathrm{photons/s}$ with a $95\mathrm{\%}$ efficiency and a $14~\mathrm{kHz}$ bandwidth. With less than $10^{-1}~\mathrm{photons \cdot s^{-1}\cdot Hz^{-1}}$ of added noise, this optomechanical frequency converter is suitable for quantum state transduction. We show the ability to operate this converter as a tunable beam splitter, with direct applications for photon routing and communication through complex quantum networks.
Zaremba's conjecture (1971) states that every positive integer number d can be represented as a denominator of a finite continued fraction b/d = [d1,d2,...,dk], with all partial quotients d1,d2,...,dk being bounded by an absolute constant A. Several new theorems concerning this conjecture were proved by Bourgain and Kontorovich in 2011. The easiest of them states that the set of numbers satisfying Zaremba's conjecture with A = 50 has positive proportion in natural numbers. In 2014 I. D. Kan and D. A. Frolenkov proved this result with A = 5. In this paper the same theorem is proved with A = 4.
In this letter we investigate the quantum dynamics of a quasiparticle in the presence of a charged screw dislocation submitted to a uniform magnetic field. Analysing the quantum scattering for this quasiparticle we observed the appearance of a topological quantum phase in the solution and demonstrate that this phenomenon is the solid state analog of the He-McKeller-Wilkens effect.
We calculate the component Lagrangian of a four-dimensional non-anticommutative (with a singlet deformation parameter) and fully N=2 supersymmetric gauge field theory with the simple gauge group SU(2). We find that the deformed (classical) scalar potential is unbounded from below, in contrast to the undeformed case.
The influence of the size and shape of a dispersing and absorbing dielectric body on the local-field corrected spontaneous-decay of an excited atom embedded in the body is studied on the basis of the real-cavity model. By means of a Born expansion of the Green tensor of the system it is shown that to linear order in the susceptibility of the body the decay rate exactly follows Tomas's formula found for the special case of an atom at the center of a homogeneous dielectric sphere [Phys. Rev. A 63, 053811 (2001)]. It is further shown that for an atom situated at the interior of an arbitrary dielectric body this formula remains valid beyond the linear order. The case of an atom embedded in a weakly polarizable sphere is discussed in detail.