ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the prediction of solar flare size and time-to-flare using 38 features describing magnetic complexity of the photospheric magnetic field. This work uses support vector regression to formulate a mapping from the 38-dimensional feature space to a continuous-valued label vector representing flare size or time-to-flare. When we consider flaring regions only, we find an average error in estimating flare size of approximately half a \emph{geostationary operational environmental satellite} (\emph{GOES}) class. When we additionally consider non-flaring regions, we find an increased average error of approximately 3/4 a \emph{GOES} class. We also consider thresholding the regressed flare size for the experiment containing both flaring and non-flaring regions and find a true positive rate of 0.69 and a true negative rate of 0.86 for flare prediction. The results for both of these size regression experiments are consistent across a wide range of predictive time windows, indicating that the magnetic complexity features may be persistent in appearance long before flare activity. This is supported by our larger error rates of some 40 hr in the time-to-flare regression problem. The 38 magnetic complexity features considered here appear to have discriminative potential for flare size, but their persistence in time makes them less discriminative for the time-to-flare problem.
Quasar proximity zones at $z>5.5$ correspond to over-dense and over-ionized environments. Galaxies found inside proximity zones can therefore display features which would otherwise be masked by absorption in the IGM. We demonstrate the utility of this quasar-galaxy synergy by reporting the discovery of the first three `proximate Lyman-$\alpha$ emitters' (LAEs) within the proximity zone of quasar J0836 at $z=5.802$ (\textit{Aerith A, B} and \textit{C}). \textit{Aerith A}, located behind the quasar with an impact parameter $D_\perp = 278$ pkpc, provides the first detection of a Lyman-$\alpha$ transverse proximity effect. We model the transmission and show it constrains the onset of J0836's quasar phase to $0.2 \text{Myr}<t<20\text{Myr}$ in the past. The second object, \textit{Aerith B} at a distance $D=750$ pkpc from the quasar, displays a bright, broad double-peaked \lal emission line. Based on relations calibrated at $z\leq3$, the peak separation implies a low ionizing $f_{\text{esc}} \lesssim 1\%$, the most direct such constraint on a reionization-era galaxy. We fit the Ly-$\alpha$ line with an outflowing shell model, finding a completely typical central density $\text{log N}_{\text{HI}}/\text{cm}^{-2} = 19.3_{-0.2}^{+0.8}$, outflow velocity $v=16_{-11}^{+4}$ km s$^{-1}$, and gas temperature $\text{log} T/\text{K} = 3.8_{-0.7}^{+0.8}$ compared to $2<z<3$ analogue LAEs. Finally, we detect an emission line at $\lambda=8177$ \AA\ in object \textit{Aerith C} which, if it is \lal at $z=5.726$, would correspond closely with the end of the quasar's proximity zone ($\Delta z<0.02$ from the boundary) and suggests the quasar influences the IGM up to $\sim85$ cMpc away, making it the largest quasar proximity zone. Via the analyses conducted here, we illustrate how proximate LAEs offer unique insight into the ionizing properties of both quasars and galaxies during the epoch of reionization.
We present the results of photometric observations of three TeV blazars, 3C 66A, S5 0954+658 and BL Lacertae, during the period 2013--2017. Our extensive observations were performed in a total of 360 nights which produced $\sim$6820 image frames in BVRI bands. We study flux and spectral variability of these blazars on these lengthy timescales. We also examine the optical Spectral Energy Distributions of these blazars, which are crucial in understanding the emission mechanism of long-term variability in blazars. All three TeV blazars exhibited strong flux variability during our observations. The colour variations are mildly chromatic on long timescales for two of them. The nature of the long-term variability of 3C 66A and S5 0954+658 is consistent with a model of a non-thermal variable component that has a continuous injection of relativistic electrons with power law distributions around 4.3 and 4.6, respectively. However, the long-term flux and colour variability of BL Lac suggests that these can arise from modest changes in velocities or viewing angle toward the emission region, leading to variations in the Doppler boosting of the radiation by a factor ~1.2 over the period of these observations.
The hydrodynamics of stellar collisions and mergers is discussed in the context of blue straggler formation. Emphasis is placed on the very important question of hydrodynamic mixing during the merger process. Recent results of three-dimensional hydrodynamic calculations suggest that the merger remnants produced by stellar collisions are typically {\em not\/} well-mixed. However, comparisons between the observed colors and numbers of blue stragglers in dense clusters and the predictions of theoretical calculations for their stellar evolution appear to require that the initial blue-straggler models be close to chemically homogeneous. The resolution of this apparent conflict is likely to involve the development of convection or other thermal instabilitites that can provide efficient mixing during the contraction of the merger remnant to a thermal equilibrium state on the main sequence.
The paper is devoted to a reaction-diffusion equation with delay arising in modelling the immune response. We prove the existence of travelling waves in the bistable case using the Leray-Schauder method. In difference with the previous works, we do not assume here quasi-monotonicity of the delayed reaction term.
Generalization of Gaussian trial wave functions in quantum molecular dynamics models is introduced, which allows for long-range correlations characteristic for composite nuclear fragments. We demonstrate a significant improvement in the description of light fragments with correlations. Utilizing either type of Gaussian wave functions, with or without correlations, however, we find that we cannot describe fragment formation in a dynamic situation. Composite fragments are only produced in simulations if they are present as clusters in the substructure of original nuclei. The difficulty is traced to the delocalization of wave functions during emission. Composite fragments are produced abundantly in the Gaussian molecular dynamics in the limit $\hbar \rightarrow 0$.
We study the prime numbers that lie in Beatty sequences of the form $\lfloor \alpha n + \beta \rfloor$ and have prescribed algebraic splitting conditions. We prove that the density of primes in both a fixed Beatty sequence and a Chebotarev class of some Galois extension is precisely the product of the densities $\alpha^{-1}\cdot\frac{|C|}{|G|}$. Moreover, we show that the primes in the intersection of these sets satisfy a Bombieri--Vinogradov type theorem. This allows us to prove the existence of bounded gaps for such primes. As a final application, we prove a common generalization of the aforementioned bounded gaps result and the Green--Tao theorem.
The following relaxation of the classical problem of determining Ramsey number of a fixed graph has first been proposed by Erdos, Hajnal and Rado over 50 years ago. Given a graph $G$ and an integer $t \geq 2$ determine the minimum number $N$ such that in any $t$-coloured complete graph on $N$ vertices there is a copy of $G$ using only edges of some $t-1$ colours. We determine the answer precisely when $G$ is a path.
We study clustering of the extremes in a stationary sequence with subexponential tails in the maximum domain of attraction of the Gumbel We obtain functional limit theorems in the space of random sup-measures and in the space $D(0,\infty)$. The limits have the Gumbel distribution if the memory is only moderately long. However, as our results demonstrate rather strikingly, the "heuristic of a single big jump" could fail even in a moderately long range dependence setting. As the tails become lighter, the extremal behavior of a stationary process may depend on multiple large values of the driving noise.
We study the spectral evolution on second and sub--second timescales in 11 long and 12 short Gamma Ray Bursts (GRBs) with peak flux >8.5e-6 erg/cm2 s (8 keV-35 MeV) detected by the Fermi satellite. The peak flux correlates with the time-averaged peak energy in both classes of bursts. The peak energy evolution, as a function of time, tracks the evolution of the flux on short timescales in both short and long GRBs. We do not find evidence of an hard-to-soft spectral evolution. While short GRBs have observed peak energies larger than few MeV during most of their evolution, long GRBs can start with a softer peak energy (of few hundreds keV) and become as hard as short ones (i.e. with Ep,obs larger than few MeV) at the peak of their light curve. Six GRBs in our sample have a measured redshift. In these few cases we find that their correlations between the rest frame Ep and the luminosity Liso are less scattered than their correlations in the observer frame between the peak energy Ep,obs and the flux P. We find that the rest frame Ep of long bursts can be as high or even larger than that of short GRBs and that short and long GRBs follow the same Ep-Liso correlation, despite the fact that they likely have different progenitors.
When the equatorial spin velocity, $v$, of a charged conducting sphere approaches $c$, the Lorentz force causes a remarkable rearrangement of the total charge $q$.   Charge of that sign is confined to a narrow equatorial belt at latitudes $b \leqslant \sqrt{3} (1 - v^2/c^2)^{{1/2}}$ while charge of the opposite sign occupies most of the sphere's surface. The change in field structure is shown to be a growing contribution of the `magic' electromagnetic field of the charged Kerr-Newman black hole with Newton's G set to zero. The total charge within the narrow equatorial belt grows as $(1-v^2/c^2)^{-{1/4}}$ and tends to infinity as $v$ approaches $c$. The electromagnetic field, Poynting vector, field angular momentum and field energy are calculated for these configurations.   Gyromagnetic ratio, g-factor and electromagnetic mass are illustrated in terms of a 19th Century electron model. Classical models with no spin had the small classical electron radius $e^2/mc^2\sim$ a hundredth of the Compton wavelength, but models with spin take that larger size but are so relativistically concentrated to the equator that most of their mass is electromagnetic.   The method of images at inverse points of the sphere is shown to extend to charges at points with imaginary co-ordinates.
Let $p$ be an odd prime. We study the structure of the cyclotomic Greenberg-Selmer group attached to a general irreducible Artin motive over $\mathbb{Q}$ endowed with an ordinary $p$-stabilization. Under the Leopoldt and the weak $p$-adic Schanuel Conjectures, we show that it is of torsion over the Iwasawa algebra. Under mild hypotheses on $p$ we compute the constant term of its characteristic series in terms of a $p$-adic regulator and we highlight an extra zeros phenomenon. We then focus on Artin motives attached to classical weight one modular forms, to which our preceding results apply unconditionally. We formulate an Iwasawa Main Conjecture in this context and prove one divisibility using a Theorem of Kato.
We investigate the distribution of companion galaxies around quasars using {\em Hubble Space Telescope} ({\em HST}) Advanced Camera for Surveys Wide Field Camera (ACS/WFC) archival images. Our master sample contains 532 quasars which have been observed by {\em HST} ACS/WFC, spanning a wide range of luminosity $(-31<M_i(z=2)<-23)$ and redshift ($0.3<z<3$). We search for companions around the quasars with projected distance of $10\text{ kpc}<d<100\text{ kpc}$. PSF subtraction is performed to enhance the completeness for close companions. The completeness is estimated to be high $(>90\%)$ even for the faintest companions of interest. The number of physical companions is estimated by subtracting a background density from the number density of projected companions. We divide all the companions into three groups (faint, intermediate and bright) according to their fluxes. A control sample of galaxies is constructed to have similar redshift distribution and stellar mass range as the quasar sample using the data from {\em HST} deep fields. We find that quasars and control sample galaxies have similar numbers of faint and bright companions, while quasars show a $3.7\sigma$ deficit of intermediate companions compared to galaxies. The numbers of companions in all three groups do not show strong evolution with redshift, and the number of intermediate companions around quasars decreases with quasar luminosity. Assuming that merger-triggered quasars have entered the final coalescence stage during which individual companions are no longer detectable at large separations, our result is consistent with a picture in which a significant fraction of quasars is triggered by mergers.
We prove here the validity of a large deviation principle for the family of invariant measures associated to a two dimensional Navier-Stokes equation on a torus, perturbed by a smooth additive noise.
Small thermodynamic systems exhibit peculiar behavior different from that observed in long-scale systems. Non-equilibrium processes taking place in those systems are strongly influenced by the presence of fluctuations which can be large. Contributions to the free energy which vanish at the infinite number of particles limit cannot be neglected and may exert an important influence on the dynamics. We show that in spite of these important differences, the method of non-equilibrium thermodynamics still applies when reducing the size of the system. By using this method, assumption of local equilibrium at the mesoscale thereby leads to the formulation of a mesoscopic nonequilibrium thermodynamics from which expressions for the non-equilibrium currents and kinetic equations for the probability density can be obtained.
Hyper-parallel quantum information processing is a promising and beneficial research field. In this paper, we present a method to implement a hyper-parallel controlled-phase-flip (hyper-CPF) gate for frequency-, spatial-, and time-bin-encoded qubits by coupling flying photons to trapped nitrogen vacancy (NV) defect centers. The scheme, which differs from their conventional parallel counterparts, is specifically advantageous in decreasing against the dissipate noise, increasing the quantum channel capacity, and reducing the quantum resource overhead. The gate qubits with frequency, spatial, and time-bin degrees of freedom (DOF) are immune to quantum decoherence in optical fibers, whereas the polarization photons are easily disturbed by the ambient noise.
[Abridged] Methods: We use interferometric observations in the $N$-band with VLTI/MIDI to resolve the mid-IR nucleus of IC 3639. The origin of the nuclear infrared emission is determined from: 1) the comparison of the correlated fluxes from VLTI/MIDI with the fluxes measured at subarcsec resolution (VLT/VISIR, VLT/ISAAC); 2) diagnostics based on IR fine-structure line ratios, the IR continuum emission, IR bands produced by polycyclic aromatic hydrocarbons (PAH) and silicates; and 3) the high-angular resolution spectral energy distribution. Results: The unresolved flux of IC 3639 is $90 \pm 20\, \rm{mJy}$ at $10.5\, \rm{\mu m}$, measured with three different baselines in VLTI (UT1-UT2, UT3-UT4, and UT2-UT3; $46$-$58\, \rm{m}$), making this the faintest measurement so far achieved with mid-IR interferometry. The correlated flux is a factor of $3$-$4$ times fainter than the VLT/VISIR total flux measurement. The observations suggest that most of the mid-IR emission has its origin on spatial scales between $10$ and $80\, \rm{pc}$ ($40$-$340\, \rm{mas}$). A composite scenario where the star formation component dominates over the AGN is favoured by the diagnostics based on ratios of IR fine-structure emission lines, the shape of the IR continuum, and the PAH and silicate bands. Conclusions: A composite AGN-starburst scenario is able to explain both the mid-IR brightness distribution and the IR spectral properties observed in the nucleus of IC 3639. The nuclear starburst would dominate the mid-IR emission and the ionisation of low-excitation lines (e.g. [NeII]$_{12.8 \rm{\mu m}}$) with a net contribution of $\sim 70\%$. The AGN accounts for the remaining $\sim 30\%$ of the mid-IR flux, ascribed to the unresolved component in the MIDI observations, and the ionisation of high-excitation lines (e.g. [NeV]$_{14.3 \rm{\mu m}}$ and [OIV]$_{25.9 \rm{\mu m}}$).
The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) at the Xinglong observatory in China is a new 4-m telescope equipped with 4,000 optical fibers. In 2010, we initiated the LAMOST-Kepler project. We requested to observe the full field-of-view of the nominal Kepler mission with the LAMOST to collect low-resolution spectra for as many objects from the KIC10 catalogue as possible. So far, 12 of the 14 requested LAMOST fields have been observed resulting in more than 68,000 low-resolution spectra. Our preliminary results show that the stellar parameters derived from the LAMOST spectra are in good agreement with those found in the literature based on high-resolution spectroscopy. The LAMOST data allows to distinguish dwarfs from giants and can provide the projected rotational velocity for very fast rotators.
In this paper we develop a Bethe approximation, based on the cluster variation method, which is apt to study lattice models of branched polymers. We show that the method is extremely accurate in cases where exact results are known as, for instance, in the enumeration of spanning trees. Moreover, the expressions we obtain for the asymptotic number of spanning trees and lattice trees on a graph coincide with analogous expressions derived through different approaches. We study the phase diagram of lattice trees with nearest-neighbour attraction and branching energies. We find a collapse transition at a tricritical theta point, which separates an expanded phase from a compact phase. We compare our results for the theta transition in two and three dimensions with available numerical estimates.
A word is \emph{square-free} if it does not contain non-empty factors of the form $XX$. In 1906 Thue proved that there exist arbitrarily long square-free words over $3$-letter alphabet. We consider a new type of square-free words. A square-free word is \emph{extremal} if it cannot be extended to a new square-free word by inserting a single letter on arbitrary position. We prove that there exist infinitely many extremal words over $3$-letter alphabet. Some parts of our construction relies on computer verifications. We also pose some related open problems.
If one randomly punches holes in an infinite tensed membrane, when does the tension cease to exist? This problem was introduced by R. Connelly in connection with applications of rigidity theory to natural sciences. We outline a mathematical theory of tension based on graph rigidity theory and introduce several probabilistic models for this problem. We show that if the ``centers'' of the holes are distributed in R^2 according to Poisson law with parameter \lambda>0, and the distribution of sizes of the holes is independent of the distribution of their centers, the tension vanishes on all of R^2 for any value of \lambda. In fact, it follows from a more general result on the behavior of iterative convex hulls of connected subsets of R^d, when the initial configuration of subsets is distributed according to Poisson law and the sizes of the elements of the original configuration are independent of this Poisson distribution. For the latter problem we establish the existence of a critical threshold in terms of the number of iterative convex hull operations required for covering all of R^d. The processes described in the paper are somewhat related to bootstrap and rigidity percolation models.
We propose a new model for the formation of fast, low-ionization emission regions (FLIERs) in planetary nebulae that is able to account for many of their attendant characteristics and circumvent the problems on the collimation/formation mechanisms found in previous studies. In this model, FLIERs are formed in the stagnation zone of partially collimated stellar winds with reduced momentum flow along the axis. A concave bow-shock structure is formed due to the lack of momentum flow along the axis of a midly bipolar stellar wind. The stagnation knots are formed when the shocked environment medium accumulates at the apex of the outer shell and is compressed to a dense knot in the {\em concave} section of the bow-shock. We present two-dimensional hydrodynamic simulations of the formation of a stagnation knot and compare the resultant dynamical properties with those of FLIERs in planetary nebulae.
The existing techniques of account for the phonon dispersion are computationally costly, while its impact on a variety of thermodynamic properties appears negligible. We develop a mathematical formalism, which allows for clear understanding of the effect. The theoretical elaborations are then confronted with a widely used phenomenological model of the dispersion relation. The results show that accuracy of the models, which neglect the phonon dispersion, allows for calculation of many thermodynamic quantities up to an admissible precision. Although the context refers mainly to the Helmholtz energy , other properties are concerned as well with less details. Time-efficient schemes of control over the accuracy loss due to the neglected phonon dispersion are discussed.
Controlling the thermal conductivity of semiconductors is of practical interest in optimizing the performance of thermoelectric and phononic devices. The insertion of inclusions of nanometer size in a semiconductor is an effective means of achieving such control; it has been proposed that the thermal conductivity of silicon could be reduced to 1 W/m/K using this approach and that a minimum in the heat conductivity would be reached for some optimal size of the inclusions. Yet the practical verification of this design rule has been limited. In this work, we address this question by studying the thermal properties of silicon metalattices that consist of a periodic distribution of spherical inclusions with radii from 7 to 30 nm, embedded into silicon. Experimental measurements confirm that the thermal conductivity of silicon metalattices is as low as 1 W/m/K for silica inclusions, and that this value can be further reduced to 0.16 W/m/K for silicon metalattices with empty pores. A detailed model of ballistic phonon transport suggests that this thermal conductivity is close to the lowest achievable by tuning the radius and spacing of the periodic inhomogeneities. This study is a significant step in elucidating the scaling laws that dictate ballistic heat transport at the nanoscale in silicon and other semiconductors.