ShantanuT01/DACTYL-Pretraining huggingface dataset:
A partial Steiner triple system of order $u$ is a pair $(U,\mathcal{A})$ where $U$ is a set of $u$ elements and $\mathcal{A}$ is a set of triples of elements of $U$ such that any two elements of $U$ occur together in at most one triple. If each pair of elements occur together in exactly one triple it is a Steiner triple system. An embedding of a partial Steiner triple system $(U,\mathcal{A})$ is a (complete) Steiner triple system $(V,\mathcal{B})$ such that $U \subseteq V$ and $\mathcal{A} \subseteq \mathcal{B}$. For a given partial Steiner triple system of order $u$ it is known that an embedding of order $v \geq 2u+1$ exists whenever $v$ satisfies the obvious necessary conditions. Determining whether "small" embeddings of order $v < 2u+1$ exist is a more difficult task. Here we extend a result of Colbourn on the $\mathsf{NP}$-completeness of these problems. We also exhibit a family of counterexamples to a conjecture concerning when small embeddings exist.
The Schwarzschild--de Sitter space--time describes the gravitational field of a spherically symmetric mass in a universe with cosmological constant $\Lambda$. Based on this space--time we calculate Solar system effects like gravitational redshift, light deflection, gravitational time delay, Perihelion shift, geodetic or de Sitter precession, as well as the influence of $\Lambda$ on a Doppler measurement, used to determine the velocity of the Pioneer 10 and 11 spacecraft. For $\Lambda=\Lambda_0 \sim 10^{-52} {\rm m}^{-2}$ the cosmological constant plays no role for all of these effects, while a value of $\Lambda \sim - 10^{-37} {\rm m}^{-2}$, if hypothetically held responsible for the Pioneer anomaly, is not compatible with the Perihelion shift.
When the vacuum state of a scalar or electromagnetic field is modified by the presence of a reflecting boundary, an interacting test particle undergoes velocity fluctuations. Such effect is regarded as a sort of quantum analog of the classical Brownian motion. Several aspects about this system have been recently investigated in the literature, for instance, finite temperature effects, curved spacetime framework, near-boundary regime, late time behavior, and subvacuum phenomena. Here, further steps are given in this analysis by considering the effect of vacuum fluctuations of a scalar field in the presence of a perfectly reflecting flat boundary over the motion of a scalar test particle when the background field does not satisfy the Huygens' principle. Specifically, the background field is allowed to have mass and the system is studied in $D+1$ dimensions. A method of implementing a smooth transition between distinct states of the field is also developed, rendering regularized analytic expressions describing the velocity fluctuations of the test particle. This method is applied to study some special behaviors of the system. Possible applications include fields known to occur in nature as, for instance, the massive Higgs' field, for which the velocity fluctuations are here predicted to acquire a characteristic oscillation, thus behaving differently from their electromagnetic counterparts.
We explore the suitability of a modern vector meson dominance (VMD) model as a method for chiral extrapolation of nucleon electromagnetic form factor simulations in lattice QCD. It is found that the VMD fits to experimental data can be readily generalized to describe the lattice simulations. However, the converse is not true. That is, the VMD form is unsuitable as a method of extrapolation of lattice simulations at large quark mass to the physical regime.
L\'evy processes on bialgebras are families of infinitely divisible representations. We classify the generators of L\'evy processes on the compact forms of the quantum algebras $U_q(g)$, where $g$ is a simple Lie algebra. Then we show how the processes themselves can be reconstructed from their generators and study several classical stochastic processes that can be associated to these processes.
The existence of dark matter (DM) at scales of few pc down to $\simeq 10^{-5}$ pc around the centers of galaxies and in particular in the Galactic Center region has been considered in the literature. Under the assumption that such a DM clump, principally constituted by non-baryonic matter (like WIMPs) does exist at the center of our galaxy, the study of the $\gamma$-ray emission from the Galactic Center region allows us to constrain both the mass and the size of this DM sphere. Further constraints on the DM distribution parameters may be derived by observations of bright infrared stars around the Galactic Center. Hall and Gondolo \cite{hallgondolo} used estimates of the enclosed mass obtained in various ways and tabulated by Ghez et al. \cite{Ghez_2003,Ghez_2005}. Moreover, if a DM cusp does exist around the Galactic Center it could modify the trajectories of stars moving around it in a sensible way depending on the DM mass distribution. Here, we discuss the constraints that can be obtained with the orbit analysis of stars (as S2 and S16) moving inside the DM concentration with present and next generations of large telescopes. In particular, consideration of the S2 star apoastron shift may allow improving limits on the DM mass and size.
We analyze nonstationary $^{137}$Cs atmospheric activity concentration fluctuations measured near Chernobyl after the 1986 disaster and find three new results: (i) the histogram of fluctuations is well described by a log-normal distribution, (ii) there is a pronounced spectral component with period T=1 y, and (iii) the fluctuations are long-range correlated. These findings allow us to quantify two fundamental statistical properties of the data - the probability distribution and the correlation properties of the time series. We interpret our findings as evidence that the atmospheric radionuclide resuspension processes are tightly coupled to the surrounding ecosystems and to large time scale weather patterns.
We critically evaluate the isovector GMO sumrule for the charged $\pi N N$ coupling constant using recent precision data from $\pi ^-$p and $\pi^-$d atoms and with careful attention to systematic errors. From the $\pi ^-$d scattering length we deduce the pion-proton scattering lengths ${1/2}(a_{\pi ^-p}+a_{\pi ^-n})=(-20\pm 6$(statistic)$ \pm 10$ (systematic))~$\cdot 10^{-4}m_{\pi_c}^{-1}$ and ${1/2}(a_{\pi ^-p}-a_{\pi ^-n})=(903 \pm 14)\cdot 10^{-4}m_{\pi_c}^{-1}$. From this a direct evaluation gives $g^2_c(GMO)/4\pi =14.20\pm 0.07$(statistic)$\pm 0.13$(systematic) or $f^2_c/4\pi= 0.0786\pm 0.0008$.
We present the study of the effects of high energy cosmic rays (CRs) over the astrophysical ices, observed toward the embedded class I protostar Elias 29, by using computational modeling and laboratory data. Its spectrum was observed with {\it Infrared Space Observatory - ISO}, covering 2.3 - 190 $\mu$m. The modeling employed the three-dimensional Monte Carlo radiative transfer code RADMC-3D (Dullemond et al. 2012) and laboratory data of bombarded ice grains by CRs analogs, and unprocessed ices (not bombarded). We are assuming that Elias 29 has a self-irradiated disk with inclination $i =$ 60$^{\circ}$, surrounded by an envelope with bipolar cavity. The results show that absorption features toward Elias 29, are better reproduced by assuming a combination between unprocessed astrophysical ices at low temperature (H$_2$O, CO, CO$_2$) and bombarded ices (H$_2$O:CO$_2$) by high energy CRs. Evidences of the ice processing around Elias 29 can be observed by the good fitting around 5.5-8.0 $\mu$m, by polar and apolar ice segregation in 15.15-15.25 $\mu$m, and by presence of the CH$_4$ and HCOOH ices. Given that non-nitrogen compounds were employed in this work, we assume that absorption around 5.5-8.0 $\mu$m should not be associated with NH$_4^+$ ion (Shutte & Khanna2003), but more probably with aliphatic ethers (e.g. R1-OCH$_2$-R2), CH$_3$CHO and related species. The results obtained in this paper are important, because they show that the environment around protostars is better modeled considering processed samples and, consequently, demonstrates the chemical evolution of the astrophysical ices.
In this work we combine the well established Kondo problem with the more speculative field of a discrete space time. We show that a discrete energy space induces a flow towards a new fixed point by breaking the conservation of charge and spin and lifting the fermion parity. This parity lifting fixed point appears on a scale set by the discretization of energy space. In contrast to the Planck scale the associated energy scale is at very low energy scales, possibly given by the inverse size of the universe.
I present a density-matrix renormalization-group (DMRG) method for calculating dynamical properties and excited states in low-dimensional lattice quantum many-body systems. The method is based on an exact variational principle for dynamical correlation functions and the excited states contributing to them. This dynamical DMRG is an alternate formulation of the correction vector DMRG but is both simpler and more accurate. The finite-size scaling of spectral functions is discussed and a method for analyzing the scaling of dense spectra is described. The key idea of the method is a size-dependent broadening of the spectrum.The dynamical DMRG and the finite-size scaling analysis are demonstrated on the optical conductivity of the one-dimensional Peierls-Hubbard model. Comparisons with analytical results show that the spectral functions of infinite systems can be reproduced almost exactly with these techniques. The optical conductivity of the Mott-Peierls insulator is investigated and it is shown that its spectrum is qualitatively different from the simple spectra observed in Peierls (band) insulators and one-dimensional Mott-Hubbard insulators.
Deep models are the defacto standard in visual decision problems due to their impressive performance on a wide array of visual tasks. On the other hand, their opaqueness has led to a surge of interest in explainable systems. In this work, we emphasize the importance of model explanation in various forms such as visual pointing and textual justification. The lack of data with justification annotations is one of the bottlenecks of generating multimodal explanations. Thus, we propose two large-scale datasets with annotations that visually and textually justify a classification decision for various activities, i.e. ACT-X, and for question answering, i.e. VQA-X. We also introduce a multimodal methodology for generating visual and textual explanations simultaneously. We quantitatively show that training with the textual explanations not only yields better textual justification models, but also models that better localize the evidence that support their decision.
In this paper, we consider a semilinear parabolic equation with nonlinear nonlocal Neumann boundary condition and nonnegative initial datum. We first prove global existence results. We then give some criteria on this problem which determine whether the solutions blow up in finite time for large or for all nontrivial initial data. Finally, we show that under certain conditions blow-up occurs only on the boundary.
We find exact solutions for Skyrmions for the Skyrme-like models. Constructing first the recursion formulae at small and large distance behavior, we proceed by implementing these constraints to a chosen parametrization of the solutions. The procedure is applied to the spherically symmetric hedgehog solution and to topological number N > 1 solutions based on rational maps.
A dynamical coupled channel approach is used to study $\pi$ and $\omega$--meson production induced by pions and photons scattering from the proton. Six intermediate channels including $\pi N$, $\eta N$, $\pi\Delta$, $\sigma N$, $\rho N$ and $\omega N$ are employed to describe unpolarized and polarized data. Bare parameters in an effective hadronic Lagrangian are determined in a fit to data for $\pi N \to \pi N$, $\gamma N \to \pi N$, $\pi^- p \to \omega n$, and $\gamma p \to \omega p$ reactions at center-of-mass energies from threshold to $W < 2.0$ GeV. The $T$ matrix determined in these fits is used to calculate the photon beam asymmetry for $\omega$-meson production and the $\omega N \to\omega N$ total cross section and $\omega N$ scattering lengths.
We propose a statistical tool to compare the scaling behaviour of turbulence in pairs of molecular cloud maps. Using artificial maps with well defined spatial properties, we calibrate the method and test its limitations to ultimately apply it to a set of observed maps. We develop the wavelet-based weighted cross-correlation (WWCC) method to study the relative contribution of structures of different sizes and their degree of correlation in two maps as a function of spatial scale, and the mutual displacement of structures in the molecular cloud maps. We test the WWCC for circular structures having a single prominent scale and fractal structures showing a self-similar behavior without prominent scales. Observational noise and a finite map size limit the scales where the cross-correlation coefficients and displacement vectors can be reliably measured. For fractal maps containing many structures on all scales, the limitation from the observational noise is negligible for signal-to-noise ratios >5. (abbrev). Application of the WWCC to the observed line maps of the giant molecular cloud G333 allows to add specific scale information to the results obtained earlier using the principle component analysis. It confirms the chemical and excitation similarity of $^{13}$CO and C$^{18}$O on all scales, but shows a deviation of HCN at scales of up to 7' (~7 pc). This can be interpreted as a chemical transition scale. The largest structures also show a systematic offset along the filament, probably due to a large-scale density gradient. The WWCC can compare correlated structures in different maps of molecular clouds identifying scales that represent structural changes such as chemical and phase transitions and prominent or enhanced dimensions.
In almost all of plasma theories for astrophysical objects, we have assumed the charge quasi-neutrality of unmagnetized plasmas in global scales. This assumption has been justified because if there is a charged plasma, it induces electric field which attracts the opposite charge, and this opposite charge reduces the charge separation. Here, we report a newly discovered instability which causes a charge separation in a rotating plasma inside of an innermost stable circular orbit (ISCO) around a black hole. The growth rate of the instability is smaller than that of the disk instability even in the unstable disk region and is forbidden in the stable disk region outside of the ISCO. However, this growth rate becomes comparable to that of the disk instability when the plasma density is much lower than a critical density inside of the ISCO. In such case, the charge separation instability would become apparent and cause the charged accretion into the black hole, thus charge the hole up.
Helium diffusion in metals is the basic requirement of nucleation and growth of bubble, which gives rise to adverse degradation effects on mechanical properties of structural materials in reactors under irradiation. Lattice based Kinetic Monte Carlo approach is widely adopted to study the evolution of helium-vacancy clustering. However, the imple-mentation of Arrhenius law to prediction the event rate of single interstitial helium solute diffusion in metal is not always appropriate due to low-energy barrier. Based on a stochastic model, a modified formula is derived from the Brownian motion upon a cosine-type potential. Using the parameters obtained from molecular dynamics simulation for the diffusivity of single helium solute in BCC W, the prediction of our model is consistent with the results from dynamical simulation and previous model. This work would help to develop a more accurate KMC scheme for the growth of helium-vacancy clusters, as well as other low-energy reactions in materials science.
We report the first detection of deuterated water (HDO) toward an extragalactic hot core. The HDO 2$_{11}$-2$_{12}$ line has been detected toward hot cores N105-2A and 2B in the N105 star-forming region in the low-metallicity Large Magellanic Cloud (LMC) dwarf galaxy with the Atacama Large Millimeter/submillimeter Array (ALMA). We have compared the HDO line luminosity ($L_{\rm HDO}$) measured toward the LMC hot cores to those observed toward a sample of seventeen Galactic hot cores covering three orders of magnitude in $L_{\rm HDO}$, four orders of magnitude in bolometric luminosity ($L_{\rm bol}$), and a wide range of Galactocentric distances (thus metallicities). The observed values of $L_{\rm HDO}$ for the LMC hot cores fit very well into the $L_{\rm HDO}$ trends with $L_{\rm bol}$ and metallicity observed toward the Galactic hot cores. We have found that $L_{\rm HDO}$ seems to be largely dependent on the source luminosity, but metallicity also plays a role. We provide a rough estimate of the H$_2$O column density and abundance ranges toward the LMC hot cores by assuming that HDO/H$_2$O toward the LMC hot cores is the same as that observed in the Milky Way; the estimated ranges are systematically lower than Galactic values. The spatial distribution and velocity structure of the HDO emission in N105-2A is consistent with HDO being the product of the low-temperature dust grain chemistry. Our results are in agreement with the astrochemical model predictions that HDO is abundant regardless of the extragalactic environment and should be detectable with ALMA in external galaxies.
It is shown in this paper that the transition kernel corresponding to a spatially inhomogeneous random walk on ${\mathbf{Z}}^d$ admits upper and lower Gaussian estimates.
We present a search in IceCube data for neutrino emission from Galactic TeV gamma-ray sources detected by the HAWC gamma-ray observatory. HAWC serves as the excellent instrument to complement IceCube with its energy range extending to very high energies. Assuming that the highest energy photons originate from the decay of pions, rather than from accelerated leptons, the very high energy gamma-rays observed by HAWC are expected to be correlated with neutrinos. Using eight years of IceCube data, we report on two analyses that investigate a possible neutrino--gamma ray correlation. The first is a stacked analysis of identified HAWC point sources and the second is a template method which accounts for the full morphology of HAWC sources, including their measured extension.
ALMA imaging of the cold molecular medium in the nearby starburst galaxy NGC 1808 is presented. The observations reveal the distribution of molecular gas, traced by $^{12}$CO (1-0) and $^{12}$CO (3-2), and continuum (93 and 350 GHz) across the central 1 kpc starburst region at high resolution of $\sim1$ arcsec. A molecular gas torus (radius $\sim30$ pc) is discovered in the circumnuclear disk (CND; central 100 pc), with a high CO (3-2)/CO (1-0) ratio of $\sim1$, surrounded by massive ($10^6$-$10^7$ $M_\odot$) clouds with high star formation efficiency (SFE$\sim10^{-8}$ yr$^{-1}$), molecular spiral arms, and a 500 pc pseudoring. The CND harbors a continuum core and molecular gas exhibiting peculiar motion. The new data confirm the line splitting along the minor galactic axis, interpreted as a nuclear gas outflow with average velocity $\sim180$ km s$^{-1}$, and show evidence of a velocity gradient of $\sim+0.4$ km s$^{-1}$ pc$^{-1}$ along the axis. In addition, supershells expanding from the 500 pc ring with maximum velocities of $\sim75$ km s$^{-1}$ are revealed. The distribution and CO luminosities of molecular clouds in the central 1 kpc starburst region indicate an evolutionary sequence, from gas accretion onto the 500 pc ring from the large-scale bar, to enhanced star formation in the ring, and outflow as feedback.
We establish the regularity of weak solutions for the vorticity equation associated to a family of desingularised models for vortex filament dynamics in 3D incompressible viscous flows. These include and generalise the classical model "of an allowance for the thickness of the vortices" due to Louis Rosenhead in 1930. Our approach is based on an interplay between the geometry of vorticity and analytic inequalities in Sobolev spaces.
Asteroseismology is a powerful tool that can precisely characterize the mass, radius, and other properties of field stars. However, our inability to properly model the near-surface layers of stars creates a frequency-dependent frequency difference between the observed and the modeled frequencies, usually referred to as the "surface term". This surface term can add significant errors to the derived stellar properties unless removed properly. In this paper we simulate surface terms across a significant portion of the HR diagram, exploring four different masses ($M=0.8, 1.0, 1.2$, and $1.5$ M$_\odot$) at five metallicities ($[\rm{Fe/H}]=0.5, 0.0, -0.5 ,-1.0, and -1.5$) from main sequence to red giants for stars with $T_{\rm{eff}}<6500 K$ and explore how well the most common ways of fitting and removing the surface term actually perform. We find that the two-term model proposed by Ball & Gizon (2014) works much better than other models across a large portion of the HR diagram, including the red giants, leading us to recommend its use for future asteroseismic analyses.
We specify conditions under which the nucleon-nucleon interaction, based on the t-channel meson-exchange mechanism, is equivalent to an interaction generated via an s-channel exchange of six-quark bags. The duality is possible provided the alternation of zeros and poles of the non-dispersive part of D function takes place in the normalization where the imaginary part of D is non-negative and the CDD poles are the only poles of D.
In this article, we introduce a systematic new method to investigate the conjectural p-adic meromorphic continuation of Professor Bernard Dwork's unit root zeta function attached to an ordinary family of algebraic varieties defined over a finite field of characteristic p.
We give a geometric proof of the Decomposition Theorem of Beilinson, Bernstein, Deligne and Gabber for the direct image of the intersection cohomology complex under a proper map of complex algebraic varieties. The method rests on new Hodge-theoretic results on the cohomology of projective varieties which extend naturally the classical theory and provide new applications.
As a critical part of the Tracking Active Galactic Nuclei with Austral Milliarcsecond Interferometry (TANAMI) program, in November 2007 the Australia Telescope Compact Array (ATCA) started monitoring the radio spectra of a sample of southern hemisphere active galactic nuclei (AGN) that were selected as likely candidates for detection (as well as a control sample) by the Large Area Telescope (LAT) aboard the Fermi Gamma Ray Space Observatory. The initial sample was chosen based on properties determined from AGN detections by the Energetic Gamma Ray Experiment Telescope (EGRET). Most of the initial sample has been detected by Fermi/LAT and with the addition of new detections the sample has grown to include 226 AGN, 133 of which have data for more than one epoch. For the majority of these AGN, our monitoring program provides the only dynamic radio spectra available. The ATCA receiver suite makes it possible to observe several sources at frequencies between 4.5 and 41 GHz in a few hours, resulting in an excellent measure of spectral index at each epoch. By examining how the spectral index changes over time, we aim to investigate the mechanics of radio and gamma-ray emission from AGN jets.