ShantanuT01/DACTYL-Pretraining huggingface dataset:
Recently it has become apparent that proto-stellar-like outflow activity extends to the brown dwarf (BD) mass regime. While the presence of accretion appears to be the common ingredient in all objects known to drive jets fundamental questions remain unanswered. The more prominent being the exact mechanism by which jets are launched, and whether this mechanism remains universal among such a diversity of sources and scales. To address these questions we have been investigating outflow activity in a sample of protostellar objects that differ considerably in mass and mass accretion rate. Central to this is our study of brown dwarf jets. To date Classical T Tauri stars (CTTS) have offered us the best touchstone for decoding the launching mechanism. Here we shall summarise what is understood so far of BD jets and the important constraints observations can place on models. We will focus on the comparison between jets driven by objects with central mass < 0.1M \odot and those driven by CTTSs. In particular we wish to understand how the the ratio of the mass outflow to accretion rate compares to what has been measured for CTTSs.
In the Maxwell interaction model the collision rate is independent of the relative velocity of the colliding pair and, as a consequence, the collisional moments are bilinear combinations of velocity moments of the same or lower order. In general, however, the drift term of the Boltzmann equation couples moments of a given order to moments of a higher order, thus preventing the solvability of the moment hierarchy, unless approximate closures are introduced. On the other hand, there exist a number of states where the moment hierarchy can be recursively solved, the solution generally exposing non-Newtonian properties. The aim of this paper is to present an overview of results pertaining to some of those states, namely the planar Fourier flow (without and with a constant gravity field), the planar Couette flow, the force-driven Poiseuille flow, and the uniform shear flow.
Observations of the eclipsing dwarf nova IP Peg during outburst reveal metal lines in emission, such as Mg II 4481 A. Analysis using Doppler tomography locates emission of helium and metal lines on the inner Roche lobe of the secondary star. Such multi-line Roche-lobe imaging presents a new tool in mapping the red star's ionization structure.
Comparing the functional behavior of neural network models, whether it is a single network over time or two (or more networks) during or post-training, is an essential step in understanding what they are learning (and what they are not), and for identifying strategies for regularization or efficiency improvements. Despite recent progress, e.g., comparing vision transformers to CNNs, systematic comparison of function, especially across different networks, remains difficult and is often carried out layer by layer. Approaches such as canonical correlation analysis (CCA) are applicable in principle, but have been sparingly used so far. In this paper, we revisit a (less widely known) from statistics, called distance correlation (and its partial variant), designed to evaluate correlation between feature spaces of different dimensions. We describe the steps necessary to carry out its deployment for large scale models -- this opens the door to a surprising array of applications ranging from conditioning one deep model w.r.t. another, learning disentangled representations as well as optimizing diverse models that would directly be more robust to adversarial attacks. Our experiments suggest a versatile regularizer (or constraint) with many advantages, which avoids some of the common difficulties one faces in such analyses. Code is at https://github.com/zhenxingjian/Partial_Distance_Correlation.
The detection potential of the active neutrino magnetic moment ($\nu_{a}$MM) and the active sterile transition magnetic moment ($\nu_{s}$MM) of the solar neutrino CE$\nu$NS process in future Dark Matter direct detection experiments is studied and compared with the respective allowed range to explain the Xenon1T excess. We find that the sensitivity to the $\nu_{a}$MM approaches to the level between $10^{-10}\mu_B$ and $10^{-11}\mu_B$, which is dominantly limited by the detection threshold. On the other hand, the future solar neutrino CE$\nu$NS detection would be powerful in probing the $\nu_{s}$MM for the sterile neutrino mass below 10 MeV, which could unambiguously test the $\nu_{s}$MM explanation of the Xenon1T excess. The sensitivity in the general framework with both $\nu_{a}$MM and $\nu_{s}$MM contributions is also derived.
We consider the down/up crossing property of weighted Markov branching processes. The joint probability distribution of multi crossing numbers of such processes are obtained. In particular, for Markov branching processes, the probability distribution of death number is given and for bulk-arrival queueing model, the joint probability distributions of service number and arrival number is also given.
Optical coupling of an ensemble of silicon-vacancy (SiV) centers to single-crystal diamond microdisk cavities is demonstrated. The cavities are fabricated from a single-crystal diamond membrane generated by ion implantation and, electrochemical liftoff followed by homo-epitaxial overgrowth. Whispering gallery modes which spectrally overlap with the zero-phonon line (ZPL) of the SiV centers and exhibit quality factors ~2200 are measured. Lifetime reduction from 1.8 ns to 1.48 ns is observed from SiV centers in the cavity compared to those in the membrane outside the cavity. These results are pivotal in developing diamond integrated photonics networks.
A possibility to measure the spin and spin-spin correlations of a chargino pair is investigated in the process electron positron -> chargino_1 anti-chargino_1 -> (neutralino_1 quark anti-quark) (neutralino_1 quark anti-quark) at future linear-collider energies. The total and the differential cross sections are calculated by the GRACE system which allows for the full spin correlation. Experimental sensitivity of the measurements are examined by assuming the limited detector resolution, the initial state radiation and the beam-beam effect (beamstrahlung). It is found that generally the spin-spin correlation can only be measured with a lower sensitivity than the chargino spin itself. The dependence of the correlation measurements on the relevant SUSY parameters can be seen for a light sneutrino case, but the situation becomes worse for a heavier sneutrino.
We propose a model where a supernova explodes in some vicinity of our solar system (some tens of parsecs) in the recent past (some tens of thousands years) with the energy release in cosmic rays of order of $ 10 ^ {51} $ erg. The flux from this supernova is added to an isotropic flux from other sources. We consider the case where the Sun's location is not in some typical for Our Galaxy average environment, but in the Local Superbubble about 100 pc across, in which the diffusion coefficient $D (E) = D_0 \times E ^ {0.6} $, with the value of $ D_0 \sim 10 ^ {25} cm^ 2 s^ {-1} $. We describe the energy dependence of the anisotropy of cosmic rays in the TeV region, together with the observed features of the energy spectrum of protons found in direct measurements. Our model provides a natural explanation to the hardening of the proton spectrum at 200 GeV, together with the observed steepening of the spectrum above 50 TeV.
The classical problem of whether $m$th-powers with or without zero in a finite field $\mathbb{F}_q$ form a difference set has been extensively studied, and is related to many topics, such as flag transitive finite projective planes. In this paper new necessary and sufficient conditions are established including those via a system of polynomial equations on Gauss sums. The author thereby solves the problem for even $q$ which is neglected in the literature, and extends the nonexistence list for even $m$ up to $22$. Moreover, conjectures toward the complete classification are posed.
We consider a system of $d$ non-linear stochastic fractional heat equations in spatial dimension $1$ driven by multiplicative $d$-dimensional space-time white noise. We establish a sharp Gaussian-type upper bound on the two-point probability density function of $(u(s, y), u (t, x))$. From this result, we deduce optimal lower bounds on hitting probabilities of the process $\{u(t, x): (t, x) \in [0, \infty[ \times \mathbb{R}\}$ in the non-Gaussian case, in terms of Newtonian capacity, which is as sharp as that in the Gaussian case. This also improves the result in Dalang, Khoshnevisan and Nualart [\textit{Probab. Theory Related Fields} \textbf{144} (2009) 371--424] for systems of classical stochastic heat equations. We also establish upper bounds on hitting probabilities of the solution in terms of Hausdorff measure.
SubHalo Abundance Matching (SHAM) is an empirical method for constructing galaxy catalogues based on high-resolution $N$-body simulations. We apply SHAM on the UNIT simulation to simulate SDSS BOSS/eBOSS Luminous Red Galaxies (LRGs) within a wide redshift range of $0.2 < z < 1.0$. Besides the typical SHAM scatter parameter $\sigma$, we include $v_{\rm smear}$ and $V_{\rm ceil}$ to take into account the redshift uncertainty and the galaxy incompleteness respectively. These two additional parameters are critical for reproducing the observed 2PCF multipoles on 5--25$\,h^{-1}\,{\rm Mpc}$. The redshift uncertainties obtained from the best-fitting $v_{\rm smear}$ agree with those measured from repeat observations for all SDSS LRGs except for the LOWZ sample. We explore several potential systematics but none of them can explain the discrepancy found in LOWZ. Our explanation is that the LOWZ galaxies might contain another type of galaxies which needs to be treated differently. The evolution of the measured $\sigma$ and $V_{\rm ceil}$ also reveals that the incompleteness of eBOSS galaxies decreases with the redshift. This is the consequence of the magnitude lower limit applied in eBOSS LRG target selection. Our SHAM also set upper limits for the intrinsic scatter of the galaxy--halo relation given a complete galaxy sample: $\sigma_{\rm int}<0.31$ for LOWZ at $0.2<z<0.33$, $\sigma_{\rm int}<0.36$ for LOWZ at $0.33<z<0.43$, and $\sigma_{\rm int}<0.46$ for CMASS at $0.43<z<0.51$. The projected 2PCFs of our SHAM galaxies also agree with the observational ones on the 2PCF fitting range.
In this paper, we will consider the fractional Caffarelli-Kohn-Nirenberg inequality \begin{equation*} {\Lambda} \left(\int_{\mathbb R^n}\frac{|u(x)|^{p}}{|x|^{{\beta} {p}}}\,dx\right)^{\frac{2}{p}}\leq \int_{\mathbb R^n}\int_{\mathbb R^n}\frac{(u(x)-u(y))^2}{|x-y|^{n+2\gamma}|x|^{{\alpha}}|y|^{{\alpha}}}\,dy\,dx \end{equation*} where $\gamma\in(0,1)$, $n\geq 2$, and $\alpha,\beta\in\mathbb R$ satisfy \begin{equation*} \alpha\leq \beta\leq \alpha+\gamma, \ -2\gamma<\alpha<\frac{n-2\gamma}{2}, \end{equation*} and the exponent $p$ is chosen to be \begin{equation*} p=\frac{2n}{n-2\gamma+2(\beta-\alpha)}, \end{equation*} such that the inequality is invariant under scaling. We first study the existence and nonexistence of extremal solutions. Our next goal is to show some results on the symmetry and symmetry breaking region for the minimizers; these suggest the existence of a Felli-Schneider type curve separating both regions but, surprisingly, we find a novel behavior as $\alpha\to -2\gamma$. The main idea in the proofs, as in the classical case, is to reformulate the fractional Caffarelli-Kohn-Nirenberg inequality in cylindrical variables. Then, in order to find the radially symmetric solutions we need to solve a non-local ODE.   For this equation we also get uniqueness of minimizers in the radial symmetry class; indeed, we show that the unique continuation argument of Frank-Lenzmann (Acta'13) can be applied to more general operators with good spectral properties. We provide, in addition, a completely new proof of non-degeneracy which works for all critical points. It is based on the variation of constants approach and the non-local Wronskian of Ao-Chan-DelaTorre-Fontelos-Gonz\'alez-Wei (Duke'19).
We extend the direct integration method of the holomorphic anomaly equations to general Omega backgrounds for pure SU(2) N=2 Super-Yang-Mills theory and topological string theory on non-compact Calabi-Yau threefolds. We find that an extension of the holomorphic anomaly equation, modularity and boundary conditions provided by the perturbative terms as well as by the gap condition at the conifold are sufficient to solve the generalized theory in the above cases. In particular we use the method to solve the topological string for the general Omega backgrounds on non-compact toric Calabi-Yau spaces. The conifold boundary condition follows from that the N=2 Schwinger-Loop calculation with BPS states coupled to a self-dual and an anti-self-dual field strength. We calculate such BPS states also for the decompactification limit of Calabi-Yau spaces with regular K3 fibrations and half K3s embedded in Calabi-Yau backgrounds.
The imprint of non-linearities in the propagation of gravitational waves --- the tail effect --- is responsible for new spin contributions to the energy flux and orbital phasing of spinning black hole binaries. The spin-orbit (linear in spin) contribution to this effect is currently known at leading post-Newtonian order, namely 3PN for maximally spinning black holes on quasi-circular orbits. In the present work, we generalize these tail-originated spin-orbit terms to the next-to-leading 4PN order. This requires in particular extending previous results on the dynamical evolution of precessing compact binaries. We show that the tails represent the only spin-orbit terms at that order for quasi-circular orbits, and we find perfect agreement with the known result for a test particle around a Kerr black hole, computed by perturbation theory. The BH-horizon absorption terms have to be added to the PN result computed here. Our work completes the knowledge of the spin-orbit effects to the phasing of compact binaries up to the 4PN order, and will allow the building of more faithful PN templates for the inspiral phase of black hole binaries, improving the capabilities of ground-based and space-based gravitational wave detectors.
X-ray variabilities with spectral state transitions in bright low mass X-ray binaries containing a neutron star are investigated by using the one-day bin light curves of MAXI/GSC (Gas Slit Camera) and Swift/BAT (Burst Alert Telescope). Four sources (4U 1636$-$536, 4U 1705$-$44, 4U 1608$-$52, and GS 1826$-$238) exhibited small-amplitude X-ray variabilities with spectral state transitions. Such "mini-outbursts" were characterized by smaller amplitudes (several times) and shorter duration (less than several tens of days) than those of "normal outbursts." Theoretical model of disk instability by Mineshige and Osaki (PASJ, 37, 1, 1985) predicts both large-amplitude outbursts and small-amplitude variabilities. We interpret the normal outbursts as the former prediction of this model, and the mini-outbursts as the latter. Here, we can also call the mini-outburst as "purr-type outburst" referring to theoretical work. We suggest that similar variabilities lasting for several tens of days without spectral state transitions, which are often observed in the hard state, may be a repeat of mini-outbursts.
Symmetries are a key concept to connect mathematical elegance with physical insight. We consider measurement assemblages in quantum mechanics and show how their symmetry can be described by means of the so-called discrete bundles. It turns out that many measurement assemblages used in quantum information theory as well as for studying the foundations of quantum mechanics are entirely determined by symmetry; moreover, starting from a certain symmetry group, novel types of measurement sets can be constructed. The insight gained from symmetry allows us to easily determine whether the measurements in the set are incompatible under noisy conditions, i.e., whether they can be regarded as genuinely distinct ones. In addition, symmetry enables us to identify finite sets of measurements having a high sensitivity to reveal the quantumness of distributed quantum states.
We provide a proof of global regularity of solutions of coupled Navier-Stokes equations and Fokker-Planck equations, in two spatial dimensions, in the absence of boundaries. The proof yields a priori estimates for the growth of spatial gradients.
Let a sequence of iid. random variables $\xi_1,...,\xi_n$ be given on a measurable space $(X,\cal X)$ with distribution $\mu$ together with a function $f(x_1,...,x_k)$ on the product space $(X^k,{\cal X}^k)$. Let $\mu_n$ denote the empirical measure defined by these random variables and consider the random integral $$ J_{n,k}(f)={{n^{k/2}}\over{k!}}\int' f(u_1,...,u_k) (\mu_n(du_1)-\mu(du_1))...(\mu_n(du_k)-\mu(du_k)), $$ where prime means that the diagonals are omitted from the domain of integration. In this work a good bound is given on the probability $P(|J_{n,k}(f)|>x)$ for all $x>0$. This result shows that the tail behaviour of the distribution funtcion of the random integral $J_{n,k}(f)$ and that of the integral of the function $f$ with respect to a Gaussian random field show a similar behaviour. The proof is based on an adaptation of some methods of the theory of Wiener--Ito integrals. In particular, a sort of diagram formula is proved for the random integrals $J_{n,k}(f)$ together with some of its important properties, a result which may be interesting in itself. The relation of this estimate to some results about $U$-statistics is also discussed.
This article focuses on a combinatorial structure specific to triangulated plane graphs with quadrangular outer face and no separating triangle, which are called irreducible triangulations. The structure has been introduced by Xin He under the name of regular edge-labelling and consists of two bipolar orientations that are transversal. For this reason, the terminology used here is that of transversal structures. The main results obtained in the article are a bijection between irreducible triangulations and ternary trees, and a straight-line drawing algorithm for irreducible triangulations. For a random irreducible triangulation with $n$ vertices, the grid size of the drawing is asymptotically with high probability $11n/27\times 11n/27$ up to an additive error of $\cO(\sqrt{n})$. In contrast, the best previously known algorithm for these triangulations only guarantees a grid size $(\lceil n/2\rceil -1)\times \lfloor n/2\rfloor$.
We study the free energy of the pure glue QCD string with a torus target space and the gauge groups $SU(N)$ and (chiral) $U(N)$. It is highly constrained by a strong/weak gauge coupling duality which results in modular covariance. The string free energy is computed exactly in terms of modular forms for worldsheet genera 1 - 8. It has a surprisingly mild singularity in the weak gauge coupling/small area limit.
The notion of "reference frame" is a central theoretical construct for interpreting the physical implications of spacetime diffeomorphism invariance in General Relativity. However, the alternative formulation of classical General Relativity known as Shape Dynamics suggest that a subset of spacetime diffeomorphisms - namely hypersurface deformations - are, in a certain sense, dual to spatial conformal (or Weyl) invariance. Moreover, holographic gauge/gravity dualities suggest that bulk spacetime diffeomorphism invariance can be replaced by the properties of boundary CFTs. How can these new frameworks be compatible with the traditional notion of reference frame so fundamental to our interpretation of General Relativity? In this paper, we address this question by investigating the classical case of maximally symmetric spacetimes with a positive cosmological constant. We find that it is possible to define a notion of "Shape Observer" that represents a conformal reference frame that is dual to the notion of inertial reference frame in spacetime. We then provide a precise dictionary relating the two notions. These Shape Observers are holographic in the sense that they are defined on the asymptotic conformal boundaries of spacetime but know about bulk physics. This leads to a first principles derivation of an exact classical holographic correspondence that can easily be generalized to more complicated situations and may lead to insights regarding the interpretation of the conformal invariance manifest in Shape Dynamics.
We theoretically examine the momentum dependence of resonant inelastic x-ray scattering (RIXS) spectrum for one-dimensional and two-dimensional cuprates based on the single-band Hubbard model with realistic parameter values. The spectrum is calculated by using the numerical diagonalization technique for finite-size clusters. We focus on excitations across the Mott gap and clarify spectral features coming from the excitations as well as the physics behind them. Good agreement between the theoretical and existing experimental results clearly demonstrates that the RIXS is a potential tool to study the momentum-dependent charge excitations in strongly correlated electron systems.
We present a new measurement of the stellar initial mass function (IMF) based on ultra-deep, high-resolution photometry of >5,000 stars in the outskirts of the Small Magellanic Cloud (SMC) galaxy. The Hubble Space Telescope (HST) Advanced Camera for Surveys (ACS) observations reveal this rich, co-spatial population behind the foreground globular cluster 47 Tuc, which we targeted for 121 HST orbits. The stellar main sequence of the SMC is measured in the F606W, F814W color-magnitude diagram (CMD) down to ~30th magnitude, and is cleanly separated from the foreground star cluster population using proper motions. We simulate the SMC population by extracting stellar masses (single and unresolved binaries) from specific IMFs, and converting those masses to luminosities in our bandpasses. The corresponding photometry for these simulated stars is drawn directly from a rich cloud of 4 million artificial stars, thereby accounting for the real photometric scatter and completeness of the data. Over a continuous and well populated mass range of M = 0.37 - 0.93 Msun (i.e., down to a ~75% completeness limit at F606W = 28.7), we demonstrate that the IMF is well represented by a single power-law form with slope \alpha = -1.90 (^{+0.15}_{-0.10}) (3 sigma error) (i.e., dN/dM \propto M^{\alpha}). This is shallower than the Salpeter slope of \alpha = -2.35, which agrees with the observed stellar luminosity function at higher masses. Our results indicate that the IMF does {\it not} turn over to a more shallow power-law form within this mass range. We discuss implications of this result for the theory of star formation, the inferred masses of galaxies, and the (lack of a) variation of the IMF with metallicity.
Recently, Balogh, Kostochka and Liu in [Packing chromatic number of cubic graphs, Discrete Math.~341 (2018) 474--483] answered in negative the question that was posed in several earlier papers whether the packing chromatic number is bounded in the class of graphs with maximum degree $3$. In this note, we present an explicit infinite family of subcubic graphs with unbounded packing chromatic number.