Space-efficient Feature Maps for String Alignment Kernels

String kernels are attractive data analysis tools for analyzing string data. Among them, alignment kernels are known for their high prediction accuracies in string classifications when tested in combination with SVM in various applications. However, alignment kernels have a crucial drawback in that they scale poorly due to their quadratic computation complexity in the number of input strings, which limits large-scale applications in practice. We address this need by presenting the first approximation for string alignment kernels, which we call space-efficient feature maps for edit distance with moves (SFMEDM), by leveraging a metric embedding named edit sensitive parsing (ESP) and feature maps (FMs) of random Fourier features (RFFs) for large-scale string analyses. The original FMs for RFFs consume a huge amount of memory proportional to the dimension d of input vectors and the dimension D of output vectors, which prohibits its large-scale applications. We present novel space-efficient feature maps (SFMs) of RFFs for a space reduction from O(dD) of the original FMs to O(d) of SFMs with a theoretical guarantee with respect to concentration bounds. We experimentally test SFMEDM on its ability to learn SVM for large-scale string classifications with various massive string data, and we demonstrate the superior performance of SFMEDM with respect to prediction accuracy, scalability and computation efficiency.Comment: Full version for ICDM'19 pape

Spin down of protostars through gravitational torques

Young protostars embedded in circumstellar discs accrete from an angular momentum-rich mass reservoir. Without some braking mechanism, all stars should be spinning at or near break-up velocity. In this paper, we perform simulations of the self-gravitational collapse of an isothermal cloud using the ORION adaptive mesh refinement code and investigate the role that gravitational torques might play in the spin-down of the dense central object. While magnetic effects likely dominate for low mass stars, high mass and Population III stars might be less well magnetised. We find that gravitational torques alone prevent the central object from spinning up to more than half of its breakup velocity, because higher rotation rates lead to bar-like deformations that enable efficient angular momentum transfer to the surrounding medium. We also find that the long-term spin evolution of the central object is dictated by the properties of the surrounding disc. In particular, spiral modes with azimuthal wavenumber $m=2$ couple more effectively to its spin than the lopsided $m=1$ mode, which was found to inhibit spin evolution. We suggest that even in the absence of magnetic fields, gravitational torques may provide an upper limit on stellar spin, and that moderately massive circumstellar discs can cause long-term spin down.Comment: 13 pages, 17 figures, 1 table. Accepted by MNRAS. Updated reference

Spiral Arms, Infall, and Misalignment of the Circumbinary Disk from the Circumstellar Disks in the Protostellar Binary System L1551 NE

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SMA and Spitzer Observations of Bok Glouble CB17: A Candidate First Hydrostatic Core?

We present high angular resolution SMA and Spitzer observations toward the Bok globule CB17. SMA 1.3mm dust continuum images reveal within CB17 two sources with an angular separation of about 21" (about 5250 AU at a distance of 250 pc). The northwestern continuum source, referred to as CB17 IRS, dominates the infrared emission in the Spitzer images, drives a bipolar outflow extending in the northwest-southeast direction, and is classified as a low luminosity Class0/I transition object (L_bol ~ 0.5 L_sun). The southeastern continuum source, referred to as CB17 MMS, has faint dust continuum emission in the SMA 1.3mm observations (about 6 sigma detection; ~3.8 mJy), but is not detected in the deep Spitzer infrared images at wavelengths from 3.6 to 70 micron. Its bolometric luminosity and temperature, estimated from its spectral energy distribution, are less than 0.04 L_sun and 16 K, respectively. The SMA CO(2-1) observations suggest that CB17 MMS may drive a low-velocity molecular outflow (about 2.5 km/s), extending in the east-west direction. Comparisons with prestellar cores and Class0 protostars suggest that CB17 MMS is more evolved than prestellar cores but less evolved than Class0 protostars. The observed characteristics of CB17 MMS are consistent with the theoretical predictions from radiative/magneto hydrodynamical simulations of a first hydrostatic core, but there is also the possibility that CB17 MMS is an extremely low luminosity protostar deeply embedded in an edge-on circumstellar disk. Further observations are needed to study the properties of CB17 MMS and to address more precisely its evolutionary stage.Comment: 33 pages, 11 figures, to be published by Ap

More supplements to a class of logarithmically completely monotonic functions associated with the gamma function

In this article, a necessary and sufficient condition and a necessary condition are established for a function involving the gamma function to be logarithmically completely monotonic on $(0,\infty)$. As applications of the necessary and sufficient condition, some inequalities for bounding the psi and polygamma functions and the ratio of two gamma functions are derived.Comment: 8 page

Protostellar collapse: rotation and disk formation

We present some important conclusions from recent calculations pertaining to the collapse of rotating molecular cloud cores with axial symmetry, corresponding to evolution of young stellar objects through classes 0 and begin of class I. Three main issues have been addressed: (1) The typical timescale for building up a preplanetary disk - once more it turned out that it is of the order of one free-fall time which is decisively shorter than the widely assumed timescale related to the so-called 'inside-out collapse'; (2) Redistribution of angular momentum and the accompanying dissipation of kinetic (rotational) energy - together these processes govern the mechanical and thermal evolution of the protostellar core to a large extent; (3) The origin of calcium-aluminium-rich inclusions (CAIs) - due to the specific pattern of the accretion flow, material that has undergone substantial chemical and mineralogical modifications in the hot (exceeding 900 K) interior of the protostellar core may have a good chance to be advectively transported outward into the cooler remote parts (beyond 4 AU, say) of the growing disk and to survive there until it is incorporated into a meteoritic body.Comment: 4 pages, 4 figure