Knot Tightening By Constrained Gradient Descent

We present new computations of approximately length-minimizing polygons with fixed thickness. These curves model the centerlines of "tight" knotted tubes with minimal length and fixed circular cross-section. Our curves approximately minimize the ropelength (or quotient of length and thickness) for polygons in their knot types. While previous authors have minimized ropelength for polygons using simulated annealing, the new idea in our code is to minimize length over the set of polygons of thickness at least one using a version of constrained gradient descent. We rewrite the problem in terms of minimizing the length of the polygon subject to an infinite family of differentiable constraint functions. We prove that the polyhedral cone of variations of a polygon of thickness one which do not decrease thickness to first order is finitely generated, and give an explicit set of generators. Using this cone we give a first-order minimization procedure and a Karush-Kuhn-Tucker criterion for polygonal ropelength criticality. Our main numerical contribution is a set of 379 almost-critical prime knots and links, covering all prime knots with no more than 10 crossings and all prime links with no more than 9 crossings. For links, these are the first published ropelength figures, and for knots they improve on existing figures. We give new maps of the self-contacts of these knots and links, and discover some highly symmetric tight knots with particularly simple looking self-contact maps.Comment: 45 pages, 16 figures, includes table of data with upper bounds on ropelength for all prime knots with no more than 10 crossings and all prime links with no more than 9 crossing

A first measurement of the Proper Motion of the Leo II dwarf spheroidal galaxy

We use 14-year baseline images obtained with the Wide Field Planetary Camera 2 on board the Hubble Space telescope to derive a proper motion for one of the Milky Way's most distant dwarf spheroidal companions, Leo II, relative to an extragalactic background reference frame. Astrometric measurements are performed in the effective point spread function (ePSF) formalism using our own developed code. An astrometric reference grid is defined using 3,224 stars that are members of Leo II that are brighter than magnitude 25 in the F814W band. We identify 17 compact extra-galactic sources, for which we measure a systemic proper motion relative to this stellar reference grid. We derive a proper motion [\mu_{\alpha},\mu_{\delta}]=[+104+/-113,-33+/-151] microarcseconds/yr for Leo II in the heliocentric reference frame. Though marginally detected, the proper motion yields constraints on the orbit of Leo II. Given a distance of 230 Kpc and a heliocentric radial velocity +79 km/s, and after subtraction of the solar motion, our measurement indicates a total orbital motion 266.1+/-128.7 km/s in the Galactocentric reference frame, with a radial component +21.5+/-4.3 km/s and tangential component 265.2+/-129.4 km/s. The small radial component indicates that Leo II either has a low-eccentricity orbit, or is currently close to perigalacticon or apogalacticon distance. We see evidence for systematic errors in the astrometry of the extragalactic sources which, while close to being point sources, are slightly resolved in the HST images. We argue that more extensive observations at later epochs will be necessary to better constrain the proper motion of Leo II. We provide a detailed catalog of the stellar and extragalactic sources identified in the HST data which should provide a solid early-epoch reference for future astrometric measurements.Comment: 10 pages, accepted for publication in the Astrophysical Journa

Shapes of Knotted Cyclic Polymers(Knots and soft-matter physics: Topology of polymers and related topics in physics, mathematics and biology)

この論文は国立情報学研究所の電子図書館事業により電子化されました。Momentary configurations of long polymers at thermal equilibrium usually deviate from spherical symmetry and can be better described, on average, by a prolate ellipsoid. The asphericity and nature of asphericity (or prolateness) that describe these momentary ellipsoidal shapes of a polymer are determined by specific expressions involving the three principal moments of inertia calculated for configurations of the polymer. Earlier theoretical studies and numerical simulations have established that as the length of the polymer increases, the average shape for the statistical ensemble of random configurations asymptotically approaches a characteristic universal shape that depends on the solvent quality. It has been established, however, that these universal shapes differ for linear, circular, and branched chains. We investigate here the effect of knotting on the shape of cyclic polymers modeled as random isosegmental polygons. We observe that random polygons forming different knot types reach asymptotic shapes that are distinct from the ensemble average shape. For the same chain length, more complex knots are, on average, more spherical than less complex knots. This paper is a shorter, revised version of the article Ref. [12]. For more details, see Ref. [12]

In Vivo Activity of Metal Complexes Containing 1,10-Phenanthroline and 3,6,9-Trioxaundecanedioate Ligands against Pseudomonas aeruginosa Infection in Galleria mellonella Larvae

Drug-resistant Pseudomonas aeruginosa is rapidly developing resulting in a serious global threat. Immunocompromised patients are specifically at risk, especially those with cystic fibrosis (CF). Novel metal complexes incorporating 1,10-phenanthroline (phen) ligands have previously demonstrated antibacterial and anti-biofilm effects against resistant P. aeruginosa from CF patients in vitro. Herein, we present the in vivo efficacy of {[Cu(3,6,9-tdda)(phen)2]·3H2O·EtOH}n (Cu-tdda-phen), {[Mn(3,6,9-tdda)(phen)2]·3H2O·EtOH}n (Mn-tdda-phen) and [Ag2(3,6,9-tdda)(phen)4]·EtOH (Ag-tdda-phen) (tddaH2 = 3,6,9-trioxaundecanedioic acid). Individual treatments of these metal-tdda-phen complexes and in combination with the established antibiotic gentamicin were evaluated in vivo in larvae of Galleria mellonella infected with clinical isolates and laboratory strains of P. aeruginosa. G. mellonella were able to tolerate all test complexes up to 10 µg/larva. In addition, the immune response was affected by stimulation of immune cells (hemocytes) and genes that encode for immune-related peptides, specifically transferrin and inducible metallo-proteinase inhibitor. The amalgamation of metal-tdda-phen complexes and gentamicin further intensified this response at lower concentrations, clearing a P. aeruginosa infection that were previously resistant to gentamicin alone. Therefore this work highlights the anti-pseudomonal capabilities of metal-tdda-phen complexes alone and combined with gentamicin in an in vivo model

The Mass Distribution and Assembly of the Milky Way from the Properties of the Magellanic Clouds

We present a new measurement of the mass of the Milky Way (MW) based on observed properties of its largest satellite galaxies, the Magellanic Clouds (MCs), and an assumed prior of a {\Lambda}CDM universe. The large, high-resolution Bolshoi cosmological simulation of this universe provides a means to statistically sample the dynamical properties of bright satellite galaxies in a large population of dark matter halos. The observed properties of the MCs, including their circular velocity, distance from the center of the MW, and velocity within the MW halo, are used to evaluate the likelihood that a given halo would have each or all of these properties; the posterior PDF for any property of the MW system can thus be constructed. This method provides a constraint on the MW virial mass, 1.2 +0.7 -0.3(stat.) +0.3 -0.4 (sys.) x 10^12 M\odot (68% confidence), which is consistent with recent determinations that involve very different assumptions. In addition, we calculate the posterior PDF for the density profile of the MW and its satellite accretion history. Although typical satellites of 10^12 M\odot halos are accreted over a wide range of epochs over the last 10 Gyr, we find a \sim72% probability that the Magellanic Clouds were accreted within the last Gyr, and a 50% probability that they were accreted together.Comment: 9 pages, replaced with version published in ApJ. Animations available at http://risa.stanford.edu/milkyway

The ACS Virgo Cluster Survey. VIII. The Nuclei of Early-Type Galaxies

(Abridged) The ACS Virgo Cluster Survey is an HST program to obtain high-resolution, g and z-band images for 100 early-type members of the Virgo Cluster, spanning a range of ~460 in blue luminosity. Based on this large, homogeneous dataset, we present a sharp upward revision in the frequency of nucleation in early-type galaxies brighter than M_B ~ -15 (66 < f_n < 82%), and find no evidence for nucleated dwarfs to be more concentrated to the center of Virgo than their non-nucleated counterparts. Resolved stellar nuclei are not present in galaxies brighter than M_B ~ -20.5, however, there is no clear evidence from the properties of the nuclei, or from the overall incidence of nucleation, for a change at M_B ~ -17.6, the traditional dividing point between dwarf and giant galaxies. On average, nuclei are ~3.5 mag brighter than a typical globular cluster and have a median half-light radius ~4.2 pc. Nuclear luminosities correlate with nuclear sizes and, in galaxies fainter than M_B ~ -17.6, nuclear colors. Comparing the nuclei to the "nuclear clusters" found in late-type spiral galaxies reveals a close match in terms of size, luminosity and overall frequency, pointing to a formation mechanism that is rather insensitive to the detailed properties of the host galaxy. The mean nuclear-to-galaxy luminosity ratio is indistinguishable from the mean SBH-to-bulge mass ratio, calculated in early-type galaxies with detected supermassive black holes (SBHs). We argue that compact stellar nuclei might be the low-mass counterparts of the SBHs detected in the bright galaxies, and that one should think in terms of "Central Massive Objects" -- either SBHs or compact stellar nuclei -- that accompany the formation of almost all early-type galaxies and contain a mean fraction ~0.3% of the total bulge mass.Comment: ApJ Supplements, accepted. Updated references. The manuscript is 61 pages, including 6 tables and 28 figures. Figures included in this submission are low resolution; a version of the paper containing high-resolution color figures can be downloaded from the ACSVCS website: http://www.cadc.hia.nrc.gc.ca/community/ACSVCS/publications.html#acsvcs

Small-Scale Structure in the SDSS and LCDM: Isolated L* Galaxies with Bright Satellites

We use a volume-limited spectroscopic sample of isolated galaxies in the Sloan Digital Sky Survey (SDSS) to investigate the frequency and radial distribution of luminous (M_r <~ -18.3) satellites like the Large Magellanic Cloud (LMC) around ~L* Milky Way analogs and compare our results object-by-object to LCDM predictions based on abundance matching in simulations. We show that 12% of Milky Way-like galaxies host an LMC-like satellite within 75 kpc (projected), and 42 % within 250 kpc (projected). This implies ~10% have a satellite within the distance of the LMC, and ~40% of L* galaxies host a bright satellite within the virialized extent of their dark matter halos. Remarkably, the simulation reproduces the observed frequency, radial dependence, velocity distribution, and luminosity function of observed secondaries exceptionally well, suggesting that LCDM provides an accurate reproduction of the observed Universe to galaxies as faint as L~10^9 Lsun on ~50 kpc scales. When stacked, the observed projected pairwise velocity dispersion of these satellites is sigma~160 km/s, in agreement with abundance-matching expectations for their host halo masses. Finally, bright satellites around L* primaries are significantly redder than typical galaxies in their luminosity range, indicating that environmental quenching is operating within galaxy-size dark matter halos that typically contain only a single bright satellite. This redness trend is in stark contrast to the Milky Way's LMC, which is unusually blue even for a field galaxy. We suggest that the LMC's discrepant color might be further evidence that it is undergoing a triggered star-formation event upon first infall.Comment: 14 pages, 11 figures; accepted to Ap