Fractal Strings and Multifractal Zeta Functions

For a Borel measure on the unit interval and a sequence of scales that tend to zero, we define a one-parameter family of zeta functions called multifractal zeta functions. These functions are a first attempt to associate a zeta function to certain multifractal measures. However, we primarily show that they associate a new zeta function, the topological zeta function, to a fractal string in order to take into account the topology of its fractal boundary. This expands upon the geometric information garnered by the traditional geometric zeta function of a fractal string in the theory of complex dimensions. In particular, one can distinguish between a fractal string whose boundary is the classical Cantor set, and one whose boundary has a single limit point but has the same sequence of lengths as the complement of the Cantor set. Later work will address related, but somewhat different, approaches to multifractals themselves, via zeta functions, partly motivated by the present paper.Comment: 32 pages, 9 figures. This revised version contains new sections and figures illustrating the main results of this paper and recent results from others. Sections 0, 2, and 6 have been significantly rewritte

Matrix-Assisted Laser Desorption/Ionization Time-of-Flight Mass Spectrometry Identification of Mycobacteria in Routine Clinical Practice

Background: Non-tuberculous mycobacteria recovered from respiratory tract specimens are emerging confounder organisms for the laboratory diagnosis of tuberculosis worldwide. There is an urgent need for new techniques to rapidly identify mycobacteria isolated in clinical practice. Matrix-assisted laser desorption time-of-flight mass spectrometry (MALDI-TOF MS) has previously been proven to effectively identify mycobacteria grown in high-concentration inocula from collections. However, a thorough evaluation of its use in routine laboratory practice has not been performed. Methodology: We set up an original protocol for the MALDI-TOF MS identification of heat-inactivated mycobacteria after dissociation in Tween-20, mechanical breaking of the cell wall and protein extraction with formic acid and acetonitrile. By applying this protocol to as few as 10 5 colony-forming units of reference isolates of Mycobacterium tuberculosis, Mycobacterium avium, and 20 other Mycobacterium species, we obtained species-specific mass spectra for the creation of a local database. Using this database, our protocol enabled the identification by MALDI-TOF MS of 87 M. tuberculosis, 25M. avium and 12 non-tuberculosis clinical isolates with identification scores $2 within 2.5 hours. Conclusions: Our data indicate that MALDI-TOF MS can be used as a first-line method for the routine identification of heatinactivated mycobacteria. MALDI-TOF MS is an attractive method for implementation in clinical microbiology laboratories i

Magnetic and Electronic Properties of Metal-Atom Adsorbed Graphene

We systematically investigate the magnetic and electronic properties of graphene adsorbed with diluted 3d-transition and noble metal atoms using first principles calculation methods. We find that most transition metal atoms (i.e. Sc, Ti, V, Mn, Fe) favor the hollow adsorption site, and the interaction between magnetic adatoms and \pi-orbital of graphene induces sizable exchange field and Rashba spin-orbit coupling, which together open a nontrivial bulk gap near the Dirac points leading to the quantum-anomalous Hall effect. We also find that the noble metal atoms (i.e. Cu, Ag, Au) prefer the top adsorption site, and the dominant inequality of the AB sublattice potential opens another kind of nontrivial bulk gap exhibiting the quantum-valley Hall effect.Comment: Submitted to PRL on Aug. 10, 2011. 11 pages(4.5 pages for the main text and 6.5 pages for the supporting materials

Supplement: "Localization and broadband follow-up of the gravitational-wave transient GW150914" (2016, ApJL, 826, L13)

This Supplement provides supporting material for Abbott et al. (2016a). We briefly summarize past electromagnetic (EM) follow-up efforts as well as the organization and policy of the current EM follow-up program. We compare the four probability sky maps produced for the gravitational-wave transient GW150914, and provide additional details of the EM follow-up observations that were performed in the different bands

Localization and Broadband Follow-up of the Gravitational-wave Transient GW150914

A gravitational-wave (GW) transient was identified in data recorded by the Advanced Laser Interferometer Gravitational-wave Observatory (LIGO) detectors on 2015 September 14. The event, initially designated G184098 and later given the name GW150914, is described in detail elsewhere. By prior arrangement, preliminary estimates of the time, significance, and sky location of the event were shared with 63 teams of observers covering radio, optical, near-infrared, X-ray, and gamma-ray wavelengths with ground- and space-based facilities. In this Letter we describe the low-latency analysis of the GW data and present the sky localization of the first observed compact binary merger. We summarize the follow-up observations reported by 25 teams via private Gamma-ray Coordinates Network circulars, giving an overview of the participating facilities, the GW sky localization coverage, the timeline, and depth of the observations. As this event turned out to be a binary black hole merger, there is little expectation of a detectable electromagnetic (EM) signature. Nevertheless, this first broadband campaign to search for a counterpart of an Advanced LIGO source represents a milestone and highlights the broad capabilities of the transient astronomy community and the observing strategies that have been developed to pursue neutron star binary merger events. Detailed investigations of the EM data and results of the EM follow-up campaign are being disseminated in papers by the individual teams. </p

A gravitational-wave standard siren measurement of the Hubble constant

The detection of GW170817 (ref. 1) heralds the age of gravitational-wave multi-messenger astronomy, with the observations of gravitational-wave and electromagnetic emission from the same transient source. On 17 August 2017 the network of Advanced Laser Interferometer Gravitational-wave Observatory (LIGO)2 and Virgo3 detectors observed GW170817, a strong signal from the merger of a binary neutron-star system. Less than two seconds after the merger, a γ-ray burst event, GRB 170817A, was detected consistent with the LIGO–Virgo sky localization region4–6). The sky region was subsequently observed by optical astronomy facilities7, resulting in the identification of an optical transient signal within about 10 arcseconds of the galaxy NGC 4993 (refs 8–13). GW170817 can be used as a standard siren14–18, combining the distance inferred purely from the gravitational-wave signal with the recession velocity arising from the electromagnetic data to determine the Hubble constant. This quantity, representing the local expansion rate of the Universe, sets the overall scale of the Universe and is of fundamental importance to cosmology. Our measurements do not require any form of cosmic ‘distance ladder’19; the gravitational-wave analysis directly estimates the luminosity distance out to cosmological scales. Here we report H0 = kilometres per second per megaparsec, which is consistent with existing measurements20,21, while being completely independent of them

Multi-messenger Observations of a Binary Neutron Star Merger

On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of ∼ 1.7 {{s}} with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg2 at a luminosity distance of {40}-8+8 Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 {M}ȯ . An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at ∼ 40 {{Mpc}}) less than 11 hours after the merger by the One-Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over ∼10 days. Following early non-detections, X-ray and radio emission were discovered at the transient’s position ∼ 9 and ∼ 16 days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC 4993 followed by a short gamma-ray burst (GRB 170817A) and a kilonova/macronova powered by the radioactive decay of r-process nuclei synthesized in the ejecta.</p