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

Electron-electron interactions in one- and three-dimensional mesoscopic disordered rings: a perturbative approach

We have computed persistent currents in a disordered mesoscopic ring in the presence of small electron-electron interactions, treated in first order perturbation theory. We have investigated both a contact (Hubbard) and a nearest neighbour interaction in 1D and 3D. Our results show that a repulsive Hubbard interaction produces a paramagnetic contribution to the average current (whatever the dimension) and increases the value of the typical current. On the other hand, a nearest neighbour repulsive interaction results in a diamagnetic contribution in 1D and paramagnetic one in 3D, and tends to decrease the value of the typical current in any dimension. Our study is based on numerical simulations on the Anderson model and is justified analytically in the presence of very weak disorder. We have also investigated the influence of the amount of disorder and of the statistical (canonical or grand-canonical) ensemble.Comment: 7 pages in REVTEX, 4 figure

Dynamic response of isolated Aharonov-Bohm rings coupled to an electromagnetic resonator

We have measured the flux dependence of both real and imaginary conductance of $GaAs/GaAlAs$ isolated mesoscopic rings at 310 MHz. The rings are coupled to a highly sensitive electromagnetic superconducting micro-resonator and lead to a perturbation of the resonance frequency and quality factor. This experiment provides a new tool for the investigation of the conductance of mesoscopic systems without any connection to invasive probes. It can be compared with recent theoretical predictions emphasizing the differences between isolated and connected geometries and the relation between ac conductance and persistent currents. We observe $\Phi_0/2$ periodic oscillations on both components of the magnetoconductance. The oscillations of the imaginary conductance whose sign corresponds to diamagnetism in zero field, are 3 times larger than the Drude conductance $G_0$. The real part of the periodic magnetoconductance is of the order of $0.2 G_0$ and is apparently negative in low field. It is thus notably different from the weak localisation oscillations observed in connected rings, which are much smaller and opposite in sign.Comment: 4 pages, revtex, epsf, 4 Postscript file

Genetic and Functional Assessment of the Role of the rs13431652-A and rs573225-A Alleles in the G6PC2 Promoter That Are Strongly Associated With Elevated Fasting Glucose Levels

OBJECTIVE Genome-wide association studies have identified a single nucleotide polymorphism (SNP), rs560887, located in a G6PC2 intron that is highly correlated with variations in fasting plasma glucose (FPG). G6PC2 encodes an islet-specific glucose-6-phosphatase catalytic subunit. This study examines the contribution of two G6PC2 promoter SNPs, rs13431652 and rs573225, to the association signal. RESEARCH DESIGN AND METHODS We genotyped 9,532 normal FPG participants (FPG <6.1 mmol/l) for three G6PC2 SNPs, rs13431652 (distal promoter), rs573225 (proximal promoter), rs560887 (3rd intron). We used regression analyses adjusted for age, sex, and BMI to assess the association with FPG and haplotype analyses to assess comparative SNP contributions. Fusion gene and gel retardation analyses characterized the effect of rs13431652 and rs573225 on G6PC2 promoter activity and transcription factor binding. RESULTS Genetic analyses provide evidence for a strong contribution of the promoter SNPs to FPG variability at the G6PC2 locus (rs13431652: β = 0.075, P = 3.6 × 10−35; rs573225 β = 0.073 P = 3.6 × 10−34), in addition to rs560887 (β = 0.071, P = 1.2 × 10−31). The rs13431652-A and rs573225-A alleles promote increased NF-Y and Foxa2 binding, respectively. The rs13431652-A allele is associated with increased FPG and elevated promoter activity, consistent with the function of G6PC2 in pancreatic islets. In contrast, the rs573225-A allele is associated with elevated FPG but reduced promoter activity. CONCLUSIONS Genetic and in situ functional data support a potential role for rs13431652, but not rs573225, as a causative SNP linking G6PC2 to variations in FPG, though a causative role for rs573225 in vivo cannot be ruled out

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