Distribution of Time-Averaged Observables for Weak Ergodicity Breaking

We find a general formula for the distribution of time-averaged observables for systems modeled according to the sub-diffusive continuous time random walk. For Gaussian random walks coupled to a thermal bath we recover ergodicity and Boltzmann's statistics, while for the anomalous subdiffusive case a weakly non-ergodic statistical mechanical framework is constructed, which is based on L\'evy's generalized central limit theorem. As an example we calculate the distribution of $\bar{X}$: the time average of the position of the particle, for unbiased and uniformly biased particles, and show that $\bar{X}$ exhibits large fluctuations compared with the ensemble average $$.Comment: 5 pages, 2 figure

Materials for Biomedical Applications

This paper discusses two ceramic material systems for selective laser sintering (SLS) that are being developed for biomedical applications for use in repair of bone defects. SLS is the preferred method of fabricating ceramic implants that exhibit well defined porous microstructures. Implants fabricated in this. manner have proven effective in-vivo showing excellent biocompatibility as well as considerable osseous integration and remodeling of the imp'ant materialMechanical Engineerin

The dimension of loop-erased random walk in 3D

We measure the fractal dimension of loop-erased random walk (LERW) in 3 dimensions, and estimate that it is 1.62400 +- 0.00005. LERW is closely related to the uniform spanning tree and the abelian sandpile model. We simulated LERW on both the cubic and face-centered cubic lattices; the corrections to scaling are slightly smaller for the face-centered cubic lattice.Comment: 4 pages, 4 figures. v2 has more data, minor additional change

The integrated density of states of the random graph Laplacian

We analyse the density of states of the random graph Laplacian in the percolating regime. A symmetry argument and knowledge of the density of states in the nonpercolating regime allows us to isolate the density of states of the percolating cluster (DSPC) alone, thereby eliminating trivially localised states due to finite subgraphs. We derive a nonlinear integral equation for the integrated DSPC and solve it with a population dynamics algorithm. We discuss the possible existence of a mobility edge and give strong evidence for the existence of discrete eigenvalues in the whole range of the spectrum.Comment: 4 pages, 1 figure. Supplementary material available at http://www.theorie.physik.uni-goettingen.de/~aspel/data/spectrum_supplement.pd

The Alexander-Orbach conjecture holds in high dimensions

We examine the incipient infinite cluster (IIC) of critical percolation in regimes where mean-field behavior has been established, namely when the dimension d is large enough or when d>6 and the lattice is sufficiently spread out. We find that random walk on the IIC exhibits anomalous diffusion with the spectral dimension d_s=4/3, that is, p_t(x,x)= t^{-2/3+o(1)}. This establishes a conjecture of Alexander and Orbach. En route we calculate the one-arm exponent with respect to the intrinsic distance.Comment: 25 pages, 2 figures. To appear in Inventiones Mathematica

RNA markers enable phenotypic test of antibiotic susceptibility in Neisseria gonorrhoeae after 10 minutes of ciprofloxacin exposure

Antimicrobial-resistant Neisseria gonorrhoeae is an urgent public-health threat, with continued worldwide incidents of infection and rising resistance to antimicrobials. Traditional culture-based methods for antibiotic susceptibility testing are unacceptably slow (1–2 days), resulting in the use of broad-spectrum antibiotics and the further development and spread of resistance. Critically needed is a rapid antibiotic susceptibility test (AST) that can guide treatment at the point-of-care. Rapid phenotypic approaches using quantification of DNA have been demonstrated for fast-growing organisms (e.g. E. coli) but are challenging for slower-growing pathogens such as N. gonorrhoeae. Here, we investigate the potential of RNA signatures to provide phenotypic responses to antibiotics in N. gonorrhoeae that are faster and greater in magnitude compared with DNA. Using RNA sequencing, we identified antibiotic-responsive transcripts. Significant shifts (>4-fold change) in transcript levels occurred within 5 min of antibiotic exposure. We designed assays for responsive transcripts with the highest abundances and fold changes, and validated gene expression using digital PCR. Using the top two markers (porB and rpmB) we correctly determined the antibiotic susceptibility and resistance of 49 clinical isolates after 10 min exposure to ciprofloxacin. RNA signatures are therefore promising as an approach on which to build rapid AST devices for N. gonorrhoeae at the point-of-care, which is critical for disease management, surveillance, and antibiotic stewardship efforts

Optimizing information flow in small genetic networks. II: Feed forward interactions

Central to the functioning of a living cell is its ability to control the readout or expression of information encoded in the genome. In many cases, a single transcription factor protein activates or represses the expression of many genes. As the concentration of the transcription factor varies, the target genes thus undergo correlated changes, and this redundancy limits the ability of the cell to transmit information about input signals. We explore how interactions among the target genes can reduce this redundancy and optimize information transmission. Our discussion builds on recent work [Tkacik et al, Phys Rev E 80, 031920 (2009)], and there are connections to much earlier work on the role of lateral inhibition in enhancing the efficiency of information transmission in neural circuits; for simplicity we consider here the case where the interactions have a feed forward structure, with no loops. Even with this limitation, the networks that optimize information transmission have a structure reminiscent of the networks found in real biological systems

Complete Experimental Structure Determination of the p(3x2)pg Phase of Glycine on Cu{110}

We present a quantitative low energy electron diffraction (LEED) surface-crystallograpic study of the complete adsorption geometry of glycine adsorbed on Cu{110} in the ordered p(3×2) phase. The glycine molecules form bonds to the surface through the N atoms of the amino group and the two O atoms of the de-protonated carboxylate group, each with separate Cu atoms such that every Cu atom in the first layer is involved in a bond. Laterally, N atoms are nearest to the atop site (displacement 0.41 Å). The O atoms are asymmetrically displaced from the atop site by 0.54 Å and 1.18 Å with two very different O-Cu bond lengths of 1.93 Å and 2.18 Å. The atom positions of the upper-most Cu layers show small relaxations within 0.07 Å of the bulk-truncated surface geometry. The unit cell of the adsorbate layer consists of two glycine molecules, which are related by a glide-line symmetry operation. This study clearly shows that a significant coverage of adsorbate structures without this glide-line symmetry must be rejected, both on the grounds of the energy dependence of the spot intensities (LEED-IV curves) and of systematic absences in the LEED pattern

Tracer concentration profiles measured in central London as part of the REPARTEE campaign

There have been relatively few tracer experiments carried out that have looked at vertical plume spread in urban areas. In this paper we present results from two tracer (cyclic perfluorocarbon) experiments carried out in 2006 and 2007 in central London centred on the BT Tower as part of the REPARTEE (Regent’s Park and Tower Environmental Experiment) campaign. The height of the tower gives a unique opportunity to study vertical dispersion profiles and transport times in central London. Vertical gradients are contrasted with the relevant Pasquill stability classes. Estimation of lateral advection and vertical mixing times are made and compared with previous measurements. Data are then compared with a simple operational dispersion model and contrasted with data taken in central London as part of the DAPPLE campaign. This correlates dosage with non-dimensionalised distance from source. Such analyses illustrate the feasibility of the use of these empirical correlations over these prescribed distances in central London

Laplace Operators on Fractals and Related Functional Equations

We give an overview over the application of functional equations, namely the classical Poincar\'e and renewal equations, to the study of the spectrum of Laplace operators on self-similar fractals. We compare the techniques used to those used in the euclidean situation. Furthermore, we use the obtained information on the spectral zeta function to define the Casimir energy of fractals. We give numerical values for this energy for the Sierpi\'nski gasket