Self-similar disk packings as model spatial scale-free networks

The network of contacts in space-filling disk packings, such as the Apollonian packing, are examined. These networks provide an interesting example of spatial scale-free networks, where the topology reflects the broad distribution of disk areas. A wide variety of topological and spatial properties of these systems are characterized. Their potential as models for networks of connected minima on energy landscapes is discussed.Comment: 13 pages, 12 figures; some bugs fixed and further discussion of higher-dimensional packing

Dimer coverings on the Sierpinski gasket with possible vacancies on the outmost vertices

We present the number of dimers $N_d(n)$ on the Sierpinski gasket $SG_d(n)$ at stage $n$ with dimension $d$ equal to two, three, four or five, where one of the outmost vertices is not covered when the number of vertices $v(n)$ is an odd number. The entropy of absorption of diatomic molecules per site, defined as $S_{SG_d}=\lim_{n \to \infty} \ln N_d(n)/v(n)$, is calculated to be $\ln(2)/3$ exactly for $SG_2(n)$. The numbers of dimers on the generalized Sierpinski gasket $SG_{d,b}(n)$ with $d=2$ and $b=3,4,5$ are also obtained exactly. Their entropies are equal to $\ln(6)/7$, $\ln(28)/12$, $\ln(200)/18$, respectively. The upper and lower bounds for the entropy are derived in terms of the results at a certain stage for $SG_d(n)$ with $d=3,4,5$. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of $S_{SG_d}$ with $d=3,4,5$ can be evaluated with more than a hundred significant figures accurate.Comment: 35 pages, 20 figures and 1 tabl

GMO detection using a bioluminescent real time reporter (BART) of loop mediated isothermal amplification (LAMP) suitable for field use

<p>Abstract</p> <p>Background</p> <p>There is an increasing need for quantitative technologies suitable for molecular detection in a variety of settings for applications including food traceability and monitoring of genetically modified (GM) crops and their products through the food processing chain. Conventional molecular diagnostics utilising real-time polymerase chain reaction (RT-PCR) and fluorescence-based determination of amplification require temperature cycling and relatively complex optics. In contrast, isothermal amplification coupled to a bioluminescent output produced in real-time (BART) occurs at a constant temperature and only requires a simple light detection and integration device.</p> <p>Results</p> <p>Loop mediated isothermal amplification (LAMP) shows robustness to sample-derived inhibitors. Here we show the applicability of coupled LAMP and BART reactions (LAMP-BART) for determination of genetically modified (GM) maize target DNA at low levels of contamination (0.1-5.0% GM) using certified reference material, and compare this to RT-PCR. Results show that conventional DNA extraction methods developed for PCR may not be optimal for LAMP-BART quantification. Additionally, we demonstrate that LAMP is more tolerant to plant sample-derived inhibitors, and show this can be exploited to develop rapid extraction techniques suitable for simple field-based qualitative tests for GM status determination. We also assess the effect of total DNA assay load on LAMP-BART quantitation.</p> <p>Conclusions</p> <p>LAMP-BART is an effective and sensitive technique for GM detection with significant potential for quantification even at low levels of contamination and in samples derived from crops such as maize with a large genome size. The resilience of LAMP-BART to acidic polysaccharides makes it well suited to rapid sample preparation techniques and hence to both high throughput laboratory settings and to portable GM detection applications. The impact of the plant sample matrix and genome loading within a reaction must be controlled to ensure quantification at low target concentrations.</p