F Factor

This V-plot was cross-correlated against matrices defining the fragment center and size information for a genomic region, such that the cross-correlation signal at position x along the genome is given by
$\text{Signal}(x)=F\cdot V$
where F is the matrix of fragment center and size information for fragments of size 105 to 250 bp with centers between x − 60 and x + 60 and V is the V-plot matrix. This raw signal is then normalized using a background signal that is intended to represent the expected signal from the cross-correlation, given (1) the number of fragments observed, and (2) the Tn5 sequence preference. The background signal at position x is defined as
$\text{Background}(x)=B\cdot V\ast \sum F,$
where B represents a matrix with relative probabilities of generating fragments of different sizes and center positions such that ∑B = 1. The scaling factor ∑F, the sum of all reads in the signal matrix, ensures that the background signal represents the expected signal given the observed number of fragments. To determine B, the probability of observing individual insertion sites was first modeled as follows. Tn5 has a sequence preference across ∼21 bp that it contacts (Buenrostro et al. 2013 (link)); therefore, we developed a Position Weight Matrix (PWM) for sequence content ±10 bp from Tn5 insertion points in ATAC-seq performed on genomic DNA. Relative probabilities are calculated for each genomic position using this PWM, and then this 1D sequence preference is used to calculate the relative probability of observing particular ATAC-seq fragments (which require two Tn5 insertions) by multiplying the probabilities of the two insertions needed for that fragment with the probability of observing a fragment of that size (determined from the fragment-size distribution). The normalized nucleosome signal is given by subtracting this background signal from the cross-correlation signal:
$\text{Normalized Signal}(x)=F\cdot V-B\cdot V\ast \sum F.$

The pDOC series of plasmids are based on the plasmid pEX100T [19 (link)]. A schematic representation of the plasmids is shown in Figure 2 and the entire DNA sequence of each plasmid is provided in Additional file 1 and also on GenBank; nos.. The plasmid pDOC-F was constructed by amplification of the 3 × FLAG DNA sequence, Flp recombinase target sites (Flp1 and Flp2) and the kanamycin cassette from the plasmid pSUB11 [22 (link)], flanked by KpnI and XhoI restriction sites, using the primers D55908 and D55909. This amplicon was cloned into the pGEM-T Easy cloning vector (Promega). The resulting plasmid was then restricted with AatII and KpnI, and ligated with annealed complementary oligonucleotides (D57236 and D57237), designed to introduce an I-SceI site and a multi-cloning region (CR1). This plasmid was then restricted with XhoI and NsiI and ligated with annealed complementary oligonucleotides (D57238 and D57239), designed to introduce a second I-SceI site and a multi-cloning region (CR2). The resulting plasmid was restricted with I-SceI, and the fragment cloned into the I-SceI sites of the plasmid pEX100T.
To facilitate further plasmid construction, the 3 × FLAG DNA sequence was removed from pDOC-F, and an AgeI restriction site introduced immediately downstream of the KpnI site. This was achieved by PCR amplification of the DNA immediately downstream of the 3 × FLAG DNA sequence, flanked by KpnI and BglII restriction sites using primers D57436 and D57437. This fragment was then cloned into the unique KpnI and BglII sites of pDOC-F, effectively removing the 3 × FLAG DNA sequence. This new plasmid, pDOC-K, retained the Flp recombination target sites and the kanamycin cassette.
The plasmid pDOC-K was restricted with KpnI and AgeI, and KpnI-AgeI flanked DNA harboring a 6 × His coding sequence, the coding sequence of GFP (from Invitrogen Emerald Green GFP gateway vector - V355-20; amplified with primers D59990 and D59991) or the coding sequence of ProteinA [23 (link)] (amplified using primers D57584 and D57585), were ligated. This resulted in the generation of the plasmids pDOC-H, pDOC-G and pDOC-P respectively.
The plasmid pDOC-C was created by removing the Flp recombinase sites and the kanamycin cassette from pDOC-K, by digestion with KpnI-XhoI, and ligation with annealed complementary oligonucleotides that introduced a unique EcoRV site (D60111 and D60112).

The strains used in these experiments were derivatives of E. coli K-12 (Table 1). Strain XL-1 Blue was used for routine molecular biology and the fimA-lacZ transcriptional fusion strain VL386, and its derivatives, were used for experiments with the fimS genetic switch. The VL386 Δfis::kan knockout mutant was derived by P1vir-mediated transduction [75, 76 ] using a CSH50 fis::kan mutant lysate. VL386 lrp::cml was also prepared by transduction, using a CSH50 lrp::cml lysate. Complementation of the fis mutation was carried out using plasmid pFIS349, which is a single-copy plasmid based on the mini-F origin plasmid pZC320 [77 (link)]. Bacteria were cultured in lysogeny broth (LB, made from Difco media components) or LB agar (containing agar at 1.5 % w/v) [75 ]. MacConkey lactose agar plates [75 ] were used for Lac phenotype determination. Unless otherwise stated, liquid cultures were grown overnight at 37 °C with aeration at 200 r.p.m in an orbital incubator (New Brunswick). Where appropriate, antibiotics (Sigma-Aldrich) were used at the following concentrations: carbenicillin (100 μg ml⁻¹), chloramphenicol (25 μg ml⁻¹) and kanamycin (20 μg ml⁻¹). Plasmid DNA was introduced to bacterial cells by CaCl₂ transformation [78 ] or electroporation using a Bio-Rad Gene Pulser as described in Hanahan, 1983 [79 (link)].

In this paper, we have numerically and analytically investigated the performance of the proposed low-profile multi-layer carpet cloak using low index layers in order to reduce the thickness of the carpet cloak. The proposed carpet cloak simulation is carried out using Comsol Multiphysics. In this simulation, the carpet cloak is illuminated by a gaussian beam and the bottom boundary condition is defined as PEC (modeling the ground plane) and the three other boundaries are considered as scattering boundary conditions. In order to analyze the performance of the proposed low index slab consisting of silver-coated CdSe/CdS quantum dots dispersed in a polymer host with specific filling factor, a 3D full-wave numerical simulation is performed using CST software. The low index slab is shined by a plane wave propagating in the z direction and periodic boundary condition is used around the structure to mimic an infinite slab. The inner and outer radii of nanoparticles are $r_{\mathit{QD}}=4\mathrm{nm}$ and $r_{\mathit{Ag}}=5.8\mathrm{nm}$ respectively with filling factor $f=0.2$ . In order to verify the accuracy of the simulations, we have compared electromagnetic responses of two structures including the slab using numerous nanoparticles (36 ones) and the slab using retrieved effective permittivity instead of real nano-particles. In order to retrieve the effective permittivity of the slab including numerous nanoparticles, we have used MATLAB software. Also, periodic boundary condition is used around the low index slab.