A network Poisson model for weighted directed networks with covariates

The edges in networks are not only binary, either present or absent, but also take weighted values in many scenarios (e.g., the number of emails between two users). The covariate-p0 model has been proposed to model binary directed networks with the degree heterogeneity and covariates. However, it may cause information loss when it is applied in weighted networks. In this paper, we propose to use the Poisson distribution to model weighted directed networks, which admits the sparsity of networks, the degree heterogeneity and the homophily caused by covariates of nodes. We call it the network Poisson model. The model contains a density parameter μ, a 2n-dimensional node parameter θ and a fixed dimensional regression coefficient γ of covariates. Since the number of parameters increases with n, asymptotic theory is non standard. When the number n of nodes goes to infinity, we establish the ℓ∞-errors for the maximum likelihood estimators (MLEs), θ̂ and γ̂, which are Op(( log n/n)1/2) for θ̂ and Op( log n/n) for γ̂, up to an additional factor. We also obtain the asymptotic normality of the MLE. Numerical studies and a data analysis demonstrate our theoretical findings.</p

Analyzing and interpreting spatial and temporal variability of the United States county population distributions using Taylor's law - Fig 3

US maps showing the slope (a and b) and the sign of quadratic coefficient (c and d) of the spatial (Q)TL (a and c) and temporal (Q)TL (b and d). Sign of the quadratic coefficient is determined by the coefficient significance after Bonferroni correction. Specifically, "zero" is defined when the p-value of the quadratic coefficient (e of Eq 2) is greater than 0.05/number of tests (55 for spatial (Q)TL and 64 for temporal (Q)TL), meaning that the coefficient is not significantly different from zero. "minus" is defined when the p-value is smaller than 0.05/number of tests and the point estimate of e is less than zero. "plus" is defined when the p-value is smaller than 0.05/number of tests and the point estimate of e is larger than zero. This US map is made with the package fiftystater [43] in R. fiftystater is free software that can be redistributed and/or modified under the terms of the GNU General Public License as published by the Free Software Foundation, version 3.</p

Point estimate of regression coefficient of Taylor's law (TL) and quadratic Taylor's law (QTL).

b is the slope estimate of the spatial hierarchical TL (SHTL), spatial TL (STL) or temporal TL (TTL). e is the quadratic coefficient of the spatial hierarchical quadratic TL (SHQTL), spatial quadratic TL (SQTL) or temporal quadratic TL (TQTL). Dark dashed line shows the average value for the corresponding estimate.</p

Flexible Biosensors for the Impedimetric Detection of Protein Targets Using Silk-Conductive Polymer Biocomposites

To expand the applications of flexible biosensors in point-of-care healthcare applications beyond monitoring of biophysical parameters, it is important to devise strategies for the detection of various proteins and biomarkers. Here, we demonstrate a flexible, fully organic, biodegradable, label-free impedimetric biosensor for the critical biomarker, vascular endothelial growth factor (VEGF). This biosensor was constructed by photolithographically patterning a conducting ink consisting of a photoreactive silk sericin coupled with a conducting polymer. These functional electrodes are printed on flexible fibroin substrates that are controllably thick and can be free-standing, or conform to soft surfaces. Detection was accomplished via the antibody to VEGF which was immobilized within the conducting matrix. The results indicated that the developed flexible biosensor was highly sensitive and selective to the target protein, even in challenging biofluids such as human serum. The biosensors themselves are biocompatible and degradable. Through this work, the developed flexible biosensor based on a simple and label-free strategy can find practical applications in the monitoring of wound healing or early disease diagnosis

Analyzing and interpreting spatial and temporal variability of the United States county population distributions using Taylor's law - Fig 2

Time series of (a) the slope estimate of spatial hierarchical TL and of (b) the quadratic coefficient estimate of the spatial hierarchical quadratic TL. The solid circle represents the point estimate and the vertical bar shows the corresponding 95% confidence interval.</p

Summary of the regression statistics of the Taylor's law (TL) (Eq 1) and quadratic Taylor's law (QTL) (Eq 2) models using county population count.

Summary of the regression statistics of the Taylor's law (TL) (Eq 1) and quadratic Taylor's law (QTL) (Eq 2) models using county population count.</p

Temporal mean-temporal variance relationships on log-log scale.

These illustrative examples are selected from a continuum of variation; they do not represent distinct categories. (a) States showing sublinear (superlinear) increase in log(spatial variance) as a function of log(spatial mean) are defined as decentralizing (centralizing) states, compared to the balancing states where log(spatial variance) grows linearly with log(spatial mean). (b) States are classified by the temporal fluctuation of county population count of their most populous (on average) counties: hibernating county (county with the least temporal fluctuation), hybrid county (county with intermediate temporal fluctuation), less vibrant county (county with large temporal fluctuation) and vibrant county (county with the largest temporal fluctuation).</p

Cells were transfected and grown for 24 h, minichromosomal transcripts were detected by RNA FISH, DNA was counterstained with DAPI, and images were collected

(A) Two sets of four views of one field are shown. (bottom) Percentages (± SD) of green foci that overlap red foci, and vice versa. (i–iv) Transfection with II,,pA. An untransfected cell (arrowhead) contains no or transcripts. The other contains many cytoplasmic transcripts but few transcripts; its nucleus contains some red and green foci (marking nascent RNA at transcription sites) against a general background (marking transcripts on their way to the cytoplasm). (insets) Two foci with both red and green fluorescence; this is expected, as the plasmid encodes both and (on the backbone). (v–viii) Cotransfection with II,,pA and II,,pA, which differ solely in coding region. The two central (transfected) cells contain and RNA mainly in the cytoplasm, with some in the nuclear foci. (insets) Nuclear focus with both types of RNA. Insets show an enlarged view of the boxed portions. (B) Discriminating between nuclear foci and background. Intensities are expressed relative to those given by fluorescent reference beads, and the fraction of foci in 200 cells with relative intensities of 0–0.05, 0.06–0.1, etc., is indicated. Promoterless 0,,pA gives faint signal due to autofluorescence (equivalent to that seen in mock-transfected cells, not depicted; gray bar) and read-through from the SV40 early promoter into (red bars). For plasmids with promoters (e.g., II,,pA), only foci with intensities greater than the maximum read-through (green dotted line) were considered. (C) Cells were transfected with II,,pA and incubated with or without α-amanitin and RNase, DNA was stained with DAPI, and transcripts were detected; the treatments abolish signal. Three sets of two views of one field are shown. Bars: (A) 5 μm; (C) 10 μm.<p><b>Copyright information:</b></p><p>Taken from "Similar active genes cluster in specialized transcription factories"</p><p></p><p>The Journal of Cell Biology 2008;181(4):615-623.</p><p>Published online 19 May 2008</p><p>PMCID:PMC2386102.</p><p></p

Diaoluo tree sample data

Tree sample data from Diaoluo Mountain tropical forest in 2010 and 2015 separately. Each row records one individual with its diameter at breast height (cm), height (m), wood density (g/cm3), and aboveground biomass (g

Analyzing and interpreting spatial and temporal variability of the United States county population distributions using Taylor's law - Fig 4

Comparison of the slope of spatial TL (a) and temporal TL (b) across four regions (Midwest, Northeast, South and West) of the US. The overall comparison is tested by the Kruskal-Wallis test and each pairwise comparison is done by the Wilcoxon rank sum test. The number above each pair shows the corresponding p-value. The three horizonal bars in each box plot, from top to bottom, represent the third quartile (Q3), median (Q2), and first quartile (Q1) respectively. The upper and lower whiskers are defined respectively as min(max(slope), Q3+1.5*(Q3-Q1)) and max(min(slope), Q1-1.5*(Q3-Q1)). Outliers (denoted by dots) denote slope values that are greater than Q3+1.5*(Q3-Q1) or smaller than Q1-1.5*(Q3-Q1).</p