The impact of a cut-off on visualizing a power-law distribution and estimating the exponent.

<p>(A) Probability mass function (PMF, inset; calculated as , where is the Riemann zeta function) and the corresponding complementary cumulative distribution [CCDF, defined as ] for a power-law distribution without cut-off, i.e., the power law holds for arbitrarily large <i>k</i>. The exponents are −1.5 and −0.5 for the PMF and CCDF, respectively. (B) PMFs (inset; defined as if <i>k</i> ≤ <i>k_max</i> and if <i>k</i>><i>k_max</i>, where <i>k_max</i> is the cut-off size) and corresponding CCDFs [defined as ] for power-law distributions with cut-off sizes, <i>k_max</i> = 10², 10³, 10⁴, and 10⁵ [dashed lines: power law with exponent <i>α</i> = −1.5 (inset) and −0.5 shown for comparison]. (C) CCDFs for cluster sizes in monkey 1 (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0099761#pone-0099761-g001" target="_blank">Fig. 1E</a> for corresponding PMFs). (D) Power-law exponents were estimated for synthetic data with varying cut-off size, <i>N</i>, ranging from 8 to 10⁴, assuming the correct model with upper bound (<i>s</i>_max = <i>N</i>, red) or an incorrect model without cut-off (<i>s</i>_max = ∞, black). Exponents were estimated using a maximum-likelihood approach (shown are the means with error bars indicating the standard deviation across <i>n</i> = 10 synthetic distributions). (E) Power-law exponents were estimated for size distribution of monkey 1 with varying cut-off size, <i>N</i>, ranging from 10 to 91, assuming the correct model with upper bound (<i>s</i>_max = <i>N</i>, red) or an incorrect model without cut-off (<i>s</i>_max = ∞, black).</p

Characteristics of spatial patterns for avalanches observed before and after the cut-off.

<p>(<b>A</b>) Avalanches observed with a window of <i>N</i> = 24 (see inset). Top panel: the probability distribution is redrawn from Fig. 1E (Monkey 1). Bottom panel: five randomly chosen spatial avalanche patterns each are shown for <i>s</i> = 3, 6, …, 24. In addition, all 19 spatial patterns for avalanches larger than the observation window size (i.e., <i>s</i>>24) are depicted. The number of times that any specific electrode participated in a given avalanche is color-coded. (<b>B</b>) Same as <i>A</i> for the largest observation window with <i>N</i> = 91 electrodes. Only 15 example patterns with s>91 are depicted. (<b>C</b>) The average spatial extent of avalanches, quantified by the number of unique electrodes involved in an avalanche, is plotted as a function of avalanche size for different observation windows. Horizontal dashed lines indicate window size <i>N</i>. The diagonal red line indicates equality. (<b>D</b>) Average percentage of electrodes that do not exhibit repeated activation in an avalanche is plotted as a function of the avalanche size for different observation windows. Vertical dashed lines correspond to the different observation window sizes. The observation windows used are the same as those in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0099761#pone-0099761-g001" target="_blank">Figure 1E</a>.</p

The two-layer model exhibits dynamics similar to LFP-based cortical neuronal avalanches.

<p>(<b>A</b>) The diagram of the model, showing a part of the two-dimensional network of binary neurons and the generation of signals at the “electrode level”, i.e., the local spiking activity (LSA). The LSA sampled by simulated electrodes is produced by summation of spiking activities from spatially compact, non-overlapping 10 by 10 neuronal groups (dark gray and blue nodes) and subsequent temporal smoothing. (<b>B</b>) The size distribution of spike avalanches (<i>n</i> = 150,000; red) in the critically tuned network follows a power law with exponent −1.5 (dashed line). (<b>C</b>) Example trace of raw (blue) and temporally smoothed (black) LSA activities (half-width of the Gaussian smoothing window: 30 time steps). LSA peaks (red dots) were detected by applying a threshold of LSA = 0.1. (<b>D</b>) Raster of LSA peaks detected at the electrode level (individual dots represent LSA peaks). (<b>E</b>) Avalanche size distributions observed at the electrode level of the model with local connectivity are plotted for four different observation windows (<i>n</i> = 50,105 avalanches for <i>N</i> = 100). Inset: probability of LSA propagation across the two-dimensional array of simulated electrodes. The positions of arrows indicate the corresponding window sizes. The dotted line is a power law with exponent of −1.5. (<b>F</b>) The estimated branching parameter, <i>σ</i>, is plotted against the observation window size <i>N</i>. (<b>G</b>) The average spatial extent, quantified by the number of unique electrodes involved in an avalanche, is plotted against avalanche size for different observation windows. The horizontal dotted lines indicate window sizes (same as <i>E</i>). The diagonal dotted line indicates equality. (<b>H</b>) Percentage of electrodes without repeated activation during an avalanche is plotted as a function of avalanche size. (<b>I</b>) The same as in <i>E</i> for all-to-all connectivity (inset shows the probability of LSA propagation across the electrodes).</p

Size relationship of avalanches is only preserved for avalanches smaller than the observation window size.

<p>(<b>A</b>) Observing an avalanche of size <i>s_N1 ≤ N₁</i> predicts the size <i>s_N2</i> of the corresponding avalanche observed in window <i>N₂ < N₁</i>. This prediction power is lost for <i>s_N1</i>><i>N₁</i>. The sizes of nLFP clusters were measured for a window of size <i>N</i>₁ and plotted against the corresponding cluster sizes that were obtained for a window half as large, i.e., <i>N</i>₂ = 0.5×<i>N</i>₁ (monkey 1). Vertical arrows indicate the sizes of the larger window. Shown are averages for each size <i>s_N</i>₁ (gray symbols) and smoothed lines for better visualization (×: <i>N</i>₁ = 20, +: <i>N</i>₁ = 40, o: <i>N</i>₁ = 80). The smaller window with <i>N</i>₂ electrodes was completely contained within the larger window with <i>N</i>₁ electrodes. (<b>B</b>) The same as <i>A</i> for the model. (<b>C</b>) The same analysis for various values of the upper cut-off frequency, <i>f</i>_high (<i>N</i>₁ = 40, <i>N</i>₂ = 20; monkey 1). (<b>D</b>) The same as <i>C</i> for the model with various settings for temporal smoothing of the raw LSA signal.</p

Local activity propagation leads to avalanche dynamics that can be observed by windows with varying sizes.

<p>(<b>A</b>) Small avalanches identified within small windows are parts of larger avalanches identified in large windows. Examples of the spatiotemporal pattern of an avalanche as observed through windows of increasing size. Note that for the smallest window, the avalanche was separated into two smaller avalanches. (<b>B</b>) Probability map of nLFP propagations, showing the probability, <i>p</i>, of detecting a decedent nLFP at certain location in the next time bin (2 ms, upper row; 4 ms, lower row) after a single nLFP has been detected. The initial nLFP is always positioned at the center of the map (0, 0) and the unit of distance, <i>Δd</i>, is the inter-electrode distance of the recording array (0.4 mm). (<b>C</b>) Estimation of balanced propagation depends on window size. The estimated branching parameter, <i>σ</i>, increases with window <i>N</i>, approaching the critical value of <i>σ</i> = 1. (<b>D</b>) Branching parameter as a function of avalanche size, <i>σ</i>(<i>s</i>), is plotted for the four observation windows used in <i>A</i> (color coded). Individual dots represent average <i>σ</i> for avalanches with different sizes, <i>s</i> = 1, …, <i>N</i> for monkey 1 (monkey 2 gave similar results; not shown).</p

Table_1_LncmiRHG-MIR100HG: A new budding star in cancer.docx

MIR100HG, also known as lncRNA mir-100-let-7a-2-mir-125b-1 cluster host gene, is a new and critical regulator in cancers in recent years. MIR100HG is dysregulated in various cancers and plays an oncogenic or tumor-suppressive role, which participates in many tumor cell biology processes and cancer-related pathways. The errant expression of MIR100HG has inspired people to investigate the function of MIR100HG and its diagnostic and therapeutic potential in cancers. Many studies have indicated that dysregulated expression of MIR100HG is markedly correlated with poor prognosis and clinicopathological features. In this review, we will highlight the characteristics and introduce the role of MIR100HG in different cancers, and summarize the molecular mechanism, pathways, chemoresistance, and current research progress of MIR100HG in cancers. Furthermore, some open questions in this rapidly advancing field are proposed. These updates clarify our understanding of MIR100HG in cancers, which may pave the way for the application of MIR100HG-targeting approaches in future cancer diagnosis, prognosis, and therapy.</p

Forest plot showing the meta-analysis of hazard ratio estimates for OS in Asian and Western subgroup.

<p>Forest plot showing the meta-analysis of hazard ratio estimates for OS in Asian and Western subgroup.</p

Forest plot showing the meta-analysis of hazard ratio estimates for OS in overall patients.

<p>Forest plot showing the meta-analysis of hazard ratio estimates for OS in overall patients.</p

c-Met as a Prognostic Marker in Gastric Cancer: A Systematic Review and Meta-Analysis

<div><p>Background</p><p>c-Met has been recognized as an important therapeutic target in gastric cancer, but the prognostic property of the c-Met status is still unclear. We aimed to characterize the prognostic effect of c-Met by systematic review and meta-analysis.</p> <p>Methods</p><p>We identified 15 studies assessing survival in gastric cancer by c-Met status. Effect measure of interest was hazard ratio (HR) for survival. Meta-regression was performed to estimate the relationship between HR and disease stage. Random-effects meta-analyses were used to account for heterogeneity.</p> <p>Results</p><p>15 eligible studies provided outcome data stratified by c-Met status in 2210 patients. Meta-analysis of the HRs indicated a significantly poorer Os in patients with high c-Met expression (average HR=2.112, 95%CI: 1.622–2.748). Subgroup analysis showed the prognostic effect of c-Met was identical in protein-level and gene-level based methodology. The same effect was also seen in Asian and Western ethnicity subgroup analysis. Meta-regression showed HR was not associated with disease stage.</p> <p>Conclusions</p><p>Patients with tumors that harbor high c-Met expression are more likely to have a worse Os, with this prognostic effect independent of disease stage. c-Met status should be evaluated in clinical prognosis.</p> </div

Forest plot showing the meta-analysis of hazard ratio estimates for OS in gene-level subgroup and protein-level subgroup.

<p>Forest plot showing the meta-analysis of hazard ratio estimates for OS in gene-level subgroup and protein-level subgroup.</p