The Sign Test, Paired Data, and Asymmetric Dependence: A Cautionary Tale

In the paired data setting, the sign test is often described in statistical textbooks as a test for comparing differences between the medians of two marginal distributions. There is an implicit assumption that the median of the differences is equivalent to the difference of the medians when employing the sign test in this fashion. We demonstrate however that given asymmetry in the bivariate distribution of the paired data, there are often scenarios where the median of the differences is not equal to the difference of the medians. Further, we show that these scenarios will lead to a false interpretation of the sign test for its intended use in the paired data setting. We illustrate the false-interpretation concept via theory, a simulation study, and through a real-world example based on breast cancer RNA sequencing data obtained from the Cancer Genome Atlas (TCGA).</p

A note on dyadic approximation in Cantor’s set

We consider the convergence theory for dyadic approximation in the middlethird Cantor set, K, for approximation functions of the form ψτ (n) = n−τ (τ ⩾ 0). In particular, we show that for values of τ beyond a certain threshold we have that almost no point in K is dyadically ψτ-well approximable with respect to the natural probability measure on K. This refines a previous result in this direction obtained by the first, third, and fourth named authors.</p

Additional file 2 of Ectopic intrapulmonary thyroid masquerading as metastatic carcinoma of the lung: a rare case scenario

Supplementary Material

Additional file 1 of Ectopic intrapulmonary thyroid masquerading as metastatic carcinoma of the lung: a rare case scenario

Supplementary Material

Capsule-like Safe Genetic VectorsCell-Penetrating Core–Shell Particles Selectively Release Functional Small RNA and Entrap Its Encoding DNA

The breakthrough of genetic therapy is set back by the lack of suitable genetic vector systems. We present the development of permeability-tunable, capsule-like, polymeric, micron-sized, core–shell particles for delivery of recombinant nucleic acids into target cells. These particles were demonstrated to effectively release rod-shaped small hairpin RNA and to selectively retain the RNA-encoding DNA template, which was designed to form a bulky tripartite structure. Thus, they can serve as delivery vectors preloaded with cargo RNA or alternatively as RNA-producing micro-bioreactors. The internalization of particles by human tissue culture cells inversely correlated with particle size and with the cell to particle ratio, although at a higher than stoichiometric excess of particles over cells, cell viability was impaired. Among primary human peripheral blood mononuclear cells, up to 50% of the monocytes displayed positive uptake of particles. Finally, these particles efficiently delivered siRNA into HEK293T cells triggering functional knockdown of the target gene lamin A/C. Particle-mediated knockdown was superior to that observed after conventional siRNA delivery via lipofection. Core–shell particles protect encapsulated nucleic acids from degradation and target cell genomes from direct contact with recombinant DNA, thus representing a promising delivery vector system that can be explored for genetic therapy and vaccination

The effects of various NaCl concentrations on the osmolyte contents of <i>Salvia miltiorrhiza</i> leaves.

<p>The osmolyte contents measured in the experiment include the soluble protein and soluble sugar contents. <i>Salvia miltiorrhiza</i> seedlings were cultivated in 1/2 Hoagland nutrient solution for 3 weeks and were later exposed to salt stress by adding NaCl up to 25, 50, 75 and 100 mM of the hydroponic solution for 30 days. Non-treated plants were used as controls (0 mM NaCl). Error bars represent the standard errors (SE) of the means.</p

The effects of various NaCl concentrations on the photosynthetic pigments of <i>Salvia miltiorrhiza</i> leaves.

<p>The photosynthetic pigments measured in the experiment include chlorophyll a (Chl-a), chlorophyll b (Chl-b) and total chlorophyll contents (T-Chl). <i>Salvia miltiorrhiza</i> seedlings were cultivated in 1/2 Hoagland nutrient solution for 3 weeks and were later exposed to salt stress by adding NaCl up to concentration of 25, 50, 75 and 100 mM of the hydroponic solution for 30 days. Non-treated plants were used as controls (0 mM NaCl). Error bars represent the standard errors (SE) of the means.</p

The effects of various NaCl concentrations on the plant height, root length, fresh weight and dry weight of <i>Salvia miltiorrhiza</i> seedlings.

<p>The seedlings were cultivated in 1/2 Hoagland nutrient solution for 3 weeks and were later exposed to salt stress by adding NaCl to concentrations of 25, 50, 75 and 100 mM of the hydroponic solution for 30 days. Non-treated plants were used as controls (0 mM NaCl). Each value represents the mean of three replicates. Treatments with the same letters are not statistically different (P≥0.05).</p

DataSheet_1_Evaluating the role of IDO1 macrophages in immunotherapy using scRNA-seq and bulk-seq in colorectal cancer.docx

BackgroundMacrophage infiltration is crucial for colorectal cancer (CRC) immunotherapy. Detailed classification of macrophage subsets will facilitate the selection of patients suitable for immunotherapy. However, the classification of macrophages in CRC is not currently detailed.MethodsIn this study, we combined single-cell RNA sequencing (scRNA-seq) and bulk-seq to analyze patients with colorectal cancer. scRNA-seq data were used to study cell-cell communication and to differentiate immune-infiltrating cells and macrophage subsets. Bulk-seq data were used to further analyze immune infiltration, clinical features, tumor mutational burden, and expression of immune checkpoint molecules in patients with CRC having different macrophage subsets.ResultsSeven macrophage subpopulations were identified, among which indoleamine 2,3 dioxygenase 1 (IDO1) macrophages had the most significant difference in the degree of infiltration among normal, microsatellite-unstable, and microsatellite-stable populations. We then performed gene set variation analysis using 12 marker genes of IDO1 macrophages and divided the patients into two clusters: high-IDO1 macrophages (H-IDO1M) and low-IDO1 macrophages (L-IDO1M). H-IDO1M showed higher infiltration of immune cells, higher expression of immune checkpoints, and less advanced pathological stages than L-IDO1M (p ConclusionsThis study elucidated that IDO1-macrophage-based molecular subtypes can predict the response to immunotherapy in patients with CRC. The results provide new insights into tumor immunity and help in clinical decisions regarding designing effective immunotherapy for these patients.</p

Table_1_Evaluating the role of IDO1 macrophages in immunotherapy using scRNA-seq and bulk-seq in colorectal cancer.xlsx

BackgroundMacrophage infiltration is crucial for colorectal cancer (CRC) immunotherapy. Detailed classification of macrophage subsets will facilitate the selection of patients suitable for immunotherapy. However, the classification of macrophages in CRC is not currently detailed.MethodsIn this study, we combined single-cell RNA sequencing (scRNA-seq) and bulk-seq to analyze patients with colorectal cancer. scRNA-seq data were used to study cell-cell communication and to differentiate immune-infiltrating cells and macrophage subsets. Bulk-seq data were used to further analyze immune infiltration, clinical features, tumor mutational burden, and expression of immune checkpoint molecules in patients with CRC having different macrophage subsets.ResultsSeven macrophage subpopulations were identified, among which indoleamine 2,3 dioxygenase 1 (IDO1) macrophages had the most significant difference in the degree of infiltration among normal, microsatellite-unstable, and microsatellite-stable populations. We then performed gene set variation analysis using 12 marker genes of IDO1 macrophages and divided the patients into two clusters: high-IDO1 macrophages (H-IDO1M) and low-IDO1 macrophages (L-IDO1M). H-IDO1M showed higher infiltration of immune cells, higher expression of immune checkpoints, and less advanced pathological stages than L-IDO1M (p ConclusionsThis study elucidated that IDO1-macrophage-based molecular subtypes can predict the response to immunotherapy in patients with CRC. The results provide new insights into tumor immunity and help in clinical decisions regarding designing effective immunotherapy for these patients.</p