Data depth and floating body

Little known relations of the renown concept of the halfspace depth for multivariate data with notions from convex and affine geometry are discussed. Halfspace depth may be regarded as a measure of symmetry for random vectors. As such, the depth stands as a generalization of a measure of symmetry for convex sets, well studied in geometry. Under a mild assumption, the upper level sets of the halfspace depth coincide with the convex floating bodies used in the definition of the affine surface area for convex bodies in Euclidean spaces. These connections enable us to partially resolve some persistent open problems regarding theoretical properties of the depth

A-Lister: a tool for analysis of differentially expressed omics entities across multiple pairwise comparisons.

BackgroundResearchers commonly analyze lists of differentially expressed entities (DEEs), such as differentially expressed genes (DEGs), differentially expressed proteins (DEPs), and differentially methylated positions/regions (DMPs/DMRs), across multiple pairwise comparisons. Large biological studies can involve multiple conditions, tissues, and timepoints that result in dozens of pairwise comparisons. Manually filtering and comparing lists of DEEs across multiple pairwise comparisons, typically done by writing custom code, is a cumbersome task that can be streamlined and standardized.ResultsA-Lister is a lightweight command line and graphical user interface tool written in Python. It can be executed in a differential expression mode or generic name list mode. In differential expression mode, A-Lister accepts as input delimited text files that are output by differential expression tools such as DESeq2, edgeR, Cuffdiff, and limma. To allow for the most flexibility in input ID types, to avoid database installation requirements, and to allow for secure offline use, A-Lister does not validate or impose restrictions on entity ID names. Users can specify thresholds to filter the input file(s) by column(s) such as p-value, q-value, and fold change. Additionally, users can filter the pairwise comparisons within the input files by fold change direction (sign). Queries composed of intersection, fuzzy intersection, difference, and union set operations can also be performed on any number of pairwise comparisons. Thus, the user can filter and compare any number of pairwise comparisons within a single A-Lister differential expression command. In generic name list mode, A-Lister accepts delimited text files containing lists of names as input. Queries composed of intersection, fuzzy intersection, difference, and union set operations can then be performed across these lists of names.ConclusionsA-Lister is a flexible tool that enables the user to rapidly narrow down large lists of DEEs to a small number of most significant entities. These entities can then be further analyzed using visualization, pathway analysis, and other bioinformatics tools

On a nonlocal degenerate parabolic problem

Conditions for the existence and uniqueness of weak solutions for a class of nonlinear nonlocal degenerate parabolic equations are established. The asymptotic behaviour of the solutions as time tends to infinity are also studied. In particular, the finite time extinction and polynomial decay properties are proved

A Careers Perspective on Entrepreneurship

[Excerpt] What if being an entrepreneur were treated like any other occupation—teacher, nurse, manager? What if the decision to found a new venture were thought of as one of many options that individuals consider as they try to structure a meaningful and rewarding career? How would the field of entrepreneurship research be different? In our view, there is much to be learned by conceiving of entrepreneurship not solely as a final destination, but as a step along a career trajectory. Doing so opens the study of entrepreneurship to a wider range of scholarly insights, and promises important insights for entrepreneurial practice, training, and policy. This special issue takes an important step in this direction

Enlargement of a low-dimensional stochastic web

We consider an archetypal example of a low-dimensional stochastic web, arising in a 1D oscillator driven by a plane wave of a frequency equal or close to a multiple of the oscillator’s natural frequency. We show that the web can be greatly enlarged by the introduction of a slow, very weak, modulation of the wave angle. Generalizations are discussed. An application to electron transport in a nanometre-scale semiconductor superlattice in electric and magnetic fields is suggested