Tangles, tree-decompositions, and grids in matroids

A tangle in a matroid is an obstruction to small branch-width. In particular, the maximum order of a tangle is equal to the branch-width. We prove that: (i) there is a tree-decomposition of a matroid that “displays” all of the maximal tangles, and (ii) when M is representable over a finite field, each tangle of sufficiently large order “dominates” a large grid-minor. This extends results of Robertson and Seymour concerning Graph Minors

The structure of graphs with a vital linkage of order 2

A linkage of order k of a graph G is a subgraph with k components, each of which is a path. A linkage is vital if it spans all vertices, and no other linkage connects the same pairs of end vertices. We give a characterization of the graphs with a vital linkage of order 2: they are certain minors of a family of highly structured graphs

Quasi-graphic matroids

Frame matroids and lifted-graphic matroids are two interesting generalizations of graphic matroids. Here we introduce a new generalization, quasi-graphic matroids, that unifies these two existing classes. Unlike frame matroids and lifted-graphic matroids, it is easy to certify that a matroid is quasi-graphic. The main result of the paper is that every 3-connected representable quasi-graphic matroid is either a lifted-graphic matroid or a rame matroid

Branch-width and well-quasi-ordering in matroids and graphs

AbstractWe prove that a class of matroids representable over a fixed finite field and with bounded branch-width is well-quasi-ordered under taking minors. With some extra work, the result implies Robertson and Seymour's result that graphs with bounded tree-width (or equivalently, bounded branch-width) are well-quasi-ordered under taking minors. We will not only derive their result from our result on matroids, but we will also use the main tools for a direct proof that graphs with bounded branch-width are well-quasi-ordered under taking minors. This proof also provides a model for the proof of the result on matroids, with all specific matroid technicalities stripped off

On inequivalent representations of matroids over non-prime fields

For each finite field $F$ of prime order there is a constant $c$ such that every 4-connected matroid has at most $c$ inequivalent representations over $F$. We had hoped that this would extend to all finite fields, however, it was not to be. The $(m,n)$-mace is the matroid obtained by adding a point freely to $M(K_{m,n})$. For all $n \geq 3$, the $(3,n)$-mace is 4-connected and has at least $2n$ representations over any field $F$ of non-prime order $q \geq 9$. More generally, for $n \geq m$, the $(m,n)$-mace is vertically $(m+1)$-connected and has at least $2n$ inequivalent representations over any finite field of non-prime order $q\geq m^m$

Rasgrp1 mutation increases naïve T-cell CD44 expression and drives mTOR-dependent accumulation of Helios+ T cells and autoantibodies

Missense variants are a major source of human genetic variation. Here we analyze a new mouse missense variant, Rasgrp1Anaef, with an ENU-mutated EF hand in the Rasgrp1 Ras guanine nucleotide exchange factor. Rasgrp1Anaef mice exhibit anti-nuclear autoantibodies and gradually accumulate a CD44hi Helios+ PD-1+ CD4+ T cell population that is dependent on B cells. Despite reduced Rasgrp1-Ras-ERK activation in vitro, thymocyte selection in Rasgrp1Anaef is mostly normal in vivo, although CD44 is overexpressed on naïve thymocytes and T cells in a T-cell-autonomous manner. We identify CD44 expression as a sensitive reporter of tonic mTOR-S6 kinase signaling through a novel mouse strain, chino, with a reduction-of-function mutation in Mtor. Elevated tonic mTOR-S6 signaling occurs in Rasgrp1Anaef naïve CD4+ T cells. CD44 expression, CD4+ T cell subset ratios and serum autoantibodies all returned to normal in Rasgrp1AnaefMtorchino double-mutant mice, demonstrating that increased mTOR activity is essential for the Rasgrp1Anaef T cell dysregulation

Rasgrp1 mutation increases naïve T-cell CD44 expression and drives mTOR-dependent accumulation of Helios⁺ T cells and autoantibodies

Missense variants are a major source of human genetic variation. Here we analyze a new mouse missense variant, Rasgrp1ᴬⁿᵃᵉᶠ, with an ENU-mutated EF hand in the Rasgrp1 Ras guanine nucleotide exchange factor. Rasgrp1ᴬⁿᵃᵉᶠ mice exhibit anti-nuclear autoantibodies and gradually accumulate a CD44hi Helios⁺ PD-1⁺ CD4⁺ T cell population that is dependent on B cells. Despite reduced Rasgrp1-Ras-ERK activation in vitro, thymocyte selection in Rasgrp1ᴬⁿᵃᵉᶠ is mostly normal in vivo, although CD44 is overexpressed on naïve thymocytes and T cells in a T-cell-autonomous manner. We identify CD44 expression as a sensitive reporter of tonic mTOR-S6 kinase signaling through a novel mouse strain, chino, with a reduction-of-function mutation in Mtor. Elevated tonic mTOR-S6 signaling occurs in Rasgrp1ᴬⁿᵃᵉᶠ naïve CD4⁺ T cells. CD44 expression, CD4⁺ T cell subset ratios and serum autoantibodies all returned to normal in Rasgrp1ᴬⁿᵃᵉᶠMtorᶜʰⁱⁿᵒ double-mutant mice, demonstrating that increased mTOR activity is essential for the Rasgrp1ᴬⁿᵃᵉᶠ T cell dysregulation

Rasgrp1 mutation increases naïve T-cell CD44 expression and drives mTOR-dependent accumulation of Helios+ T cells and autoantibodies

Missense variants are a major source of human genetic variation. Here we analyze a new mouse missense variant, Rasgrp1(Anaef), with an ENU-mutated EF hand in the Rasgrp1 Ras guanine nucleotide exchange factor. Rasgrp1(Anaef) mice exhibit anti-nuclear autoantibodies and gradually accumulate a CD44(hi) Helios(+) PD-1(+) CD4(+) T cell population that is dependent on B cells. Despite reduced Rasgrp1-Ras-ERK activation in vitro, thymocyte selection in Rasgrp1(Anaef) is mostly normal in vivo, although CD44 is overexpressed on naïve thymocytes and T cells in a T-cell-autonomous manner. We identify CD44 expression as a sensitive reporter of tonic mTOR-S6 kinase signaling through a novel mouse strain, chino, with a reduction-of-function mutation in Mtor. Elevated tonic mTOR-S6 signaling occurs in Rasgrp1(Anaef) naïve CD4(+) T cells. CD44 expression, CD4(+) T cell subset ratios and serum autoantibodies all returned to normal in Rasgrp1(Anaef)Mtor(chino) double-mutant mice, demonstrating that increased mTOR activity is essential for the Rasgrp1(Anaef) T cell dysregulation. DOI: http://dx.doi.org/10.7554/eLife.01020.00

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data

Quasi-Graphic Matroids (retracted)

Frame matroids and lifted-graphic matroids are two interesting generalizations of graphic matroids. Here, we introduce a new generalization, quasi-graphic matroids, that unifies these two existing classes. Unlike frame matroids and lifted-graphic matroids, it is easy to certify that a matroid is quasi-graphic. The main result of the article is that every 3-connected representable quasi-graphic matroid is either a lifted-graphic matroid or a frame matroid