Introduction ..................................................................................................................... 628 I. The Privilege of Disaffirmance ................................................................................. 630 A. Historical Restriction.................................................................................... 630 1. Protectionist View .........

Introduction ........................................................................................................ 63 Historical Background.................................................................................... 63 Purpose and Overview of Empirical Study..................................................... 65 I. Roe v. Wade and the “Reasonable” Physician.............................

Undirected graphs of pathwidth at most one are characterized by two forbidden minors i.e., (i) K3 the complete graph on three vertices and (ii) S2,2,2 the spider graph with three legs of length two each [BFKL87]. Directed pathwidth is a natural generalization of pathwidth to digraphs. In this paper, we prove that digraphs of directed pathwidth at most one are characterized by a finite number of...

The space of m × p totally nonnegative real matrices has a stratification into totally nonnegative cells. The largest such cell is the space of totally positive matrices. There is a well-known criterion due to Gasca and Peña for testing a real matrix for total positivity. This criterion involves testing mp minors. In contrast, there is no known small set of minors for testing for total nonnegat...

In a recent paper [6], Kwon and Oum claim that every graph of bounded rank-width is a pivot-minor of a graph of bounded tree-width (while the converse has been known true already before). We study the analogous questions for “depth” parameters of graphs, namely for the tree-depth and related new shrub-depth. We show that shrub-depth is monotone under taking vertex-minors, and that every graph c...

We describe explicitly the admissible families of minors for the totally nonnegative cells of real matrices, that is, the families of minors that produce nonempty cells in the cell decompositions of spaces of totally nonnegative matrices introduced by A. Postnikov. In order to do this, we relate the totally nonnegative cells to torus orbits of symplectic leaves of the Poisson varieties of compl...

Belgium has recently extended its euthanasia legislation to minors, making it the first legislation in the world that does not specify any age limit. I consider two strands in the opposition to this legislation. First, I identify five arguments in the public debate to the effect that euthanasia for minors is somehow worse than euthanasia for adults--viz, arguments from weightiness, capability o...

Secant varieties to Veronese embeddings of projective space are classical varieties whose equations are not completely understood. Minors of catalecticant matrices furnish some of their equations, and in some situations even generate their ideals. Geramita conjectured that this is the case for the secant line variety of the Veronese variety, namely that its ideal is generated by the 3×3 minors ...

BACKGROUND Various international laws and guidelines stress the importance of respecting the developing autonomy of children and involving minors in decision-making regarding treatment and research participation. However, no universal agreement exists as to at what age minors should be deemed decision-making competent. Minors of the same age may show different levels of maturity. In addition, p...

It is well-known that in finite graphs, large complete minors/topological minors can be forced by assuming a large average degree. Our aim is to extend this fact to infinite graphs. For this, we generalise the notion of the relative end degree, which had been previously introduced by the first author for locally finite graphs, and show that large minimum relative degree at the ends and large mi...