An intertwine of a pair of matroids is a matroid such that it, but none of its proper minors, has minors that are isomorphic to each matroid in the pair. For pairs for which neither matroid can be obtained, up to isomorphism, from the other by taking free extensions, free coextensions, and minors, we construct a family of rank-k intertwines for each sufficiently large integer k. We also treat s...

Since 1991, commitment to involuntary psychiatric care has been allowed in Finland for minors in broader terms than for adults. While in adults mental illness has to be diagnosable before involuntary treatment can be imposed, minors can be committed to and detained in involuntary psychiatric treatment if they suffer from "severe mental disorders", and fulfil the further commitment criteria defi...

Let Qk,n = {α = (α1, · · · , αk) : 1 ≤ α1 < · · · < αk ≤ n} denote the strictly increasing sequences of k elements from 1, . . . , n. For α, β ∈ Qk,n we denote by A[α, β] the submatrix of A with rows indexed by α, columns by β. The submatrix obtained by deleting the α-rows and β-columns is denoted by A[α′, β′]. For nonsingular A ∈ IRn×n, the Jacobi identity relates the minors of the inverse A−1...

For many patients, living donor liver transplantation represents their only hope of receiving a lifesaving graft. In certain (albeit rare) cases, a minor will be the only suitable donor. Living liver donation by minors has been reported in several countries. In the academic literature and professional guidelines, little attention is paid to the development of an ethical framework for this pract...

A matrix A ∈Mn (R) has a nest of positive principal minors if PAP has positive leading principal minors for some permutation matrix P . Motivated by the fact that such a matrix A can be positively scaled so all its eigenvalues lie in the open right-half-plane, conditions are investigated so that a square sign pattern either requires or allows a nest of positive principal minors.