Relations among Principal Minorsof a Matrix – p. 1/1 Definitions Let A = (a ij) ∈ C n 2 be a complex n × n matrix. A σ ∈ C: principal minor of A indexed by σ, with A ∅ = 1. A * ∈ C 2 n : vector whose entries are the principal minors of A. Definitions Let A = (a ij) ∈ C n 2 be a complex n × n matrix. A σ ∈ C: principal minor of A indexed by σ, with A ∅ = 1. A * ∈ C 2 n : vector whose entries are...

In 2010, Senate Bill 1309 included language to repeal an existing Arizona law that enables minors younger than 18 years of age to seek diagnosis and treatment of sexually transmitted diseases (STDs) without parental consent. Numerous implications were identified that would have stemmed from parental consent provisions originally proffered in Senate Bill 1309. These implications included diminis...

We present a new O(n3) algorithm for computing all eigenvalues of certain sign regular matrices to high relative accuracy in floating point arithmetic. The accuracy and cost are unaffected by the conventional eigenvalue condition numbers. A matrix is called sign regular when the signs of its nonzero minors depend only of the order of the minors. The sign regular matrices we consider are the one...

PROBLEM Alcohol-related youth traffic fatalities continue as a major public-health concern. While state and federal laws can be useful in tackling this problem, the efficacy of many laws has not been empirically demonstrated. We examined the impact of state laws prohibiting alcohol advertising to target minors. METHOD Using statistics obtained from the Fatality Analysis Reporting System (FARS...

Social host laws for minors aim to reduce teenage alcohol consumption by imposing liability on adults who host parties. Parents cite safety reasons as part of their motivation for hosting parties, preferring their teens and their teens' friends to drink in a supervised and safe locale. Both sides predict an effect of social host liability for minors on alcohol-related traffic accident rates for...

For any affine variety equipped with coordinates, there is a surjective, continuous map from its Berkovich space to its tropicalisation. Exploiting torus actions, we develop techniques for finding an explicit, continuous section of this map. In particular, we prove that such a section exists for linear spaces, Grassmannians of planes (reproving a result due to Cueto, Häbich, and Werner), matrix...

Understanding electronic cigarettes' effect on tobacco smoking is a central economic and policy issue. This paper examines the causal impact of e-cigarette access on conventional cigarette use by adolescents. Regression analyses consider how state bans on e-cigarette sales to minors influence smoking rates among 12 to 17 year olds. Such bans yield a statistically significant 0.9 percentage poin...

Let G be a graph and p ∈ [1,∞]. The parameter fp(G) is the least integer k such that for all m and all vectors (rv)v∈V (G) ⊆ R , there exist vectors (qv)v∈V (G) ⊆ R k satisfying ‖rv − rw‖p = ‖qv − qw‖p, for all vw ∈ E(G). It is easy to check that fp(G) is always finite and that it is minor monotone. By the graph minor theorem of Robertson and Seymour [9], there are a finite number of excluded m...

The algebraic relations between the principal minors of an n× n matrix are somewhat mysterious, see e.g. [LS09]. We show, however, that by adding in certain almost principal minors, the relations are generated by a single relation, the so-called hexahedron relation, which is a composition of six cluster mutations. We give in particular a Laurent-polynomial parameterization of the space of n× n ...

The role of adult men in adolescent childbearing has received heightened attention in recent years, and a new policy efforts have focused on statutory rape laws as a way to reduce adolescent childbearing. Analyses of the 1988 National Maternal and Infant Health Survey indicate, however, that these policies would not apply to most teenage births. Among mothers aged 15-17 who had a child in 1988,...