Algebraic Algorithms for Computing the Complex Zeros of Gaussian Polynomials

Let G be a univariate Gaussian rational polynomial (a polynomial with Gaussian rational coefficients) having m distinct zeros. Algebraic algorithms are designed and implemented which, given G and a positive rational error bound E, use Sturm's Theorem, the Routh-Hurwitz Theorems, and infinite precision integer arithmetic or modular arithmetic to compute m disjoint squares in the complex plane, each containing one zero of G and having width less than E. Also included are algorithms for the following operations: associating with each square the multiplicity of the unique zero of G contained in the square; determining the number of zeros of G in regions of the complex plane such as circles and rectangles; refining selected individual zeros of G, that is, given G, a square S containing a single zero of G, and a positive rational error bound E, computing a subsquare of S which contains the zero and has width less than E. The theoretical computing times of the algorithms are analyzed and presented along with empirical computing times

Cardiac hypertrophy and sudden death in mice with a genetically clamped renin transgene

Several mouse models have already proved valuable for investigating hypertrophic responses to cardiac stress. Here, we characterize one caused by a well defined single copy transgene, RenTgMK, that genetically clamps plasma renin and thence angiotensin II at high levels. All of the transgenic males develop concentric cardiac hypertrophy with fibrosis but without dilatation. Over half die suddenly aged 6-8 months. Telemetry showed disturbances in diurnal rhythms a few days before death and, later, electrocardiographic disturbances comparable to those in humans with congestive heart failure. Expression of seven hypertrophy-related genes in this and two categorically different models (lack of atrial natriuretic peptide receptor A; overexpression of calsequestrin) were compared. Statistical analyses show that ventricular expressions of the genes coding for atrial natriuretic peptide, β myosin heavy chain, medium chain acyl-CoA dehydrogenase, and adrenomedullin correlate equally well with the degree of hypertrophy, although their ranges of expression are, respectively, 50-, 30-, 10-, and 3-fold