Nucleotide Frequencies in Human Genome and Fibonacci Numbers

This work presents a mathematical model that establishes an interesting connection between nucleotide frequencies in human single-stranded DNA and the famous Fibonacci's numbers. The model relies on two assumptions. First, Chargaff's second parity rule should be valid, and, second, the nucleotide frequencies should approach limit values when the number of bases is sufficiently large. Under these two hypotheses, it is possible to predict the human nucleotide frequencies with accuracy. It is noteworthy, that the predicted values are solutions of an optimization problem, which is commonplace in many nature's phenomena.Comment: 12 pages, 2 figure

Scalar Decay in Chaotic Mixing

I review the local theory of mixing, which focuses on infinitesimal blobs of scalar being advected and stretched by a random velocity field. An advantage of this theory is that it provides elegant analytical results. A disadvantage is that it is highly idealised. Nevertheless, it provides insight into the mechanism of chaotic mixing and the effect of random fluctuations on the rate of decay of the concentration field of a passive scalar.Comment: 35 pages, 15 figures. Springer-Verlag conference style svmult.cls (included). Published in "Transport in Geophysical Flows: Ten Years After," Proceedings of the Grand Combin Summer School, 14-24 June 2004, Valle d'Aosta, Italy. Fixed some typo

Restenosis, reocclusion and adverse cardiovascular events after successful balloon angioplasty of occluded versus nonoccluded coronary arteries: Results from the multicenter american research trial with cilazapril after angioplasty to prevent transluminal coronary obstruction and restenosis (MARCATOR)

OBJECTIVES: This study sought to compare the frequency of restenosis, reocclusion and adverse cardiovascular events after angioplasty of occluded versus nonoccluded coronary arteries. BACKGROUND: Angioplasty of chronically occluded coronary arteries is believed to be associated with a higher frequency of restenosis and reocclusion than angioplasty of subtotal stenoses. Whether this leads to adverse cardiovascular events is unknown. METHODS: The Multicenter American Research Trial With Cilazapril After Angioplasty to Prevent Restenosis (MARCATOR) was a placebo-controlled trial with angiographic follow-up to determine the effect of the angiotensin-converting enzyme inhibitor cilazapril on the frequency of restenosis. In this trial, restenosis was defined as 1) angiographic reduction of minimal lumen diameter > or = 0.72 mm between angioplasty and the follow-up visit; and 2) > 50% diameter stenosis on the follow-up angiogram. We identified

Hard Instances of the Constrained Discrete Logarithm Problem

The discrete logarithm problem (DLP) generalizes to the constrained DLP, where the secret exponent $x$ belongs to a set known to the attacker. The complexity of generic algorithms for solving the constrained DLP depends on the choice of the set. Motivated by cryptographic applications, we study sets with succinct representation for which the constrained DLP is hard. We draw on earlier results due to Erd\"os et al. and Schnorr, develop geometric tools such as generalized Menelaus' theorem for proving lower bounds on the complexity of the constrained DLP, and construct sets with succinct representation with provable non-trivial lower bounds

Alfv\'en Reflection and Reverberation in the Solar Atmosphere

Magneto-atmospheres with Alfv\'en speed [a] that increases monotonically with height are often used to model the solar atmosphere, at least out to several solar radii. A common example involves uniform vertical or inclined magnetic field in an isothermal atmosphere, for which the Alfv\'en speed is exponential. We address the issue of internal reflection in such atmospheres, both for time-harmonic and for transient waves. It is found that a mathematical boundary condition may be devised that corresponds to perfect absorption at infinity, and, using this, that many atmospheres where a(x) is analytic and unbounded present no internal reflection of harmonic Alfv\'en waves. However, except for certain special cases, such solutions are accompanied by a wake, which may be thought of as a kind of reflection. For the initial-value problem where a harmonic source is suddenly switched on (and optionally off), there is also an associated transient that normally decays with time as O(t-1) or O(t-1 ln t), depending on the phase of the driver. Unlike the steady-state harmonic solutions, the transient does reflect weakly. Alfv\'en waves in the solar corona driven by a finite-duration train of p-modes are expected to leave such transients.Comment: Accepted by Solar Physic

Finite element simulation of three-dimensional free-surface flow problems

An adaptive finite element algorithm is described for the stable solution of three-dimensional free-surface-flow problems based primarily on the use of node movement. The algorithm also includes a discrete remeshing procedure which enhances its accuracy and robustness. The spatial discretisation allows an isoparametric piecewise-quadratic approximation of the domain geometry for accurate resolution of the curved free surface. The technique is illustrated through an implementation for surface-tension-dominated viscous flows modelled in terms of the Stokes equations with suitable boundary conditions on the deforming free surface. Two three-dimensional test problems are used to demonstrate the performance of the method: a liquid bridge problem and the formation of a fluid droplet