The entropies of renewal systems

Renewal systems are symbolic dynamical systems originally introduced by Adler. IfW is a finite set of words over a finite alphabetA, then the renewal system generated byW is the subshiftX _W ⊂A ^Z formed by bi-infinite concatenations of words fromW. Motivated by Adler’s question of whether every irreducible shift of finite type is conjugate to a renewal system, we prove that for every shift of finite type there is a renewal system having the same entropy. We also show that every shift of finite type can be approximated from above by renewal systems, and that by placing finite-type constraints on possible concatenations, we obtain all sofic systems. The authors were supported in part by NFS grants DMS-8706284, DMS-8814159 and DMS-8820716.     

Fractal landscapes in biological systems: long-range correlations in DNA and interbeat heart intervals

Here we discuss recent advances in applying ideas of fractals and disordered systems to two topics of biological interest, both topics having common the appearance of scale-free phenomena, i.e., correlations that have no characteristic length scale, typically exhibited by physical systems near a critical point and dynamical systems far from equilibrium. (i) DNA nucleotide sequences have traditionally been analyzed using models which incorporate the possibility of short-range nucleotide correlations. We found, instead, a remarkably long-range power law correlation. We found such long-range correlations in intron-containing genes and in non-transcribed regulatory DNA sequences as well as intragenomic DNA, but not in cDNA sequences or intron-less genes. We also found that the myosin heavy chain family gene evolution increases the fractal complexity of the DNA landscapes, consistent with the intron-late hypothesis of gene evolution. (ii) The healthy heartbeat is traditionally thought to be regulated according to the classical principle of homeostasis, whereby physiologic systems operate to reduce variability and achieve an equilibrium-like state. We found, however, that under normal conditions, beat-to-beat fluctuations in heart rate display long-range power law correlations.     

From 1/f noise to multifractal cascades in heartbeat dynamics

We explore the degree to which concepts developed in statistical physics can be usefully applied to physiological signals. We illustrate the problems related to physiologic signal analysis with representative examples of human heartbeat dynamics under healthy and pathologic conditions. We first review recent progress based on two analysis methods, power spectrum and detrended fluctuation analysis, used to quantify long-range power-law correlations in noisy heartbeat fluctuations. The finding of power-law correlations indicates presence of scale-invariant, fractal structures in the human heartbeat. These fractal structures are represented by self-affine cascades of beat-to-beat fluctuations revealed by wavelet decomposition at different time scales. We then describe very recent work that quantifies multifractal features in these cascades, and the discovery that the multifractal structure of healthy dynamics is lost with congestive heart failure. The analytic tools we discuss may be used on a wide range of physiologic signals. (c) 2001 American Institute of Physics.     

Simulation of forming processes by FEM with a Bingham fluid model

We model the forming process as a fluid flow. A finite element program, FIDAP, which analyses flow problems, was used to calculate velocity and strain rates at points throughout the material during the deformation process. This allows predictions to be made on the shape and quality of the resulting part. The stress-strain relation we used models the plastic flow of metals (Bingham fluids). The FEM approximation of such a fluid is tested by comparing results for a simple analytical example. In forming processes provision must be made for friction between dye and workpiece, and the program was modified accordingly. Two classical ring forming simulations are compared to published results.     

Cardiac magnetic resonance imaging: infarct size is an independent predictor of mortality in patients with coronary artery disease

Background

Cardiac magnetic resonance imaging (CMR) can accurately determine infarct size. Prior studies using indirect methods to assess infarct size have shown that patients with larger myocardial infarctions have a worse prognosis than those with smaller myocardial infarctions.

Objectives

This study assessed the prognostic significance of infarct size determined by CMR.

Methods

Cine and contrast CMR were performed in 100 patients with coronary artery disease (CAD) undergoing routine cardiac evaluation. Infarct size was determined by planimetry. We used Cox proportional hazards regression analyses (stepwise forward selection approach) to evaluate the risk of all-cause death associated with traditional cardiovascular risk factors, symptoms of heart failure, medication use, left ventricular ejection fraction, left ventricular mass, angiographic severity of CAD and extent of infarct size determined by CMR.

Results

Ninety-one patients had evidence of myocardial infarction by CMR. Mean follow-up was 4.8±1.6 years after CMR, during which time 30 patients died. The significant multivariable predictors of all-cause mortality were extent of myocardial infarction by CMR, extent of left ventricular systolic dysfunction, symptoms of heart failure, and diabetes mellitus (P<.05). The presence of infarct greater than or equal to 24% of left ventricular mass and left ventricular ejection fraction less than or equal to 30% were the most optimal cut-off points for the prediction of death with bivariate adjusted hazard ratios of 2.11 (95% confidence interval 1.02-4.38) and 4.06 (95% confidence interval 1.73-9.54), respectively.

Conclusions

The extent of myocardial infarction determined by CMR is an independent predictor of death in patients with CAD.     

Long-range power-law correlations in condensed matter physics and biophysics

We discuss the appearance of long-range power-law correlations in various systems of interest to condensed matter physicists and biophysicists, with emphasis on the recent discovery of long-range correlations in DNA sequences that contain non-coding regions.     

Nonlinear dynamics of the heartbeat: I. The AV junction: Passive conduit or active oscillator?

Under physiologic conditions, the AV junction is traditionally regarded as a passive conduit for the conduction of impulses from the atria to the ventricles. An alternative view, namely that subsidiary pacemakers play an active role in normal electrophysiologic dynamics during sinus rhythm, has been suggested based on nonlinear models of cardiac oscillators. A central problem has been the development of a simple but explicit mathematical model for coupled nonlinear oscillators relevant both to stable and perturbed cardiac dynamics. We use equations describing an analog electrical circuit with an external d.c. voltage source (V₀) and two nonlinear oscillators with intrinsic frequencies in the ratio of 3:2, comparable to the SA node and AV junction rates. The oscillators are coupled by means of a resistor. 1:1 (SA:AV) phase-locking of the oscillators occurs over a critical range of V₀. Externally driving the SA oscillator at increasing rates results in 3:2 AV Wenckebach periodicity and a 2:1 AV block. These findings appear with no assumptions about conduction time or refractoriness. This dynamical model is consistent with the new interpretation that normal sinus rhythm may represent 1:1 coupling of two or more active nonlinear oscillators and also accounts for the appearance of an AV block with critical changes in a single parameter such as the pacing rate.