Overlapping of two truncated crisis scenarios: generator of peaks in mean lifetimes of chaotic transients.

Maxima of mean transient time versus driving amplitude were found for weakly dissipated Duffing oscillator. In the neighborhood of peak of mean transient time an approximate power-law dependence was found. This behavior was compared with scaling in the vicinity of crisis point and interpreted as crossing of two neighboring crisis points which appears with decrease of driving amplitude. At this point chaotic attractor was destroyed and chaotic transient, exhibiting a maximum in the lifetime was borned. It was shown that the peak of mean lifetime has a regular behavior described by quadratic function.

Key-string segmentation algorithm and higher-order repeat 16mer (54 copies) in human alpha satellite DNA in chromosome 7.

A new key-string segmentation algorithm for identification of alpha satellite DNAs and higher-order repeat (HOR) units was introduced and exemplified. Starting with an initial key string, we determine the dominant key string and HOR. Our key-string algorithm was used to scan the recent GenBank data for human alpha satellite DNA sequence AC017075.8 (193 277 bp) from the centromeric region of chromosome 7. The sequence was computationally segmented into one HOR domain (super-repeat domain) and two non-HOR domains. Dominant key-string GTTTCT provided segmentation in terms of alpha monomers. The HOR is tandemly repeated in 54 copies in the super-repeat (HOR) domain. Five insertions and three deletions in the HOR structure associated with a dominant key string were identified. Concensus HOR was constructed. Divergence of individual HOR copies from concensus amounts to 0.7% on the average, while divergence between 16 monomer variants within each HOR is on the average 20%. In the front and back domain, 199 monomer variants were identified that are not organized in HOR and diverge by 20-40%.

Link between truncated fractals and coupled oscillators in biological systems.

This article aims at providing a new theoretical insight into the fundamental question of the origin of truncated fractals in biological systems. It is well known that fractal geometry is one of the characteristics of living organisms. However, contrary to mathematical fractals which are self-similar at all scales, the biological fractals are truncated, i.e. their self-similarity extends at most over a few orders of magnitude of separation. We show that nonlinear coupled oscillators, modeling one of the basic features of biological systems, may generate truncated fractals: a truncated fractal pattern for basin boundaries appears in a simple mathematical model of two coupled nonlinear oscillators with weak dissipation. This fractal pattern can be considered as a particular hidden fractal property. At the level of sufficiently fine precision technique the truncated fractality acts as a simple structure, leading to predictability, but at a lower level of precision it is effectively fractal, limiting the predictability of the long-term behavior of biological systems. We point out to the generic nature of our result.

Many-hole interactions and the average lifetimes of chaotic transients that precede controlled periodic motion.

We consider n small regions (referred to as the holes) on a chaotic attractor and study the average lifetime it takes for a randomly initiated trajectory to land in their union. The holes are thought of as n possible escape routes for the trajectory. The escape route through one of the holes may be considerably reduced by other holes, depending on their positions. This effect, referred to as shadowing, can significantly prolong the average lifetime. The main result of this paper is the construction and analysis (numerical and theoretical) of the many-hole interactions. They are interpreted as the amount of shadowing between the holes. The "effective range" of these interactions is associated with the largest Lyapunov exponent. The shadowing effect is shown to be very large when the holes are located on n points of an unstable periodic orbit. Considerable attention is paid to this case since it is of interest to the field of controlling chaos.

Bursts in the chaotic trajectory lifetimes preceding controlled periodic motion

The average lifetime [tau(H)] it takes for a randomly started trajectory to land in a small region (H) on a chaotic attractor is studied. tau(H) is an important issue for controlling chaos. We point out that if the region H is visited by a short periodic orbit, the lifetime tau(H) strongly deviates from the inverse of the naturally invariant measure contained within that region [&mgr;(N)(H)(-1)]. We introduce the formula that relates tau(H)/&mgr;(N)(H)(-1) to the expanding eigenvalue of the short periodic orbit visiting H.

Quantitative tissue carcinoembryonic antigen (T CEA) assay as a screening test for severe dysplasia in colorectal adenomas.

Relationship between the serum (S CEA) and the tissue (T CEA) carcinoembryonic antigen concentrations with regard to the degree of dysplasia in colorectal adenomas was investigated. Our study included 56 single or multiple colorectal adenomas in 46 patients. The measurements of T CEA concentrations were performed using the quantitative CEA-EIA method (Abbott) modified for wet tissue, obtained from heads of the adenomas. As a control point the mucosa near adenoma and the rectal mucosa were used. Our results suggest that the T CEA concentrations from the head of the adenoma demonstrate a highly significant difference between mild and severe dysplasia (P < 0.001), between mild dysplasia and invasive adenocarcinoma (P < 0.001) and a significant difference between mild and moderate dysplasia (P < 0.05). On the other hand, the S CEA concentrations corresponding to these cases showed no such differences. In conclusion, we suggest the quantitative measurement of T CEA concentrations as a screening test for severe dysplasia in colorectal adenomas.

Prognostic and therapeutic score for colorectal adenomas and the role of serum and tissue carcinoembryonic antigen.

OBJECTIVE: To study the tissue carcinoembryonic antigen (TCEA) concentrations with regard to multiplicity, diameter, pathohistological finding, degree of dysplasia and serum CEA (SCEA) concentrations. METHODS: Our study included 46 patients with single or multiple adenomas. For 56 adenomas TCEA concentrations were measured in addition to standard determinations of multiplicity, diameter, pathohistology, degree of dysplasia and SCEA. The measurements of TCEA concentrations were performed using the CEA-EIA method (Abbott) modified for wet tissue obtained from the head of the adenoma (TCEA-A), margin of resection at the neck or base of the adenoma (TCEA-B), mucosa near the adenoma (TCEA-C) and rectal mucosa (TCEA-D). The Mann-Whitney test and M estimates were used to differentiate CEA distribution between various classes of adenomas within each characterization. RESULTS: TCEA concentrations from the head of the adenoma (TCEA-A) demonstrated highly significant difference between mild and severe dysplasia (P = 0.0003), between mild dysplasia and invasive adenocarcinoma (P = 0.001) and significant difference between mild and moderate dysplasia (P = 0.04). There was a statistically significant difference in TCEA-A also between tubular and villous adenomas (P = 0.04). On the other hand, no significant correlations with regard to multiplicity, diameter and pathohistological features were found. CONCLUSION: These results suggest that there is a highly significant difference between the tissue CEA concentration from the head of the adenoma (TCEA-A) in the presence or absence of severe dysplasia. Furthermore, combining a number of pathological variables together with TCEA and routine SCEA, a new score was proposed to be used as a guide to the frequency of follow-up colonoscopy following polypectomy.