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Scaling, growth and cyclicity in biology: a new computational approach.

Delsanto PP, Gliozzi AS, Guiot C - Theor Biol Med Model (2008)

Bottom Line: In nonlinear problems it allows the nonscaling invariance to be retrieved by means of suitable redefined fractal-dimensioned variables.As an example of its implementation, the method is applied to the analysis of human growth curves.The excellent quality of the results (R2 = 0.988) demonstrates the usefulness and reliability of the approach.

View Article: PubMed Central - HTML - PubMed

Affiliation: Dept, Physics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy. pier.delsanto@polito.it

ABSTRACT

Background: The Phenomenological Universalities approach has been developed by P.P. Delsanto and collaborators during the past 2-3 years. It represents a new tool for the analysis of experimental datasets and cross-fertilization among different fields, from physics/engineering to medicine and social sciences. In fact, it allows similarities to be detected among datasets in totally different fields and acts upon them as a magnifying glass, enabling all the available information to be extracted in a simple way. In nonlinear problems it allows the nonscaling invariance to be retrieved by means of suitable redefined fractal-dimensioned variables.

Results: The main goal of the present contribution is to extend the applicability of the new approach to the study of problems of growth with cyclicity, which are of particular relevance in the fields of biology and medicine.

Conclusion: As an example of its implementation, the method is applied to the analysis of human growth curves. The excellent quality of the results (R2 = 0.988) demonstrates the usefulness and reliability of the approach.

Show MeSH
Examples of b(a) curves belonging to the class U0/TM. Examples of b(a) curves belonging to the class U0/TM, as described by Eq. (15). We have assumed for all the plots ω = 2, A1 = 1 and Ψ1 = 0. As predicted by Eq. (16), in the case M = 1 we obtain an ellipse with a ratio ω between the two semi-axes. Examples of the M = 2 case are shown in the plots (b), (c), (d) and (e), for different choices of the parameters A2 and Ψ2. As expected, three ellipses appear in the case U0/T3 (plot f).
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Figure 1: Examples of b(a) curves belonging to the class U0/TM. Examples of b(a) curves belonging to the class U0/TM, as described by Eq. (15). We have assumed for all the plots ω = 2, A1 = 1 and Ψ1 = 0. As predicted by Eq. (16), in the case M = 1 we obtain an ellipse with a ratio ω between the two semi-axes. Examples of the M = 2 case are shown in the plots (b), (c), (d) and (e), for different choices of the parameters A2 and Ψ2. As expected, three ellipses appear in the case U0/T3 (plot f).

Mentions: i.e. it represents an ellipse (see Fig. 1a), with ω being the ratio between the two semi-axes. In the case U0/T2, the "interference" between the ellipses generated by the first and second harmonics gives rise to plots, which include two complete ellipses (Fig.1b) or, according to whether A2 <<A1 or A2 > A1, one complete and one collapsed in a cusp (Fig. 1c) or in a knot (Fig. 1d), respectively. The plot b vs. a also depends, of course, also on the phase shift between the two harmonics and more complex curves may result (Fig. 1e) if its value is not close to 0 or to π. For N > 2, the plots obviously become more complex, nevertheless they may often be relatively easy to decipher, as in the U0/T3 case shown in Fig. 1f.


Scaling, growth and cyclicity in biology: a new computational approach.

Delsanto PP, Gliozzi AS, Guiot C - Theor Biol Med Model (2008)

Examples of b(a) curves belonging to the class U0/TM. Examples of b(a) curves belonging to the class U0/TM, as described by Eq. (15). We have assumed for all the plots ω = 2, A1 = 1 and Ψ1 = 0. As predicted by Eq. (16), in the case M = 1 we obtain an ellipse with a ratio ω between the two semi-axes. Examples of the M = 2 case are shown in the plots (b), (c), (d) and (e), for different choices of the parameters A2 and Ψ2. As expected, three ellipses appear in the case U0/T3 (plot f).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2289804&req=5

Figure 1: Examples of b(a) curves belonging to the class U0/TM. Examples of b(a) curves belonging to the class U0/TM, as described by Eq. (15). We have assumed for all the plots ω = 2, A1 = 1 and Ψ1 = 0. As predicted by Eq. (16), in the case M = 1 we obtain an ellipse with a ratio ω between the two semi-axes. Examples of the M = 2 case are shown in the plots (b), (c), (d) and (e), for different choices of the parameters A2 and Ψ2. As expected, three ellipses appear in the case U0/T3 (plot f).
Mentions: i.e. it represents an ellipse (see Fig. 1a), with ω being the ratio between the two semi-axes. In the case U0/T2, the "interference" between the ellipses generated by the first and second harmonics gives rise to plots, which include two complete ellipses (Fig.1b) or, according to whether A2 <<A1 or A2 > A1, one complete and one collapsed in a cusp (Fig. 1c) or in a knot (Fig. 1d), respectively. The plot b vs. a also depends, of course, also on the phase shift between the two harmonics and more complex curves may result (Fig. 1e) if its value is not close to 0 or to π. For N > 2, the plots obviously become more complex, nevertheless they may often be relatively easy to decipher, as in the U0/T3 case shown in Fig. 1f.

Bottom Line: In nonlinear problems it allows the nonscaling invariance to be retrieved by means of suitable redefined fractal-dimensioned variables.As an example of its implementation, the method is applied to the analysis of human growth curves.The excellent quality of the results (R2 = 0.988) demonstrates the usefulness and reliability of the approach.

View Article: PubMed Central - HTML - PubMed

Affiliation: Dept, Physics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy. pier.delsanto@polito.it

ABSTRACT

Background: The Phenomenological Universalities approach has been developed by P.P. Delsanto and collaborators during the past 2-3 years. It represents a new tool for the analysis of experimental datasets and cross-fertilization among different fields, from physics/engineering to medicine and social sciences. In fact, it allows similarities to be detected among datasets in totally different fields and acts upon them as a magnifying glass, enabling all the available information to be extracted in a simple way. In nonlinear problems it allows the nonscaling invariance to be retrieved by means of suitable redefined fractal-dimensioned variables.

Results: The main goal of the present contribution is to extend the applicability of the new approach to the study of problems of growth with cyclicity, which are of particular relevance in the fields of biology and medicine.

Conclusion: As an example of its implementation, the method is applied to the analysis of human growth curves. The excellent quality of the results (R2 = 0.988) demonstrates the usefulness and reliability of the approach.

Show MeSH