Multiscaled randomness: A possible source of 1/f noise in biology.

We evaluate the possibility that the 1/ f fluctuations observed in many biological time series result simply from the fact that biological processes have many inputs with differing time scales. We present a stochastic model whose output is the summation of multiple random inputs ~i.e., different regulatory mechanisms! .W e derive the conditions under which the model reproduces the complex fluctuations and 1/ f scaling observed in biological systems. Simulations demonstrate that if model parameters are unconstrained, the likelihood of generating 1/f noise is quite small. Thus, while the model can be used to generate 1/ f b noise with various scaling exponents, it is unlikely that the 1/ f behavior observed in many biological systems is due only to the fact that these systems are regulated by many different inputs acting on different time scales.

[1]  Paul Manneville,et al.  Intermittency, self-similarity and 1/f spectrum in dissipative dynamical systems , 1980 .

[2]  T. Musha,et al.  1/f Fluctuation of Heartbeat Period , 1982, IEEE Transactions on Biomedical Engineering.

[3]  Tang,et al.  Self-Organized Criticality: An Explanation of 1/f Noise , 2011 .

[4]  L S Liebovitch,et al.  Fractal analysis of a voltage-dependent potassium channel from cultured mouse hippocampal neurons. , 1987, Biophysical journal.

[5]  M. Weissman.  1/f noise and other slow, nonexponential kinetics in condensed matter. , 1988 .

[6]  Malvin C. Teich.  Fractal character of the auditory neural spike train , 1989 .

[7]  Tamás Vicsek,et al.  Self-affine growth of bacterial colonies , 1990 .

[8]  Eldred,et al.  Physical mechanisms underlying neurite outgrowth: A quantitative analysis of neuronal shape. , 1990, Physical review letters.

[9]  West,et al.  Complex fractal dimension of the bronchial tree. , 1991, Physical review letters.

[10]  LINEAR VERSUS NONLINEAR AMPLIFICATION: A GENERALIZATION OF THE NOVIKOV-MONTROLL-SHLESINGER-WEST CASCADE , 1992 .

[11]  Jeffrey M. Hausdorff,et al.  Long-range anticorrelations and non-Gaussian behavior of the heartbeat. , 1993, Physical review letters.

[12]  Albert-László Barabási,et al.  Avalanches and power-law behaviour in lung inflation , 1994, Nature.

[13]  Jan Beran,et al.  Statistics for long-memory processes , 1994 .

[14]  D L Gilden,et al.  1/f noise in human cognition. , 1995, Science.

[15]  L. Glass,et al.  Understanding Nonlinear Dynamics , 1995 .

[16]  H. Stanley,et al.  Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. , 1995, Chaos.

[17]  Jeffrey M. Hausdorff,et al.  Is walking a random walk? Evidence for long-range correlations in stride interval of human gait. , 1995, Journal of applied physiology.