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1.
Figure 1

Figure 1. From: Origins of Stochasticity and Burstiness in High-Dimensional Biochemical Networks.

Illustration of the notion of burstiness.

Simon Rosenfeld. EURASIP J Bioinform Syst Biol. 2009;2009(1):362309-362309.
2.
Figure 3

Figure 3. From: Origins of Stochasticity and Burstiness in High-Dimensional Biochemical Networks.

Convergence of the sums of lognormal processes (a) to approximate normality (b).

Simon Rosenfeld. EURASIP J Bioinform Syst Biol. 2009;2009(1):362309-362309.
3.
Figure 6

Figure 6. From: Origins of Stochasticity and Burstiness in High-Dimensional Biochemical Networks.

Example of approximation of the difference of two lognormals by the GPD. (a) QQ-plot of theoretical GPD versus empirical ; (b) empirical histogram of versus theoretical GPD density.

Simon Rosenfeld. EURASIP J Bioinform Syst Biol. 2009;2009(1):362309-362309.
4.
Figure 5

Figure 5. From: Origins of Stochasticity and Burstiness in High-Dimensional Biochemical Networks.

Parameters of GPD expressed through the standard deviation,. Dots are the parameters obtained by fitting the GPD to the simulated ; solid lines are the parameters obtained through the analytical approximations (10)-(11).

Simon Rosenfeld. EURASIP J Bioinform Syst Biol. 2009;2009(1):362309-362309.
5.
Figure 8

Figure 8. From: Origins of Stochasticity and Burstiness in High-Dimensional Biochemical Networks.

Evidence that the exceedances form a Poisson process: waiting times are exponentially distributed. The number of peaks predicted from asymptotic theory is 703; the number actually found in simulation is 695.

Simon Rosenfeld. EURASIP J Bioinform Syst Biol. 2009;2009(1):362309-362309.
6.
Figure 4

Figure 4. From: Origins of Stochasticity and Burstiness in High-Dimensional Biochemical Networks.

Illustration of convergence to normality. The histograms belong to processes shown in Figure 3. (a) Lognormal processes (skeweness 6.2, kurtosis 106). (b) Distribution of sums of 80 lognormals (skeweness 1.2, kurtosis 2). In both cases, solid lines belong to standard normal.

Simon Rosenfeld. EURASIP J Bioinform Syst Biol. 2009;2009(1):362309-362309.
7.
Figure 2

Figure 2. From: Origins of Stochasticity and Burstiness in High-Dimensional Biochemical Networks.

Histogram of the process depicted in Figure 1. The distribution is close to the Student's t with number of degrees of freedom 1.13. This is an indicator of "heavy tails." Solid line belongs to the standard normal distribution, .

Simon Rosenfeld. EURASIP J Bioinform Syst Biol. 2009;2009(1):362309-362309.
8.
Figure 7

Figure 7. From: Origins of Stochasticity and Burstiness in High-Dimensional Biochemical Networks.

(a) Process . (b) Process of exceedances . (c)Residual noise, . (d) Trajectory of the random walk generated by . Note that the variance of residual noise, , is only 2.3% of total variance , despite the fact that exceedances, , occupy only 5% of the probability space.

Simon Rosenfeld. EURASIP J Bioinform Syst Biol. 2009;2009(1):362309-362309.

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