Interestingly, without this constraint we were not able to determine a parameter configuration matching the simulation results to in vitro measurements.

Before we extensively discuss the simulation results , we first thoroughly validate the model and its current parametrization.

The simulation results with the adapted model are depicted in Fig.

According to our simulation results , only a concisely regulated interplay between redox-dependent and self-induced auto-/paracrine WNT signaling can explain the nuclear fi-catenin dynamics observed experimentally during the initial phase of differentiation:

In summary, our simulation results suggest a twofold activation mechanism that drives the early differentiation process in human progenitor cells.

Simulation result for Raft/Receptor dynamics.

We also tested the sensitivity of the structure obtained to the evolutionary goal by comparing simulation results with different goals having the same rank.

We show simulation results of networks with L = 4 (5 layers of nodes) and 6 nodes in each layer (D = 6).

Each column in this figure shows simulation results for a different goal, and each row shows a different network layer.

We show simulation results of a simple nonlinear problem mimicking a 4-pixel retina.

(B) Typical example of simulation results .

We show simulation results when the goal consisted of a matrix of deficient rank (1 , 2 or 3) to which some level of noise was added (see Methods), so mathematically speaking goals had full rank, such that some of the eigenvalues were relatively small.

Generically, in fields as diverse as artificial neural networks [30] and evolution of biological networks, simulations result in highly connected networks with no bow-tie [31—37].

Additional figures and simulation results as follows: 1.Parameter sensitivity test, 2.

This simulated result was confirmed with empirically-reconstructed human brain networks derived from high-density EEG recordings, demonstrating again that the anterior-to-posterior directionality occurs because of the posterior-hub structure.

We also varied the time delay parameter across a broad range (2~50ms), but this did not yield a qualitative difference in the simulation results as long as the delay was less than a quarter cycle (< 25 ms) of the given natural frequency (in this case, one cycle is about 100 ms since the frequency is around 10Hz).

Fig 3 shows the simulation results in random and scale-free networks, which represent two extreme cases of inhomogeneous degree networks.

To explain these simulation results , we utilized Ko et al.’s mean-field technique approach to derive the relationships for the coupled Stuart-Landau oscillators with inhomogeneous coupling strength, which in turn can be applied to inhomogeneous degree networks by interpreting inhomogeneous coupling strength as inhomogeneous degree for each oscillator [43].

The simulation results suggest that the phase-lead/lag relation, causality, and information flow transfer are possibly all correlated with each other.

The simulation results confirmed that the central relationship of degree, node dynamics and directionality (i.e., higher degree nodes have larger amplitudes and phase lag behind lower degree nodes) still holds firmly.

We then produced a random population With these a priori probabilities, and compared the expected frequency of a haplotype unobserved in a sample (Z(R)), the expected number of unique haplotypes in the population (U(R)) and the fraction of the population covered by these haplotypes to the simulations results .

Ratio of analytical estimated U(R) values divided by simulation results for different values of sample size and a (Inset: Analytical estimation (gray solid line) and simulation values (black circles) of U(R) (black circles) for a = 1.5).

Ratio of analytical estimated fraction of covered population values divided by simulation results for different values of sample size and a (Inset: Analytical estimation (gray solid line) and simulation values (black circles) of fraction of covered population for a = 1 .5.

Ratio of analytical estimated values of the probability that there exists at least one unobserved haplotype divided by simulations results for different values of sample size and a (Inset: Analytical estimation (gray solid line) and simulation values (black circles) of the probability that there exists at least one unobserved haplotype for a = 1.5.

Therefore, these give the correspondences of the analytical results for distribution of the variables in different temperature ranges With the simulation results for distribution of the variables in different variable ranges.

Microscopic Atomic Binding Model and Simulation Results

We will first present the analytical results and then the simulation results .

The fitting procedure for the simulation results .

Simulation results also indicated that ConPADE works well for contigs of small size, on the order of a few thousand nucleotides in length.

Collectively, these simulation results show that high ploidy levels can be reliably estimated only with high sequencing coverage, even for long contigs.

Coverage simulation results .

Coverage simulation results .

Simulation results for this model of ‘action initiation and changes of mind’

Simulation results for this model of ‘action preparation’ (Fig.

Simulation results for this model of action preparation and commitment (Fig.

The relationship among myosin isoform values being predictive of the energy required for processivity may be investigated through viewing simulation results according to the energy consumed by a system on average for a given processivity.

When determining E* from Fig 6B simulation results are representative of ensembles with pro-cessive lifetimes of approximately 500ms.

When simulation results from Fig 6A are reconsidered with E*, there is strong agreement among all isoform types adhering to one master curve (Fig 7).

Simulation results show that these behaviors arise from a threshold relationship between uptake and host receptor number.

Lines extended from the power-law simulation results no longer remain parallel away from biologically relevant receptor concentrations.

When GFP values were scaled with their respective MOI for the fraction of infected host cells, the curves collapsed into a single linear line that has high correlation (Fig 3D), similar to our previous simulation results (Fig 2C).

3(c)-(f) demonstrates that the analytical results slightly underestimate the simulation results to a small degree, especially if the mutated strain’s growth rate is high and R2 is close to K, but becomes more accurate as R2 increases and generally provides a good approximation.

Nevertheless, even in this case, Equation 7 accurately matches up with simulation results in this parameter range, although some inaccuracies arise for K = 1,000 (81 Fig).

Contains additional information on derivations, and further comparisons against simulation results (Mathematica NB format).