| Abstract | We confirm analytical results with computational simulations using general model networks and anatomical brain networks, as well as high-density electroencephalography collected from humans in the conscious and anesthetized states. |
| Discussion | Furthermore, the analytical results are independent of the type of network, as long as the network is inhomogeneous in terms of connections. |
| Discussion | As such, our simple models and the analytical results may not explain fine-scale neuronal firing relationships and the short-term dynamics of complex local connections such as the influence of a common source with different time delays. |
| Identification of mathematical relationships among node degree, amplitude of local oscillations and directionality of interactions | The analytical results demonstrate that, for the Stuart-Landau oscillators with the same natural frequencies and inhomogeneous coupling, when the coupling strength between oscillators is sufficiently high and the delay time given as constant between them is sufficiently small, |
| Identification of mathematical relationships among node degree, amplitude of local oscillations and directionality of interactions | The analytic results also demonstrate the following: 2 7 2 ing function of x for x E [— g, . |
| Supporting Information | Detailed derivations of the analytical results for “General Relationship of Global |
| Analytical Models of Distribution of Affinity, Equilibrium Constants, Specificity and Kinetics | 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 | This confirms the analytical results discussed above. |
| Results and Discussion | We will first present the analytical results and then the simulation results. |
| Model | Although here we explicitly assumed the presence of the external layer, these analytical results can also be applied for arbitrary realization of a spatiotemporal correlation. |
| STDP and Bayesian ICA | Moreover, our analytical results suggested the reason that independent sources are detected. |
| Supporting Information | (E) Analytic results for various types of STDP. |
| Comparing pathogen growth against death rate | We verified this intuition by comparing the analytical results for cases where (p2 is increased by a set factor (so that only R2 is changed by this rescaling), to outcomes where 02 is scaled (which will not just affect R2 but will also increase p by the same factor, as outlined above). |
| Comparison of analytical results with simulations data | Comparison of analytical results with simulations data |
| Comparison of analytical results with simulations data | 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. |