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of local, cell-type dependent statistics, we develop a low-rank approximation based on the dominant eigenmodes of the connectivity matrix . Using perturbation theory , we show that the obtained low-rank ...
. Each task represents a different, common challenge in control engineering, namely non -linear behaviour, unstable equilibrium, dead time, and chaotic behaviour. These applications have furthermore been ...
. In 1963, Lorenz found a 3-D (three-dimensional) weather modeling system, which resulted in the establishment of the first chaotic system [7]. Since then, chaos theory has been studied intensively ...
possess a random structure inherited from the random connectivity matrix . Download: PPT PowerPoint slide PNG larger image TIFF original image Fig 1. Dynamical regimes of an excitatory-inhibitory network ...
, even with perfect assignment of all sampled individuals, sampling error alone can introduce noise into the estimated population connectivity matrix . Future work should aim to improve the number ...
structures, which is a unique feature of the ANGEL model. Moreover, we analyze spectral and eigenfunction properties of the synthetic and reference networks, based on the Random Matrix Theory modeling approach ...
parameterized by the (possibly complex) eigenvalues of the network connectivity matrix . Recently, this method has been extended to treat diffusively coupled networks of non -smooth Filippov type (Filippov, 1988 ...
from countless fields are used to model their worlds with the tools offered by graph theory in order to impose a structure to otherwise chaotic data. In this challenging scenario, identifying shared ...
matrix w is the cross product between the encoder and decoder matrices, (5) Our primary tool for studying state space transformations is control theory , which specifies the dynamics of x(t) as (6) where ...
) where N, the stoichiometric matrix , contains all the relevant information on the structure of the fluxes within the network. Vector v is a set of complicated non -linear functions describing growth rates ...
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