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The set of population phase lag configurations needed to generate sequences in each direction is called a phase chart.
(E ) If a population has a fixed phase chart, the possible remappings are restricted to affine transformations.
In this case, each complete remapping recruits a different phase chart, fixing a new set of phase lags in the population.
Hence, in open environments, the notion of a phase chart must be extended to include a fixed phase ordering for each running direction.
Given such a fixed phase chart, a set of remappings known as affine transformations preserve the correct theta dynamics (see Supplementary file 1, Appendix: A7).
Interestingly, the remappings observed in grid modules (Fyhn et al., 2007), but not CA1, are consistent with those predicted for networks with a single fixed set of theta phase lags called a phase chart.
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The time history response plots, the phase charts and the Poincare mapping charts are plotted.
The number of possible global remappings that maintain theta sequences is then determined by the number of available phase charts.
Nevertheless, it remains possible that CA1 theta dynamics are based on fixed phase charts, provided that multiple such phase charts are available to the network, similar to the multiple attractor charts which have been suggested to support remapping of firing rate (Samsonovich and McNaughton, 1997).
Nevertheless, more complex scenarios with multiple phase charts could explain CA1 population activity during theta oscillations and 'preplay', which suggests a limited remapping capacity for CA1 (Dragoi and Tonegawa, 2011, 2013).
These phases chart the shifts in strategy among SAHAYOG and its close allies, and responses of the state to these strategies.
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