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Abstract Recent advancements in neurotechnology enable precise spatiotemporal patterns of micros- timulations with single-cell resolution. The choice of perturbation sites must satisfy two key criteria: efficacy in evoking significant responses and selectivity for the desired target effects. This choice is currently based on laborious trial-and-error procedures, unfeasible for sequences of multi-site stimulations. Efficient methods to design complex perturbation patterns are ur- gently needed. Can we design a spatiotemporal pattern of stimulation to steer neural activity and behavior towards a desired target? We outline a method for achieving this goal in two steps. First, we identify the most effective perturbation sites, or hubs, only based on short observations of spontaneous neural activity. Second, we provide an efficient method to design multi-site stimulation patterns by combining approaches from nonlinear dynamical systems, control theory and data-driven methods. We demonstrate the feasibility of our approach using multi-site stimulation patterns in recurrent network models. 

Populations of neurons represent sensory, motor, and cognitive variables via patterns of activity distributed across the population. The size of the population used to encode a variable is typically much greater than the dimension of the variable itself, and thus, the corresponding neural population activity occupies lower-dimensional subsets of the full set of possible activity states. Given population activity data with such lower-dimensional structure, a fundamental question asks how close the low-dimensional data lie to a linear subspace. The linearity or nonlinearity of the low-dimensional structure reflects important computational features of the encoding, such as robustness and generalizability. Moreover, identifying such linear structure underlies common data analysis methods such as Principal Component Analysis (PCA). Here, we show that for data drawn from many common population codes the resulting point clouds and manifolds are exceedingly nonlinear, with the dimension of the best-fitting linear subspace growing at least exponentially with the true dimension of the data. Consequently, linear methods like PCA fail dramatically at identifying the true underlying structure, even in the limit of arbitrarily many data points and no noise.