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The paper studies the control of a class of discrete event processes, i.e., processes that are discrete, asynchronous and possibly nondeterministic. The controlled process is described as the generator of a formal language, while the controller, or supervisor, is constructed from a recognizer for a specified target language that incorporates the desired closed-loop system behavior. The existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language. Two examples are provided.

Summary We present a high-dimensional model of the representational space in human ventral temporal (VT) cortex in which dimensions are response-tuning functions that are common across individuals and patterns of response are modeled as weighted sums of basis patterns associated with these response-tunings. We map response pattern vectors, measured with fMRI, from individual subjects’ voxel spaces into this common model space using a new method, ‘hyperalignment’. Hyperalignment parameters based on responses during one experiment – movie-viewing – identified 35 common response-tuning functions that captured fine-grained distinctions among a wide range of stimuli in the movie and in two category perception experiments. Between-subject classification (BSC, multivariate pattern classification based on other subjects’ data) of response pattern vectors in common model space greatly exceeded BSC of anatomically-aligned responses and matched within-subject classification. Results indicate that population codes for complex visual stimuli in VT cortex are based on response-tuning functions that are common across individuals.

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Current models of the functional architecture of human cortex emphasize areas that capture coarse-scale features of cortical topography but provide no account for population responses that encode information in fine-scale patterns of activity. Here, we present a linear model of shared representational spaces in human cortex that captures fine-scale distinctions among population responses with response-tuning basis functions that are common across brains and models cortical patterns of neural responses with individual-specific topographic basis functions. We derive a common model space for the whole cortex using a new algorithm, searchlight hyperalignment, and complex, dynamic stimuli that provide a broad sampling of visual, auditory, and social percepts. The model aligns representations across brains in occipital, temporal, parietal, and prefrontal cortices, as shown by between-subject multivariate pattern classification and intersubject correlation of representational geometry, indicating that structural principles for shared neural representations apply across widely divergent domains of information. The model provides a rigorous account for individual variability of well-known coarse-scale topographies, such as retinotopy and category selectivity, and goes further to account for fine-scale patterns that are multiplexed with coarse-scale topographies and carry finer distinctions.