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New on the VVTNS YouTube Channel https://www.wwtns.online/past-seminars-2025-2026 *Continuous representations in small, discrete circuits* lecture delivered on February 4, 2026 by Marcella Noorman University of Chicago *Abstract: *Many animals rely on persistent internal representations of continuous angular variables for working memory, motor control, and navigation. Theories have proposed that such representations are maintained by a class of recurrently connected networks called ring attractor networks. These networks rely on large numbers of neurons to maintain continuous and stable representations and to accurately integrate incoming signals. The head direction system of the fruit fly, however, seems to achieve these properties with a remarkably small network. These findings challenge our understanding of ring attractors and their putative implementation in neural circuits. In this talk, I will show analytically how small networks can overcome the constraints of their size to generate a ring attractor and are hence capable of stably maintaining an internal representation of a continuous, periodic variable. Further, I will show how ring attractors emerge in small threshold linear networks through the coordination of a discrete set of line attractors. More broadly, this work informs our understanding of the functional capabilities of small, discrete systems. *About VVTNS : Launched as the World Wide Theoretical Neuroscience Seminar (WWTNS) in November 2020 and renamed in homage to Carl van Vreeswijk in Memoriam (April 20, 2022), Speakers have the occasion to talk about theoretical aspects of their work which cannot be discussed in a setting where the majority of the audience consists of experimentalists. The seminars, **held on Wednesdays at 11 am ET,** are 45-50 min long followed by a discussion. The talks are recorded with authorization of the speaker and are available to everybody on our YouTube channel.*