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The Theater Model of Consciousness imagines a stage observed by a vast audience of unconscious processors. Our Conscious Turing Machine (CTM) formalizes a version of this model: it is conscious of the stage, but not the audience’s thoughts. CTM is shaped by two demands: 1.Be as simple as possible (Occam’s razor), and 2. Explain a lot—including answers to Kevin Mitchell’s 15x3 questions. Unlike other models, CTM has no Central Executive (CE)—a hypothesized director of stage activity-as that lacks both explanation and neural evidence. We argue the CE cannot exist, and explain why. In CTM, control emerges from competition among processors, which estimate the importance of their info via an optimal, self-correcting process. The winner is chosen with probability proportional to that importance. Its info is broadcast from the stage to the entire audience.
Kate is a METEOR postdoc at MIT, working with Manish Raghavan, and starting in summer 2026, she will be an assistant professor of computer science at University of Illinois Urbana-Champaign (UIUC). She works on algorithmic problems relating to the societal...
Microbiomes, which are collections of interacting microbes in a specific environment, often substantially impact the environmental patches or living hosts that they occupy. To model the interactions between microbes across multiple scales, which include their local dynamics within
an environment and the exchange of microbes between environments, using metacommunity theory. Metacommunity models commonly assume continuous microbe dispersion between environments. Such a framework is well-suited to abiotic environmental patches, but it fails to capture the fact that living hosts interact with each other during discrete time intervals. In this talk, I present a modeling framework that successfully encodes such discrete interactions and uses two parameters to separately control the interaction frequencies between hosts and the amount of microbe exchange during each interaction. I illustrate the behavior of this model with both analytical approximations and numerical experiments.
We describe the topology of the space of all smooth asymptotically stable vector fields on Rⁿ, as well as the space of all proper smooth Lyapunov functions for such vector fields. In particular, both spaces are path-connected and simply connected when n is not equal to 4, 5 and weakly contractible when n is less than 4. The proofs rely on Lyapunov theory and differential topology, such as the work of Smale and Perelman on the generalized Poincaré conjecture and results of Smale, Cerf, and Hatcher on the topology of diffeomorphism groups of discs. (Hatcher's result is a proof of the Smale conjecture.) Applications include a partial answer to a question of Conley, a parametric Hartman-Grobman theorem for nonhyperbolic but asymptotically stable equilibria, and a parametric Morse lemma for degenerate minima.