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We study the relationship between assumptions of state separability and both preparation and measurement contextuality, and the relationship of both of these to the frame problem, the problem of predicting what does not change in consequence of an action. We state a quantum analog of the latter and prove its undecidability. We show how contextuality is generically induced in state preparation and measurement by basis choice, thermodynamic exchange, and the imposition of a priori causal models, and how fine-tuning assumptions appear ubiquitously in settings characterized as non-contextual. [ABSTRACT FROM AUTHOR]

We apply previously developed Chu space and Channel Theory methods, focusing on the construction of Cone-Cocone Diagrams (CCCDs), to study the role of epistemic feelings, particularly feelings of confidence, in dual process models of problem solving. We specifically consider "Bayesian brain" models of probabilistic inference within a global neuronal workspace architecture. We develop a formal representation of Process-1 problem solving in which a solution is reached if and only if a CCCD is completed. We show that in this representation, Process-2 problem solving can be represented as multiply iterated Process-1 problem solving and has the same formal solution conditions. We then model the generation of explicit, reportable subjective probabilities from implicit, experienced confidence as a simulation-based, reverse engineering process and show that this process can also be modeled as a CCCD construction. [ABSTRACT FROM AUTHOR]

Several features of an analytic (infinite-dimensional) Grassmannian of (commensurable) subspaces of a Hilbert space were developed in the context of integrable PDEs (KP hierarchy). We extended some of those features when polarized separable Hilbert spaces are generalized to a class of polarized Hilbert modules and then consider the classical Baker and τ-functions as operator-valued. Following from Part I we produce a pre-determinant structure for a class of τ-functions defined in the setting of the similarity class of projections of a certain Banach *-algebra. This structure is explicitly derived from the transition map of a corresponding principal bundle. The determinant of this map leads to an operator τ-function. We extend to this setting the operator cross-ratio which had previously been used to produce the scalar-valued τ-function, as well as the associated notion of a Schwarzian derivative along curves inside the space of similarity classes of a given projection. We link directly this cross-ratio with Fay’s trisecant identity for the τ-function. By restriction to the image of the Krichever map, we use the Schwarzian to introduce the notion of an operator-valued projective structure on a compact Riemann surface: this allows a deformation inside the Grassmannian (as it varies its complex structure). Lastly, we use our identification of the Jacobian of the Riemann surface in terms of extensions of the Burchnall–Chaundy C*-algebra (Part I) provides a link to the study of the KP hierarchy. [ABSTRACT FROM AUTHOR]