Neural simulation of a system that learns representations of sensory experience

The pyriform cortex forms stable representations of smells to allow their subsequent recognition. Clustering systems are shown to perform a similar function, so they provide a guide to understanding the operation of the pyriform. A neural model of a sample of pyriform cortex was built that adheres to most known biological constraints, including learning by long-term potentiation. Results of early simulations suggest some interesting properties. The effort has implications for the knowledge representations used in artificial intelligence work

Quantum Knowledge, Quantum Belief, Quantum Reality: Notes of a QBist Fellow Traveler

I consider the "Quantum Bayesian" view of quantum theory as expounded in a 2006 paper of Caves, Fuchs, and Schack. I argue that one can accept a generally personalist, decision-theoretic view of probability, including probability as manifested in quantum physics, while nevertheless accepting that in some situations, including some in quantum physics, probabilities may in a useful sense be thought of as objectively correct. This includes situations in which the ascription of a quantum state should be thought of as objectively correct. I argue that this does not cause any prima facie objectionable sort of action at a distance, though it may involve adopting the attitude that certain dispositional properties of things are not "localized" at those things. Whether this insouciant view of nonlocality and objectivity can survive more detailed analysis is a matter for further investigation.Comment: 13 page

Semidefinite programming characterization and spectral adversary method for quantum complexity with noncommuting unitary queries

Generalizing earlier work characterizing the quantum query complexity of computing a function of an unknown classical ``black box'' function drawn from some set of such black box functions, we investigate a more general quantum query model in which the goal is to compute functions of N by N ``black box'' unitary matrices drawn from a set of such matrices, a problem with applications to determining properties of quantum physical systems. We characterize the existence of an algorithm for such a query problem, with given error and number of queries, as equivalent to the feasibility of a certain set of semidefinite programming constraints, or equivalently the infeasibility of a dual of these constraints, which we construct. Relaxing the primal constraints to correspond to mere pairwise near-orthogonality of the final states of a quantum computer, conditional on black-box inputs having distinct function values, rather than bounded-error determinability of the function value via a single measurement on the output states, we obtain a relaxed primal program the feasibility of whose dual still implies the nonexistence of a quantum algorithm. We use this to obtain a generalization, to our not-necessarily-commutative setting, of the ``spectral adversary method'' for quantum query lower bounds.Comment: Dagstuhl Seminar Proceedings 06391, "Algorithms and Complexity for Continuous Problems," ed. S. Dahlke, K. Ritter, I. H. Sloan, J. F. Traub (2006), available electronically at http://drops.dagstuhl.de/portals/index.php?semnr=0639

Achieving and Maintaining Cognitive Vitality With Aging

This report contains the summary results of a workshop held at Canyon Ranch Health Resort in Tucson, Arizona. Physicians and scientists shed light on the process of cognitive aging. They review current scientific and clinical knowledge of normal human cognitive aging, the biological mechanisms that underlie this process, and risk factors associated with mental decline. They make recommendations for lifestyle changes and outline a research agenda for the development of new therapies to prevent mental decline and maintain cognitive vitality

Geometry of the Complex of Curves I: Hyperbolicity

The Complex of Curves on a Surface is a simplicial complex whose vertices are homotopy classes of simple closed curves, and whose simplices are sets of homotopy classes which can be realized disjointly. It is not hard to see that the complex is finite-dimensional, but locally infinite. It was introduced by Harvey as an analogy, in the context of Teichmuller space, for Tits buildings for symmetric spaces, and has been studied by Harer and Ivanov as a tool for understanding mapping class groups of surfaces. In this paper we prove that, endowed with a natural metric, the complex is hyperbolic in the sense of Gromov. In a certain sense this hyperbolicity is an explanation of why the Teichmuller space has some negative-curvature properties in spite of not being itself hyperbolic: Hyperbolicity in the Teichmuller space fails most obviously in the regions corresponding to surfaces where some curve is extremely short. The complex of curves exactly encodes the intersection patterns of this family of regions (it is the "nerve" of the family), and we show that its hyperbolicity means that the Teichmuller space is "relatively hyperbolic" with respect to this family. A similar relative hyperbolicity result is proved for the mapping class group of a surface. We also show that the action of pseudo-Anosov mapping classes on the complex is hyperbolic, with a uniform bound on translation distance.Comment: Revised version of IMS preprint. 36 pages, 6 Figure