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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
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