3,410 research outputs found
The Nature and Function of Content in Computational Models
Much of computational cognitive science construes human cognitive capacities as representational
capacities, or as involving representation in some way. Computational theories of vision,
for example, typically posit structures that represent edges in the distal scene. Neurons are often
said to represent elements of their receptive fields. Despite the ubiquity of representational talk
in computational theorizing there is surprisingly little consensus about how such claims are to
be understood. The point of this chapter is to sketch an account of the nature and function of
representation in computational cognitive models
The Euler and Springer numbers as moment sequences
I study the sequences of Euler and Springer numbers from the point of view of
the classical moment problem.Comment: LaTeX2e, 30 pages. Version 2 contains some small clarifications
suggested by a referee. Version 3 contains new footnotes 9 and 10. To appear
in Expositiones Mathematica
Egocentric Spatial Representation in Action and Perception
Neuropsychological findings used to motivate the “two visual systems” hypothesis have been taken to endanger a pair of widely accepted claims about spatial representation in visual experience. The first is the claim that visual experience represents 3-D space around the perceiver using an egocentric frame of reference. The second is the claim that there is a constitutive link between the spatial contents of visual experience and the perceiver’s bodily actions. In this paper, I carefully assess three main sources of evidence for the two visual systems hypothesis and argue that the best interpretation of the evidence is in fact consistent with both claims. I conclude with some brief remarks on the relation between visual consciousness and rational agency
The log-L\'evy moment problem via Berg-Urbanik semigroups
We consider the Stieltjes moment problem for the Berg-Urbanik semigroups
which form a class of multiplicative convolution semigroups on
that is in bijection with the set of Bernstein functions. Berg and Dur\'an
proved that the law of such semigroups is moment determinate (at least) up to
time , and, for the Bernstein function , Berg made the striking
observation that for time the law of this semigroup is moment
indeterminate. We extend these works by estimating the threshold time
\scr{T}_\phi \in [2,\infty] that it takes for the law of such Berg-Urbanik
semigroups to transition from moment determinacy to moment indeterminacy in
terms of simple properties of the underlying Bernstein function , such as
its Blumenthal-Getoor index. One of the several strategies we implement to deal
with the different cases relies on a non-classical Abelian type criterion for
the moment problem, recently proved by the authors. To implement this approach
we provide detailed information regarding distributional properties of the
semigroup such as existence and smoothness of a density, and, the large
asymptotic behavior for all of this density along with its successive
derivatives. In particular, these results, which are original in the L\'evy
processes literature, may be of independent interests.Comment: Studia Mathematic
Quantum value indefiniteness
The indeterministic outcome of a measurement of an individual quantum is
certified by the impossibility of the simultaneous, definite, deterministic
pre-existence of all conceivable observables from physical conditions of that
quantum alone. We discuss possible interpretations and consequences for quantum
oracles.Comment: 19 pages, 2 tables, 2 figures; contribution to PC0
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