13,311 research outputs found
Abstract State Machines 1988-1998: Commented ASM Bibliography
An annotated bibliography of papers which deal with or use Abstract State
Machines (ASMs), as of January 1998.Comment: Also maintained as a BibTeX file at http://www.eecs.umich.edu/gasm
Tight Size-Degree Bounds for Sums-of-Squares Proofs
We exhibit families of -CNF formulas over variables that have
sums-of-squares (SOS) proofs of unsatisfiability of degree (a.k.a. rank)
but require SOS proofs of size for values of from
constant all the way up to for some universal constant.
This shows that the running time obtained by using the Lasserre
semidefinite programming relaxations to find degree- SOS proofs is optimal
up to constant factors in the exponent. We establish this result by combining
-reductions expressible as low-degree SOS derivations with the
idea of relativizing CNF formulas in [Kraj\'i\v{c}ek '04] and [Dantchev and
Riis'03], and then applying a restriction argument as in [Atserias, M\"uller,
and Oliva '13] and [Atserias, Lauria, and Nordstr\"om '14]. This yields a
generic method of amplifying SOS degree lower bounds to size lower bounds, and
also generalizes the approach in [ALN14] to obtain size lower bounds for the
proof systems resolution, polynomial calculus, and Sherali-Adams from lower
bounds on width, degree, and rank, respectively
Changing a semantics: opportunism or courage?
The generalized models for higher-order logics introduced by Leon Henkin, and
their multiple offspring over the years, have become a standard tool in many
areas of logic. Even so, discussion has persisted about their technical status,
and perhaps even their conceptual legitimacy. This paper gives a systematic
view of generalized model techniques, discusses what they mean in mathematical
and philosophical terms, and presents a few technical themes and results about
their role in algebraic representation, calibrating provability, lowering
complexity, understanding fixed-point logics, and achieving set-theoretic
absoluteness. We also show how thinking about Henkin's approach to semantics of
logical systems in this generality can yield new results, dispelling the
impression of adhocness. This paper is dedicated to Leon Henkin, a deep
logician who has changed the way we all work, while also being an always open,
modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on
his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and
Alonso, E., 201
A Jones matrix formalism for simulating three-dimensional polarized light imaging of brain tissue
The neuroimaging technique three-dimensional polarized light imaging (3D-PLI)
provides a high-resolution reconstruction of nerve fibres in human post-mortem
brains. The orientations of the fibres are derived from birefringence
measurements of histological brain sections assuming that the nerve fibres -
consisting of an axon and a surrounding myelin sheath - are uniaxial
birefringent and that the measured optic axis is oriented in direction of the
nerve fibres (macroscopic model). Although experimental studies support this
assumption, the molecular structure of the myelin sheath suggests that the
birefringence of a nerve fibre can be described more precisely by multiple
optic axes oriented radially around the fibre axis (microscopic model). In this
paper, we compare the use of the macroscopic and the microscopic model for
simulating 3D-PLI by means of the Jones matrix formalism. The simulations show
that the macroscopic model ensures a reliable estimation of the fibre
orientations as long as the polarimeter does not resolve structures smaller
than the diameter of single fibres. In the case of fibre bundles, polarimeters
with even higher resolutions can be used without losing reliability. When
taking the myelin density into account, the derived fibre orientations are
considerably improved.Comment: 20 pages, 8 figure
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