117,943 research outputs found
Canonical Proof nets for Classical Logic
Proof nets provide abstract counterparts to sequent proofs modulo rule
permutations; the idea being that if two proofs have the same underlying
proof-net, they are in essence the same proof. Providing a convincing proof-net
counterpart to proofs in the classical sequent calculus is thus an important
step in understanding classical sequent calculus proofs. By convincing, we mean
that (a) there should be a canonical function from sequent proofs to proof
nets, (b) it should be possible to check the correctness of a net in polynomial
time, (c) every correct net should be obtainable from a sequent calculus proof,
and (d) there should be a cut-elimination procedure which preserves
correctness. Previous attempts to give proof-net-like objects for propositional
classical logic have failed at least one of the above conditions. In [23], the
author presented a calculus of proof nets (expansion nets) satisfying (a) and
(b); the paper defined a sequent calculus corresponding to expansion nets but
gave no explicit demonstration of (c). That sequent calculus, called LK\ast in
this paper, is a novel one-sided sequent calculus with both additively and
multiplicatively formulated disjunction rules. In this paper (a self-contained
extended version of [23]), we give a full proof of (c) for expansion nets with
respect to LK\ast, and in addition give a cut-elimination procedure internal to
expansion nets - this makes expansion nets the first notion of proof-net for
classical logic satisfying all four criteria.Comment: Accepted for publication in APAL (Special issue, Classical Logic and
Computation
The Fiber Walk: A Model of Tip-Driven Growth with Lateral Expansion
Tip-driven growth processes underlie the development of many plants. To date,
tip-driven growth processes have been modelled as an elongating path or series
of segments without taking into account lateral expansion during elongation.
Instead, models of growth often introduce an explicit thickness by expanding
the area around the completed elongated path. Modelling expansion in this way
can lead to contradictions in the physical plausibility of the resulting
surface and to uncertainty about how the object reached certain regions of
space. Here, we introduce "fiber walks" as a self-avoiding random walk model
for tip-driven growth processes that includes lateral expansion. In 2D, the
fiber walk takes place on a square lattice and the space occupied by the fiber
is modelled as a lateral contraction of the lattice. This contraction
influences the possible follow-up steps of the fiber walk. The boundary of the
area consumed by the contraction is derived as the dual of the lattice faces
adjacent to the fiber. We show that fiber walks generate fibers that have
well-defined curvatures, enable the identification of the process underlying
the occupancy of physical space. Hence, fiber walks provide a base from which
to model both the extension and expansion of physical biological objects with
finite thickness.Comment: Plos One (in press
Speeding up Glauber Dynamics for Random Generation of Independent Sets
The maximum independent set (MIS) problem is a well-studied combinatorial
optimization problem that naturally arises in many applications, such as
wireless communication, information theory and statistical mechanics.
MIS problem is NP-hard, thus many results in the literature focus on fast
generation of maximal independent sets of high cardinality. One possibility is
to combine Gibbs sampling with coupling from the past arguments to detect
convergence to the stationary regime. This results in a sampling procedure with
time complexity that depends on the mixing time of the Glauber dynamics Markov
chain.
We propose an adaptive method for random event generation in the Glauber
dynamics that considers only the events that are effective in the coupling from
the past scheme, accelerating the convergence time of the Gibbs sampling
algorithm
Foundations for Relativistic Quantum Theory I: Feynman's Operator Calculus and the Dyson Conjectures
In this paper, we provide a representation theory for the Feynman operator
calculus. This allows us to solve the general initial-value problem and
construct the Dyson series. We show that the series is asymptotic, thus proving
Dyson's second conjecture for QED. In addition, we show that the expansion may
be considered exact to any finite order by producing the remainder term. This
implies that every nonperturbative solution has a perturbative expansion. Using
a physical analysis of information from experiment versus that implied by our
models, we reformulate our theory as a sum over paths. This allows us to relate
our theory to Feynman's path integral, and to prove Dyson's first conjecture
that the divergences are in part due to a violation of Heisenberg's uncertainly
relations
Cognitive constraints, contraction consistency, and the satisficing criterion
© 2007, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0
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