53,261 research outputs found
A geometry of information, I: Nerves, posets and differential forms
The main theme of this workshop (Dagstuhl seminar 04351) is `Spatial
Representation: Continuous vs. Discrete'. Spatial representation has two
contrasting but interacting aspects (i) representation of spaces' and (ii)
representation by spaces. In this paper, we will examine two aspects that are
common to both interpretations of the theme, namely nerve constructions and
refinement. Representations change, data changes, spaces change. We will
examine the possibility of a `differential geometry' of spatial representations
of both types, and in the sequel give an algebra of differential forms that has
the potential to handle the dynamical aspect of such a geometry. We will
discuss briefly a conjectured class of spaces, generalising the Cantor set
which would seem ideal as a test-bed for the set of tools we are developing.Comment: 28 pages. A version of this paper appears also on the Dagstuhl
seminar portal http://drops.dagstuhl.de/portals/04351
New Results for the MAP Problem in Bayesian Networks
This paper presents new results for the (partial) maximum a posteriori (MAP)
problem in Bayesian networks, which is the problem of querying the most
probable state configuration of some of the network variables given evidence.
First, it is demonstrated that the problem remains hard even in networks with
very simple topology, such as binary polytrees and simple trees (including the
Naive Bayes structure). Such proofs extend previous complexity results for the
problem. Inapproximability results are also derived in the case of trees if the
number of states per variable is not bounded. Although the problem is shown to
be hard and inapproximable even in very simple scenarios, a new exact algorithm
is described that is empirically fast in networks of bounded treewidth and
bounded number of states per variable. The same algorithm is used as basis of a
Fully Polynomial Time Approximation Scheme for MAP under such assumptions.
Approximation schemes were generally thought to be impossible for this problem,
but we show otherwise for classes of networks that are important in practice.
The algorithms are extensively tested using some well-known networks as well as
random generated cases to show their effectiveness.Comment: A couple of typos were fixed, as well as the notation in part of
section 4, which was misleading. Theoretical and empirical results have not
change
Breakup of Shearless Meanders and "Outer" Tori in the Standard Nontwist Map
The breakup of shearless invariant tori with winding number
(in continued fraction representation) of the
standard nontwist map is studied numerically using Greene's residue criterion.
Tori of this winding number can assume the shape of meanders (folded-over
invariant tori which are not graphs over the x-axis in phase space),
whose breakup is the first point of focus here. Secondly, multiple shearless
orbits of this winding number can exist, leading to a new type of breakup
scenario. Results are discussed within the framework of the renormalization
group for area-preserving maps. Regularity of the critical tori is also
investigated.Comment: submitted to Chao
A convergence acceleration operator for multiobjective optimisation
A novel multiobjective optimisation accelerator is
introduced that uses direct manipulation in objective space
together with neural network mappings from objective space to decision space. This operator is a portable component that can be hybridized with any multiobjective optimisation algorithm. The purpose of this Convergence Acceleration Operator (CAO) is to enhance the search capability and the speed of convergence of the host algorithm. The operator acts directly in objective space to suggest improvements to solutions obtained by a multiobjective evolutionary algorithm (MOEA). These suggested improved objective vectors are then mapped into decision variable space and tested. The CAO is incorporated with two leading MOEAs, the Non-Dominated Sorting Genetic Algorithm (NSGA-II) and the Strength Pareto Evolutionary Algorithm (SPEA2) and tested. Results show that the hybridized algorithms consistently improve the speed of convergence of the original algorithm whilst maintaining the desired distribution of solutions
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