3,486 research outputs found
Commutator estimates in -algebras
Let be a -algebra and let be the algebra
of all locally measurable operators affiliated with . It is shown
that for any self-adjoint element there exists a
self-adjoint element from the center of , such that
for any there exists a unitary element from
, satisfying . A
corollary of this result is that for any derivation on
with the range in a (not necessarily norm-closed) ideal
, the derivation is inner, that is
, and . Similar results are
also obtained for inner derivations on .Comment: 30 page
Derivations in the Banach ideals of -compact operators
Let be a von Neumann algebra equipped with a faithful normal
semi-finite trace and let be the algebra of all
-compact operators affiliated with . Let be a symmetric operator space (on ) and let
be a symmetrically-normed Banach ideal of -compact
operators in . We study (i) derivations on
with the range in and (ii) derivations on the Banach algebra
. In the first case our main results assert that such derivations
are continuous (with respect to the norm topologies) and also inner (under some
mild assumptions on ). In the second case we show that any such
derivation is necessarily inner when is a type factor. As an
interesting application of our results for the case (i) we deduce that any
derivation from into an -space, ,
() associated with is inner
Temporal and Spatial Data Mining with Second-Order Hidden Models
In the frame of designing a knowledge discovery system, we have developed
stochastic models based on high-order hidden Markov models. These models are
capable to map sequences of data into a Markov chain in which the transitions
between the states depend on the \texttt{n} previous states according to the
order of the model. We study the process of achieving information extraction
fromspatial and temporal data by means of an unsupervised classification. We
use therefore a French national database related to the land use of a region,
named Teruti, which describes the land use both in the spatial and temporal
domain. Land-use categories (wheat, corn, forest, ...) are logged every year on
each site regularly spaced in the region. They constitute a temporal sequence
of images in which we look for spatial and temporal dependencies. The temporal
segmentation of the data is done by means of a second-order Hidden Markov Model
(\hmmd) that appears to have very good capabilities to locate stationary
segments, as shown in our previous work in speech recognition. Thespatial
classification is performed by defining a fractal scanning ofthe images with
the help of a Hilbert-Peano curve that introduces atotal order on the sites,
preserving the relation ofneighborhood between the sites. We show that the
\hmmd performs aclassification that is meaningful for the agronomists.Spatial
and temporal classification may be achieved simultaneously by means of a 2
levels \hmmd that measures the \aposteriori probability to map a temporal
sequence of images onto a set of hidden classes
Commutator estimates in -factors
Let be a -factor and let be
the space of all measurable operators affiliated with . It is
shown that for any self-adjoint element there exists a
scalar , such that for all , there
exists a unitary element from , satisfying
. A corollary
of this result is that for any derivation on with the
range in an ideal , the derivation is inner,
that is , and . Similar
results are also obtained for inner derivations on .Comment: 21 page
Mining Complex Hydrobiological Data with Galois Lattices
We have used Galois lattices for mining hydrobiological data. These data are
about macrophytes, that are macroscopic plants living in water bodies. These
plants are characterized by several biological traits, that own several
modalities. Our aim is to cluster the plants according to their common traits
and modalities and to find out the relations between traits. Galois lattices
are efficient methods for such an aim, but apply on binary data. In this
article, we detail a few approaches we used to transform complex
hydrobiological data into binary data and compare the first results obtained
thanks to Galois lattices
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