151,055 research outputs found
Real-time modelling and interpolation of spatio-temporal marine pollution
Due to the complexity of the interactions
involved in various dynamic systems, known physical,
biological or chemical laws cannot adequately describe
the dynamics behind these processes. The study of these
systems thus depends on measurements often taken at
various discrete spatial locations through time by noisy
sensors. For this reason, scientists often necessitate interpolative, visualisation and analytical tools to deal
with the large volumes of data common to these systems. The starting point of this study is the seminal
research by C. Shannon on sampling and reconstruction
theory and its various extensions. Based on recent work
on the reconstruction of stochastic processes, this paper
develops a novel real-time estimation method for non-
stationary stochastic spatio-temporal behaviour based
on the Integro-Di erence Equation (IDE). This meth-
odology is applied to collected marine pollution data
from a Norwegian fjord. Comparison of the results obtained by the proposed method with interpolators from
state-of-the-art Geographical Information System (GIS)
packages will show, that signifi cantly superior results are
obtained by including the temporal evolution in the spatial interpolations.peer-reviewe
Active Semi-Supervised Learning Using Sampling Theory for Graph Signals
We consider the problem of offline, pool-based active semi-supervised
learning on graphs. This problem is important when the labeled data is scarce
and expensive whereas unlabeled data is easily available. The data points are
represented by the vertices of an undirected graph with the similarity between
them captured by the edge weights. Given a target number of nodes to label, the
goal is to choose those nodes that are most informative and then predict the
unknown labels. We propose a novel framework for this problem based on our
recent results on sampling theory for graph signals. A graph signal is a
real-valued function defined on each node of the graph. A notion of frequency
for such signals can be defined using the spectrum of the graph Laplacian
matrix. The sampling theory for graph signals aims to extend the traditional
Nyquist-Shannon sampling theory by allowing us to identify the class of graph
signals that can be reconstructed from their values on a subset of vertices.
This approach allows us to define a criterion for active learning based on
sampling set selection which aims at maximizing the frequency of the signals
that can be reconstructed from their samples on the set. Experiments show the
effectiveness of our method.Comment: 10 pages, 6 figures, To appear in KDD'1
On the metric character of the quantum Jensen-Shannon divergence
In a recent paper, the generalization of the Jensen Shannon divergence (JSD)
in the context of quantum theory has been studied (Phys. Rev. A 72, 052310
(2005)). This distance between quantum states has shown to verify several of
the properties required for a good distinguishability measure. Here we
investigate the metric character of this distance. More precisely we show,
formally for pure states and by means of simulations for mixed states, that its
square root verifies the triangle inequality.Comment: 8 pages, 1 figures, numerical results substantially improved in Sec.
III. To appear in Phys. Rev.
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