62 research outputs found
Shape recognition and classification in electro-sensing
This paper aims at advancing the field of electro-sensing. It exhibits the
physical mechanism underlying shape perception for weakly electric fish. These
fish orient themselves at night in complete darkness by employing their active
electrolocation system. They generate a stable, high-frequency, weak electric
field and perceive the transdermal potential modulations caused by a nearby
target with different admittivity than the surrounding water. In this paper, we
explain how weakly electric fish might identify and classify a target, knowing
by advance that the latter belongs to a certain collection of shapes. Our model
of the weakly electric fish relies on differential imaging, i.e., by forming an
image from the perturbations of the field due to targets, and physics-based
classification. The electric fish would first locate the target using a
specific location search algorithm. Then it could extract, from the
perturbations of the electric field, generalized (or high-order) polarization
tensors of the target. Computing, from the extracted features, invariants under
rigid motions and scaling yields shape descriptors. The weakly electric fish
might classify a target by comparing its invariants with those of a set of
learned shapes. On the other hand, when measurements are taken at multiple
frequencies, the fish might exploit the shifts and use the spectral content of
the generalized polarization tensors to dramatically improve the stability with
respect to measurement noise of the classification procedure in
electro-sensing. Surprisingly, it turns out that the first-order polarization
tensor at multiple frequencies could be enough for the purpose of
classification. A procedure to eliminate the background field in the case where
the permittivity of the surrounding medium can be neglected, and hence improve
further the stability of the classification process, is also discussed.Comment: 10 pages, 15 figure
Target Identification Using Dictionary Matching of Generalized Polarization Tensors
The aim of this paper is to provide a fast and efficient procedure for
(real-time) target identification in imaging based on matching on a dictionary
of precomputed generalized polarization tensors (GPTs). The approach is based
on some important properties of the GPTs and new invariants. A new shape
representation is given and numerically tested in the presence of measurement
noise. The stability and resolution of the proposed identification algorithm is
numerically quantified.Comment: Keywords: generalized polarization tensors, target identification,
shape representation, stability analysis. Submitted to Foundations of
Computational Mathematic
Thomas Decomposition of Algebraic and Differential Systems
In this paper we consider disjoint decomposition of algebraic and non-linear
partial differential systems of equations and inequations into so-called simple
subsystems. We exploit Thomas decomposition ideas and develop them into a new
algorithm. For algebraic systems simplicity means triangularity, squarefreeness
and non-vanishing initials. For differential systems the algorithm provides not
only algebraic simplicity but also involutivity. The algorithm has been
implemented in Maple
Modeling active electrolocation in weakly electric fish
In this paper, we provide a mathematical model for the electrolocation in
weakly electric fishes. We first investigate the forward complex conductivity
problem and derive the approximate boundary conditions on the skin of the fish.
Then we provide a dipole approximation for small targets away from the fish.
Based on this approximation, we obtain a non-iterative location search
algorithm using multi-frequency measurements. We present numerical experiments
to illustrate the performance and the stability of the proposed multi-frequency
location search algorithm. Finally, in the case of disk- and ellipse-shaped
targets, we provide a method to reconstruct separately the conductivity, the
permittivity, and the size of the targets from multi-frequency measurements.Comment: 37 pages, 11 figure
Symbolic Methods for Chemical Reaction Networks (Dagstuhl Seminar 12462)
During 11-16 November 2012, the Dagstuhl Seminar 12462 "Symbolic Methods for Chemical Reaction Networks" was held in Schloss Dagstuhl - Leibneiz Center for Informatics. The seminar brought together researchers in symbolic computation, chemical engineering, and systems biology. During the seminar, participants presented ïŹve-minute talks introducing their research interests, ïŹve participants gave longer talks, and all participants had the opportunity to take part in various discussion groups. Abstracts of presentations and summaries of the discussion groups are compiled in this report
Lattices of quantized vortices in polariton superfluids
In this review, we will focus on the description of the recent studies conducted in the
quest for the observation of lattices of quantized vortices in resonantly injected polariton
superfluids. In particular, we will show how the implementation of optical traps for
polaritons allows for the realization of vortexâantivortex lattices in confined geometries
and how the development of a flexible method to inject a controlled orbital angular
momentum (OAM) in such systems results in the observation of patterns of same-sign
vortices
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