232,796 research outputs found
Discrete Elastic Inner Vector Spaces with Application in Time Series and Sequence Mining
This paper proposes a framework dedicated to the construction of what we call
discrete elastic inner product allowing one to embed sets of non-uniformly
sampled multivariate time series or sequences of varying lengths into inner
product space structures. This framework is based on a recursive definition
that covers the case of multiple embedded time elastic dimensions. We prove
that such inner products exist in our general framework and show how a simple
instance of this inner product class operates on some prospective applications,
while generalizing the Euclidean inner product. Classification experimentations
on time series and symbolic sequences datasets demonstrate the benefits that we
can expect by embedding time series or sequences into elastic inner spaces
rather than into classical Euclidean spaces. These experiments show good
accuracy when compared to the euclidean distance or even dynamic programming
algorithms while maintaining a linear algorithmic complexity at exploitation
stage, although a quadratic indexing phase beforehand is required.Comment: arXiv admin note: substantial text overlap with arXiv:1101.431
On Recursive Edit Distance Kernels with Application to Time Series Classification
This paper proposes some extensions to the work on kernels dedicated to
string or time series global alignment based on the aggregation of scores
obtained by local alignments. The extensions we propose allow to construct,
from classical recursive definition of elastic distances, recursive edit
distance (or time-warp) kernels that are positive definite if some sufficient
conditions are satisfied. The sufficient conditions we end-up with are original
and weaker than those proposed in earlier works, although a recursive
regularizing term is required to get the proof of the positive definiteness as
a direct consequence of the Haussler's convolution theorem. The classification
experiment we conducted on three classical time warp distances (two of which
being metrics), using Support Vector Machine classifier, leads to conclude
that, when the pairwise distance matrix obtained from the training data is
\textit{far} from definiteness, the positive definite recursive elastic kernels
outperform in general the distance substituting kernels for the classical
elastic distances we have tested.Comment: 14 page
Frame Indifferent Formulation of Maxwell's Elastic Fluid and the Rational Continuum Mechanics of the Electromagnetic Field
We show that the linearized equations of the incompressible elastic medium
admit a `Maxwell form' in which the shear component of the stress vector plays
the role of the electric field, and the vorticity plays the role of the
magnetic field. Conversely, the set of dynamic Maxwell equations are strict
mathematical corollaries from the governing equations of the incompressible
elastic medium. This suggests that the nature of `electromagnetic field' may
actually be related to an elastic continuous medium. The analogy is complete if
the medium is assumed to behave as fluid in shear motions, while it may still
behave as elastic solid under compressional motions. Then the governing
equations of the elastic fluid are re-derived in the Eulerian frame by
replacing the partial time derivatives by the properly invariant (frame
indifferent) time rates. The `Maxwell from' of the frame indifferent
formulation gives the frame indifferent system that is to replace the Maxwell
system. This new system comprises terms already present in the classical
Maxwell equations, alongside terms that are the progenitors of the
Biot--Savart, Oersted--Ampere's, and Lorentz--force laws. Thus a frame
indifferent (truly covariant) formulation of electromagnetism is achieved from
a single postulate that the electromagnetic field is a kind of elastic (partly
liquid partly solid) continuum.Comment: accepte
Analyzing power for the proton elastic scattering from neutron-rich 6He nucleus
Vector analyzing power for the proton-6He elastic scattering at 71
MeV/nucleon has been measured for the first time, with a newly developed
polarized proton solid target working at low magnetic field of 0.09 T. The
results are found to be incompatible with a t-matrix folding model prediction.
Comparisons of the data with g-matrix folding analyses clearly show that the
vector analyzing power is sensitive to the nuclear structure model used in the
reaction analysis. The alpha-core distribution in 6He is suggested to be a
possible key to understand the nuclear structure sensitivity.Comment: 5 pages, 3 figures, accepted for publication as a Rapid Communication
in Physical Review
$p+^{4,6,8}He elastic scattering at intermediate energies
Using a relativistic nuclear optical potential consisting of a Lorentz
scalar, , and the time-like component of a four-vector potential,
, we calculate elastic scattering differential cross sections and
polarizations for He at intermediate energies for which experimental
data are available. We also calculate the differential cross sections and
analyzing powers for He at intermediate energies and compare with the
few available experimental data.Comment: 09 pages, 04 figure
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