5,794 research outputs found
On the representations and -equivariant normal form for solenoidal Hopf-zero singularities
In this paper, we deal with the solenoidal conservative Lie algebra
associated to the classical normal form of Hopf-zero singular system. We
concentrate on the study of some representations and -equivariant
normal form for such singular differential equations. First, we list some of
the representations that this Lie algebra admits. The vector fields from this
Lie algebra could be expressed by the set of ordinary differential equations
where the first two of them are in the canonical form of a one-degree of
freedom Hamiltonian system and the third one depends upon the first two
variables. This representation is governed by the associated Poisson algebra to
one sub-family of this Lie algebra. Euler's form, vector potential, and Clebsch
representation are other representations of this Lie algebra that we list here.
We also study the non-potential property of vector fields with Hopf-zero
singularity from this Lie algebra. Finally, we examine the unique normal form
with non-zero cubic terms of this family in the presence of the symmetry group
. The theoretical results of normal form theory are illustrated
with the modified Chua's oscillator
A Quasi-Newton Method for Large Scale Support Vector Machines
This paper adapts a recently developed regularized stochastic version of the
Broyden, Fletcher, Goldfarb, and Shanno (BFGS) quasi-Newton method for the
solution of support vector machine classification problems. The proposed method
is shown to converge almost surely to the optimal classifier at a rate that is
linear in expectation. Numerical results show that the proposed method exhibits
a convergence rate that degrades smoothly with the dimensionality of the
feature vectors.Comment: 5 pages, To appear in International Conference on Acoustics, Speech,
and Signal Processing (ICASSP) 201
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