In this talk, I will present a large margin method for hierarchical
classification. The main focus here is to utilize the dependency
structure among classes to improve the classification performance of
flat classification. In such a situation, flat classification is
infeasible in the presence of a large number of dependent classes, which
occurs often in gene function discovery. Various hierarchical losses
will be discussed, in addition to an application to
gene function prediction.

In my talk, I will talk about , on one hand,how to use elliptic function theory to construct solutions of a specific mean field equation on torus, when the parameters are integer multiples of 4 pi. On the other hand, the PDE deep theory of bubbling analysis can be applied to obtain results related to the function theory on torus, for example, we can prove the Green function of torus has at most five critical points. Open problems of this aspect is also discussed.

We discuss joint work with Jon Chaika and Helge Krueger. The main result concerns explicit criteria for the absence of absolutely continuous spectrum for Schrodinger operators whose potentials are generated by an interval exchange transformation. In particular, we provide the first example of an invertible ergodic transformation of a compact metric space for which the associated Schrodinger operators have purely singular spectrum for every non-constant continuous sampling function.

The concept of time reversal (TR) of scalar wave is reexamined
from basic principles. Five different time reversal
mirrors (TRM) are introduced and their relations are analyzed.

The asymptotic analysis of the near-field focusing property is
presented. It is shown that to have a subwavelength focal spot
the TRM should involve dipole fields. The monopole TR is
extremely ineffective to focus below wavelength as the focal
spot size decreases logarithmically with the distance between
the source and TRM.

Contrary to the matched field processing and the phase processor,
both of which resemble TR, TR in a weak- or non-scattering medium
is usually biased in the longitudinal direction. This is true for
all five TR schemes. On the other hand, the TR focal spot has
been shown repeatedly in the literature, both theoretically and
experimentally, to be centered at the source point when the
medium is multiply scattering. A reconciliation of the two
seemingly conflicting results is found in the random fluctuations
in the intensity of the Green function for a multiply scattering
medium and the notion of scattering-enlarged effective aperture.

This is a report on a joint work with Isabelle Catto, Norbert Mauser and Saber Trabelsi. The Multiconfiguration time dependent Hartree Fock Method (MCTDHF) is a nonlinear approximation of a linear system of /N/ quantum particles with binary interaction. It combines the principle of the Hartree Fock and the Galerkin approximation. The main difficulty is the introduction of a global (in space) density matrix $\Gamma(t) $ which may degenerate. By construction this approximation formally preserves the mass and the energy of the system. The conservation of energy can be used to balance the singularities Coulomb potential and to provide sufficient conditions for the global in time invertibility of $\Gamma(t)$.

In numerical computations this matrix is very often regularized (changed into $\Gamma(t) +\epsilon(t)$). In this situation the energy is no more conserved
and the mathematical analysis done in $L^2$ relies on Strichartz type estimates.