4,693 research outputs found
Efficient Portfolio Selection
Merak believed that an efficient frontier analysis method that combined the robustness of the Monte Carlo approach with the confidence of the Markowitz approach would be a very powerful tool for any industry. However, it soon became clear that there are other ways to address the problem that do not require a Monte Carlo component.
Three subgroups were formed, and each developed a different approach for solving the problem. These were the Portfolio Selection Algorithm Approach, the Statistical Inference Approach, and the Integer Programming Approach
The Goldman symplectic form on the PGL(V)-Hitchin component
This article is the second of a pair of articles about the Goldman symplectic
form on the PGL(V )-Hitchin component. We show that any ideal triangulation on
a closed connected surface of genus at least 2, and any compatible bridge
system determine a symplectic trivialization of the tangent bundle to the
Hitchin component. Using this, we prove that a large class of flows defined in
the companion paper [SWZ17] are Hamiltonian. We also construct an explicit
collection of Hamiltonian vector fields on the Hitchin component that give a
symplectic basis at every point. These are used to show that the global
coordinate system on the Hitchin component defined iin the companion paper is a
global Darboux coordinate system.Comment: 95 pages, 24 figures, Citations update
Coherent Control and Entanglement in the Attosecond Electron Recollision Dissociation of D2+
We examine the attosecond electron recollision dissociation of D2+ recently
demonstrated experimentally [H. Niikura et al., Nature (London) 421, 826
(2003)] from a coherent control perspective. In this process, a strong laser
field incident on D2 ionizes an electron, accelerates the electron in the laser
field to eV energies, and then drives the electron to recollide with the parent
ion, causing D2+ dissociation. A number of results are demonstrated. First, a
full dimensional Strong Field Approximation (SFA) model is constructed and
shown to be in agreement with the original experiment. This is then used to
rigorously demonstrate that the experiment is an example of coherent pump-dump
control. Second, extensions to bichromatic coherent control are proposed by
considering dissociative recollision of molecules prepared in a coherent
superposition of vibrational states. Third, by comparing the results to similar
scenarios involving field-free attosecond scattering of independently prepared
D2+ and electron wave packets, recollision dissociation is shown to provide an
example of wave-packet coherent control of reactive scattering. Fourth, this
analysis makes clear that it is the temporal correlations between the continuum
electron and D2+ wave packet, and not entanglement, that are crucial for the
sub-femtosecond probing resolution demonstrated in the experiment. This result
clarifies some misconceptions regarding the importance of entanglement in the
recollision probing of D2+. Finally, signatures of entanglement between the
recollision electron and the atomic fragments, detectable via coincidence
measurements, are identified
Rational points near planar curves and Diophantine approximation
In this paper, we establish asymptotic formulae with optimal errors for the
number of rational points that are close to a planar curve, which unify and
extend the results of Beresnevich-Dickinson-Velani and Vaughan-Velani.
Furthermore, we complete the Lebesgue theory of Diophantine approximation on
weakly non-degenerate planar curves that was initially developed by
Beresnevich-Zorin in the divergence case.Comment: 27 pages, corrected typos, to appear in Adv. Mat
Non-commutative deformation of Chern-Simons theory
The problem of the consistent definition of gauge theories living on the
non-commutative (NC) spaces with a non-constant NC parameter is
discussed. Working in the L formalism we specify the undeformed
theory, d abelian Chern-Simons, by setting the initial brackets.
The deformation is introduced by assigning the star commutator to the
bracket. For this initial set up we construct the corresponding L
structure which defines both the NC deformation of the abelian gauge
transformations and the field equations covariant under these transformations.
To compensate the violation of the Leibniz rule one needs the higher brackets
which are proportional to the derivatives of . Proceeding in the slowly
varying field approximation when the star commutator is approximated by the
Poisson bracket we derive the recurrence relations for the definition of these
brackets for arbitrary . For the particular case of -like NC
space we obtain an explicit all orders formulas for both NC gauge
transformations and NC deformation of Chern-Simons equations. The latter are
non-Lagrangian and are satisfied if the NC field strength vanishes everywhere.Comment: 33 pages, published version, exposition improved, new material
regarding the definition of the non-commutative field strength and the
treatment of the non-commutativity of general form adde
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