89 research outputs found
Analytic Approach for Controlling Realistic Quantum Chaotic Systems
An analytic approach for controlling quantum states, which was originally
applied to fully random matrix systems [T. Takami and H. Fujisaki, Phys. Rev. E
75, 036219 (2007)], is extended to deal with more realistic quantum systems
with a banded random matrix (BRM). The validity of the new analytic field is
confirmed by directly solving the Schroedinger equation with a BRM interaction.
We find a threshold of the width of the BRM for the quantum control to be
successful.Comment: 4 pages with 4 PostScript figures, to appear in the Proceedings of
ICCMSE 2007 in a section of Symposium 8 "Quantum Control and Light-Matter
Interactions: Recent Computational and Theoretical Results
Will gravitational waves confirm Einstein's General Relativity?
Even if Einstein's General Relativity achieved a great success and overcame
lots of experimental tests, it also showed some shortcomings and flaws which
today advise theorists to ask if it is the definitive theory of gravity. In
this proceeding paper it is shown that, if advanced projects on the detection
of Gravitational Waves (GWs) will improve their sensitivity, allowing to
perform a GWs astronomy, accurate angular and frequency dependent response
functions of interferometers for GWs arising from various Theories of Gravity,
i.e. General Relativity and Extended Theories of Gravity, will be the ultimate
test for General Relativity. This proceeding paper is also a short review of
the Essay which won Honorable Mention at the 2009 Gravity Research Foundation
Awards.Comment: To appear in Proceedings of the 7th International Conference of
Numerical Analysis and Applied Mathematics, Rethymno, Crete (near to Chania),
Greece, 18-22 September 200
Reducing Spatial Data Complexity for Classification Models
Intelligent data analytics gradually becomes a day-to-day reality of today's businesses. However, despite rapidly
increasing storage and computational power current state-of-the-art predictive models still can not handle massive and noisy
corporate data warehouses. What is more adaptive and real-time operational environment requires multiple models to be
frequently retrained which fiirther hinders their use. Various data reduction techniques ranging from data sampling up to
density retention models attempt to address this challenge by capturing a summarised data structure, yet they either do
not account for labelled data or degrade the classification performance of the model trained on the condensed dataset. Our
response is a proposition of a new general framework for reducing the complexity of labelled data by means of controlled
spatial redistribution of class densities in the input space. On the example of Parzen Labelled Data Compressor (PLDC) we
demonstrate a simulatory data condensation process directly inspired by the electrostatic field interaction where the data are
moved and merged following the attracting and repelling interactions with the other labelled data. The process is controlled
by the class density function built on the original data that acts as a class-sensitive potential field ensuring preservation of
the original class density distributions, yet allowing data to rearrange and merge joining together their soft class partitions.
As a result we achieved a model that reduces the labelled datasets much further than any competitive approaches yet with
the maximum retention of the original class densities and hence the classification performance. PLDC leaves the reduced
dataset with the soft accumulative class weights allowing for efficient online updates and as shown in a series of experiments
if coupled with Parzen Density Classifier (PDC) significantly outperforms competitive data condensation methods in terms of
classification performance at the comparable compression levels
Fast cooling of trapped ions using the dynamical Stark shift gate
A laser cooling scheme for trapped ions is presented which is based on the
fast dynamical Stark shift gate, described in [Jonathan etal, PRA 62, 042307].
Since this cooling method does not contain an off resonant carrier transition,
low final temperatures are achieved even in traveling wave light field. The
proposed method may operate in either pulsed or continuous mode and is also
suitable for ion traps using microwave addressing in strong magnetic field
gradients.Comment: 4 pages 5 figure
Gravitomagnetic effect in gravitational waves
After an introduction emphasizing the importance of the gravitomag- netic
effect in general relativity, with a resume of some space-based appli- cations,
we discuss the so-called magnetic components of gravitational waves (GWs),
which have to be taken into account in the context of the total response
functions of interferometers for GWs propagating from ar- bitrary directions.Comment: To appear in Proceedings of the 7th International Conference of
Numerical Analysis and Applied Mathematics, Rethymno, Crete (near to Chania),
Greece, 18-22 September 200
Feedback Stabilization Methods for the Numerical Solution of Systems of Ordinary Differential Equations
In this work we study the problem of step size selection for numerical
schemes, which guarantees that the numerical solution presents the same
qualitative behavior as the original system of ordinary differential equations,
by means of tools from nonlinear control theory. Lyapunov-based and Small-Gain
feedback stabilization methods are exploited and numerous illustrating
applications are presented for systems with a globally asymptotically stable
equilibrium point. The obtained results can be used for the control of the
global discretization error as well.Comment: 33 pages, 9 figures. Submitted for possible publication to BIT
Numerical Mathematic
Matrix Structure Exploitation in Generalized Eigenproblems Arising in Density Functional Theory
In this short paper, the authors report a new computational approach in the
context of Density Functional Theory (DFT). It is shown how it is possible to
speed up the self-consistent cycle (iteration) characterizing one of the most
well-known DFT implementations: FLAPW. Generating the Hamiltonian and overlap
matrices and solving the associated generalized eigenproblems
constitute the two most time-consuming fractions of each iteration. Two
promising directions, implementing the new methodology, are presented that will
ultimately improve the performance of the generalized eigensolver and save
computational time.Comment: To appear in the proceedings of 8th International Conference on
Numerical Analysis and Applied Mathematics (ICNAAM 2010
The Jacobi-Maupertuis Principle in Variational Integrators
In this paper, we develop a hybrid variational integrator based on the Jacobi-Maupertuis Principle of Least Action. The Jacobi-Maupertuis principle states that for a mechanical system with total energy E and potential energy V(q), the curve traced out by the system on a constant energy surface minimizes the action given by ∫√[2(E-V(q))] ds where ds is the line element on the constant energy surface with respect to the kinetic energy of the system. The key feature is that the principle is a parametrization independent geodesic problem. We show that this principle can be combined with traditional variational integrators and can be used to efficiently handle high velocity regions where small time steps would otherwise be required. This is done by switching between the Hamilton principle and the Jacobi-Maupertuis principle depending upon the kinetic energy of the system. We demonstrate our technique for the Kepler problem and discuss some ongoing and future work in studying the energy and momentum behavior of the resulting integrator
A p-adic look at the Diophantine equation x^{2}+11^{2k}=y^{n}
We find all solutions of Diophantine equation x^{2}+11^{2k} = y^{n} where
x>=1, y>=1, n>=3 and k is natural number. We give p-adic interpretation of this
equation.Comment: 4 page
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