A New Family of Multistep Methods with Improved Phase Lag Characteristics for the Integration of Orbital Problems

In this work we introduce a new family of ten-step linear multistep methods for the integration of orbital problems. The new methods are constructed by adopting a new methodology which improves the phase lag characteristics by vanishing both the phase lag function and its first derivatives at a specific frequency. The efficiency of the new family of methods is proved via error analysis and numerical applications.Comment: 21 pages, 3 figures, 1 tabl

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

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

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