Title of Thesis: On Random Additive Perturbation for Privacy Preserving Data Mining Author: Souptik Datta, Master of Science, 2004 Thesis directed by: Dr. Hillol Kargupta, Associate Professor Department of Computer Science and Electrical Engineering Privacy is becoming an increasingly important issue in many data mining applications. This has triggered the development of many privacy-preserving...

With suitably chosen unperturbed Hamiltonians, we show numerical evidence of convergence of Rayleigh–Schrödinger perturbation expansions for low-lying eigenstates and the corresponding eigenenergies of the quartic, sextic, and octic anharmonic oscillators, when the anharmonic terms are not very strong. In obtaining the perturbation expansions, unperturbed Hamiltonians are taken as the diagonal ...

in this paper, first a new homotopy perturbation method for solving a fractional order nonlinear telegraph equation is introduced. by applying the proposed method, the nonlinear equation is translated to linear equations for per iteration of homotopy perturbation method. then, the obtained problems are solved with separation method. in the examples, it is illustrated that the exact solution is ...

While the determination of free-energy differences by MD simulation has become a standard procedure for which many techniques have been developed, total entropies and entropy differences are still hardly ever computed. An overview of techniques to determine entropy differences is given, and the accuracy and convergence behavior of five methods based on thermodynamic integration and perturbation...

Power series expansions naturally arise whenever solutions of ordinary differential equations are studied in the regime of perturbation theory. In the case of quasi-periodic solutions the issue of convergence of the series is plagued of the so-called small divisor problem. In this paper we review a method recently introduced to deal with such a problem, based on renormalisation group ideas and ...

Recently, several studies of non-Hermitian Hamiltonians having PT symmetry have been conducted. Most striking about these complex Hamiltonians is how closely their properties resemble those of conventional Hermitian Hamiltonians. This paper presents further evidence of the similarity of these Hamiltonians to Hermitian Hamiltonians by examining the summation of the divergent weak-coupling pertur...

We devise a non-Hermitian Rayleigh-Schrödinger perturbation theory for the singleand the multireference case to tackle both the many-body problem and the decay problem encountered, for example, in the study of electronic resonances in molecules. A complex absorbing potential (CAP) is employed to facilitate a treatment of resonance states that is similar to the well-established boundstate techni...

in this article, we demonstrate an analytic-numeric solution for some dynamical systems using the multistagehomotopy perturbation method. the method yields results that are in complete agreement with their numericalcounterparts.

In the present study, some perturbation methods are applied to Duffing equations having a displacement time-delayed variable to study the stability of such systems. Two approaches are considered to analyze Duffing oscillator having a strong delayed variable. The homotopy perturbation method is applied through the frequency analysis and nonlinear frequency is formulated as a function of all the ...

Dynamic programming problems are common in economics, finance and natural resource management. However, exact solutions to these problems are exceptional. Instead, solutions typically rely on numerical approximation techniques which vary in use, complexity and computational requirements. Perturbation, projection and linear programming approaches are among the most useful of these numerical tech...