16 research outputs found
An Object Oriented Implemtation of Fractal Image Compression
The technique of Fractal Image Compression, although new, has been described in several ways. Thus far, all descriptions of this compression algorithm read by the author have been in procedural form. The purpose of this paper is to present the Fractal Image Compression algorithm in an object-oriented form and to point out the advantages of this organization. The main advantages of taking an object-oriented approach to this problem are flexibility and maintainability. Different aspects of this algorithm are handled by different objects, thereby allowing for easy customization and testing of each part. Another advantage of this approach is that the structure of objects serves as a tutorial for what the algorithm does. By examining the object structure, one can get a feel for the algorithm\u27s operation without studying the underlying mathematics
Preliminary investigations on the applicability of the fixed point transformations-based adaptive control for time-delayed systems
In this paper, for the first time, a possible tackling of the problem of known time-delay by the use of a Fixed Point Transformation-based adaptive controller is investigated. This approach at first transform the control task into a fixed point problem then solves it via iteration. The preliminary results that were obtained by numerical simulations for a strongly nonlinear controlled system, a van der Pol oscillator, are promising. It is expedient to make further, systematic investigations
Concentration of Measure Inequalities in Information Theory, Communications and Coding (Second Edition)
During the last two decades, concentration inequalities have been the subject
of exciting developments in various areas, including convex geometry,
functional analysis, statistical physics, high-dimensional statistics, pure and
applied probability theory, information theory, theoretical computer science,
and learning theory. This monograph focuses on some of the key modern
mathematical tools that are used for the derivation of concentration
inequalities, on their links to information theory, and on their various
applications to communications and coding. In addition to being a survey, this
monograph also includes various new recent results derived by the authors. The
first part of the monograph introduces classical concentration inequalities for
martingales, as well as some recent refinements and extensions. The power and
versatility of the martingale approach is exemplified in the context of codes
defined on graphs and iterative decoding algorithms, as well as codes for
wireless communication. The second part of the monograph introduces the entropy
method, an information-theoretic technique for deriving concentration
inequalities. The basic ingredients of the entropy method are discussed first
in the context of logarithmic Sobolev inequalities, which underlie the
so-called functional approach to concentration of measure, and then from a
complementary information-theoretic viewpoint based on transportation-cost
inequalities and probability in metric spaces. Some representative results on
concentration for dependent random variables are briefly summarized, with
emphasis on their connections to the entropy method. Finally, we discuss
several applications of the entropy method to problems in communications and
coding, including strong converses, empirical distributions of good channel
codes, and an information-theoretic converse for concentration of measure.Comment: Foundations and Trends in Communications and Information Theory, vol.
10, no 1-2, pp. 1-248, 2013. Second edition was published in October 2014.
ISBN to printed book: 978-1-60198-906-
A Mixed Hybrid Finite Volumes Solver for Robust Primal and Adjoint CFD
PhDIn the context of gradient-based numerical optimisation, the adjoint method is an e cient
way of computing the gradient of the cost function at a computational cost independent
of the number of design parameters, which makes it a captivating option for industrial
CFD applications involving costly primal solves. The method is however a ected by
instabilities, some of which are inherited from the primal solver, notably if the latter does
not fully converge. The present work is an attempt at curbing primal solver limitations
with the goal of indirectly alleviating adjoint robustness issues.
To that end, a novel discretisation scheme for the steady-state incompressible Navier-
Stokes problem is proposed: Mixed Hybrid Finite Volumes (MHFV). The scheme draws
inspiration from the family of Mimetic Finite Di erences and Mixed Virtual Elements
strategies, rid of some limitations and numerical artefacts typical of classical Finite Volumes
which may hinder convergence properties. Derivation of MHFV operators is illustrated
and each scheme is validated via manufactured solutions: rst for pure anisotropic
di usion problems, then convection-di usion-reaction and nally Navier-Stokes. Traditional
and novel Navier-Stokes solution algorithms are also investigated, adapted to
MHFV and compared in terms of performance.
The attention is then turned to the discrete adjoint Navier-Stokes system, which is assembled
in an automated way following the principles of Equational Di erentiation, i.e. the
di erentiation of the primal discrete equations themselves rather than the algorithm
used to solve them. Practical/computational aspects of the assembly are discussed, then
the adjoint gradient is validated and a few solution algorithms for the MHFV adjoint
Navier-Stokes are proposed and tested. Finally, two examples of full shape optimisation
procedures on internal ow test cases (S-bend and U-bend) are reported.European Union's Seventh Framework Programme
grant agreement number 317006