|Commenced in January 1999 || Frequency: Monthly || Edition: International|| Paper Count: 18 |
Mathematical, Computational, Physical, Electrical and Computer Engineering
Algebraic Approach for the Reconstruction of Linear and Convolutional Error Correcting Codes
In this paper we present a generic approach for the problem of the blind estimation of the parameters of linear and convolutional error correcting codes. In a non-cooperative context, an adversary has only access to the noised transmission he has intercepted. The intercepter has no knowledge about the parameters used by the legal users. So, before having acess to the information he has first to blindly estimate the parameters of the error correcting code of the communication. The presented approach has the main advantage that the problem of reconstruction of such codes can be expressed in a very simple way. This allows us to evaluate theorical bounds on the complexity of the reconstruction process but also bounds on the estimation rate. We show that some classical reconstruction techniques are optimal and also explain why some of them have theorical complexities greater than these experimentally observed.
Group Similarity Transformation of a Time Dependent Chemical Convective Process
The time dependent progress of a chemical reaction over a flat horizontal plate is here considered. The problem is solved through the group similarity transformation method which reduces the number of independent by one and leads to a set of nonlinear ordinary differential equation. The problem shows a singularity at the chemical reaction order n=1 and is analytically solved through the perturbation method. The behavior of the process is then numerically investigated for n≠1 and different Schmidt numbers. Graphical results for the velocity and concentration of chemicals based on the analytical and numerical solutions are presented and discussed.
HIV Modelling - Parallel Implementation Strategies
We report on the development of a model to
understand why the range of experience with respect to HIV
infection is so diverse, especially with respect to the latency period.
To investigate this, an agent-based approach is used to extract highlevel
behaviour which cannot be described analytically from the set
of interaction rules at the cellular level. A network of independent
matrices mimics the chain of lymph nodes. Dealing with massively
multi-agent systems requires major computational effort. However,
parallelisation methods are a natural consequence and advantage of
the multi-agent approach and, using the MPI library, are here
implemented, tested and optimized. Our current focus is on the
various implementations of the data transfer across the network.
Three communications strategies are proposed and tested, showing
that the most efficient approach is communication based on the
natural lymph-network connectivity.
On the Flow of a Third Grade Viscoelastic Fluid in an Orthogonal Rheometer
The flow of a third grade fluid in an orthogonal rheometer is studied. We employ the admissible velocity field proposed in . We solve the problem and obtain the velocity field as well as the components for the Cauchy tensor. We compare the results with those from . Some diagrams concerning the velocity and Cauchy stress components profiles are presented for different values of material constants and compared with the corresponding values for a linear viscous fluid.
The Riemann Barycenter Computation and Means of Several Matrices
An iterative definition of any n variable mean function is given in this article, which iteratively uses the two-variable form of the corresponding two-variable mean function. This extension method omits recursivity which is an important improvement compared with certain recursive formulas given before by Ando-Li-Mathias, Petz- Temesi. Furthermore it is conjectured here that this iterative algorithm coincides with the solution of the Riemann centroid minimization problem. Certain simulations are given here to compare the convergence rate of the different algorithms given in the literature. These algorithms will be the gradient and the Newton mehod for the Riemann centroid computation.
On Diffusion Approximation of Discrete Markov Dynamical Systems
The paper is devoted to stochastic analysis of finite
dimensional difference equation with dependent on ergodic Markov
chain increments, which are proportional to small parameter ". A
point-form solution of this difference equation may be represented
as vertexes of a time-dependent continuous broken line given on the
segment [0,1] with "-dependent scaling of intervals between vertexes.
Tending " to zero one may apply stochastic averaging and diffusion
approximation procedures and construct continuous approximation of
the initial stochastic iterations as an ordinary or stochastic Ito differential
equation. The paper proves that for sufficiently small " these
equations may be successfully applied not only to approximate finite
number of iterations but also for asymptotic analysis of iterations,
when number of iterations tends to infinity.
A Two-Species Model for a Fishing System with Marine Protected Areas
A model of a system concerning one species of demersal
(inshore) fish and one of pelagic (offshore) fish undergoing fishing
restricted by marine protected areas is proposed in this paper. This
setup was based on the FISH-BE model applied to the Tabina fishery
in Zamboanga del Sur, Philippines. The components of the model
equations have been adapted from widely-accepted mechanisms in
population dynamics. The model employs Gompertz-s law of growth
and interaction on each type of protected and unprotected subpopulation.
Exchange coefficients between protected and unprotected
areas were assumed to be proportional to the relative area of the
entry region. Fishing harvests were assumed to be proportional to
both the number of fishers and the number of unprotected fish. An
extra term was included for the pelagic population to allow for the
exchange between the unprotected area and the outside environment.
The systems were found to be bounded for all parameter values. The
equations for the steady state were unsolvable analytically but the
existence and uniqueness of non-zero steady states can be proven.
Plots also show that an MPA size yielding the maximum steady state
of the unprotected population can be found. All steady states were
found to be globally asymptotically stable for the entire range of
Comparison of Finite Difference Schemes for Water Flow in Unsaturated Soils
Flow movement in unsaturated soil can be expressed
by a partial differential equation, named Richards equation. The
objective of this study is the finding of an appropriate implicit
numerical solution for head based Richards equation. Some of the
well known finite difference schemes (fully implicit, Crank Nicolson
and Runge-Kutta) have been utilized in this study. In addition, the
effects of different approximations of moisture capacity function,
convergence criteria and time stepping methods were evaluated. Two
different infiltration problems were solved to investigate the
performance of different schemes. These problems include of vertical
water flow in a wet and very dry soils. The numerical solutions of
two problems were compared using four evaluation criteria and the
results of comparisons showed that fully implicit scheme is better
than the other schemes. In addition, utilizing of standard chord slope
method for approximation of moisture capacity function, automatic
time stepping method and difference between two successive
iterations as convergence criterion in the fully implicit scheme can
lead to better and more reliable results for simulation of fluid
movement in different unsaturated soils.
Parallel Block Backward Differentiation Formulas for Solving Ordinary Differential Equations
A parallel block method based on Backward
Differentiation Formulas (BDF) is developed for the parallel solution
of stiff Ordinary Differential Equations (ODEs). Most common
methods for solving stiff systems of ODEs are based on implicit
formulae and solved using Newton iteration which requires repeated
solution of systems of linear equations with coefficient matrix, I -
hβJ . Here, J is the Jacobian matrix of the problem. In this paper,
the matrix operations is paralleled in order to reduce the cost of the
iterations. Numerical results are given to compare the speedup and
efficiency of parallel algorithm and that of sequential algorithm.
Direct Block Backward Differentiation Formulas for Solving Second Order Ordinary Differential Equations
In this paper, a direct method based on variable step
size Block Backward Differentiation Formula which is referred as
BBDF2 for solving second order Ordinary Differential Equations
(ODEs) is developed. The advantages of the BBDF2 method over the
corresponding sequential variable step variable order Backward
Differentiation Formula (BDFVS) when used to solve the same
problem as a first order system are pointed out. Numerical results are
given to validate the method.
Magnetohydrodynamic Damping of Natural Convection Flows in a Rectangular Enclosure
We numerically study the three-dimensional
magnetohydrodynamics (MHD) stability of oscillatory natural
convection flow in a rectangular cavity, with free top surface, filled
with a liquid metal, having an aspect ratio equal to A=L/H=5, and
subjected to a transversal temperature gradient and a uniform
magnetic field oriented in x and z directions. The finite volume
method was used in order to solve the equations of continuity,
momentum, energy, and potential. The stability diagram obtained in
this study highlights the dependence of the critical value of the
Grashof number Grcrit , with the increase of the Hartmann number
Ha for two orientations of the magnetic field. This study confirms
the possibility of stabilization of a liquid metal flow in natural
convection by application of a magnetic field and shows that the
flow stability is more important when the direction of magnetic field
is longitudinal than when the direction is transversal.
Local Error Control in the RK5GL3 Method
The RK5GL3 method is a numerical method for solving
initial value problems in ordinary differential equations, and is
based on a combination of a fifth-order Runge-Kutta method and
3-point Gauss-Legendre quadrature. In this paper we describe an
effective local error control algorithm for RK5GL3, which uses local
extrapolation with an eighth-order Runge-Kutta method in tandem
with RK5GL3, and a Hermite interpolating polynomial for solution
estimation at the Gauss-Legendre quadrature nodes.
Relationship between Sums of Squares in Linear Regression and Semi-parametric Regression
In this paper, the sum of squares in linear regression is
reduced to sum of squares in semi-parametric regression. We
indicated that different sums of squares in the linear regression are
similar to various deviance statements in semi-parametric regression.
In addition to, coefficient of the determination derived in linear
regression model is easily generalized to coefficient of the
determination of the semi-parametric regression model. Then, it is
made an application in order to support the theory of the linear
regression and semi-parametric regression. In this way, study is
supported with a simulated data example.
Error Propagation in the RK5GL3 Method
The RK5GL3 method is a numerical method for solving
initial value problems in ordinary differential equations, and is based
on a combination of a fifth-order Runge-Kutta method and 3-point
Gauss-Legendre quadrature. In this paper we describe the propagation
of local errors in this method, and show that the global order of
RK5GL3 is expected to be six, one better than the underlying Runge-
Architecture, Implementation and Application of Tools for Experimental Analysis
This paper presents an architecture to assist in the
development of tools to perform experimental analysis. Existing
implementations of tools based on this architecture are also described
in this paper. These tools are applied to the real world problem of
fault attack emulation and detection in cryptographic algorithms.
Comparison of Reliability Systems Based Uncertainty
Stochastic comparison has been an important
direction of research in various area. This can be done by the use of
the notion of stochastic ordering which gives qualitatitive rather than
purely quantitative estimation of the system under study. In this
paper we present applications of comparison based uncertainty
related to entropy in Reliability analysis, for example to design
better systems. These results can be used as a priori information in
Reflection of Plane Waves at Free Surface of an Initially Stressed Dissipative Medium
The paper discuses the effect of initial stresses on the reflection coefficients of plane waves in a dissipative medium. Basic governing equations are formulated in context of Biot's incremental deformation theory. These governing equations are solved analytically to obtain the dimensional phase velocities of plane waves propagating in plane of symmetry. Closed-form expressions for the reflection coefficients of P and SV waves- incident at the free surface of an initially stressed dissipative medium are obtained. Numerical computations, using these expressions, are carried out for a particular model. Computations made with the results predicted in presence and absence of the initial stresses and the results have been shown graphically. The study shows that the presence of compressive initial stresses increases the velocity of longitudinal wave (P-wave) but diminishes that of transverse wave (SV-wave). Also the numerical results presented indicate that initial stresses and dissipation might affect the reflection coefficients significantly.
Parallel Direct Integration Variable Step Block Method for Solving Large System of Higher Order Ordinary Differential Equations
The aim of this paper is to investigate the
performance of the developed two point block method designed for
two processors for solving directly non stiff large systems of higher
order ordinary differential equations (ODEs). The method calculates
the numerical solution at two points simultaneously and produces
two new equally spaced solution values within a block and it is
possible to assign the computational tasks at each time step to a
single processor. The algorithm of the method was developed in C
language and the parallel computation was done on a parallel shared
memory environment. Numerical results are given to compare the
efficiency of the developed method to the sequential timing. For
large problems, the parallel implementation produced 1.95 speed-up
and 98% efficiency for the two processors.