Abstract: 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.
Abstract: HSDPA is a new feature which is introduced in
Release-5 specifications of the 3GPP WCDMA/UTRA standard to
realize higher speed data rate together with lower round-trip times.
Moreover, the HSDPA concept offers outstanding improvement of
packet throughput and also significantly reduces the packet call
transfer delay as compared to Release -99 DSCH. Till now the
HSDPA system uses turbo coding which is the best coding technique
to achieve the Shannon limit. However, the main drawbacks of turbo
coding are high decoding complexity and high latency which makes
it unsuitable for some applications like satellite communications,
since the transmission distance itself introduces latency due to
limited speed of light. Hence in this paper it is proposed to use LDPC
coding in place of Turbo coding for HSDPA system which decreases
the latency and decoding complexity. But LDPC coding increases the
Encoding complexity. Though the complexity of transmitter
increases at NodeB, the End user is at an advantage in terms of
receiver complexity and Bit- error rate. In this paper LDPC Encoder
is implemented using “sparse parity check matrix" H to generate a
codeword at Encoder and “Belief Propagation algorithm "for LDPC
decoding .Simulation results shows that in LDPC coding the BER
suddenly drops as the number of iterations increase with a small
increase in Eb/No. Which is not possible in Turbo coding. Also same
BER was achieved using less number of iterations and hence the
latency and receiver complexity has decreased for LDPC coding.
HSDPA increases the downlink data rate within a cell to a theoretical
maximum of 14Mbps, with 2Mbps on the uplink. The changes that
HSDPA enables includes better quality, more reliable and more
robust data services. In other words, while realistic data rates are
only a few Mbps, the actual quality and number of users achieved
will improve significantly.
Abstract: Many algorithms are available for sorting the unordered elements. Most important of them are Bubble sort, Heap sort, Insertion sort and Shell sort. These algorithms have their own pros and cons. Shell Sort which is an enhanced version of insertion sort, reduces the number of swaps of the elements being sorted to minimize the complexity and time as compared to insertion sort. Shell sort improves the efficiency of insertion sort by quickly shifting values to their destination. Average sort time is O(n1.25), while worst-case time is O(n1.5). It performs certain iterations. In each iteration it swaps some elements of the array in such a way that in last iteration when the value of h is one, the number of swaps will be reduced. Donald L. Shell invented a formula to calculate the value of ?h?. this work focuses to identify some improvement in the conventional Shell sort algorithm. ''Enhanced Shell Sort algorithm'' is an improvement in the algorithm to calculate the value of 'h'. It has been observed that by applying this algorithm, number of swaps can be reduced up to 60 percent as compared to the existing algorithm. In some other cases this enhancement was found faster than the existing algorithms available.
Abstract: In this paper, various algorithms for designing quadrature mirror filter are reviewed and a new algorithm is presented for the design of near perfect reconstruction quadrature mirror filter bank. In the proposed algorithm, objective function is formulated using the perfect reconstruction condition or magnitude response condition of prototype filter at frequency (ω = 0.5π) in ideal condition. The cutoff frequency is iteratively changed to adjust the filters coefficients using optimization algorithm. The performances of the proposed algorithm are evaluated in term of computation time, reconstruction error and number of iterations. The design examples illustrate that the proposed algorithm is superior in term of peak reconstruction error, computation time, and number of iterations. The proposed algorithm is simple, easy to implement, and linear in nature.
Abstract: Encryption and decryption in RSA are done by modular exponentiation which is achieved by repeated modular multiplication. Hence efficiency of modular multiplication directly determines the efficiency of RSA cryptosystem. This paper designs a Modified Montgomery Modular Multiplication in which addition of operands is computed by 4:2 compressor. The basic logic operations in addition are partitioned over two iterations such that parallel computations are performed. This reduces the critical path delay of proposed Montgomery design. The proposed design and RSA are implemented on Virtex 2 and Virtex 5 FPGAs. The two factors partitioning and parallelism have improved the frequency and throughput of proposed design.
Abstract: The response surface methodology (RSM) is a
collection of mathematical and statistical techniques useful in the
modeling and analysis of problems in which the dependent variable
receives the influence of several independent variables, in order to
determine which are the conditions under which should operate these
variables to optimize a production process. The RSM estimated a
regression model of first order, and sets the search direction using the
method of maximum / minimum slope up / down MMS U/D.
However, this method selects the step size intuitively, which can
affect the efficiency of the RSM. This paper assesses how the step
size affects the efficiency of this methodology. The numerical
examples are carried out through Monte Carlo experiments,
evaluating three response variables: efficiency gain function, the
optimum distance and the number of iterations. The results in the
simulation experiments showed that in response variables efficiency
and gain function at the optimum distance were not affected by the
step size, while the number of iterations is found that the efficiency if
it is affected by the size of the step and function type of test used.
Abstract: A complex valued neural network is a neural network
which consists of complex valued input and/or weights and/or thresholds
and/or activation functions. Complex-valued neural networks
have been widening the scope of applications not only in electronics
and informatics, but also in social systems. One of the most important
applications of the complex valued neural network is in signal
processing. In Neural networks, generalized mean neuron model
(GMN) is often discussed and studied. The GMN includes a new
aggregation function based on the concept of generalized mean of all
the inputs to the neuron. This paper aims to present exhaustive results
of using Generalized Mean Neuron model in a complex-valued neural
network model that uses the back-propagation algorithm (called
-Complex-BP-) for learning. Our experiments results demonstrate the
effectiveness of a Generalized Mean Neuron Model in a complex
plane for signal processing over a real valued neural network. We
have studied and stated various observations like effect of learning
rates, ranges of the initial weights randomly selected, error functions
used and number of iterations for the convergence of error required on
a Generalized Mean neural network model. Some inherent properties
of this complex back propagation algorithm are also studied and
discussed.
Abstract: In this study, a new root-finding method for solving nonlinear equations is proposed. This method requires two starting values that do not necessarily bracketing a root. However, when the starting values are selected to be close to a root, the proposed method converges to the root quicker than the secant method. Another advantage over all iterative methods is that; the proposed method usually converges to two distinct roots when the given function has more than one root, that is, the odd iterations of this new technique converge to a root and the even iterations converge to another root. Some numerical examples, including a sine-polynomial equation, are solved by using the proposed method and compared with results obtained by the secant method; perfect agreements are found.
Abstract: In this paper a new approach for transmission pricing
is presented. The main idea is voltage angle allocation, i.e.
determining the contribution of each contract on the voltage angle of
each bus. DC power flow is used to compute a primary solution for
angle decomposition. To consider the impacts of system non-linearity
on angle decomposition, the primary solution is corrected in different
iterations of decoupled Newton-Raphson power flow. Then, the
contribution of each contract on power flow of each transmission line
is computed based on angle decomposition. Contract-related flows
are used as a measure for “extent of use" of transmission network
capacity and consequently transmission pricing. The presented
approach is applied to a 4-bus test system and IEEE 30-bus test
system.
Abstract: Simultaneous transient conduction and radiation heat
transfer with heat generation is investigated. Analysis is carried out
for both steady and unsteady situations. two-dimensional gray
cylindrical enclosure with an absorbing, emitting, and isotropically
scattering medium is considered. Enclosure boundaries are assumed
at specified temperatures. The heat generation rate is considered
uniform and constant throughout the medium. The lattice Boltzmann
method (LBM) was used to solve the energy equation of a transient
conduction-radiation heat transfer problem. The control volume finite
element method (CVFEM) was used to compute the radiative
information. To study the compatibility of the LBM for the energy
equation and the CVFEM for the radiative transfer equation, transient
conduction and radiation heat transfer problems in 2-D cylindrical
geometries were considered. In order to establish the suitability of the
LBM, the energy equation of the present problem was also solved
using the the finite difference method (FDM) of the computational
fluid dynamics. The CVFEM used in the radiative heat transfer was
employed to compute the radiative information required for the
solution of the energy equation using the LBM or the FDM (of the
CFD). To study the compatibility and suitability of the LBM for the
solution of energy equation and the CVFEM for the radiative
information, results were analyzed for the effects of various
parameters such as the boundary emissivity. The results of the LBMCVFEM
combination were found to be in excellent agreement with
the FDM-CVFEM combination. The number of iterations and the
steady state temperature in both of the combinations were found
comparable. Results are found for situations with and without heat
generation. Heat generation is found to have significant bearing on
temperature distribution.
Abstract: Based on Traub-s methods for solving nonlinear
equation f(x) = 0, we develop two families of third-order
methods for solving system of nonlinear equations F(x) = 0. The
families include well-known existing methods as special cases.
The stability is corroborated by numerical results. Comparison
with well-known methods shows that the present methods are
robust. These higher order methods may be very useful in the
numerical applications requiring high precision in their computations
because these methods yield a clear reduction in number of iterations.
Abstract: In this paper, we present two new one-step iterative
methods based on Thiele-s continued fraction for solving nonlinear
equations. By applying the truncated Thiele-s continued fraction
twice, the iterative methods are obtained respectively. Analysis of
convergence shows that the new methods are fourth-order convergent.
Numerical tests verifying the theory are given and based on the
methods, two new one-step iterations are developed.
Abstract: In this article two algorithms, one based on variation iteration method and the other on Adomian's decomposition method, are developed to find the numerical solution of an initial value problem involving the non linear integro differantial equation where R is a nonlinear operator that contains partial derivatives with respect to x. Special cases of the integro-differential equation are solved using the algorithms. The numerical solutions are compared with analytical solutions. The results show that these two methods are efficient and accurate with only two or three iterations
Abstract: The decoding of Low-Density Parity-Check (LDPC) codes is operated over a redundant structure known as the bipartite graph, meaning that the full set of bit nodes is not absolutely necessary for decoder convergence. In 2008, Soyjaudah and Catherine designed a recovery algorithm for LDPC codes based on this assumption and showed that the error-correcting performance of their codes outperformed conventional LDPC Codes. In this work, the use of the recovery algorithm is further explored to test the performance of LDPC codes while the number of iterations is progressively increased. For experiments conducted with small blocklengths of up to 800 bits and number of iterations of up to 2000, the results interestingly demonstrate that contrary to conventional wisdom, the error-correcting performance keeps increasing with increasing number of iterations.
Abstract: The conjugate gradient optimization algorithm
usually used for nonlinear least squares is presented and is
combined with the modified back propagation algorithm yielding
a new fast training multilayer perceptron (MLP) algorithm
(CGFR/AG). The approaches presented in the paper consist of
three steps: (1) Modification on standard back propagation
algorithm by introducing gain variation term of the activation
function, (2) Calculating the gradient descent on error with
respect to the weights and gains values and (3) the determination
of the new search direction by exploiting the information
calculated by gradient descent in step (2) as well as the previous
search direction. The proposed method improved the training
efficiency of back propagation algorithm by adaptively modifying
the initial search direction. Performance of the proposed method
is demonstrated by comparing to the conjugate gradient algorithm
from neural network toolbox for the chosen benchmark. The
results show that the number of iterations required by the
proposed method to converge is less than 20% of what is required
by the standard conjugate gradient and neural network toolbox
algorithm.
Abstract: A novel typical day prediction model have been built and validated by the measured data of a grid-connected solar photovoltaic (PV) system in Macau. Unlike conventional statistical method used by previous study on PV systems which get results by averaging nearby continuous points, the present typical day statistical method obtain the value at every minute in a typical day by averaging discontinuous points at the same minute in different days. This typical day statistical method based on discontinuous point averaging makes it possible for us to obtain the Gaussian shape dynamical distributions for solar irradiance and output power in a yearly or monthly typical day. Based on the yearly typical day statistical analysis results, the maximum possible accumulated output energy in a year with on site climate conditions and the corresponding optimal PV system running time are obtained. Periodic Gaussian shape prediction models for solar irradiance, output energy and system energy efficiency have been built and their coefficients have been determined based on the yearly, maximum and minimum monthly typical day Gaussian distribution parameters, which are obtained from iterations for minimum Root Mean Squared Deviation (RMSD). With the present model, the dynamical effects due to time difference in a day are kept and the day to day uncertainty due to weather changing are smoothed but still included. The periodic Gaussian shape correlations for solar irradiance, output power and system energy efficiency have been compared favorably with data of the PV system in Macau and proved to be an improvement than previous models.