Abstract: One of the major challenges faced in solving initial and boundary problems is how to find approximate solutions with minimal deviation from the exact solution without so much rigor and complications. The Taylor series method provides a simple way of obtaining an infinite series which converges to the exact solution for initial value problems and this method of solution is somewhat limited for a two point boundary problem since the infinite series has to be truncated to include the boundary conditions. In this paper, the Ying Buzu Shu algorithm is used to solve a two point boundary nonlinear diffusion problem for the fourth and sixth order solution and compare their relative error and rate of convergence to the exact solution.
Abstract: In this paper, efforts were made to examine and compare the algorithmic iterative solutions of conjugate gradient method as against other methods such as Gauss-Seidel and Jacobi approaches for solving systems of linear equations of the form Ax = b, where A is a real n x n symmetric and positive definite matrix. We performed algorithmic iterative steps and obtained analytical solutions of a typical 3 x 3 symmetric and positive definite matrix using the three methods described in this paper (Gauss-Seidel, Jacobi and Conjugate Gradient methods) respectively. From the results obtained, we discovered that the Conjugate Gradient method converges faster to exact solutions in fewer iterative steps than the two other methods which took much iteration, much time and kept tending to the exact solutions.
Abstract: In this paper, a non-cooperative game method is
formulated where all players compete to transmit at higher
power. Every base station represents a player in the game.
The game is solved by obtaining the Nash equilibrium (NE)
where the game converges to optimality. The proposed method,
named Power Efficient Handover Game Theoretic (PEHO-GT)
approach, aims to control the handover in dense small cell
networks. Players optimize their payoff by adjusting the
transmission power to improve the performance in terms of
throughput, handover, power consumption and load balancing.
To select the desired transmission power for a player, the payoff
function considers the gain of increasing the transmission power.
Then, the cell selection takes place by deploying Technique for
Order Preference by Similarity to an Ideal Solution (TOPSIS).
A game theoretical method is implemented for heterogeneous
networks to validate the improvement obtained. Results reveal
that the proposed method gives a throughput improvement while
reducing the power consumption and minimizing the frequent
handover.
Abstract: Various processes are modelled using a discrete phase,
where particles are seeded from a source. Such particles can represent
liquid water droplets, which are affecting the continuous phase by
exchanging thermal energy, momentum, species etc. Discrete phases
are typically modelled using parcel, which represents a collection of
particles, which share properties such as temperature, velocity etc.
When coupling the phases, the exchange rates are integrated over
the cell, in which the parcel is located. This can cause spikes and
fluctuating exchange rates. This paper presents an alternative method of coupling a discrete
and a continuous plug flow phase. This is done using triangular
parcels, which span between nodes following the dynamics of single
droplets. Thus, the triangular parcels are propagated using the corner
nodes. At each time step, the exchange rates are spatially integrated
over the surface of the triangular parcels, which yields a smooth
continuous exchange rate to the continuous phase. The results shows that the method is more stable, converges
slightly faster and yields smooth exchange rates compared with
the steam tube approach. However, the computational requirements
are about five times greater, so the applicability of the alternative
method should be limited to processes, where the exchange rates are
important. The overall balances of the exchanged properties did not
change significantly using the new approach.
Abstract: Aiming at optimizing the weight and deflection of cantilever beam subjected to maximum stress and maximum deflection, Multi-objective Particle Swarm Optimization (MOPSO) with Utopia Point based local search is implemented. Utopia point is used to govern the search towards the Pareto Optimal set. The elite candidates obtained during the iterations are stored in an archive according to non-dominated sorting and also the archive is truncated based on least crowding distance. Local search is also performed on elite candidates and the most diverse particle is selected as the global best. This method is implemented on standard test functions and it is observed that the improved algorithm gives better convergence and diversity as compared to NSGA-II in fewer iterations. Implementation on practical structural problem shows that in 5 to 6 iterations, the improved algorithm converges with better diversity as evident by the improvement of cantilever beam on an average of 0.78% and 9.28% in the weight and deflection respectively compared to NSGA-II.
Abstract: The traditional k-means algorithm has been widely used as a simple and efficient clustering method. However, the algorithm often converges to local minima for the reason that it is sensitive to the initial cluster centers. In this paper, an algorithm for selecting initial cluster centers on the basis of minimum spanning tree (MST) is presented. The set of vertices in MST with same degree are regarded as a whole which is used to find the skeleton data points. Furthermore, a distance measure between the skeleton data points with consideration of degree and Euclidean distance is presented. Finally, MST-based initialization method for the k-means algorithm is presented, and the corresponding time complexity is analyzed as well. The presented algorithm is tested on five data sets from the UCI Machine Learning Repository. The experimental results illustrate the effectiveness of the presented algorithm compared to three existing initialization methods.
Abstract: Piecewise polynomial regression model is very flexible model for modeling the data. If the piecewise polynomial regression model is matched against the data, its parameters are not generally known. This paper studies the parameter estimation problem of piecewise polynomial regression model. The method which is used to estimate the parameters of the piecewise polynomial regression model is Bayesian method. Unfortunately, the Bayes estimator cannot be found analytically. Reversible jump MCMC algorithm is proposed to solve this problem. Reversible jump MCMC algorithm generates the Markov chain that converges to the limit distribution of the posterior distribution of piecewise polynomial regression model parameter. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of piecewise polynomial regression model.
Abstract: Large scale Indian manufacturers started
implementing Six Sigma to their supply core to fulfill the endless
need of high quality products. As well, they initiated encouraging
their suppliers to apply the well-ascertain SS management practice
and kept no resource for supplier enterprises, generally small midsized
enterprises to think for the admittance of Six Sigma as a quality
promotion drive. There are many issues to study for requisite changes
before the introduction of Six Sigma in auto SMEs. This paper
converges on impeding factors while implementing SS drive and also
pinpoints the gains achieved through successful implementation. The
result of this study suggest some operational guidelines for effective
implementation of Six Sigma from evidences acquired through
research questionnaire and interviews with industrial professionals,
apportioned to assort auto sector mid-sized enterprises (MSEs) in
India.
Abstract: Genetic algorithm is widely used in optimization
problems for its excellent global search capabilities and highly parallel
processing capabilities; but, it converges prematurely and has a poor
local optimization capability in actual operation. Simulated annealing
algorithm can avoid the search process falling into local optimum. A
hybrid genetic algorithm based on simulated annealing is designed by
combining the advantages of genetic algorithm and simulated
annealing algorithm. The numerical experiment represents the hybrid
genetic algorithm can be applied to solve the function optimization
problems efficiently.
Abstract: The customers use the best compromise criterion
between price and quality of service (QoS) to select or change
their Service Provider (SP). The SPs share the same market and
are competing to attract more customers to gain more profit. Due
to the divergence of SPs interests, we believe that this situation is a
non-cooperative game of price and QoS. The game converges to an
equilibrium position known Nash Equilibrium (NE). In this work, we
formulate a game theoretic framework for the dynamical behaviors
of SPs. We use Genetic Algorithms (GAs) to find the price and
QoS strategies that maximize the profit for each SP and illustrate
the corresponding strategy in NE. In order to quantify how this NE
point is performant, we perform a detailed analysis of the price of
anarchy induced by the NE solution. Finally, we provide an extensive
numerical study to point out the importance of considering price and
QoS as a joint decision parameter.
Abstract: In this article, we deal with a variant of the classical
course timetabling problem that has a practical application in many
areas of education. In particular, in this paper we are interested in
high schools remedial courses. The purpose of such courses is to
provide under-prepared students with the skills necessary to succeed
in their studies. In particular, a student might be under prepared in
an entire course, or only in a part of it. The limited availability
of funds, as well as the limited amount of time and teachers at
disposal, often requires schools to choose which courses and/or which
teaching units to activate. Thus, schools need to model the training
offer and the related timetabling, with the goal of ensuring the
highest possible teaching quality, by meeting the above-mentioned
financial, time and resources constraints. Moreover, there are some
prerequisites between the teaching units that must be satisfied. We
first present a Mixed-Integer Programming (MIP) model to solve
this problem to optimality. However, the presence of many peculiar
constraints contributes inevitably in increasing the complexity of
the mathematical model. Thus, solving it through a general-purpose
solver may be performed for small instances only, while solving
real-life-sized instances of such model requires specific techniques
or heuristic approaches. For this purpose, we also propose a heuristic
approach, in which we make use of a fast constructive procedure
to obtain a feasible solution. To assess our exact and heuristic
approaches we perform extensive computational results on both
real-life instances (obtained from a high school in Lecce, Italy) and
randomly generated instances. Our tests show that the MIP model is
never solved to optimality, with an average optimality gap of 57%.
On the other hand, the heuristic algorithm is much faster (in about the
50% of the considered instances it converges in approximately half of
the time limit) and in many cases allows achieving an improvement
on the objective function value obtained by the MIP model. Such an
improvement ranges between 18% and 66%.
Abstract: In this paper, we regard as a coded transmission over a
frequency-selective channel. We plan to study analytically the
convergence of the turbo-detector using a maximum a posteriori
(MAP) equalizer and a MAP decoder. We demonstrate that the
densities of the maximum likelihood (ML) exchanged during the
iterations are e-symmetric and output-symmetric. Under the Gaussian
approximation, this property allows to execute a one-dimensional
scrutiny of the turbo-detector. By deriving the analytical terminology
of the ML distributions under the Gaussian approximation, we confirm
that the bit error rate (BER) performance of the turbo-detector
converges to the BER performance of the coded additive white
Gaussian noise (AWGN) channel at high signal to noise ratio (SNR),
for any frequency selective channel.
Abstract: In this paper, we present new preconditioned modified accelerated overrelaxation (MAOR) method for solving linear systems. We compare the spectral radii of the iteration matrices of the preconditioned and the original methods. The comparison results show that the preconditioned MAOR method converges faster than the MAOR method whenever the MAOR method is convergent. Finally, we give one numerical example to confirm our theoretical results.
Abstract: This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.
Abstract: This paper is concerning the application of a deterministic decisional pattern to a multi-agent system which would provide intelligence to a distributed energy smart grid at local consumer level. Development of multi-agent application involves agent specifications, analysis, design and realization. It can be implemented by following several decisional patterns. The purpose of present article is to suggest a new approach to control the smart grid system in a decentralized competitive approach. The proposed algorithmic solution results from a deterministic dichotomous approach based on environment observation. It uses an iterative process to solve automatic learning problems. Through memory of collected past tries, the algorithm monotonically converges to very steep system operation point in attraction basin resulting from weak system nonlinearity. In this sense, system is given by (local) constitutive elementary rules the intelligence of its global existence so that it can self-organize toward optimal operating sequence.
Abstract: Multi-Radio Multi-Channel Wireless Mesh Networks (MRMC-WMNs) operate at the backbone to access and route high volumes of traffic simultaneously. Such roles demand high network capacity, and long “online" time at the expense of accelerated transmission energy depletion and poor connectivity. This is the problem of transmission power control. Numerous power control methods for wireless networks are in literature. However, contributions towards MRMC configurations still face many challenges worth considering. In this paper, an energy-efficient power selection protocol called PMMUP is suggested at the Link-Layer. This protocol first divides the MRMC-WMN into a set of unified channel graphs (UCGs). A UCG consists of multiple radios interconnected to each other via a common wireless channel. In each UCG, a stochastic linear quadratic cost function is formulated. Each user minimizes this cost function consisting of trade-off between the size of unification states and the control action. Unification state variables come from independent UCGs and higher layers of the protocol stack. The PMMUP coordinates power optimizations at the network interface cards (NICs) of wireless mesh routers. The proposed PMMUP based algorithm converges fast analytically with a linear rate. Performance evaluations through simulations confirm the efficacy of the proposed dynamic power control.
Abstract: One of the essential components of much of DSP
application is noise cancellation. Changes in real time signals are
quite rapid and swift. In noise cancellation, a reference signal which
is an approximation of noise signal (that corrupts the original
information signal) is obtained and then subtracted from the noise
bearing signal to obtain a noise free signal. This approximation of
noise signal is obtained through adaptive filters which are self
adjusting. As the changes in real time signals are abrupt, this needs
adaptive algorithm that converges fast and is stable. Least mean
square (LMS) and normalized LMS (NLMS) are two widely used
algorithms because of their plainness in calculations and
implementation. But their convergence rates are small. Adaptive
averaging filters (AFA) are also used because they have high
convergence, but they are less stable. This paper provides the
comparative study of LMS and Normalized NLMS, AFA and new
enhanced average adaptive (Average NLMS-ANLMS) filters for noise
cancelling application using speech signals.
Abstract: In the self-stabilizing algorithmic paradigm, each node has a local view of the system, in a finite amount of time the system converges to a global state with desired property. In a graph G =
(V, E), a subset S C V is a 2-packing if Vi c V: IN[i] n SI
Abstract: Topological changes in mobile ad hoc networks
frequently render routing paths unusable. Such recurrent path failures
have detrimental effects on quality of service. A suitable technique
for eliminating this problem is to use multiple backup paths between
the source and the destination in the network. This paper proposes an
effective and efficient protocol for backup and disjoint path set in ad
hoc wireless network. This protocol converges to a highly reliable
path set very fast with no message exchange overhead. The paths
selection according to this algorithm is beneficial for mobile ad hoc
networks, since it produce a set of backup paths with more high
reliability. Simulation experiments are conducted to evaluate the
performance of our algorithm in terms of route numbers in the path
set and its reliability. In order to acquire link reliability estimates, we
use link expiration time (LET) between two nodes.
Abstract: In this work, propagation of uncertainty during calibration
process of TRANUS, an integrated land use and transport model
(ILUTM), has been investigated. It has also been examined, through a
sensitivity analysis, which input parameters affect the variation of the
outputs the most. Moreover, a probabilistic verification methodology
of calibration process, which equates the observed and calculated
production, has been proposed. The model chosen as an application is
the model of the city of Grenoble, France. For sensitivity analysis and
uncertainty propagation, Monte Carlo method was employed, and a
statistical hypothesis test was used for verification. The parameters of
the induced demand function in TRANUS, were assumed as uncertain
in the present case. It was found that, if during calibration, TRANUS
converges, then with a high probability the calibration process is
verified. Moreover, a weak correlation was found between the inputs
and the outputs of the calibration process. The total effect of the
inputs on outputs was investigated, and the output variation was found
to be dictated by only a few input parameters.