Evolutionary of Prostate Cancer Stem Cells in Prostate Duct
A systems approach model for prostate cancer in prostate duct, as a sub-system of the organism is developed. It is accomplished in two steps. First this research work starts with a nonlinear system of coupled Fokker-Plank equations which models continuous process of the system like motion of cells. Then extended to PDEs that include discontinuous processes like cell mutations, proliferation and deaths. The discontinuous processes is modeled by using intensity poisson processes. The model incorporates the features of the prostate duct. The system of PDEs spatial coordinate is along the proximal distal axis. Its parameters depend on features of the prostate duct. The movement of cells is biased towards distal region and mutations of prostate cancer cells is localized in the proximal region. Numerical solutions of the full system of equations are provided, and are exhibit traveling wave fronts phenomena. This motivates the use of the standard transformation to derive a canonically related system of ODEs for traveling wave solutions. The results obtained show persistence of prostate cancer by showing that the non-negative cone for the traveling wave system is time invariant. The traveling waves have a unique global attractor is proved also. Biologically, the global attractor verifies that evolution of prostate cancer stem cells exhibit the avascular tumor growth. These numerical solutions show that altering prostate stem cell movement or mutation of prostate cancer cells lead to avascular tumor. Conclusion with comments on clinical implications of the model is discussed.
Water Boundary Layer Flow Over Rotating Sphere with Mass Transfer
An analysis is performed to study the influence of nonuniform double slot suction on a steady laminar boundary layer flow over a rotating sphere when fluid properties such as viscosity and Prandtl number are inverse linear functions of temperature. Nonsimilar solutions have been obtained from the starting point of the streamwise co-ordinate to the exact point of separation. The difficulties arising at the starting point of the streamwise co-ordinate, at the edges of the slot and at the point of separation have been overcome by applying an implicit finite difference scheme in combination with the quasi-linearization technique and an appropriate selection of the finer step sizes along the stream-wise direction. The present investigation shows that the point of ordinary separation can be delayed by nonuniform double slot suction if the mass transfer rate is increased and also if the slots are positioned further downstream. In addition, the investigation reveals that double slot suction is found to be more effective compared to a single slot suction in delaying ordinary separation. As rotation parameter increase the point of separation moves upstream direction.
Numerical Algorithms for Solving a Type of Nonlinear Integro-Differential Equations
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
Finding Equilibrium in Transport Networks by Simulation and Investigation of Behaviors
The goal of this paper is to find Wardrop equilibrium
in transport networks at case of uncertainty situations, where the
uncertainty comes from lack of information. We use simulation tool
to find the equilibrium, which gives only approximate solution, but
this is sufficient for large networks as well. In order to take the
uncertainty into account we have developed an interval-based
procedure for finding the paths with minimal cost using the
Dempster-Shafer theory. Furthermore we have investigated the users-
behaviors using game theory approach, because their path choices
influence the costs of the other users- paths.
Computations of Bezier Geodesic-like Curves on Spheres
It is an important problem to compute the geodesics on
a surface in many fields. To find the geodesics in practice, however,
the traditional discrete algorithms or numerical approaches can only
find a list of discrete points. The first author proposed in 2010 a new,
elegant and accurate method, the geodesic-like method, for
approximating geodesics on a regular surface. This paper will present
by use of this method a computation of the Bezier geodesic-like curves
Visual Hull with Imprecise Input
Imprecision is a long-standing problem in CAD design
and high accuracy image-based reconstruction applications. The visual
hull which is the closed silhouette equivalent shape of the objects
of interest is an important concept in image-based reconstruction.
We extend the domain-theoretic framework, which is a robust and
imprecision capturing geometric model, to analyze the imprecision in
the output shape when the input vertices are given with imprecision.
Under this framework, we show an efficient algorithm to generate the
2D partial visual hull which represents the exact information of the
visual hull with only basic imprecision assumptions. We also show
how the visual hull from polyhedra problem can be efficiently solved
in the context of imprecise input.
On Minimum Cycle Bases of the Wreath Product of Wheels with Stars
The length of a cycle basis of a graph is the sum of the lengths of its elements. A minimum cycle basis is a cycle basis with minimum length. In this work, a construction of a minimum cycle basis for the wreath product of wheels with stars is presented. Moreover, the length of minimum cycle basis and the length of its longest cycle are calculated.
Estimation of Bayesian Sample Size for Binomial Proportions Using Areas P-tolerance with Lowest Posterior Loss
This paper uses p-tolerance with the lowest posterior
loss, quadratic loss function, average length criteria, average
coverage criteria, and worst outcome criterion for computing of
sample size to estimate proportion in Binomial probability function
with Beta prior distribution. The proposed methodology is examined,
and its effectiveness is shown.
Multi-labeled Data Expressed by a Set of Labels
Collected data must be organized to be utilized efficiently, and hierarchical classification of data is efficient approach to organize data. When data is classified to multiple categories or annotated with a set of labels, users request multi-labeled data by giving a set of labels. There are several interpretations of the data expressed by a set of labels. This paper discusses which data is expressed by a set of labels by introducing orders for sets of labels and shows that there are four types of orders, which are characterized by whether the labels of expressed data includes every label of the given set of labels within the range of the set. Desirable properties of the orders, data is also expressed by the higher set of labels and different sets of labels express different data, are discussed for the orders.
Lightning Protection Systems Design for Substations by Using Masts and Matlab
The economical criterion is accounted as the objective
function to develop a computer program for designing lightning
protection systems for substations by using masts and Matlab in this
work. Masts are needed to be placed at desired locations; the program
will then show mast heights whose sum is the smallest, i.e. satisfies
the economical criterion. The program is helpful for engineers to
quickly design a lightning protection system for a substation. To
realize this work, methodology and limited conditions of the program,
as well as an example of the program result, were described in this
Comparative Studies of Support Vector Regression between Reproducing Kernel and Gaussian Kernel
Support vector regression (SVR) has been regarded
as a state-of-the-art method for approximation and regression. The
importance of kernel function, which is so-called admissible support
vector kernel (SV kernel) in SVR, has motivated many studies
on its composition. The Gaussian kernel (RBF) is regarded as a
“best" choice of SV kernel used by non-expert in SVR, whereas
there is no evidence, except for its superior performance on some
practical applications, to prove the statement. Its well-known that
reproducing kernel (R.K) is also a SV kernel which possesses many
important properties, e.g. positive definiteness, reproducing property
and composing complex R.K by simpler ones. However, there are a
limited number of R.Ks with explicit forms and consequently few
quantitative comparison studies in practice. In this paper, two R.Ks,
i.e. SV kernels, composed by the sum and product of a translation
invariant kernel in a Sobolev space are proposed. An exploratory
study on the performance of SVR based general R.K is presented
through a systematic comparison to that of RBF using multiple
criteria and synthetic problems. The results show that the R.K is
an equivalent or even better SV kernel than RBF for the problems
with more input variables (more than 5, especially more than 10) and
Solution of Density Dependent Nonlinear Reaction-Diffusion Equation Using Differential Quadrature Method
In this study, the density dependent nonlinear reactiondiffusion
equation, which arises in the insect dispersal models, is
solved using the combined application of differential quadrature
method(DQM) and implicit Euler method. The polynomial based
DQM is used to discretize the spatial derivatives of the problem. The
resulting time-dependent nonlinear system of ordinary differential
equations(ODE-s) is solved by using implicit Euler method. The
computations are carried out for a Cauchy problem defined by a onedimensional
density dependent nonlinear reaction-diffusion equation
which has an exact solution. The DQM solution is found to be in a
very good agreement with the exact solution in terms of maximum
absolute error. The DQM solution exhibits superior accuracy at large
time levels tending to steady-state. Furthermore, using an implicit
method in the solution procedure leads to stable solutions and larger
time steps could be used.
Certain Estimates of Oscillatory Integrals and Extrapolation
In this paper we study the boundedness properties of
certain oscillatory integrals with polynomial phase. We obtain sharp
estimates for these oscillatory integrals. By the virtue of these
estimates and extrapolation we obtain Lp boundedness for these
oscillatory integrals under rather weak size conditions on the kernel
A Novel Microarray Biclustering Algorithm
Biclustering aims at identifying several biclusters that
reveal potential local patterns from a microarray matrix. A bicluster is
a sub-matrix of the microarray consisting of only a subset of genes
co-regulates in a subset of conditions. In this study, we extend the
motif of subspace clustering to present a K-biclusters clustering (KBC)
algorithm for the microarray biclustering issue. Besides minimizing
the dissimilarities between genes and bicluster centers within all
biclusters, the objective function of the KBC algorithm additionally
takes into account how to minimize the residues within all biclusters
based on the mean square residue model. In addition, the objective
function also maximizes the entropy of conditions to stimulate more
conditions to contribute the identification of biclusters. The KBC
algorithm adopts the K-means type clustering process to efficiently
make the partition of K biclusters be optimized. A set of experiments
on a practical microarray dataset are demonstrated to show the
performance of the proposed KBC algorithm.
Numerical Optimization Design of PEM Fuel Cell Performance Applying the Taguchi Method
The purpose of this paper is applied Taguchi method on the optimization for PEMFC performance, and a representative Computational Fluid Dynamics (CFD) model is selectively performed for statistical analysis. The studied factors in this paper are pressure of fuel cell, operating temperature, the relative humidity of anode and cathode, porosity of gas diffusion electrode (GDE) and conductivity of GDE. The optimal combination for maximum power density is gained by using a three-level statistical method. The results confirmed that the robustness of the optimum design parameters influencing the performance of fuel cell are founded by pressure of fuel cell, 3atm; operating temperature, 353K; the relative humidity of anode, 50%; conductivity of GDE, 1000 S/m, but the relative humidity of cathode and porosity of GDE are pooled as error due to a small sum of squares. The present simulation results give designers the ideas ratify the effectiveness of the proposed robust design methodology for the performance of fuel cell.
On the Robust Stability of Homogeneous Perturbed Large-Scale Bilinear Systems with Time Delays and Constrained Inputs
The stability test problem for homogeneous large-scale perturbed bilinear time-delay systems subjected to constrained inputs is considered in this paper. Both nonlinear uncertainties and interval systems are discussed. By utilizing the Lyapunove equation approach associated with linear algebraic techniques, several delay-independent criteria are presented to guarantee the robust stability of the overall systems. The main feature of the presented results is that although the Lyapunov stability theorem is used, they do not involve any Lyapunov equation which may be unsolvable. Furthermore, it is seen the proposed schemes can be applied to solve the stability analysis problem of large-scale time-delay systems.
On the Use of Correlated Binary Model in Social Network Analysis
In social network analysis the mean nodal degree and
density of the graph can be considered as a measure of the activity of
all actors in the network and this is an important property of a graph
and for making comparisons among networks. Since subjects in a
family or organization are subject to common environment factors, it
is prime interest to study the association between responses.
Therefore, we study the distribution of the mean nodal degree and
density of the graph under correlated binary units. The cross product
ratio is used to capture the intra-units association among subjects.
Computer program and an application are given to show the benefits
of the method.
Species Spreading due to Environmental Hostility, Dispersal Adaptation and Allee Effects
A phenomenological model for species spreading which incorporates the Allee effect, a species- maximum attainable growth rate, collective dispersal rate and dispersal adaptability is presented. This builds on a well-established reaction-diffusion model for spatial spreading of invading organisms. The model is phrased in terms of the “hostility" (which quantifies the Allee threshold in relation to environmental sustainability) and dispersal adaptability (which measures how a species is able to adapt its migratory response to environmental conditions). The species- invading/retreating speed and the sharpness of the invading boundary are explicitly characterised in terms of the fundamental parameters, and analysed in detail.
A Two-Channel Secure Communication Using Fractional Chaotic Systems
In this paper, a two-channel secure communication
using fractional chaotic systems is presented. Conditions for chaos
synchronization have been investigated theoretically by using Laplace
transform. To illustrate the effectiveness of the proposed scheme, a
numerical example is presented. The keys, key space, key selection
rules and sensitivity to keys are discussed in detail. Results show that
the original plaintexts have been well masked in the ciphertexts yet
recovered faithfully and efficiently by the present schemes.
Bifurcation Analysis of Horizontal Platform System
Horizontal platform system (HPS) is popularly applied
in offshore and earthquake technology, but it is difficult and
time-consuming for regulation. In order to understand the nonlinear
dynamic behavior of HPS and reduce the cost when using it, this paper
employs differential transformation method to study the bifurcation
behavior of HPS. The numerical results reveal a complex dynamic
behavior comprising periodic, sub-harmonic, and chaotic responses.
Furthermore, the results reveal the changes which take place in the
dynamic behavior of the HPS as the external torque is increased.
Therefore, the proposed method provides an effective means of
gaining insights into the nonlinear dynamics of horizontal platform
Parameter Selections of Fuzzy C-Means Based on Robust Analysis
The weighting exponent m is called the fuzzifier that
can have influence on the clustering performance of fuzzy c-means
(FCM) and m├Ä[1.5,2.5] is suggested by Pal and Bezdek . In this
paper, we will discuss the robust properties of FCM and show that the
parameter m will have influence on the robustness of FCM. According
to our analysis, we find that a large m value will make FCM more
robust to noise and outliers. However, if m is larger than the theoretical
upper bound proposed by Yu et al. , the sample mean will become
the unique optimizer. Here, we suggest to implement the FCM
algorithm with m├Ä[1.5,4] under the restriction when m is smaller
than the theoretical upper bound.
Three Computational Mathematics Techniques: Comparative Determination of Area under Curve
The objective of this manuscript is to find area under the plasma concentration- time curve (AUC) for multiple doses of salbutamol sulphate sustained release tablets (Ventolin® oral tablets SR 8 mg, GSK, Pakistan) in the group of 18 healthy adults by using computational mathematics techniques. Following the administration of 4 doses of Ventolin® tablets 12 hourly to 24 healthy human subjects and bioanalysis of obtained plasma samples, plasma drug concentration-time profile was constructed. AUC, an important pharmacokinetic parameter, was measured using integrated equation of multiple oral dose regimens. The approximated AUC was also calculated by using computational mathematics techniques such as repeated rectangular, repeated trapezium and repeated Simpson's rule and compared with exact value of AUC calculated by using integrated equation of multiple oral dose regimens to find best computational mathematics method that gives AUC values closest to exact. The exact values of AUC for four consecutive doses of Ventolin® oral tablets were 150.5819473, 157.8131756, 164.4178231 and 162.78 ng.h/ml while the closest values approximated AUC values were 149.245962, 157.336171, 164.2585768 and 162.289224 ng.h/ml, respectively as found by repeated rectangular rule. The errors in the approximated values of AUC were negligible. It is concluded that all computational tools approximated values of AUC accurately but the repeated rectangular rule gives slightly better approximated values of AUC as compared to repeated trapezium and repeated Simpson's rules.
Self-evolving Artificial Immune System via Developing T and B Cell for Permutation Flow-shop Scheduling Problems
Artificial Immune System is applied as a Heuristic
Algorithm for decades. Nevertheless, many of these applications
took advantage of the benefit of this algorithm but seldom proposed
approaches for enhancing the efficiency. In this paper, a
Self-evolving Artificial Immune System is proposed via developing
the T and B cell in Immune System and built a self-evolving
mechanism for the complexities of different problems. In this
research, it focuses on enhancing the efficiency of Clonal selection
which is responsible for producing Affinities to resist the invading of
Antigens. T and B cell are the main mechanisms for Clonal
Selection to produce different combinations of Antibodies.
Therefore, the development of T and B cell will influence the
efficiency of Clonal Selection for searching better solution.
Furthermore, for better cooperation of the two cells, a co-evolutional
strategy is applied to coordinate for more effective productions of
Antibodies. This work finally adopts Flow-shop scheduling
instances in OR-library to validate the proposed algorithm.
The Distance between a Point and a Bezier Curveon a Bezier Surface
The distance between two objects is an important
problem in CAGD, CAD and CG etc. It will be presented in this paper
that a simple and quick method to estimate the distance between a
point and a Bezier curve on a Bezier surface.