**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**1501

# Search results for: probability matrix.

##### 1501 A Computer Model of Quantum Field Theory

**Authors:**
Hans H. Diel

**Abstract:**

This paper describes a computer model of Quantum Field Theory (QFT), referred to in this paper as QTModel. After specifying the initial configuration for a QFT process (e.g. scattering) the model generates the possible applicable processes in terms of Feynman diagrams, the equations for the scattering matrix, and evaluates probability amplitudes for the scattering matrix and cross sections. The computations of probability amplitudes are performed numerically. The equations generated by QTModel are provided for demonstration purposes only. They are not directly used as the base for the computations of probability amplitudes. The computer model supports two modes for the computation of the probability amplitudes: (1) computation according to standard QFT, and (2) computation according to a proposed functional interpretation of quantum theory.

**Keywords:**
Computational Modeling,
Simulation of Quantum Theory,
Quantum Field Theory,
Quantum Electrodynamics

##### 1500 Computation of Probability Coefficients using Binary Decision Diagram and their Application in Test Vector Generation

**Authors:**
Ashutosh Kumar Singh,
Anand Mohan

**Abstract:**

**Keywords:**
Binary Decision Diagrams,
Spectral Coefficients,
Fault detection

##### 1499 On Generalized New Class of Matrix Polynomial Set

**Authors:**
Ghazi S. Kahmmash

**Abstract:**

New generalization of the new class matrix polynomial set have been obtained. An explicit representation and an expansion of the matrix exponential in a series of these matrix are given for these matrix polynomials.

**Keywords:**
Generating functions,
Recurrences relation and Generalization of the new class matrix polynomial set.

##### 1498 The Partial Non-combinatorially Symmetric N10 -Matrix Completion Problem

**Authors:**
Gu-Fang Mou,
Ting-Zhu Huang

**Abstract:**

An n×n matrix is called an N1 0 -matrix if all principal minors are non-positive and each entry is non-positive. In this paper, we study the partial non-combinatorially symmetric N1 0 -matrix completion problems if the graph of its specified entries is a transitive tournament or a double cycle. In general, these digraphs do not have N1 0 -completion. Therefore, we have given sufficient conditions that guarantee the existence of the N1 0 -completion for these digraphs.

**Keywords:**
Matrix completion,
matrix completion,
N10 -matrix,
non-combinatorially symmetric,
cycle,
digraph.

##### 1497 Fuzzy Adjacency Matrix in Graphs

**Authors:**
Mahdi Taheri,
Mehrana Niroumand

**Abstract:**

**Keywords:**
Graph,
adjacency matrix,
fuzzy numbers

##### 1496 Inverse Matrix in the Theory of Dynamic Systems

**Authors:**
R. Masarova,
M. Juhas,
B. Juhasova,
Z. Sutova

**Abstract:**

**Keywords:**
Dynamic system,
transfer matrix,
inverse matrix,
modeling.

##### 1495 New Multisensor Data Fusion Method Based on Probabilistic Grids Representation

**Authors:**
Zhichao Zhao,
Yi Liu,
Shunping Xiao

**Abstract:**

A new data fusion method called joint probability density matrix (JPDM) is proposed, which can associate and fuse measurements from spatially distributed heterogeneous sensors to identify the real target in a surveillance region. Using the probabilistic grids representation, we numerically combine the uncertainty regions of all the measurements in a general framework. The NP-hard multisensor data fusion problem has been converted to a peak picking problem in the grids map. Unlike most of the existing data fusion method, the JPDM method dose not need association processing, and will not lead to combinatorial explosion. Its convergence to the CRLB with a diminishing grid size has been proved. Simulation results are presented to illustrate the effectiveness of the proposed technique.

**Keywords:**
Cramer-Rao lower bound (CRLB),
data fusion,
probabilistic grids,
joint probability density matrix,
localization,
sensor network.

##### 1494 Numerical Treatment of Matrix Differential Models Using Matrix Splines

**Authors:**
Kholod M. Abualnaja

**Abstract:**

This paper consider the solution of the matrix differential models using quadratic, cubic, quartic, and quintic splines. Also using the Taylor’s and Picard’s matrix methods, one illustrative example is included.

**Keywords:**
Matrix Splines,
Cubic Splines,
Quartic Splines.

##### 1493 The Relationship of Eigenvalues between Backward MPSD and Jacobi Iterative Matrices

**Authors:**
Zhuan-de Wang,
Hou-biao Li,
Zhong-xi Gao

**Abstract:**

In this paper, the backward MPSD (Modified Preconditioned Simultaneous Displacement) iterative matrix is firstly proposed. The relationship of eigenvalues between the backward MPSD iterative matrix and backward Jacobi iterative matrix for block p-cyclic case is obtained, which improves and refines the results in the corresponding references.

**Keywords:**
Backward MPSD iterative matrix,
Jacobi iterative matrix,
eigenvalue,
p-cyclic matrix.

##### 1492 On Positive Definite Solutions of Quaternionic Matrix Equations

**Authors:**
Minghui Wang

**Abstract:**

**Keywords:**
Matrix equation,
Quaternionic matrix,
Real representation,
positive (semi)definite solutions.

##### 1491 Connectivity Estimation from the Inverse Coherence Matrix in a Complex Chaotic Oscillator Network

**Authors:**
Won Sup Kim,
Xue-Mei Cui,
Seung Kee Han

**Abstract:**

We present on the method of inverse coherence matrix for the estimation of network connectivity from multivariate time series of a complex system. In a model system of coupled chaotic oscillators, it is shown that the inverse coherence matrix defined as the inverse of cross coherence matrix is proportional to the network connectivity. Therefore the inverse coherence matrix could be used for the distinction between the directly connected links from indirectly connected links in a complex network. We compare the result of network estimation using the method of the inverse coherence matrix with the results obtained from the coherence matrix and the partial coherence matrix.

**Keywords:**
Chaotic oscillator,
complex network,
inverse coherence matrix,
network estimation.

##### 1490 Solving Linear Matrix Equations by Matrix Decompositions

**Authors:**
Yongxin Yuan,
Kezheng Zuo

**Abstract:**

In this paper, a system of linear matrix equations is considered. A new necessary and sufficient condition for the consistency of the equations is derived by means of the generalized singular-value decomposition, and the explicit representation of the general solution is provided.

**Keywords:**
Matrix equation,
Generalized inverse,
Generalized
singular-value decomposition.

##### 1489 The Convergence Results between Backward USSOR and Jacobi Iterative Matrices

**Authors:**
Zuan-De Wang,
Hou-biao Li,
Zhong-xi Gao

**Abstract:**

In this paper, the backward Ussor iterative matrix is proposed. The relationship of convergence between the backward Ussor iterative matrix and Jacobi iterative matrix is obtained, which makes the results in the corresponding references be improved and refined.Moreover,numerical examples also illustrate the effectiveness of these conclusions.

**Keywords:**
Backward USSOR iterative matrix,
Jacobi iterative matrix,
convergence,
spectral radius

##### 1488 An Algorithm of Ordered Schur Factorization For Real Nonsymmetric Matrix

**Authors:**
Lokendra K. Balyan

**Abstract:**

**Keywords:**
Schur Factorization,
Eigenvalues of nonsymmetric matrix,
Orthoganal matrix.

##### 1487 Tree Sign Patterns of Small Order that Allow an Eventually Positive Matrix

**Authors:**
Ber-Lin Yu,
Jie Cui,
Hong Cheng,
Zhengfeng Yu

**Abstract:**

**Keywords:**
Eventually positive matrix,
sign pattern,
tree.

##### 1486 Numerical Simulation of Effect of Various Rib Configurations on Enhancing Heat Transfer of Matrix Cooling Channel

**Authors:**
Seok Min Choi,
Minho Bang,
Seuong Yun Kim,
Hyungmin Lee,
Won-Gu Joo,
Hyung Hee Cho

**Abstract:**

**Keywords:**
Matrix cooling,
rib,
heat transfer,
gas turbine.

##### 1485 The Possibility-Probability Relationship for Bloodstream Concentrations of Physiologically Active Substances

**Authors:**
Arkady Bolotin

**Abstract:**

**Keywords:**
Possibility distributions,
possibility-probability relationship.

##### 1484 Bounds on the Second Stage Spectral Radius of Graphs

**Authors:**
S.K.Ayyaswamy,
S.Balachandran,
K.Kannan

**Abstract:**

Let G be a graph of order n. The second stage adjacency matrix of G is the symmetric n × n matrix for which the ijth entry is 1 if the vertices vi and vj are of distance two; otherwise 0. The sum of the absolute values of this second stage adjacency matrix is called the second stage energy of G. In this paper we investigate a few properties and determine some upper bounds for the largest eigenvalue.

**Keywords:**
Second stage spectral radius,
Irreducible matrix,
Derived graph

##### 1483 An Overview of Handoff Techniques in Cellular Networks

**Authors:**
Nasıf Ekiz,
Tara Salih,
Sibel Küçüköner,
Kemal Fidanboylu

**Abstract:**

Continuation of an active call is one of the most important quality measurements in the cellular systems. Handoff process enables a cellular system to provide such a facility by transferring an active call from one cell to another. Different approaches are proposed and applied in order to achieve better handoff service. The principal parameters used to evaluate handoff techniques are: forced termination probability and call blocking probability. The mechanisms such as guard channels and queuing handoff calls decrease the forced termination probability while increasing the call blocking probability. In this paper we present an overview about the issues related to handoff initiation and decision and discuss about different types of handoff techniques available in the literature.

**Keywords:**
Handoff,
Forced Termination Probability,
Blocking probability,
Handoff Initiation,
Handoff Decision,
Handoff Prioritization Schemes.

##### 1482 Some New Subclasses of Nonsingular H-matrices

**Authors:**
Guangbin Wang,
Liangliang Li,
Fuping Tan

**Abstract:**

In this paper, we obtain some new subclasses of non¬singular H-matrices by using a diagonally dominant matrix

**Keywords:**
H-matrix,
diagonal dominance,
a diagonally dominant matrix.

##### 1481 Performance of Block Codes Using the Eigenstructure of the Code Correlation Matrixand Soft-Decision Decoding of BPSK

**Authors:**
Vitalice K. Oduol,
C. Ardil

**Abstract:**

A method is presented for obtaining the error probability for block codes. The method is based on the eigenvalueeigenvector properties of the code correlation matrix. It is found that under a unary transformation and for an additive white Gaussian noise environment, the performance evaluation of a block code becomes a one-dimensional problem in which only one eigenvalue and its corresponding eigenvector are needed in the computation. The obtained error rate results show remarkable agreement between simulations and analysis.

**Keywords:**
bit error rate,
block codes,
code correlation matrix,
eigenstructure,
soft-decision decoding,
weight vector.

##### 1480 Redundancy Component Matrix and Structural Robustness

**Authors:**
Xinjian Kou,
Linlin Li,
Yongju Zhou,
Jimian Song

**Abstract:**

We introduce the redundancy matrix that expresses clearly the geometrical/topological configuration of the structure. With the matrix, the redundancy of the structure is resolved into redundant components and assigned to each member or rigid joint. The values of the diagonal elements in the matrix indicates the importance of the corresponding members or rigid joints, and the geometrically correlations can be shown with the non-diagonal elements. If a member or rigid joint failures, reassignment of the redundant components can be calculated with the recursive method given in the paper. By combining the indexes of reliability and redundancy components, we define an index concerning the structural robustness. To further explain the properties of the redundancy matrix, we cited several examples of statically indeterminate structures, including two trusses and a rigid frame. With the examples, some simple results and the properties of the matrix are discussed. The examples also illustrate that the redundancy matrix and the relevant concepts are valuable in structural safety analysis.

**Keywords:**
Structural robustness,
structural reliability,
redundancy component,
redundancy matrix.

##### 1479 Newton-Raphson State Estimation Solution Employing Systematically Constructed Jacobian Matrix

**Authors:**
Nursyarizal Mohd Nor,
Ramiah Jegatheesan,
Perumal Nallagownden

**Abstract:**

**Keywords:**
State Estimation (SE),
Weight Least Square (WLS),
Newton-Raphson State Estimation (NRSE),
Jacobian matrix H.

##### 1478 Determination of Sensitive Transmission Lines Due to the Effect of Protection System Hidden Failure in a Critical System Cascading Collapse

**Authors:**
N. A. Salim,
M. M. Othman,
I. Musirin,
M. S. Serwan

**Abstract:**

Protection system hidden failures have been identified as one of the main causes of system cascading collapse resulting to power system instability. In this paper, a systematic approach is presented in order to identify the probability of a system cascading collapse by taking into consideration the effect of protection system hidden failure. This includes the accurate calculation of the probability of hidden failure as it will provide significant impinge on the findings of the probability of system cascading collapse. The probability of a system cascading collapse is then used to identify the initial tripping of sensitive transmission lines which will contribute to a critical system cascading collapse. Based on the results obtained from this study, it is important to decide on the accurate value of the hidden failure probability as it will affect the probability of a system cascading collapse.

**Keywords:**
Critical system cascading collapse,
hidden failure,
probability of cascading collapse,
sensitive transmission lines.

##### 1477 Conjugate Gradient Algorithm for the Symmetric Arrowhead Solution of Matrix Equation AXB=C

**Authors:**
Minghui Wang,
Luping Xu,
Juntao Zhang

**Abstract:**

*AXB=C*and the associate optimal approximation problem are considered for the symmetric arrowhead matrix solutions in the premise of consistency. The convergence results of the method are presented. At last, a numerical example is given to illustrate the efficiency of this method.

**Keywords:**
Iterative method,
symmetric arrowhead matrix,
conjugate gradient algorithm.

##### 1476 An Approaching Index to Evaluate a forward Collision Probability

**Authors:**
Yuan-Lin Chen

**Abstract:**

This paper presents an approaching forward collision probability index (AFCPI) for alerting and assisting driver in keeping safety distance to avoid the forward collision accident in highway driving. The time to collision (TTC) and time headway (TH) are used to evaluate the TTC forward collision probability index (TFCPI) and the TH forward collision probability index (HFCPI), respectively. The Mamdani fuzzy inference algorithm is presented combining TFCPI and HFCPI to calculate the approaching collision probability index of the vehicle. The AFCPI is easier to understand for the driver who did not even have any professional knowledge in vehicle professional field. At the same time, the driver’s behavior is taken into account for suiting each driver. For the approaching index, the value 0 is indicating the 0% probability of forward collision, and the values 0.5 and 1 are indicating the 50% and 100% probabilities of forward collision, respectively. The AFCPI is useful and easy-to-understand for alerting driver to avoid the forward collision accidents when driving in highway.

**Keywords:**
Approaching index,
forward collision probability,
time to collision,
time headway.

##### 1475 Ruin Probability for a Markovian Risk Model with Two-type Claims

**Authors:**
Dongdong Zhang,
Deran Zhang

**Abstract:**

In this paper, a Markovian risk model with two-type claims is considered. In such a risk model, the occurrences of the two type claims are described by two point processes {Ni(t), t ¸ 0}, i = 1, 2, where {Ni(t), t ¸ 0} is the number of jumps during the interval (0, t] for the Markov jump process {Xi(t), t ¸ 0} . The ruin probability ª(u) of a company facing such a risk model is mainly discussed. An integral equation satisfied by the ruin probability ª(u) is obtained and the bounds for the convergence rate of the ruin probability ª(u) are given by using key-renewal theorem.

**Keywords:**
Risk model,
ruin probability,
Markov jump process,
integral equation.

##### 1474 Membership Surface and Arithmetic Operations of Imprecise Matrix

**Authors:**
Dhruba Das

**Abstract:**

**Keywords:**
Imprecise number,
Imprecise vector,
Membership
surface,
Imprecise matrix.

##### 1473 On the Positive Definite Solutions of Nonlinear Matrix Equation

**Authors:**
Tian Baoguang,
Liang Chunyan,
Chen Nan

**Abstract:**

In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case r>-δ_{i} are discussed. An algorithm that avoids matrix inversion with the case -1<-δ_{i}<0 is proposed.

**Keywords:**
Nonlinear matrix equation,
Positive definite solution,
The maximal-minimal solution,
Iterative method,
Free-inversion

##### 1472 Application of Adaptive Genetic Algorithm in Function Optimization

**Authors:**
Panpan Xu,
Shulin Sui

**Abstract:**

The crossover probability and mutation probability are the two important factors in genetic algorithm. The adaptive genetic algorithm can improve the convergence performance of genetic algorithm, in which the crossover probability and mutation probability are adaptively designed with the changes of fitness value. We apply adaptive genetic algorithm into a function optimization problem. The numerical experiment represents that adaptive genetic algorithm improves the convergence speed and avoids local convergence.

**Keywords:**
Genetic algorithm,
Adaptive genetic algorithm,
Function optimization.