Search results for: stochastic frontier
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 293

Search results for: stochastic frontier

293 Interstate Comparison of Environmental Performance using Stochastic Frontier Analysis: The United States Case Study

Authors: Alexander Y. Vaninsky

Abstract:

Environmental performance of the U.S. States is investigated for the period of 1990 – 2007 using Stochastic Frontier Analysis (SFA). The SFA accounts for both efficiency measure and stochastic noise affecting a frontier. The frontier is formed using indicators of GDP, energy consumption, population, and CO2 emissions. For comparability, all indicators are expressed as ratios to total. Statistical information of the Energy Information Agency of the United States is used. Obtained results reveal the bell - shaped dynamics of environmental efficiency scores. The average efficiency scores rise from 97.6% in 1990 to 99.6% in 1999, and then fall to 98.4% in 2007. The main factor is insufficient decrease in the rate of growth of CO2 emissions with regards to the growth of GDP, population and energy consumption. Data for 2008 following the research period allow for an assumption that the environmental performance of the U.S. States has improved in the last years.

Keywords: Stochastic frontier analysis, environmental performance, interstate comparisons.

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292 Cost Efficiency of European Cooperative Banks

Authors: Karolína Vozková, Matěj Kuc

Abstract:

This paper analyzes recent trends in cost efficiency of European cooperative banks using efficient frontier analysis. Our methodology is based on stochastic frontier analysis which is run on a set of 649 European cooperative banks using data between 2006 and 2015. Our results show that average inefficiency of European cooperative banks is increasing since 2008, smaller cooperative banks are significantly more efficient than the bigger ones over the whole time period and that share of net fee and commission income to total income surprisingly seems to have no impact on bank cost efficiency.

Keywords: Cooperative banks, cost efficiency, efficient frontier analysis, stochastic frontier analysis, net fee and commission income.

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291 Profit Efficiency and Competitiveness of Commercial Banks in Malaysia

Authors: Rosita Suhaimi, Firdaus Abdullah, Chong Fen Nee, Nurhani Aba Ibrahim

Abstract:

This paper attempts to identify the significance of Information and Communications Technology (ICT) and competitiveness to the profit efficiency of commercial banks in Malaysia. The profit efficiency of commercial banks in Malaysia, the dependent variable, was estimated using the Stochastic Frontier Approach (SFA) on a sample of unbalanced panel data, covering 23 commercial banks, between 1995 to 2007. Based on the empirical results, ICT was not found to exert a significant impact on profit efficiency, whereas competitiveness, non ICT stock expenditure and ownership were significant contributors. On the other hand, the size of banks was found to have significantly reduced profit efficiency, opening up for various interpretations of the interrelated role of ICT and competition.

Keywords: Competitiveness, Profit Efficiency, Stochastic Frontier Analysis

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290 Effect of Urea Deep Placement Technology Adoption on the Production Frontier: Evidence from Irrigation Rice Farmers in the Northern Region of Ghana

Authors: Shaibu Baanni Azumah, William Adzawla

Abstract:

Rice is an important staple crop, with current demand higher than the domestic supply in Ghana. This has led to a high and unfavourable import bill. Therefore, recent policies and interventions in the agricultural sub-sector aim at promoting various improved agricultural technologies in order to improve domestic production and reduce the importation of rice. In this study, we examined the effect of the adoption of Urea Deep Placement (UDP) technology by rice farmers on the position of the production frontier. This involved 200 farmers selected through a multi stage sampling technique in the Northern region of Ghana. A Cobb-Douglas stochastic frontier model was fitted. The result showed that the adoption of UDP technology shifts the output frontier outward and also move the farmers closer to the frontier. Farmers were also operating under diminishing returns to scale which calls for redress. Other factors that significantly influenced rice production were farm size, labour, use of certified seeds and NPK fertilizer. Although there was an opportunity for improvement, the farmers were highly efficient (92%), compared to previous studies. Farmers’ efficiency was improved through increased education, household size, experience, access to credit, and lack of extension service provision by MoFA. The study recommends the revision of Ghana’s agricultural policy to include the UDP technology. Agricultural Extension officers of the Ministry of Food and Agriculture (MoFA) should be trained on the UDP technology to support IFDC’s drive to improve adoption by rice farmers. Rice farmers are also encouraged to expand their farm lands, improve plant population, and also increase the usage of fertilizer to improve yields. Mechanisms through which credit can be made easily accessible and effectively utilised should be identified and promoted.

Keywords: Efficiency, rice farmers, stochastic frontier, UDP technology.

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289 Mean-Variance Optimization of Portfolios with Return of Premium Clauses in a DC Pension Plan with Multiple Contributors under Constant Elasticity of Variance Model

Authors: Bright O. Osu, Edikan E. Akpanibah, Chidinma Olunkwa

Abstract:

In this paper, mean-variance optimization of portfolios with the return of premium clauses in a defined contribution (DC) pension plan with multiple contributors under constant elasticity of variance (CEV) model is studied. The return clauses which permit death members to claim their accumulated wealth are considered, the remaining wealth is not equally distributed by the remaining members as in literature. We assume that before investment, the surplus which includes funds of members who died after retirement adds to the total wealth. Next, we consider investments in a risk-free asset and a risky asset to meet up the expected returns of the remaining members and obtain an optimized problem with the help of extended Hamilton Jacobi Bellman equation. We obtained the optimal investment strategies for the two assets and the efficient frontier of the members by using a stochastic optimal control technique. Furthermore, we studied the effect of the various parameters of the optimal investment strategies and the effect of the risk-averse level on the efficient frontier. We observed that the optimal investment strategy is the same as in literature, secondly, we observed that the surplus decreases the proportion of the wealth invested in the risky asset.

Keywords: DC pension fund, Hamilton Jacobi Bellman equation, optimal investment strategies, stochastic optimal control technique, return of premiums clauses, mean-variance utility.

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288 Calculation of Reorder Point Level under Stochastic Parameters: A Case Study in Healthcare Area

Authors: Serap Akcan, Ali Kokangul

Abstract:

We consider a single-echelon, single-item inventory system where both demand and lead-time are stochastic. Continuous review policy is used to control the inventory system. The objective is to calculate the reorder point level under stochastic parameters. A case study is presented in Neonatal Intensive Care Unit.

Keywords: Inventory control system, reorder point level, stochastic demand, stochastic lead time

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287 Non-Stationary Stochastic Optimization of an Oscillating Water Column

Authors: María L. Jalón, Feargal Brennan

Abstract:

A non-stationary stochastic optimization methodology is applied to an OWC (oscillating water column) to find the design that maximizes the wave energy extraction. Different temporal cycles are considered to represent the long-term variability of the wave climate at the site in the optimization problem. The results of the non-stationary stochastic optimization problem are compared against those obtained by a stationary stochastic optimization problem. The comparative analysis reveals that the proposed non-stationary optimization provides designs with a better fit to reality. However, the stationarity assumption can be adequate when looking at averaged system response.

Keywords: Non-stationary stochastic optimization, oscillating water column, temporal variability, wave energy.

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286 Dynamic Slope Scaling Procedure for Stochastic Integer Programming Problem

Authors: Takayuki Shiina

Abstract:

Mathematical programming has been applied to various problems. For many actual problems, the assumption that the parameters involved are deterministic known data is often unjustified. In such cases, these data contain uncertainty and are thus represented as random variables, since they represent information about the future. Decision-making under uncertainty involves potential risk. Stochastic programming is a commonly used method for optimization under uncertainty. A stochastic programming problem with recourse is referred to as a two-stage stochastic problem. In this study, we consider a stochastic programming problem with simple integer recourse in which the value of the recourse variable is restricted to a multiple of a nonnegative integer. The algorithm of a dynamic slope scaling procedure for solving this problem is developed by using a property of the expected recourse function. Numerical experiments demonstrate that the proposed algorithm is quite efficient. The stochastic programming model defined in this paper is quite useful for a variety of design and operational problems.

Keywords: stochastic programming problem with recourse, simple integer recourse, dynamic slope scaling procedure

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285 Stochastic Estimation of Cavity Flowfield

Authors: Yin Yin Pey, Leok Poh Chua, Wei Long Siauw

Abstract:

Linear stochastic estimation and quadratic stochastic estimation techniques were applied to estimate the entire velocity flow-field of an open cavity with a length to depth ratio of 2. The estimations were done through the use of instantaneous velocity magnitude as estimators. These measurements were obtained by Particle Image Velocimetry. The predicted flow was compared against the original flow-field in terms of the Reynolds stresses and turbulent kinetic energy. Quadratic stochastic estimation proved to be more superior than linear stochastic estimation in resolving the shear layer flow. When the velocity fluctuations were scaled up in the quadratic estimate, both the time-averaged quantities and the instantaneous cavity flow can be predicted to a rather accurate extent.

Keywords: Open cavity, Particle Image Velocimetry, Stochastic estimation, Turbulent kinetic energy.

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284 Stochastic Programming Model for Power Generation

Authors: Takayuki Shiina

Abstract:

We consider power system expansion planning under uncertainty. In our approach, integer programming and stochastic programming provide a basic framework. We develop a multistage stochastic programming model in which some of the variables are restricted to integer values. By utilizing the special property of the problem, called block separable recourse, the problem is transformed into a two-stage stochastic program with recourse. The electric power capacity expansion problem is reformulated as the problem with first stage integer variables and continuous second stage variables. The L-shaped algorithm to solve the problem is proposed.

Keywords: electric power capacity expansion problem, integerprogramming, L-shaped method, stochastic programming

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283 Stochastic Scheduling to Minimize Expected Lateness in Multiple Identical Machines

Authors: Ghulam Zakria, Zailin Guan , Yasser Riaz Awan, Wan Lizhi

Abstract:

There are many real world problems in which parameters like the arrival time of new jobs, failure of resources, and completion time of jobs change continuously. This paper tackles the problem of scheduling jobs with random due dates on multiple identical machines in a stochastic environment. First to assign jobs to different machine centers LPT scheduling methods have been used, after that the particular sequence of jobs to be processed on the machine have been found using simple stochastic techniques. The performance parameter under consideration has been the maximum lateness concerning the stochastic due dates which are independent and exponentially distributed. At the end a relevant problem has been solved using the techniques in the paper..

Keywords: Quantity Production Flow Shop, LPT Scheduling, Stochastic Scheduling, Maximum Lateness, Random Due Dates

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282 Comparison of Reliability Systems Based Uncertainty

Authors: A. Aissani, H. Benaoudia

Abstract:

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 simulation studies.

Keywords: Uncertainty, Stochastic comparison, Reliability, serie's system, imperfect repair.

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281 On Diffusion Approximation of Discrete Markov Dynamical Systems

Authors: Jevgenijs Carkovs

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.

Keywords: Markov dynamical system, diffusion approximation, equilibrium stochastic stability.

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280 The Strict Stability of Impulsive Stochastic Functional Differential Equations with Markovian Switching

Authors: Dezhi Liu Guiyuan Yang Wei Zhang

Abstract:

Strict stability can present the rate of decay of the solution, so more and more investigators are beginning to study the topic and some results have been obtained. However, there are few results about strict stability of stochastic differential equations. In this paper, using Lyapunov functions and Razumikhin technique, we have gotten some criteria for the strict stability of impulsive stochastic functional differential equations with markovian switching.

Keywords: Impulsive; Stochastic functional differential equation; Strict stability; Razumikhin technique.

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279 Mean Square Stability of Impulsive Stochastic Delay Differential Equations with Markovian Switching and Poisson Jumps

Authors: Dezhi Liu

Abstract:

In the paper, based on stochastic analysis theory and Lyapunov functional method, we discuss the mean square stability of impulsive stochastic delay differential equations with markovian switching and poisson jumps, and the sufficient conditions of mean square stability have been obtained. One example illustrates the main results. Furthermore, some well-known results are improved and generalized in the remarks.

Keywords: Impulsive, stochastic, delay, Markovian switching, Poisson jumps, mean square stability.

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278 Segmentation of Noisy Digital Images with Stochastic Gradient Kernel

Authors: Abhishek Neogi, Jayesh Verma, Pinaki Pratim Acharjya

Abstract:

Image segmentation and edge detection is a fundamental section in image processing. In case of noisy images Edge Detection is very less effective if we use conventional Spatial Filters like Sobel, Prewitt, LOG, Laplacian etc. To overcome this problem we have proposed the use of Stochastic Gradient Mask instead of Spatial Filters for generating gradient images. The present study has shown that the resultant images obtained by applying Stochastic Gradient Masks appear to be much clearer and sharper as per Edge detection is considered.

Keywords: Image segmentation, edge Detection, noisy images, spatialfilters, stochastic gradient kernel.

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277 Noise Analysis of Single-Ended Input Differential Amplifier using Stochastic Differential Equation

Authors: Tarun Kumar Rawat, Abhirup Lahiri, Ashish Gupta

Abstract:

In this paper, we analyze the effect of noise in a single- ended input differential amplifier working at high frequencies. Both extrinsic and intrinsic noise are analyzed using time domain method employing techniques from stochastic calculus. Stochastic differential equations are used to obtain autocorrelation functions of the output noise voltage and other solution statistics like mean and variance. The analysis leads to important design implications and suggests changes in the device parameters for improved noise characteristics of the differential amplifier.

Keywords: Single-ended input differential amplifier, Noise, stochastic differential equation, mean and variance.

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276 A Scenario-Based Approach for the Air Traffic Flow Management Problem with Stochastic Capacities

Authors: Soumia Ichoua

Abstract:

In this paper, we investigate the strategic stochastic air traffic flow management problem which seeks to balance airspace capacity and demand under weather disruptions. The goal is to reduce the need for myopic tactical decisions that do not account for probabilistic knowledge about the NAS near-future states. We present and discuss a scenario-based modeling approach based on a time-space stochastic process to depict weather disruption occurrences in the NAS. A solution framework is also proposed along with a distributed implementation aimed at overcoming scalability problems. Issues related to this implementation are also discussed.

Keywords: Air traffic management, sample average approximation, scenario-based approach, stochastic capacity.

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275 PTH Moment Exponential Stability of Stochastic Recurrent Neural Networks with Distributed Delays

Authors: Zixin Liu, Jianjun Jiao Wanping Bai

Abstract:

In this paper, the issue of pth moment exponential stability of stochastic recurrent neural network with distributed time delays is investigated. By using the method of variation parameters, inequality techniques, and stochastic analysis, some sufficient conditions ensuring pth moment exponential stability are obtained. The method used in this paper does not resort to any Lyapunov function, and the results derived in this paper generalize some earlier criteria reported in the literature. One numerical example is given to illustrate the main results.

Keywords: Stochastic recurrent neural networks, pth moment exponential stability, distributed time delays.

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274 A Computational Stochastic Modeling Formalism for Biological Networks

Authors: Werner Sandmann, Verena Wolf

Abstract:

Stochastic models of biological networks are well established in systems biology, where the computational treatment of such models is often focused on the solution of the so-called chemical master equation via stochastic simulation algorithms. In contrast to this, the development of storage-efficient model representations that are directly suitable for computer implementation has received significantly less attention. Instead, a model is usually described in terms of a stochastic process or a "higher-level paradigm" with graphical representation such as e.g. a stochastic Petri net. A serious problem then arises due to the exponential growth of the model-s state space which is in fact a main reason for the popularity of stochastic simulation since simulation suffers less from the state space explosion than non-simulative numerical solution techniques. In this paper we present transition class models for the representation of biological network models, a compact mathematical formalism that circumvents state space explosion. Transition class models can also serve as an interface between different higher level modeling paradigms, stochastic processes and the implementation coded in a programming language. Besides, the compact model representation provides the opportunity to apply non-simulative solution techniques thereby preserving the possible use of stochastic simulation. Illustrative examples of transition class representations are given for an enzyme-catalyzed substrate conversion and a part of the bacteriophage λ lysis/lysogeny pathway.

Keywords: Computational Modeling, Biological Networks, Stochastic Models, Markov Chains, Transition Class Models.

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273 Passivity Analysis of Stochastic Neural Networks With Multiple Time Delays

Authors: Biao Qin, Jin Huang, Jiaojiao Ren, Wei Kang

Abstract:

This paper deals with the problem of passivity analysis for stochastic neural networks with leakage, discrete and distributed delays. By using delay partitioning technique, free weighting matrix method and stochastic analysis technique, several sufficient conditions for the passivity of the addressed neural networks are established in terms of linear matrix inequalities (LMIs), in which both the time-delay and its time derivative can be fully considered. A numerical example is given to show the usefulness and effectiveness of the obtained results.

Keywords: Passivity, Stochastic neural networks, Multiple time delays, Linear matrix inequalities (LMIs).

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272 Existence of Solution of Nonlinear Second Order Neutral Stochastic Differential Inclusions with Infinite Delay

Authors: Yong Li

Abstract:

The paper is concerned with the existence of solution of nonlinear second order neutral stochastic differential inclusions with infinite delay in a Hilbert Space. Sufficient conditions for the existence are obtained by using a fixed point theorem for condensing maps.

Keywords: Mild solution, Convex multivalued map, Neutral stochastic differential inclusions.

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271 Formulating the Stochastic Finite Elements for Free Vibration Analysis of Plates with Variable Elastic Modulus

Authors: Mojtaba Aghamiri Esfahani, Mohammad Karkon, Seyed Majid Hosseini Nezhad, Reza Hosseini-Ara

Abstract:

In this study, the effect of uncertainty in elastic modulus of a plate on free vibration response is investigated. For this purpose, the elastic modulus of the plate is modeled as stochastic variable with normal distribution. Moreover, the distance autocorrelation function is used for stochastic field. Then, by applying the finite element method and Monte Carlo simulation, stochastic finite element relations are extracted. Finally, with a numerical test, the effect of uncertainty in the elastic modulus on free vibration response of a plate is studied. The results show that the effect of uncertainty in elastic modulus of the plate cannot play an important role on the free vibration response.

Keywords: Stochastic finite elements, plate bending, free vibration, Monte Carlo, Neumann expansion method.

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270 Stochastic Comparisons of Heterogeneous Samples with Homogeneous Exponential Samples

Authors: Nitin Gupta, Rakesh Kumar Bajaj

Abstract:

In the present communication, stochastic comparison of a series (parallel) system having heterogeneous components with random lifetimes and series (parallel) system having homogeneous exponential components with random lifetimes has been studied. Further, conditions under which such a comparison is possible has been established.

Keywords: Exponential distribution, Order statistics, Star ordering, Stochastic ordering.

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269 An Application of Extreme Value Theory as a Risk Measurement Approach in Frontier Markets

Authors: Dany Ng Cheong Vee, Preethee Nunkoo Gonpot, Noor-Ul-Hacq Sookia

Abstract:

In this paper, we consider the application of Extreme Value Theory as a risk measurement tool. The Value at Risk, for a set of indices, from six Stock Exchanges of Frontier markets is calculated using the Peaks over Threshold method and the performance of the model index-wise is evaluated using coverage tests and loss functions. Our results show that “fattailedness” alone of the data is not enough to justify the use of EVT as a VaR approach. The structure of the returns dynamics is also a determining factor. This approach works fine in markets which have had extremes occurring in the past thus making the model capable of coping with extremes coming up (Colombo, Tunisia and Zagreb Stock Exchanges). On the other hand, we find that indices with lower past than present volatility fail to adequately deal with future extremes (Mauritius and Kazakhstan). We also conclude that using EVT alone produces quite static VaR figures not reflecting the actual dynamics of the data.

Keywords: Extreme Value theory, Financial Crisis 2008, Frontier Markets, Value at Risk.

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268 The Impact of Transaction Costs on Rebalancing an Investment Portfolio in Portfolio Optimization

Authors: B. Marasović, S. Pivac, S. V. Vukasović

Abstract:

Constructing a portfolio of investments is one of the most significant financial decisions facing individuals and institutions. In accordance with the modern portfolio theory maximization of return at minimal risk should be the investment goal of any successful investor. In addition, the costs incurred when setting up a new portfolio or rebalancing an existing portfolio must be included in any realistic analysis. In this paper rebalancing an investment portfolio in the presence of transaction costs on the Croatian capital market is analyzed. The model applied in the paper is an extension of the standard portfolio mean-variance optimization model in which transaction costs are incurred to rebalance an investment portfolio. This model allows different costs for different securities, and different costs for buying and selling. In order to find efficient portfolio, using this model, first, the solution of quadratic programming problem of similar size to the Markowitz model, and then the solution of a linear programming problem have to be found. Furthermore, in the paper the impact of transaction costs on the efficient frontier is investigated. Moreover, it is shown that global minimum variance portfolio on the efficient frontier always has the same level of the risk regardless of the amount of transaction costs. Although efficient frontier position depends of both transaction costs amount and initial portfolio it can be concluded that extreme right portfolio on the efficient frontier always contains only one stock with the highest expected return and the highest risk.

Keywords: Croatian capital market, Fractional quadratic programming, Markowitz model, Portfolio optimization, Transaction costs.

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267 Stability Analysis of Impulsive Stochastic Fuzzy Cellular Neural Networks with Time-varying Delays and Reaction-diffusion Terms

Authors: Xinhua Zhang, Kelin Li

Abstract:

In this paper, the problem of stability analysis for a class of impulsive stochastic fuzzy neural networks with timevarying delays and reaction-diffusion is considered. By utilizing suitable Lyapunov-Krasovskii funcational, the inequality technique and stochastic analysis technique, some sufficient conditions ensuring global exponential stability of equilibrium point for impulsive stochastic fuzzy cellular neural networks with time-varying delays and diffusion are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters, diffusion effect and impulsive disturbed intention. It is believed that these results are significant and useful for the design and applications of fuzzy neural networks. An example is given to show the effectiveness of the obtained results.

Keywords: Exponential stability, stochastic fuzzy cellular neural networks, time-varying delays, impulses, reaction-diffusion terms.

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266 Mean Square Exponential Synchronization of Stochastic Neutral Type Chaotic Neural Networks with Mixed Delay

Authors: Zixin Liu, Huawei Yang, Fangwei Chen

Abstract:

This paper studies the mean square exponential synchronization problem of a class of stochastic neutral type chaotic neural networks with mixed delay. On the Basis of Lyapunov stability theory, some sufficient conditions ensuring the mean square exponential synchronization of two identical chaotic neural networks are obtained by using stochastic analysis and inequality technique. These conditions are expressed in the form of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. The feedback controller used in this paper is more general than those used in previous literatures. One simulation example is presented to demonstrate the effectiveness of the derived results.

Keywords: Exponential synchronization, stochastic analysis, chaotic neural networks, neutral type system.

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265 Stochastic Mixed 0-1 Integer Programming Applied to International Transportation Problems under Uncertainty

Authors: Y. Wu

Abstract:

Today-s business has inevitably been set in the global supply chain management environment. International transportation has never played such an important role in the global supply chain network, because movement of shipments from one country to another tends to be more frequent than ever before. This paper studies international transportation problems experienced by an international transportation company. Because of the limited fleet capacity, the transportation company has to hire additional trucks from two countries in advance. However, customer-s shipment information is uncertain, and decisions have to be made before accurate information can be obtained. This paper proposes a stochastic mixed 0-1 programming model to solve the international transportation problems under uncertain demand. A series of experiments demonstrate the effectiveness of the proposed stochastic model.

Keywords: Global supply chain management, international transportation, stochastic programming.

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264 A New Application of Stochastic Transformation

Authors: Nilar Win Kyaw

Abstract:

In cryptography, confusion and diffusion are very important to get confidentiality and privacy of message in block ciphers and stream ciphers. There are two types of network to provide confusion and diffusion properties of message in block ciphers. They are Substitution- Permutation network (S-P network), and Feistel network. NLFS (Non-Linear feedback stream cipher) is a fast and secure stream cipher for software application. NLFS have two modes basic mode that is synchronous mode and self synchronous mode. Real random numbers are non-deterministic. R-box (random box) based on the dynamic properties and it performs the stochastic transformation of data that can be used effectively meet the challenges of information is protected from international destructive impacts. In this paper, a new implementation of stochastic transformation will be proposed.

Keywords: S-P network, Feistel network, R-block, stochastic transformation

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