JOINT PROGRAM

11th WSEAS International Conference on

APPLIED MATHEMATICS (MATH '07)

Dallas, Texas, USA, March 22-24, 2007

Thursday, March 22, 2007

Plenary Lecture 1

Fluctuation Expansion at the Horizon as a new and Efficient Tool for Integration and ODE and PDE Solving

Professor Metin Demiralp

Informatics Institute

Istanbul Technical University

ITU Bilisim Enstitusu Ayazaga Yerleskesi

Maslak, 34469, Istanbul, TURKEY

Abstract: The univariate integration of a function over a closed interval can be realized through various analytical or numerical methods. Almost all numerical methods assume the continuity and the smoothness of the function under consideration and tries to use somehow a polynomial approximation. They fail if the function has nonintegrable singularity in the integration interval. In the case of integrable singularities in the interval the numerical methods may become slowly converging. They may be negatively affected even from the singularities outside the integration domain. Hence, to remove or to decrease these types of negative effects, one can use a weight function which somehow reflects and compensates the singular nature of the function to be integrated.

Fluctuation expansion uses sharply localized weight functions representable by Dirac's delta function which picks the value of a function at a given point. Dirac’s delta function can be approximated by appropriately defined projection operator kernels. Fluctuation expansion is based on these types of approximations. It expands and approximates the weight function in this way and produces a Gauss quadrature like approximation formula with universal weight coefficients which are different for different weights. The accuracy can be controlled by monitoring the number of the terms in expansion of weight in terms of projection operator kernels.

Fluctuation expansion can also be applied to multivariate integration. The basic philosophy remains same in this case. Only difference is the multivariance in various entities and as long as sufficient care is paid for possible complications the efficiency is again powerful and the method remains promising.

All linear partial differential equations describing probabilistic events can be handled by using fluctuation expansion. This is because of the fact that the existence of probability in the event description implies the utilization of the expectation values like in quantum mechanics or nonequilibrium statistical mechanics via Liuouville equation. If the expectation values are considered instead of the probability describing entities then the multivariate integrals in the representations of expectation values can be approximated by using the fluctuation expansion.

Plenary Lecture 2

Incomplete inventory information - the next challenge

Professor Suresh P. Sethi

Charles & Nancy Davidson Distinguished Professor

Director, Center for Intelligent Supply Networks

School of Management

University of Texas at Dallas

Richardson, TX 75080, USA

Abstract: The purpose of this lecture is to review recent developments in the analysis of partially observed optimal control problems that arise in the management of inventory systems.

Inventory control is one of the most important topics in management science/operations research. A systematic analysis of inventory problems began with the development of the classical EOQ formula of Harris in 1913. Since then, an enormous amount of literature has accumulated on inventory control problems.

One of the critical assumptions in this vast literature has been that the current level of inventory is fully observed. Some of the most celebrated results such as optimality of base-stock or (s,S) policies have been obtained under the assumption of full observation. Yet it is often the case in practice that the inventory level is only partially observed. Most of the well-known inventory policies are not only non-optimal, but are also not applicable in the partial observation environment.

The reasons for partial observation of the current inventory level are many. Inventory records or cash register information differ from actual inventory because of a variety of factors including transaction errors, theft, spoilage, misplacement, unobserved lost demands, and information delays. As a result, what are usually observed are some events or surrogate measures, called signals, related to the inventory level. At best, these relationships may provide only the distribution of current inventory levels.

In the best case, therefore, the relevant state in the inventory control problems is not the current inventory level, but rather its distribution given the observed signals. Thus, the analysis for finding optimal production or ordering policies takes place generally in the space of infinite-dimensional probability distributions.

SESSION: Probabilities, Statistics and Operational Research

Chair: Alexey Sadovski, Remi Leandre

Friday, March 23, 2007

SESSION: Computational Algorithms and Applications

Chair: Toshinori Yamada, Mihai Bugaru

SESSION: Control Methods and Optimization Techniques

Chair: Yezid Donoso, Kuang Yuan Kung

Symposium: Management, Marketing and Finances (MMF '07)

Chair: Richard Ehrhardt, Chih-Hung Hsu

Saturday, March 24, 2007

SESSION: Numerical Analysis, Linear Algebra and Applications

Chair: Vasilis Zafiris, Jianfeng Li

SESSION: Educational Methods

Chair: Felipe Jiménez, Sylvia Encheva

SESSION: Differential Equations and Applications

Chair: Stanislaw Kasperczuk, Katarina Jegdic

PROGRAM

6th WSEAS International Conference on

TELECOMMUNICATIONS and INFORMATICS (TELE-INFO '07)

Dallas, Texas, USA, March 22-24, 2007

Thursday, March 22, 2007

Plenary Lecture 1

Fluctuation Expansion at the Horizon as a new and Efficient Tool for Integration and ODE and PDE Solving

Professor Metin Demiralp

Informatics Institute

Istanbul Technical University

ITU Bilisim Enstitusu Ayazaga Yerleskesi

Maslak, 34469, Istanbul, TURKEY

Abstract: The univariate integration of a function over a closed interval can be realized through various analytical or numerical methods. Almost all numerical methods assume the continuity and the smoothness of the function under consideration and tries to use somehow a polynomial approximation. They fail if the function has nonintegrable singularity in the integration interval. In the case of integrable singularities in the interval the numerical methods may become slowly converging. They may be negatively affected even from the singularities outside the integration domain. Hence, to remove or to decrease these types of negative effects, one can use a weight function which somehow reflects and compensates the singular nature of the function to be integrated.

Fluctuation expansion uses sharply localized weight functions representable by Dirac's delta function which picks the value of a function at a given point. Dirac’s delta function can be approximated by appropriately defined projection operator kernels. Fluctuation expansion is based on these types of approximations. It expands and approximates the weight function in this way and produces a Gauss quadrature like approximation formula with universal weight coefficients which are different for different weights. The accuracy can be controlled by monitoring the number of the terms in expansion of weight in terms of projection operator kernels.

Fluctuation expansion can also be applied to multivariate integration. The basic philosophy remains same in this case. Only difference is the multivariance in various entities and as long as sufficient care is paid for possible complications the efficiency is again powerful and the method remains promising.

All linear partial differential equations describing probabilistic events can be handled by using fluctuation expansion. This is because of the fact that the existence of probability in the event description implies the utilization of the expectation values like in quantum mechanics or nonequilibrium statistical mechanics via Liuouville equation. If the expectation values are considered instead of the probability describing entities then the multivariate integrals in the representations of expectation values can be approximated by using the fluctuation expansion.

Plenary Lecture 2

Incomplete inventory information - the next challenge

Professor Suresh P. Sethi

Charles & Nancy Davidson Distinguished Professor

Director, Center for Intelligent Supply Networks

School of Management

University of Texas at Dallas

Richardson, TX 75080, USA

Abstract: The purpose of this lecture is to review recent developments in the analysis of partially observed optimal control problems that arise in the management of inventory systems.

Inventory control is one of the most important topics in management science/operations research. A systematic analysis of inventory problems began with the development of the classical EOQ formula of Harris in 1913. Since then, an enormous amount of literature has accumulated on inventory control problems.

One of the critical assumptions in this vast literature has been that the current level of inventory is fully observed. Some of the most celebrated results such as optimality of base-stock or (s,S) policies have been obtained under the assumption of full observation. Yet it is often the case in practice that the inventory level is only partially observed. Most of the well-known inventory policies are not only non-optimal, but are also not applicable in the partial observation environment.

The reasons for partial observation of the current inventory level are many. Inventory records or cash register information differ from actual inventory because of a variety of factors including transaction errors, theft, spoilage, misplacement, unobserved lost demands, and information delays. As a result, what are usually observed are some events or surrogate measures, called signals, related to the inventory level. At best, these relationships may provide only the distribution of current inventory levels.

In the best case, therefore, the relevant state in the inventory control problems is not the current inventory level, but rather its distribution given the observed signals. Thus, the analysis for finding optimal production or ordering policies takes place generally in the space of infinite-dimensional probability distributions.

SESSION: Latest Trends on Telecommunications

Chair: Pelin Yildiz, Dragoljub Pokrajac

Friday, March 23, 2007

SESSION: Advances on Computer Science

Chair: Suphamit Chittayasothorn, Zhonghang Xia

Saturday, March 24, 2007

SESSION: Information Science and Applications

Chair: George Rzevski, Said Hassan

PROGRAM

6th WSEAS International Conference on

SIGNAL PROCESSING (SIP '07)

Dallas, Texas, USA, March 22-24, 2007

Thursday, March 22, 2007

Plenary Lecture 1

Fluctuation Expansion at the Horizon as a new and Efficient Tool for Integration and ODE and PDE Solving

Professor Metin Demiralp

Informatics Institute

Istanbul Technical University

ITU Bilisim Enstitusu Ayazaga Yerleskesi

Maslak, 34469, Istanbul, TURKEY

Abstract: The univariate integration of a function over a closed interval can be realized through various analytical or numerical methods. Almost all numerical methods assume the continuity and the smoothness of the function under consideration and tries to use somehow a polynomial approximation. They fail if the function has nonintegrable singularity in the integration interval. In the case of integrable singularities in the interval the numerical methods may become slowly converging. They may be negatively affected even from the singularities outside the integration domain. Hence, to remove or to decrease these types of negative effects, one can use a weight function which somehow reflects and compensates the singular nature of the function to be integrated.

Fluctuation expansion uses sharply localized weight functions representable by Dirac's delta function which picks the value of a function at a given point. Dirac’s delta function can be approximated by appropriately defined projection operator kernels. Fluctuation expansion is based on these types of approximations. It expands and approximates the weight function in this way and produces a Gauss quadrature like approximation formula with universal weight coefficients which are different for different weights. The accuracy can be controlled by monitoring the number of the terms in expansion of weight in terms of projection operator kernels.

Fluctuation expansion can also be applied to multivariate integration. The basic philosophy remains same in this case. Only difference is the multivariance in various entities and as long as sufficient care is paid for possible complications the efficiency is again powerful and the method remains promising.

All linear partial differential equations describing probabilistic events can be handled by using fluctuation expansion. This is because of the fact that the existence of probability in the event description implies the utilization of the expectation values like in quantum mechanics or nonequilibrium statistical mechanics via Liuouville equation. If the expectation values are considered instead of the probability describing entities then the multivariate integrals in the representations of expectation values can be approximated by using the fluctuation expansion.

Plenary Lecture 2

Incomplete inventory information - the next challenge

Professor Suresh P. Sethi

Charles & Nancy Davidson Distinguished Professor

Director, Center for Intelligent Supply Networks

School of Management

University of Texas at Dallas

Richardson, TX 75080, USA

Abstract: The purpose of this lecture is to review recent developments in the analysis of partially observed optimal control problems that arise in the management of inventory systems.

Inventory control is one of the most important topics in management science/operations research. A systematic analysis of inventory problems began with the development of the classical EOQ formula of Harris in 1913. Since then, an enormous amount of literature has accumulated on inventory control problems.

One of the critical assumptions in this vast literature has been that the current level of inventory is fully observed. Some of the most celebrated results such as optimality of base-stock or (s,S) policies have been obtained under the assumption of full observation. Yet it is often the case in practice that the inventory level is only partially observed. Most of the well-known inventory policies are not only non-optimal, but are also not applicable in the partial observation environment.

The reasons for partial observation of the current inventory level are many. Inventory records or cash register information differ from actual inventory because of a variety of factors including transaction errors, theft, spoilage, misplacement, unobserved lost demands, and information delays. As a result, what are usually observed are some events or surrogate measures, called signals, related to the inventory level. At best, these relationships may provide only the distribution of current inventory levels.

In the best case, therefore, the relevant state in the inventory control problems is not the current inventory level, but rather its distribution given the observed signals. Thus, the analysis for finding optimal production or ordering policies takes place generally in the space of infinite-dimensional probability distributions.

SESSION: Advances on Signal Processing

Chair: Neelu Jain, Sang-Won Nam

Friday, March 23, 2007

SESSION: Applications of Signal Processing

Chair: Jin Young Kim, Parvinder Singh

Saturday, March 24, 2007

SESSION: Image Processing Techniques

Chair: Devinder Kaur, Frank Moore