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Курс 1
Dynamics and Prediction in Gene-Environment and Financial Networks with the Help of Optimization
Authors: Gerhard-Wilhelm Weber, S. Zeynep Alparslan-Gök, Nedim Dikmen, Basak Akteke-Öztürk, Ömür Ugur, Süreyya Özögür, Pakize Taylan
This talk surveys and improves recent advances in understanding the mathematical foundations and interdisciplinary implications of the newly introduced gene-environment networks as well as the connections of OR approach to financial mathematics and its related instruments. It also mathematically deepens recent advances in modeling and prediction by rigorously introducing the environment and aspects of errors and uncertainty into the genetic context within the framework of matrix and interval arithmetics. Given the data from DNA microarray experiments and environmental records, we extract nonlinear ordinary differential equations which contain parameters that have to be determined. This is done by some "modern" kinds of approximations, such as the generalized Chebychev and the generalized semi-infinite optimizations. Then, time-discretized dynamical system is studied. By a combinatorial algorithm which constructs and follows polyhedra sequences, allows us to detect the region of parametric stability. Finally, we analyze the topological landscape of gene-environment networks in terms of this structural stability. In addition to the survey of our recent studies, we also wish to introduce stochastic differential equations into our framework. This pioneering work is practically motivated and theoretically elaborated: it is devoted for better understanding of scientific foundations and for mathematical contribution to better healthcare, more healthy living conditions and to protect (our) biosystems. Besides, the applicability of the optimizations in interdisciplinary fields of science and technology will also be emphasized during the tutorial. The authors cordially invite the interested researchers to future collaboration.
Regression in Financial Mathematics by Additive Models and Continuous Optimization Authors: Gerhard-Wilhelm Weber and Pakize Taylan
Many problems in finance are modeled via deterministic differential equations. This type of modeling omits stochastic fluctuations and is not appro priate for stock prices. Therefore, we use stochastic differential equation. We model Stochastic Differential Equations by an additive approximation, consisting of an intercept and functions summed up which are separating the predictors. We also present a mathematical modeling by splines based on a new clustering approach for the input, their density, and the variation of output. Second order terms are bounded for robustness. For this we use Convex Optimization methods, namely, Conic Quadratic Programming.
Data Mining for Quality Improvement Data with Nonsmooth Optimization vs. PAM and k-Means Authors: Basak Akteke-Öztürk and Gerhard-Wilhelm Weber
This study is about our initial work for the objective of identifying the data mining approaches that can effectively improve product and process quality in industrial organizations, and to develop more effective and widely applicable knowledge discovery approaches. We use a clustering algorithm developped by using nonsmooth optimization approach in comparision with PAM and k-means to analyze the data we obtained from a casting company located in Turkey. We present the rule sets established for our models by using rule induction to discover the characteristics of the found clusters.
* This project is supported by the TÜBITAK Project on Use and Developing of Data Mining Methods for Quality Control in Manufacturing, hosted at METU, Ankara.
Data Mining in Quality Improvement Authors: Gülser Köksal and Sinan Kayalıgil This project on Use and Development of Data Mining Methods for Quality Control in Manfacturing is supported by Turkish Science and Research Council TÜBITAK. It aims to determine which DM approaches can effectively be used in QI, to test performance of DM approaches on selected quality design and improvement problems with especially voluminous data an multiple input and quality characteristics, and to develop more effective approaches to solve such problems. In this talk, the project is closer introduced and the methods from OR, statistics and optimization presented and applied. The authors have the hope that this research could become helpful in the Ukraine also, maybe in a framework of collaboration.
Kerkenes Team: a Short Presentation and Demonstration on the Kerkenes Eco-Center Project Activities
Authors: Francoise Summers, Soofia T. Elias-Özkan and Gerhard-Wilhelm Weber
This talk gives an example of a project on developing living on Turkish rural countyside, in the village on Kerkenes in Central Anatolia. The Kerkenes Team has the pleasure to invite you to a presentation and demonstration on the Kerkenes Eco-Center Project activities which include the promotion of solar energy, organic gardens and drip irrigation and energy efficient building construction. At the occasion of this example and talk we can discuss what our sciences, especially, Mathematics, Engineering, Social Sciences, Operational Research (OR), can contribute to an improvement of living conditions. We note that in 2006 the new EURO Working Group “OR for Development” was founded.
Prof. Dr. Gerhard-Wilhelm Weber, Institute of Applied Mathematics, METU, Ankara, Turkey; Chair of The Continuous Optimization Working Group of EURO (EOROPT)
All authors are from METU, Ankara, namely, from Institute of Applied Mathematics, except Francoise Summers and Soofia T. Elias-Özkan who are from Department of Architecture of METU and Gülser Köksal and Sinan Kayalıgil who are from Department of Industrial Engineering. Pakize Taylan is also from Dicle University in Diyarbakir, Turkey. Курс 2
The tool switching problem and its applications
Authors: Prof. Sc.D. Boris Goldengorin
Teacher Prof. Sc.D. Boris Goldengorin, |