G.W. Weber; "Dynamics, Stability&Control...", "Some New Pathways...",

Faculty of Engineering and Natural Sciences
FENS EE 552 SEMINARS

Talk 1: "Dynamics, Stability and Control in Environmental, Biological and Financial Dynamics --- Semi-Infinite and Conic Programming Applied in an Emerging Area of Modern OR"

Prof. Dr. Gerhard-Wilhelm Weber
Institute of Applied Mathematics,  Middle East Technical University, Ankara, Turkey
and
Faculty of Economics, Business and Law, University of Siegen, Germany

Abstract:
This paper further introduces continuous optimization into the fields of computational biology and environmental protection which belong to the most challenging and emerging areas of science. Our paper tries to detect and overcome some structural frontiers of our methods applied to the recently introduced gene-environment networks. Based on experimental data given, we investigate ordinary differential equations having nonlinearities on the right-hand side and a generalized treatment of the absolute shift term which represents the environmental effects. The genetic process is studied by a time-discretization, in particular, of Runge-Kutta type. The possibility of detecting stability and instability regions is being shown by a utilization of the combinatorial algorithm of Brayton and Tong which is based on the orbits of polyhedra. The time-continuous and discrete systems can be represented by means of matrices allowing biological implications, they encode and are motived by our networks. A specific contribution consists in a careful but rigorous integration of the environment into modeling and dynamics, using generalized semi-infinite and conic quadratic programming. We characterize structural stability in the topological landscape of gene-environement networks. Aspects of spline approximation, Tikhonov regularization and the modeling of uncertainties with intervals are included. A special module implemented into this study is the TEM model on CO2 emission reduction and its control. This practically motivated and theoretically elaborated work is devoted for a contribution to better health care, progress in medicine, a better education and more healthy living conditions. Future research directions are addressed, e.g., towards further elements from statistics and probability, numerical implementation and with a closer representation of the financial sector.

Coauthors: Ö. Ugur, B. Akteke-Öztürk, S.Z. Alparslan-Gök, S. Özögür, P. Taylan and A. Tezel

Talk 2: Some New Pathways of Research at IAM of METU and Collaboration Proposed --- MARS --- SVM with Infinitely Many Kernels, Coding Theory and Cryptography Indicated"

By this shorter presentation, some of the recent studies at Institute of Applied Mathematics will become briefly introduced which we hope to be of some interest for the precious Colleagues from Sabancı University.

Firstly and mainly, we discuss modern spline regression with the help of continuous optimization, especially, multivariate adaptive regression spline (MARS) of J. Friedman. This is a tool from statistics, important in classification and regression, with applicability in many areas of finance, science and technology, very useful in high dimensions and shows a great promise for fitting nonlinear multivariate functions. The MARS algorithm for estimating the model function consists of two sub algorithms. As an alternative to the backward stepwise algorithm, we propose to construct a penalized residual sum of squares for a Tikhonov regularization problem which we treat using continuous optimization, considered to become a complementary technology and alternative to the back-ward stepwise algorithm. Especially, we employ conic quadratic programming (CQP), permitting the use of interior point methods. The new approach will be analyzed, computationally applied and compared with the classical one of MARS.

Secondly, still remaining in statistical learning and computational statistics, we will sketch some new pathways of research initiated by us in Machine Learning. It is characterized by an infinite number of kernels in the optimization problem called Support Vector Machine. Today, we are employing both infinite and semi-infinite optimization here.

 Thirdly, a short introduction about the research of IAM Department of Cryptography will be given. The colleagues there and all the ones related with aforementioned research projects would be very honored and glad if closer scientific exchange could be possible on all those various challenging fields of science.

Coauthors: P. Taylan, D. Sezer, G. Köksal, I. Batmaz, F. Yerlikaya,  S. Özögür, J. Shawe-Taylor, F. Özbudak and E. Akyildiz

BIO: Gerhard-Wilhelm Weber works at IAM of METU, Ankara, Turkey (department of financial mathematics and scientific computing; assistant to the director), and Guest Professor at the Faculty of Economics, Management and Law of University of Siegen, Germany. He works in optimization, optimal control, finance, inverse problems, OR, computational statistics, computational biology, dynamical systems, data mining and sectors of environment and development. He received his Diploma and Doctorate in mathematics and economics at RWTH Aachen, and his Habilitation at TU Darmstadt. He held professorships by proxy at Institute of Mathematics, University of Cologne, and at Faculty of Mathematics, TU Chemnitz, Germany, then he worked at Cologne Bioinformatics Center; since 2003 he is at METU, Ankara. He chairs EUROPT and represents German OR in Turkey.

February 20, 2008, 13:40,   FENS G029