Keynote Lecture

Most Recent Developments within Enhanced Multivariance Products Representation (EMPR) Perspective

Professor Metin Demiralp
Istanbul Technical University
Informatics Institute

Abstract: A few years ago, Metin Demiralp has constructed an extension to High Dimensional Model Representation (HDMR) by inserting certain given univariate functions, support functions, to the formulation. This extension has been called “Enhanced Multivariance Products Representation (EMPR)” because of the additive terms with unique common multivariance same as the number of the target function’s independent variables. After this construction, during the time period, from then until now, he and his group (Group for Science and Methods of Computing in ˙Istanbul Tehcnical University Informatics Institute) members performed various applications and created new developments.
EMPR preserves the orthogonal geometry of HDMR. It also uses the product type overall weight functions which are composed of univariate factors, each of which depends on a different independent variable argument of the target function; even though quite recently nonproduct type overall weights are succesfully introduced to the formulation of HDMR. Beyond these preservations, the basic extension is to multiply each HDMR component with certain univariate support functions such that the resulting form of the component becomes dependent of all independent variables of target function. The support functions are given entities and, depending on how they are defined, the EMPR truncations show different level of approximation qualities. Hence, the support function selection is perhaps the most important component of EMPR.
EMPR has born from the image processing via HDMR upon noticing its certain in sufficiencies within technicalities. The bivariate HDMR has been used therein and soon it has been noticed that the all of the three different type HDMR truncations were giving almost nothing and the bivariate remainder term was involving overdominating pixel information about the target image with slightly depending on which kind of weight has been used. This motivated us to change, or truely speaking, extend HDMR philosophy by importing support functions. The result has been really more acceptable when the dimensionality grows. Even though there has been a noticable quality increase even in the case of bivariance, bivariate EMPR has appeared to be quite limited and urged us to seek more than one sets of support functions to extend HDMR. The result has been quite succesfull and TMEMPR (Tridiagonal Matrix EMPR) for discrete set domains and TKEMPR (Tridiagonal Kernel EMPR) for continuous functions which can be considered as the kernel of an appropriate univariate integral operator have born after these efforts.
The presentation focuses on these and some related issues in somehow chronological order.

Brief Biography of the Speaker: Metin Demiralp was born in Türkiye (Turkey) on 4 May 1948. His education from elementary school to university was entirely in Turkey. He got his BS, MS degrees and PhD from the same institution, ˙Istanbul Technical University. He was originally chemical engineer, however, through theoretical chemistry, applied mathematics, and computational science years he was mostly working on methodology for computational sciences and he is continuing to do so. He has a group (Group for Science and Methods of Computing) in Informatics Institute of ˙Istanbul Technical University (he is the founder of this institute). He collaborated with the Prof. Herschel A. Rabitz’s group at Princeton University (NJ, USA) at summer and winter semester breaks during the period 1985-2003 after his 14 month long postdoctoral visit to the same group in 1979-1980. He was also (and still is) in collaboration with a neuroscience group at the Psychology Department in the University of Michigan at Ann Arbour in last three years (with certain publications in journals and proceedings).
Metin Demiralp has more than 100 papers in well known and prestigious scientific journals, and, more than 230 contributions together with various keynote, plenary, and, tutorial talks to the proceedings of various international conferences. He gave many invited talks in various prestigious scientific meetings and academic institutions. He has a good scientific reputation in his country and he was one of the principal members of Turkish Academy of Sciences since 1994. He has resigned on June 2012 because of the governmental decree changing the structure of the academy and putting politicial influence possibility by bringing a member assignation system. Metin Demiralp is also a member of European Mathematical Society. He has also two important awards of turkish scientific establishments.
The important recent foci in research areas of Metin Demiralp can be roughly listed as follows: Probabilistic Evolution Method in Explicit ODE Solutions and in Quantum and Liouville Mechanics, Fluctuation Expansions in Matrix Representations, High Dimensional Model Representations, Space Extension Methods, Data Processing via Multivariate Analytical Tools, Multivariate Numerical Integration via New Efficient Approaches, Matrix Decompositions, Multiway Array Decompositions, Enhanced Multivariate Product Representations, Quantum Optimal Control.