20. Yüzyılın Başlarında ‘Fonksiyonel Analiz’
Aydın Aytuna
METU, Institute of Applied Mathematics
Place: IAM S212
Date/Time: 28.02.2017/ 15:40-16:30
Abstract: Bu popüler matematik/tarih konuşmasında, geçen yüzyılın başlarında ortaya çıkan ''Hilbert Uzayları'' nın kısa bir doğuş öyküsü ele alınacaktır.

Stochastic Delay Differential Equations

Program of Financial Mathematics,

Co-advisor: Assist. Prof. Ceren Vardar Acar

Place: IAM S-212

Date / Time: 13.01.2017 / 13.45

Abstract.

Enumeration of irreducible polynomials with prescribed coefficients

Emrah Sercan Yılmaz

College Dublin University

Place: IAM S212

Date/Time: 10.01.2017 -15.30

Abstract: In this seminar, we will give the general theory of enumeration of irreducible polynomials with prescribed coefficients from beginning. We will explain how these numbers are related with (fibre products of) supersingular curves.

Modern Portfolio Optimization with Value at Risk and Conditional Value at Risk - Explanation, Evaluation and Comparison

Sinem Keskin

Program of Financial Mathematics,

Advisor: Prof. Dr. Gerhard W. Weber

Place: IAM S-209

Date / Time: 06.01.2017 / 16.00

Abstract.

Optimization for Big-Data Analytics: Multi-Group Data Classification with

Mathematical programming

Metin Türkay

Koc University

Click for Presentation PDF

Place: IAM - S209

Date / Time:  04.01.2017 / 13:40

Abstract: Data classification is an approach for predicting the class of incoming instances by using the models constructed based on a data set with known class memberships. The first phase in data classification is the training phase where a set of classification rules are constructed using the training set of data. Class membership of the instances in the training set are known and classification rules try to infer relations among the classes and the attribute values of the data instances. Attributes represent the characteristics of an instance and is known both for training and test data set. In the second phase of data classification attribute values of test data instances are used to predict their class membership via the classifier that is built in training phase and this phase is called the testing phase.In this seminar, we focus on solving multiclass data classification problems based on an hyper-boxes approach presented by Uney and Turkay (2006) that has been attracting a lot of attention recently. We enclose data set of each class by hyper-boxes that can be represented by upper and lower bounds of attributes. An error function is minimized by a mixed integer linear programming problem to construct the hyper boxes that represent different classes. The goal is to separate the classes using minimum number of hyper boxes and misclassified points. The solution of the mathematical programming model provides a classifier that is used to label the class membership of new coming samples. We first present the main approach and illustrate the effectiveness on a variety of benchmark problems. The extensions of this approach to handle big data and also improve the computational performance will be discussed.

A Parametric Simplex Algorithm for Linear Vector Optimization Problems

Firdevs Ulus

Department of Industrial Engineering
Bilkent University
Invited by: Murat Manguoğlu
Place: IAM-S209

Date / Time: 03.01.2017 / 15.40

Abstract. A parametric simplex algorithm for solving linear vector optimization problems (LVOPs) is presented. This algorithm can be seen s a variant of the multi-objective simplex algorithm. Different from it, the proposed algorithm works in the parameter space and does not aim to find the set of all efficient solutions. Instead, it finds a ‘solution’ which is a subset of efficient solutions that allows to generate the whole efficient frontier. In that sense, it can also be seen as a generalization of the parametric self-dual simplex algorithm, which originally is designed for solving single objective linear ptimization problems, and is modified to solve two objective bounded LVOPs with the positive orthant as the ordering cone. The algorithm proposed here works for any dimension, any solid pointed polyhedral ordering cone and for bounded as well as unbounded problems.Numerical results are provided to compare the proposed algorithm with an objective space based LVOP (Benson's) algorithm and with the multiobjective simplex (the Evans-Steuer) algorithm. The results show that for non-degenerate problems the proposed algorithm outperforms Benson's algorithm and is on par with the Evan-Steuer algorithm. For highly degenerate problems Benson's algorithm outperforms the simplex-type algorithms; however, the parametric simplex algorithm is computationally much more efficient than the Evans-Steuer algorithm for these problems.

Em Algorithm for Markov Chain Observed Via Gaussian Noise and Point Processes Information

Zehra Eksi-Altay

Vienna University of Economics and Business
Invited by: Yeliz Yolcu Okur
Place: IAM-S209

Date / Time: 27.12.2016 / 15.40

Abstract. In this paper we deal with the parameter estimation of a  finite-state Markov chain observed via Gaussian noise and point processes information. To this, we use the Expectation Maximization (EM) algorithm. This amounts to the derivation of finite-dimensional filters for the related quantities. In this context, we obtain both exact and unnormalized filters. Next, we compute discretized robust versions of the unnormalized filters. Moreover, we introduce a novel goodness of fit test to check how well the estimated model explains the given data set. Finally, we run a simulation study to test speed and accuracy of the algorithm. In particular, we provide a comparison for the estimates resulting from the robust and naive discretization and the value of point process information.

Portfolio Optimization for a Large Investor under Partial Information and Price Impact

Zehra Eksi  and Hyejin Ku

Place: IAM-S208

Date / Time: 26.12.2016 / 12.00

Abstract. This paper studies portfolio optimization problems in a market with partial information and price impact. We consider a large investor with an objective of expected utility maximization from terminal wealth. The drift of the underlying price process is modeled as a diffusion affected by a continuous-time Markov chain and the actions of the large investor. Using the stochastic filtering theory, we reduce the optimal control problem under partial information to the one with complete observation.For logarithmic and power utility cases we solve the utility maximization problem explicitly and we obtain optimal investment strategies in the feedback form. We compare the value functions to those for the case without price impact in Bauerle and Rieder (2004) and Bauerle and Rieder (2005). It turns out that the investor would be better off due to the presence of a price impact both in complete-information and partial-information settings.

Robust Conditional Value-at-Risk Under Parallelpipe Uncertainty: An Application to Portfolio Optimization

Güray Kara

Program of Financial Mathematics,

Advisor: Prof. Dr. Gerhard W. Weber

Place: IAM S-209

Date / Time: 21.12.2016 / 13.15

Abstract.

Efficient methods to generate cryptographically good binary linear transformations

Tolga Sakallı
Trakya University
Department of Computer Engineering

Place: IAM-S209

Date / Time: 20.12.2016 / 15.40

Abstract. In this presentation, we propose new methods using a divide-and-conquer strategy to generate $n \times n$ binary matrices (for composite $n$) with a high/maximum branch number and the same Hamming weight in each row and column. We introduce new types of binary matrices, namely $(BHwC)_{t,m}$ and $(BCwC)_{q,m}$ types, which are a combination of Hadamard and circulant matrices, and the recursive use of circulant matrices, respectively. With the help of these hybrid structures, the search space to generate a binary matrix with a high/maximum branch number is drastically reduced. By using the proposed methods, we focus on generating $12 \times 12$, $16 \times 16$ and $32 \times 32$ binary matrices with a maximum or maximum achievable branch number and low implementation costs to be used in block ciphers. Then, we discuss the implementation properties of binary matrices generated and present experimental results for binary matrices in these sizes. Finally, we apply the proposed methods to larger sizes, i.e., $48 \times 48$, $64 \times 64$ and $80 \times 80$ binary matrices having some applications in secure multi-party computation and fully homomorphic encryption.