METU Student Chapter of SIAM

General Seminars

Speaker: Neslihan Özmen, Fatma Yerlikaya, Doğa Gürsoy

Title: “The Inverse Problem of Magnetoencepkalography: Sourse Localization and The Shape of Ball ”

Date: May 25, 15:40

Place:Institute of Applied Mathematics S209

Abstract:

Magnetoencephalography (MEG) is a non-invasive neurophysiological technique that measures the magnetic fields generated by neuronal activity of the brain. The inverse problem of magnetoencephalography (MEG) is to estimate impressed currents from observations of magnetic fields outside the skull. A common way to model impressed currents is to generate a grid that covers the region of interest in the brain and attach mutually orthogonal electric dipoles with unknown amplitudes at each grid point. The MEG inverse problem of reconsructing electrical sources in human brain is an ill-posed problem. Users of MEG are faced with a vast array of inverse methods that can be used to process their data. For solving this problem there are some regularization techniques (i.e., Tikhonov regularization).

Speaker: Nurgül Gökgöz, Serdar Tanıl, Ahmet Onur

Title: “Iterative Methods for Discrete Tomography Implementation & Comparison Kaczmarz’s Method and Conjugate Gradient Least Squares Method ”

Date: May 25, 15:40

Place: Institute of Applied Mathematics S209

Abstract:

In this study, the main objective is to reconstruct an image from its projections using some means of tomography. To do this Kaczmarz method and conjugate gradient least squares method were used. In order to illustrate the two methods, a software was written in java language. This software gets an image file as an input and creates projections of it from different directions. Then it tries to reconstruct the image using Kaczmarz and conjugate gradient least squares methods. The result shows that as the number of projection increases the accuracy of reconstruction increases. Also in a brain image, Kaczmarz gives better results than conjugate gradient least squares with the same number of projections.

The Inverse Problem of Magnetoencepkalography: Source Localization and The Shape of Ball

Iterative Methods for Discrete Tomography Implementation & Comparison Kaczmarz’s Method and Conjugate Gradient Least Squares Method

“Lectures on Cooperative Game Theory”, by Stef Tijs (Tilburg

University), November 2006

Speaker: Ayse Kisacik

Title: “Enron Case ”

Date: 18 May 2005, 12:40

Place:Institute of Applied Mathematics, M-205

Abstract:

Enron was a huge multinational company. It was born after a merge between Houston Natural Gas Company and Internorth. Its growth was so fast and at the end it became derivatives trading firm. Moreover, because of its success, it won Fortune Magazine s most innovative company in America award six-times. But surprisingly, on October 2001 it declared bankruptcy. This event was not only Enron s bankruptcy, but also it was a scandal of gatekeepers (especially auditing firms), capital markets and politics. A lot of specialists have written articles and papers about this financial scandal. This financial scandal brings a lot of question marks into minds about current corporate governance, accounting systems, independence of gatekeepers and also monitory, regulatory systems. Nowadays, the countries which have strong ties between capital markets try to find some answers to these questions..

Speaker: Ebru Elif Gökçek

Title: “Too Big to Fail?Long-Term Capital Management and the Federal Reserve”

Date:18 May 2005, 12:40

Place: Institute of Applied Mathematics, M-205

Abstract:

Hedge funds are private investment funds that aim to make profits for their shareholders by trading securities. Long-Term Capital Management (LTCM) was a large and prominent hedge fund. As a result of its huge positions in exchange-traded and OTC derivatives, its failure in 1998 is said to have nearly blown up the worlds financial system. The Federal Reserve intervened to stop the failure of LTCM as it was believed to be too big to fail.This study tries to show how and why LTCM ended up in bailout. Considering the detrimental consequences of its rescue, it is also discussed whether it was really too big to fail or not.

Speaker: Fatma Gaye Basaran

Title: “The Fall of MGRM”

Date:18 May 2005, 12:40

Place: Institute of Applied Mathematics, M-205

Abstract:

Although the case of Metallgesellschaft continues to be surrounded by controversy, there is general agreement about the facts of the case. In December, 1993, Metallgescellschaft AG revealed publicly that its “Energy Group” was responsible for losses of approximately $1.5 billion, due mainly to cash-flow problems resulting from large oil forward contracts it had written.In this derivatives debacle study, the trading strategies employed by the conglomerate, how proper supervision could have averted disaster and how similar financial crises may be avoided in the future are explored.

Speaker: Efsun Kürüm

Title: ” Simple Construction of the Efficient Frontier ”

Date: 11 May 2005, 12:40

Place:

Institute of Applied Mathematics, M-205

Abstract:

Simple methods of constructing known results are provided in this study.At the core of these methods is the idendification of a simple concise basis that spans the Capital Market Line( CML).It is shown that a portfolio whose risky assets weights are the product of the inverse variance-covariance matrix of (nonredundant) security rates of return times the vector of the excess expected rates of return over the risk-free rate is a CML portfolio.This portfolio and the risk-free security span the CML.In addition,with this basis,there is immediate construction of the efficient frontier of risky assets(the ‘hyperbola’), ‘tangency’ portfolios, ‘reflection’ portfolios, and a CAPM relationship.

Speaker: Aylin Akınlı

Title: “Seductive but Dangerous”

Date:11 May 2005, 12:40

Place: Institute of Applied Mathematics, M-205

Abstract:

Value at risk (VAR) has gained rapid acceptance as a valuable approach to risk management. Not all VARs are equal,however.A study of VAR techniques used by dealers and end-users reveals that VAR calculations differ significantly for the same portfolio.VARs are extremely dependent on parameters,data,assumptions,and methodology.Calculation of eight common VARs for three hypothetical portfolios demonstrates the potentially seductive but dangerous nature of any single approach to risk management.In sum, although VAR and other quanitative techniques are necessary aspects of an effective risk-management program , they are not sufficient to control risk.Original article by Tanya Styblo Beder.

Speaker: Utku Bora Geyikçi

Title: “An investigation of the results of market liberalization in Turkey”

Date:11 May 2005, 12:40

Place: Institute of Applied Mathematics, M-205

Abstract:

The current globalization debate typically emphasizes spillover effects among financial and capital markets, whereby valuation mistakes or shocks in one market are transmitted to other markets. In Turkey especially after the crises the Decree 32 issued by government in August 1989 is one of the most disputed subjects . The resolution, announced in the Official Gazette, declares the securities market in Turkey fully open to foreign institutional and individual investors. This decree is the date of liberalization of the capital market for Turkey. Therefore investigating the results of this market liberalization is the main aim of this article

Speaker: Cengizhan Aksu

Title: “Insurer’s Optimal Excess of Loss Strategy under a Static and Dynamic Situation”

Date: 27 April 2005, 12:40

Place: M-205

Abstract:

In this study, the problem of finding an optimal retention level maximizing the expected profit of the insurance company is considered under Excess of Loss Strategy. In the first part of the study, the optimal retention level is obtained under a static situation in which there is a fixed claim amount. In the second part, we consider a risk process modelled as a compound Poisson process. We find the optimal dynamic excess of loss reinsurance strategy to maximize the survival probability.

Speaker: Gökhan Yılmaz

Title: “Static and Dynamic Optimal Reinsurance Strategy for a Non Proportional Treaty under a fixed Proportion”

Date: 27 April 2005, 12:40

Place: M-205

Abstract:

The main subject of our study is to find out an optimal retention level that maximizes the expected profit of the insurance company by using the excess of loss reinsurance strategy which is modified with a fixed proportion. In static situation, the optimal retention level is obtained based on a fixed claim amount. In dynamic situation, the optimal reinsurance strategy that minimizes the ruin probability of the insurance company is found out by considering the number of claim amounts as a compound Poisson process.

Speaker: Didem Akçay

Title: “Inference of switching networks by using a piecewise linear formulation ”

Date: 20 April 2005, 12:40

Place: M-205

Abstract:

Inference of regulatory networks has received attention of researchers from many fields. The challenge offered by this problem is its being a typical modelling problem in lack of sufficient information about the process. Hence, we need to derive the missing information from the empirical observations. Therefore, the methodologies used or developed during this study are applicable to various fields of science and engineering. Modelling by inference consists of selecting or defining the most appropriate model structure and inferring the parameters. An appropriate model structure should have the following properties.The model parameters should be inferable. Given the observation and the model class, all parameters used in the model should have a unique solution.(restriction of the solution space) The forward model should be accurately computable.(restriction of the solution space) The model should be capable of exhibiting the essential qualitative features of the system.(limit of the restriction) The model should be relevant with the process.(limit of the restriction) A piecewise linear formulation, described by a switching state transition matrix and a Boolean fuction indicating the switching conditions is proposed for inference of gene regulatory networks. This project mainly concerns using a formulation of switching networks obeying all the above mentioned requirements and developing inference algorithms for all parameters of the formulations.

Speaker: Derya Altıntan

Title: “Population Dynamics and Impulsive Differential Equations”

Date: 20 April 2005, 12:40

Place: M-205

Abstract:

The main subject of our report are on existence to investigate the problem of existence of periodic solutions of impulsive differential equations with harvesting terms. Introducing the harvesting elements make the equations more realistic. Exceptionally, if one take into account human activity. Mathematically the involving the terms is benefitial because we can discuss existence of bounded solutions, periodic solutions, and their stability. First part of the report consists of information about the population models for single species. In the second part the models considered with harvesting. In next section Lotka-Volterra equations with impulse actions are considered. The last part of the report consists of two numerical examples.

Speaker: Mesut Taştan

Title: “Stability of Dynamical Systems:A Constructive Approach”

Date: 13 April 2005, 12:40

Place: M205

Abstract:

A common method for checking stability for dynamical systems is to construct a quadratic Liapunov function from nonlinear theory approach but finding a suitable Liapunov function is not easy for most cases. In this presentation, I will try to explain Brayton and Tong?s algorithmic approach for determining the stability of a set of matrices obtained from time-varying difference equations.

Speaker: Sırma Zeynep Alparslan

Title: “The Technology Emissions Means Model ”

Date: 13 April 2005, 12:40

Place: M205

Abstract:

The conferences of Rio de Janerio and Kyoto demand for a new and important economic instrument which focus on environmental protection in both macro and micro economy.A sustainable development can only be guaranteed if the instrument is embeeded in an optimal energy management.For that reason , the Technology Emissions Means Model (TEM model) was developed,giving the possibility to simulate such an extraordinary market situation. A new bargaining approach to international emissions trading markets are presented within the so called Kyoto Game,which is the part of the TEM model.The TEM model can be regarded as a mathematical model which supports the development of a management tool in the area of the international climate change convention,namely in the creation of a Joint Implementation program.According to numerical examinations ,it is seen that the TEM model tends to a chaotic behavior which is gained by a variation of the memory parameter.As a result a control theoretic approach is necessary , which is indicated by an additional control term.The Framework Convention on Climate Change (FCCC) of Kyoto Protocol demands for reductions in greenhouse gas emisssions by the industrialized countries.On the other hand developing countries are expanding their energy consumption,leading to increased levels of greenhouse gas emissions.The TEM model is a model in the field of economic models which integrates economic and technical investments in a coupled time-discrete nonlinear system of equations.

Speaker: Nurşin Baş

Title: “Modelling of Traffic Flow”

Date: 13 April 2005, 12:40

Place: M205

Abstract:

Traffic flow is determined by the movements and interactions of the vehicles on a carriageway in one direction. Modeling traffic flow can be done at various levels of detail: microscopic, mesoscopic and macroscopic: Microscopic models distinguish the individual drivers and describe their behavior in great detail. Macroscopic models describe the traffic flow by continuous aggregate functions like average density, velocity and flow in the space-time domain. The dynamics of traffic flow is modeled by a nonlinear system of two or three PDEs. Mesoscopic models form a huge ?transition? class between micro- macroscopic models.

Speaker: Tamer Ergun

Title: “Commonly used cryptography algorithms related with Public Key Systems”

Date: 29 December 2004 at 15:40

Place: Institute of Applied Mathematics M-205

Abstract:

Broadly speaking,the term Cryptography refers to a wide range of security issues in the transmission and safeguarding of information. Cryptography splits into two parts as Symmetric Key and Asymmetric Key also known as Public Key .The idea of Public Key was presented by Diffie and Hellman in 1976 and after this revolution, applications of algebra and number theory have arisen. In this talk, we will briefly mention the most commonly used algorithms related with Public Key Systems such as Digital Signature, RSA, Discrete Log, Diffie-Hellman and ElGamal.

Speaker: Emre Tiftik

Title: “The decomposition algorithm for linear programs”

Date: 29 December 2004 at 15:40

Place: Institute of Applied Mathematics M-205

Abstract:

A procedure is presented for the efficient computational solution of linear programs having a certain structural property characteristic of a large class of problems of practical interest. The property makes possible the decomposition of the problem into a sequence of small linear programs whose iterated solutions solve the given problem through a generalizatio?n of the simplex method for linear programming.

Speaker: Sedat Sarıkaya

Title: “Comparison of Inverse Electrocardiography Methods”

Date: 22 December 2004 at 15:40

Place: Institute of Applied Mathematics M-205

Abstract:

The goal of inverse problem of electrocardiography is to estimate cardiac electrical activity based on measured torso surface potentials and a geometric model of the torso. Due to attenuation and spatial smoothing that occurs in the thorax, inverse electrocardiography is an ill-posed inverse problem and the forward model matrix is badly conditioned. Thus small disturbances in the measurements lead to amplified errors in inverse solutions. Regularization, which can be defined as imposition of a priori constraints, is needed to combat this ill-posedness. The goal of this thesis is to study various regularization approaches applied to inverse electrocardiography problem and compare their performances.

Speaker: Seval Çevik

Title: “Basle Committee”

Date: 22 December 2004 at 15:40

Place: Institute of Applied Mathematics M-205

Abstract:

The role of Basle Committee in the international regulation and supervision of banking institutions.

Speaker: İrem Yıldırım

Title: “Heavy-Tailed Distributions and Extreme Value Theory in Finance”

Date: 15 December 2004 at 15:40

Place: Institute of Applied Mathematics M-205

Abstract:

It is of great importance for those in charge of managing risk to understand how financial as set returns are distributed. Practitioners often assume for convenience that the distribution is normal. Since the 1960s, however, empirical evidence has led many to reject this assumption in favor of various heavy-tailed alternatives. In a heavy-tailed distribution the likelihood that one encounters significant deviations from the mean is much greater than in the case of the normal distribution. It is now commonly accepted that financial asset returns are, in fact, heavy-tailed. The goal of presentation is to examine how these heavy tails affect financial portfolio theory risk management and to describe some of the methods offered by Extreme Value Theory that one can use to deal with heavy tails.

Speaker: Zehra Ekşi

Title: “Value at Risk and Alternative Measures of Risk”

Date: 15 December 2004 at 15:40

Place: Institute of Applied Mathematics M-205

Abstract:

Quantifying and managing the market risk is one of the most important issues in todays financial markets. VAR is the most widely used method to define market risk. But due to its weaknesses sourcing from its underlying assumptions, alternative risk measures have been developed. In this representation both VAR and its alternatives will be examined.

Speaker: Ayşegül İşcanoğlu

Title: “Credit Scoring with Discriminant Analysis”

Date: 15 December 2004 at 15:40

Place: Institute of Applied Mathematics M-205

Abstract:

Credit scoring procedure is a quantative approach used to measure and evaluate the creditworthiness of a firm. The important problem in the credit scoring procedure is to discriminate and classify the firms with respect to their business performances, such as profitability, solvency, management ability, liquidty and so on. Over the 40 years, for this aim various methods have been used. In this talk, I will introduce you with one of the oldest and widely used method that is discriminant analysis.

Speaker: Serkan Zeytun

Title: “A Fair Spread Model For High Yield Emerging Market Sovereigns”

Date: 08 December 2004 at 15:40

Place: Institute of Applied Mathematics M-205

Abstract:

This model drives the term structure of default probabilities, and hence fair value credit spreads, from country economic fundamentals. Unlike previous, econometric analyses of fair value, this model is based on a new approach. This model tackles what have been belived is the core of the problem of fair value: namely, a country’s fiscal dynamics.

Speaker: Rezzan Kan

Title: “Estimating and Forecasting Volatility of Stock Indices Using Asymmetric Garch Models and (Skewed) Student-T Densities”

Date: 08 December 2004 at 15:40

Place: Institute of Applied Mathematics M-205

Abstract:

Some well-known characteristics are common to many financial time series. Volatility clustering is often observed (i.e. large changes tend to be followed by large changes and small changes tend to be followed by small changes; see Mandelbrot, 1963, for early evidence). Second, financial time series often exhibit leptokurtosis, meaning that the distribution of their returns is fat-tailed (i.e. the kurtosis exceed the kurtosis of a standard Gaussian distribution, see Mandelbrot, 1963, or Fama, 1965). Moreover, the so-called “leverage effect”, first noted in Black (1976), refers to the fact that changes in stock prices tend to be negatively correlated with changes in volatility (i.e. volatility is higher after negative shocks than after positive shocks of same magnitude).

Speaker: Hale Baş

Title: “Generalized Hyperbolic Distributions & Brazilian Data”

Date: 1 December 2004 at 15:40

Place: Institute of Applied Mathematics M-205

Abstract:

Aim is to discuss the use of the Generalized Hyperbolic Distributions to fit the Brazilian asset returns. Describe how to use these distributions in VaR estimation & derivative price computation

Speaker: Deniz Toz

Title: “How do modern cryptography work?”

Date: 1 December 2004 at 15:40

Place: Institute of Applied Mathematics M-205

Abstract:

Every day hundreds of thousands of people interact electronically, whether it is through e-mail, e-commerce, ATM machines, or cellular phones. The perpetual increase of information transmitted electronically has lead to an increased reliance on cryptography. All modern algorithms use a key to control encryption and decryption. There are two classes of key-based encryption algorithms, symmetric (or secret-key) and asymmetric (or public-key) algorithms. In this talk, a general introduction to public key infrastructure will be presented. In addition, the basic principles of cryptography in real life and it’s target issues (such as data integrity, authentication, non-repudiation) will be briefly discussed.

Speaker: Arda Kurt

Title: “Methods in Forward Problem of Electrocardiography”

Date: 1 December 2004 at 15:40

Place: Institute of Applied Mathematics M-205

Abstract:

Electrocardiography (E.C.G.) involves the interpretation of the potentials recorded at the body surface due to electrical activity of the heart. The general objective of the socalled forward and inverse problems of ECG is a better qualitative and quantitative understanding of the heart’s electrical activity. One of these main problems of ECG, the forward problem, entails the calculation of the body-surface potentials, starting usually from either equivalent current dipoles that represent the electrical activity or from known potentials on the heart outer surface (the epicardium). This talk will mainly cover the methods (surface/volume methods) developed to solve the forward problem of ECG with a background information on ECG.

Speaker: *Selime Gürol

Title: “Classification and clustering of Landscape images”

Date: 24 November 2004 at 15:40

Place: Institute of Applied Mathematics M-205

Abstract:

Remote sensing maximizes diversity of information and area of coverage at minimal cost, and allows the interpreter to address several problems far more rapidly than by any other method. Recent developments in remote sensing instrumentation offered a challenge to the mathematical and statistical methods to interpret the acquired information. Interpretation of LANDSAT/STATLOG images, which is viable for early detection of ecological problems, urban planning, disasters, communications, human use of the land etc., is an important problem in this context. Statistical learning methods like additive models, trees (CART), learning vector quantization, neural networks, k-neighbourhood methods are already popular in unsupervised classification and clustering of image scene inverse problems of this field. Due to the degradation and corruption of the images, the performance is limited both by the accuracy of clustering and by the extent of the classification. In this project we are concerned with improving the performance of the available methods by both investigating the optimum implementation of statistical methods and by employing various mathematical and statistical methods like Bayesian networks, robust estimation, etc.

Speaker: *Osman Özgür

Title: “Discrete Tomography in VLSI Microchip Design”

Date: 24 November 2004 at 15:40

Place: Institute of Applied Mathematics M-205

Abstract:

Optimization theory is a key technology for inverse problems of reconstruction in science, engineering and economy. Discrete tomography is a modern research field dealing with the reconstruction of finite objects in, e.g., VLSI chip design, where this thesis will focus on. Here, we use new optimization problems and methods to approximately resolve this NP-hard problem. Our new introductions base on interpretations, algorithms and learning methods coming from the theories of coding and optimal experimental design. Here, we combine optimization with exploiting geometrical-algebraical symmetries or, more generally, equivariances. Furthermore, we also obtain numerical experience based on algorithmic codes.

Speaker: *Emre Dağlı

Title: “Generalized Semi-Infinite Optimization of Anticipatory Systems”

Date: 24 November 2004 at 15:40

Place:Institute of Applied Mathematics M-205

Abstract:

This talk is an introduction into a modern field optimization problems, and their utilization for anticipatory systems. These problems are from generalized semi-infinite optimization, and they admit an infinite set of inequality constraints, which depends on the state. Before using these problems for anticipation (prediction), firstly, some basic understanding of them is necessary. Under suitable assumptions, there are local stability properties of the Kuhn-Tucker points, and global stability properties of the feasible set and corresponding structural stability of the entire optimization problem. In the course of this well understanding of structure and stability, the perturbational approach gives rise to reconstructions. By studying three applications of generalized semi-infinite optimization, secondly, we interpret these aspects of inverse problems in the sense of prediction.

Speaker: *Fatma Bilge Yılmaz

Title: “Mathematical Modeling and Approximation of Gene Expression Patterns and Gene Networks”

Date: 22 October 2004 at 16:00

Place: Institute of Applied Mathematics M-205

*Fatma Bilge Yılmaz: Institute of Applied Mathematics, Computational Biology and Medicine Working Group, METU