## Thesis Defences

##### Last Updated:

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Thesis defenses in all programs should be announced online 10 days before the oral examination. The details of the thesis presentations are listed here and the calendar located in "Home" page. The students are strongly encouraged to attend the presentations.

## Schedule

** Speaker: **Ahmet Kürşat İrge

** Affiliation: **MSc in Financial Mathematics

**Advisor:** Seza Danışoğlu

**Place/Zoom Link: **https://zoom.us/j/94066158367?pwd=YVlpcm9CQk1MSGhmcGwwcXNidTBUQT09

**Meeting number: **940 6615 8367

**Password: **752576

**Time: **Wednesday, May 11, 2022; 09:00

**Abstract:** This study examines whether the industry effect variables can allow investing in neglected high BM firms with the classic FSCORE method. The industry winners in the neglected firms cluster are called Underdogs. The industry effect variables examine the industry effects while the FSCORE method takes the internal picture of the high book-to-market firms. Thus, a comprehensive fundamental analysis process is established. The Generalized Method of Moment estimation explains the direction and strength of relations between the industry effects variables and future returns. The results show that the industry-winners and twelve-month market-adjusted returns have a positive relationship with statistically significant with an approximate 8% return increase for firms above the industry average. The industry winners method can separate future winners and losers in the neglected firms' cluster, so the Underdog firms produce an approximate 6% market-adjusted return increase in the twelve months. It is essential to highlight that this return increase comes from the neglected group. Consequently, the industry effect variables increased the number of investable firms by approximately 90%. The industry effect variables can separate future winners and losers in the high book-to-market firms. Moreover, the industry effects method also increased the scope and power of the FSCORE.

** Speaker: **Selim Orhan

** Affiliation: **MSc in Financial MathematicsMSc in Financial Mathematics

**Advisor:** Seza Danışoğlu

**Place/Zoom Link: **https://zoom.us/j/94066158367?pwd=YVlpcm9CQk1MSGhmcGwwcXNidTBUQT09

**Meeting number: **940 6615 8367

**Password: **752576

**Time: **May 10, 2022, 10:00 am

**Abstract:** Banks are considered as the marginal and sophisticated investors of financial markets. This is evident in the Haddad and Sraer (2020) study that examines the US government bond excess returns. This study extends the Haddad/Sraer analysis to the Turkish government bond market. According to the forecasting results, exposure ratio provides explanatory power over bond excess returns, especially for longer maturities. On the other hand, output gap and industrial growth present strong in-sample forecasting power for shorter-term maturities. The inclusion of macroeconomic variables into the regression along with exposure ratio increases the significance and explanatory power of exposure ratio for the explanation of bond excess returns. Output gap is the most contributive in-sample forecasting macro variable in terms of the explanation of bond excess returns. Together with output gap and exposure ratio, the inclusion of consumer price index (CPI), producer price index (PPI) or consumer confidence index improves the statistical and economic significance of in-sample regression results.

** Speaker: **Süleyman Cengizci

** Affiliation: **Ph.D. in Scientific Computing

**Advisor:** Prof. Ömur Ugur and Prof. Tayfun E. Tezduyar

**Place/Zoom Link: https://zoom.us/j/92983087322?pwd=VTB5RExYcm90cEpzeEFnTENMYmo1UT09**

**Meeting number: **929 8308 7322

**Password: **379914

**Time: **Feb 28, 2022, 10:00 Istanbul (virtual on zoom)

**Abstract:** For both military and civil aviation purposes, rockets, missiles, and spacecraft moving at hypersonic speeds are being utilized in recent years. While these vehicles move at speeds five times the speed of sound or more, they experience many extreme physical and chemical conditions during their flight. Because of molecular friction, such high velocities cause very high temperatures, and these high temperatures result in the excitation of the components of the gas mixture in which the vehicle moves. This situation causes various thermochemical interactions in the flow field and affects the dynamics of the flight. These interactions need to be examined accurately, for both the flight safety and the vehicle reaching the right target at the right time.

Wind tunnel experiments are both costly and insufficient to regenerate the high temperatures and shock interactions of hypersonic flights. These wind tunnel setups can also take a long time to design, test, and finally obtain the experimental data with. Therefore, computational fluid dynamics (CFD) tools are essential in analyzing the flight dynamics of hypersonic vehicles and designing them for such high speeds. Classical discretization methods need to be supplemented with stabilization and shock-capturing techniques since they suffer from spurious oscillations in simulating such high-speed flows.

In this thesis, hypersonic flows in thermochemical nonequilibrium are computationally studied. To this end, hypersonic flows of a five-species (O, N, NO, O_{2}, N_{2}) gas mixture around a cylinder are examined with a 17-reaction chemical model. The gas particles may be in different energy modes in hypersonic regimes due to the high temperatures: translational, rotational, vibrational, and electron-electronic. Since they have the similar time scales to reach equilibrium, the translational and rotational energy modes can be represented by one temperature, and the vibrational and electron-electronic energy modes by another. Therefore, a two-temperature chemical kinetic model is adopted.

In the computations, the compressible-flow Streamline-Upwind/Petrov--Galerkin method is employed to stabilize the finite element formulation. The stabilized formulation is supplemented with the YZβ shock-capturing to obtain good solution profiles at shocks. The nonlinear system of equations resulting from the space and time discretizations is solved with the Newton--Raphson nonlinear iterative process and ILU-preconditioned generalized minimal residual (GMRES) iterative search technique. The solvers are developed in the FEniCS environment.

** Speaker: **İsa Eren Yıldırım

** Affiliation: **MSc in Scientific Computing

**Advisor:** Prof. Dr. Ömür UĞUR

**Co Advisor : **Dr. Umair Bin WAHEED

**Place/Zoom Link: https://zoom.us/j/99405315740?pwd=ei9wRnVIZTUzYnlmVVhZbzZzU1FuQT09**

**Meeting number: **994 0531 5740

**Password: **992314

**Time: **Friday, February 11, 2022 / 11:00 (virtual on zoom)

**Abstract:** In Seismic prospecting, huge amounts of data are collected and processed to infer the structural and lithological composition of the subsurface. The key step in this procedure is velocity model building (VMB). First arrival traveltime inversion is one of the VMB tools commonly used for predicting near-surface velocity structures in seismic exploration. The underlying mathematical model describing the connection between the data (traveltimes) and the model parameters (velocity) is the eikonal equation, which is a first-order non-linear partial differential equation. Conventionally, the in version is carried out using ray-based methods or gradient-based algorithms. Though the gradient-based algorithms find the gradient that is needed to update the model parameters without requiring ray tracing, it can be computationally demanding. On the other hand, despite its robustness and efficiency ray-based methods suffer from complex regions as the ray theory relies on the high-frequency approximation. Instead of using these approaches for a traveltime inversion problem, I propose a machine learning (ML) based approach, specifically harnessing the physics informed neural net works (PINNs) exploiting the mathematical model represented by the eikonal equa tion to estimate the near-surface subsurface velocities. Training neural networks with the aid of the physics defining the underlying problem overcomes some of the challenges inherent in the traditional approaches such as requiring an acceptable a priori information, and incorrect parameter updates in the optimization. Through synthetic tests and the application of a real data, I show the reliability of the PINN based travel time inversion which can be a potential alternative tool to the traditional tomography frameworks.

** Speaker: **Ertuğrul Umut Yıldırım

** Affiliation: **MSc in Scientific Computing

**Advisor:** Assoc. Prof. Dr. Seza DANIŞOĞLU

**Co Advisor : **Assist. Prof. Dr. Guenther GLATZ

**Place/Zoom Link:https://zoom.us/j/99405315740?pwd=ei9wRnVIZTUzYnlmVVhZbzZzU1FuQT09**

**Meeting number: **994 0531 5740

**Password: **992314

**Time: **Friday, February 11, 2022/10:00 (virtual on zoom)

**Abstract:** Computed tomography has been widely used in clinical and industrial applications as a non-destructive visualization technology. Revealing the internal structure of porous materials with the help of computed tomography scanning is at the heart of digital rock physics. The quality of computed tomography scans has a strong effect on the accuracy of the estimated physical properties of the investigated sample. X-ray exposure time is a crucial factor for scan quality. Ideally, long exposure time scans, yielding large signal-to-noise ratios, are available if physical properties are to be delineated. However, especially in micro-computed tomography applications, long exposure times constitute a problem for monitoring some physical processes that are happening quickly. To alleviate this problem, this thesis proposes a convolutional neural network approach for scan quality enhancement allowing for a reduction in X-ray exposure time while improving signal-to-noise ratio of the scanned image simultaneously. Moreover, the impact of using different loss functions, namely the mean squared error and the structural similarity index measure, on the performance of the network is analyzed. Both the visual and quantitative assessments show that the trained network greatly improves the quality of low-dose scans.

** Speaker: **Abdullah Efe Gül

** Affiliation:** MSc in Financial Mathematics

**Advisor:** Assoc. Prof. Dr. Seza DANIŞOĞLU

**Place/Zoom Link:https://zoom.us/j/94372855962?pwd=Wm5menpQWURxNjZjRXFlN01NRjJjUT09**

**Meeting number: **943 7285 5962

**Password: **thesis

**Time: **Friday, February 11, 2022 / 10:00 (virtual on zoom)

**Abstract:** This thesis proposes two new measures of investor attention: Search Traffic (ST) and Click Per Search (CPS). These two measures as well as the commonly used Google Search Volume Index (SVI) measure are constructed by optimizing the number of keywords while using a search engine optimization. ST is measured based on financial website URLs without using any search keyword and is a direct measure of investor attention. The relationships between investor attention and stock market activities consisting of return and volatility are investigated for the Dow Jones Index (DJI) and its constituent stocks. The study provides robust evidence that attention has significant and asymmetric impact on index returns as well as excess returns. It has significant and negative influence on returns under bearish conditions while significant and positive effect during bullish conditions. Attention is also a significant driver of both index and stock volatility such that volatility increases following an increase in attention. In addition, investors respond to price reversals more quickly compared to positive index returns. Observations on CPS suggest that the more investors search for a financial keyword, the less they click on financial websites per searched keyword.

**Keywords:** Returns, Volatility, Investor attention, Search Engine Optimization

** Speaker: **Cansu Bozkurt

** Affiliation:** PhD (or MSc) in Programme

**Advisor:** Assoc.Prof.Dr. Murat CENK

**Co-Advisor**: Dr. Cansu BETİN ONUR

**Place/Zoom Link:**https://zoom.us/j/92303884017?pwd=dGFPcFNVNCttLzQ5WG4yRkNtQ1lFUT09

**Meeting number:**923 0388 4017

**Password: **216977

**Time: **10.02.2022 / 16.30

**Abstract:** The time period after the mid-20th century was named as information age or digital age. In that age, the world is being digitalized very fastly. The amount of data trans- ferred and processed online is increasing rapidly. As a result, data protection became an essential topic for researchers. To process or make a computation on the encrypted data deciphering ciphertext first causes a security flaw. Homomorphic encryption (HE) algorithms were designed to make computations on data without deciphering it. However, HE algorithms are able to work for a limited amount of processing steps. Fully homomorphic encryption (FHE) algorithms are developed to solve this problem. It is possible to apply any efficiently computable function on encrypted data. This thesis presents definitions, properties, applications of FHE. Some constructions of FHE schemes based on the integers are also analyzed. Furthermore, the computational complexity of two algorithms, namely the DGHV scheme and Batch DGHVscheme (a scheme that supports encrypting and homomorphically processing a vector of plaintexts as a single ciphertext ) has been computed and their efficiency are compared based on the complexities. While the DGHV scheme encrypts the one-bit message, the batch DGHV scheme encrypts an l-bit message vector m at a time. The primary purpose is to research which option is more efficient for encrypting l-bit messages.

** Speaker: **Furkan Höçük

** Affiliation: **MSc in Financial Mathematics

**Place/Zoom Link: https://zoom.us/j/93230944278?pwd=WEp5S3BTMjMrNkJtaHlSNUtwMVo5UT09**

**Meeting number: **932 3094 4278

**Password: **868382

**Time: **Thursday, February 10, 2022 / 14:00 (virtual on zoom)

**Abstract:** This empirical study compares the relative performances of the Fama-French five-factor model without foreign exchange risk and the five-factor model incorporating foreign exchange risk on capturing the cross-section of stock returns in Borsa İstanbul. We follow a similar methodology to the Fama-French's in constructing intersection portfolios and factor variables based on the several balance-sheet and income statement items of firms listed in Borsa İstanbul over July 2009 – June 2020. We propose a new proxy for foreign exchange risk on the deviations of the average stock return movements. It is known that, in emerging countries like Turkey, the tendency of firms to borrow from foreign markets where they can borrow at relatively advantageous rates and the volatile foreign exchange rates has distressed the composition of many firms' assets and liabilities in foreign currency. Our intention to suggest a proxy for foreign exchange risk is the possible effect of the composition of firms' assets and liabilities in foreign currency on average stock returns. In light of the several statistical indicators to test the predicting power, we find that both versions are good at capturing deviations in expected returns. Adding the FX risk factor to Fama-French five-factor model can slightly improve the explanatory power. We also predicted excess returns of intersection portfolios using support vector regression method. Subsequently, we combined predictions of simple linear regression and support vector regression and found out that SVR outperforms SLR for both versions of Fama-French five-factor with and without FX risk.

** Speaker: **Nazlı Ceren Demir

** Affiliation:** MSc in Cryptography

**Advisor:** Assist. Prof. Dr. Oğuz YAYLA

**Place/Zoom Link: https://zoom.us/j/3122100970**

**Meeting number:**Without number

**Password: **Without password

**Time: **10.02.2022 / 16.00

**Abstract:**

** Speaker: **Hamdi Burak Bayrak

** Affiliation:** M.Sc. in Scientific Computing

**Advisor:** Assoc. Prof. Şeyda Ertekin

**Co-Advisor**: Assoc. Prof. Hamdullah Yücel

**Place/Zoom Link:** https://us04web.zoom.us/j/7619250253?pwd=NEdVOHAwTjVVbWtpQWxlb0dYMjZjdz09

**Meeting number:**761 925 0253

**Password: **6m6cbU

**Time: **February 10, 2022 10:30

**Abstract:** Semi-supervised learning is a powerful approach to make use of unlabeled data to improve the performance of a deep learning model. One mostly used method of this approach is pseudo-labeling. However, pseudo-labeling, especially its originally proposed form tends to remarkably suffer from noisy training when the assigned labels are false. In order to mitigate this problem, in our work, we investigate the gradient sent to the neural network and propose a heuristic method, called competing labels, where we arrange the loss function and choose the pseudo-labels in a way that the gradient the model receives contains more than one negative element. We test our method on MNIST, Fashion-MNIST, and KMNIST datasets and show that our method has a better generalization performance compared to the originally proposed pseudo-labeling method.

** Speaker: **Özgün Ada Ceylan

** Affiliation:** M.Sc. in Scientific Computing

**Advisor:** Prof. Dr. Ömür UĞUR

**Place/Zoom Link: https://zoom.us/j/92373330296?pwd=N3NqRCtDaTNGaENyeGlPNzVYK1hkZz09**

**Meeting number: **923 7333 0296

**Password: **008212

**Time: **Wednesday, February 09, 2022 / 10:00 (virtual on zoom)

**Abstract:** Advancing technologies in distributed electrical generation and increasing amount of required electricity make electrical systems more complicated. Thus, the number of buses has in[1]creased and the size of incidence matrix for electrical power flow calculation has expanded. Hence, investigation and performance analysis on different solvers are needed. In this thesis, a performance comparison between iterative solvers for electrical power flow is studied. These solvers are Newton-Raphson, Fast-Decoupled and Newton-Krylov Spaces methods. Besides, the effect of parallel programming in Newton-Krylov Spaces Method is also investigated.

** Speaker: **Giray Efe

** Affiliation:** MSc in Cryptography

**Advisor:** Assoc. Prof. Dr. Murat Cenk

**Place/Zoom Link:** https://zoom.us/j/96559971366?pwd=Q3hteks1QlRDeGNCdTNicEdmcktGUT09

**Meeting number:** 965 5997 1366

**Password: **577709

**Time: **February 09, 2022 09:50

**Abstract: : **Polynomial multiplication on the quotient ring is one of the most fundamental, general-purpose operations frequently used in cryptographic algorithms. Therefore, a possible improvement over a multiplication algorithm directly affects the performance of algorithms used in a cryptographic application. Well-known multiplication algorithms such as Schoolbook, Karatsuba, and Toom-Cook are dominant choices against NTT in small and ordinary input sizes. On the other hand, how these approaches are implemented under the quotient ring of polynomials, matters. Instead of applying the reduction procedure as the final stage, using Toeplitz Matrix Product (i.e., TMVP) is a clever way to realize the modular multiplication more efficiently. Furthermore, the hybrid use of these algorithms yields more efficient results than the static choice of any single algorithm. For this purpose, we derive and analyze various constructions of multiplication and share the best possible sequences under different circumstances, and show that TMVP is a decent choice instead of classical modular polynomial multiplication approaches in cryptographic applications.

** Speaker: **Berkin Aksoy

** Affiliation:** MSc in Cryptography

**Advisor:** Assoc. Prof. Dr. Murat Cenk

**Place/Zoom Link:** https://zoom.us/j/99299800485?pwd=eCtlVzhQcUR2aG01Z0JqZXBvWFJ4UT09

**Meeting number:** 992 9980 0485

**Password: **185163

**Time: **February 09, 2022 09:00

**Abstract: : **Since the beginning of the National Institute of Standards and Technology (NIST), The Post-Quantum Cryptography (PQC) Standardization process, efficient implementations of lattice-based algorithms have been studied extensively. Lattice-based NIST PQC finalists use polynomial or matrix-vector multiplications on the ring with type Z

_{q}[x] / f(x). For convenient ring types, Number Theoretic Transform (NTT) can be used to perform multiplications as done in Crystals-KYBER among the finalists of the NIST PQC Standardization Process. On the other hand, if the q value of the scheme is a power of 2, as in NTRU and Saber, which are among the other lattice-based finalists, NTT can not be used explicitly. Hence multiplications are performed by the combination of Toom-Cook and Karatsuba algorithms. Recently, a novel technique called lazy interpolation has been introduced to increase the performance of Toom-Cook and Karatsuba algorithms. This thesis shows that the block recombination method is equivalent to lazy interpolation and can be used efficiently on multiplication algorithms. On the practical side, we compare different hybrid multiplication algorithms, then implement the block recombination method for Saber. Performance results are given in cycle values on general-purpose Intel processors with C implementation. Our work speeds up key generation, encapsulation, and decapsulation parts of Saber than the previous C implementations in the literature with a rate of between 10%-13%.

** Speaker: **Esra Yeniaras

** Affiliation:** PhD in Cryptography

**Advisor:** Assoc. Prof. Dr. Murat Cenk

**Place/Zoom Link:** **https://zoom.us/j/96725437392?pwd=V1dvS2lHd1AvNkZIWDdtOWFTTzN1Zz09**

**Meeting number:** 967 2543 7392

**Password: **691826

**Time: **January 21, 2022 14:00

**Abstract: : **Some of the post-quantum cryptographic protocols require polynomial multiplication in characteristic three fields, thus the efficiency of such multiplication algorithms gain more importance recently. In this thesis, we propose four new polynomial multiplication algorithms in characteristic three fields and we show that they are more efficient than the current state-of-the-art methods. We first analyze the well-known algorithms such as the schoolbook method, Karatsuba 2-way and 3-way split methods, Bernstein’s three 3-way split method, Toom-Cook-like formulas, and other recent algorithms. We realize that there are not any 4-way or 5-way split multiplication algorithms in characteristic three fields unlike the binary (characteristic two) fields which have various 4, 5, or more split versions. We then propose three different 4-way split polynomial multiplication algorithms which are derived by using the interpolation technique in F9. Furthermore, we propose a new 5-way split polynomial multiplication algorithm and then compare the arithmetic complexities and the implementation results for all of the aforementioned methods. We show that the new 4-way and 5-way split algorithms provide a 48.6% reduction in the arithmetic complexity for multiplication over F9 and a 26.8% reduction for multiplication over F3 for the input size 1280. Moreover, the new 4-way and 5-way algorithms yield faster implementation results compared to the current state-of-the-art methods. We apply the proposed methods to NTRU Prime protocol, a key encapsulation mechanism, submitted to NIST PQC Standardization Process by Bernstein et al., which executes characteristic three polynomial multiplication in its decapsulation stage. We implement the new methods in C and observe a 26.85% speedup for stnrup653 and a 35.52% speedup for sntrup761 in the characteristic three polynomial multiplication step of the NTRU Prime decapsulation.

** Speaker: **Sıtkı Can Toraman

** Affiliation: **MScin Scientific Computing

**Advisor:** Assoc.Prof. Dr. Hamdullah Yücel

**Place/Zoom Link:** https://zoom.us/j/5990725041

**Meeting number:** 599 072 5041

**Password:**

**Time: **Jan 6, 2022 11:00

**Abstract: : **Many physical phenomena such as the flow of anaircraft, or heating process, or wave ropagationare modeled mathematically by differential equations, in particular partialdifferential equations (PDEs). Analytical solutions to PDEs are often unknown orvery hard to obtain. Because of that, we simulate such systems by numerical methodssuch as finite difference, finite volume, or finite element, etc. When we want tocontrol the behavior of certain system components, such as the shape of a wingof an aircraft or an applied heat distribution, it becomes equivalent tooptimizing certain parameters of the underlying PDEs. Optimization of realworld systems in this way is called PDE-constrained optimization or optimalcontrol problems. To have a more accurate mathematical model, we employuncertain coefficients in PDEs since nature has different sources of intrinsicrandomness. In this thesis, we study a numerical investigation of a stronglyconvex and smooth tracking-type functional subject to a convection-diffusionequation with random coefficients. In spatial dimension, we use the FiniteElement Method (FEM), in probability dimension, we use the Monte Carlo (MC)method, and as an optimization method, we use the stochastic gradient (SG)method, where the true gradient is replaced by a stochastic one to minimize theexpected value over a random function. To accelerate the onvergence of the stochasticapproach, momentum terms, i.e., Polyak’s and Nesterov’s momentums, are added. Afull error analysis including Monte Carlo, finite element, and stochastic momentumgradient iteration errors are done. Numerical examples are presented toillustrate the performance of the roposed stochastic approximations in thePDEconstrained optimization setting.

** Speaker: **Ahmet Şimşek

** Affiliation: **M.Sc. in Cryptography

**Advisor:** Oğuz Yayla

**Place/Zoom Link:** https://zoom.us/j/94454255374?pwd=MTA0NFFQKzZ6VC9YMXRIU3IrbndqZz09

**Meeting number:** 944 5425 5374

**Password:**123asd

**Abstract: **Hyperledger was set up with the aim of being an open-source platform targeted at accelerating industry-wide collaboration hosted by The Linux Foundation for developing robust and dependable blockchain and distributed ledger-based technological platform that may be applied across several industry sectors to improve the efficiency, performance, and transactions of different business operations. Various distributed ledger frameworks and libraries have been developed for this purpose. In this thesis, the Ursa cryptographic library, which is one of the libraries being developed to offer its users with dependable, secure, user friendly and pluggable cryptographic applications to its users, has been examined and the performances of both the anonymous identity creation process and the presented cryptographic algorithms are examined.

** Speaker: **Sharoy Augustine Samuel

** Affiliation: **Ph.D. in Financial Mathematics

**Advisor:** Ali Devin Sezer

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**Date: **July 2, 2021 10:30 Ankara

The **Abstract: **We study a class of nonlinear BSDEs with a superlinear driver process $f$ adapted to a filtration${\mathbb F}$ and over a random time interval $[0,S]$ where $S$ is a stopping time of ${\mathbb F}$. The filtration is assumed to support at least a $d$-dimensional Brownian motion as well as a Poisson random measure. The terminal condition $\xi$ is allowed to take the value $+\infty$, i.e., singular. Our goal is to show existence of solutions to the BSDE in this setting. We will do so by proving that the minimal supersolution to the BSDE is a solution, i.e., attains the terminal values with probability $1$. We focus on non-Markovian terminal conditions of the following form:1) $\xi = \infty \cdot {\bm 1}_{\{\tau \le S\}}$ and 2) $\xi_2 = \infty \cdot {\bm 1}_{\{ \tau >S \}}$ where $\tau$ is another stopping time.

We call a stopping time $S$ solvable with respect to a given BSDE and filtration if the BSDE has a minimal supersolution with terminal value $\infty$ at terminal time $S$. The concept of solvability plays a key role in many of the arguments. We also use the solvability concept to relax integribility conditions assumed in previous works for continuity results for BSDE with singular terminal conditions for terminal values of the form $\infty \cdot {\bm 1}_{\{\tau \le T \}}$ where $T$ is deterministic.We provide numerical examples in cases where the solution is explicitly computable and a basic application in optimal liquidation.

** Speaker: **Süleyman Yıldız

** Affiliation: **PhD in Scientific Computing

**Advisor:** Bülent Karasözen

** Place: https://zoom.us/j/92728802662?pwd=YkRxSUlwZ0s3MVJGZXNmdkxLRFo1QT09**

**Meeting number:** **:** 927 2880 2662

**Password:** 361150

**Date: **June 18, 2021 13:30 Ankara

**Abstract: **The shallow water equations (SWEs) consist of a set of two-dimensional partial differential equations (PDEs) describing a thin inviscid fluid layer flowing over the topography in a frame rotating about an arbitrary axis. SWEs are widely used in modeling large-scale atmosphere/ocean dynamics and numerical weather prediction. Highresolution simulations of the SWEs requires long time horizons over global scales, which when combined with accurate resolution in time and space makes simulations very time-consuming. While high-resolution ocean-modeling simulations are still feasible on large HPC machines, performing many query applications, such as repeated evaluations of the model over a range of parameter values, at these resolutions, is not feasible. Techniques such as reduced-order modeling produces an efficient reduced model based on existing high-resolution simulation data. In this thesis, ROMs are investigated for the rotating SWE, with constant (RSWE) and non-traditional SWE with full Coriolis force (NTSWE), and for rotating ther- mal SWE (RTSWE) while preserving their non-canonical Hamiltonian-structure, the energy and Casimirs, i.e. mass, enstrophy, vorticity, and buoyancy. Two different approaches are followed for constructing ROMs; the traditional intrusive model order reduction with Galerkin projection and the data-driven, non-intrusive ROMs. The full order models (FOM) of the SWE, which needed to construct the ROMs is obtained by discretizing the SWE in space by finite differences by preserving the skew-symmetric structure of the Poisson matrix. Applying intrusive proper orthogonal decomposition (POD) with the Galerkin projection, energy preserving ROMs are constructed for the NRSWE and RTSWE in skewgradient form. Due to nonlinear terms, the dimension of the reduced-order system scales with the dimension of the FOM. The nonlinearities in the ROM are computed by applying the discrete empirical interpolation (DEIM) method to reduce the computational cost. The computation of the reduced-order solutions is accelerated further by the use of tensor techniques. For the RSWE in linear-quadratic form, the dimension of the reduced solutions is obtained using tensor algebra without necessitating hyper-reduction techniques like the DEIM. Applying POD in a tensorial framework by exploiting matricizations of tensors, the computational cost is further reduced for the rotating SWE in linear-quadratic as well in skew-gradient form. In the data-driven, nonintrusive ROMs are learnt only from the snapshots by solving an appropriate leastsquares optimization problem in a low-dimensional subspace. Data-driven ROMs are constructed for the NTSWE and RTSWE with the operator inference (OpInf) using, (non-Markovian) and with re-projection (Markovian) dynamics, respectively. Computational challenges are discussed that arise from the optimization problem being ill-conditioned. Moreover, the non-intrusive model order reduction framework is extended to a parametric case, whereas we make use of the parameter dependency at the level of the PDE without interpolating between the reduced operators. The overall procedure of the intrusive and non-intrusive ROMs for the rotating SWEs in linear-quadratic and skew-gradient form yields a clear separation of the offline and online computational cost of the reduced solutions. The predictive capabilities of both models outside the range of the training data are shown. Both ROMs behave similarly and can accurately predict in the test and training data and capture system behavior in the prediction phase. The preservation of physical quantites in the ROMs of the SWEs such as energy (Hamiltonian), and other conserved quantities, i.e., mass, buoyancy, and total vorticity, enables that the models fit better to data and stable solutions are obtained in long-term predictions which are robust to parameter changes while exhibiting several orders of magnitude computational speedup over the FOM.

** Speaker: **Umut Gölbaşı

** Affiliation: **MSc in Financial Mathematics

**Advisor:** A. Sevtap Kestel

** Place: https://zoom.us/j/95369171602?pwd=ek1UUm90a3VDR1c5dWtRNGdzQkZMUT09**

**Meeting number:** **:** 953 6917 1602

**Password:** 783645

**Date: **15 March 2021, 10:00

**Abstract: **Electricity generation cost and environmental effects of electricity generation continue to be among central themes in energy planning. The choice of electricity generation technology and energy source affect the environment through released greenhouse gases and other waste. United States is the world’s second-largest CO2 emitter and electricity consumer. This thesis aims to estimate the optimal capacity expansion of electric power sector in the United States for 2022-2050. We develop a fuzzy multi-objective linear program to minimize cost and environmental effects. In sensitivity analyses, we show how different policies and price evolution may alter the mix. Later on, we examine the effects of the new capacity mix and implied generation on the cost of electricity and emissions. We find that direct modeling of capacity factors give meaningful results. According to this thesis, renewable energy is expected to reach more than 1100 GW installed capacity by 2050. This reduces average cost of electricity generation by more than 70 percent and reduces CO2 emissions by more than 80 percent compared to expected end-2021 levels.

** Speaker: **Burcu Aydogan

** Affiliation: **PhD in Financial Mathematics

**Advisor:** Ömür Ugur

** Place: https://zoom.us/j/94118246108?pwd=LzhyL255SkE1eHpQRHA2RW5vSG5aUT09**

**Meeting number:** 941 1824 6108

**Password:** 316831

**Date: **15 March 2021, 13:00

**Abstract: **In this thesis, we intend to develop optimal market making strategies in a limit order book for high-frequency trading using stochastic control approach. Firstly, we address for evolving optimal bid and ask prices where the underlying asset follows the Heston stochastic volatility model including jump components to explore the effect of the arrival of the orders. The goal of the market maker is to maximize her expected return while controlling the inventories where the remaining is charged with a liquidation cost. Two types of utility functions are considered: quadratic and exponential with a risk averse degree, respectively. Then, we take into consideration a model considering an underlying asset with jumps in stochastic volatility. We derive the optimal quotes for both models under the assumptions. For the numerical simulations, we apply finite differences and linear interpolation as well as extrapolation methods to obtain a solution of the nonlinear Hamilton-Jacobi-Bellman (HJB) equation. We discuss the influence of each parameter on the best bid and ask prices in the models and demonstrate the risk metrics including profit and loss distribution (PnL), standard deviation of PnL and Sharpe ratio which play important roles for the trader to make decisions on the strategies in high-frequency trading. Moreover, we provide the comparisons of the strategies with the existing ones. The thesis reveals that our models describe and fit the real market data better since a real data has jumps and the volatility is fluctuating in reality. As a real data application, we conduct our simulations for the developed strategies in this thesis on the high-frequency data of Borsa Istanbul (BIST). For this purpose, we first estimate the parameters of each model and then perform the numerical experiments on the optimal quotes. Our aim is to investigate the qualitative behaviour of an investor who is trading in an emerging market by our strategies in terms of the PnL, standard deviation of PnL and inventory process. Furthermore, we provide the applications on global stocks in order to see that the models are applicable, reasonable and profitable also for the developed markets. Lastly, we take account of the optimal market making models with stochastic latency in the price. The jump components are included on these models, as well. We contribute to this study by providing the numerical experiments with artificial data. Finally, the thesis ends up with a conclusion and a showcase on future research.

** Speaker: **Deniz Kenan Kilic

** Affiliation: **PhD in Financial Mathematics

**Advisor:** Ömür Ugur

** Place: https://zoom.us/j/99252972182?pwd=Tk9Yc0d6MzlvSWhra29yYldLcGVsQT09**

**Meeting number:** 992 5297 2182

**Password:** 711612

**Date: **15 February 2021, 11:00

**Abstract: **The thesis aims to combine wavelet theory with nonlinear models, particularly neural networks, to find an appropriate time series model structure. Data like financial time series are nonstationary, noisy, and chaotic. Therefore using wavelet analysis helps for better modeling in the sense of both frequency and time. Data is divided into several components by using multiresolution analysis (MRA). Subsequently, each part is modeled by using a suitable neural network structure. In this step, the design of the model is formed according to the pattern of subseries. Then predictions of each subseries are combined. The combined prediction result is compared to the original time series’s prediction result using only a nonlinear model. Moreover, wavelets are used as an activation function for LSTM networks to form a hybrid LSTM-Wavenet model. Furthermore, the hybrid LSTM-Wavenet model is fused with MRA as a proposed method. In brief, it is studied whether using MRA and hybrid LSTM-Wavenet model decreases the loss or not for both S&P500 (∧GSPC) and NASDAQ (∧IXIC) data. Four different modeling methods are used: LSTM, LSTM+MRA, hybrid LSTM-Wavenet, hybrid LSTM-Wavenet+MRA (the proposed method). Results show that using MRA and wavelets as an activation function together decreases error values the most.

**Speaker: **Merve Gözde Sayın

**Affiliation: **MSc in Financial Mathematics

**Advisor:** Ceylan Yozgatligil

**Place: https://zoom.us/j/91434127130?pwd=QVB1VmlRNzgrenl6b014c0ZiY3lWdz09**

Meeting number: 914 3412 7130

Password: 205326

**Date: **15 February 2021, 13:00

**Abstract: ** Estimating stock indices that reflect the market has been an essential issue for a long time. Although various models have been studied in this direction, historically, statistical methods and then various machine learning methods have to introduced artificial intelligence into our lives. Related literature shows that neural networks and tree-based models are mostly used. In this direction, in this thesis, four different models are examined. The first one is the most preferred neural network method for financial data called LSTM, and the second one is one of the most preferred tree-based models called XGBoost, and the third and the fourth models are the hybridizations of LSTM and XGBoost. Besides, these models have been applied to eight different stock market indices, and the model that gives the best results is determined according to the Mean Absolute Scaled Error (MASE) evaluation criteria.

** Speaker: **Esra Günsay

** Affiliation: **MSc in Cryptography

**Advisor:** Murat Cenk

** Place: https://zoom.us/j/91560425604?pwd=VXZqK2dOd1NYWVViVTE4UTZLR2NoUT09**

**Meeting number:** 915 6042 5604

**Password:** 052190

** Date: **12 February 2021, 16:30

**Abstract: **Appropriate, effective, and efficient use of cryptographic protocols contributes tomany novel advances in real-world privacy-preserving constructions. One of the most important cryptographic protocols is zero-knowledge proofs. Zero-knowledge proofs have the utmost importance in terms of decentralized systems, especially in context of the privacy lately. In many decentralized systems, such as electronic voting, e-cash, e-auctions, or anonymous credentials, zero-knowledge range proofs are used as building blocks. The main purpose of this thesis is to explain range proofs with detailed primitives and examine their applications in decentralized, so-called blockchain systems such as confidential assets, Monero, zkLedger, and Zether.In this thesis, we have examined, summarised, and compared range proofs based on zero-knowledge proofs.

** Speaker: **Gizem Kara

** Affiliation: **MSc in Cryptography

**Advisor:** Ali Doğanaksoy

**Co-Advisor: **Oğuz Yayla

**Place: https://zoom.us/j/91560425604?pwd=VXZqK2dOd1NYWVViVTE4UTZLR2NoUT09**

**Meeting number:** 915 6042 5604

**Password:** 052190

** Date: **12 February 2021, 17:30

**Abstract: **A number of arithmetization-oriented ciphers emerge for use in advanced cryptographic protocols such as secure multi-party computation (MPC), fully homomorphic encryption (FHE) and zero-knowledge proofs (ZK) in recent years. The standard block ciphers like AES and the hash functions SHA2/SHA3 are proved to be efficient in software and hardware but not optimal to use in this field for this reason, new kind of cryptographic primitives proposed. However, unlike traditional ones, there is no standard approach to design and analyze such block ciphers and the hash functions, therefore their security analysis needs to be done carefully. In 2018, StarkWare launched a public STARK-Friendly Hash (SFH) Challenge to select an efficient and secure hash function to be used within ZK-STARKs, transparent and post-quantum secure proof systems. The block cipher JARVIS is one of the first ciphers designed for STARK applications but, shortly after its publication, the cipher has been shown vulnerable to Gröbner basis attack. This master thesis aims to describe a Gröbner basis attack on new block ciphers, MiMC, GMiMCerf (SFH candidates) and the variants of JARVIS. We present the complexity of Gröbner basis attack on JARVIS-like ciphers, results from our experiments for the attack on reduced-round MiMC and a structure we found in the Gröbner basis for GMiMCerf.

** Speaker: **Pınar Ongan

** Affiliation: **MSc in Cryptography

**Advisor:** Ali Doğanaksoy

**Co-Advisor:** Burcu Gülmez Temür

** Place: https://zoom.us/j/98707521401?pwd=OCtPRnV2a013QnVNUnhiTTFOQjVtUT09**

**Meeting number:** 987 0752 1401

**Password:** 068665

** Date: **11 February 2021, 16:30

**Abstract: **This thesis consists of two main parts: In the first part, a study of several classes of permutation and complete permutation polynomials is given, while in the second part, a method of construction of several new classes of bent functions is described. The first part consists of the study of several classes of binomials and trinomials over finite fields. A complete list of permutation polynomials of the form f(x)=x^{(q^n-1)/(q-1)+ 1} + b x in GF(q^n)[x] is obtained for the case n=5, and a criterion on permutation polynomials of the same type is derived for the general case. Furthermore, it is shown that when q is odd, trinomials of the form f(x)= x^5 h(x^{q-1}) in GF(q^2)[x], where h(x)=x^5+x+1 never permutes GF(q^2). A method of constructing several new classes of bent functions via linear translators and permutation polynomials forms the second part of the thesis. First, a way to lift a permutation over GF(2^t) to a permutation over GF(2^m) is described, where t divides m. Then, via this method, 3-tuples of particular permutations that lead to new classes of bent functions are obtained. As a last step, the fact that none of the bent functions obtained here will be contained in Maiorana-McFarland class is proved.

**Speaker: **Fatih Cingöz

** Affiliation: **MSc in Financial Mathematics

**Advisor:** Adil Oran

** Place: https://metu.webex.com/metu/j.php?MTID=m5385a4be312d961b1c561de397bb22af**

Meeting number: 121 130 773

Password: Fp8vgrbq9g6

** Date: **4 February 2021, 14:00

** Abstract:**