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08. School of Science & Technology (2015-2019)

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Open Access
A Short Note On Solving 1-D Porous Medium Equation by Finite Element Methods
(Nazarbayev University School of Science and Technology, 2016-05-20) Matayev, Chingis
Porous Medium Equation (PME) is one of the simplest types of of nonlinear evolution equation of parabolic type. It emerges in the description of di erent natural phenomena, and its theory and properties depart strongly from the heat equation, ut = u, its most famous relative. Hence the interest of its study, both for the pure mathematician and the applied scientist (Vazquez, 2006). The aim of this paper is to study the Porous Medium Equation in one dimension.
Open Access
Actuarial Applications of a two-parameter generalized Logistic model
(Nazarbayev University School of Science and Technology, 2018-05-10) Alekberova, Nargiz
This project presents a generalization of the classical logistic and the Gompertz model by using two parameter power law exponent. The suggested generalized with two parameters models was shown by numerical example to be potentially a better choice for fitting a certain data. The solutions of these models are used in terms of force of mortality function in actuarial math as insurance contingency models or as hazard function for quality control in science and engineering. The complexity of solution is presented in the form of hypergeometric function and corresponding to it nonlinear implicit regression analysis. Due to the mentioned complexity we develop the approximation of the actual solution and consider only its special cases.
Open Access
Analysis of Dynamic Pull-in for a Graphene-based MEMS Model
(Nazarbayev University School of Science and Technology, 2018) Omarov, Daniyar
A novel procedure based on the Sturm’s theorem for real-valued polynomials is developed to predict and identify periodic solutions and non-periodic solutions in the pull-in analysis of a graphene-based MEMS lumped parameter model with general initial conditions. It is demonstrated that under specific conditions on the lumped parameters and the initial conditions, the model has certain periodic solutions and otherwise there is no such solutions. This theoretical procedure is made practical by numerical implementations with Python scripts to verify the predicted behaviour of the periodic solutions. Numerical simulations are performed with sample data to justify by this procedure the analytically predicted existence of periodic solutions. Also, Low Order Fourier Approximation is used to find the solution for the linear spring case. Comparison with the highly accurate Runge-Kutta method is done to verify derived values from the new numerical approximation.
Open Access
Analytic Solutions for a Nonlinear Transport Equation
(Nazarbayev University School of Science and Technology, 2019-08-07) Biyar, Magzhan; da Silva, Daniel Oliveira; Castro Castilla, Alejandro Javier
We prove that the Cauchy problem for a transport equation with algebraic nonlinearity of degree p with initial data in Gevrey spaces is locally well-posed. In particular, we show that the analyticity of solutions persists for a short time and we derive a sufficient condition for solutions to be analytic for all times.
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Application of advanced molecular techniques for analyzing phytoplankton population in Burabay National Nature Park Resort
(Nazarbayev University School of Science and Technology, 2016) Sarsembekova, Assel
In this work, the molecular techniques as DNA extraction, DNA quantification, PCR analysis were optimized and subsequent sequencing was performed on MiSeq platform (Illumina, USA). We aimed to apply molecular methods to analyse phytoplankton population inhabiting Lake Shortan and Lake Burabay
Open Access
Boundary Element Method for Stokes Flow in Incompressible Newtonian Fluids
(Nazarbayev University School of Science and Technology, 2015-04) Tazhimbetov, Nurbek Akhmetuly
In this thesis, I present different discretization techniques for boundary integral method for Stokes flow in case of an incompressible Newtonian fluid. Boundary integral method (BIM) is one of many techniques that are used to solve Partial Differencial Equations (PDE) numerically. However, the basic advantage of the BIM is that it reduces the problem from n-dimensional domain to n - 1; for example, the two-dimensional square-box that contains viscous liquid can be solved by using the values of an unkown function at the boundary of square. Nevertheless, the BIM exhibits some challenges in finding the Green's function for a particular domain or differential operator, solving the integral equations and, especially, in computing the values of a complex domain. The latter one is quite diffcult because the flow diverges at corners (exhibits singularity). The goal of this work is to derive general analytical solution for Stokes equation (in integral equations form) and to compute the discretized integral equations using different quadrature rules for cavity problem.
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Brillouin visco-elastometry and Raman spectroscopy of potassium permanganate aqueous solutions
(Nazarbayev University School of Science and Technology, 2017-04) Omarkulova, Aziza
This thesis tries to find connection between mechanical and chemical properties of KMnO4 aqueous solutions with variable opacity. To the best of our knowledge, there was no research done on this or similar topic. The aqueous solutions of KMnO4 with various concentrations of KMnO4 were studied using Brillouin and Raman spectroscopies. Elastic and viscous properties and their change due to sample concentration is investigated by Brillouin experiment. Graphs and tables showing these changes are also included in this work. Raman spectra of the sample solutions gives information about molecular interaction on a microscopic level. The thesis includes derivation of the frequency shift and linewidth for Brillouin and Raman scatterings, as well as the assignment of vibrational modes for Raman scattering. For Brillouin scattering it was found that the solutions become stiffer and less viscous with increase of concentration of KMnO4 in water and Raman scattering showed that the solutions possess stretching vibration modes of permanganate ions and intramolecular O-H bending modes of water molecules. At the end possible relation between elastic property and active stretching vibrational modes is discussed. Also application of viscous property of aqueous KMnO4 for more effective water treatment is proposed.
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Co-expression of FVIII with human IGG FC Fragment or mouse IL-10 in encapsulated G8 myoblast cells as a potential treatment of hemophilia A
(Nazarbayev University School of Science and Technology, 2016) Kanketayeva, Zhansaya
In this master thesis study we have shown that recombination G8 myoblasts, encapsulated in alginate-PLL microcapsules can successfully secrete detectable levels of both Fc and IL-10 out of the capsules and sustain good viability, showing the potential of co-delivering FVIII by encapsulated cells.
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Concentration dependent mitostatic effect and inhibition of cell motibility by different tubulin binding drugs-comparative study
(Nazarbayev University School of Science and Technology, 2016) Balabiyev, Arnat
Here, we demonstrate the comparative effects of nocodazole, taxol and vinorelbine on mitotic progression and cell motility using mouse fibroblasts and three cancer cell lines
Open Access
Convergence Rate of Fourier Neural Networks
(Nazarbayev University School of Science and Technology, 2019-04-26) Zhumekenov, Abylay; Assylbekov, Zhenisbek; Tourassis, Vassilios D.
The paper investigates a convergence rate for 2-layer feedforward Fourier Neural Network (FNN). Such networks are motivated by the approximation properties of wellknown Fourier series. Several implementations of FNNs were proposed since 1990’s: by Gallant and White; A. Silvescu; Tan, Zuo and Cai; Liu. The main focus of this research is Silvescu’s FNN, because such activation function does not fit into the category of networks, where the linearly transformed input is exposed to activation. The latter ones were extensively described by Hornik in 1989. In regard to non-trivial Silvescu’s FNN, its convergence rate is proven to be of order 𝑂(1/𝑛). The paper continues investigating classes of functions approximated by Silvescu FNN, which appeared to be from Schwartz space and space of positive definite functions.
Open Access
Copula functions in Credit Metrics’ VaR estimation
(Nazarbayev University School of Science and Technology, 2019-08-08) Magzanov, Shynggys; Wei, Dongming; Assylbekov, Zhenisbek
Credit risk modelling of a portfolio of exposures is essential part of activity of every financial institution. However this procedure is complicated since the joint behavior of chosen exposures must be known. In this paper Value at Risk percentile of the portfolio consisting of three corporate bonds issued by Lukoil, Gazprom and Norilsk Nickel was estimated at three different significance levels within the frame of Credit Metrics approach proposed by J.P.Morgan. Following the Asset value model, Monte-Carlo simulations were performed to obtain possible portfolio values in one year time horizon. Where the joint distribution of asset returns of three companies was constructed by means of pair-copula construction method discussed in Aas, Czado, Frigessi,Bakken (2009). Results reveal that for particular portfolio of bonds at 90%, 95% and 99% confidence levels the value of our portfolio will not fall below 2057.915 ,1798.117 and 1375.011 dollars respectively.
Open Access
Copulas and Correlation in Statistical Risk Theory
(Nazarbayev University School of Science and Technology, 2018) Rat, Sara
The Financial Risk Management (FRM) aims to identify, measure and manage risks in different sectors. One of the core things during such operations is measuring different dependencies. Linear correlation is known as one of the most popular measure of dependence, however it is known that it is a reasonable mea- sure of dependence only when variables are Normally distributed, but this is not the case with credit and portfolio risks, therefore other measures of dependency are needed. This paper presents a Copula function for bivariate case as one of the tools to analyze dependencies in portfolio risk management. Copulas were first introduced by Sklar in 1959 [8], and in 1999 they were studied in financial context for the first time by Embrechts et al. in 1999 [4]. Motivated by the copula analysis of European stock portfolios [6], this paper aims to analyze portfolio consisting of Asian S&P Asia 50 and S&P BSE 100 indices, and apply copula to this portfolio.
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The correlation expansion method used in quantum computation
(Nazarbayev University School of Science and Technology, 2017-04) Baitenov, Adil
In this master thesis, 3 methods of solving of Quantum Ising model have been outlined and compared, they include ABC. We investigate the entanglement dynamics and find energy and spin values for 1-dimensional Quantum Ising chain and 2 and 3-dimensional Quantum Ising models. System starts in a paramagnetic regime and switches to ferromagnetic spin-spin coupling constant J. In this work, we consider instantaneous (step function) switch, which demonstrates the instantaneous switch from paramagnetic to ferromagnetic state. Solution of the system is made by quantum simulation using Microsofts’ Corporations computational simulator called The Language-Integrated Quantum Operations (LIQUi|>) Simulator, 1/Z expansion method and Exact Diagonalization method. Accuracy and precision of results of first two methods are compared with Exact Diagonalization that provides the exact solution of the system. With that it can be seen to what extent 1/Z expansion method is applicable for solving of Quantum Ising model.
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Data Aggregation in Wireless Sensor Networks with Multiple Sinks
(Nazarbayev University School of Science and Technology, 2017-04) Yestemirova, Gaukhar
The invention of wireless sensor networks (WSNs) has caused a technological breakthrough in almost all industry fields that need to acquire regular and reliable real-time data from the field of interest. Today WSNs are used in many applications, including environmental, industrial, health care, and military. A WSN is a network comprised of sensors devices, usually called nodes, and a designated device called a sink to which nodes transmit their sensed data. Nodes are low-cost, battery-powered devices with limited memory and computational power. Usually WSNs are deployed and left unattended for a long time. During this time the WSN can experience different faulty scenarios. For example, nodes and sink can crash or communication between them can go down. In such cases, the network becomes useless as the sink will not be able to collect data from nodes. One way to increase the reliability of such WSNs is to deploy them with more than one sink so that when one sink goes down other sinks could forward collected data. A number of data collection protocols have been proposed so far. However, they have been proposed mainly for WSNs with a single sink. Existing protocols developed for WSNs with a single sink does not show the similar system efficiency to WSNs with multiple sinks. In this thesis work, we propose three data aggregation protocols for WSNs with multiple sinks: i) an adjusted form of Minimum Spanning Tree (MST); ii) two adjusted forms of Shortest Path Tree (SPT) and i) Maximum Spanning Backbone (MSB) that try to minimize the number of message transmissions during data collection. In all cases we first build a tree and then highlight the set of nodes that connect all the sinks and call them backbone nodes. These backbone nodes first collect the data from the nodes, then send aggregated data to all the sinks. We show the performance of our proposed protocols using simulation program. The simulation results from least to most backbone nodes as the following: MSB, two adjustments of SPT and MST.
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Deploying Nonlinear Circuits on Wireless Power Transmitters and Receivers
(Nazarbayev University School of Science and Technology, 2017-04) Shaikhov, Aidyn
In this thesis, several methods that increase the tolerance of a wireless power transfer system are illustrated. For that reason, a Duffing oscillator (the second order differential equation with a third order of nonlinearity) equation is introduced. Also, an electrical analysis of a Duffing oscillator is presented. The detailed characteristics discussion is provided. Even though the Duffing oscillator circuit does not improve the efficiency of wireless power transfer drastically, it provides a significant wider bandwidth as compared to linear oscillators. The Duffing oscillator’s bandwidth is enhanced by a factor of 2.7 as compared to the linear oscillator with the same quality factor. Therefore, the Duffing oscillator improves the tolerance to coupling factor fluctuations arising from varying transmission distance and adjustment of coupled coils. The results are demonstrated using a MATLAB script.
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Development of a Lightweight Biped Robot
(Nazarbayev University School of Science and Technology, 2017-05) Aubakir, Bauyrzhan
Robotics, as a research and technical field, finds inspiration in nature. In particular, bipedal robots, which structure and kinematics reproduce the lower limbs of a human body, are the first step toward functional humanoid robots. This document describes the development phases of a lightweight biped robot under construction at the department of Robotics and Mechatronics in Nazarbayev University. The mechanical design is the primary focus of this work; nevertheless, a big effort was also dedicated to formalize and realize the electrical, sensorial and software subsystems. By using 3D printing techniques and lightweight materials a lower power consumption and higher power over weight ratio was reached in comparison with state-of-the-art robots having comparable dimensions. Furthermore, thanks to a lower links inertia the system is inherently safer when operating in environment where humans are present. A detailed description of the robot kinematics and the methodology followed to dimension the actuation system is provided together with preliminary results on the execution of different postures and gaits.
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Development of a Neuromorphic Control System for a Biped Robot
(Nazarbayev University School of Science and Technology, 2017-04) Keldibek, Amina
Humanoid robots are developed around the world with the purpose to assist humans in their domestic and public activities and operate in unstructured and hazardous environments. To accomplish this effectively, intelligent humanoids should be autonomous, to accomplish high-level human tasks without help, and adaptable, to be able to react to dynamic changes and external disturbances in operating environments. The primary objective of this thesis is to investigate how biologically plausible methods such as reservoir computing and rewardmodulated learning can be used for generating robust sensory-motor outputs and achieving adaptability of the biped system. Recurrent neural networks architecture is studied on two robot systems: first is Asimo humanoid and second is biped developed at Nazarbayev University.
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Development of flow cytometry and microscopy techniques to monitor freshwater phytoplankton communities in Kazakhstani lakes
(Nazarbayev University School of Science and Technology, 2016) Dashkova, Veronika
In this project, we tested an approach based on separating fluorescent viability and metabolic dyes between different excitation lasers in order to reach minimal spectral overlap with the autofluorescent signal using flow and imaging cytometry
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Discrete Vortices in Photonic Graphene
(Nazarbayev University School of Science and Technology, 2017-04) Dybyspayeva, Kumiszhan
Graphene is a relatively new 2D material consisting of carbon atoms in honeycomb structure. Because of this structure, it has various interesting properties such as linear dispersion relation in the low energy spectrum that governs relativistic nature of electrons in graphene. Since there is an analogy between an electron wavepacket dynamics in time and paraxial wave propagation in z-direction, a honeycomb lattice of evanescently coupled optical waveguides, so called "photonic graphene", can be used to study dynamics of optical wavepackets and to mimic quantum relativistic behaviour in table-top experiments. Another interesting property of graphene is the pseudospin that is associated with generation of vortices. The goal of the present thesis is to investigate the unusual behaviour of the wavepacket in photonic graphene by observing the role of pseudospin for discrete optical vortices in the photonic lattice.
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A Distributed Software Architecture for Performing Text Analysis on Web content
(Nazarbayev University School of Science and Technology, 2017-05) Aldabergenov, Aibek
With the high availability of data on the World Wide Web, researchers are actively using Web content for performing various text analysis operations. The large amount of data introduces challenges in data acquisition, storage and processing for researchers who want to use data from different sources on the Internet. In an environment where several people might want to share their data and code, the problem is further complicated by researchers' use of different software applications for performing data collection, storage and analysis tasks. The goal of this thesis is to study the components that make up different parts of web mining systems, and present a scalable software architecture for large-scale Web content analytics tasks performed in a multi-user setting. Additionally, an implementation of the proposed software architecture using modern open source software frameworks and tools is presented in this work.