02. Master's Thesis
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Item Open Access QUANTUM EVOLUTIONARY ALGORITHM FOR QUANTUM CIRCUIT SYNTHESIS(School of Sciences and Technology, 2018-06) Krylov, GeorgiyQuantum computing area has a lot research attention due to opportunities that possessing such device could provide. For example, quantum computers could deliver new insights to previously unsolvable problems. The reason for that is higher parallel capabilities of such devices. In addition, since quantum computers are naturally reversible, no heat dissipation occurs during computation [21]. This property could serve as a viable solution to the problem that computer chip production industry faces. Moreover, since the chip manufacturing industry reaches nanometer scale of size of elements, the effects that could cause unexpected information behavior in classical paradigm are part of the technology of quantum devices [31, 14]. Considering possible benefits that could be achieved by quantum computing devices, the new areas of Quantum Information Theory, Quantum Cryptography, Quantum Algorithms and Logic Design and many others emerged at the end of the twentieth century [31]. These areas are concentrating their efforts on solving problems of designing communication protocols, ensuring the security of the new systems, constructing appropriate algorithms. Computers that could be advancing in finding solutions in problems listed above require quantum circuits that have optimal structure and could implement error correction. This is the main motivation for this thesis work to explore the problem of circuit design. The approach that we investigate is circuit construction by the means of Quantum Evolutionary Algorithms. We propose a version of an algorithm that accounts with specificity and constraints of quantum paradigm. We use its Graphic Processing Unit (GPU) accelerated classical implementation to evaluate the behavior and performance of the proposed algorithm. Later we discuss additional complexity introduced by accounting with these constraints. We support our ideas with results of synthesis of small circuits and compare the performance with classical genetic algorithm on similar task.Item Open Access KNOTTED OPTICAL VORTEX LINES IN NONLINEAR SATURABLE MEDIUM(Nazarbayev University School of Science and Technology, 2018-06) Issakhanov, AlfarabiIn last 50 years, a significant progress was noticed in medicine, communications and entertainment. Such advanced development of these fields was directly related to ability of controlling light. Photonics is exactly about this ability. At the present time, photonics is walking together with a fundamental physical concept, optical soliton. Optical solitons are shape-preserving laser beams. They are found potentially useful in data transmission, which is very significant nowadays. Hence, research in the field of optical solitons is still a vital issue. When optical soliton is perturbed in a specific manner, there appear zeros of optical field around the soliton, which are called optical vortices. In general optical vortices are lines in space. Hence, we might expect them to become knotted. Knotting optical vortices around perturbed seems spontaneous and cannot be directly predicted. To explain this phenomenon, a similar system is constructed based on perturbation theory. In this system, however, we have a mathematical problem which yet lacks a full understanding. We address this problem by introducing concepts from three disciplines: laser physics, knot theory and singular optics. We believe that understanding the mechanism underlying spontaneous knotting of optical vortices will be a step forward in other systems too, such as quantum turbulence in superfluids and formation of optical vortices around other types of optical solitons.Item Open Access Synchronization of Coupled Nonlinear Oscillators with Applications to Photonic Arrays(Nazarbayev University School of Science and Technology, 2019-05-01) Zharas, Banu; Bountis, Anastasios; Tourassis, Vassilios D.In recent years, the study of synchronization of coupled oscillators have been the subject of intense research interest, leading to many new and unexpected phenomena. Our research is first focused on the analysis of a network of coupled nonlinear oscillators exhibiting the breakdown of synchronization into fascinating “chimera states” exhibiting the coexistence of synchronized and unsynchronized parts. We then apply these ideas to laser arrays of photonic “oscillators”, which have numerous applications in optical communications, sensing and imaging. First of all, we demonstrate the occurrence of synchronization and chimera states in a simpler problem, consisting of a ring of coupled 4D simplified Lorenz systems, in which each oscillator is described by a Li-Sprott oscillator [1]. An interesting feature of each oscillator is the coexistence of a limit cycle and two symmetric strange attractors for some specific range of parameters, which influences the global synchronization dynamics and leads to the formation of chimera states. Inspired by this model, we study some fascinating oscillatory phenomena of coupled photonic oscillators consisting of dimers of semiconductor lasers, each of which is capable of performing limit cycle oscillations. Coupling in an appropriate way a large number of dimers in long arrays we find that they can exhibit combinations of oscillatory patterns involving long amplitude oscillations (LAO) and also localized oscillations of very small amplitude close to the fixed points (LOCFP). As preliminary results of this investigation, we show the coexistence of LOA and LOCFP patterns reminiscent of “chimera–like” states and LOCFP “breather– like” phenomena. Both of these behaviors are shown to be spatially robust, when we calculate the Discrete Laplacian of their amplitudes for long times.Item Open Access The Dynamics of Hamiltonian Lattices With Application to Hollomon Oscillators(Nazarbayev University School of Science and Technology, 2019-05-29) Zholmaganbetova, Aigerim; Bountis, AnastasiosMany problems in theoretical physics are expressed in the form of Hamiltonian systems. Among these the first to be extensively studied were low-dimensional, possessing as few as two (or three) degrees of freedom. In the last decades, however, great attention has been devoted to Hamiltonian systems of high dimensionality. The most famous among them are the ones that deal with the dynamics and statistics of a large number N of mass particles connected with nearest neighbor interactions. At low energies E, these typically execute quasiperiodic motions near some fundamental stable periodic orbits (SPOs) which represent nonlinear continuations of the N normal mode solutions of the corresponding linear system. However, as the energy is increased, these solutions destabilize causing the motion in their vicinity to drift into chaotic domains, thus giving rise to important questions concerning the systems behavior in the thermodynamic limit, where E and N diverge with E=N = constant. One of the open problems in Hamiltonian dynamics, therefore, examines the relation between local (linear) stability properties of simple periodic solutions of Hamiltonian systems, and the more “global” dynamics. In this thesis, after reviewing the main results on these topics for the case of N-particle Fermi-Pasta-Ulam Hamiltonians, I proceed to apply the corresponding methods to a lattice of Hollomon oscillators, which are of interest to applications in problems of nonlinear elasticity.Item 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.Item Open Access Explorations on chaotic behaviors of Recurrent Neural Networks(Nazarbayev University School of Science and Technology, 2019-04-29) Myrzakhmetov, Bagdat; Assylbekov, Zhenisbek; Takhanov, Rustem; Tourassis, Vassilios D.In this thesis work we analyzed the dynamics of the Recurrent Neural Network architectures. We explored the chaotic nature of state-of-the-art Recurrent Neural Networks: Vanilla Recurrent Network, Recurrent Highway Networks and Structurally Constrained Recurrent Network. Our experiments showed that they exhibit chaotic behavior in the absence of input data. We also proposed a way of removing chaos chaos from Recurrent Neural Networks. Our findings show that initialization of the weight matrices during the training plays an important role, as initialization with the matrices whose norm is smaller than one will lead to the non-chaotic behavior of the Recurrent Neural Networks. The advantage of the non-chaotic cells is stable dynamics. At the end, we tested our chaos-free version of the Recurrent Highway Networks (RHN) in a real-world application. In a sequence-to-sequence modeling experiments, particularly in the language modeling task, chaos-free version of RHN perform on par with the original version by using the same hyperparameters.Item Open Access Numerical computations of complexification of Legendrian knots(Nazarbayev University School of Science and Technology, 2019-04-29) Yerzhigit, Bauyrzhan; Lawrence, Mark; Tourassis, Vassilios D.With the recent interest in knots, it is interesting to study their complexification. We have chosen to study Legendrian knots as they have the property that we can reconstruct the original knot from its projection. This property is especially useful in the case of the complexification of a knot as in this case the diagram of the projection of the knot is no longer real. In this paper we show a way to compute complex rational functions that have a Legendrian knot as an image under unit circle.Item Open Access Multigrid method for Mild-Slope equation in Coastal Wave Modelling(Nazarbayev University School of Science and Technology, 2019-04-19) Tabarek, Rysbergen; Erlangga, Yogi; Tourassis, Vassilios D.In this thesis we propose and study an efficient iterative multigrid method for the time independent modified mild slope equation with and without energy dissipation term. The algorithm relies on a multigrid method preconditioned with shifted-Laplacian preconditioner and solved by Bi-CGSTAB algorithm. Multigrid analysis results are shown by numerical experiments. Numerical experiments are conducted in depth sloped elliptic shoal introduced by Berkhoff et. alItem Open Access Pulse vaccination of a time-delayed SIRS epidemic model with nonlinear incidence rate(Nazarbayev University School of Science and Technology, 2019-05-03) Yeleussinova, Meruyert; Kashkynbayev, Ardak; Tourassis, Vassilios D.This work deals with an application of pulse vaccination for a varying size of the population of time-delayed 𝑆𝐼𝑅𝑆 epidemic model. The dynamics of the infectious disease depends on the threshold value, 𝑅0, known as the basic reproduction number. In the classical epidemic models, this value is evaluated by means of the next generation matrix. However, this method does not work for non-autonomous systems. Since we consider the pulse vaccination strategy for epidemic models our system is naturally non-autonomous. We follow the general approach to derive 𝑅0 in terms of spectral radii of Poincare maps. Further, we show the existence of an infectious-free periodic solution and its global attractiveness for 𝑅0 < 1 and the persistence of infectious disease for 𝑅0 > 1.Item Open Access Global stability analysis for a tick-borne model(Nazarbayev University School of Science and Technology, 2019-05-06) Koptleuova, Daiana; Kashkynbayev, Ardak; Tourassis, Vassilios D.This thesis consider three type of epidemiological models: SIR, SIS and SIRS with nonlinear incidence rate and piecewise constant delay of generalized type. In this paper the total population size is varied with time elapse. We study the global asymptotic stability of the disease-free and endemic equilibrium states of models by constructing suitable Lyapunov functions and Lyapunov–LaSalle technique. The main contribution of this master thesis is to develop more realistic compartmental models by extending the literature of models with piecewise constant delay. The theoretical findings are illustrated through numerical simulations.Item Open Access The lumped model parameters approach for static and dynamic power-law beam problems(Nazarbayev University School of Science and Technology, 2019-04-29) Begzhigitov, Madi; Skrzypacz, Piotr; Tourassis, Vassilios D.It is important to estimate the natural frequencies of the structural elements in the design of mechanical or electromechanical structures. There is a wide use of single lumped-parameter spring-mass models in the industry for materials . Their behaviour is linear by Hooke’s law within the geometric and loading conditions. In this work, the lumped-parameter theory is generalized for Hollomon’s power-law materials and the lumped-parameters for the corresponding nonlinear restoring force in the spring-like model for the standard geometric and loading conditions of the power-law Euler beams are provided. For each case in the given lumped-parameter model the corresponding effective mass is also calculated. Then, the resulting spring-mass system is solved to validate the solutions as approximations to the corresponding beam system. Numerical validations of the proposed lumped models for the cantilever beam with circular and rectangular cross-sections are presented.Item Open Access Experimental study of Pac-Man conditions for learn-ability of discrete linear dynamical systems(Nazarbayev University School of Science and Technology, 2019-05-01) Damiyev, Zhaksybek; Takhanov, Rustem; Tourassis, Vassilios D.In this work, we are going to reconstruct parameters of a discrete dynamical system with a hidden layer, given by a quadruple of matrices (𝐴,𝐵,𝐶,𝐷), from system’s past behaviour. First, we reproduced experimentally the well-known result of Hardt et al. that the reconstruction can be made under some conditions, called Pac-Man conditions. Then we demonstrated experimentally that the system approaches the global minimum even if an input 𝑥 is a sequence of i.i.d. random variables with a nongaussian distribution. We also formulated hypotheses beyond Pac-Man conditions that Gradient Descent solves the problem if the operator norm (or alternatively, the spectral radius) of transition matrix 𝐴 is bounded by 1 and obtained the negative result, i.e. a counterexample to those conjectures.Item Restricted Robotic Construction of Tensegrity Structures(Nazarbayev University School of Science and Technology, 2017-04) Issa, MargulanTensegrity based design is emerging as an active research field. Tensegrity structures can be constructed with minimal weight compared to the traditional ones. They can also have stability and durability without relying on gravity. These merits make them ideal for the construction of orbital structures such as space stations. Even though the researchers have recently crafted elegant theories for the statics and dynamics of tensegrity, there are many hurdles for their active utilization in space construction. Due to the need for attaching strings in complex geometries and precise tensioning of these, the labor and skill intensive construction of these tensegrities in space cannot be accomplished by humans. With recent advances in robotics especially in embedded computing, sensing and motion planning, robots can be summoned to tackle the automated construction problem of tensegrities. To the best of the author’s knowledge, an automated construction framework for tensegrities does not exist. This thesis focuses on this problem. Firstly, we describe our assembly-friendly tensegrity struts with integrated strings and tensioners. Secondly, we present the development and implementation of a specialized robot end-effector for tensegrity construction. This end-effector with embedded sensors and computation is capable of measuring the string tension based on vibration frequency, attaching/detaching strings and also tensioning them. Using these components, we developed a framework for robotic construction of tensegrity structures. We show the efficacy of our framework by realworld experiments. In particular, we constructed a 3-strut and 9-string tensegrity prism which can serve as a building block for more complex structures.Item Restricted Mechanical Design and Kinematic Analysis of a Spherical Parallel Manipulator with Coaxial Input Shafts(Nazarbayev University School of Science and Technology, 2017-05) Tursynbek, IliyasIn this thesis a spherical parallel manipulator with coaxial input shafts (Coaxial SPM) is under study. It is a part of a bigger family of spherical parallel manipulators (SPM) with a special feature of unlimited roll rotation around its axis. This feature makes the Coaxial SPM of high interest for applications in motion control system. First, an approach for obtaining unique forward and inverse kinematics solutions is introduced, in order to relate the angular position of the manipulator servomotors to the position and orientation of Coaxial SPM mobile platform and vice versa. Then, a configuration space of the manipulator is defined by using a numerical procedure, in order to guarantee the absence of singularities and of collision between the manipulator links during the manipulator motion. Afterwards, the Cartesian space of the manipulator is generated. Results of these analyses are applied to the assembled mechanical prototype of Coaxial SPM for experimental verifications.Item Restricted Data Aggregation in Wireless Sensor Networks with Multiple Sinks(Nazarbayev University School of Science and Technology, 2017-04) Yestemirova, GaukharThe 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.Item Restricted Robotic Assembly Planning of Tensegrity Structures(Nazarbayev University School of Science and Technology, 2017-04) Nurimbetov, BirzhanTensegrity structures provide durability and stability with minimal weight. Thanks to these properties, use of tensegrity structures for space applications is becoming an active research area. One of the main challenges is the automated construction of such structures in space. In this thesis, we present a framework for the automated assembly planning of tensegrity structures using an industrial manipulator (Staubli TX90XL) equipped with a purpose-specific end-effector. We leverage the recent advances in sampling-based motion planning to create the motion plans (i.e. the reference trajectories for the manipulator joints). Specifically, we divided the assembly planning problem into three stages. In the first stage, the initial position and orientation of the given tensegrity structure with respect to the assembly robot is determined using a motion-planning integrated forward elimination search. In the second stage, a feasible assembly sequence of the strings is found using backward disassembly search. Lastly, individual robot motion plans for attaching each string to the bars for the given tensegrity configuration is generated using RRT* algorithm. The efficacy of the framework was demonstrated using an extensive set of simulation and real-world experiments dealing with the assembly of a 3-strut and 9-string tensegrity prism structure, which can be utilized as a building block of complex tensegrity structures.Item Restricted Development of a Lightweight Biped Robot(Nazarbayev University School of Science and Technology, 2017-05) Aubakir, BauyrzhanRobotics, 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.Item Restricted Development of a Neuromorphic Control System for a Biped Robot(Nazarbayev University School of Science and Technology, 2017-04) Keldibek, AminaHumanoid 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.Item Restricted Interaction of Turbulence with Shock Waves in the Context of Core-Collapse Supernovae(Nazarbayev University School of Science and Technology, 2017-04) Berdibek, ShapagatThe supernova explosion of massive stars is a complex physical event. Nuclear shell burning in the nal stages of the lives of massive stars is accompanied by strong turbulent convection. The resulting uctuations aid supernova explosion by amplifying the non-radial ow in the post-shock region. We investigate the physical mechanism behind this ampli cation using a linear perturbation theory. We model the shock wave as a one-dimensional planar discontinuity and consider its interaction with vorticity and entropy perturbations in the upstream ow. We nd that, as the perturbations cross the shock, their total turbulent kinetic energy is ampli ed by a factor of 2, while the average linear size of turbulent eddies decreases by about the same factor. We also study the e ects of the interaction of acoustic perturbations with the shock wave. We determine that the post-shock turbulent kinetic energy is dominated by vorticity waves. In addition, we nd that the kinetic energy ampli cation of perturbations increases as / M21 . Finally, we discuss the implication of our results for the supernova explosion mechanism. We show that the upstream perturbations can decrease the critical neutrino luminosity for producing explosion by several percent.Item Restricted Discrete Vortices in Photonic Graphene(Nazarbayev University School of Science and Technology, 2017-04) Dybyspayeva, KumiszhanGraphene 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.