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Item Open Access Adaptive numerical homogenization for upscaling single phase flow and transport(ELSEVIER, 2019-03-05) Amanbek, Yerlan; Singh, Gurpreet; Wheeler, Mary F.; Duijn, HansvanWe propose an adaptive multiscale method to improve the efficiency and the accuracy of numerical computations by combining numerical homogenization and domain decomposition for modeling flow and transport. Our approach focuses on minimizing the use of fine scale properties associated with advection and diffusion/dispersion. Here a fine scale flow and transport problem is solved in subdomains defined by a transient region where spatial changes in transported species concentrations are large while a coarse scale problem is solved in the remaining subdomains. Away from the transient region, effective macroscopic properties are obtained using local numerical homogenization. An Enhanced Velocity Mixed Finite Element Method (EVMFEM) as a domain decomposition scheme is used to couple these coarse and fine subdomains [1]. Specifically, homogenization is employed here only when coarse and fine scale problems can be decoupled to extract temporal invariants in the form of effective parameters. In this paper, a number of numerical tests are presented for demonstrating the capabilities of this adaptive numerical homogenization approach in upscaling flow and transport in heterogeneous porous medium.Item Open Access Adoption of e-Government in the Republic of Kazakhstan(MDPI, 2020-07-09) Amanbek, Yerlan; Balgayev, Ilyas; Batyrkhanov, Kanat; Tan, MargaretInformation and Communication Technology has been gaining importance in the economy of Kazakhstan, the largest landlocked country. In this paper, we investigate the factors that influence Kazakhstan’s e-Government portal use at the informational stage and describe the challenges encountered by citizens while using the portal. Statistical analysis is performed on a web-based questionnaire survey targeted at citizens of Kazakhstan. The technology acceptance model is used as a methodology to measure attitude towards portal usage. This paper also discusses the barriers that can restrict the successful adoption of e-Government services. The results show that awareness among citizens is high and they perceive the portal to be useful, but only a limited percentage of citizens actually use it regularly. The results of this paper could be used to help the IT managers of the portal to improve the management of informational content and maintain more effective adoption among citizens.Item Open Access ALGORITHMIC PROPERTIES OF ROGERS SEMILATTICES(Nazarbayev University School of Sciences and Humanities, 2024-04-25) Tleuliyeva, ZhansayaThe thesis uses various approaches to explore the algorithmic complexity of families of subsets of natural numbers. One of these approaches involves investigating upper semilattices of computable numberings of a given family and their complexity in different hierarchies. These semilattices, known as Rogers semilattices, can help distinguish different structural properties of families of partial computable functions and computably enumerable sets. As a result, by using Rogers semilattices of computable numberings, we can measure the algorithmic complexity of the corresponding family.Item Open Access ALMOST PERIODIC SOLUTIONS OF FUZZY SHUNTING INHIBITORY CNNS WITH DELAYS(AIMS Mathematics, 2022) Kashkynbayev, Ardak; Koptileuova, Moldir; Issakhanov, Alfarabi; Cao, JindeIn the present paper, we prove the existence of unique almost periodic solutions to fuzzy shunting inhibitory cellular neural networks (FSICNN) with several delays. Further, by means of Halanay inequality we analyze the global exponential stability of these solutions and obtain corresponding convergence rate. The results of this paper are new, and they are concluded with numerical simulations confirming them.Item Restricted ALTERNATING SCHEME FOR METHOD OF MOMENTS(Nazarbayev University School of Sciences and Humanities, 2021-05) Kozybayeva, KymbatIn the financial market, there is always an unexpected issue between measures of dif ferent obligations, stocks, currency. Big financial companies before doing investments are highly interested in exploring the behavior of a certain market. For such analysis, we use different methods which are calling dimension reduction techniques. This work adopted the principal component analysis and maximum mean discrepancy distance to assess ten different bond yields by calculating their changes. In the beginning, we will explain in detail the nature of our data and show some results from the theorem about the Wiener process. After we will apply the classic method and our new (al ternating to PCA) method. In the end, we will compare graphs of each method and conclude the effectiveness of Maximum Mean Discrepancy distanceItem Restricted ALTERNATING SCHEME FOR METHOD OF MOMENTS(Nazarbayev University School of Sciences and Humanities, 2021-05) Kozybayeva, KymbatIn the financial market, there is always an unexpected issue between measures of dif ferent obligations, stocks, currency. Big financial companies before doing investments are highly interested in exploring the behavior of a certain market. For such analysis, we use different methods which are calling dimension reduction techniques. This work adopted the principal component analysis and maximum mean discrepancy distance to assess ten different bond yields by calculating their changes. In the beginning, we will explain in detail the nature of our data and show some results from the theorem about the Wiener process. After we will apply the classic method and our new (al ternating to PCA) method. In the end, we will compare graphs of each method and conclude the effectiveness of Maximum Mean Discrepancy distanceItem Open Access ANALYSIS OF DEAD CORE FORMATION IN CATALYTIC REACTION AND DIFUSION PROCESSES WITH GENERALIZED DIFUSION FUX(Scientific Reports, 2022) Skrzypacz, Piotr; Kabduali, Bek; Kadyrbek, Alua; Szafert, Sławomir; Andreev, Vsevolod; Golman, BorisDead-core and non-dead-core solutions to the nonlinear diffusion–reaction equation based on the generalized diffusion flux with gradient-dependent diffusivity and the power-law reaction kinetics in catalyst slabs are established. The formation of dead zones where the reactant concentration vanishes is characterized by the critical Thiele modulus that is derived as a function of reaction order and diffusion exponent in the generalized diffusion flux. The effects of reaction order and diffusion exponent on the reactant concentration distribution in the slab and dead-zone length are analyzed. It is particularly demonstrated that by contrast to the model based on the standard Fick’s diffusion, dead-core solutions exist in the case of first-order reactions. Also, the relationship between critical Thiele moduli for models based on the generalized and standard Fick’s diffusion fluxes is established.Item Open Access Analysis of Dead Core Phenomena in Reaction-Diffusion Problems(Nazarbayev University School of Sciences and Humanities, 2020-05-10) Sabit, FarizaFor some semilinear parabolic problems of reaction-diffusion, a dead core - a region of zero reactant concentration - may be formed in finite time. We study the large time behavior of the solution and give an estimate for the asymptotic behavior of the solution of a semilinear heat equation with Robin boundary condition.Item Restricted ANALYSIS OF ELLIOTT WAVE THEORY ON TIME-SERIES DATA FROM FOREX(School of Sciences and Humanities, 2023) Zhalgasbek, AyazThis capstone project analyzes the application of the Elliott wave theory on time-series data from the Forex market. The project uses patternbased probabilistic models to test the validity of the Elliott wave theory and to evaluate its predictive power. The results of our analysis indicate that the pattern-based probabilistic models do not completely support the Elliott wave theory. Specifically, we found that the patterns identified by the Elliott wave theory did not have statistically significant predictive power for daily exchange rates of currencies. This study encourages further research on this topic with different criteria and larger data setsItem Open Access ANALYSIS OF LANDAU–LIFSHITZ AND NEO-HOOKEAN MODELS FOR STATIC AND DYNAMIC ACOUSTOELASTIC TESTING(Physica Scripta, 2022) Melnikov, Andrey; Malcolm, Alison E; Poduska, Kristin MA comparison of three different isotropic non-linear elastic models uncovers subtle but important differences in the acoustoelastic responses of a material slab that is subjected to dynamic deformations during a pump-probe experiment. The probe wave deformations are small and are superimposed on larger underlying deformations using three different models: Landau–Lifshitz (using itsfourth-order extension), compressible neo-Hookean model(properly accountingfor volumetric deformations), and an alternative neo-Hookeanmodel(fully decoupled energies due to distortional isochoric and volumetric deformations). The analyses yield elasticity tensors and respective expressionsfor the propagation speeds of P-wave and S-wave probesfor each model. Despite having many similarities, the different models give different predictions of which probe wave types will have speeds that are perturbed by different pump wave types. The analyses also show a conceptual inconsistency in the Landau–Lifshitz model, that a simple shear deformation induces a stress and a shear wave probe speed that depend on the second-order elastic constantλ, which controls resistance to volumetric changes and thus should not be present in the expressionsfor shear stress and shear wave probe speeds. Thus, even though the Landau–Lifshitz model is widely used, it may not always be the best option to model experimental data.Item Open Access ANALYSIS OF THE MATHEMATICAL MODEL DESCRIBING THYROID-PITUITARY HORMONAL TRANSPORTATION BY A SYSTEM OF NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS(Nazarbayev University School of Sciences and Humanities, 2022-05) Baidildayeva, AishaThe main goal of this capstone project is to conduct the analysis of the mathematical model which describes the transportation of the thyroid pituitary axis of the hormones within the endocrine system. The model is constructed by a system of ordinary nonlinear differential equations that represent the fluctuations of the levels of the concentration of thyroxine hormone in the blood and illustrate its dependency on the concentration of certain enzymes. This capstone project will assess the stability of the system by applying the well-known Routh-Hurwitz criteria, conduct nu merical simulations, and use MATLAB with the purpose to visualize the general behaviour of the system. The derivation of the analytical solution separately for normal and degenerate states of the system is also presented in the paper. Lastly, the phenomena of relaxation oscillations that was noticed to take place during the derivation of the analytical solution will be explained. The research has shown that there is a direct correlation between the periodicity in the changes of the levels of thyroxine hormone in the blood and the presence of the symptoms of the schizophrenia. The current capstone project can be improved by modifying the model such that it includes the discrete and distributed delay cases during the trans portation process.Item Open Access Analytical and numerical investigations of thecollapse of blood vessels with nonlinear wallmaterial embedded in nonlinear soft tissues(Alexandria Engineering Journal, 2018-11-22) Ghazy, Mohammed; Elgindi, Mohamed B.; Wei, DongmingIn this paper, shapes of nonlinear blood vessels, surrounded by nonlinear soft tissues,and buckled due to radial pressure are solved for analytically and numerically. The blood flow ratesthrough the bucked shapes are then computed numerically. A Fung-type isotropic hyperelasticstress-strain constitutive equation is used to establish a nonlinear mathematical model for radialbuckling of blood vessels...Item Open Access APPLICATION OF 4-DIMENSIONAL COPULAS IN CALCULATING VALUE-AT-RISK FOR THE PORTFOLIO OF 4 SP500 COMPANIES(School of Sciences and Humanities, 2023) Bolatbekov, KairzhanPortfolio risk management is a process aimed at maintaining profit streams and reducing uncertainties in investment decisions. Value-at-Risk (VaR) is a widely used metric to quantify the potential loss of profits. Although historical simulations and Gaussian distribution are common methods for estimating VaR, modelling the joint multivariate distribution of portfolio investments can be challenging. Copula models offer a solution to these challenges for joint distributions. In this study, we calculated VaR and Conditional Value-at-Risk (CVaR) for a portfolio consisting of the four least correlated stocks among the 15 largest companies in the SP 500 using historical simulations and copula models. We evaluated portfolio based on equal weighting. The optimal ARIMA-GARCH model was selected using Akaike Information Criteria (AIC) values. Furthermore, the performance of the VaR estimations was compared and analyzed using goodness-of-fit tests.Item Open Access APPROXIMATION ERROR OF FOURIER NEURAL NETWORKS(John Wiley and Sons Inc, 2021-03-23) Zhumekenov, Abylay; Takhanov, Rustem; Castro, Alejandro J.; Assylbekov, ZhenisbekThe paper investigates approximation error of two-layer feedforward Fourier Neural Networks (FNNs). Such networks are motivated by the approximation properties of Fourier series. Several implementations of FNNs were proposed since 1980s: by Gallant and White, Silvescu, Tan, Zuo and Cai, and Liu. The main focus of our work is Silvescu's FNN, because its 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 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 BENIGN OVERFITTING WITH RETRIEVAL AUGMENTED MODELS(Nazarbayev University School of Sciences and Humanities, 2022) Assylbekov, Zhenisbek; Tezekbayev, Maxat; Nikoulina, Vassilina; Gallé, MatthiasDespite the fact that modern deep neural networks have the ability to memorize (almost) the entire training set they generalize well to unseen data, contradicting traditional learning theory. This phenomenon --- dubbed benign overfitting --- has been theoretically studied so far in simplified settings only. At the same time, ML practitioners (especially in NLP) figured out how to exploit this feature for more efficient training: retrieval-augmented models (e.g., kNN-LM, RETRO) explicitly store (part of) the training sample in the storage and thus try to (partially) remove a load of memorization from the neural network. In this paper we link these apparently separate threads of research, and propose several possible research directions regarding benign overfitting in retrieval-augmented models.Item Embargo BOUSSINESQ EQUATION IN ELASTIC RODS.(Nazarbayev University School of Sciences and Humanities, 2024-04-19) Zhardemova, NazerkeIn this project, the goal is to consider the equation of the transverse deflections of the rod when it is firmly connected to an elastic foundation. We study the well-posedness of the corresponding Cauchy problem, that is, existence, uniqueness and persistence properties of the solutions inherit by the initial data. Moreover, we will also find the conditions under which the solutions can extend globally in time in $L^2$ and the energy space $X$. Furthermore, we establish the persistence decay properties of the solutions in $X^s$.Item Open Access Calculation of manifold’s tangent space at a given point from noisy data(Nazarbayev University School of Sciences and Humanities, 2020-05-04) Toleubek, MoldirRecently, several studies have been conducted in a field of machine learning to construct manifolds from data in a complex multidimensional space. Therefore manifold learning becomes remarkably attractable among researchers. One of the main tools to identify manifold’s structure is tangent space. In this work, first, we simulate a method for finding tangent space of manifold at some point from noisy data by Principal Component Analysis. In fact, Principal Component Analysis(PCA) provides dimension reduction by its ‘principal components’. Then we introduce concurrent method to PCA that is called Maximum Mean Discrepancy distance. It is based on measuring the distance between smooth distributions.Item Open Access CALCULATIONS OF VALUE AT RISK FOR THE PORTFOLIO OF 5 S&P 500 STOCKS USING 5-DIMENSIONAL COPULA FUNCTIONS(Nazarbayev University School of Sciences and Humanities, 2024-04-19) Kakenov, AssanaliThe purpose of this project is to compare copula estimations of Value at Risk (VaR) for a portfolio of 5 S&P 500 stocks to historical, normal distribution, and Monte Carlo methods employing dependence measures and ARIMA-GARCH time series models. This study will provide interpretations of financial data between 2019-2024 in a scope of 5 equations: Gaussian, Clayton, t-Copula, Gumbel, and Frank copulas. Correlations between closing prices of the largest 30 S&P 500 companies by market capitalization were calculated, and the portfolio was constructed by selecting 5 stocks with the least average correlation. The Markowitz portfolio optimization model was utilized to estimate the weights of the assets in the portfolio. Log returns, skewness, kurtosis, Shapiro-Wilk, and ADF were measured to describe stationarity and normality of the data. Data autocorrelation was assessed using ACF and PACF for volatility before ARIMA-GARCH modeling. All methodology was followed by appropriate hypothesis tests. Finally, 5-dimensional copulas were used for the VaR estimations for different confidence intervals. While AIC and BIC showed that t-copula was the best fit, the Clayton copula passed the goodness-of-fit test with the largest p-value. Subsequently, the Clayton copula generated VaR estimations closest to the historical data. The method used in this study can be extended for more than five assets without theoretical obstacles.Item Open Access THE CAUCHY PROBLEM FOR A MOLECULAR BEAM EPITAXY MODEL WITH SLOPE SELECTION(Nazarbayev University School of Sciences and Humanities, 2021-05) Biyar, MagzhanThis thesis is devoted to the study of a nonlinear diffusion equation. We have to prove that the Cauchy problems for a molecular beam epitaxy (MBE) equation with slope selection is locally well-posed for initial data in 𝑊...Item Open Access The Classification Using the Hierarchy and Exclusion Graphs(Nazarbayev University School of Sciences and Humanities, 2020) Raimbekov, TemirlanThis thesis first reviews the Conditional Random Fields (CRF) model. Then, we introduce the Hierarchy and Exclusion (HEX) graphs and describe the probabilistic classification model based on these graphs (HEX model). Next, we demonstrate that the HEX model is a special case of the CRF model. This allows us to train the HEX model using the framework of the CRF model. After that, we explain the algorithm for this process that calculates the marginals (Exact Inference algorithm). The main objective of the research was to design the sparsification and densification steps for the exact inference algorithm. We propose algorithms for these steps. Then, we introduce the betting model that is modified HEX model. We calculate marginals for this model using the Exact Inference algorithm without sparsification and densification steps. After that, we perform the same experiments using these steps. Finally, by estimating the execution time for the experiments we demonstrate that using the sparsification and densification steps in the exact inference algorithm boosts its performance.....