Search results for: stochastic matrices

Authors: Damir Latypov

Abstract:

A hybrid classical-quantum algorithm to solve boundary integral equations (BIE) arising in problems of electromagnetic and acoustic scattering is proposed. The quantum speed-up is due to a Quantum Linear System Algorithm (QLSA). The original QLSA of Harrow et al. provides an exponential speed-up over the best-known classical algorithms but only in the case of sparse systems. Due to the non-local nature of integral operators, matrices arising from discretization of BIEs, are, however, dense. A QLSA for dense matrices was introduced in 2017. Its runtime as function of the system's size N is bounded by O(√Npolylog(N)). The run time of the best-known classical algorithm for an arbitrary dense matrix scales as O(N².³⁷³). Instead of exponential as in case of sparse matrices, here we have only a polynomial speed-up. Nevertheless, sufficiently high power of this polynomial, ~4.7, should make QLSA an appealing alternative. Unfortunately for the QLSA, the asymptotic separability of the Green's function leads to high compressibility of the BIEs matrices. Classical fast algorithms such as Multilevel Fast Multipole Method (MLFMM) take advantage of this fact and reduce the runtime to O(Nlog(N)), i.e., the QLSA is only quadratically faster than the MLFMM. To be truly impactful for computational electromagnetics and acoustics engineers, QLSA must provide more substantial advantage than that. We propose a computational scheme which combines elements of the classical fast algorithms with the QLSA to achieve the required performance.

Keywords: quantum linear system algorithm, boundary integral equations, dense matrices, electromagnetic scattering theory

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Authors: Meriem Bahij, Ahmed Nafidi, Boujemâa Achchab, Sílvio M. A. Gama, José A. O. Matos

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Stochastic modeling concerns the use of probability to model real-world situations in which uncertainty is present. Therefore, the purpose of stochastic modeling is to estimate the probability of outcomes within a forecast, i.e. to be able to predict what conditions or decisions might happen under different situations. In the present study, we present a model of a stochastic diffusion process based on the bi-Weibull distribution function (its trend is proportional to the bi-Weibull probability density function). In general, the Weibull distribution has the ability to assume the characteristics of many different types of distributions. This has made it very popular among engineers and quality practitioners, who have considered it the most commonly used distribution for studying problems such as modeling reliability data, accelerated life testing, and maintainability modeling and analysis. In this work, we start by obtaining the probabilistic characteristics of this model, as the explicit expression of the process, its trends, and its distribution by transforming the diffusion process in a Wiener process as shown in the Ricciaardi theorem. Then, we develop the statistical inference of this model using the maximum likelihood methodology. Finally, we analyse with simulated data the computational problems associated with the parameters, an issue of great importance in its application to real data with the use of the convergence analysis methods. Overall, the use of a stochastic model reflects only a pragmatic decision on the part of the modeler. According to the data that is available and the universe of models known to the modeler, this model represents the best currently available description of the phenomenon under consideration.

Keywords: diffusion process, discrete sampling, likelihood estimation method, simulation, stochastic diffusion process, trends functions, bi-parameters weibull density function

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Authors: Ahmed Noor Al-qayyim, Barlas Özden Çağlayan

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Structural failure is caused mainly by damage that often occurs on structures. Many researchers focus on obtaining very efficient tools to detect the damage in structures in the early state. In the past decades, a subject that has received considerable attention in literature is the damage detection as determined by variations in the dynamic characteristics or response of structures. This study presents a new damage identification technique. The technique detects the damage location for the incomplete structure system using output data only. The method indicates the damage based on the free vibration test data by using “Two Points - Condensation (TPC) technique”. This method creates a set of matrices by reducing the structural system to two degrees of freedom systems. The current stiffness matrices are obtained from optimization of the equation of motion using the measured test data. The current stiffness matrices are compared with original (undamaged) stiffness matrices. High percentage changes in matrices’ coefficients lead to the location of the damage. TPC technique is applied to the experimental data of a simply supported steel beam model structure after inducing thickness change in one element. Where two cases are considered, the method detects the damage and determines its location accurately in both cases. In addition, the results illustrate that these changes in stiffness matrix can be a useful tool for continuous monitoring of structural safety using ambient vibration data. Furthermore, its efficiency proves that this technique can also be used for big structures.

Keywords: damage detection, optimization, signals processing, structural health monitoring, two points–condensation

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Authors: Majid Khalili, Hamed Tayebi

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This paper considers a stochastic flexible job-shop scheduling (SFJSS) problem in the presence of production disruptions, and reactive scheduling is implemented in order to find the optimal solution under uncertainty. In this problem, there are two main disruptions including machine failure which influences operation time, and modification or cancellation of the order delivery date during production. In order to decrease the negative effects of these difficulties, two derived strategies from reactive scheduling are used; the first one is relevant to being able to allocate multiple machine to each job, and the other one is related to being able to select the best alternative process from other job while some disruptions would be created in the processes of a job. For this purpose, a Mixed Integer Linear Programming model is proposed.

Keywords: flexible job-shop scheduling, reactive scheduling, stochastic environment, mixed integer linear programming

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Authors: Jaroslav Krutil, František Pochylý, Simona Fialová, Vladimír Habán

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A mathematical model of the additional effects of the liquid in the hydrodynamic gap is presented in the paper. An in-compressible viscous fluid is considered. Based on computational modeling are determined the matrices of mass, stiffness and damping. The mathematical model is experimentally verified.

Keywords: computational modeling, mathematical model, hydrodynamic gap, matrices of mass, stiffness and damping

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Authors: Ramazan I. Kadiev, Arcady Ponosov

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Mathematical models of gene regulatory networks can in many cases be described by ordinary differential equations with switching nonlinearities, where the initial value problem is ill-posed. Several regularization methods are known in the case of deterministic networks, but the presence of stochastic noise leads to several technical difficulties. In the presentation, it is proposed to apply the methods of the stochastic singular perturbation theory going back to Yu. Kabanov and Yu. Pergamentshchikov. This approach is used to regularize the above ill-posed problem, which, e.g., makes it possible to design stable numerical schemes. Several examples are provided in the presentation, which support the efficiency of the suggested analysis. The method can also be of interest in other fields of biomathematics, where differential equations contain switchings, e.g., in neural field models.

Keywords: ill-posed problems, singular perturbation analysis, stochastic differential equations, switching nonlinearities

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Authors: H. M. Soroush

Abstract:

The problem of scheduling products and services for on-time deliveries is of paramount importance in today’s competitive environments. It arises in many manufacturing and service organizations where it is desirable to complete jobs (products or services) with different weights (penalties) on or before their due dates. In such environments, schedules should frequently decide whether to schedule a job based on its processing time, due-date, and the penalty for tardy delivery to improve the system performance. For example, it is common to measure the weighted number of late jobs or the percentage of on-time shipments to evaluate the performance of a semiconductor production facility or an automobile assembly line. In this paper, we address the problem of scheduling a set of jobs on a server where processing times or due-dates of jobs are random variables and fixed weights (penalties) are imposed on the jobs’ late deliveries. The goal is to find the schedule that minimizes the expected weighted number of tardy jobs. The problem is NP-hard to solve; however, we explore three scenarios of the problem wherein: (i) both processing times and due-dates are stochastic; (ii) processing times are stochastic and due-dates are deterministic; and (iii) processing times are deterministic and due-dates are stochastic. We prove that special cases of these scenarios are solvable optimally in polynomial time, and introduce efficient heuristic methods for the general cases. Our computational results show that the heuristics perform well in yielding either optimal or near optimal sequences. The results also demonstrate that the stochasticity of processing times or due-dates can affect scheduling decisions. Moreover, the proposed problem is general in the sense that its special cases reduce to some new and some classical stochastic single machine models.

Keywords: number of late jobs, scheduling, single server, stochastic

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Authors: A. A. Hussen, I. N. Jleta

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Micro-electromechanical system (MEMS) accelerometers and gyroscopes are suitable for the inertial navigation system (INS) of many applications due to the low price, small dimensions and light weight. The main disadvantage in a comparison with classic sensors is a worse long term stability. The estimation accuracy is mostly affected by the time-dependent growth of inertial sensor errors, especially the stochastic errors. In order to eliminate negative effect of these random errors, they must be accurately modeled. Where the key is the successful implementation that depends on how well the noise statistics of the inertial sensors is selected. In this paper, the Allan variance technique will be used in modeling the stochastic errors of the inertial sensors. By performing a simple operation on the entire length of data, a characteristic curve is obtained whose inspection provides a systematic characterization of various random errors contained in the inertial-sensor output data.

Keywords: Allan variance, accelerometer, gyroscope, stochastic errors

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Authors: Nadarajah I. Ramesh

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Much of the research on stochastic point process models for rainfall has focused on Poisson cluster models constructed from either the Neyman-Scott or Bartlett-Lewis processes. The doubly stochastic Poisson process provides a rich class of point process models, especially for fine-scale rainfall modelling. This paper provides an account of recent development on this topic and presents the results based on some of the fine-scale rainfall models constructed from this class of stochastic point processes. Amongst the literature on stochastic models for rainfall, greater emphasis has been placed on modelling rainfall data recorded at hourly or daily aggregation levels. Stochastic models for sub-hourly rainfall are equally important, as there is a need to reproduce rainfall time series at fine temporal resolutions in some hydrological applications. For example, the study of climate change impacts on hydrology and water management initiatives requires the availability of data at fine temporal resolutions. One approach to generating such rainfall data relies on the combination of an hourly stochastic rainfall simulator, together with a disaggregator making use of downscaling techniques. Recent work on this topic adopted a different approach by developing specialist stochastic point process models for fine-scale rainfall aimed at generating synthetic precipitation time series directly from the proposed stochastic model. One strand of this approach focused on developing a class of doubly stochastic Poisson process (DSPP) models for fine-scale rainfall to analyse data collected in the form of rainfall bucket tip time series. In this context, the arrival pattern of rain gauge bucket tip times N(t) is viewed as a DSPP whose rate of occurrence varies according to an unobserved finite state irreducible Markov process X(t). Since the likelihood function of this process can be obtained, by conditioning on the underlying Markov process X(t), the models were fitted with maximum likelihood methods. The proposed models were applied directly to the raw data collected by tipping-bucket rain gauges, thus avoiding the need to convert tip-times to rainfall depths prior to fitting the models. One advantage of this approach was that the use of maximum likelihood methods enables a more straightforward estimation of parameter uncertainty and comparison of sub-models of interest. Another strand of this approach employed the DSPP model for the arrivals of rain cells and attached a pulse or a cluster of pulses to each rain cell. Different mechanisms for the pattern of the pulse process were used to construct variants of this model. We present the results of these models when they were fitted to hourly and sub-hourly rainfall data. The results of our analysis suggest that the proposed class of stochastic models is capable of reproducing the fine-scale structure of the rainfall process, and hence provides a useful tool in hydrological modelling.

Keywords: fine-scale rainfall, maximum likelihood, point process, stochastic model

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Authors: Katja Ignatieva, Patrick Wong

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We investigated the dynamics of high frequency energy prices, including crude oil and electricity prices. The returns of underlying quantities are modelled using various parametric models such as stochastic framework with jumps and stochastic volatility (SVCJ) as well as non-parametric alternatives, which are purely data driven and do not require specification of the drift or the diffusion coefficient function. Using different statistical criteria, we investigate the performance of considered parametric and nonparametric models in their ability to forecast price series and volatilities. Our models incorporate possible seasonalities in the underlying dynamics and utilise advanced estimation techniques for the dynamics of energy prices.

Keywords: stochastic volatility, affine jump-diffusion models, high frequency data, model specification, markov chain monte carlo

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Authors: Sie Long Kek, Wah June Leong, Kok Lay Teo

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Linear quadratic Gaussian model is a standard mathematical model for the stochastic optimal control problem. The combination of the linear quadratic estimation and the linear quadratic regulator allows the state estimation and the optimal control policy to be designed separately. This is known as the separation principle. In this paper, an efficient computational method is proposed to solve the linear quadratic Gaussian problem. In our approach, the Hamiltonian function is defined, and the necessary conditions are derived. In addition to this, the output error is defined and the least-square optimization problem is introduced. By determining the first-order necessary condition, the gradient of the sum squares of output error is established. On this point of view, the stochastic approximation approach is employed such that the optimal control policy is updated. Within a given tolerance, the iteration procedure would be stopped and the optimal solution of the linear-quadratic Gaussian problem is obtained. For illustration, an example of the linear-quadratic Gaussian problem is studied. The result shows the efficiency of the approach proposed. In conclusion, the applicability of the approach proposed for solving the linear quadratic Gaussian problem is highly demonstrated.

Keywords: iteration procedure, least squares solution, linear quadratic Gaussian, output error, stochastic approximation

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Authors: Daniela Rivera-Tobar Mario Perez-Won, Roberto Lemus-Mondaca, Gipsy Tabilo-Munizaga

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Different dietary trends worldwide seek to consume foods with anti-inflammatory properties, rich in antioxidants, proteins, and unsaturated fatty acids that lead to better metabolic, intestinal, mental, and cardiac health. In this sense, food matrices with high protein content based on macro and microalgae are an excellent alternative to meet the new needs of consumers. An emerging and environmentally friendly technology for producing protein matrices is ultrasonic agglomeration. It consists of the formation of permanent bonds between particles, improving the agglomeration of the matrix compared to conventionally agglomerated products (compression). Among the advantages of this process are the reduction of nutrient loss and the avoidance of binding agents. The objective of this research was to optimize the ultrasonic agglomeration process in matrices composed of Spirulina (Arthrospira platensis) powder and Cochayuyo (Durvillae Antartica) flour, by means of the response variable (Young's modulus) and the independent variables were the process conditions (percentage of ultrasonic amplitude: 70, 80 and 90; ultrasonic agglomeration times and cycles: 20, 25 and 30 seconds, and 3, 4 and 5). It was evaluated using a central composite design and analyzed using response surface methodology. In addition, the effects of agglomeration on thermophysical and microstructural properties were evaluated. It was determined that ultrasonic compression with 80 and 90% amplitude caused conformational changes according to Fourier infrared spectroscopy (FTIR) analysis, the best condition with respect to observed microstructure images (SEM) and differential scanning calorimetry (DSC) analysis, was the condition of 90% amplitude 25 and 30 seconds with 3 and 4 cycles of ultrasound. In conclusion, the agglomerated matrices present good macro and microstructural properties which would allow the design of food systems with better nutritional and functional properties.

Keywords: ultrasonic agglomeration, physical properties of food, protein matrices, macro and microalgae

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Authors: Kun Huang

Abstract:

This paper investigates whether the combination of local and stochastic volatility models can be calibrated exactly to any arbitrage-free implied volatility surface of European option. The risk neutral Brownian Bridge density is applied for calibration of the leverage function of our Hybrid model. Furthermore, the tails of marginal risk neutral density are generated by Generalized Extreme Value distribution in order to capture the properties of asset returns. The local volatility is generated from the arbitrage-free implied volatility surface using stochastic volatility inspired parameterization.

Keywords: arbitrage free implied volatility, calibration, extreme value distribution, hybrid model, local volatility, risk-neutral density, stochastic volatility

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Authors: Zubier Arfan, Paul Johnson

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The electronification of financial markets and the rise of algorithmic trading has sparked a lot of interest from the mathematical community, for the market making-problem in particular. The research presented in this short paper solves the classic stochastic control problem in order to derive the strategy for a market-maker. It also shows how to calibrate and simulate the strategy with real limit order book data for back-testing. The ambiguity of limit-order priority in back-testing is dealt with by considering optimistic and pessimistic priority scenarios. The model, although it does outperform a naive strategy, assumes constant volatility, therefore, is not best suited to the LOB data. The Heston model is introduced to describe the price and variance process of the asset. The Trader's constant absolute risk aversion utility function is optimised by numerically solving a 3-dimensional Hamilton-Jacobi-Bellman partial differential equation to find the optimal limit order quotes. The results show that the stochastic volatility market-making model is more suitable for a risk-averse trader and is also less sensitive to calibration error than the constant volatility model.

Keywords: market-making, market-microsctrucure, stochastic volatility, quantitative trading

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Authors: Tomoaki Hashimoto

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Model predictive control is a kind of optimal feedback control in which control performance over a finite future is optimized with a performance index that has a moving initial time and a moving terminal time. This paper examines the stability of model predictive control for linear discrete-time systems with additive stochastic disturbances. A sufficient condition for the stability of the closed-loop system with model predictive control is derived by means of a linear matrix inequality. The objective of this paper is to show the results of computational simulations in order to verify the validity of the obtained stability condition.

Keywords: computational simulations, optimal control, predictive control, stochastic systems, discrete-time systems

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Authors: N. C. Sarkar, A. Bhaskar, Z. Zheng

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The driving behavior in area-based (i.e., non-lane based) traffic is induced by the presence of other individuals in the choice space from the driver’s visual perception area. The driving behavior of a subject vehicle is constrained by the potential leaders and leaders are frequently changed over time. This paper is to determine a stochastic model for a parameter of modified intelligent driver model (MIDM) in area-based traffic (as in developing countries). The parametric and non-parametric distributions are presented to fit the parameters of MIDM. The goodness of fit for each parameter is measured in two different ways such as graphically and statistically. The quantile-quantile (Q-Q) plot is used for a graphical representation of a theoretical distribution to model a parameter and the Kolmogorov-Smirnov (K-S) test is used for a statistical measure of fitness for a parameter with a theoretical distribution. The distributions are performed on a set of estimated parameters of MIDM. The parameters are estimated on the real vehicle trajectory data from India. The fitness of each parameter with a stochastic model is well represented. The results support the applicability of the proposed modeling for parameters of MIDM in area-based traffic flow simulation.

Keywords: area-based traffic, car-following model, micro-simulation, stochastic modeling

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Authors: Amir Azaron

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In this research, a stochastic programming approach is developed for designing supply chains with uncertain parameters. Demands and selling prices of products at markets are considered as the uncertain parameters. The proposed mathematical model will be multi-period two-stage stochastic programming, which takes into account the selection of retailer sites, suppliers, production levels, inventory levels, transportation modes to be used for shipping goods, and shipping quantities among the entities of the supply chain network. The objective function is to maximize the chain’s net present value. In order to maximize the chain’s NPV, the sum of first-stage investment costs on retailers, and the expected second-stage processing, inventory-holding and transportation costs should be kept as low as possible over multiple periods. The effects of supply uncertainty where suppliers are unreliable will also be investigated on the efficiency of the supply chain.

Keywords: supply chain management, stochastic programming, multiobjective programming, inventory control

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Authors: Walid S. Alfuhaid, Saud A. Alghamdi, John M. Watkins, M. Edwin Sawan

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Designing a controller for stochastic decentralized interconnected large scale systems usually involves a high degree of complexity and computation ability. Noise, observability, and controllability of all system states, connectivity, and channel bandwidth are other constraints to design procedures for distributed large scale systems. The quasi-steady state model investigated in this paper is a reduced order model of the original system using singular perturbation techniques. This paper results in an optimal control synthesis to design an observer based feedback controller by standard stochastic control theory techniques using Linear Quadratic Gaussian (LQG) approach and Kalman filter design with less complexity and computation requirements. Numerical example is given at the end to demonstrate the efficiency of the proposed method.

Keywords: decentralized, optimal control, output, singular perturb

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Authors: Obaid Algahtani

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An interval may be defined as a convex combination as follows: I=[a,b]={x_α=(1-α)a+αb: α∈[0,1]}. Consequently, we may adopt interval operations by applying the scalar operation point-wise to the corresponding interval points: I ∙J={x_α∙y_α ∶ αϵ[0,1],x_α ϵI ,y_α ϵJ}, With the usual restriction 0∉J if ∙ = ÷. These operations are associative: I+( J+K)=(I+J)+ K, I*( J*K)=( I*J )* K. These two properties, which are missing in the usual interval operations, will enable the extension of the usual linear system concepts to the interval setting in a seamless manner. The arithmetic introduced here avoids such vague terms as ”interval extension”, ”inclusion function”, determinants which we encounter in the engineering literature that deal with interval linear systems. On the other hand, these definitions were motivated by our attempt to arrive at a definition of interval random variables and investigate the corresponding statistical properties. We feel that they are the natural ones to handle interval systems. We will enable the extension of many results from usual state space models to interval state space models. The interval state space model we will consider here is one of the form X_((t+1) )=AX_t+ W_t, Y_t=HX_t+ V_t, t≥0, where A∈ 〖IR〗^(k×k), H ∈ 〖IR〗^(p×k) are interval matrices and 〖W 〗_t ∈ 〖IR〗^k,V_t ∈〖IR〗^p are zero – mean Gaussian white-noise interval processes. This feeling is reassured by the numerical results we obtained in a simulation examples.

Keywords: interval analysis, interval matrices, state space model, Kalman Filter

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Authors: Abeer Amayri, Akif A. Bulgak

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Due to today’s globalization as well as outsourcing practices of the companies, the Supply Chain (SC) performances have become more dependent on the efficient movement of material among places that are geographically dispersed, where there is more chance for disruptions. One such disruption is the quality and delivery uncertainties of outsourcing. These uncertainties could lead the products to be unsafe and, as is the case in a number of recent examples, companies may have to end up in recalling their products. As a result of these problems, there is a need to develop a methodology for selecting suppliers globally in view of risks associated with low quality and late delivery. Accordingly, we developed a two-stage stochastic model that captures the risks associated with uncertainty in quality and delivery as well as a solution procedure for the model. The stochastic model developed simultaneously optimizes supplier selection and purchase quantities under price discounts over a time horizon. In particular, our target is the study of global organizations with multiple sites and multiple overseas suppliers, where the pricing is offered in suppliers’ local currencies. Our proposed methodology is applied to a case study for a US automotive company having two assembly plants and four potential global suppliers to illustrate how the proposed model works in practice.

Keywords: global supply chains, quality, stochastic programming, supplier selection

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Authors: Mustafa Abu Ghalia, Yaser Dahman

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A new class of polyurethane (PU) reinforced with green bacterial cellulose nanofibers (BC) were prepared using a solvent casting method, with the goal of fabricating green nanocomposites. Four series classes of BC (1, 2.5, 5, and 10 wt%) were reinforced into PU matrices via BC surface modification and subsequently BC-grafted into PU throughout silane coupling agent to improve BC dispersion and its interfacial interaction. The experiment results from the tensile tester were evaluated according to the response surface method (RSM) for optimizing the impacts of variable parameters, pore size, porosity, and BC contents on the mechanical properties. The compressive strength for PU-5 BC wt% was about 9.8 MPa, and decrease when being generated prosperity to recorded at 4.9 MPa. Nielson model was applied to investigate the BC stress concentration on the PU matrices. Likewise, krenche and Hapli-Tasi model were employed to evaluate the BC nanofiber reinforcement potential and BC orientation into PU matrices. The analysis of variance (ANOVA) demonstrated that only BC loading has a significant effect in increases tensile strength, young’s modulus, and a flexural modulus of the PU-BC nanocomposites. The optimal factors of the variables experiment confirmed to be 5 wt% for BC, 230 for pore size, and 80 % for porosity. Scanning electron microscopy (SEM) micrographs showed that the uniform distribution of nanofibers in the PU matrices with the addition of BC 5 wt %. Hydrolytic degradation revealed that the weight loss in PU-BC scaffold is higher than PU-BC wt %.

Keywords: polyurethane scaffold, mechanical properties, tissue engineering, polyurethane

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Authors: Miljan B. Petrović, Dušan B. Petrović, Goran S. Nikolić

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This paper describes a method for AWGN (Additive White Gaussian Noise) variance estimation in noisy stochastic signals, referred to as Multiplicative-Noising Variance Estimation (MNVE). The aim was to develop an estimation algorithm with minimal number of assumptions on the original signal structure. The provided MATLAB simulation and results analysis of the method applied on speech signals showed more accuracy than standardized AR (autoregressive) modeling noise estimation technique. In addition, great performance was observed on very low signal-to-noise ratios, which in general represents the worst case scenario for signal denoising methods. High execution time appears to be the only disadvantage of MNVE. After close examination of all the observed features of the proposed algorithm, it was concluded it is worth of exploring and that with some further adjustments and improvements can be enviably powerful.

Keywords: noise, signal-to-noise ratio, stochastic signals, variance estimation

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Authors: Liang Liu, Xiaopeng Luo

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In this paper, we propose an accelerated stochastic gradient method with momentum. The momentum term is the weighted average of generated gradients, and the weights decay inverse proportionally with the iteration times. Stochastic gradient descent with momentum (SGDM) uses weights that decay exponentially with the iteration times to generate the momentum term. Using exponential decay weights, variants of SGDM with inexplicable and complicated formats have been proposed to achieve better performance. However, the momentum update rules of our method are as simple as that of SGDM. We provide theoretical convergence analyses, which show both the exponential decay weights and our inverse proportional decay weights can limit the variance of the parameter moving directly to a region. Experimental results show that our method works well with many practical problems and outperforms SGDM.

Keywords: exponential decay rate weight, gradient descent, inverse proportional decay rate weight, momentum

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Authors: S. Rozhkova, O. Rozhkova, A. Harlova, V. Lasukov

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We have conducted the optimal synthesis of root-mean-squared objective filter to estimate the state vector in the case if within the observation channel with memory the anomalous noises with unknown mathematical expectation are complement in the function of the regular noises. The synthesis has been carried out for linear stochastic systems of continuous-time.

Keywords: mathematical expectation, filtration, anomalous noise, memory

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Authors: Seon Soon Choi

Abstract:

The essential purpose is to present the good fatigue crack propagation model describing a stochastic fatigue crack growth behavior in a rolled magnesium alloy, AZ31, under various load ratio conditions. Fatigue crack propagation experiments were carried out in laboratory air under four conditions of load ratio, R, using AZ31 to investigate the crack growth behavior. The stochastic fatigue crack growth behavior was analyzed using an interpolation of random variable, Z, introduced to an empirical fatigue crack propagation model. The empirical fatigue models used in this study are Paris-Erdogan model, Walker model, Forman model, and modified Forman model. It was found that the random variable is useful in describing the stochastic fatigue crack growth behaviors under various load ratio conditions. The good probabilistic model describing a stochastic fatigue crack growth behavior under various load ratio conditions was also proposed.

Keywords: magnesium alloys, fatigue crack propagation model, load ratio, interpolation of random variable

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Authors: Sasiwimol Auepong, Raywat Tanadkithirun

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In this work, the problem that squirrels ruin durian, which is an economical fruit in Thailand, is considered. We seek the strategy for the durian farmers to eliminate the squirrels under the consideration that squirrels also provide ecosystem service. The population dynamics of squirrels are constructed to have carrying capacity since we consider the population in a confined area. A performance index indicating the total benefit of a given elimination strategy is provided. It comprises the cost of countermeasures, the loss of resources, and the ecosystem service provided by squirrels. The optimal performance index is numerically solved through the variational inequality using the finite difference method. The optimal strategy to control the squirrel population is also given numerically.

Keywords: controlled stochastic differential equation, durian, finite difference method, performance index, singular stochastic control model, squirrel

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Authors: S. O. Oyamakin, A. U. Chukwu

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Richard's growth equation being a generalized logistic growth equation was improved upon by introducing an allometric parameter using the hyperbolic sine function. The integral solution to this was called hyperbolic Richard's growth model having transformed the solution from deterministic to a stochastic growth model. Its ability in model prediction was compared with the classical Richard's growth model an approach which mimicked the natural variability of heights/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using the coefficient of determination (R2), Mean Absolute Error (MAE) and Mean Square Error (MSE) results. The Kolmogorov-Smirnov test and Shapiro-Wilk test was also used to test the behavior of the error term for possible violations. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic Richard's nonlinear growth models better than the classical Richard's growth model.

Keywords: height, Dbh, forest, Pinus caribaea, hyperbolic, Richard's, stochastic

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Authors: Colin O’Hare, Zili Zho, Thomas Sneddon

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The Australian superannuation system has received high praise for its participation rates and level of funding in retirement yet it is only 25 years old. In recent years, with increasing longevity and persistent lower rates of investment return, how adequate will the funds accumulated through a superannuation system be? In this paper we take Australia as a case study and build a stochastic model of accumulation and decummulation of funds and determine the expected number of years a fund may last an individual in retirement.

Keywords: component, mortality, stochastic models, superannuation

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Authors: Haowen Xi

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We propose and solve exactly a class of non-linear generalization of the Black-Scholes process of stochastic differential equations describing price bubble and crashes dynamics. As a result of nonlinear positive feedback, the faster-than-exponential price positive growth (bubble forming) and negative price growth (crash forming) are found to be the power-law finite-time singularity in which bubbles and crashes price formation ending at finite critical time tc. While most literature on the market bubble and crash process focuses on the nonlinear positive feedback mechanism aspect, very few studies concern the noise level on the same process. The present work adds to the market bubble and crashes literature by studying the external sources noise influence on the critical time tc of the bubble forming and crashes forming. Two main results will be discussed: (1) the analytical expression of expected value of the critical time is found and unexpected critical slowing down due to the coupling external noise is predicted; (2) numerical simulations of the nonlinear stochastic equation is presented, and the probability distribution of Prob(tc) is found to be the inverse gamma function.

Keywords: bubble, crash, finite-time-singular, numerical simulation, price dynamics, stochastic differential equations

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Authors: Daniel Fundi Murithi

Abstract:

Missing data is a real bane in many surveys. To overcome the problems caused by missing data, partial deletion, and single imputation methods, among others, have been proposed. However, problems such as discarding usable data and inaccuracy in reproducing known population parameters and standard errors are associated with them. For regression and stochastic imputation, it is assumed that there is a variable with complete cases to be used as a predictor in estimating missing values in the other variable, and the relationship between the two variables is linear, which might not be realistic in practice. In this project, we estimate population total in presence of missing values in two-phase sampling. Instead of regression or stochastic models, non-parametric model based regression model is used in imputing missing values. Empirical study showed that nonparametric model-based regression imputation is better in reproducing variance of population total estimate obtained when there were no missing values compared to mean, median, regression, and stochastic imputation methods. Although regression and stochastic imputation were better than nonparametric model-based imputation in reproducing population total estimates obtained when there were no missing values in one of the sample sizes considered, nonparametric model-based imputation may be used when the relationship between outcome and predictor variables is not linear.

Keywords: finite population total, missing data, model-based imputation, two-phase sampling

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