Numerical Analysis and Computation Commons^™

Assessing Computational Thinking, Daniel Duckworth

Daniel Duckworth

This paper provides some context for the role of computation thinking (CT) in the Australian Curriculum, an abridged literature review of CT as a problem-solving framework from the International Computer and Information Literacy Study (ICILS) 2018 assessment framework and some examples of how CT has been used to solve real-world problems. Finally, this paper presents ways to teach and assess CT.

Local Lagged Adapted Generalized Method Of Moments: An Innovative Estimation And Forecasting Approach And Its Applications.Pdf, Olusegun M. Otunuga

Olusegun Michael Otunuga

Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Signal Flow Graph Approach To Efficient Dst I-Iv Algorithms, Sirani M. Perera

Sirani Mututhanthrige Perera

In this paper, fast and efficient discrete sine transformation (DST) algorithms are presented based on the factorization of sparse, scaled orthogonal, rotation, rotation-reflection, and butterfly matrices. These algorithms are completely recursive and solely based on DST I-IV. The presented algorithms have low arithmetic cost compared to the known fast DST algorithms. Furthermore, the language of signal flow graph representation of digital structures is used to describe these efficient and recursive DST algorithms having (n􀀀1) points signal flow graph for DST-I and n points signal flow graphs for DST II-IV.

An Interval Arithmetic Newton Method For Solving Systems Of Nonlinear Equations, Ronald I. Greenberg, Eldon R. Hansen

Ronald Greenberg

We introduce an interval Newton method for bounding solutions of systems of nonlinear equations. It entails three sub-algorithms. The first is a Gauss-Seidel type step. The second is a real (non-interval) Newton iteration. The third solves the linearized equations by elimination. We explain why each sub-algorithm is desirable and how they fit together to provide solutions in as little as 1/3 to 1/4 the time required by a commonly used method due to Krawczyk.

C.V. - Wojciech Budzianowski, Wojciech M. Budzianowski

Wojciech Budzianowski

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Renewable Energy And Sustainable Development (Resd) Group, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

15004.Pdf, Marcus C. Randall

Marcus Randall

Efficient Thermal Image Segmentation Through Integration Of Nonlinear Enhancement With Unsupervised Active Contour Model, Fatema Albalooshi, Evan Krieger, Paheding Sidike, Vijayan K. Asari

Vijayan K. Asari

Thermal images are exploited in many areas of pattern recognition applications. Infrared thermal image segmentation can be used for object detection by extracting regions of abnormal temperatures. However, the lack of texture and color information, low signal-to-noise ratio, and blurring effect of thermal images make segmenting infrared heat patterns a challenging task. Furthermore, many segmentation methods that are used in visible imagery may not be suitable for segmenting thermal imagery mainly due to their dissimilar intensity distributions. Thus, a new method is proposed to improve the performance of image segmentation in thermal imagery. The proposed scheme efficiently utilizes nonlinear intensity …

Procesy Cieplne I Aparaty (Lab), Wojciech M. Budzianowski

Wojciech Budzianowski

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Inżynieria Chemiczna Lab., Wojciech M. Budzianowski

Wojciech Budzianowski

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Optimization And Simulation Of An Evolving Kidney Paired Donation (Kpd) Program, Yijiang Li, Jack Kalbfleisch, Peter Xuekun Song, Yan Zhou, Alan Leichtman, Michael Rees

Yan Zhou 周彦文档

The old concept of barter exchange has extended to the modern area of living-donor kidney transplantation, where one incompatible donor-candidate pair is matched to another pair with a complementary incompatibility, such that the donor from one pair gives an organ to a compatible candidate in the other pair and vice versa. Kidney paired donation (KPD) programs provide a unique and important platform for living incompatible donor-candidate pairs to exchange organs in order to achieve mutual benefit. We propose a novel approach to organizing kidney exchanges in an evolving KPD program with advantages, including (i) it allows for a more exible …

Optimal Control Of A Switched Autonomous System With Time Delay Arising In Fed-Batch Processes, Chongyang Liu

Chongyang Liu

In this paper, we propose a switched autonomous system with time delay to model the 1,3-propanediol (1,3-PD) production in a fed-batch process. Taking the switching instants and the terminal time as the control variables, we formulate a constrained time-delayed optimal control (CTOC) problem to optimize the 1,3-PD production process. Using a time-scaling transformation and parametrizing the switching instants into new parameters, an equivalent CTOC problem is investigated. A numerical solution method is then developed to seek the optimal control strategy. This method is based on the constraint transcription technique and the gradients of the cost functional together with those of …

On Combining Neighbouring Extremals With Control Parameterization, Chongyang Liu, Qun Lin, Ryan Loxton, Kok Lay Teo

Chongyang Liu

In this paper, we consider the neighbouring extremals for a class of optimal control problems with control constraints. We first solve the optimal control problem using control parameterization method to obtain the optimal open-loop control and the optimal reference state. Then, a neighbouring feedback control law is derived for small state perturbations caused by changes on reference state at switching times.

Nonlinear State-Dependent Impulsive System In Fed-Batch Culture And Its Optimal Control, Bangyu Shen, Xiaojing Wang, Chongyang Liu

Chongyang Liu

In this paper, a nonlinear impulsive controlled system, in which the volume of feeding is taken as the control function, is proposed to formulate the fed-batch fermentation process.In the system, both impulsive moments and jumps size of state are state-dependent. Some important properties of the system are investigated. To maximize the concentration of target product at the terminal time, an optimal control model involving the nonlinear state-dependent impulsive controlled system is presented.The optimal control problem is subject to the continuous state inequality constraint and the control constraint. The existence of optimal control is also obtained. In order to derive the …

Inżynieria Chemiczna Ćw., Wojciech M. Budzianowski

Wojciech Budzianowski

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Tematyka Prac Doktorskich, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Zespół Energii Odnawialnej I Zrównoważonego Rozwoju (Eozr), Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.

Introduction To Real Analysis, William F. Trench

William F. Trench

This is a text for a two-term course in introductory real analysis for junior or senior math- ematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathe- matical maturity that can be gained from an introductory real analysis course. The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calcu- lus sequence …

A Chebyshev Pseudo-Spectral Method To Solve The Space-Time Tempered Fractional Diffusion Equation

Cecile M Piret

Generating A Dynamic Synthetic Population – Using An Age-Structured Two-Sex Model For Household Dynamics, Mohammad-Reza Namazi-Rad, Payam Mokhtarian, Pascal Perez

Payam Mokhtarian

Generating a reliable computer-simulated synthetic population is necessary for knowledge processing and decision-making analysis in agent-based systems in order to measure, interpret and describe each target area and the human activity patterns within it. In this paper, both synthetic reconstruction (SR) and combinatorial optimisation (CO) techniques are discussed for generating a reliable synthetic population for a certain geographic region (in Australia) using aggregated- and disaggregated-level information available for such an area. A CO algorithm using the quadratic function of population estimators is presented in this paper in order to generate a synthetic population while considering a two-fold nested structure for …

Homotopy Perturbation Method With Two Expanding Parameters, Ji-Huan He

Ji-Huan He

A homotopy perturbation method with two expanding parameters is suggested. The method is especially effective for a nonlinear equation with two nonlinear terms, which might have different effects on the solution. A nonlinear oscillator is used as an example to elucidate the solution procedure.

Fractional Calculus For Nanoscale Flow And Heat Transfer, Hong-Yan Liu, Ji-Huan He, Zheng-Biao Li

Ji-Huan He

Purpose – Academic and industrial researches on nanoscale flows and heat transfers are an area of increasing global interest, where fascinating phenomena are always observed, e.g. admirable water or air permeation and remarkable thermal conductivity. The purpose of this paper is to reveal the phenomena by the fractional calculus. Design/methodology/approach – This paper begins with the continuum assumption in conventional theories, and then the fractional Gauss’ divergence theorems are used to derive fractional differential equations in fractal media. Fractional derivatives are introduced heuristically by the variational iteration method, and fractal derivatives are explained geometrically. Some effective analytical approaches to fractional …

Modelling And Optimal Control Of A Time-Delayed Switched System In Fed-Batch Process, Chongyang Liu, Zhaohua Gong

Chongyang Liu

The main control goal of the fed-batch process is to maximize the yield of target product as well as to minimize the operation costs simultaneously. Considering the existence of time delay and the switching nature in the fed-batch process, a time-delayed switched system is proposed to formulate the 1,3-propanediol (1,3-PD) production process. Some important properties of the system are also discussed. Taking the switching instants and the terminal time as the control variables, a free terminal time delayed optimal control problem is then presented. Using a time-scaling transformation and parameterizing the switching instants into new parameters, an equivalently optimal control …

Sensitivity Analysis And Parameter Identification For A Nonlinear Time-Delay System In Microbial Fed-Batch Process, Chongyang Liu

Chongyang Liu

Developing suitable dynamic models of bioprocess is a difficult issue in bioscience. In this paper, considering the microbial metabolism mechanism, i.e., the production of new biomass is delayed by the amount of time it takes to metabolize the nutrients, in glycerol bioconversion to 1,3-propanediol, we propose a nonlinear time-delay system to formulate the fed-batch fermentation process. Some important properties are also discussed. Then, in view of the effect of time-delay and the high number of kinetic parameters in the system, the parametric sensitivity analysis is used to determine the key parameters. Finally, a parameter identification model is presented and a …

Switching Time And Parameter Optimization In Nonlinear Switched Systems With Multiple Time-Delays, Chongyang Liu, Ryan Loxton, Kok Lay Teo

Chongyang Liu

In this paper, we consider a dynamic optimization problem involving a general switched system that evolves by switching between several subsystems of nonlinear delay-differential equations. The optimization variables in this system consist of: (1) the times at which the subsystem switches occur; and (2) a set of system parameters that influence the subsystem dynamics. We first establish the existence of the partial derivatives of the system state with respect to both the switching times and the system parameters. Then, on the basis of this result, we show that the gradient of the cost function can be computed by solving the …

A Computational Method For Solving Time-Delay Optimal Control Problems With Free Terminal Time, Chongyang Liu, Ryan Loxton, Kok Lay Teo

Chongyang Liu

This paper considers a class of optimal control problems for general nonlinear time-delay systems with free terminal time. We first show that for this class of problems, the well-known time-scaling transformation for mapping the free time horizon into a fixed time interval yields a new time-delay system in which the time-delays are variable. Then, we introduce a control parameterization scheme to approximate the control variables in the new system by piecewise-constant functions. This yields an approximate finite-dimensional optimization problem with three types of decision variables: the control heights, the control switching times, and the terminal time in the original system …

Optimal Parameter Selection For Nonlinear Multistage Systems With Time-Delays, Chongyang Liu, Ryan Loxton, Kok Lay Teo

Chongyang Liu

In this paper, we consider a novel dynamic optimization problem for nonlinear multistage systems with time-delays. Such systems evolve over multiple stages, with the dynamics in each stage depending on both the current state of the system and the state at delayed times. The optimization problem involves choosing the values of the time-delays, as well as the values of additional parameters that influence the system dynamics, to minimize a given cost functional. We first show that the partial derivatives of the system state with respect to the time-delays and system parameters can be computed by solving a set of auxiliary …

A New Class Of Scalable Parallel Pseudorandom Number Generators Based On Pohlig-Hellman Exponentiation Ciphers, Paul Beale

Paul Beale

Parallel supercomputer-based Monte Carlo applications depend on pseudorandom number generators that produce independent pseudorandom streams across many separate processes. We propose a new scalable class of parallel pseudorandom number generators based on Pohlig--Hellman exponentiation ciphers. The method generates uniformly distributed floating point pseudorandom streams by encrypting simple sequences of integer \textit{messages} into \textit{ciphertexts} by exponentiation modulo prime numbers. The advantages of the method are: the method is trivially parallelizable by parameterization with each pseudorandom number generator derived from an independent prime modulus, the method is fully scalable on massively parallel computing clusters due to the large number of primes available …

Termodynamika Procesowa I Techniczna Lab., Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.