Comparing Solution Methods for Dynamic Equilibrium Economies

This paper compares solution methods for dynamic equilibrium economies. We compute and simulate the stochastic neoclassical growth model with leisure choice using Undetermined Coefficients in levels and in logs, Finite Elements, Chebyshev Polynomials, Second and Fifth Order Perturbations and Value Function Iteration for several calibrations. We document the performance of the methods in terms of computing time, implementation complexity and accuracy and we present some conclusions about our preferred approaches based on the reported evidence.Dynamic Equilibrium Economies, Computational Methods, Linear and Nonlinear Solution Methods

BioEM: GPU-accelerated computing of Bayesian inference of electron microscopy images

In cryo-electron microscopy (EM), molecular structures are determined from large numbers of projection images of individual particles. To harness the full power of this single-molecule information, we use the Bayesian inference of EM (BioEM) formalism. By ranking structural models using posterior probabilities calculated for individual images, BioEM in principle addresses the challenge of working with highly dynamic or heterogeneous systems not easily handled in traditional EM reconstruction. However, the calculation of these posteriors for large numbers of particles and models is computationally demanding. Here we present highly parallelized, GPU-accelerated computer software that performs this task efficiently. Our flexible formulation employs CUDA, OpenMP, and MPI parallelization combined with both CPU and GPU computing. The resulting BioEM software scales nearly ideally both on pure CPU and on CPU+GPU architectures, thus enabling Bayesian analysis of tens of thousands of images in a reasonable time. The general mathematical framework and robust algorithms are not limited to cryo-electron microscopy but can be generalized for electron tomography and other imaging experiments

Performance modelling with adaptive hidden Markov models and discriminatory processor sharing queues

In modern computer systems, workload varies at different times and locations. It is important to model the performance of such systems via workload models that are both representative and efficient. For example, model-generated workloads represent realistic system behaviour, especially during peak times, when it is crucial to predict and address performance bottlenecks. In this thesis, we model performance, namely throughput and delay, using adaptive models and discrete queues. Hidden Markov models (HMMs) parsimoniously capture the correlation and burstiness of workloads with spatiotemporal characteristics. By adapting the batch training of standard HMMs to incremental learning, online HMMs act as benchmarks on workloads obtained from live systems (i.e. storage systems and financial markets) and reduce time complexity of the Baum-Welch algorithm. Similarly, by extending HMM capabilities to train on multiple traces simultaneously it follows that workloads of different types are modelled in parallel by a multi-input HMM. Typically, the HMM-generated traces verify the throughput and burstiness of the real data. Applications of adaptive HMMs include predicting user behaviour in social networks and performance-energy measurements in smartphone applications. Equally important is measuring system delay through response times. For example, workloads such as Internet traffic arriving at routers are affected by queueing delays. To meet quality of service needs, queueing delays must be minimised and, hence, it is important to model and predict such queueing delays in an efficient and cost-effective manner. Therefore, we propose a class of discrete, processor-sharing queues for approximating queueing delay as response time distributions, which represent service level agreements at specific spatiotemporal levels. We adapt discrete queues to model job arrivals with distributions given by a Markov-modulated Poisson process (MMPP) and served under discriminatory processor-sharing scheduling. Further, we propose a dynamic strategy of service allocation to minimise delays in UDP traffic flows whilst maximising a utility function.Open Acces

Strategies for teaching engineering mathematics

This thesis is an account of experiments into the teaching of mathematics to engineering undergraduates which have been conducted over twenty years against a background of changing intake ability, varying output requirements and increasing restrictions on the formal contact time available. The aim has been to improve the efficiency of the teaching-learning process. The main areas of experimentation have been the integration in the syllabus of numerical and analytical methods, the incorporation of case studies into the curriculum and the use of micro-based software to enhance the teaching process. Special attention is paid to courses in Mathematical Engineering and their position in the spectrum of engineering disciplines. A core curriculum in mathematics for undergraduate engineers is proposed and details are provided of its implementation. The roles of case studies and micro-based software are highlighted. The provision of a mathematics learning resource centre is considered a necessary feature of the implementation of the proposed course. Finally, suggestions for further research are made

Verification and validation of models

Simulation Models;econometrics

Computer aided reliability, availability, and safety modeling for fault-tolerant computer systems with commentary on the HARP program

Many of the most challenging reliability problems of our present decade involve complex distributed systems such as interconnected telephone switching computers, air traffic control centers, aircraft and space vehicles, and local area and wide area computer networks. In addition to the challenge of complexity, modern fault-tolerant computer systems require very high levels of reliability, e.g., avionic computers with MTTF goals of one billion hours. Most analysts find that it is too difficult to model such complex systems without computer aided design programs. In response to this need, NASA has developed a suite of computer aided reliability modeling programs beginning with CARE 3 and including a group of new programs such as: HARP, HARP-PC, Reliability Analysts Workbench (Combination of model solvers SURE, STEM, PAWS, and common front-end model ASSIST), and the Fault Tree Compiler. The HARP program is studied and how well the user can model systems using this program is investigated. One of the important objectives will be to study how user friendly this program is, e.g., how easy it is to model the system, provide the input information, and interpret the results. The experiences of the author and his graduate students who used HARP in two graduate courses are described. Some brief comparisons were made with the ARIES program which the students also used. Theoretical studies of the modeling techniques used in HARP are also included. Of course no answer can be any more accurate than the fidelity of the model, thus an Appendix is included which discusses modeling accuracy. A broad viewpoint is taken and all problems which occurred in the use of HARP are discussed. Such problems include: computer system problems, installation manual problems, user manual problems, program inconsistencies, program limitations, confusing notation, long run times, accuracy problems, etc