A flexible method for rapid force computation in elliptical magnets

The design of open-access elliptical cross-section magnet systems has recently come under consideration. Obtaining values for the forces generated within these unusual magnets is important to progress the designs towards feasible instruments. This paper presents a novel and flexible method for the rapid computation of forces within elliptical magnets. The method is demonstrated by the analysis of a clinical magnetic resonance imaging magnet of elliptical cross-section and open design. The analysis reveals the non-symmetric nature of the generated Maxwell forces, which are an important consideration, particularly in the design of superconducting systems.

Read-only-memory-based quantum computation: Experimental explorations using nuclear magnetic resonance and future prospects

Read-only-memory-based (ROM-based) quantum computation (QC) is an alternative to oracle-based QC. It has the advantages of being less magical, and being more suited to implementing space-efficient computation (i.e., computation using the minimum number of writable qubits). Here we consider a number of small (one- and two-qubit) quantum algorithms illustrating different aspects of ROM-based QC. They are: (a) a one-qubit algorithm to solve the Deutsch problem; (b) a one-qubit binary multiplication algorithm; (c) a two-qubit controlled binary multiplication algorithm; and (d) a two-qubit ROM-based version of the Deutsch-Jozsa algorithm. For each algorithm we present experimental verification using nuclear magnetic resonance ensemble QC. The average fidelities for the implementation were in the ranges 0.9-0.97 for the one-qubit algorithms, and 0.84-0.94 for the two-qubit algorithms. We conclude with a discussion of future prospects for ROM-based quantum computation. We propose a four-qubit algorithm, using Grover's iterate, for solving a miniature real-world problem relating to the lengths of paths in a network.

Computation of the linear elastic properties of random porous materials with a wide variety of microstructure

A finite-element method is used to study the elastic properties of random three-dimensional porous materials with highly interconnected pores. We show that Young's modulus, E, is practically independent of Poisson's ratio of the solid phase, nu(s), over the entire solid fraction range, and Poisson's ratio, nu, becomes independent of nu(s) as the percolation threshold is approached. We represent this behaviour of nu in a flow diagram. This interesting but approximate behaviour is very similar to the exactly known behaviour in two-dimensional porous materials. In addition, the behaviour of nu versus nu(s) appears to imply that information in the dilute porosity limit can affect behaviour in the percolation threshold limit. We summarize the finite-element results in terms of simple structure-property relations, instead of tables of data, to make it easier to apply the computational results. Without using accurate numerical computations, one is limited to various effective medium theories and rigorous approximations like bounds and expansions. The accuracy of these equations is unknown for general porous media. To verify a particular theory it is important to check that it predicts both isotropic elastic moduli, i.e. prediction of Young's modulus alone is necessary but not sufficient. The subtleties of Poisson's ratio behaviour actually provide a very effective method for showing differences between the theories and demonstrating their ranges of validity. We find that for moderate- to high-porosity materials, none of the analytical theories is accurate and, at present, numerical techniques must be relied upon.

Universal quantum computation and simulation using any entangling Hamiltonian and local unitaries

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? We provide an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling n-qubit Hamiltonian and local unitary operations. It follows that universal quantum computation can be performed using any entangling interaction and local unitary operations.

Practical scheme for quantum computation with any two-qubit entangling gate

Which gates are universal for quantum computation? Although it is well known that certain gates on two-level quantum systems (qubits), such as the controlled-NOT, are universal when assisted by arbitrary one-qubit gates, it has only recently become clear precisely what class of two-qubit gates is universal in this sense. We present an elementary proof that any entangling two-qubit gate is universal for quantum computation, when assisted by one-qubit gates. A proof of this result for systems of arbitrary finite dimension has been provided by Brylinski and Brylinski; however, their proof relies on a long argument using advanced mathematics. In contrast, our proof provides a simple constructive procedure which is close to optimal and experimentally practical.

ROM-based computation: Quantum versus classical

We introduce a model of computation based on read only memory (ROM), which allows us to compare the space-efficiency of reversible, error-free classical computation with reversible, error-free quantum computation. We show that a ROM-based quantum computer with one writable qubit is universal, whilst two writable bits are required for a universal classical ROM-based computer. We also comment on the time-efficiency advantages of quantum computation within this model.

Bridging the gap between different statistical approaches: An integrated framework for modelling

This paper proposes a template for modelling complex datasets that integrates traditional statistical modelling approaches with more recent advances in statistics and modelling through an exploratory framework. Our approach builds on the well-known and long standing traditional idea of 'good practice in statistics' by establishing a comprehensive framework for modelling that focuses on exploration, prediction, interpretation and reliability assessment, a relatively new idea that allows individual assessment of predictions. The integrated framework we present comprises two stages. The first involves the use of exploratory methods to help visually understand the data and identify a parsimonious set of explanatory variables. The second encompasses a two step modelling process, where the use of non-parametric methods such as decision trees and generalized additive models are promoted to identify important variables and their modelling relationship with the response before a final predictive model is considered. We focus on fitting the predictive model using parametric, non-parametric and Bayesian approaches. This paper is motivated by a medical problem where interest focuses on developing a risk stratification system for morbidity of 1,710 cardiac patients given a suite of demographic, clinical and preoperative variables. Although the methods we use are applied specifically to this case study, these methods can be applied across any field, irrespective of the type of response.

Effect of changing data collection parameters on statistical motor unit number estimates

The effect of number of samples and selection of data for analysis on the calculation of surface motor unit potential (SMUP) size in the statistical method of motor unit number estimates (MUNE) was determined in 10 normal subjects and 10 with amyotrophic lateral sclerosis (ALS). We recorded 500 sequential compound muscle action potentials (CMAPs) at three different stable stimulus intensities (10–50% of maximal CMAP). Estimated mean SMUP sizes were calculated using Poisson statistical assumptions from the variance of 500 sequential CMAP obtained at each stimulus intensity. The results with the 500 data points were compared with smaller subsets from the same data set. The results using a range of 50–80% of the 500 data points were compared with the full 500. The effect of restricting analysis to data between 5–20% of the CMAP and to standard deviation limits was also assessed. No differences in mean SMUP size were found with stimulus intensity or use of different ranges of data. Consistency was improved with a greater sample number. Data within 5% of CMAP size gave both increased consistency and reduced mean SMUP size in many subjects, but excluded valid responses present at that stimulus intensity. These changes were more prominent in ALS patients in whom the presence of isolated SMUP responses was a striking difference from normal subjects. Noise, spurious data, and large SMUP limited the Poisson assumptions. When these factors are considered, consistent statistical MUNE can be calculated from a continuous sequence of data points. A 2 to 2.5 SD or 10% window are reasonable methods of limiting data for analysis. Muscle Nerve 27: 320–331, 2003

An augmented Lanczos algorithm for the efficient computation of a dot-product of a function of a large sparse symmetric matrix

The Lanczos algorithm is appreciated in many situations due to its speed. and economy of storage. However, the advantage that the Lanczos basis vectors need not be kept is lost when the algorithm is used to compute the action of a matrix function on a vector. Either the basis vectors need to be kept, or the Lanczos process needs to be applied twice. In this study we describe an augmented Lanczos algorithm to compute a dot product relative to a function of a large sparse symmetric matrix, without keeping the basis vectors.

Comparative analysis between statistical and artificial intelligence models in business failure prediction

A growing number of predicting corporate failure models has emerged since 60s. Economic and social consequences of business failure can be dramatic, thus it is not surprise that the issue has been of growing interest in academic research as well as in business context. The main purpose of this study is to compare the predictive ability of five developed models based on three statistical techniques (Discriminant Analysis, Logit and Probit) and two models based on Artificial Intelligence (Neural Networks and Rough Sets). The five models were employed to a dataset of 420 non-bankrupt firms and 125 bankrupt firms belonging to the textile and clothing industry, over the period 2003–09. Results show that all the models performed well, with an overall correct classification level higher than 90%, and a type II error always less than 2%. The type I error increases as we move away from the year prior to failure. Our models contribute to the discussion of corporate financial distress causes. Moreover it can be used to assist decisions of creditors, investors and auditors. Additionally, this research can be of great contribution to devisers of national economic policies that aim to reduce industrial unemployment.

Comparative Analysis between Statistical and Artificial Intelligence Models in Business Failure Prediction

A growing number of predicting corporate failure models has emerged since 60s. Economic and social consequences of business failure can be dramatic, thus it is not surprise that the issue has been of growing interest in academic research as well as in business context. The main purpose of this study is to compare the predictive ability of five developed models based on three statistical techniques (Discriminant Analysis, Logit and Probit) and two models based on Artificial Intelligence (Neural Networks and Rough Sets). The five models were employed to a dataset of 420 non-bankrupt firms and 125 bankrupt firms belonging to the textile and clothing industry, over the period 2003–09. Results show that all the models performed well, with an overall correct classification level higher than 90%, and a type II error always less than 2%. The type I error increases as we move away from the year prior to failure. Our models contribute to the discussion of corporate financial distress causes. Moreover it can be used to assist decisions of creditors, investors and auditors. Additionally, this research can be of great contribution to devisers of national economic policies that aim to reduce industrial unemployment.