Comparing methods to estimate the human lens power

Purpose: To compare accuracies of different methods for calculating human lens power when lens thickness is not available. Methods: Lens power was calculated by four methods. Three methods were used with previously published biometry and refraction data of 184 emmetropic and myopic eyes of 184 subjects (age range [18, 63] years, spherical equivalent range [–12.38, +0.75] D). These three methods consist of the Bennett method, which uses lens thickness, our modification of the Stenström method and the Bennett¬Rabbetts method, both of which do not require knowledge of lens thickness. These methods include c constants, which represent distances from lens surfaces to principal planes. Lens powers calculated with these methods were compared with those calculated using phakometry data available for a subgroup of 66 emmetropic eyes (66 subjects). Results: Lens powers obtained from the Bennett method corresponded well with those obtained by phakometry for emmetropic eyes, although individual differences up to 3.5D occurred. Lens powers obtained from the modified¬Stenström and Bennett¬Rabbetts methods deviated significantly from those obtained with either the Bennett method or phakometry. Customizing the c constants improved this agreement, but applying these constants to the entire group gave mean lens power differences of 0.71 ± 0.56D compared with the Bennett method. By further optimizing the c constants, the agreement with the Bennett method was within ± 1D for 95% of the eyes. Conclusion: With appropriate constants, the modified¬Stenström and Bennett¬Rabbetts methods provide a good approximation of the Bennett lens power in emmetropic and myopic eyes.

Tools and methods for capturing Twitter data during natural disasters

During the course of several natural disasters in recent years, Twitter has been found to play an important role as an additional medium for many–to–many crisis communication. Emergency services are successfully using Twitter to inform the public about current developments, and are increasingly also attempting to source first–hand situational information from Twitter feeds (such as relevant hashtags). The further study of the uses of Twitter during natural disasters relies on the development of flexible and reliable research infrastructure for tracking and analysing Twitter feeds at scale and in close to real time, however. This article outlines two approaches to the development of such infrastructure: one which builds on the readily available open source platform yourTwapperkeeper to provide a low–cost, simple, and basic solution; and, one which establishes a more powerful and flexible framework by drawing on highly scaleable, state–of–the–art technology.

Computationally efficient methods for solving time-variable-order time-space fractional reaction-diffusion equation

Fractional differential equations are becoming more widely accepted as a powerful tool in modelling anomalous diffusion, which is exhibited by various materials and processes. Recently, researchers have suggested that rather than using constant order fractional operators, some processes are more accurately modelled using fractional orders that vary with time and/or space. In this paper we develop computationally efficient techniques for solving time-variable-order time-space fractional reaction-diffusion equations (tsfrde) using the finite difference scheme. We adopt the Coimbra variable order time fractional operator and variable order fractional Laplacian operator in space where both orders are functions of time. Because the fractional operator is nonlocal, it is challenging to efficiently deal with its long range dependence when using classical numerical techniques to solve such equations. The novelty of our method is that the numerical solution of the time-variable-order tsfrde is written in terms of a matrix function vector product at each time step. This product is approximated efficiently by the Lanczos method, which is a powerful iterative technique for approximating the action of a matrix function by projecting onto a Krylov subspace. Furthermore an adaptive preconditioner is constructed that dramatically reduces the size of the required Krylov subspaces and hence the overall computational cost. Numerical examples, including the variable-order fractional Fisher equation, are presented to demonstrate the accuracy and efficiency of the approach.

A hierarchical evolutionary algorithmic design (HEAD) system for generating and evolving building design models

This thesis develops a detailed conceptual design method and a system software architecture defined with a parametric and generative evolutionary design system to support an integrated interdisciplinary building design approach. The research recognises the need to shift design efforts toward the earliest phases of the design process to support crucial design decisions that have a substantial cost implication on the overall project budget. The overall motivation of the research is to improve the quality of designs produced at the author's employer, the General Directorate of Major Works (GDMW) of the Saudi Arabian Armed Forces. GDMW produces many buildings that have standard requirements, across a wide range of environmental and social circumstances. A rapid means of customising designs for local circumstances would have significant benefits. The research considers the use of evolutionary genetic algorithms in the design process and the ability to generate and assess a wider range of potential design solutions than a human could manage. This wider ranging assessment, during the early stages of the design process, means that the generated solutions will be more appropriate for the defined design problem. The research work proposes a design method and system that promotes a collaborative relationship between human creativity and the computer capability. The tectonic design approach is adopted as a process oriented design that values the process of design as much as the product. The aim is to connect the evolutionary systems to performance assessment applications, which are used as prioritised fitness functions. This will produce design solutions that respond to their environmental and function requirements. This integrated, interdisciplinary approach to design will produce solutions through a design process that considers and balances the requirements of all aspects of the design. Since this thesis covers a wide area of research material, 'methodological pluralism' approach was used, incorporating both prescriptive and descriptive research methods. Multiple models of research were combined and the overall research was undertaken following three main stages, conceptualisation, developmental and evaluation. The first two stages lay the foundations for the specification of the proposed system where key aspects of the system that have not previously been proven in the literature, were implemented to test the feasibility of the system. As a result of combining the existing knowledge in the area with the newlyverified key aspects of the proposed system, this research can form the base for a future software development project. The evaluation stage, which includes building the prototype system to test and evaluate the system performance based on the criteria defined in the earlier stage, is not within the scope this thesis. The research results in a conceptual design method and a proposed system software architecture. The proposed system is called the 'Hierarchical Evolutionary Algorithmic Design (HEAD) System'. The HEAD system has shown to be feasible through the initial illustrative paper-based simulation. The HEAD system consists of the two main components - 'Design Schema' and the 'Synthesis Algorithms'. The HEAD system reflects the major research contribution in the way it is conceptualised, while secondary contributions are achieved within the system components. The design schema provides constraints on the generation of designs, thus enabling the designer to create a wide range of potential designs that can then be analysed for desirable characteristics. The design schema supports the digital representation of the human creativity of designers into a dynamic design framework that can be encoded and then executed through the use of evolutionary genetic algorithms. The design schema incorporates 2D and 3D geometry and graph theory for space layout planning and building formation using the Lowest Common Design Denominator (LCDD) of a parameterised 2D module and a 3D structural module. This provides a bridge between the standard adjacency requirements and the evolutionary system. The use of graphs as an input to the evolutionary algorithm supports the introduction of constraints in a way that is not supported by standard evolutionary techniques. The process of design synthesis is guided as a higher level description of the building that supports geometrical constraints. The Synthesis Algorithms component analyses designs at four levels, 'Room', 'Layout', 'Building' and 'Optimisation'. At each level multiple fitness functions are embedded into the genetic algorithm to target the specific requirements of the relevant decomposed part of the design problem. Decomposing the design problem to allow for the design requirements of each level to be dealt with separately and then reassembling them in a bottom up approach reduces the generation of non-viable solutions through constraining the options available at the next higher level. The iterative approach, in exploring the range of design solutions through modification of the design schema as the understanding of the design problem improves, assists in identifying conflicts in the design requirements. Additionally, the hierarchical set-up allows the embedding of multiple fitness functions into the genetic algorithm, each relevant to a specific level. This supports an integrated multi-level, multi-disciplinary approach. The HEAD system promotes a collaborative relationship between human creativity and the computer capability. The design schema component, as the input to the procedural algorithms, enables the encoding of certain aspects of the designer's subjective creativity. By focusing on finding solutions for the relevant sub-problems at the appropriate levels of detail, the hierarchical nature of the system assist in the design decision-making process.

Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise

In this paper we extend the ideas of Brugnano, Iavernaro and Trigiante in their development of HBVM($s,r$) methods to construct symplectic Runge-Kutta methods for all values of $s$ and $r$ with $s\geq r$. However, these methods do not see the dramatic performance improvement that HBVMs can attain. Nevertheless, in the case of additive stochastic Hamiltonian problems an extension of these ideas, which requires the simulation of an independent Wiener process at each stage of a Runge-Kutta method, leads to methods that have very favourable properties. These ideas are illustrated by some simple numerical tests for the modified midpoint rule.

Numerical methods for solving the multi-term time-fractional wave-diffusion equations

In this paper, the multi-term time-fractional wave diffusion equations are considered. The multiterm time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation

Anomalous subdiffusion equations have in recent years received much attention. In this paper, we consider a two-dimensional variable-order anomalous subdiffusion equation. Two numerical methods (the implicit and explicit methods) are developed to solve the equation. Their stability, convergence and solvability are investigated by the Fourier method. Moreover, the effectiveness of our theoretical analysis is demonstrated by some numerical examples. © 2011 American Mathematical Society.

Numerical methods and analysis for a class of fractional advection-dispersion models

In this paper, a class of fractional advection–dispersion models (FADMs) is considered. These models include five fractional advection–dispersion models, i.e., the time FADM, the mobile/immobile time FADM with a time Caputo fractional derivative 0 < γ < 1, the space FADM with two sides Riemann–Liouville derivatives, the time–space FADM and the time fractional advection–diffusion-wave model with damping with index 1 < γ < 2. These equations can be used to simulate the regional-scale anomalous dispersion with heavy tails. We propose computationally effective implicit numerical methods for these FADMs. The stability and convergence of the implicit numerical methods are analysed and compared systematically. Finally, some results are given to demonstrate the effectiveness of theoretical analysis.

The SAGE Handbook of Criminological Research Methods

Conducting research into crime and criminal justice carries unique challenges. This Handbook focuses on the application of 'methods' to address the core substantive questions that currently motivate contemporary criminological research. It maps a canon of methods that are more elaborated than in most other fields of social science, and the intellectual terrain of research problems with which criminologists are routinely confronted. Drawing on exemplary studies, chapters in each section illustrate the techniques (qualitative and quantitative) that are commonly applied in empirical studies, as well as the logic of criminological enquiry. Organized into five sections, each prefaced by an editorial introduction, the Handbook covers: • Crime and Criminals • Contextualizing Crimes in Space and Time: Networks, Communities and Culture • Perceptual Dimensions of Crime • Criminal Justice Systems: Organizations and Institutions • Preventing Crime and Improving Justice Edited by leaders in the field of criminological research, and with contributions from internationally renowned experts, The SAGE Handbook of Criminological Research Methods is set to become the definitive resource for postgraduates, researchers and academics in criminology, criminal justice, policing, law, and sociology.

A comparison of methods for classifying clinical samples based on proteomics data : a case study for statistical and machine learning approaches

The discovery of protein variation is an important strategy in disease diagnosis within the biological sciences. The current benchmark for elucidating information from multiple biological variables is the so called “omics” disciplines of the biological sciences. Such variability is uncovered by implementation of multivariable data mining techniques which come under two primary categories, machine learning strategies and statistical based approaches. Typically proteomic studies can produce hundreds or thousands of variables, p, per observation, n, depending on the analytical platform or method employed to generate the data. Many classification methods are limited by an n≪p constraint, and as such, require pre-treatment to reduce the dimensionality prior to classification. Recently machine learning techniques have gained popularity in the field for their ability to successfully classify unknown samples. One limitation of such methods is the lack of a functional model allowing meaningful interpretation of results in terms of the features used for classification. This is a problem that might be solved using a statistical model-based approach where not only is the importance of the individual protein explicit, they are combined into a readily interpretable classification rule without relying on a black box approach. Here we incorporate statistical dimension reduction techniques Partial Least Squares (PLS) and Principal Components Analysis (PCA) followed by both statistical and machine learning classification methods, and compared them to a popular machine learning technique, Support Vector Machines (SVM). Both PLS and SVM demonstrate strong utility for proteomic classification problems.