A compositional data analysis package for R providing multiple approaches

”compositions” is a new R-package for the analysis of compositional and positive data. It contains four classes corresponding to the four different types of compositional and positive geometry (including the Aitchison geometry). It provides means for computation, plotting and high-level multivariate statistical analysis in all four geometries. These geometries are treated in an fully analogous way, based on the principle of working in coordinates, and the object-oriented programming paradigm of R. In this way, called functions automatically select the most appropriate type of analysis as a function of the geometry. The graphical capabilities include ternary diagrams and tetrahedrons, various compositional plots (boxplots, barplots, piecharts) and extensive graphical tools for principal components. Afterwards, ortion and proportion lines, straight lines and ellipses in all geometries can be added to plots. The package is accompanied by a hands-on-introduction, documentation for every function, demos of the graphical capabilities and plenty of usage examples. It allows direct and parallel computation in all four vector spaces and provides the beginner with a copy-and-paste style of data analysis, while letting advanced users keep the functionality and customizability they demand of R, as well as all necessary tools to add own analysis routines. A complete example is included in the appendix

Behavioral Measures and their Correlation with IPM Iteration Counts on Semi-Definite Programming Problems

We study four measures of problem instance behavior that might account for the observed differences in interior-point method (IPM) iterations when these methods are used to solve semidefinite programming (SDP) problem instances: (i) an aggregate geometry measure related to the primal and dual feasible regions (aspect ratios) and norms of the optimal solutions, (ii) the (Renegar-) condition measure C(d) of the data instance, (iii) a measure of the near-absence of strict complementarity of the optimal solution, and (iv) the level of degeneracy of the optimal solution. We compute these measures for the SDPLIB suite problem instances and measure the correlation between these measures and IPM iteration counts (solved using the software SDPT3) when the measures have finite values. Our conclusions are roughly as follows: the aggregate geometry measure is highly correlated with IPM iterations (CORR = 0.896), and is a very good predictor of IPM iterations, particularly for problem instances with solutions of small norm and aspect ratio. The condition measure C(d) is also correlated with IPM iterations, but less so than the aggregate geometry measure (CORR = 0.630). The near-absence of strict complementarity is weakly correlated with IPM iterations (CORR = 0.423). The level of degeneracy of the optimal solution is essentially uncorrelated with IPM iterations.

Introduction to JavaScript Programming

These are the resources for an introductory lecture in JavaScript programming. Exercises are provided to practice simple JavaScript programming, including a template for a DHTML implementation of Conway's Game of Life (with encrypted solution).

Mathematical Methods 4

Exercises, exams and solutions for a third year maths course.

Mathematical Methods 2

Exercises, exams and solutions for a first year maths course.

Mathematical Population Biology

math3052 lecture notes (2008-9)

Programming & Software

An overview of programming and software development.

Programming Principles: Starting Out

In this lecture we describe the structure of the Programming Principles course at Southampton, look at the definitions and paradigms of programming, and take a look ahead to the key things that we will be covering in the weeks ahead.

Programming Principles: Introduction to Java

In this lecture we look at key concepts in Java: how to write, compile and run Java programs, define a simple class, create a main method, and use if/else structures to define behaviour.

Programming Principles: Variables, Primitives, Objects and Scope

In this session we look more closely at the way that Java deals with variables, and in particular with the differences between primitives (basic types like int and char) and objects. We also take an initial look at the scoping rules in Java, which dictate the visibility of variables in your program

Programming Principles: Computational Thinking

In this session we look at how to think systematically about a problem and create a solution. We look at the definition and characteristics of an algorithm, and see how through modularisation and decomposition we can then choose a set of methods to create. We also compare this somewhat procedural approach, with the way that design works in Object Oriented Systems,

Programming Principles: Methods

In this session we look at how to create more powerful objects through more powerful methods. We look at parameters and call by value vs. call by reference; return types; and overloading.

Programming Principles: Encapsulation and Constructors

In this session we look at the public and protected keywords, and the principle of encapsulation. We also look at how Constructors can help you initialise objects, while maintaining the encapsulation principle.

Programming Principles: Loops and Arrays

In this session we look at the different types of loop in the Java language, and see how they can be used to iterate over Arrays.

Programming Principles: Collections and Iterators

In this session we look at how we can use collection objects like ArrayList as a more advanced type of array. We also introduce the idea of generics (forcing a collection to hold a particular type) and see how Java handles the autoboxing and unboxing of primitives. Finally we look at Iterators, a common design pattern for dealing with iteration over a collection.