Trans-floating-point arithmetic removes nine quadrillion redundancies from 64-bit IEEE 754 floating-point arithmetic

IEEE 754 floating-point arithmetic is widely used in modern, general-purpose computers. It is based on real arithmetic and is made total by adding both a positive and a negative infinity, a negative zero, and many Not-a-Number (NaN) states. Transreal arithmetic is total. It also has a positive and a negative infinity but no negative zero, and it has a single, unordered number, nullity. Modifying the IEEE arithmetic so that it uses transreal arithmetic has a number of advantages. It removes one redundant binade from IEEE floating-point objects, doubling the numerical precision of the arithmetic. It removes eight redundant, relational,floating-point operations and removes the redundant total order operation. It replaces the non-reflexive, floating-point, equality operator with a reflexive equality operator and it indicates that some of the exceptions may be removed as redundant { subject to issues of backward compatibility and transient future compatibility as programmers migrate to the transreal paradigm.

Construction of the transcomplex numbers from the complex numbers

A geometrical construction of the transcomplex numbers was given elsewhere. Here we simplify the transcomplex plane and construct the set of transcomplex numbers from the set of complex numbers. Thus transcomplex numbers and their arithmetic arise as consequences of their construction, not by an axiomatic development. This simplifes transcom- plex arithmetic, compared to the previous treatment, but retains totality so that every arithmetical operation can be applied to any transcomplex number(s) such that the result is a transcomplex number. Our proof establishes the consistency of transcomplex and transreal arithmetic and establishes the expected containment relationships amongst transcomplex, complex, transreal and real numbers. We discuss some of the advantages the transarithmetics have over their partial counterparts.

Transdifferential and transintegral calculus

The set of transreal numbers is a superset of the real numbers. It totalises real arithmetic by defining division by zero in terms of three def- inite, non-finite numbers: positive infinity, negative infinity and nullity. Elsewhere, in this proceedings, we extended continuity and limits from the real domain to the transreal domain, here we extended the real derivative to the transreal derivative. This continues to demonstrate that transreal analysis contains real analysis and operates at singularities where real analysis fails. Hence computer programs that rely on computing deriva- tives { such as those used in scientific, engineering and financial applica- tions { are extended to operate at singularities where they currently fail. This promises to make software, that computes derivatives, both more competent and more reliable. We also extended the integration of absolutely convergent functions from the real domain to the transreal domain.

Transreal arithmetic as a consistent basis for paraconsistent logics

Paraconsistent logics are non-classical logics which allow non-trivial and consistent reasoning about inconsistent axioms. They have been pro- posed as a formal basis for handling inconsistent data, as commonly arise in human enterprises, and as methods for fuzzy reasoning, with applica- tions in Artificial Intelligence and the control of complex systems. Formalisations of paraconsistent logics usually require heroic mathe- matical efforts to provide a consistent axiomatisation of an inconsistent system. Here we use transreal arithmetic, which is known to be consis- tent, to arithmetise a paraconsistent logic. This is theoretically simple and should lead to efficient computer implementations. We introduce the metalogical principle of monotonicity which is a very simple way of making logics paraconsistent. Our logic has dialetheaic truth values which are both False and True. It allows contradictory propositions, allows variable contradictions, but blocks literal contradictions. Thus literal reasoning, in this logic, forms an on-the- y, syntactic partition of the propositions into internally consistent sets. We show how the set of all paraconsistent, possible worlds can be represented in a transreal space. During the development of our logic we discuss how other paraconsistent logics could be arithmetised in transreal arithmetic.

Transreal limits expose category errors in IEEE 754 floating-point arithmetic and in mathematics

The IEEE 754 standard for oating-point arithmetic is widely used in computing. It is based on real arithmetic and is made total by adding both a positive and a negative infinity, a negative zero, and many Not-a-Number (NaN) states. The IEEE infinities are said to have the behaviour of limits. Transreal arithmetic is total. It also has a positive and a negative infinity but no negative zero, and it has a single, unordered number, nullity. We elucidate the transreal tangent and extend real limits to transreal limits. Arguing from this firm foundation, we maintain that there are three category errors in the IEEE 754 standard. Firstly the claim that IEEE infinities are limits of real arithmetic confuses limiting processes with arithmetic. Secondly a defence of IEEE negative zero confuses the limit of a function with the value of a function. Thirdly the definition of IEEE NaNs confuses undefined with unordered. Furthermore we prove that the tangent function, with the infinities given by geometrical con- struction, has a period of an entire rotation, not half a rotation as is commonly understood. This illustrates a category error, confusing the limit with the value of a function, in an important area of applied mathe- matics { trigonometry. We brie y consider the wider implications of this category error. Another paper proposes transreal arithmetic as a basis for floating- point arithmetic; here we take the profound step of proposing transreal arithmetic as a replacement for real arithmetic to remove the possibility of certain category errors in mathematics. Thus we propose both theo- retical and practical advantages of transmathematics. In particular we argue that implementing transreal analysis in trans- floating-point arith- metic would extend the coverage, accuracy and reliability of almost all computer programs that exploit real analysis { essentially all programs in science and engineering and many in finance, medicine and other socially beneficial applications.

Interference and communications among active network applications

This paper focuses on active networks applications and in particular on the possible interactions among these applications. Active networking is a very promising research field which has been developed recently, and which poses several interesting challenges to network designers. A number of proposals for e±cient active network architectures are already to be found in the literature. However, how two or more active network applications may interact has not being investigated so far. In this work, we consider a number of applications that have been designed to exploit the main features of active networks and we discuss what are the main benefits that these applications may derive from them. Then, we introduce some forms of interaction including interference and communications among applications, and identify the components of an active network architecture that are needed to support these forms of interaction. We conclude by presenting a brief example of an active network application exploiting the concept of interaction.

A simple, intuitive camera calibration tool for natural images

The paper reports an interactive tool for calibrating a camera, suitable for use in outdoor scenes. The motivation for the tool was the need to obtain an approximate calibration for images taken with no explicit calibration data. Such images are frequently presented to research laboratories, especially in surveillance applications, with a request to demonstrate algorithms. The method decomposes the calibration parameters into intuitively simple components, and relies on the operator interactively adjusting the parameter settings to achieve a visually acceptable agreement between a rectilinear calibration model and his own perception of the scene. Using the tool, we have been able to calibrate images of unknown scenes, taken with unknown cameras, in a matter of minutes. The standard of calibration has proved to be sufficient for model-based pose recovery and tracking of vehicles.

Review of computer vision in intelligent environment design

This paper discusses and compares the use of vision based and non-vision based technologies in developing intelligent environments. By reviewing the related projects that use vision based techniques in intelligent environment design, the achieved functions, technical issues and drawbacks of those projects are discussed and summarized, and the potential solutions for future improvement are proposed, which leads to the prospective direction of my PhD research.

The use of computer-based learning tools for teaching and clinical purposes: Interactive computing strategy for Iraq

Medical universities and teaching hospitals in Iraq are facing a lack of professional staff due to the ongoing violence that forces them to flee the country. The professionals are now distributed outside the country which reduces the chances for the staff and students to be physically in one place to continue the teaching and limits the efficiency of the consultations in hospitals. A survey was done among students and professional staff in Iraq to find the problems in the learning and clinical systems and how Information and Communication Technology could improve it. The survey has shown that 86% of the participants use the Internet as a learning resource and 25% for clinical purposes while less than 11% of them uses it for collaboration between different institutions. A web-based collaborative tool is proposed to improve the teaching and clinical system. The tool helps the users to collaborate remotely to increase the quality of the learning system as well as it can be used for remote medical consultation in hospitals.

Improving computer interaction for older people - studying mouse clicks

Interactions using a standard computer mouse can be particularly difficult for novice and older adult users. Tasks that involve positioning the mouse over a target and double-clicking to initiate some action can be a real challenge for many users. Hence, this paper describes a study that investigates the double-click interactions of older and younger adults and presents data that can help inform the development of methods of assistance. Twelve older adults (mean age = 63.9 years) and 12 younger adults (mean age = 20.8 years) performed click and double-click target selections with a computer mouse. Initial results show that older users make approximately twice as many errors as younger users when attempting double-clicks. For both age groups, the largest proportion of errors was due to difficulties with keeping the cursor steady between button presses. Compared with younger adults, older adults experienced more difficulties with performing two button presses within a required time interval. Understanding these interactions better is a step towards improving accessibility, and may provide some suggestions for future directions of research in this area.

Networks of contextualised ontologies for the Semantic Web

Currently many ontologies are available for addressing different domains. However, it is not always possible to deploy such ontologies to support collaborative working, so that their full potential can be exploited to implement intelligent cooperative applications capable of reasoning over a network of context-specific ontologies. The main problem arises from the fact that presently ontologies are created in an isolated way to address specific needs. However we foresee the need for a network of ontologies which will support the next generation of intelligent applications/devices, and, the vision of Ambient Intelligence. The main objective of this paper is to motivate the design of a networked ontology (Meta) model which formalises ways of connecting available ontologies so that they are easy to search, to characterise and to maintain. The aim is to make explicit the virtual and implicit network of ontologies serving the Semantic Web.

Multi-level Input Fusion in multi-modal systems

Context-aware multimodal interactive systems aim to adapt to the needs and behavioural patterns of users and offer a way forward for enhancing the efficacy and quality of experience (QoE) in human-computer interaction. The various modalities that constribute to such systems each provide a specific uni-modal response that is integratively presented as a multi-modal interface capable of interpretation of multi-modal user input and appropriately responding to it through dynamically adapted multi-modal interactive flow management , This paper presents an initial background study in the context of the first phase of a PhD research programme in the area of optimisation of data fusion techniques to serve multimodal interactivite systems, their applications and requirements.

Running climate models on grids using G-Rex

Compute grids are used widely in many areas of environmental science, but there has been limited uptake of grid computing by the climate modelling community, partly because the characteristics of many climate models make them difficult to use with popular grid middleware systems. In particular, climate models usually produce large volumes of output data, and running them also involves complicated workflows implemented as shell scripts. A new grid middleware system that is well suited to climate modelling applications is presented in this paper. Grid Remote Execution (G-Rex) allows climate models to be deployed as Web services on remote computer systems and then launched and controlled as if they were running on the user's own computer. Output from the model is transferred back to the user while the run is in progress to prevent it from accumulating on the remote system and to allow the user to monitor the model. G-Rex has a REST architectural style, featuring a Java client program that can easily be incorporated into existing scientific workflow scripts. Some technical details of G-Rex are presented, with examples of its use by climate modellers.