Computer Theorem Proving and HoTT

Theorem-proving is a one-player game. The history of computer programs being the players goes back to 1956 and the ‘LT’ LOGIC THEORY MACHINE of Newell, Shaw and Simon. In game-playing terms, the ‘initial position’ is the core set of axioms chosen for the particular logic and the ‘moves’ are the rules of inference. Now, the Univalent Foundations Program at IAS Princeton and the resulting ‘HoTT’ book on Homotopy Type Theory have demonstrated the success of a new kind of experimental mathematics using computer theorem proving.

Inferring population history with DIY ABC: a user-friendly approach to approximate Bayesian computation

Genetic data obtained on population samples convey information about their evolutionary history. Inference methods can extract part of this information but they require sophisticated statistical techniques that have been made available to the biologist community (through computer programs) only for simple and standard situations typically involving a small number of samples. We propose here a computer program (DIY ABC) for inference based on approximate Bayesian computation (ABC), in which scenarios can be customized by the user to fit many complex situations involving any number of populations and samples. Such scenarios involve any combination of population divergences, admixtures and population size changes. DIY ABC can be used to compare competing scenarios, estimate parameters for one or more scenarios and compute bias and precision measures for a given scenario and known values of parameters (the current version applies to unlinked microsatellite data). This article describes key methods used in the program and provides its main features. The analysis of one simulated and one real dataset, both with complex evolutionary scenarios, illustrates the main possibilities of DIY ABC.

In-service and pre-service teachers' opinion on the use of models in teaching chemistry

The presented study examined the opinion of in-service and prospective chemistry teachers about the importance of usage of molecular and crystal models in secondary-level school practice, and investigated some of the reasons for their (non-) usage. The majority of participants stated that the use of models plays an important role in chemistry education and that they would use them more often if the circumstances were more favourable. Many teachers claimed that three-dimensional (3d) models are still not available in sufficient number at their schools; they also pointed to the lack of available computer facilities during chemistry lessons. The research revealed that, besides the inadequate material circumstances, less than one third of participants are able to use simple (freeware) computer programs for drawing molecular structures and their presentation in virtual space; however both groups of teachers expressed the willingness to improve their knowledge in the subject area. The investigation points to several actions which could be undertaken to improve the current situation.

Jpowder: a Java-based program for the display and examination of powder diffraction data

The ability to display and inspect powder diffraction data quickly and efficiently is a central part of the data analysis process. Whilst many computer programs are capable of displaying powder data, their focus is typically on advanced operations such as structure solution or Rietveld refinement. This article describes a lightweight software package, Jpowder, whose focus is fast and convenient visualization and comparison of powder data sets in a variety of formats from computers with network access. Jpowder is written in Java and uses its associated Web Start technology to allow ‘single-click deployment’ from a web page, http://www.jpowder.org. Jpowder is open source, free and available for use by anyone.

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 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.

The use of ICT by adults with learning disabilities in day and residential services

The use of Information and Communication Technology (ICT) by adults with learning disabilities has been positively promoted over the past decade. More recently, policy statements and guidance from the UK government have underlined the importance of ICT for adults with learning disabilities specifically, as well as for the population in general, through the potential it offers for social inclusion. The aim of the present study was to provide a picture of how ICT is currently being used within one organisation providing specialist services for adults with learning disabilities and more specifically to provide a picture of its use in promoting community participation. Nine day and 14 residential services were visited as part of a qualitative study to answer three main questions: What kinds of computer programs are being used? What are they being used for? Does this differ between day and residential services? Computers and digital cameras were used for a wide range of activities and ‘mainstream’ programs were used more widely than those developed for specific user groups. In day services, ICT was often embedded in wider projects and activities, whilst use in houses was based around leisure interests. In both contexts, ICT was being used to facilitate communication, although this was more linked to within-service activities, rather than those external to service provision.

An ontological approach to competency management

Competency management is a very important part of a well-functioning organisation. Unfortunately competency descriptions are not uniformly specified nor defined across borders: National, sectorial or organisational, leading to an opaque competency description market with a multitude of competency frameworks and competency benchmarks. An ontology is a formalised description of a domain, which enables automated reasoning engines to be built which by utilising the interrelations between entities can make “intelligent” choices in different situations within the domain. Introducing formalised competency ontologies automated tools, such as skill gap analysis, training suggestion generation, job search and recruitment, can be developed, which compare and contrast different competency descriptions on the semantic level. The major problem with defining a common formalised ontology for competencies is that there are so many viewpoints of competencies and competency frameworks. Work within the TRACE project has focused on finding common trends within different competency frameworks in order to allow an intermediate competency description to be made, which other frameworks can reference. This research has shown that competencies can be divided up into “knowledge”, “skills” and what we call “others”. An ontology has been created based on this with a simple structure of different “kinds” of “knowledges” and “skills” using semantic interrelations to define the basic semantic structure of the ontology. A prototype tool for analysing a skill gap analysis has been developed. Personal profiles can be produced using the tool and a skill gap analysis is performed on a desired competency profile by using an ontologically based inference engine, which is able to list closest fit and possible proficiency gaps

Adaptive project planning and management based on best practices - COBRA system

Planning a project with proper considerations of all necessary factors and managing a project to ensure its successful implementation will face a lot of challenges. Initial stage in planning a project for bidding a project is costly, time consuming and usually with poor accuracy on cost and effort predictions. On the other hand, detailed information for previous projects may be buried in piles of archived documents which can be increasingly difficult to learn from the previous experiences. Project portfolio has been brought into this field aiming to improve the information sharing and management among different projects. However, the amount of information that could be shared is still limited to generic information. This paper, we report a recently developed software system COBRA to automatically generate a project plan with effort estimation of time and cost based on data collected from previous completed projects. To maximise the data sharing and management among different projects, we proposed a method of using product based planning from PRINCE2 methodology. (Automated Project Information Sharing and Management System -�COBRA) Keywords: project management, product based planning, best practice, PRINCE2

Application of computer-aided facilities management (CAFM) for intelligent buildings operation

Purpose – The purpose of this paper is to investigate the concepts of intelligent buildings (IBs), and the opportunities offered by the application of computer-aided facilities management (CAFM) systems. Design/methodology/approach – In this paper definitions of IBs are investigated, particularly definitions that are embracing open standards for effective operational change, using a questionnaire survey. The survey further investigated the extension of CAFM to IBs concepts and the opportunities that such integrated systems will provide to facilities management (FM) professionals. Findings – The results showed variation in the understanding of the concept of IBs and the application of CAFM. The survey showed that 46 per cent of respondents use a CAFM system with a majority agreeing on the potential of CAFM in delivery of effective facilities. Research limitations/implications – The questionnaire survey results are limited to the views of the respondents within the context of FM in the UK. Practical implications – Following on the many definitions of an IB does not necessarily lead to technologies of equipment that conform to an open standard. This open standard and documentation of systems produced by vendors is the key to integrating CAFM with other building management systems (BMS) and further harnessing the application of CAFM for IBs. Originality/value – The paper gives experience-based suggestions for both demand and supply sides of the service procurement to gain the feasible benefits and avoid the currently hindering obstacles, as the paper provides insight to the current and future tools for the mobile aspects of FM. The findings are relevant for service providers and operators as well.

Computer generation and quantitative morphometric analysis of virtual neurons

An important goal in computational neuroanatomy is the complete and accurate simulation of neuronal morphology. We are developing computational tools to model three-dimensional dendritic structures based on sets of stochastic rules. This paper reports an extensive, quantitative anatomical characterization of simulated motoneurons and Purkinje cells. We used several local and global algorithms implemented in the L-Neuron and ArborVitae programs to generate sets of virtual neurons. Parameters statistics for all algorithms were measured from experimental data, thus providing a compact and consistent description of these morphological classes. We compared the emergent anatomical features of each group of virtual neurons with those of the experimental database in order to gain insights on the plausibility of the model assumptions, potential improvements to the algorithms, and non-trivial relations among morphological parameters. Algorithms mainly based on local constraints (e.g., branch diameter) were successful in reproducing many morphological properties of both motoneurons and Purkinje cells (e.g. total length, asymmetry, number of bifurcations). The addition of global constraints (e.g., trophic factors) improved the angle-dependent emergent characteristics (average Euclidean distance from the soma to the dendritic terminations, dendritic spread). Virtual neurons systematically displayed greater anatomical variability than real cells, suggesting the need for additional constraints in the models. For several emergent anatomical properties, a specific algorithm reproduced the experimental statistics better than the others did. However, relative performances were often reversed for different anatomical properties and/or morphological classes. Thus, combining the strengths of alternative generative models could lead to comprehensive algorithms for the complete and accurate simulation of dendritic morphology.