Routines and Applications of Symbolic Algebra Software

Computing has become an essential resource in modern research and has found application across a wide range of scientific disciplines. Developments in symbolic algebra tools have been particularly valuable in physics where calculations in fields such as general relativity, quantum field theory and physics beyond the standard model are becoming increasing complex and unpractical to work with by hand. The computer algebra system Cadabra is a tensor-first approach to symbolic algebra based on the programming language Python which has been used extensively in research in these fields while also having a shallow learning curve making it an excellent way to introduce students to methods in computer algebra. The work in this thesis has been concentrated on developing Cadabra, which has involved looking at two different elements which make up a computer algebra program. Firstly, the implementation of algebraic routines is discussed. This has primarily been focused on the introduction of an algorithm for detecting the equivalence of tensorial expressions related by index permutation symmetries. The method employed differs considerably from traditional canonicalisation routines which are commonly used for this purpose by using Young projection operators to make such symmetries manifest. The other element of writing a computer algebra program which is covered is the infrastruc- ture and environment. The importance of this aspect of software design is often overlooked by funding committees and academic software users resulting in an anti-pattern of code not being shared and contributed to in the way in which research itself is published and promulgated. The focus in this area has been on implementing a packaging system for Cadabra which allows the writing of generic libraries which can be shared by the community, and interfacing with other scientific computing packages to increase the capabilities of Cadabra

Hiding canonicalisation in tensor computer algebra

Simplification of expressions in computer algebra systems often involves a step known as "canonicalisation", which reduces equivalent expressions to the same form. However, such forms may not be natural from the perspective of a pen-and-paper computation, or may be unwieldy, or both. This is, for example, the case for expressions involving tensor multi-term symmetries. We propose an alternative strategy to handle such tensor expressions, which hides canonical forms from the user entirely, and present an implementation of this idea in the Cadabra computer algebra system

Small fish in a big pond: an architectural approach to users privacy, rights and security in the age of big data

We focus on the challenges and issues associated with Big Data, and propose a novel architecture that uses the principles of Separation of Concerns and distributed computing to overcome many of the challenges associated with storage, analysis and integrity. We address the issue of asymmetrical distribution of power between the originators of data and the organizations and institutions that make use of that data by taking a systemic perspective to include both sides in our architectural design, shifting from a customer-provider relationship to a more symbiotic one in which control over access to customer data resides with the customer. We illustrate the affordances of the proposed architecture by describing its application in the domain of Social Networking Sites, where we furnish a mechanism to address problems of privacy and identity, and create the potential to open up online social networking to a richer set of possible applications

Predictors of dominance rank and agonistic interactions in captive Livingstone’s fruit bats

Male dominance hierarchies have been studied in many animals but rarely in bats (Chiroptera). The dominance rank of social animals may dictate access to resources and mates; therefore, it has important implications for an individual’s fitness and is crucial for successful captive management. Between January and December 2018, at both Bristol Zoo Gardens (Bristol, UK) and Jersey Zoo (Jersey, British Isles), we observed 19 male Livingstone’s fruit bats Pteropus livingstonii using focal follows for 345 h overall, noting the outcome of all agonistic interactions. We recorded instigators of interactions, along with winners and losers, and analyzed these data using the R-package “EloRating” to create Elo-rating temporal plots of dominance ranks. We used generalized linear mixed models and multiple linear regression to analyze interaction data and test hypotheses regarding predictors of dominance rank, frequency of agonistic interaction, and choice of interaction partner. Age was positively correlated with dominance rank up to around year 9, when an asymptote was attained. Highly ranked bats instigated the most agonistic interactions, and largely directed these interactions at bats with much lower rankings than themselves. Hierarchies were extremely stable throughout the data collection period at both sites. We conclude that Livingstone’s fruit bats have a stable linear dominance hierarchy, with high-ranking, typically older males instigating the most interactions with lowest ranking males to secure dominance rank. This study adds to the limited discourse on Pteropus social behaviors, indicating that some bat species may have social systems similar in complexity to some nonhuman primates.<br/

Finite-Dimensional Bicomplex Hilbert Spaces

This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including the spectral decomposition theorem. Applications to concepts relevant to quantum mechanics, like the evolution operator, are pointed out.Comment: 21 page

ArtMaps: A Technology for Looking at Tate’s Collection

This article presents ArtMaps, a crowdsourcing web-based app for desktop and mobile use that allows users to locate, move and annotate artworks in the Tate collection in relation to one or more sets of locations. Here the authors show that ArtMaps extends the ‘space’ of the museum and facilitates a new, pluriperspectival, way of looking at art

ArtMaps: interpreting the spatial footprints of artworks

Creating and utilizing simple links between items and locations in map-based systems has become a mainstream component of modern computing. In this paper, we explore support for ‘art mapping’, an activity that requires consideration of more complex interpretations of spatial relationships as users engage with identifying locations of relevance to artworks. Through a user study of the ArtMaps platform, and an exploratory study with professional artists, we identify diverse interpretations of spatial meaning in relation to art. We find that art mapping highlights potential for more active engagement with art through technology, but challenges existing systems for spatial representation. Through connecting our findings with work on designing for interpretation, and on space and place in HCI, we contribute new understanding of creating engagement through the spatial interpretation of art, and define potential characteristics and uses of holistic ‘footprints’ for artworks

EMPOWERING GLOBAL NUTRITION WITH DIGITAL TECHNOLOGY : PRACTICAL IMPLEMENTATION IN CLINICAL PRACTICE AND RESEARCH

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