A Geometric Algebra Based Higher Dimensional Approximation Method for Statics and Kinematics of Robotic Manipulators, published in Advances in Applied Clifford Algebras.

• https://doi.org/10.1007/s00006-019-1039-z

• In this article, a robotic system or manipulator is represented as a network whose motion generating kinematic pairs are represented as the network’s inter-connected nodes. Within this network theoretic context, we develop a formulation employing higher dimensional multivectors defined in Clifford Algebra that approximates the computational outcomes of such complicated systems of equations, for both inverse and forward problem types.

Reassembling Transformations for Robot Manipulators Characterised Using Network Theoretic and Clifford-Algebraic Methods, published in Robotica.

• https://doi.org/10.1017/S0263574720000752

• Using Clifford-Algebraic and network theoretic methods, this article presents a novel-theoretical framework which allows any two robot architectures and design parameters to be mathematically related to one another through combinations of discrete operators or ‘reassembling transformations’.

A Generalised Quaternion and Clifford Algebra Based Mathematical Methodology to Effect Multi-Stage Reassembling Transformations in Parallel Robots, published in Advances in Applied Clifford Algebras.

• https://doi.org/10.1007/s00006-021-01119-6

• This work presents a novel methodology that marries quaternion rotors, the Lagrangian formulation, geometric algebra and associated mathematical apparatus, to tackle the problem of analysing and modelling robotic manipulators or mechanisms that undergo reassembling transformations.

Artificial Intelligence Using Hyper-Algebraic Networks, published in Neurocomputing.

• https://doi.org/10.1016/j.neucom.2019.12.116

• This paper presents a novel paradigmatic revision of traditional neural networks, using network theoretic methods and Conformal Geometric Algebra. A unique theoretical framework called the ‘hyperfield cognition framework’ expands upon the mathematical foundations of neural networks in five-dimensional Conformal Geometric Algebraic space.

Time Series, Hidden Variables and Spatio-Temporal Ordinality Networks, published in Advances in Applied Clifford Algebra.

• https://doi.org/10.1007/s00006-020-01061-z

• In this paper, a novel methodology for the modelling and forecasting of time series using higher-dimensional networks is presented. Time series data is partitioned, transformed and mapped into five-dimensional conformal space as a network which we call the ‘Spatio-Temporal Ordinality Network’ (STON). These STONs are characterised using specific Clifford Algebraic multivector functions which are found to be highly effective as featurised variables that forecast future states of the time series.

Mathematically Modelling Pyrolytic Polygeneration Processes using Artificial Intelligence, published in Fuel.

• https://doi.org/10.1016/j.fuel.2021.120488

• By utilising pyrolysis experimental data from the literature, we model pyrolytic processes and generate governing expressions that apply to numerous pyrolytic polygeneration processes for cellulose-rich streams. We furnish this work with three case studies which demonstrate the utility and merit of our modelling approach.

Multivariate Modelling of the Trace Element Chemistry of Arsenopyrite from Gold Deposits Using Higher-Dimensional Algebras, published in Mathematical Geosciences.

• https://doi.org/10.1007/s11004-020-09856-3

• In this article, a generalised formulation for multivariate systems modelling is presented and it is applied to the discovery of the manifested system characteristics of arsenopyrite samples collected from Australian gold deposits, using fuzzy arsenopyrite trace element datasets. The models generated allow a specialist to discover qualitative relations, using higher-dimensional representations of multivariate data.

Greenfields Gold Deposit Exploration Techniques using Conformal Geometric Algebra-Based Arsenopyrite Trace Element Assemblage Models, published in The Journal of Geochemical Exploration.

• https://doi.org/10.1016/j.gexplo.2020.106685

• Using a Conformal Geometric Algebra based formulation that predicts geological features from geochemical datasets, this paper extends the methods and techniques to the construction of predictive spatial maps of these geological features. The contribution further introduces a novel “intersection space minimisation procedure” and the “raytracing interpolation procedure” and they are used to a create comprehensive and accurate spatialised maps from a limited number of predictions in conjunction with neural networks and the hyperfield formulation.

A Generalized Theoretical Model for the Relationship Between Critical Micelle Concentrations, Pressure, and Temperature for Surfactants, published in The Journal of Surfactants and Detergents.

• https://doi.org/10.1002/jsde.12360

• In this article, we develop a conformal geometric algebra‐based formulation that models surfactants, their solubilities, and critical micelle concentration (CMC), with relation to temperature and pressure. One of the contributions of this work is the utilization of this formulation to develop a governing expression, in the form of a three‐dimensional relationship, between CMC, pressure, and temperature for a general surfactant.

A Generalised Methodology Using Conformal Geometric Algebra for Mathematical Chemistry, published in The Journal of Mathematical Chemistry.

• https://doi.org/10.1007/s10910-020-01155-w

• This paper employs network theoretic methods and standard Conformal Geometric Algebra with a unique algebraic extension that introduces special non-integer basis vectors. The methodology developed lays preliminary foundations for both generic and more specialised characterisations and modelling of chemical systems.

A Clifford Algebra-Based Mathematical Model for the Determination of Critical Temperatures in Superconductors, published in The Journal of Mathematical Chemistry.

• https://doi.org/10.1007/s10910-020-01156-9

• In this article, we present a novel and generalised mathematical formulation, which maps the atomic and structural characteristics of superconducting lattice structures to their critical temperature.