Advanced physical characterisation of milled pharmaceutical solids

Milling has been the key unit operation in controlling particle size of pharmaceutical powders at scale. The work carried out in this thesis is a comprehensive study of the stability of pharmaceutical solids post-milling and upon storage, from molecular level up to bulk handling scale. It is an attempt to fill key gaps in knowledge with regard to the anomalous behaviour and physical instability of milled powder through the development of advanced novel techniques. The physical instability of milled or amorphous pharmaceutical powders often manifest in changes in derived powder properties. Moisture induced dimensional changes of amorphous lactose compacts were monitored by in-situ environmental controlled optical profilometry. The complex volumetric behaviour involves glassy-rubbery phase transition followed by amorphous-crystalline transformation under the influence of water. These associated changes were not observed in physical aging of amorphous lactose compacts by measuring specific surface area. At the molecular level these physical changes are governed by relaxation processes. By operating within the linear viscoelastic region, low strain uni-axial indentation of small molecule organic glasses at a range of temperature generated master curves using WLF analysis. Viscoelastic behaviour of these materials were determined to be controlled by local β-relaxation around the glass transition rather than globally for polymers. At the bulk level, due to the non-equilibrium nature of milled and amorphous powders, their surface energies tends to be significantly higher than the equivalent crystalline forms. This can be detrimental as highly cohesive and poor flowing powders are difficult to process. The unconfined compression test was adapted to measure cohesion of small weak pharmaceutical powder compacts. More significantly, a positive relationship was confirmed between surface energetics and cohesion of modified D-mannitol. At the particle level, the mechanism(s) by which milling or micronisation creates low levels of amorphicity remains unclear. MOUDI fractionation of bulk micronised α-lactose monohydrate and characterisation of fine fractions has clearly demonstrated that micronisation as well as mechanical particle size reduction also generates low levels of highly amorphous ultrafine particles within bulk crystalline powder which will have a significant effect on powder physical stability post-milling and upon storage. In conclusion, using the novel techniques developed here, significant progress has been towards understanding the physical behaviour of milled and amorphous pharmaceutical solids

FPGA Acceleration for Random Forest Inference

Random forest algorithm has been used broadly in both the research field and in the industry due to its ability to tackle both categorical and numerical dataset. FPGAs also have the highest growing potential and can be applied for the acceleration of random forest inference due to its low power consumption and parallelism support. Research have shown that a compact random forest algorithm is best executed through multi-threading and pipelining, and a FPGA implementation shows significant advantages compared to GP-GPU and CPU implementations in the area. It was able to process each decision tree within the forest independently in parallel. My research is dedicated to achieving this result by benchmarking individual performance running the same RF prediction algorithm on different platforms. The HDL code running on the FPGA will be translated from the source C++ code through Vitis HLS to be synthesized onto the FPGA board. The training data and the binary files will be processed beforehand for an equal competition for all platforms. I will be using various optimization techniques including loop unrolling and data-level parallelism to fully utilize the capabilities of FPGAs. With sufficient data and analysis, my result will show that FPGAs perform better compared to other platforms such as CPU or GP-GPU

TP Matrices and TP Completability

A matrix is called totally nonnegative (TN) if the determinant of every square submatrix is nonnegative and totally positive (TP) if the determinant of every square submatrix is positive. The TP (TN) completion problem asks which partial matrices have a TP (TN) completion. In this paper, several new TP-completable pat- terns in 3-by-n matrices are identied. The relationship between expansion and completability is developed based on the prior re- sults about single unspecied entry. These results extend our un- derstanding of TP-completable patterns. A new Ratio Theorem related to TP-completability is introduced in this paper, and it can possibly be a helpful tool in TP-completion problems

Neural Diagrammatic Reasoning

Diagrams have been shown to be effective tools for humans to represent and reason about complex concepts. They have been widely used to represent concepts in science teaching, to communicate workflow in industries and to measure human fluid intelligence. Mechanised reasoning systems typically encode diagrams into symbolic representations that can be easily processed with rule-based expert systems. This relies on human experts to define the framework of diagram-to-symbol mapping and the set of rules to reason with the symbols. This means the reasoning systems cannot be easily adapted to other diagrams without a new set of human-defined representation mapping and reasoning rules. Moreover such systems are not able to cope with diagram inputs as raw and possibly noisy images. The need for human input and the lack of robustness to noise significantly limit the applications of mechanised diagrammatic reasoning systems. A key research question then arises: can we develop human-like reasoning systems that learn to reason robustly without predefined reasoning rules? To answer this question, I propose Neural Diagrammatic Reasoning, a new family of diagrammatic reasoning systems which does not have the drawbacks of mechanised reasoning systems. The new systems are based on deep neural networks, a recently popular machine learning method that achieved human-level performance on a range of perception tasks such as object detection, speech recognition and natural language processing. The proposed systems are able to learn both diagram to symbol mapping and implicit reasoning rules only from data, with no prior human input about symbols and rules in the reasoning tasks. Specifically I developed EulerNet, a novel neural network model that solves Euler diagram syllogism tasks with 99.5% accuracy. Experiments show that EulerNet learns useful representations of the diagrams and tasks, and is robust to noise and deformation in the input data. I also developed MXGNet, a novel multiplex graph neural architecture that solves Raven Progressive Matrices (RPM) tasks. MXGNet achieves state-of-the-art accuracies on two popular RPM datasets. In addition, I developed Discrete-AIR, an unsupervised learning architecture that learns semi-symbolic representations of diagrams without any labels. Lastly I designed a novel inductive bias module that can be readily used in today’s deep neural networks to improve their generalisation capability on relational reasoning tasks.EPSRC Studentship and Cambridge Trust Scholarshi

A Behavioural Asset Pricing Model with a Time-Varying Second Moment

We develop a simple behavioural asset pricing model with fundamentalists and chartists to study price behaviour in financial markets. Within our model, the market impact of the weighting process of the conditional mean and variance of the chartists and investors' reactions are analysed. Price dynamics of the deterministic model under/over-reactions are analyzed. It shows different price dynamics and routes to complicated price behaviour when the chartists act as either trend followers or contrarians. It is found that (in a separate paper Chiarella et al (2004)) this analysis can be used to establish some connections between the statistical properties of the nonlinear stochastic system (such as distribution density and autocorrelation patterns of returns, in particular the stylised facts, such as fat tails, skewness, high kurtosis and long memory, observed in high frequency financial data) and the stability and bifurcation of the underlying deterministic system are established.fundamentalists; chartists, stability; bifurcation; investors' under- and over-reactions; stylized facts