Simple approximate MAP inference for Dirichlet processes mixtures

The Dirichlet process mixture model (DPMM) is a ubiquitous, flexible Bayesian nonparametric statistical model. However, full probabilistic inference in this model is analytically intractable, so that computationally intensive techniques such as Gibbs sampling are required. As a result, DPMM-based methods, which have considerable potential, are restricted to applications in which computational resources and time for inference is plentiful. For example, they would not be practical for digital signal processing on embedded hardware, where computational resources are at a serious premium. Here, we develop a simplified yet statistically rigorous approximate maximum a-posteriori (MAP) inference algorithm for DPMMs. This algorithm is as simple as DP-means clustering, solves the MAP problem as well as Gibbs sampling, while requiring only a fraction of the computational effort. (For freely available code that implements the MAP-DP algorithm for Gaussian mixtures see http://www.maxlittle.net/.) Unlike related small variance asymptotics (SVA), our method is non-degenerate and so inherits the “rich get richer” property of the Dirichlet process. It also retains a non-degenerate closed-form likelihood which enables out-of-sample calculations and the use of standard tools such as cross-validation. We illustrate the benefits of our algorithm on a range of examples and contrast it to variational, SVA and sampling approaches from both a computational complexity perspective as well as in terms of clustering performance. We demonstrate the wide applicabiity of our approach by presenting an approximate MAP inference method for the infinite hidden Markov model whose performance contrasts favorably with a recently proposed hybrid SVA approach. Similarly, we show how our algorithm can applied to a semiparametric mixed-effects regression model where the random effects distribution is modelled using an infinite mixture model, as used in longitudinal progression modelling in population health science. Finally, we propose directions for future research on approximate MAP inference in Bayesian nonparametrics.

Modelling the growth of prion protein aggregates in the brain in variant Creutzfeldt-Jakob disease

Deposition of insoluble prion protein (PrP) in the brain in the form of protein aggregates or deposits is characteristic of the ‘transmissible spongiform encephalopathies’ (TSEs). Understanding the growth and development of these PrP aggregates is important both in attempting to the elucidate of the pathogenesis of prion disease and in the development of treatments designed to prevent or inhibit the spread of prion pathology within the brain. Aggregation and disaggregation of proteins and the diffusion of substances into the developing aggregates (surface diffusion) are important factors in the development of protein aggregates. Mathematical models suggest that if aggregation/disaggregation or surface diffusion is the predominant factor, the size frequency distribution of the resulting protein aggregates in the brain should be described by either a power-law or a log-normal model respectively. This study tested this hypothesis for two different types of PrP deposit, viz., the diffuse and florid-type PrP deposits in patients with variant Creutzfeldt-Jakob disease (vCJD). The size distributions of the florid and diffuse plaques were fitted by a power-law function in 100% and 42% of brain areas studied respectively. By contrast, the size distributions of both types of plaque deviated significantly from a log-normal model in all brain areas. Hence, protein aggregation and disaggregation may be the predominant factor in the development of the florid plaques. A more complex combination of factors appears to be involved in the pathogenesis of the diffuse plaques. These results may be useful in the design of treatments to inhibit the development of protein aggregates in vCJD.

Three-factor models versus time series models:quantifying time-dependencies of interactions between stimuli in cell biology and psychobiology for short longitudinal data

Signal integration determines cell fate on the cellular level, affects cognitive processes and affective responses on the behavioural level, and is likely to be involved in psychoneurobiological processes underlying mood disorders. Interactions between stimuli may subjected to time effects. Time-dependencies of interactions between stimuli typically lead to complex cell responses and complex responses on the behavioural level. We show that both three-factor models and time series models can be used to uncover such time-dependencies. However, we argue that for short longitudinal data the three factor modelling approach is more suitable. In order to illustrate both approaches, we re-analysed previously published short longitudinal data sets. We found that in human embryonic kidney 293 cells cells the interaction effect in the regulation of extracellular signal-regulated kinase (ERK) 1 signalling activation by insulin and epidermal growth factor is subjected to a time effect and dramatically decays at peak values of ERK activation. In contrast, we found that the interaction effect induced by hypoxia and tumour necrosis factor-alpha for the transcriptional activity of the human cyclo-oxygenase-2 promoter in HEK293 cells is time invariant at least in the first 12-h time window after stimulation. Furthermore, we applied the three-factor model to previously reported animal studies. In these studies, memory storage was found to be subjected to an interaction effect of the beta-adrenoceptor agonist clenbuterol and certain antagonists acting on the alpha-1-adrenoceptor / glucocorticoid-receptor system. Our model-based analysis suggests that only if the antagonist drug is administer in a critical time window, then the interaction effect is relevant.

Modelling growth of prion protein aggregates in the brain in variant Creutzfeldt-Jakob disease

Deposition of insoluble prion protein (PrP) in the brain in the form of protein aggregates or deposits is characteristic of the ‘transmissible spongiform encephalopathies’ (TSEs). Understanding the growth and development of PrP aggregates is important both in attempting to elucidate the pathogenesis of prion disease and in the development of treatments designed to inhibit the spread of prion pathology within the brain. Aggregation and disaggregation of proteins and the diffusion of substances into the developing aggregates (surface diffusion) are important factors in the development of protein deposits. Mathematical models suggest that if either aggregation/disaggregation or surface diffusion is the predominant factor, then the size frequency distribution of the resulting protein aggregates will be described by either a power-law or a log-normal model respectively. This study tested this hypothesis for two different populations of PrP deposit, viz., the diffuse and florid-type PrP deposits characteristic of patients with variant Creutzfeldt-Jakob disease (vCJD). The size distributions of the florid and diffuse deposits were fitted by a power-law function in 100% and 42% of brain areas studied respectively. By contrast, the size distributions of both types of aggregate deviated significantly from a log-normal model in all areas. Hence, protein aggregation and disaggregation may be the predominant factor in the development of the florid deposits. A more complex combination of factors appears to be involved in the pathogenesis of the diffuse deposits. These results may be useful in the design of treatments to inhibit the development of PrP aggregates in vCJD.

Modelling short crack growth behaviour in nickel-base superalloys

This paper provides a description of the features and mechanisms of facetted short crack growth in Ni-base superalloys, and briefly reviews existing short crack growth models in terms of their application to Ni-base alloys. The concept of “soft barriers” is introduced to produce a new two-phase model for local microstructural effects on short crack growth in Waspaloy. This is derived from detailed observations of crack growth through individual grains. The model differs from all previous approaches in highlighting the importance of crack path perturbations within grains. Potential applications of the model in alloy development are discussed.

Modelling foreign direct investment in China

This thesis consists of three empirical and one theoretical studies. While China has received an increasing amount of foreign direct investment (FDI) and become the second largest host country for FDI in recent years, the absence of comprehensive studies on FDI inflows into this country drives this research. In the first study, an econometric model is developed to analyse the economic, political, cultural and geographic determinants of both pledged and realised FDI in China. The results of this study suggest that China's relatively cheaper labour force, high degree of international integration with the outside world (represented by its exports and imports) and bilateral exchange rates are the important economic determinants of both pledged FDI and realised FDI in China. The second study analyses the regional distribution of both pledged and realised FDI within China. The econometric properties of the panel data set are examined using a standardised 't-bar' test. The empirical results indicate that provinces with higher level of international trade, lower wage rates, more R&D manpower, more preferential policies and closer ethnic links with overseas Chinese attract relatively more FDI. The third study constructs a dynamic equilibrium model to study the interactions among FDI, knowledge spillovers and long run economic growth in a developing country. The ideas of endogenous product cycles and trade-related international knowledge spillovers are modified and extended to FDI. The major conclusion is that, in the presence of FDI, economic growth is determined by the stock of human capital, the subjective discount rate and knowledge gap, while unskilled labour can not sustain growth. In the fourth study, the role of FDI in the growth process of the Chinese economy is investigated by using a panel of data for 27 provinces across China between 1986 and 1995. In addition to FDI, domestic R&D expenditure, international trade and human capital are added to the standard convergence regressions to control for different structural characteristics in each province. The empirical results support endogenous innovation growth theory in which regional per capita income can converge given technological diffusion, transfer and imitation.

Myopia:precedents for research in the twenty-first century

The myopic eye is generally considered to be a vulnerable eye and, at levels greater than 6 D, one that is especially susceptible to a range of ocular pathologies. There is concern therefore that the prevalence of myopia in young adolescent eyes has increased substantially over recent decades and is now approaching 10-25% and 60-80%, respectively, in industrialized societies of the West and East. Whereas it is clear that the major structural correlate of myopia is longitudinal elongation of the posterior vitreous chamber, other potential correlates include profiles of lenticular and corneal power, the relationship between longitudinal and transverse vitreous chamber dimensions and ocular volume. The most potent predictors for juvenile-onset myopia continue to be a refractive error ≤+0.50 D at 5 years of age and family history. Significant and continuing progress is being made on the genetic characteristics of high myopia with at least four chromosomes currently identified. Twin studies and genetic modelling have computed a heritability index of at least 80% across the whole ametropic continuum. The high index does not, however, preclude an environmental precursor, sustained near work with high cognitive demand being the most likely. The significance of associations between accommodation, oculomotor dysfunction and human myopia is equivocal despite animal models that have demonstrated that sustained hyperopic defocus can induce vitreous chamber growth. Recent optical and pharmaceutical approaches to the reduction of myopia progression in children are likely precedents for future research, for example progressive addition spectacle lens trials and the use of the topical MI muscarinic antagonist pirenzepine.

Modelling the innovation value chain

Innovation events – the introduction of new products or processes – represent the end of a process of knowledge sourcing and transformation. They also represent the beginning of a process of exploitation which may result in an improvement in the performance of the innovating business. This recursive process of knowledge sourcing, transformation and exploitation comprises the innovation value chain. Modelling the innovation value chain for a large group of manufacturing firms in Ireland and Northern Ireland highlights the drivers of innovation, productivity and firm growth. In terms of knowledge sourcing,we find strong complementarity between horizontal, forwards, backwards, public and internal knowledge sourcing activities. Each of these forms of knowledge sourcing also makes a positive contribution to innovation in both products and processes although public knowledge sources have only an indirect effect on innovation outputs. In the exploitation phase, innovation in both products and processes contribute positively tocompany growth, with product innovation having a short-term ‘disruption’ effect on labour productivity. Modelling the complete innovation value chain highlights the structure and complexity of the process of translating knowledge into business value and emphasises the role of skills, capital investment and firms’ other resources in the value creation process.

Improved production of industrially relevant recombinant proteins: application of multi-factorial design of experiments and scalable process modelling

The work described in this thesis focuses on the use of a design-of-experiments approach in a multi-well mini-bioreactor to enable the rapid establishments of high yielding production phase conditions in yeast, which is an increasingly popular host system in both academic and industrial laboratories. Using green fluorescent protein secreted from the yeast, Pichia pastoris, a scalable predictive model of protein yield per cell was derived from 13 sets of conditions each with three factors (temperature, pH and dissolved oxygen) at 3 levels and was directly transferable to a 7 L bioreactor. This was in clear contrast to the situation in shake flasks, where the process parameters cannot be tightly controlled. By further optimisating both the accumulation of cell density in batch and improving the fed-batch induction regime, additional yield improvement was found to be additive to the per cell yield of the model. A separate study also demonstrated that improving biomass improved product yield in a second yeast species, Saccharomyces cerevisiae. Investigations of cell wall hydrophobicity in high cell density P. pastoris cultures indicated that cell wall hydrophobin (protein) compositional changes with growth phase becoming more hydrophobic in log growth than in lag or stationary phases. This is possibly due to an increased occurrence of proteins associated with cell division. Finally, the modelling approach was validated in mammalian cells, showing its flexibility and robustness. In summary, the strategy presented in this thesis has the benefit of reducing process development time in recombinant protein production, directly from bench to bioreactor.

The economic impact of high growth start-ups:understanding the challenge for policy in the UK

Objectives The creation of more high-growth firms continues to be a key component of enterprise policy throughout the countries of the OECD. In the UK the developing enterprise policy framework highlights the importance of supporting businesses with growth potential. The difficulty, of course, is the ability of those delivering business support policies to accurately identify those businesses, especially at start-up, which will benefit from interventions and experiences an enhanced growth performance. This paper has a core objective of presenting new data on the number of high growth firms in the UK and providing an assessment of their economic significance. Approach This paper uses a specially created longitudinal firm-level database based on the Inter-Departmental Business Register (IDBR) held by the Office of National Statistics (ONS) for all private sector businesses in the UK for the period 1997-2008 to investigate the share of high-growth firms (including a sub-set of start-up more commonly referred to as gazelles) in successive cohorts of start-ups. We apply OECD definitions of high growth and gazelles to this database and are able to quantify for the first time their number (disaggregated by sector, region, size) and importance (employment and sales). Prior Work However, what is lacking at the core of this policy focus is any comprehensive statistical analysis of the scale and nature of high-growth firms in cohorts of new and established businesses. The evidence base in response to the question “Why do high-growth firms matter?” is surprisingly weak. Important work in this area has been initiated by Bartelsman et al., (2003),Hoffman and Jünge (2006) and Henreksen and Johansson (2009) but to date work in the UK has been limited (BERR, 2008b). Results We report that there are ~11,500 high growth firms in the UK in both 2005 and 2008. The share of high growth start-ups in the UK in 2005 (6.3%) was, contrary to the widely held perception in policy circles, higher than in the United States (5.2%). Of particular interest in the analysis are the growth trajectories (pattern of growth) of these firms as well as the extent to which they are restricted to technology-based or knowledge-based sectors. Implications and Value Using hitherto unused population data for the first time we have answered a fundamental research and policy question on the number and scale of high growth firms in the UK. We draw the conclusion that this ‘rare’ event does not readily lend itself to policy intervention on the grounds that the significant effort needed to identify such businesses ex ante would appear unjustified even if it was possible.

Knowledge capital, endogenous growth and regional disparities in productivity:multi-level evidences from China

This paper examines the role of knowledge capital in persistent regional productivity disparities in developing countries. The hypotheses are tested using regional and firm level longitudinal data from China. It is found that inequalities in knowledge creation and transfer, both inter-generational and international, played a significant role in increasing regional disparities in productivity. These inequalities are exacerbated by the accumulative nature of knowledge capital. All this leads to self-perpetuating cycles of success and failure, particularly compounded with asymmetric financial and human capital between different regions.

Modelling a biochemical reaction with computational fluid dynamics

Earlier investigations (Cartland Glover et al., 2004) into the use of computational fluid dynamics (CFD) for the modelling of gas-liquid and gas-liquid-solid flow allowed a simple biochemical reaction model to be implemented. A single plane mesh was used to represent the transport and reaction of molasses, the mould Aspergillus niger and citric acid in a bubble column with a height to diameter aspect ratio of 20:1. Two specific growth rates were used to examine the impact that biomass growth had on the local solids concentration and the effect this had on the local hydrodynamics of the bubble column.

Fetal growth restriction results in remodeled and less efficient hearts in children

Background— Fetal growth restriction (FGR) affects 5% to 10% of newborns and is associated with increased cardiovascular mortality in adulthood. The most commonly accepted hypothesis is that fetal metabolic programming leads secondarily to diseases associated with cardiovascular disease, such as obesity, diabetes mellitus, and hypertension. Our main objective was to evaluate the alternative hypothesis that FGR induces primary cardiac changes that persist into childhood. Methods and Results— Within a cohort of fetuses with growth restriction identified in fetal life and followed up into childhood, we randomly selected 80 subjects with FGR and compared them with 120 normally grown fetuses, matched for gender, birth date, and gestational age at birth. Cardiovascular assessment was performed in childhood (mean age of 5 years). Compared with control subjects, children with FGR had a different cardiac shape, with increased transversal diameters and more globular cardiac ventricles. Although left ejection fraction was similar among the study groups, stroke volume was reduced significantly, which was compensated for by an increased heart rate to maintain output in severe FGR. This was associated with subclinical longitudinal systolic dysfunction (decreased myocardial peak velocities) and diastolic changes (increased E/E' ratio and E deceleration time). Children with FGR also had higher blood pressure and increased intima-media thickness. For all parameters evaluated, there was a linear increase with the severity of growth restriction. Conclusions— These findings suggest that FGR induces primary cardiac and vascular changes that could explain the increased predisposition to cardiovascular disease in adult life. If these results are confirmed, the impact of strategies with beneficial effects on cardiac remodeling should be explored in children with FGR.

A finite element approach to modelling the hydrological regime in horizontal subsurface flow constructed wetlands for wastewater treatment

A Finite Element Analysis (FEA) model is used to explore the relationship between clogging and hydraulics that occurs in Horizontal Subsurface Flow Treatment Wetlands (HSSF TWs) in the United Kingdom (UK). Clogging is assumed to be caused by particle transport and an existing single collector efficiency model is implemented to describe this behaviour. The flow model was validated against HSSF TW survey results obtained from the literature. The model successfully simulated the influence of overland flow on hydrodynamics, and the interaction between vertical flow through the low permeability surface layer and the horizontal flow of the saturated water table. The clogging model described the development of clogging within the system but under-predicted the extent of clogging which occurred over 15 years. This is because important clogging mechanisms were not considered by the model, such as biomass growth and vegetation establishment. The model showed the usefulness of FEA for linking hydraulic and clogging phenomenon in HSSF TWs and could be extended to include treatment processes. © 2011 Springer Science+Business Media B.V.