Accuracy and optimal sampling in Monte Carlo solution of population balance equations

Implementation of a Monte Carlo simulation for the solution of population balance equations (PBEs) requires choice of initial sample number (N0), number of replicates (M), and number of bins for probability distribution reconstruction (n). It is found that Squared Hellinger Distance, H2, is a useful measurement of the accuracy of Monte Carlo (MC) simulation, and can be related directly to N0, M, and n. Asymptotic approximations of H2 are deduced and tested for both one-dimensional (1-D) and 2-D PBEs with coalescence. The central processing unit (CPU) cost, C, is found in a power-law relationship, C= aMNb0, with the CPU cost index, b, indicating the weighting of N0 in the total CPU cost. n must be chosen to balance accuracy and resolution. For fixed n, M × N0 determines the accuracy of MC prediction; if b > 1, then the optimal solution strategy uses multiple replications and small sample size. Conversely, if 0 < b < 1, one replicate and a large initial sample size is preferred. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2394–2402, 2015

The dynamics of a genetic algorithm for a simple learning problem

A formalism for describing the dynamics of Genetic Algorithms (GAs) using method s from statistical mechanics is applied to the problem of generalization in a perceptron with binary weights. The dynamics are solved for the case where a new batch of training patterns is presented to each population member each generation, which considerably simplifies the calculation. The theory is shown to agree closely to simulations of a real GA averaged over many runs, accurately predicting the mean best solution found. For weak selection and large problem size the difference equations describing the dynamics can be expressed analytically and we find that the effects of noise due to the finite size of each training batch can be removed by increasing the population size appropriately. If this population resizing is used, one can deduce the most computationally efficient size of training batch each generation. For independent patterns this choice also gives the minimum total number of training patterns used. Although using independent patterns is a very inefficient use of training patterns in general, this work may also prove useful for determining the optimum batch size in the case where patterns are recycled.

Noisy fitness evaluation in genetic algorithms and the dynamics of learning

A theoretical model is presented which describes selection in a genetic algorithm (GA) under a stochastic fitness measure and correctly accounts for finite population effects. Although this model describes a number of selection schemes, we only consider Boltzmann selection in detail here as results for this form of selection are particularly transparent when fitness is corrupted by additive Gaussian noise. Finite population effects are shown to be of fundamental importance in this case, as the noise has no effect in the infinite population limit. In the limit of weak selection we show how the effects of any Gaussian noise can be removed by increasing the population size appropriately. The theory is tested on two closely related problems: the one-max problem corrupted by Gaussian noise and generalization in a perceptron with binary weights. The averaged dynamics can be accurately modelled for both problems using a formalism which describes the dynamics of the GA using methods from statistical mechanics. The second problem is a simple example of a learning problem and by considering this problem we show how the accurate characterization of noise in the fitness evaluation may be relevant in machine learning. The training error (negative fitness) is the number of misclassified training examples in a batch and can be considered as a noisy version of the generalization error if an independent batch is used for each evaluation. The noise is due to the finite batch size and in the limit of large problem size and weak selection we show how the effect of this noise can be removed by increasing the population size. This allows the optimal batch size to be determined, which minimizes computation time as well as the total number of training examples required.

Genetics and competing strategies in a threshold model for mail processing

Multi-agent algorithms inspired by the division of labour in social insects are applied to a problem of distributed mail retrieval in which agents must visit mail producing cities and choose between mail types under certain constraints.The efficiency (i.e. the average amount of mail retrieved per time step), and the flexibility (i.e. the capability of the agents to react to changes in the environment) are investigated both in static and dynamic environments. New rules for mail selection and specialisation are introduced and are shown to exhibit improved efficiency and flexibility compared to existing ones. We employ a genetic algorithm which allows the various rules to evolve and compete. Apart from obtaining optimised parameters for the various rules for any environment, we also observe extinction and speciation. From a more theoretical point of view, in order to avoid finite size effects, most results are obtained for large population sizes. However, we do analyse the influence of population size on the performance. Furthermore, we critically analyse the causes of efficiency loss, derive the exact dynamics of the model in the large system limit under certain conditions, derive theoretical upper bounds for the efficiency, and compare these with the experimental results.

The effect of load on agent-based algorithms for distributed task allocation

Multi-agent algorithms inspired by the division of labour in social insects and by markets, are applied to a constrained problem of distributed task allocation. The efficiency (average number of tasks performed), the flexibility (ability to react to changes in the environment), and the sensitivity to load (ability to cope with differing demands) are investigated in both static and dynamic environments. A hybrid algorithm combining both approaches, is shown to exhibit improved efficiency and robustness. We employ nature inspired particle swarm optimisation to obtain optimised parameters for all algorithms in a range of representative environments. Although results are obtained for large population sizes to avoid finite size effects, the influence of population size on the performance is also analysed. From a theoretical point of view, we analyse the causes of efficiency loss, derive theoretical upper bounds for the efficiency, and compare these with the experimental results.

Between a rock and a hard place:exploring women's experience of participation and progress in managerial careers

Purpose – The growth of women in management has been argued to offer a route to reduce organizational and social inequality. The purpose of this paper is to explore the careers and experiences of female managers from a variety of organizations operating in the West Midlands region of the UK. Design/methodology/approach – This study is based on 56 interviews conducted with women managers within various sectors. The interviewees also completed pictorial careers maps, which along with interview recordings were analyzed. Findings – The key themes to emerge from this research centre upon the factors that draw women into management (which we term seductive elements) as well as some of the hindering practices that prevent women from progressing. Significantly, we find that managerial careers are associated with gendered assumptions and practices (e.g. facilitating and developing people) which contribute to construct management (done by women) as bounded-up characteristically with “feminized” behaviours. Research limitations/implications – The research is based upon a relatively small sample that is multi-sectorial. Wider studies that increase population size, together with deeper studies that hold sectorial variables constant would further add weight to the findings presented here. Practical implications – The paper draws attention to the “lived reality” of doing management, which, we argue often, for women in particular involves the reconciliation of contradictions and conflicting pressures. We draw attention to the lack of “alternative models” of organization and highlight the potential for gender-focus mentoring and management education. Originality/value – The paper is of value in giving voice to a selection of women managers by allowing them to reflect upon and explore their experience of management. The paper also documents the day-to-day reality of women's managerial careers that require the re-enactment and reproduction of stereotypical gender norms.

Correlates of spontaneous reporting of adverse drug reactions within primary care: the paradox of low prescribers who are high reporters

AIM(S) To examine Primary Care Trust (PCT) demographics influencing general practitioner (GP) involvement in pharmacovigilance. METHODS PCT adverse drug reaction (ADR) reports to the Yellow Card scheme between April 2004 and March 2006 were obtained for the UK West Midlands region. Reports were analysed by all drugs, and most commonly reported drugs (‘top drugs’). PCT data, adjusted for population size, were aggregated. Prescribing statistics and other characteristics were obtained for each PCT, and associations between these characteristics and ADR reporting rates were examined. RESULTS During 2004–06, 1175 reports were received from PCTs. Two hundred and eighty (24%) of these reports were for 14 ‘top drugs’. The mean rate of reporting for PCTs was 213 reports per million population. A total of 153 million items were prescribed during 2004–06, of which 33% were ‘top drugs’. Reports for all drugs and ‘top drugs’ were inversely correlated with the number of prescriptions issued per thousand population (rs = -0.413, 95% CI -0.673, -0.062, P < 0.05, and r = -0.420, 95% CI -0.678, -0.071, P < 0.05, respectively). Reporting was significantly negatively correlated with the percentages of male GPs within a PCT, GPs over 55 years of age, single-handed GPs within a PCT, the average list size of a GP within a PCT, the overall deprivation scores and average QOF total points. ADR reports did not correlate significantly with the proportion of the population over 65 years old. CONCLUSIONS Some PCT characteristics appear to be associated with low levels of ADR reporting. The association of low prescribing areas with high ADR reporting rates replicates previous findings.

Minority enterprise in the clothing industry: an analysis of Asian jeans manufacturers in Birmingham

This thesis discusses and assesses the resources available to Asian entrepreneurs in the West Midlands' clothing industry and how they are used by these small businessmen in order to address opportunities in the market economy within the constraints imposed. The fashion industry is volatile and is dependent upon flexible firms which can respond quickly to shortrun production schedules. Small firms are best able to respond to this market environment. Production of jeans presents an interesting departure from the mainstream fashion industry. It is traditionally gared towards longrun production schedules where multinational enterprises have artificially diversified the market, promoting the 'right' brand name and have established control of the upper end of the market, whilst imports from Newly Developing Countries have catered for cheap copies at the lower end of the market. In recent years, a fashion element to jeans has emerged, thus opening a market gap for U.K. manufacturers to respond in the same way as for other fashion articles. A large immigrant population, previously serving the now declining factories and foundries of the West Midlands but, through redundancy, no longer a part of this employment sector, has ~5ponded to economic constraints and market opportunities by drawing on ethnic network resources for competitive access to labour, finance and contacts, to attack the emergent market gap. Two models of these Asian entrepreneurs are developed. One being somecne who has professionally and actively tackled the market gap and become established. These entrepreneurs are usually educated and have personal experience in business and were amongst the first to perceive opportunities to enter the industry, actively utilising their ethnicity as a resource upon which to draw for favorable access to cheap, flexible labour and capital. The second model is composed of later entrants to jeans manufacturing. They have less formal education and experience and have been pushed into self-employment by constraints of unemployment. Their ethnicity is passively used as a resource. They are more likely confined to the marginal activity of 'cut make and trim' and have little opportunity to increase profit margins, become estalished or expand.

Constructing a normative national identity: the Leitkultur debate in Germany 2000/2001

In recent years, public discourse about German national identity has increasingly focussed on the large foreign population within Germany's borders. Whilst right-wing politicians such as Edmund Stoiber foster fears of identity loss ('Überfremdung'), more liberal observers, and indeed the ruling red-green coalition, acknowledge that multiethnicity has by now become an integral part of this identity. The debate experienced its provisional climax in late 2000 and early 2001. Friedrich Merz, then parliamentary leader of the CDU party, introduced the term 'Leitkultur' into the political discourse. The notion suggests the existence of a clearly identifiable spectrum of German cultural values and proposes that foreigners who wished to live in Germany should adhere to these values. Merz's proposal triggered a wave of highly controversial comments which have been evaluated for the purpose of this paper. It draws on roughly 350 newspaper articles and interviews and aims to introduce the English-speaking reader to the complex range of arguments. The Leitkultur debate is taken as symptomatic of the current state of public discourse about foreigners and national identity in Germany.