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.

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.

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.

Sampling and measurement methods for a study of childhood refractive error in a UK population

Background There is a paucity of data describing the prevalence of childhood refractive error in the United Kingdom. The Northern Ireland Childhood Errors of Refraction study, along with its sister study the Aston Eye Study, are the first population-based surveys of children using both random cluster sampling and cycloplegic autorefraction to quantify levels of refractive error in the United Kingdom. Methods Children aged 6–7 years and 12–13 years were recruited from a stratified random sample of primary and post-primary schools, representative of the population of Northern Ireland as a whole. Measurements included assessment of visual acuity, oculomotor balance, ocular biometry and cycloplegic binocular open-field autorefraction. Questionnaires were used to identify putative risk factors for refractive error. Results 399 (57%) of 6–7 years and 669 (60%) of 12–13 years participated. School participation rates did not vary statistically significantly with the size of the school, whether the school is urban or rural, or whether it is in a deprived/non-deprived area. The gender balance, ethnicity and type of schooling of participants are reflective of the Northern Ireland population. Conclusions The study design, sample size and methodology will ensure accurate measures of the prevalence of refractive errors in the target population and will facilitate comparisons with other population-based refractive data.

Typical kernel size and number of sparse random matrices over Galois fields: a statistical physics approach

Using methods of statistical physics, we study the average number and kernel size of general sparse random matrices over GF(q), with a given connectivity profile, in the thermodynamical limit of large matrices. We introduce a mapping of GF(q) matrices onto spin systems using the representation of the cyclic group of order q as the q-th complex roots of unity. This representation facilitates the derivation of the average kernel size of random matrices using the replica approach, under the replica symmetric ansatz, resulting in saddle point equations for general connectivity distributions. Numerical solutions are then obtained for particular cases by population dynamics. Similar techniques also allow us to obtain an expression for the exact and average number of random matrices for any general connectivity profile. We present numerical results for particular distributions.

The vesicle size of DDA:TDB liposomal adjuvants plays a role in the cell-mediated immune response but has no significant effect on antibody production

The use of cationic liposomes as experimental adjuvants for subunit peptide of protein vaccines is well documented. Recently the cationic liposome CAF01, composed of dimethyldioctadecylammonium (DDA) and trehalose dibehenate (TDB), has entered Phase I clinical trials for use in a tuberculosis (TB) vaccine. CAF01 liposomes are a heterogeneous population with a mean vesicle size of 500 nm; a strong retention of antigen at the injection site and a Th1-biassed immune response are noted. The purpose of this study was to investigate whether CAF01 liposomes of significantly different vesicle sizes exhibited altered pharmacokinetics in vivo and cellular uptake with activation in vitro. Furthermore, the immune response against the TB antigen Ag85B-ESAT-6 was followed when various sized CAF01 liposomes were used as vaccine adjuvants. The results showed no differences in vaccine (liposome or antigen) draining from the injection site, however, significant differences in the movement of liposomes to the popliteal lymph node were noted. Liposome uptake by THP-1 vitamin D3 stimulated macrophage-like cells did not show a liposome size-dependent pattern of uptake. Finally, whilst there were no significant differences in the IgG1/2 regardless of the liposome size used as a delivery vehicle for Ag85B-ESAT-6, vesicle size has a size dependent effect on cell proliferation and IL-10 production with larger liposomes (in excess of 2 µm) promoting the highest proliferation and lowest IL-10 responses, yet vesicles of ~500 nm promoting higher IFN-? cytokine production from splenocytes and higher IL-1ß at the site of injection.

Population pharmacokinetics of single-dose intravenous paracetamol in children

Background To determine the pharmacokinetics (PK) of a new i.v. formulation of paracetamol (Perfalgan) in children ≤15 yr of age. Methods After obtaining written informed consent, children under 16 yr of age were recruited to this study. Blood samples were obtained at 0, 15, 30 min, 1, 2, 4, 6, and 8 h after administration of a weight-dependent dose of i.v. paracetamol. Paracetamol concentration was measured using a validated high-performance liquid chromatographic assay with ultraviolet detection method, with a lower limit of quantification (LLOQ) of 900 pg on column and an intra-day coefficient of variation of 14.3% at the LLOQ. Population PK analysis was performed by non-linear mixed-effect modelling using NONMEM. Results One hundred and fifty-nine blood samples from 33 children aged 1.8–15 yr, weight 13.7–56 kg, were analysed. Data were best described by a two-compartment model. Only body weight as a covariate significantly improved the goodness of fit of the model. The final population models for paracetamol clearance (CL), V1 (central volume of distribution), Q (inter-compartmental clearance), and V2 (peripheral volume of distribution) were: 16.51×(WT/70)0.75, 28.4×(WT/70), 11.32×(WT/70)0.75, and 13.26×(WT/70), respectively (CL, Q in litres per hour, WT in kilograms, and V1 and V2 in litres). Conclusions In children aged 1.8–15 yr, the PK parameters for i.v. paracetamol were not influenced directly by age but were by total body weight and, using allometric size scaling, significantly affected the clearances (CL, Q) and volumes of distribution (V1, V2).

Firm growth and firm size

This article analyses the growth rates of the complete population of UK-registered firms for the period 2001 to 2005. We estimate Gibrat's law – that growth rates are independent of firm size – by deciles of the firm size distribution. Whether we are able to reject Gibrat's law varies across deciles. We also show how estimates vary according to the measure of firm size, time period and sample selection.

The normal optic nerve variations in an optometric population:Possible ocular and systemic influences

Early detection of glaucoma relies on a detailed knowledge of how the normal optic nerve (ONH) varies within the population. The purpose of this study focused on two main areas; 1. To explore the optic nerve head appearance in the normal optometric population and compare the south Asian (principally Pakistani) with the European white population, correcting for possible ocular and non-ocular influences in a multiple regression model. The main findings were: • The optic discs of the South Asian (SA) and White European (WE) populations were not statistically different in size. The SA group possessed discs with increased cupping and thinner neuro-retinal rims (NRR) compared with the WE group. The SA group also demonstrated a more vertically oval shape than the WE population. These differences were significant at the p<0.01 level. • The upper limits of inter-eye asymmetry were: ≤0.2 for cup to disc area ratio, and 3mmHg for intra-ocular pressure (IOP) for both ethnic groups and this did not increase with age. IOP asymmetry did not vary with gender, ethnicity or a family history of glaucoma and was independent of ONH asymmetry. ONH and IOP asymmetry are therefore independent risk factors when screening for glaucoma for both ethnic groups. 2. To investigate the validity of the ISNT rule: inferior> superior> nasal> temporal NRR thickness in the optometric population. The main findings were: • As disc size increased the disc become rounder and less vertically oval in shape. Vertically oval discs had thicker superior and inferior NRRs and thinner nasal and temporal NRRs compared with rounder disc shapes due to cup shape being independent of disc shape. Vertically oval discs were therefore more likely to obey the ISNT rule than larger rounder discs. • The ISNT rule has a low adherence in our sample of normal eyes (5.7%). However, by removing the nasal sector to become the IST rule, 74.5% of normal eyes obeyed. SA eyes and female gender were more likely to obey the ISNT rule due to increased disc ovality. The IST rule is independent of disc shape and therefore more suitable for assessing discs from both ethnic backgrounds. Obeying the ISNT rule or IST rule was not related to disc or cup size.

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 enantioselective population pharmacokinetics of intravenous ketorolac in children using a stereoselective assay suitable for microanalysis

Objective: To describe the effect of age and body size on enantiomer selective pharmacokinetic (PK) of intravenous ketorolac in children using a microanalytical assay. Methods: Blood samples were obtained at 0, 15 and 30 min and at 1, 2, 4, 6, 8 and 12 h after a weight-dependent dose of ketorolac. Enantiomer concentration was measured using a liquid chromatography tandem mass spectrometry method. Non-linear mixed-effect modelling was used to assess PK parameters. Key findings: Data from 11 children (1.7–15.6 years, weight 10.7–67.4 kg) were best described by a two-compartment model for R(+), S(−) and racemic ketorolac. Only weight (WT) significantly improved the goodness of fit. The final population models were CL = 1.5 × (WT/46)0.75, V1 = 8.2 × (WT/46), Q = 3.4 × (WT/46)0.75, V2 = 7.9 × (WT/46), CL = 2.98 × (WT/46), V1 = 13.2 × (WT/46), Q = 2.8 × (WT/46)0.75, V2 = 51.5 × (WT/46), and CL = 1.1 × (WT/46)0.75, V1 = 4.9 × (WT/46), Q = 1.7 × (WT/46)0.75 and V2 = 6.3 × (WT/46)for R(+), S(−) and racemic ketorolac. Conclusions: Only body weight influenced the PK parameters for R(+) and S(−) ketorolac. Using allometric size scaling significantly affected the clearances (CL, Q) and volumes of distribution (V1, V2).

The continuum of psychotic symptoms in the general population:a cross-national study

OBJECTIVE: To identify the cross-national prevalence of psychotic symptoms in the general population and to analyze their impact on health status. METHOD: The sample was composed of 256,445 subjects (55.9% women), from nationally representative samples of 52 countries worldwide participating in the World Health Organization's World Health Survey. Standardized and weighted prevalence of psychotic symptoms were calculated in addition to the impact on health status as assessed by functioning in multiple domains. RESULTS: Overall prevalences for specific symptoms ranged from 4.80% (SE = 0.14) for delusions of control to 8.37% (SE = 0.20) for delusions of reference and persecution. Prevalence figures varied greatly across countries. All symptoms of psychosis produced a significant decline in health status after controlling for potential confounders. There was a clear change in health impact between subjects not reporting any symptom and those reporting at least one symptom (effect size of 0.55). CONCLUSIONS: The prevalence of the presence of at least one psychotic symptom has a wide range worldwide varying as much as from 0.8% to 31.4%. Psychotic symptoms signal a problem of potential public health concern, independent of the presence of a full diagnosis of psychosis, as they are common and are related to a significant decrement in health status. The presence of at least one psychotic symptom is related to a significant poorer health status, with a regular linear decrement in health depending on the number of symptoms.