Optimal location of supports in beam structures using genetic algorithms

Real structures can be thought as an assembly of components, as for instances plates, shells and beams. This later type of component is very commonly found in structures like frames which can involve a significant degree of complexity or as a reinforcement element of plates or shells. To obtain the desired mechanical behavior of these components or to improve their operating conditions when rehabilitating structures, one of the eventual parameters to consider for that purpose, when possible, is the location of the supports. In the present work, a beam-type structure is considered, and for a set of cases concerning different number and types of supports, as well as different load cases, the authors optimize the location of the supports in order to obtain minimum values of the maximum transverse deflection. The optimization processes are carried out using genetic algorithms. The results obtained, clearly show a good performance of the approach proposed. © 2014 IEEE.

Optimal Cut-Off Value for Homeostasis Model Assessment (HOMA) Index of Insulin-Resistance in a Population of Patients Admitted Electively in a Portuguese Cardiology Ward

INTRODUCTION: Insulin resistance is the pathophysiological key to explain metabolic syndrome. Although clearly useful, the Homeostasis Model Assessment index (an insulin resistance measurement) hasn't been systematically applied in clinical practice. One of the main reasons is the discrepancy in cut-off values reported in different populations. We sought to evaluate in a Portuguese population the ideal cut-off for Homeostasis Model Assessment index and assess its relationship with metabolic syndrome. MATERIAL AND METHODS: We selected a cohort of individuals admitted electively in a Cardiology ward with a BMI < 25 Kg/m2 and no abnormalities in glucose metabolism (fasting plasma glucose < 100 mg/dL and no diabetes). The 90th percentile of the Homeostasis Model Assessment index distribution was used to obtain the ideal cut-off for insulin resistance. We also selected a validation cohort of 300 individuals (no exclusion criteria applied). RESULTS: From 7 000 individuals, and after the exclusion criteria, there were left 1 784 individuals. The 90th percentile for Homeostasis Model Assessment index was 2.33. In the validation cohort, applying that cut-off, we have 49.3% of individuals with insulin resistance. However, only 69.9% of the metabolic syndrome patients had insulin resistance according to that cut-off. By ROC curve analysis, the ideal cut-off for metabolic syndrome is 2.41. Homeostasis Model Assessment index correlated with BMI (r = 0.371, p < 0.001) and is an independent predictor of the presence of metabolic syndrome (OR 19.4, 95% CI 6.6 - 57.2, p < 0.001). DISCUSSION: Our study showed that in a Portuguese population of patients admitted electively in a Cardiology ward, 2.33 is the Homeostasis Model Assessment index cut-off for insulin resistance and 2.41 for metabolic syndrome. CONCLUSION: Homeostasis Model Assessment index is directly correlated with BMI and is an independent predictor of metabolic syndrome.

Blood pressure change and outcome in acute ischemic stroke: the impact of baseline values, previous hypertensive disease and previous antihypertensive treatment.

BACKGROUND: Management of blood pressure (BP) in acute ischemic stroke is controversial. The present study aims to explore the association between baseline BP levels and BP change and outcome in the overall stroke population and in specific subgroups with regard to the presence of arterial hypertensive disease and prior antihypertensive treatment. METHODS: All patients registered in the Acute STroke Registry and Analysis of Lausanne (ASTRAL) between 2003 and 2009 were analyzed. Unfavorable outcome was defined as modified Rankin score more than 2. A local polynomial surface algorithm was used to assess the effect of BP values on outcome in the overall population and in predefined subgroups. RESULTS: Up to a certain point, as initial BP was increasing, optimal outcome was seen with a progressively more substantial BP decrease over the next 24-48 h. Patients without hypertensive disease and an initially low BP seemed to benefit from an increase of BP. In patients with hypertensive disease, initial BP and its subsequent changes seemed to have less influence on clinical outcome. Patients who were previously treated with antihypertensives did not tolerate initially low BPs well. CONCLUSION: Optimal outcome in acute ischemic stroke may be determined not only by initial BP levels but also by the direction and magnitude of associated BP change over the first 24-48 h.

The composition of mineral waters sourced from Europe and North America in respect to bone health: composition of mineral water optimal for bone.

The consumption of mineral waters is increasing in industrialised countries. High intakes of Ca and other alkalising cations as well as a low acid intake are beneficial to bone. We examined which components of mineral waters are conditioning their Ca content and their alkalinising power, in order to define the optimal profile. European mineral waters were randomly selected on the Internet: 100 waters with less than 200 mg Ca/l (9.98 mEq/l) and fifty with more than 200 mg/l, all with complete data for SO4, P, Cl, Na, K, Mg and Ca, and most also for HCO3. For comparison, forty North American mineral waters were randomly chosen. The potential renal acid load (PRAL) was calculated for each mineral water. North American waters did not reveal significant results because of their low mineralisation. We performed correlations between all eight components in order to explore the properties of the mineral waters. In the European waters, twenty-six out of twenty-eight correlations showed a P value of <or= 0.01. In waters with PRAL >0 (acidifying waters), PRAL was positively correlated with SO4, Ca, K and Mg (P < 0.001). In those with PRAL < 0 (alkalinising waters), PRAL was negatively correlated with HCO3, Na, Mg, Ca, K, Cl and SO4 (P < 0.001). SO4 and HCO3 were not found together in high quantities in the same water for geochemical reasons. A high Ca content is associated with either a high SO4 or a high HCO3 content. SO4 theoretically increases Ca excretion, while HCO3 and low PRAL values are associated with positive effects on bone. Therefore, the best waters for bone health are rich in both HCO3 and Ca, and by consequence low in SO4.

Is PaCO2 management optimal under controlled mechanical ventilation (CMV) during neuro-resuscitation?

INTRODUCTION. Both hypocapnia and hypercapnia can be deleterious to brain injured patients. Strict PaCO2 control is difficult to achieve because of patient's instability and unpredictable effects of ventilator settings changes. OBJECTIVE. The aim of this study was to evaluate our ability to comply with a protocol of controlled mechanical ventilation (CMV) aiming at a PaCO2 between 35 and 40 mmHg in patients requiring neuro-resuscitation. METHODS. Retrospective analysis of consecutive patients (2005-2011) requiring intracranial pressure (ICP) monitoring for traumatic brain injury (TBI), subarachnoid haemorrhage (SAH), intracranial haemorrhage (ICH) or ischemic stroke (IS). Demographic data, GCS, SAPS II, hospital mortality, PaCO2 and ICP values were recorded. During CMV in the first 48 h after admission, we analyzed the time spent within the PaCO2 target in relation to the presence or absence of intracranial hypertension (ICP[20 mmHg, by periods of 30 min) (Table 1). We also compared the fraction of time (determined by linear interpolation) spent with normal, low or high PaCO2 in hospital survivors and non-survivors (Wilcoxon, Bonferroni correction, p\0.05) (Table 2). PaCO2 samples collected during and after apnoea tests were excluded. Results given as median [IQR]. RESULTS. 436 patients were included (TBI: 51.2 %, SAH: 20.6 %, ICH: 23.2 %, IS: 5.0 %), age: 54 [39-64], SAPS II score: 52 [41-62], GCS: 5 [3-8]. 8744 PaCO2 samples were collected during 150611 h of CMV. CONCLUSIONS. Despite a high number of PaCO2 samples collected (in average one sample every 107 min), our results show that patients undergoing CMV for neuro- resuscitation spent less than half of the time within the pre-defined PaCO2 range. During documented intracranial hypertension, hypercapnia was observed in 17.4 % of the time. Since non-survivors spent more time with hypocapnia, further analysis is required to determine whether hypocapnia was detrimental per se, or merely reflects increased severity of brain insult.

Assessment of left coronary artery beat-to-beat repositioning in order to propose an optimal acquisition window for coronary MRA

Introduction: Coronary magnetic resonance angiography (MRA) is a medical imaging technique that involves collecting data from consecutive heartbeats, always at the same time in the cardiac cycle, in order to minimize heart motion artifacts. This technique relies on the assumption that coronary arteries always follow the same trajectory from heartbeat to heartbeat. Until now, choosing the acquisition window in the cardiac cycle was based exclusively on the position of minimal coronary motion. The goal of this study was to test the hypothesis that there are time intervals during the cardiac cycle when coronary beat-to-beat repositioning is optimal. The repositioning uncertainty values in these time intervals were then compared with the intervals of low coronary motion in order to propose an optimal acquisition window for coronary MRA. Methods: Cine breath-hold x-ray angiograms with synchronous ECG were collected from 11 patients who underwent elective routine diagnostic coronarography. Twenty-three bifurcations of the left coronary artery were selected as markers to evaluate repositioning uncertainty and velocity during cardiac cycle. Each bifurcation was tracked by two observers, with the help of a user-assisted algorithm implemented in Matlab (The Mathworks, Natick, MA, USA) that compared the trajectories of the markers coming from consecutive heartbeats and computed the coronary repositioning uncertainty with steps of 50ms until 650ms after the R-wave. Repositioning uncertainty was defined as the diameter of the smallest circle encompassing the points to be compared at the same time after the R-wave. Student's t-tests with a false discovery rate (FDR, q=0.1) correction for multiple comparison were applied to see whether coronary repositioning and velocity vary statistically during cardiac cycle. Bland-Altman plots and linear regression were used to assess intra- and inter-observer agreement. Results: The analysis of left coronary artery beat-to-beat repositioning uncertainty shows a tendency to have better repositioning in mid systole (less than 0.84±0.58mm) and mid diastole (less than 0.89±0.6mm) than in the rest of the cardiac cycle (highest value at 50ms=1.35±0.64mm). According to Student's t-tests with FDR correction for multiple comparison (q=0.1), two intervals, in mid systole (150-200ms) and mid diastole (550-600ms), provide statistically better repositioning in comparison with the early systole and the early diastole. Coronary velocity analysis reveals that left coronary artery moves more slowly in end systole (14.35±11.35mm/s at 225ms) and mid diastole (11.78±11.62mm/s at 625ms) than in the rest of the cardiac cycle (highest value at 25ms: 55.96±22.34mm/s). This was confirmed by Student's t-tests with FDR correction for multiple comparison (q=0.1, FDR-corrected p-value=0.054): coronary velocity values at 225, 575 and 625ms are not much different between them but they are statistically inferior to all others. Bland-Altman plots and linear regression show that intra-observer agreement (y=0.97x+0.02 with R²=0.93 at 150ms) is better than inter-observer (y=0.8x+0.11 with R²=0.67 at 150ms). Discussion: The present study has demonstrated that there are two time intervals in the cardiac cycle, one in mid systole and one in mid diastole, where left coronary artery repositioning uncertainty reaches points of local minima. It has also been calculated that the velocity is the lowest in end systole and mid diastole. Since systole is less influenced by heart rate variability than diastole, it was finally proposed to test an acquisition window between 150 and 200ms after the R-wave.

Detection of Optimal Models in Parameter Space with Support Vector Machines

The paper proposes an approach aimed at detecting optimal model parameter combinations to achieve the most representative description of uncertainty in the model performance. A classification problem is posed to find the regions of good fitting models according to the values of a cost function. Support Vector Machine (SVM) classification in the parameter space is applied to decide if a forward model simulation is to be computed for a particular generated model. SVM is particularly designed to tackle classification problems in high-dimensional space in a non-parametric and non-linear way. SVM decision boundaries determine the regions that are subject to the largest uncertainty in the cost function classification, and, therefore, provide guidelines for further iterative exploration of the model space. The proposed approach is illustrated by a synthetic example of fluid flow through porous media, which features highly variable response due to the parameter values' combination.

The role of moral values in the economic analysis of crime: A general equilibrium approach

In this paper, we develop a general equilibrium model of crime and show thatlaw enforcement has different roles depending on the equilibrium characterization and the value of social norms. When an economy has a unique stable equilibrium where a fraction of the population is productive and the remaining predates, the government can choose an optimal law enforcement policy to maximize a welfare function evaluated at the steady state. If such steady state is not unique, law enforcement is still relevant but in a completely different way because the steady state that prevails depends on the initial proportions of productive and predator individuals in the economy. The relative importance of these proportions can be changed through law enforcement policy.

Erste Resultate der HOT-Studie in der Schweiz. [Initial results of the HOT-study in Switzerland (hypertension optimal treatment)]

The HOT study (hypertension-optimal treatment) is an international clinical study on primary prevention of cardiovascular events in 19,193 hypertensive patients worldwide. It aims at the recognition of the optimal diastolic blood pressure value (< 90, < 85 or < 80 mmHg?) in order to maximize the possible benefit of an antihypertensive therapy. In addition, the HOT study investigates whether low doses of aspirin (75 mg/day) are able to reduce the occurrence of severe cardiovascular events. In Switzerland a total of 797 patients have been enrolled in the study. Antihypertensive therapy was initiated with felodipine = Plendil (5 mg/day). This vasoelective calcium antagonist could reduce diastolic blood pressure values to < 90 or < 80 mg/Hg, respectively, in one of two or one of three patients within the first three months. In nine or six patients, respectively out of ten a reduction of diastolic blood pressure values to < 90 or < 80 mmHg was reached within one year by combination of felodipine with other antihypertensive drugs (ACE inhibitors, beta blockers and diuretics).

Continuous determination of optimal cerebral perfusion pressure in traumatic brain injury.

OBJECTIVES: We have sought to develop an automated methodology for the continuous updating of optimal cerebral perfusion pressure (CPPopt) for patients after severe traumatic head injury, using continuous monitoring of cerebrovascular pressure reactivity. We then validated the CPPopt algorithm by determining the association between outcome and the deviation of actual CPP from CPPopt. DESIGN: Retrospective analysis of prospectively collected data. SETTING: Neurosciences critical care unit of a university hospital. PATIENTS: A total of 327 traumatic head-injury patients admitted between 2003 and 2009 with continuous monitoring of arterial blood pressure and intracranial pressure. MEASUREMENTS AND MAIN RESULTS: Arterial blood pressure, intracranial pressure, and CPP were continuously recorded, and pressure reactivity index was calculated online. Outcome was assessed at 6 months. An automated curve fitting method was applied to determine CPP at the minimum value for pressure reactivity index (CPPopt). A time trend of CPPopt was created using a moving 4-hr window, updated every minute. Identification of CPPopt was, on average, feasible during 55% of the whole recording period. Patient outcome correlated with the continuously updated difference between median CPP and CPPopt (chi-square=45, p<.001; outcome dichotomized into fatal and nonfatal). Mortality was associated with relative "hypoperfusion" (CPP<CPPopt), severe disability with "hyperperfusion" (CPP>CPPopt), and favorable outcome was associated with smaller deviations of CPP from the individualized CPPopt. While deviations from global target CPP values of 60 mm Hg and 70 mm Hg were also related to outcome, these relationships were less robust. CONCLUSIONS: Real-time CPPopt could be identified during the recording time of majority of the patients. Patients with a median CPP close to CPPopt were more likely to have a favorable outcome than those in whom median CPP was widely different from CPPopt. Deviations from individualized CPPopt were more predictive of outcome than deviations from a common target CPP. CPP management to optimize cerebrovascular pressure reactivity should be the subject of future clinical trial in severe traumatic head-injury patients.

Optimal use of SSR markers for varietal identification of upland cotton

Abstract: The objective of this work was to identify polymorphic simple sequence repeat (SSR) markers for varietal identification of cotton and evaluation of the genetic distance among the varieties. Initially, 92 SSR markers were genotyped in 20 Brazilian cotton cultivars. Of this total, 38 loci were polymorphic, two of which were amplified by one primer pair; the mean number of alleles per locus was 2.2. The values of polymorphic information content (PIC) and discrimination power (DP) were, on average, 0.374 and 0.433, respectively. The mean genetic distance was 0.397 (minimum of 0.092 and maximum of 0.641). A panel of 96 varieties originating from different regions of the world was assessed by 21 polymorphic loci derived from 17 selected primer pairs. Among these varieties, the mean genetic distance was 0.387 (minimum of 0 and maximum of 0.786). The dendrograms generated by the unweighted pair group method with arithmetic average (UPGMA) did not reflect the regions of Brazil (20 genotypes) or around the world (96 genotypes), where the varieties or lines were selected. Bootstrap resampling shows that genotype identification is viable with 19 loci. The polymorphic markers evaluated are useful to perform varietal identification in a large panel of cotton varieties and may be applied in studies of the species diversity.

Mathematical modeling and optimal control of malaria

Malaria continues to infect millions and kill hundreds of thousands of people worldwide each year, despite over a century of research and attempts to control and eliminate this infectious disease. Challenges such as the development and spread of drug resistant malaria parasites, insecticide resistance to mosquitoes, climate change, the presence of individuals with subpatent malaria infections which normally are asymptomatic and behavioral plasticity in the mosquito hinder the prospects of malaria control and elimination. In this thesis, mathematical models of malaria transmission and control that address the role of drug resistance, immunity, iron supplementation and anemia, immigration and visitation, and the presence of asymptomatic carriers in malaria transmission are developed. A within-host mathematical model of severe Plasmodium falciparum malaria is also developed. First, a deterministic mathematical model for transmission of antimalarial drug resistance parasites with superinfection is developed and analyzed. The possibility of increase in the risk of superinfection due to iron supplementation and fortification in malaria endemic areas is discussed. The model results calls upon stakeholders to weigh the pros and cons of iron supplementation to individuals living in malaria endemic regions. Second, a deterministic model of transmission of drug resistant malaria parasites, including the inflow of infective immigrants, is presented and analyzed. The optimal control theory is applied to this model to study the impact of various malaria and vector control strategies, such as screening of immigrants, treatment of drug-sensitive infections, treatment of drug-resistant infections, and the use of insecticide-treated bed nets and indoor spraying of mosquitoes. The results of the model emphasize the importance of using a combination of all four controls tools for effective malaria intervention. Next, a two-age-class mathematical model for malaria transmission with asymptomatic carriers is developed and analyzed. In development of this model, four possible control measures are analyzed: the use of long-lasting treated mosquito nets, indoor residual spraying, screening and treatment of symptomatic, and screening and treatment of asymptomatic individuals. The numerical results show that a disease-free equilibrium can be attained if all four control measures are used. A common pitfall for most epidemiological models is the absence of real data; model-based conclusions have to be drawn based on uncertain parameter values. In this thesis, an approach to study the robustness of optimal control solutions under such parameter uncertainty is presented. Numerical analysis of the optimal control problem in the presence of parameter uncertainty demonstrate the robustness of the optimal control approach that: when a comprehensive control strategy is used the main conclusions of the optimal control remain unchanged, even if inevitable variability remains in the control profiles. The results provide a promising framework for the design of cost-effective strategies for disease control with multiple interventions, even under considerable uncertainty of model parameters. Finally, a separate work modeling the within-host Plasmodium falciparum infection in humans is presented. The developed model allows re-infection of already-infected red blood cells. The model hypothesizes that in severe malaria due to parasite quest for survival and rapid multiplication, the Plasmodium falciparum can be absorbed in the already-infected red blood cells which accelerates the rupture rate and consequently cause anemia. Analysis of the model and parameter identifiability using Markov chain Monte Carlo methods is presented.

Optimal Recycling Combination of Ash in South-East Finland

The present world energy production is heavily relying on the combustion of solid fuels like coals, peat, biomass, municipal solid waste, whereas the share of renewable fuels is anticipated to increase in the future to mitigate climate change. In Finland, peat and wood are widely used for energy production. In any case, the combustion of solid fuels results in generation of several types of thermal conversion residues, such as bottom ash, fly ash, and boiler slag. The predominant residue type is determined by the incineration technology applied, while its composition is primarily relevant to the composition of fuels combusted. An extensive research has been conducted on technical suitability of ash for multiple recycling methods. Most of attention was drawn to the recycling of the coal combustion residues, as coal is the primary solid fuel consumed globally. The recycling methods of coal residues include utilization in a cement industry, in concrete manufacturing, and mine backfilling, to name few. Biomass combustion residues were also studied to some extent with forest fertilization, road construction, and road stabilization being the predominant utilization options. Lastly, residues form municipal solid waste incineration attracted more attention recently following the growing number of waste incineration plants globally. The recycling methods of waste incineration residues are the most limited due to its hazardous nature and varying composition, and include, among others, landfill construction, road construction, mine backfilling. In the study, environmental and economic aspects of multiple recycling options of thermal conversion residues generated within a case-study area were studied. The case-study area was South-East Finland. The environmental analysis was performed using an internationally recognized methodology — life cycle assessment. Economic assessment was conducted applying a widely used methodology — cost-benefit analysis. Finally, the results of the analyses were combined to enable easier comparison of the recycling methods. The recycling methods included the use of ash in forest fertilization, road construction, road stabilization, and landfill construction. Ash landfilling was set as a baseline scenario. Quantitative data about the amounts of ash generated and its composition was obtained from companies, their environmental reports, technical reports and other previously published literature. Overall, the amount of ash in the case-study area was 101 700 t. However, the data about 58 400 t of fly ash and 35 100 t of bottom ash and boiler slag were included in the study due to lack of data about leaching of heavy metals in some cases. The recycling methods were modelled according to the scientific studies published previously. Overall, the results of the study indicated that ash utilization for fertilization and neutralization of 17 600 ha of forest was the most economically beneficial method, which resulted in the net present value increase by 58% compared to ash landfilling. Regarding the environmental impact, the use of ash in the construction of 11 km of roads was the most attractive method with decreased environmental impact of 13% compared to ash landfilling. The least preferred method was the use of ash for landfill construction since it only enabled 11% increase of net present value, while inducing additional 1% of negative impact on the environment. Therefore, a following recycling route was proposed in the study. Where possible and legally acceptable, recycle fly and bottom ash for forest fertilization, which has strictest requirements out of all studied methods. If the quality of fly ash is not suitable for forest fertilization, then it should be utilized, first, in paved road construction, second, in road stabilization. Bottom ash not suitable for forest fertilization, as well as boiler slag, should be used in landfill construction. Landfilling should only be practiced when recycling by either of the methods is not possible due to legal requirements or there is not enough demand on the market. Current demand on ash and possible changes in the future were assessed in the study. Currently, the area of forest fertilized in the case-study are is only 451 ha, whereas about 17 600 ha of forest could be fertilized with ash generated in the region. Provided that the average forest fertilizing values in Finland are higher and the area treated with fellings is about 40 000 ha, the amount of ash utilized in forest fertilization could be increased. Regarding road construction, no new projects launched by the Center of Economic Development, Transport and the Environment in the case-study area were identified. A potential application can be found in the construction of private roads. However, no centralized data about such projects is available. The use of ash in stabilization of forest roads is not expected to increased in the future with a current downwards trend in the length of forest roads built. Finally, the use of ash in landfill construction is not a promising option due to the reducing number of landfills in operation in Finland.

Photochemical cross-linking of plastically compressed collagen gel produces an optimal scaffold for corneal tissue engineering

The experiments were designed to use photochemically cross-linked plastically compressed collagen (PCPCC) gel to support corneal epithelial cells. A plastically compressed collagen (PCC) scaffold was photo cross-linked by UVA in the presence of riboflavin to form a biomaterial with optimal mechanical properties. The breaking force, rheology, surgical suture strength, transparency, ultrastructure, and cell-based biocompatibility were compared between PCPCC and PCC gels. The breaking force increased proportionally with an increased concentration of riboflavin. The stress required to reach breaking point of the PCPCC scaffolds was over two times higher compared to the stress necessary to break PCC scaffolds in the presence of 0.1% riboflavin. Rheology results indicated that the structural properties of PCC remain unaltered after UVA cross-linking. The PCC gels were more easily broken than PCPCC gels when sutured on to bovine corneas. The optical density values of PCPCC and PCC showed no significant differences (p > 0.05). SEM analyses showed that the collagen fibres within the PCPCC gels were similar in morphology to PCC gels. No difference in cell-based biocompatibility was seen between the PCPCC and PCC scaffolds in terms of their ability to support the ex vivo expansion of corneal epithelial cells or their subsequent differentiation evidenced by similar levels of cytokeratin 14. In conclusion, PCPCC scaffold is an optimal biomaterial for use in therapeutic tissue engineering of the cornea.

Estimation of optimal gravity wave parameters for climate models using data assimilation

There is a current need to constrain the parameters of gravity wave drag (GWD) schemes in climate models using observational information instead of tuning them subjectively. In this work, an inverse technique is developed using data assimilation principles to estimate gravity wave parameters. Because mostGWDschemes assume instantaneous vertical propagation of gravity waves within a column, observations in a single column can be used to formulate a one-dimensional assimilation problem to estimate the unknown parameters. We define a cost function that measures the differences between the unresolved drag inferred from observations (referred to here as the ‘observed’ GWD) and the GWD calculated with a parametrisation scheme. The geometry of the cost function presents some difficulties, including multiple minima and ill-conditioning because of the non-independence of the gravity wave parameters. To overcome these difficulties we propose a genetic algorithm to minimize the cost function, which provides a robust parameter estimation over a broad range of prescribed ‘true’ parameters. When real experiments using an independent estimate of the ‘observed’ GWD are performed, physically unrealistic values of the parameters can result due to the non-independence of the parameters. However, by constraining one of the parameters to lie within a physically realistic range, this degeneracy is broken and the other parameters are also found to lie within physically realistic ranges. This argues for the essential physical self-consistency of the gravity wave scheme. A much better fit to the observed GWD at high latitudes is obtained when the parameters are allowed to vary with latitude. However, a close fit can be obtained either in the upper or the lower part of the profiles, but not in both at the same time. This result is a consequence of assuming an isotropic launch spectrum. The changes of sign in theGWDfound in the tropical lower stratosphere, which are associated with part of the quasi-biennial oscillation forcing, cannot be captured by the parametrisation with optimal parameters.