Managing epidemics requires to investigate potential impact of risk and protective factors on epidemiological links. Here we focus on links defined by inferred probabilities (transmission links in Equine Influenza, similarity measures of COVID-19 dynamics between different countries). The specific nature of these epidemiological data (zero-inflated, correlated, continuous and bounded) does not allow to use classical supervised methods like linear regression or decision tree to identify impacting factors on the response variable. In this article we propose a by block-permutation-based methodology (i) to identify factors (discrete or continuous) that are potentially significant, (ii) to define a performance indicator to quantify the percentage of correlation explained by the significant factors subset. The methodology is illustrated on simulated data and on the above-mentioned epidemics.
Discrepancies in population structures, decision making, health systems and numerous other factors result in various COVID-19-mortality dynamics at country scale, and make the forecast of deaths in a country under focus challenging. However, mortality dynamics of countries that are ahead of time implicitly include these factors and can be used as real-life competing predicting models. We precisely propose such a data-driven approach implemented in a publicly available web app timely providing mortality curves comparisons and real-time short-term forecasts for about 100 countries. Here, the approach is applied to compare the mortality trajectories of second-line and front-line European countries facing the COVID-19 epidemic wave. Using data up to mid-April, we show that the second-line countries generally followed relatively mild mortality curves rather than fast and severe ones. Thus, the continuation, after mid-April, of the COVID-19 wave across Europe was likely to be mitigated and not as strong as it was in most of the front-line countries first impacted by the wave (this prediction is corroborated by posterior data).
In the robust shape optimization context, the evaluation cost of numerical models is reduced by the use of a response surface. Multi-objective methodologies for robust optimization that consist in simultaneously minimizing the expectation and variance of a function have already been developed to answer to this question. However, efficient estimation in the framework of time-consuming simulation has not been completely explored. In this paper, a robust optimization procedure based on Taylor expansion, kriging prediction and a genetic NSGA-II algorithm is proposed. The two objectives are the Taylor expansion of expectation and variance. The kriging technique is chosen to surrogate the function and its derivatives. Afterwards, NSGA-II is performed on kriging response surfaces or kriging expected improvements to construct a Pareto front. One point or a batch of points is chosen carefully to enrich the learning set of the model. When the budget is reached the non-dominated points provide designs that make compromises between optimization and robustness. Seven relevant strategies based on this main procedure are detailed and compared in two test functions (2D and 6D). In each case, the results are compared when the derivatives are observed and when they are not. The procedure is also applied to an industrial case study where the objective is to optimize the shape of a motor fan.
In the context of computer experiments, metamodels are largely used to represent the output of computer codes. Among these models, Gaussian process regression (kriging) is very efficient see e.g Snelson (Flexible and efficient Gaussian process models for machine learning. ProQuest LLC, Ann Arbor, MI. Thesis (Ph.D.)–University of London, University College London, London, 2008). In high dimension that is with a large number of input variables, but with few observations, the estimation of the parameters with a classical anisotropic kriging can be completely inaccurate. Because there are equal numbers of ranges and input variables the optimization space becomes too large compared to available information. One way to overcome this drawback is to use an isotropic kernel that only depends on one parameter. However this model is too restrictive. The aim of this paper is twofold. Our first objective is to propose a smooth kernel with as few parameters as warranted. We introduce a kernel which is a tensor product of few isotropic kernels built on well-chosen subgroup of variables. The main difficulty is to find the number and the composition of the groups. Our second objective is to propose algorithmic strategies to overcome this difficulty. Four forward strategies are proposed. They all start with the simplest isotropic kernel and stop when the best model according to BIC criterion is found. They all show very good accuracy results on simulation test cases. But one of them is more efficient. Tested on a real data set, our kernel shows very good prediction results.
Felids show remarkable phenotypic similarities and are conservative in behavioral and ecological traits. In contrast, they display a large range in body mass from around 1 kg to more than 300 kg. Body size and locomotory specializations correlate to skull, limb and vertebral skeleton morphology. With an increase in body mass, felids prey selection switches from small to large, from using a rapid skull or spine lethal bite for small prey, to sustained suffocating bite for large prey. Dietary specialization correlates to skull and front limbs morphology but no correlation was found on the spine or on the hind limb. The morphology of the sacroiliac junction in relation to ecological factors remained to be described. We are presenting a study of the overall shape of the iliac auricular surface with qualitative and quantitative analyses of its morphology. Our results demonstrate that body mass, prey selection, and bite type, crucially influence the auricular surface, where no significant effect of locomotor specialization was found. The outline of the surface is significantly more elevated dorso-caudally and the joint surface shows an irregular W-shape topography in big cats whereas the surface in small cats is smoother with a C-shape topography and less of an elevated ridge. Biomechanically, we suggest that a complex auricular surface increases joint stiffness and provides more support in heavier cats, an advantage for subduing big prey successfully during a sustained bite.
In the context of robust shape optimization, the estimation cost of some physical models is reduce with the use of a response surface. A procedure that requires the estimation of moment 1 and 2 is set up for the robust optimization. The step of the optimization procedure and the partitioning of Pareto front are already developed in the literature. However, the research of a criteria to estimate the robustness of each solution at each iteration is not much explored. The function, the first and second derivatives is given by the majority of industrial code. We propose a robust optimization procedure that based on the prediction of the function and its derivatives predicted by a kriging with a Matern 5/2 covariance kernel. The modeling of the second derivative and consequently the prediction of first and the second derivatives are possible with this kernel. In this context we propose to consider the Taylor theorem calculated in each point of the conception space to approximate the variation around these points. This criterion is used as the replacement of the moment 2 usually employed. A Pareto front of the robust solutions (minimization of the function and the robustness criteria) is generated by a genetic algorithm named NSGA-II. This algorithm gives a Pareto front in an reasonable time of calculation. We show the motivations of this method with an academic example.