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In this work we address the problem of rigorously evaluating the performances of a inertial navigation system under design in presence of multiple alternative choices. We introduce a framework based on Monte-Carlo simulations in which a standard extended Kalman filter is coupled with realistic and user-configurable noise generation mechanisms and attempts to recover a reference trajectory from noisy measurements. The evaluation of several statistical metrics of the solution, aggregated over hundreds of realizations, gives a reasonable estimate of the expected performances of the system in real-world conditions and allow the user to operate the choice between alternative setups. To show the generality of our approach, we consider an example application to the problem of stochastic calibration. Two competing stochastic modeling techniques, namely, the widely popular Allan variance linear regression, and the emerging generalised method of wavelet moments are rigorously compared in terms of the framework defined metrics and in multiple scenarios. We find that the latter provides substantial advantages and should be preferred, at least for certain classes of inertial sensors. Our framework allows to consider a wide range of problems related to the quantification of navigation system performances such as, for example, the robustness of an INS with respect to outliers or other modeling imperfections. While real world experiments are essential to assess to performance of new methods they tend to be costly and are typically unable to lead to a sufficient number of replicates to evaluate, for example, the correctness of estimated uncertainty. Therefore, our method can bridge the gap between these experiments and pure statistical consideration as done, for example, in the stochastic calibration literature.

The Global Navigation Satellite System (GNSS) daily position time series are often described as the sum of stochastic processes and geophysical signals which allow studying global and local geodynamical effects such as plate tectonics, earthquakes, or ground water variations. In this work we propose to extend the Generalized Method of Wavelet Moments (GMWM) to estimate the parameters of linear models with correlated residuals. This statistical inferential framework is applied to GNSS daily position time series data to jointly estimate functional (geophysical) as well as stochastic noise models. Our method is called GMWMX, with X standing for eXogeneous variable: it is semi-parametric, computationally efficient and scalable. Unlike standard methods such as the widely used Maximum Likelihood Estimator (MLE), our methodology offers statistical guarantees, such as consistency and asymptotic normality, without relying on strong parametric assumptions. At the Gaussian model, our results show that the estimated parameters are similar to the ones obtained with the MLE. The computational performances of our approach has important practical implications. Indeed, the estimation of the parameters of large networks of thousands of GNSS stations quickly becomes computationally prohibitive. Compared to standard methods, the processing time of the GMWMX is over $1000$ times faster and allows the estimation of large scale problems within minutes on a standard computer. We validate the performances of our method via Monte-Carlo simulations by generating GNSS daily position time series with missing observations and we consider composite stochastic noise models including processes presenting long-range dependence such as power-law or Mat\'ern processes. The advantages of our method are also illustrated using real time series from GNSS stations located in the Eastern part of the USA., Comment: 30 pages, 11 figures, 3 tables

Background Medical schools can contribute to the insufficient primary care physician workforce by influencing students’ career preferences. Primary care career choice evolves between matriculation and graduation and is influenced by several individual and contextual factors. This study explored the longitudinal dynamics of primary care career intentions and the association of students’ motives for becoming doctors with these intentions in a cohort of undergraduate medical students followed over a four-year period. Methods The sample consisted of medical students from two classes recruited into a cohort study during their first academic year, and who completed a yearly survey over a four-year period from their third (end of pre-clinical curriculum) to their sixth (before graduation) academic year. Main outcome measures were students’ motives for becoming doctors (ten motives rated on a 6-point scale) and career intentions (categorized into primary care, non-primary care, and undecided). Population-level flows of career intentions were investigated descriptively. Changes in the rating of motives over time were analyzed using Wilcoxon tests. Two generalized linear mixed models were used to estimate which motives were associated with primary care career intentions. Results The sample included 217 students (60% females). Career intentions mainly evolved during clinical training, with smaller changes at the end of pre-clinical training. The proportion of students intending to practice primary care increased over time from 12.8% (year 3) to 24% (year 6). Caring for patients was the most highly rated motive for becoming a doctor. The importance of the motives cure diseases, saving lives, and vocation decreased over time. Primary care career intentions were positively associated with the motives altruism and private practice, and negatively associated with the motives prestige, academic interest and cure diseases. Conclusion Our study indicates that career intentions are not fixed and change mainly during clinical training, supporting the influence of clinical experiences on career-related choices. The impact of students’ motives on primary care career choice suggests strategies to increase the attractivity of this career, such as reinforcing students’ altruistic values and increasing the academic recognition of primary care.

Different inertial sensor calibration techniques have been proposed to consider the sources of measurement error from inertial sensors. There has been a significant amount of literature which studies the stochastic errors calibration of such devices. The recent results of [1] have proved that among all possible methods the (Generalized Method of Wavelet Moments) (GMWM) presents various optimality and is computationally reliable. However, the GMWM estimators depend on weight matrix which considerably impact the quality of the estimated stochastic error models. In addition, such models are made of different components (typically high-frequency and low-frequency components) whose impacts on navigation vary depending on the context. For example, the high-frequency component of the error model may be more important when considering low-cost IMUs mounted on small size drones used for short-term missions. On the other hand, the situation may be reversed when considering navigational grade IMUs used, often autonomously, for long-term missions. With these differences, one may wish to select a GMWM estimator whose weight matrix has been tailored to estimate more reliably the elements of an error model believed to have the greatest impacts on navigation accuracy. In this article, we provide a formal answer to this question by proposing an optimally weighted GMWM estimator. Our results show that the proposed estimator is optimal for all parameters of the sensor error model we wish to estimate with the smallest possible uncertainty of the estimation. Therefore, regardless of the application, and independently of the context, the same optimally weighted estimator can be employed.

Background We propose a new approach for designing personalized treatment for colorectal cancer (CRC) patients, by combining ex vivo organoid efficacy testing with mathematical modeling of the results., Methods The validated phenotypic approach called Therapeutically Guided Multidrug Optimization ( TGMO) was used to identify four low-dose synergistic optimized drug combinations (ODC) in 3D human CRC models of cells that are either sensitive or resistant to first-line CRC chemotherapy (FOLFOXIRI). Our findings were obtained using second order linear regression and adaptive lasso., Results The activity of all ODCs was validated on patient-derived organoids (PDO) from cases with either primary or metastatic CRC. The CRC material was molecularly characterized using whole-exome sequencing and RNAseq. In PDO from patients with liver metastases (stage IV) identified as CMS4/CRIS-A, our ODCs consisting of regorafenib [1 mM], vemurafenib [11 mM], palbociclib [1 mM] and lapatinib [0.5 mM] inhibited cell viability up to 88%, which significantly outperforms FOLFOXIRI administered at clinical doses. Furthermore, we identified patient-specific TGMO-based ODCs that outperform the efficacy of the current chemotherapy standard of care, FOLFOXIRI., Conclusions Our approach allows the optimization of patient-tailored synergistic multi- drug combinations within a clinically relevant timeframe.