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In this study, we consider three different machine‐learning methods—a three‐hidden‐layer neural network, support vector regression, and Gaussian process regression—and compare how well they can learn from a synthetic data set for proton acceleration in the Target Normal Sheath Acceleration regime. The synthetic data set was generated from a previously published theoretical model by Fuchs et al. 2005 that we modified. Once trained, these machine‐learning methods can assist with efforts to maximize the peak proton energy, or with the more general problem of configuring the laser system to produce a proton energy spectrum with desired characteristics. In our study, we focus on both the accuracy of the machine‐learning methods and the performance on one GPU including memory consumption. Although it is arguably the least sophisticated machine‐learning model we considered, support vector regression performed very well in our tests. 

Temporal text data, such as news articles or Twitter feeds, often comprises a mixture of long-lasting trends and transient topics. Effective topic modeling strategies should detect both types and clearly locate them in time. We first demonstrate that nonnegative CANDECOMP/PARAFAC decomposition (NCPD) can automatically identify topics of variable persistence. We then introduce sparseness-constrained NCPD (S-NCPD) and its online variant to control the duration of the detected topics more effectively and efficiently, along with theoretical analysis of the proposed algorithms. Through an extensive study on both semi-synthetic and real-world datasets, we find that our S-NCPD and its online variant can identify both short- and long-lasting temporal topics in a quantifiable and controlled manner, which traditional topic modeling methods are unable to achieve. Additionally, the online variant of S-NCPD shows a faster reduction in reconstruction error and results in more coherent topics compared to S-NCPD, thus achieving both computational efficiency and quality of the resulting topics. Our findings indicate that S-NCPD and its online variant are effective tools for detecting and controlling the duration of topics in temporal text data, providing valuable insights into both persistent and transient trends. 

Population pharmacokinetic (PK) modeling has become a cornerstone of drug development and optimal patient dosing. This approach offers great benefits for datasets with sparse sampling, such as in pediatric patients, and can describe between-patient variability. While most current algorithms assume normal or log-normal distributions for PK parameters, we present a mathematically consistent nonparametric maximum likelihood (NPML) method for estimating multivariate mixing distributions without any assumption about the shape of the distribution. This approach can handle distributions with any shape for all PK parameters. It is shown in convexity theory that the NPML estimator is discrete, meaning that it has finite number of points with nonzero probability. In fact, there are at most N points where N is the number of observed subjects. The original infinite NPML problem then becomes the finite dimensional problem of finding the location and probability of the support points. In the simplest case, each point essentially represents the set of PK parameters for one patient. The probability of the points is found by a primal-dual interior-point method; the location of the support points is found by an adaptive grid method. Our method is able to handle high-dimensional and complex multivariate mixture models. An important application is discussed for the problem of population pharmacokinetics and a nontrivial example is treated. Our algorithm has been successfully applied in hundreds of published pharmacometric studies. In addition to population pharmacokinetics, this research also applies to empirical Bayes estimation and many other areas of applied mathematics. Thereby, this approach presents an important addition to the pharmacometric toolbox for drug development and optimal patient dosing.