Alona Kryshchenko

We present a framework for maximum likelihood analysis on count observations that begin high and quickly drop to zero, for example, from hollow fiber drug comparison studies. This simulation study focuses on treating observed counts as Poisson or normally distributed for the purpose of estimating infection rebound after effective treatment. CFU profiles were simulated from inoculation to 96 h post‐treatment. The PK‐PD link was an Emax inhibitory model. Random parameters were pathogen growth and natural decay rates, drug concentration for half‐maximal effect, and drug pathogen kill rate. Other parameters, including PK, were fixed. Parameters were adjusted to attain 67% efficacy at 24 h. Random parameter values were optimized for profiles observed at 24, 48, 72, and 96 h assuming each of four probability assumptions: (1) all CFU measurements were Poisson distributed (truth); (2) CFU < 128 were Poisson, higher values were normally distributed; (3) all observations were normally distributed; and (4) observations were normally distributed but CFU < 10 were censored. CFU‐time profiles were re‐simulated using the optimized parameter densities. Rebound percentage (CFU ≥ 10 at 24 h post‐treatment) was best predicted using strategy 2, above. For limited periodically collected time series count data that quickly fall to 0, the true proportion reaching 0 (lack of rebound) was best modeled by assuming Poisson distribution at low counts. At higher counts (≥ 128), assuming normality is reasonable. Censoring observations leads to biased models.

Advances in ultra‐intense laser technology have increased repetition rates and average power for chirped‐pulse laser systems, which offer a promising solution for many applications including energetic proton sources. An important challenge is the need to optimize and control the proton source by varying some of the many degrees of freedom inherent to the laser‐plasma interactions. Machine learning can play an important role in this task, as our work examines. Building on our earlier work in Desai et al. 2024, we generate a large ∼1.5 million data point synthetic data set for proton acceleration using a physics‐informed analytic model that we improved to include pre‐pulse physics. Then, we train different machine learning methods on this data set to determine which methods perform efficiently and accurately. Generally, we find that quasi‐real‐time training of neural network models using single‐shot data from a kHz repetition rate ultra‐intense laser system should typically be feasible on a single GPU. We also find that a less sophisticated model, like a polynomial regression, can be trained even faster and that the accuracy of these models is still good enough to be useful. We provide our source code and example synthetic data for others to test new machine learning methods and approaches to automated learning in this regime.

Randomized iterative algorithms, such as the randomized Kaczmarz method and the randomized Gauss-Seidel method, have gained considerable popularity due to their efficacy in solving matrix-vector and matrix-matrix regression problems. Our present work leverages the insights gained from studying such algorithms to develop regression methods for tensors, which are the natural setting for many application problems, e.g., image deblurring. In particular, we extend two variants of the block-randomized Gauss-Seidel method to solve a t-product tensor regression problem. We additionally develop methods for the special case where the measurement tensor is given in factorized form. We provide theoretical guarantees of the exponential convergence rate of our algorithms, accompanied by illustrative numerical simulations.

To establish bioequivalence (BE) of a generic test formulation with respect to a reference listed drug, it is necessary to demonstrate a comparable rate and extent to which active ingredients reach the site of action. To decrease unnecessary human testing and simulate scenarios involving specific populations or challenges with recruitment or study design, industry and regulators are increasingly considering in silico virtual bioequivalence (VBE) approaches. This tutorial introduces the VBEToolbox R package: a toolbox within the Open Systems Pharmacology framework to streamline and standardize computational VBE workflows. The package integrates in vitro and in vivo data to train pharmacokinetic models through inference of inter‐individual variability from clinical data and establishment of in vitro to in vivo extrapolations. A nonparametric approach is adopted to account for uncertainties from parameter non‐identifiability. The trained model is then applied to determine the study size with statistical power needed to demonstrate BE virtually. The use of the VBE tool is illustrated with two case studies. The first evaluates the VBE of petrolatum and ethylene glycol dermal formulations of testosterone by integrating in vitro skin permeation tests, vehicle/skin partitioning data, testosterone solubility data, and in vivo absorption data in a mechanistic in vitro/in vivo dermal absorption model. The second assesses the VBE of two oral bupropion formulations by integrating in vitro dissolution data in a physiologically based pharmacokinetic model. These case studies highlight essential considerations for model development, training, and extrapolation toward application for VBE assessment.

Randomized iterative algorithms, such as the randomized Kaczmarz method, have gained considerable popularity due to their efficacy in solving matrix-vector and matrix-matrix regression problems. Our present work leverages the insights gained from studying such algorithms to develop regression methods for tensors, which are the natural setting for many application problems, e.g., image deblurring. In particular, we extend the randomized Kaczmarz method to solve a t-product tensor system where the measurement tensor is given in factorized form. We develop variants of the randomized factorized Kaczmarz method for matrices that approximately solve tensor systems in both the consistent and inconsistent regimes. We provide theoretical guarantees of the exponential convergence rate of our algorithms, accompanied by illustrative numerical simulations. Furthermore, we situate our method within a broader context by linking our novel approaches to earlier randomized Kaczmarz methods.

This paper introduces a non-parametric estimation algorithm designed to effectively estimate the joint distribution of model parameters with application to population pharmacokinetics. Our research group has previously developed the non-parametric adaptive grid (NPAG) algorithm, which while accurate, explores parameter space using an ad-hoc method to suggest new support points. In contrast, the non-parametric optimal design (NPOD) algorithm uses a gradient approach to suggest new support points, which reduces the amount of time spent evaluating non-relevant points and by this the overall number of cycles required to reach convergence. In this paper, we demonstrate that the NPOD algorithm achieves similar solutions to NPAG across two datasets, while being significantly more efficient in both the number of cycles required and overall runtime. Given the importance of developing robust and efficient algorithms for determining drug doses quickly in pharmacokinetics, the NPOD algorithm represents a valuable advancement in non-parametric modeling. Further analysis is needed to determine which algorithm performs better under specific conditions.

Inspired from quantum Monte Carlo, by sampling discrete and continuous variables at the same time using the Metropolis–Hastings algorithm, we present a novel, fast, and accurate high performance Monte Carlo Parametric Expectation Maximization (MCPEM) algorithm. We named it Randomized Parametric Expectation Maximization (RPEM). We compared RPEM with NONMEM's Importance Sampling Method (IMP), Monolix's Stochastic Approximation Expectation Maximization (SAEM), and Certara's Quasi‐Random Parametric Expectation Maximization (QRPEM) for a realistic two‐compartment voriconazole model with ordinary differential equations using simulated data. We show that RPEM is as fast and as accurate as the algorithms IMP, QRPEM, and SAEM for the voriconazole model in reconstructing the population parameters, for the normal and log‐normal cases.

Temporal data (such as news articles or Twitter feeds) often consists of a mixture of long-lasting trends and popular but short-lasting topics of interest. A truly successful topic modeling strategy should be able to detect both types of topics and clearly locate them in time. In this paper, we first show that nonnegative CANDECOMP/PARAFAC decomposition (NCPD) is able to discover topics of variable persistence automatically. Then, we propose sparseness-constrained NCPD (S-NCPD) and its online variant in order to actively control the length of the learned topics effectively and efficiently. Further, we propose quantitative ways to measure the topic length and demonstrate the ability of S-NCPD (as well as its online variant) to discover short and long-lasting temporal topics in a controlled manner in semi-synthetic and real-world data including news headlines. We also demonstrate that the online variant of S-NCPD reduces the reconstruction error more rapidly than S-NCPD.