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We propose a mathematical model for computing drug release from multi-layer capsules. The diffusion problem in such heterogeneous layer-by-layer composite medium is described by a system of coupled partial differential equations, which we…
To meet burning needs of high-resolution pressure-induced line-shape parameters in the UV/visible regions for hot-temperature industrial and atmospheric applications as well as current and future space missions, phase-shift theory is…
Exclusion and shape restrictions play a central role in defining causal effects and interpreting estimates in potential outcomes models. To date, the testable implications of such restrictions have been studied on a case-by-case basis in a…
The expression of survival factors for radiation damaged cells is empirical and based on probabilistic assumptions. We obtain it either from the maximum entropy principle for the classical Boltzmann-Gibbs entropy and/or from the Tsallis…
The analysis and modelling of a range of plasmas (for example: astrophysical, laser-produced and fusion), require atomic data for a number of parameters, such as energy levels, radiative rates and electron impact excitation rates, or…
Much effort has been put into developing theories for dense fluids, as a result of these efforts many theories work for a certain type of particle or in a certain concentration regime. Rosenfeld proposed a dependence of the self-diffusion…
The existing techniques of account for the phonon dispersion are computationally costly, while its impact on a variety of thermodynamic properties appears negligible. We develop a mathematical formalism, which allows for clear understanding…
Understanding how changes in explanatory features affect the unconditional distribution of the outcome is important in many applications. However, existing black-box predictive models are not readily suited for analyzing such questions. In…
Diffusion models have emerged as powerful generative models, inspiring extensive research into their underlying mechanisms. One of the key questions in this area is the loss functions these models shall train with. Multiple formulations…
Formula for calculating the atomic scattering factor for spherical x-ray waves is derived and used to solve the near field effects problem in X-ray Fluorescence Holography theory. A rigorous formalism to calculate the X-ray fluorescence…
Large-scale models require substantial computational resources for analysis and studying treatment conditions. Specifically, estimating treatment effects using simulations may require a lot of infeasible resources to allocate at every…
The design of an experiment, e.g., the setting of initial conditions, strongly influences the accuracy of the whole process of determining model parameters from data. We impose a sensitivity-based approach for choosing optimal design…
Recent evidence suggests that nongenetic (epigenetic) mechanisms play an important role at all stages of cancer evolution. In many cancers, these mechanisms have been observed to induce dynamic switching between two or more cell states,…
Functional data is a powerful tool for capturing and analyzing complex patterns and relationships in a variety of fields, allowing for more precise modeling, visualization, and decision-making. For example, in healthcare, functional data…
The paper presents an approach for overcoming modeling problems of typical life science applications with partly unknown mechanisms and lacking quantitative data: A model family of reaction diffusion equations is built up on a mesoscopic…
The liquid-gas phase transition for homogeneous symmetric nuclear matter is studied in the mean-field approximation. Critical properties are computed using a comprehensive group of Skyrme and Gogny forces in an effort to elucidate the…
A new way to construct a fitting formula for the halo mass function is presented. Our formula is expressed as a solution to the modified Jedamzik matrix equation that automatically satisfies the normalization constraint. The characteristic…
The new statistical approach for calculation of radiation processes with heavy multielectron ions in plasma is developed. The method consists in consideration of atomic structure as a condensed medium, characterized by the spectrum of…
As biomedical sciences discover new layers of complexity in the mechanisms of life and disease, mathematical models trying to catch up with these developments become mathematically intractable. As a result, in the grand scheme of things,…
Our recent re-analysis of the solar photospheric spectra with non-local thermodynamic equilibrium (non-LTE) models resulted in higher metal abundances compared to previous works. When applying the new chemical abundances to Standard Solar…