Related papers: Building up a model family for inflammations

Joint models for longitudinal and time-to-event data are commonly used in longitudinal studies to forecast disease trajectories over time. While there are many advantages to joint modeling, the standard forms suffer from limitations that…

This article explores mathematical models for understanding the evolution of contagious diseases. The most widely known set of models are the compartmental ones, which are based on a set of differential equations. But these are not the only…

The large-scale properties of chemical reaction systems, such as the metabolism, can be studied with graph-based methods. To do this, one needs to reduce the information -- lists of chemical reactions -- available in databases. Even for the…

We develop a theoretical approach that uses physiochemical kinetics modelling to describe cell population dynamics upon progression of viral infection in cell culture, which results in cell apoptosis (programmed cell death) and necrosis…

Spatio-temporal extensions of familiar compartment models for disease transmission incorporating diffusive behavior, or interactions between individuals at separate locations, are explored. The models considered have the character of…

A new detailed mathematical model for dynamics of immune response to hepatitis B is proposed, which takes into account contributions from innate and adaptive immune responses, as well as cytokines. Stability analysis of different steady…

Mathematical modelling has a long history in the context of collective cell migration, with applications throughout development, disease and regenerative medicine. The aim of modelling in this context is to provide a framework in which to…

Glass-forming liquids have been extensively studied in recent decades, but there is still no theory that fully describes these systems, and the diversity of treatments is in itself a barrier to understanding. Here we introduce a new simple…

Building a machine learning solution in real-life applications often involves the decomposition of the problem into multiple models of various complexity. This has advantages in terms of overall performance, better interpretability of the…

We build a model for the hepatic fatty acid metabolism and its metabolic and genetic regulations. The model has two functioning modes: synthesis and oxidation of fatty acids. We provide a sufficient condition (the strong lipolytic…

In this paper, a scale mixture of Normal distributions model is developed for classification and clustering of data having outliers and missing values. The classification method, based on a mixture model, focuses on the introduction of…

We introduce a new nonlinear model for classification, in which we model the joint distribution of response variable, y, and covariates, x, non-parametrically using Dirichlet process mixtures. We keep the relationship between y and x linear…

Model uncertainties and simulation uncertainties occur in mathematical modeling of multiscale complex systems, since some mechanisms or scales are not represented (i.e., "unresolved") due to lack in our understanding of these mechanisms or…

Identifying model parameters from observed configurations poses a fundamental challenge in data science, especially with limited data. Recently, diffusion models have emerged as a novel paradigm in generative machine learning, capable of…

Liver infection is a common disease, which poses a great threat to human health, but there is still able to identify an optimal technique that can be used on large-level screening. This paper deals with ML algorithms using different data…

Sphere packings are essential to the development of physical models for powders, composite materials, and the atomic structure of the liquid state. There is a strong scientific need to be able to assess the fit of packing models to data,…

The development of chemical reaction models aids understanding and prediction in areas ranging from biology to electrochemistry and combustion. A systematic approach to building reaction network models uses observational data not only to…

Diffusion models have emerged as a powerful new family of deep generative models with record-breaking performance in many applications, including image synthesis, video generation, and molecule design. In this survey, we provide an overview…

Tissue growth underpins a wide array of biological and developmental processes, and numerical modeling of growing systems has been shown to be a useful tool for understanding these processes. However, the phenomena that can be captured are…

Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…