Related papers: A spatio-temporal model and inference tools for lo…
Motivated by predicting intraday trading volume curves, we consider two spatio-temporal autoregressive models for matrix time series, in which each column may represent daily trading volume curve of one asset, and each row captures…
Heterogeneity in characteristics from one region (sub-population) to another, commonly observed in complex systems, such as glasses and a collection of cells, is hard to describe theoretically. In the context of cancer, intra-tumor…
Modeling the distribution of natural images is challenging, partly because of strong statistical dependencies which can extend over hundreds of pixels. Recurrent neural networks have been successful in capturing long-range dependencies in a…
The typical temporal resolution used in modern simulations significantly exceeds characteristic time scales at which the system is driven. This is especially so when systems are simulated over time-scales that are much longer than the…
A macroscopic model of the tumor Gompertzian growth is proposed. The new approach is based on the energetic balance among the different cell activities, described by methods of statistical mechanics and related to the growth inhibitor…
A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…
The majority of solid tumours arise in epithelia and therefore much research effort has gone into investigating the growth, renewal and regulation of these tissues. Here we review different mathematical and computational approaches that…
In this thesis we develop minimal models of the relationship between motility, growth, and evolution of cancer cells. We utilise simple simulations of a population of individual cells in space to examine how changes in mechanical properties…
Over the past decade, advances in super-resolution microscopy and particle-based modeling have driven an intense interest in investigating spatial heterogeneity at the level of single molecules in cells. Remarkably, it is becoming clear…
Within-individual variability of health indicators measured over time is becoming commonly used to inform about disease progression. Simple summary statistics (e.g. the standard deviation for each individual) are often used but they are not…
In the analysis of multivariate spatial and univariate spatio-temporal data, it is commonly recognized that asymmetric dependence may exist, which can be addressed using an asymmetric (matrix or space-time, respectively) covariance function…
How far is neuroepithelial cell proliferation in the developing central nervous system a deterministic process? Or, to put it in a more precise way, how accurately can it be described by a deterministic mathematical model? To provide tracks…
Conditional autoregressive (CAR) models are commonly used to capture spatial correlation in areal unit data, and are typically specified as a prior distribution for a set of random effects, as part of a hierarchical Bayesian model. The…
A key challenge in environmental health research is unmeasured spatial confounding, driven by unobserved spatially structured variables that influence both treatment and outcome. A common approach is to fit a spatial regression that models…
A new discrete-time shot noise Cox process for spatiotemporal data is proposed. The random intensity is driven by a dependent sequence of latent gamma random measures. Some properties of the latent process are derived, such as an…
We propose a novel sparse spatiotemporal dynamic generalized linear model for efficient inference and prediction of bicycle count data. Assuming Poisson distributed counts with spacetime-varying rates, we model the log-rate using…
The development of single-cell and spatial transcriptomics has revolutionized our capacity to investigate cellular properties, functions, and interactions in both cellular and spatial contexts. However, the analysis of single-cell and…
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…
Large-scale longitudinal molecular profiling is now firmly established in biomedical research, prompted by the need to uncover coordinated biomarker trajectories reflecting the dynamics of underlying biological mechanisms and characterise…
In credit risk analysis, survival models with fixed and time-varying covariates are widely used to predict a borrower's time-to-event. When the time-varying drivers are endogenous, modelling jointly the evolution of the survival time and…