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Covarion models of character evolution describe inhomogeneities in substitution processes through time. In phylogenetics, such models are used to describe changing functional constraints or selection regimes during the evolution of…
Despite the widespread utilization of Gaussian process models for versatile nonparametric modeling, they exhibit limitations in effectively capturing abrupt changes in function smoothness and accommodating relationships with heteroscedastic…
Hawkes processes are a class of point processes that have the ability to model the self- and mutual-exciting phenomena. Although the classic Hawkes processes cover a wide range of applications, their expressive ability is limited due to…
We introduce a two-parameter ensemble of random discrete-time Markov models that simultaneously captures critical slowing down and broken detailed balance. Extending a previously studied heterogeneous Markov ensemble, we incorporate…
Learning latent expression themes that best express complex patterns in a sample is a central problem in data mining and scientific research. For example, in computational biology we seek a set of salient gene expression themes that explain…
We are facing a real challenge when coping with the continuous acceleration of scientific production and the increasingly changing nature of science. In this article, we extend the classical framework of co-word analysis to the study of…
A central focus in survival analysis is examining how covariates influence survival time. These covariate effects are often found to be either time-varying, heterogeneous - such as being specific to patients, treatments, or subgroups - or…
The recent explosion in the availability of echosounder data from diverse ocean platforms has created unprecedented opportunities to observe the marine ecosystems at broad scales. However, the critical lack of methods capable of…
We consider a time-inhomogeneous diffusion process able to describe the dynamics of infected people in a susceptible-infectious epidemic model in which the transmission intensity function is time-dependent. Such a model is well suited to…
Mutations sometimes increase contagiousness for evolving pathogens. During an epidemic, scientists use viral genome data to infer a shared evolutionary history and connect this history to geographic spread. We propose a model that directly…
Diffusion Models represent a significant advancement in generative modeling, employing a dual-phase process that first degrades domain-specific information via Gaussian noise and restores it through a trainable model. This framework enables…
Spatial extent is a complicating factor in mathematical biology. The possibility that an action at point A cannot immediately affect what happens at point B creates the opportunity for spatial nonuniformity. This nonuniformity must change…
Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…
It is well recognised that animal and plant pathogens form complex ecological communities of interacting organisms within their hosts. Although community ecology approaches have been applied to determine pathogen interactions at the…
To make informed decisions in natural environments that change over time, humans must update their beliefs as new observations are gathered. Studies exploring human inference as a dynamical process that unfolds in time have focused on…
The analysis of data from multiple experiments, such as observations of several individuals, is commonly approached using mixed-effects models, which account for variation between individuals through hierarchical representations. This makes…
Heterogeneity is a ubiquitous property of many biological systems and has profound implications for computation. While it is conceivable to optimize neuronal and synaptic heterogeneity for a specific task, such top-down optimization is…
Modelling a complex system is almost invariably a challenging task. The incorporation of experimental observations can be used to improve the quality of a model, and thus to obtain better predictions about the behavior of the corresponding…
Within epidemiological modeling, the majority of analyses assume a single epidemic process for generating ground-truth data. However, this assumed data generation process can be unrealistic, since data sources for epidemics are often…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…