## Multiscale Gaussian graphical models and algorithms for large-scale inference

## Projective integration of expensive multiscale stochastic simulation; Projective integration of expensive stochastic processes

## Optimal Sampling Strategies for Multiscale Stochastic Processes

## Optimal Sampling Strategies for Multiscale Stochastic Processes

## Multiscale queuing analysis, sampling theory, and network probing

## All-Atom Multiscale Computational Modeling Of Viral Dynamics

## Convergence of stochastic gene networks to hybrid piecewise deterministic processes

## Diffusion in multiscale spacetimes

## Stochastic Dynamics of Bionanosystems: Multiscale Analysis and Specialized Ensembles

## Statistical Inference for Perturbations of Multiscale Dynamical Systems

## Elimination of Intermediate Species in Multiscale Stochastic Reaction Networks

## Quenched Large Deviations for Multiscale Diffusion Processes in Random Environments

## Error Analysis of Diffusion Approximation Methods for Multiscale Systems in Reaction Kinetics

## Normal form transforms separate slow and fast modes in stochastic dynamical systems

## Exponential L\'evy-type models with stochastic volatility and stochastic jump-intensity

## Optimal sampling strategies for multiscale stochastic processes

## Irreversible Thermodynamics in Multiscale Stochastic Dynamical Systems

## Particle-based Multiscale Modeling of Calcium Puff Dynamics

## Probabilistic methods for multiscale evolutionary dynamics

Evolution by natural selection can occur at multiple biological scales. This is particularly the case for host-pathogen systems, where selection occurs both within each infected host as well as through transmission between hosts. Despite there being established mathematical models for understanding evolution at a single biological scale, fewer tractable models exist for multiscale evolutionary dynamics. Here I present mathematical approaches using tools from probability and stochastic processes as well as dynamical systems to handle multiscale evolutionary systems. The first problem I address concerns the antigenic evolution of influenza. Using a combination of ordinary differential equations and inhomogeneous Poisson processes, I study how immune selection pressures at the within-host level impact population-level evolutionary dynamics. The second problem involves the more general question of evolutionary dynamics when selection occurs antagonistically at two biological scales. In addition to host-pathogen systems, such situations arise naturally in the evolution of traits such as the production of a public good and the use of a common resource. I introduce a model for this general phenomenon that is intuitively visualized as a a stochastic ball-and-urn system and can be used to systematically obtain general properties of antagonistic multiscale evolution. Lastly...