The paper proposes Metropolis adjusted Langevin and Hamiltonian Monte Carlo sampling
methods defined on the Riemann manifold to resolve the shortcomings of existing Monte …

While our genomes are essentially static, our microbiomes are inherently dynamic. The
microbial communities we harbor in our bodies change throughout our lives due to many …

Introduction to Functional Data Analysis provides a concise textbook introduction to the field.
It explains how to analyze functional data, both at exploratory and inferential levels. It also …

We introduce a simple, rigorous, and unified framework for solving nonlinear partial
differential equations (PDEs), and for solving inverse problems (IPs) involving the …

Networks and network analysis are arguably one of the largest growth areas of the early
twenty-first century in the quantitative sciences. Despite roots in social network analysis …

Figure 1.1 provides a prototype for the type of data that we shall consider. It shows the
heights of 10 girls measured at a set of 31 ages in the Berkeley Growth Study (Tuddenham …

This book is intended to provide fundamental statistical concepts and tools relevant to the
analysis of genetic data arising from population-based association studies. Elementary …

We employ physics-informed neural networks (PINNs) to infer properties of biological
materials using synthetic data. In particular, we successfully apply PINNs to extract the …

Ordinary differential equations (ODEs) are a powerful tool for modeling dynamic processes
with wide applications in a variety of scientific fields. Over the last two decades, ODEs have …

The empirical performance of neural ordinary differential equations (NODEs) is significantly
inferior to discrete-layer models on benchmark tasks (eg image classification). We …