Related papers: Parameter identifiability for a profile mixture mo…
This paper explores unsupervised learning of parsing models along two directions. First, which models are identifiable from infinite data? We use a general technique for numerically checking identifiability based on the rank of a Jacobian…
All known terrestrial proteins are coded as continuous strings of ~20 amino acids. The patterns formed by the repetitions of elements in groups of finite sequences describes the natural architectures of protein families. We present a method…
Phylogenetic networks are an extension of phylogenetic trees which are used to represent evolutionary histories in which reticulation events (such as recombination and hybridization) have occurred. A central question for such networks is…
A central challenge in the study of protein evolution is the identification of historic amino acid sequence changes responsible for creating novel functions observed in present-day proteins. To address this problem, we developed a new…
Statistical models are often structurally unidentifiable, because different sets of parameters can lead to equal model outcomes. To be useful for prediction and parameter inference from data, stochastic population models need to be…
Protein structure prediction is one of the most important problems in computational biology. The most successful computational approach, also called template-based modeling, identifies templates with solved crystal structures for the query…
We study identifiability of the parameters in autoregressions defined on a network. Most identification conditions that are available for these models either rely on the network being observed repeatedly, are only sufficient, or require…
We study parameter identification problems in a structured population model without mutations. Given measurements of the total population size or critical points of the population, we aim to recover its growth rate, death rate or initial…
Proteins, by virtue of their central role in most biological processes, represent one of the key subjects of the study of molecular evolution. Inherent to the indispensability of proteins for living cells is the fact that a given protein…
Parameter estimation connects mathematical models to real-world data and decision making across many scientific and industrial applications. Standard approaches such as maximum likelihood estimation and Markov chain Monte Carlo estimate…
Identifying unique parameters for mathematical models describing biological data can be challenging and often impossible. Parameter identifiability for partial differential equations models in cell biology is especially difficult given that…
Protein domains are found on genomes with notable statistical distributions, which bear a high degree of similarity. Previous work has shown how these distributions can be accounted for by simple models, where the main ingredients are…
This work focuses on the question of how identifiability of a mathematical model, that is, whether parameters can be recovered from data, is related to identifiability of its submodels. We look specifically at linear compartmental models…
Protein evolution underpins life, and understanding its behavior as a system is of great importance. However, our current models of protein evolution are arguably too simplistic to allow quantitative interpretation and prediction of…
The selection of the most suitable evolutionary model to analyze the given molecular data is usually left to biologist's choice. In his famous book, J Felsenstein suggested that certain linear equations satisfied by the expected…
Auto-regulatory feedback loops are one of the most common network motifs. A wide variety of stochastic models have been constructed to understand how the fluctuations in protein numbers in these loops are influenced by the kinetic…
In this paper, we propose a data-driven method to learn interpretable topological features of biomolecular data and demonstrate the efficacy of parsimonious models trained on topological features in predicting the stability of synthetic…
Thermostability is an important prerequisite for enzymes employed for industrial applications. Several machine learning based models have thus been formulated for protein classification based on this particular trait. These models have…
The evolutionary trajectory of a protein through sequence space is constrained by function and three-dimensional (3D) structure. Residues in spatial proximity tend to co-evolve, yet attempts to invert the evolutionary record to identify…
Mathematical modelling is a widely used approach to understand and interpret clinical trial data. This modelling typically involves fitting mechanistic mathematical models to data from individual trial participants. Despite the widespread…