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Assessment of replicability is critical to ensure the quality and rigor of scientific research. In this paper, we discuss inference and modeling principles for replicability assessment. Targeting distinct application scenarios, we propose…
Group interactions occur frequently in social settings, yet their properties beyond pairwise relationships in network models remain unexplored. In this work, we study homophily, the nearly ubiquitous phenomena wherein similar individuals…
Many practical applications in topological data analysis arise from data in the form of point clouds, which then yield simplicial complexes. The combinatorial structure of simplicial complexes captures the topological relationships between…
The correct use and interpretation of models depends on several steps, two of which being the calibration by parameter estimation and the analysis of uncertainty. In the biological literature, these steps are seldom discussed together, but…
Mathematical models are indispensable to the system biology toolkit for studying the structure and behavior of intracellular signaling networks. A common approach to modeling is to develop a system of equations that encode the known biology…
The evaluation of collective modes is fundamental in the analysis of molecular dynamics simulations. Several methods are available to extract that information, i.e normal mode analysis, principal component and spectral analysis of…
Economic choices are often stochastic: the same person may make a different choice when facing the same alternatives repeatedly. Standard models assume that the degree of randomness reflects the size of utility differences, but choice…
Composition is a powerful principle for systems biology, focused on the interfaces, interconnections, and orchestration of distributed processes to enable integrative multiscale simulations. Whereas traditional models focus on the structure…
Complex real-world networks commonly reveal characteristic groups of nodes like communities and modules. These are of value in various applications, especially in the case of large social and information networks. However, while numerous…
We use topological data analysis as a tool to analyze the fit of mathematical models to experimental data. This study is built on data obtained from motion tracking groups of aphids in [Nilsen et al., PLOS One, 2013] and two random walk…
We address the problem of parameter estimation in models of systems biology from noisy observations. The models we consider are characterized by simultaneous deterministic nonlinear differential equations whose parameters are either taken…
We consider the problem of constructing matched groups such that the resulting groups are statistically similar with respect to their average values for multiple covariates. This group-matching problem arises in many cases, including…
This scientific paper explores two distinct approaches for identifying and approximating the simulation model, particularly in the context of the snap process crucial to medical device assembly. Simulation models play a pivotal role in…
Explaining complex or seemingly simple machine learning models is an important practical problem. We want to explain individual predictions from a complex machine learning model by learning simple, interpretable explanations. Shapley values…
We introduce a mathematical model of symbiosis between different species by taking into account the influence of each species on the carrying capacities of the others. The modeled entities can pertain to biological and ecological societies…
Analyzing embedded simplicial complexes, such as triangular meshes and graphs, is an important problem in many fields. We propose a new approach for analyzing embedded simplicial complexes in a subdivision-invariant and isometry-invariant…
Model merging has achieved significant success, with numerous innovative methods proposed to enhance capabilities by combining multiple models. However, challenges persist due to the lack of a unified framework for classification and…
Empirical studies of graphs have contributed enormously to our understanding of complex systems. Known today as network science, what was originally a theoretical study of graphs has grown into a more scientific exploration of communities…
The machine learning community has mainly relied on real data to benchmark algorithms as it provides compelling evidence of model applicability. Evaluation on synthetic datasets can be a powerful tool to provide a better understanding of a…
The modelling and analysis of biological systems has deep roots in Mathematics, specifically in the field of Ordinary Differential Equations. Alternative approaches based on formal calculi, often derived from process algebras or term…