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We treat the problem of characterizing in a systematic way the qualitative features of two-dimensional dynamical systems. To that end, we construct a representation of the topological features of phase portraits by means of diagrams that…
Raman spectroscopy is an important characterization tool with diverse applications in many areas of research. We propose a machine learning method for predicting polarizabilities with the goal of providing Raman spectra from molecular…
Over the last two decades, significant advances have been made in the design and analysis of fixed-parameter algorithms for a wide variety of graph-theoretic problems. This has resulted in an algorithmic toolbox that is by now…
In this paper a novel computational technique for finite discrete approximation of continuous dynamical systems suitable for a significant class of biochemical dynamical systems is introduced. The method is parameterized in order to affect…
Sequence discovery tools play a central role in several fields of computational biology. In the framework of Transcription Factor binding studies, motif finding algorithms of increasingly high performance are required to process the big…
Single-particle trajectories measured in microscopy experiments contain important information about dynamic processes undergoing in a range of materials including living cells and tissues. However, extracting that information is not a…
Molecular dynamics simulations are an important tool for describing the evolution of a chemical system with time. However, these simulations are inherently held back either by the prohibitive cost of accurate electronic structure theory…
Molecular dynamics (MD) is a powerful technique for studying microscopic phenomena, but its computational cost has driven significant interest in the development of deep learning-based surrogate models. We introduce generative modeling of…
Single-particle tracking allows to infer the motion of single molecules in living cells. When we observe a long trajectory (more than 100 points), it is possible that the particle switches mode of motion over time. Then, fitting a single…
A central problem in data analysis is the low dimensional representation of high dimensional data, and the concise description of its underlying geometry and density. In the analysis of large scale simulations of complex dynamical systems,…
Complex systems often have features that can be modeled by advanced mathematical tools [1]. Of special interests are the features of complex systems that have a network structure as such systems are important for modeling technological and…
We introduce the optimized dynamic mode decomposition algorithm for constructing an adaptive and computationally efficient reduced order model and forecasting tool for global atmospheric chemistry dynamics. By exploiting a low-dimensional…
Molecular dynamics simulations have the potential to provide atomic-level detail and insight to important questions in chemical physics that cannot be observed in typical experiments. However, simply generating a long trajectory is…
Decision Boundary Maps (DBMs) are an effective tool for visualising machine learning classification boundaries. Yet, DBM quality strongly depends on the dimensionality reduction (DR) technique and high dimensional space used for the data…
We introduce diffusion geometry as a new framework for geometric and topological data analysis. Diffusion geometry uses the Bakry-Emery $\Gamma$-calculus of Markov diffusion operators to define objects from Riemannian geometry on a wide…
We develop a discrete-time version of the blended dynamics theorem for the use of designing distributed computation algorithms. The blended dynamics theorem enables to predict the behavior of heterogeneous multi-agent systems. Therefore,…
We give a very short introduction to discrete and continuum models for the evolutionary and spatial dynamics of cancer through two case studies: a model for the evolutionary dynamics of cancer cells under cytotoxic therapy and a model for…
Real-world optimization often demands diverse, high-quality solutions. Quality-Diversity (QD) optimization is a multifaceted approach in evolutionary algorithms that aims to generate a set of solutions that are both high-performing and…
We consider initial value problems of nonlinear dynamical systems, which include physical parameters. A quantity of interest depending on the solution is observed. A discretisation yields the trajectories of the quantity of interest in many…
Dynamical systems often exhibit the emergence of long-lived coherent sets, which are regions in state space that keep their geometric integrity to a high extent and thus play an important role in transport. In this article, we provide a…