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Mathematical modeling and simulation is a promising approach to personalized cancer medicine. Yet, the complexity, heterogeneity and multi-scale nature of cancer pose significant computational challenges. Coupling discrete cell-based models…
We develop a statistical toolbox for a quantitative model evaluation of stochastic reaction-diffusion systems modeling space-time evolution of biophysical quantities on the intracellular level. Starting from space-time data $X_N(t,x)$, as,…
Hawkes stochastic point process models have emerged as valuable statistical tools for analyzing viral contagion. The spatiotemporal Hawkes process characterizes the speeds at which viruses spread within human populations. Unfortunately,…
Prior work on Automatically Scalable Computation (ASC) suggests that it is possible to parallelize sequential computation by building a model of whole-program execution, using that model to predict future computations, and then…
This paper studies parallelization schemes for stochastic Vector Quantization algorithms in order to obtain time speed-ups using distributed resources. We show that the most intuitive parallelization scheme does not lead to better…
The behavior of some stochastic chemical reaction networks is largely unaffected by slight inaccuracies in reaction rates. We formalize the robustness of state probabilities to reaction rate deviations, and describe a formal connection…
Turing patterns can be observed in reaction-diffusion systems where chemical species have different diffusion constants. In recent years, several studies investigated the effects of noise on Turing patterns and showed that the parameter…
We consider two parallel-in-time approaches applied to a (reaction) diffusion problem, possibly non-linear. In particular, we consider PFASST (Parallel Full Approximation Scheme in Space and Time) and space-time multilevel strategies. For…
Quantum-based molecular dynamics (QMD) is a highly accurate and transferable method for material science simulations. However, the time scales and system sizes accessible to QMD are typically limited to picoseconds and a few hundred atoms.…
Signaling networks are designed to sense an environmental stimulus and adapt to it. We propose and study a minimal model of signaling network that can sense and respond to external stimuli of varying strength in an adaptive manner. The…
With the advent of interconnected quantum computers, i.e., distributed quantum computing (DQC), multiple quantum computers can now collaborate via quantum networks to perform massively complex computational tasks. However, DQC faces…
The Massive Parallel Computation (MPC) model is a theoretical framework for popular parallel and distributed platforms such as MapReduce, Hadoop, or Spark. We consider the task of computing a large matching or small vertex cover in this…
Spatially distributed problems are often approximately modelled in terms of partial differential equations (PDEs) for appropriate coarse-grained quantities (e.g. concentrations). The derivation of accurate such PDEs starting from finer…
Probabilistic models are conceptually powerful tools for finding structure in data, but their practical effectiveness is often limited by our ability to perform inference in them. Exact inference is frequently intractable, so approximate…
Computation of a signal's estimated covariance matrix is an important building block in signal processing, e.g., for spectral estimation. Each matrix element is a sum of products of elements in the input matrix taken over a sliding window.…
Conventional approaches for simulating steady-state distributions of particles under diffusive and advective transport at high P\'eclet numbers involve solving the diffusion and advection equations in at least two dimensions. Here, we…
Modeling transformations between arbitrary data distributions is a fundamental scientific challenge, arising in applications like drug discovery and evolutionary simulation. While flow matching offers a natural framework for this task, its…
Numerical solution of reaction-diffusion equations in three dimensions is one of the most challenging applied mathematical problems. Since these simulations are very time consuming, any ideas and strategies aiming at the reduction of CPU…
Today's unrelenting increase in demand for information processing creates the need for novel computing concepts. Reservoir computing is such a concept that lends itself particularly well to photonic hardware implementations. Over recent…
Video diffusion models (VDMs) perform attention computation over the 3D spatio-temporal domain. Compared to large language models (LLMs) processing 1D sequences, their memory consumption scales cubically, necessitating parallel serving…