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This work develops further a probabilist approach to the asymptotic behavior of growth-fragmentation semigroups via the Feynman-Kac formula, which was introduced in a joint article with A.R. Watson [4]. Here, it is first shown that the…
Discrete-state, continuous-time Markov models are widely used in the modeling of biochemical reaction networks. Their complexity often precludes analytic solution, and we rely on stochastic simulation algorithms to estimate system…
Gaussian processes are flexible probabilistic regression models which are widely used in statistics and machine learning. However, a drawback is their limited scalability to large data sets. To alleviate this, full-scale approximations…
We consider stochastic dynamics of a population which starts from a small colony on a habitat with large but limited carrying capacity. A common heuristics suggests that such population grows initially as a Galton-Watson branching process…
Recently, partial Bayesian neural networks (pBNNs), which only consider a subset of the parameters to be stochastic, were shown to perform competitively with full Bayesian neural networks. However, pBNNs are often multi-modal in the latent…
We derive the full kinetic equations describing the evolution of the probability density distribution for a structured population such as cells distributed according to their ages and sizes. The kinetic equations for such a "sizer-timer"…
Simulating Markovian open quantum systems in the semiclassical regime poses a grand challenge for computational physics, as the highly oscillatory nature of the dynamics imposes prohibitive resolution requirements on traditional grid-based…
A stochastic evolutionary dynamics of two strategies given by 2 x 2 matrix games is studied in finite populations. We focus on stochastic properties of fixation: how a strategy represented by a single individual wins over the entire…
Agent-based models capture heterogeneity among individuals in a population and are widely used in studies of multi-cellular systems, disease, epidemics and demography to name a few. However, existing frameworks consider discrete time-step…
Probabilistic approaches for handling count-valued time sequences have attracted amounts of research attentions because their ability to infer explainable latent structures and to estimate uncertainties, and thus are especially suitable for…
Many models of population dynamics are formulated as deterministic iterated maps although real populations are stochastic. This is justifiable in the limit of large population sizes, as the stochastic fluctuations are negligible then.…
The proposed stochastic model for pedestrian dynamics is based on existing approaches using cellular automata, combined with substantial extensions, to compensate the deficiencies resulting of the discrete grid structure. This agent motion…
The nonlinearity of dynamics in systems biology makes it hard to infer them from experimental data. Simple linear models are computationally efficient, but cannot incorporate these important nonlinearities. An adaptive method based on the…
Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics…
We introduce a powerful and flexible MCMC algorithm for stochastic simulation. The method builds on a pseudo-marginal method originally introduced in [Genetics 164 (2003) 1139--1160], showing how algorithms which are approximations to an…
We present a data-driven approach to use the Koopman generator for prediction and optimal control of control-affine stochastic systems. We provide a novel conceptual approach and a proof-of-principle for the determination of optimal control…
In this work, we present and analyze a system of PDEs, which models tumor growth by considering chemotaxis, active transport, and random effects. The stochasticity of the system is modelled by random initial data and Wiener noises that…
The question of how to incorporate curvature information in stochastic approximation methods is challenging. The direct application of classical quasi- Newton updating techniques for deterministic optimization leads to noisy curvature…
Computational systems and methods are often being used in biological research, including the understanding of cancer and the development of treatments. Simulations of tumor growth and its response to different drugs are of particular…
We introduce generative models for accelerating simulations of complex systems through learning and evolving their effective dynamics. In the proposed Generative Learning of Effective Dynamics (G-LED), instances of high dimensional data are…