Related papers: Hybrid Calculus of Wrapped Compartments
Stochastic differential equations (SDEs) are popular tools to analyse time series data in many areas, such as mathematical finance, physics, and biology. They provide a mechanistic description of the phenomeon of interest, and their…
In the modelling of stochastic phenomena, such as quasi-reaction systems, parameter estimation of kinetic rates can be challenging, particularly when the time gap between consecutive measurements is large. Local linear approximation…
We present the bond-calculus, a process algebra for modelling biological and chemical systems featuring nonlinear dynamics, multiway interactions, and dynamic bonding of agents. Mathematical models based on differential equations have been…
"Leaping" methods show great promise for significantly accelerating stochastic simulations of complex biochemical reaction networks. However, few practical applications of leaping have appeared in the literature to date. Here, we address…
Ordinary differential equations (ODEs) provide a powerful framework for modeling dynamic systems arising in a wide range of scientific domains. However, most existing ODE methods focus on a single system, and do not adequately address the…
To model reliably behavioral systems with complex bio-social interactions, accounting for uncertainty quantification, is critical for many application areas. However, in terms of the mathematical formulation of the corresponding problems,…
Single-cell data reveal the presence of biological stochasticity between cells of identical genome and environment, in particular highlighting the transcriptional bursting phenomenon. To account for this property, gene expression may be…
This paper shows how the Bayesian network paradigm can be used in order to solve combinatorial optimization problems. To do it some methods of structure learning from data and simulation of Bayesian networks are inserted inside Estimation…
Simulation models are an absolute necessity in the human and social sciences, which can only very exceptionally use experimental science methods to construct their knowledge. Models enable the simulation of social processes by replacing the…
Clustering is a fundamental collective phenomenon in agent-based models (ABMs) of opinion dynamics. To study clustering in systems with co-evolving social and opinion variables, we derive stochastic partial differential equation (SPDE)…
The Shape Calculus is a bio-inspired calculus for describing 3D shapes moving in a space. A shape forms a 3D process when combined with a behaviour. Behaviours are specified with a timed CCS-like process algebra using a notion of channel…
Agent-based models provide a flexible framework that is frequently used for modelling many biological systems, including cell migration, molecular dynamics, ecology, and epidemiology. Analysis of the model dynamics can be challenging due to…
Ordinary differential equations are widely-used in the field of systems biology and chemical engineering to model chemical reaction networks. Numerous techniques have been developed to estimate parameters like rate constants, initial…
Biological cells can exchange messages through soluble molecules or membrane-bound receptors. In particular in the latter case, the interaction is usually located in specific regions of the interacting cells and may depend on or induce…
Modeling spreading processes in complex random networks plays an essential role in understanding and prediction of many real phenomena like epidemics or rumor spreading. The dynamics of such systems may be represented algorithmically by…
Equilibrium formally can be represented as an ensemble of uncoupled systems undergoing unbiased dynamics in which detailed balance is maintained. Many non-equilibrium processes can be described by suitable subsets of the equilibrium…
In bacterial populations, cells are able to cooperate in order to yield complex collective functionalities. Interest in population-level cellular behaviour is increasing, due to both our expanding knowledge of the underlying biological…
This work presents an omics-driven modeling pipeline that integrates machine-learning tools to facilitate the dynamic modeling of multiscale biological systems. Random forests and permutation feature importance are proposed to mine omics…
We develop an improved stochastic formalism for the Bethe-Salpeter equation, based on an exact separation of the effective-interaction $W$ to two parts, $W=(W-v_W)+v_W$ where the latter is formally any translationally-invariant interaction…
We introduce a new approach to develop stochastic optimization algorithms for a class of stochastic composite and possibly nonconvex optimization problems. The main idea is to combine two stochastic estimators to create a new hybrid one. We…