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Multi-Grid Reaction-Diffusion Master Equation: Applications to Morphogen Gradient Modelling
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2024
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Radek Erban
Stefanie Winkelmann
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Planar chemical reaction systems with algebraic and non-algebraic limit
cycles
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2024
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Gheorghe Crăciun
Radek Erban
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PDF
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Multi-grid reaction-diffusion master equation: applications to morphogen
gradient modelling
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2024
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Radek Erban
Stefanie Winkelmann
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PDF
Chat
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Symmetries of many-body systems imply distance-dependent potentials
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2023
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Jonathan Utterson
Radek Erban
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+
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Symmetries of many-body systems imply distance-dependent potentials
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2023
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Jonathan Utterson
Radek Erban
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+
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Asymmetric periodic boundary conditions for molecular dynamics and coarse-grained simulations of nucleic acids
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2023
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Radek Erban
Yuichi Togashi
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+
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Macroscopic description of a heavy particle immersed within a flow of light particles
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2023
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Radek Erban
Robert A. Van Gorder
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PDF
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On Stretching, Bending, Shearing, and Twisting of Actin Filaments I: Variational Models
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2022
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Carlos Floyd
Haoran Ni
Ravinda S. Gunaratne
Radek Erban
Garegin A. Papoian
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On standardised moments of force distribution in simple liquids
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2022
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Jonathan Utterson
Radek Erban
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On Stretching, Bending, Shearing and Twisting of Actin Filaments II: Multi-Resolution Modelling
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2022
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Ravinda S. Gunaratne
Carlos Floyd
Haoran Ni
Garegin A. Papoian
Radek Erban
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Chemical systems with limit cycles
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2022
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Radek Erban
Hye-Won Kang
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+
PDF
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On the sum of positive divisors functions
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2021
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Radek Erban
Robert A. Van Gorder
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+
PDF
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Identifiability of stochastically modelled reaction networks
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2021
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Germán Enciso
Radek Erban
Jinsu Kim
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+
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On the counting function of semiprimes
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2021
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Dragos Crisan
Radek Erban
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+
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On Stretching, Bending, Shearing and Twisting of Actin Filaments I: Variational Models
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2021
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Carlos Floyd
Haoran Ni
Ravinda S. Gunaratne
Radek Erban
Garegin A. Papoian
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On the counting function of semiprimes
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2020
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Dragos Crisan
Radek Erban
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Limiting stochastic processes of shift-periodic dynamical systems
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2019
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Julia Stadlmann
Radek Erban
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Coarse-graining molecular dynamics: stochastic models with non-Gaussian force distributions
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2019
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Radek Erban
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Coarse-graining molecular dynamics: stochastic models with non-Gaussian force distributions
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2019
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Radek Erban
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PDF
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Multiscale Stochastic Reaction–Diffusion Algorithms Combining Markov Chain Models with Stochastic Partial Differential Equations
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2019
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Hye-Won Kang
Radek Erban
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PDF
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Multi-resolution dimer models in heat baths with short-range and long-range interactions
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2019
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Ravinda S. Gunaratne
Daniel B. Wilson
Mark B. Flegg
Radek Erban
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PDF
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Multi-resolution simulations of intracellular processes
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2019
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Radek Erban
Sarah A. Harris
Raffaello Potestio
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+
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Coarse-graining molecular dynamics: stochastic models with non-Gaussian force distributions
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2019
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Radek Erban
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On short-range and long-range interactions in multi-resolution dimer models
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2018
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Ravinda S. Gunaratne
Daniel B. Wilson
Mark B. Flegg
Radek Erban
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Multi-resolution dimer models in heat baths with short-range and long-range interactions
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2018
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Ravinda S. Gunaratne
Daniel B. Wilson
Mark B. Flegg
Radek Erban
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+
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Limiting stochastic processes of shift-periodic dynamical systems
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2018
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Julia Stadlmann
Radek Erban
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+
PDF
Chat
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Noise-induced mixing and multimodality in reaction networks
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2018
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Tomislav Plesa
Radek Erban
Hans G. Othmer
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+
PDF
Chat
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Reaction time for trimolecular reactions in compartment-based reaction-diffusion models
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2018
|
Fei Li
Minghan Chen
Radek Erban
Yang Cao
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PDF
Chat
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Multi-resolution polymer Brownian dynamics with hydrodynamic interactions
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2018
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Edmund T. Rolls
Radek Erban
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+
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Noise-induced Mixing and Multimodality in Reaction Networks
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2018
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Tomislav Plesa
Radek Erban
Hans G. Othmer
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+
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Multi-resolution dimer models in heat baths with short-range and long-range interactions
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2018
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Ravinda S. Gunaratne
Daniel J. Wilson
Mark B. Flegg
Radek Erban
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+
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Limiting stochastic processes of shift-periodic dynamical systems
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2018
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Julia Stadlmann
Radek Erban
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+
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Noise-induced Mixing and Multimodality in Reaction Networks
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2018
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Tomislav Plesa
Radek Erban
Hans G. Othmer
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+
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Noise Control for DNA Computing
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2017
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Tomislav Plesa
Konstantinos C. Zygalakis
David F. Anderson
Radek Erban
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PDF
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ADM-CLE Approach for Detecting Slow Variables in Continuous Time Markov Chains and Dynamic Data
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2017
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Mihai Cucuringu
Radek Erban
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Hybrid framework for the simulation of stochastic chemical kinetics
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2016
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A. Duncan
Radek Erban
Konstantinos C. Zygalakis
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+
PDF
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Hard-sphere interactions in velocity-jump models
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2016
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Benjamin Franz
Jake P. Taylor‐King
Christian A. Yates
Radek Erban
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PDF
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Chemical reaction systems with a homoclinic bifurcation: an inverse problem
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2016
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Tomislav Plesa
Tomáš Vejchodský
Radek Erban
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PDF
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Steric Effects Induce Geometric Remodeling of Actin Bundles in Filopodia
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2016
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Ulrich Dobramysl
Garegin A. Papoian
Radek Erban
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PDF
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Coupling all-atom molecular dynamics simulations of ions in water with Brownian dynamics
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2016
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Radek Erban
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PDF
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A Cucker--Smale Model with Noise and Delay
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2016
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Radek Erban
Jan Haškovec
Yongzheng Sun
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+
PDF
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Reactive Boundary Conditions as Limits of Interaction Potentials for Brownian and Langevin Dynamics
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2016
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S. Jonathan Chapman
Radek Erban
Samuel A. Isaacson
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PDF
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Particle-Based Multiscale Modeling of Calcium Puff Dynamics
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2016
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Ulrich Dobramysl
Sten Rüdiger
Radek Erban
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Reaction Time for Trimolecular Reactions in Compartment-based Reaction-Diffusion Models
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2016
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F Li
M Chen
Radek Erban
Yu Cao
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Varying the resolution of the Rouse model on temporal and spatial scales: application to multiscale modelling of DNA dynamics
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2016
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Edmund T. Rolls
Yuichi Togashi
Radek Erban
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PDF
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Error Analysis of Diffusion Approximation Methods for Multiscale Systems in Reaction Kinetics
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2016
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Simon L. Cotter
Radek Erban
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Test Models for Statistical Inference: Two-Dimensional Reaction Systems Displaying Limit Cycle Bifurcations and Bistability
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2016
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Tomislav Plesa
Tomáš Vejchodský
Radek Erban
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Chemical Reaction Systems with a Homoclinic Bifurcation: an Inverse Problem
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2015
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Tomislav Plesa
Tomáš Vejchodský
Radek Erban
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Reactive Boundary Conditions as Limits of Interaction Potentials for Brownian and Langevin Dynamics
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2015
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S. Jonathan Chapman
Radek Erban
Samuel A. Isaacson
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PDF
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Noise-induced multistability in chemical systems: Discrete versus continuum modeling
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2015
|
A. Duncan
Shuohao Liao
Tomáš Vejchodský
Radek Erban
Ramon Grima
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ADM-CLE approach for detecting slow variables in continuous time Markov chains and dynamic data
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2015
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Mihai Cucuringu
Radek Erban
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+
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Particle-based multiscale modeling of intracellular calcium dynamics
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2015
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Ulrich Dobramysl
Sten Rüdiger
Radek Erban
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+
PDF
Chat
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ADM-CLE Approach for Detecting Slow Variables in Continuous Time Markov Chains and Dynamic Data
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2015
|
Mihai Cucuringu
Radek Erban
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+
PDF
Chat
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Mathematical modelling of turning delays in swarm robotics
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2015
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Jake P. Taylor‐King
Benjamin Franz
Christian A. Yates
Radek Erban
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+
PDF
Chat
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Convergence of methods for coupling of microscopic and mesoscopic reaction–diffusion simulations
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2015
|
Mark B. Flegg
Stefan Hellander
Radek Erban
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+
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On Cucker-Smale model with noise and delay
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2015
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Radek Erban
Jan Haškovec
Yongzheng Sun
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+
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Chemical Reaction Systems with a Homoclinic Bifurcation: an Inverse Problem
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2015
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Tomislav Plesa
Tomáš Vejchodský
Radek Erban
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+
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Reactive Boundary Conditions as Limits of Interaction Potentials for Brownian and Langevin Dynamics
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2015
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S. Jonathan Chapman
Radek Erban
Samuel A. Isaacson
|
+
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ADM-CLE approach for detecting slow variables in continuous time Markov chains and dynamic data
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2015
|
Mihai Cucuringu
Radek Erban
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+
PDF
Chat
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Stochastic Turing Patterns: Analysis of Compartment-Based Approaches
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2014
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Yang Cao
Radek Erban
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Reduction of chemical systems by delayed quasi-steady state assumptions
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2014
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Tomáš Vejchodský
Radek Erban
Philip K. Maini
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+
PDF
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From molecular dynamics to Brownian dynamics
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2014
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Radek Erban
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+
PDF
Chat
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Adaptive two-regime method: Application to front propagation
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2014
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Martin Robinson
Mark B. Flegg
Radek Erban
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+
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Spatial stochastic modeling of intracellular Ca$^{2+}$ dynamics using two-regime methods
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2014
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Ulrich Dobramysl
Martin Robinson
Radek Erban
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+
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Mathematical Modelling of Turning Delays in Swarm Robotics
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2014
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Jake P. Taylor‐King
Benjamin Franz
Christian A. Yates
Radek Erban
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+
PDF
Chat
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Editorial: Special Issue on Stochastic Modelling of Reaction–Diffusion Processes in Biology
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2014
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Radek Erban
Hans G. Othmer
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+
PDF
Chat
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Analysis of the Two-Regime Method on Square Meshes
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2014
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Mark B. Flegg
S. Jonathan Chapman
Likun Zheng
Radek Erban
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PDF
Chat
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From Brownian Dynamics to Markov Chain: An Ion Channel Example
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2014
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Wan Chen
Radek Erban
S. Jonathan Chapman
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+
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Parameter estimation and bifurcation analysis of stochastic models of gene regulatory networks: tensor-structured methods
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2014
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Shuohao Liao
Tomáš Vejchodský
Radek Erban
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+
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Reduction of chemical systems by delayed quasi-steady state assumptions
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2014
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Tomáš Vejchodský
Radek Erban
Philip K. Maini
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+
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Error Analysis of Diffusion Approximation Methods for Multiscale Systems in Reaction Kinetics
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2014
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Simon L. Cotter
Radek Erban
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+
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Mathematical Modelling of Turning Delays in Swarm Robotics
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2014
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Jake P. Taylor‐King
Benjamin Franz
Christian A. Yates
Radek Erban
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+
PDF
Chat
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Travelling Waves in Hybrid Chemotaxis Models
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2013
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Benjamin Franz
Chuan Xue
Kevin J. Painter
Radek Erban
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Multiscale Stochastic Reaction–Diffusion Modeling: Application to Actin Dynamics in Filopodia
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2013
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Radek Erban
Mark B. Flegg
Garegin A. Papoian
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+
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Convergence of methods for coupling of microscopic and mesoscopic reaction-diffusion simulations
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2013
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Mark B. Flegg
Stefan Hellander
Radek Erban
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+
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Analysis of the two-regime method on square meshes
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2013
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Mark B. Flegg
S. Jonathan Chapman
Likun Zheng
Radek Erban
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+
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Travelling waves in hybrid chemotaxis models
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2013
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Benjamin Franz
Chuan Xue
Kevin J. Painter
Radek Erban
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+
PDF
Chat
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Hybrid Modelling of Individual Movement and Collective Behaviour
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2013
|
Benjamin Franz
Radek Erban
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+
PDF
Chat
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Multiscale Reaction-Diffusion Algorithms: PDE-Assisted Brownian Dynamics
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2013
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Benjamin Franz
Mark B. Flegg
S. Jonathan Chapman
Radek Erban
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+
PDF
Chat
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Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems
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2013
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Simon L. Cotter
Tomáš Vejchodský
Radek Erban
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Stochastic Turing patterns: analysis of compartment-based approaches
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2013
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Yang Cao
Radek Erban
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+
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Travelling waves in hybrid chemotaxis models
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2013
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Benjamin Franz
Xue Chuan
Kevin J. Painter
Radek Erban
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+
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Analysis of the two-regime method on square meshes
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2013
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Mark B. Flegg
S. Jonathan Chapman
Likun Zheng
Radek Erban
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+
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Convergence of methods for coupling of microscopic and mesoscopic reaction-diffusion simulations
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2013
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Mark B. Flegg
Stefan Hellander
Radek Erban
|
+
PDF
Chat
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Going from microscopic to macroscopic on nonuniform growing domains
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2012
|
Christian A. Yates
Ruth E. Baker
Radek Erban
Philip K. Maini
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+
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Multiscale reaction-diffusion algorithms: PDE-assisted Brownian dynamics
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2012
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Benjamin Franz
Mark B. Flegg
S. Jonathan Chapman
Radek Erban
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+
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From individual to collective behaviour of coupled velocity jump processes: A locust example
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2012
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Radek Erban
Jan Haškovec
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+
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A higher-order numerical framework for stochastic simulation of chemical reaction systems
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2012
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Tamás Székely
Kevin Burrage
Radek Erban
Konstantinos C. Zygalakis
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From Brownian Dynamics to Markov Chain: an Ion Channel Example
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2012
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Wan Chen
Radek Erban
S. Jonathan Chapman
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+
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Multiscale reaction-diffusion algorithms: PDE-assisted Brownian dynamics
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2012
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Benjamin Franz
Mark B. Flegg
S. Jonathan Chapman
Radek Erban
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+
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Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems
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2011
|
Simon L. Cotter
Tomáš Vejchodský
Radek Erban
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+
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From individual to collective behaviour of coupled velocity jump processes: a locust example
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2011
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Radek Erban
Jan Haškovec
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+
PDF
Chat
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Analysis of Brownian Dynamics Simulations of Reversible Bimolecular Reactions
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2011
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Jana Lipková
Konstantinos C. Zygalakis
S. Jonathan Chapman
Radek Erban
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Comparing stochastic discrete and deterministic continuum models of cell migration
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2011
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Radek Erban
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Multiscale stochastic reaction-diffusion algorithms combining Markov chain models with SPDEs
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2011
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Hye-Won Kang
Radek Erban
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+
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Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems
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2011
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Simon L. Cotter
Tomáš Vejchodský
Radek Erban
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+
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From individual to collective behaviour of coupled velocity jump processes: a locust example
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2011
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Radek Erban
Jan Haškovec
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+
PDF
Chat
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Travelling Waves in Hyperbolic Chemotaxis Equations
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2010
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Chuan Xue
Hyung Ju Hwang
Kevin J. Painter
Radek Erban
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PDF
Chat
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Ergodic directional switching in mobile insect groups
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2010
|
Carlos Escudero
Christian A. Yates
Camille Buhl
Iain D. Couzin
Radek Erban
Ioannis G. Kevrekidis
Philip K. Maini
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Analysis of Brownian Dynamics Simulations of Reversible Bimolecular Reactions
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2010
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Jana Lipková
Konstantinos C. Zygalakis
S. Jonathan Chapman
Radek Erban
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+
PDF
Chat
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From Microscopic to Macroscopic Descriptions of Cell Migration on Growing Domains
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2009
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Ruth E. Baker
Christian A. Yates
Radek Erban
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+
PDF
Chat
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Stochastic modelling of reaction–diffusion processes: algorithms for bimolecular reactions
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2009
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Radek Erban
S. Jonathan Chapman
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+
PDF
Chat
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Detecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion maps
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2009
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Amit Singer
Radek Erban
Ioannis G. Kevrekidis
Ronald R. Coifman
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+
PDF
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From Individual to Collective Behavior of Unicellular Organisms: Recent Results and Open Problems
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2009
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Chuan Xue
Hans G. Othmer
Radek Erban
Robert Sinclair
Klaus M. Stiefel
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PDF
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Analysis of a Stochastic Chemical System Close to a SNIPER Bifurcation of Its Mean-Field Model
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2009
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Radek Erban
S. Jonathan Chapman
Ioannis G. Kevrekidis
Tomáš Vejchodský
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Deterministic and stochastic models of dynamics of chemical systems
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2008
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Tomáš Vejchodský
Radek Erban
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Analysis of a stochastic chemical system close to a SNIPER bifurcation of its mean-field model
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2008
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Radek Erban
S. Jonathan Chapman
Ioannis G. Kevrekidis
Tomáš Vejchodský
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PDF
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DYNAMICS OF POLYDISPERSE IRREVERSIBLE ADSORPTION: A PHARMACOLOGICAL EXAMPLE
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2007
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Radek Erban
S. Jonathan Chapman
Kerry D. Fisher
Ioannis G. Kevrekidis
Leonard W. Seymour
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+
PDF
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Time scale of random sequential adsorption
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2007
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Radek Erban
S. Jonathan Chapman
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PDF
Chat
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Variable-free exploration of stochastic models: A gene regulatory network example
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2007
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Radek Erban
Thomas A. Frewen
Xiao Wang
Timothy C. Elston
Ronald R. Coifman
Boaz Nadler
Ioannis G. Kevrekidis
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PDF
Chat
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On Chemisorption of Polymers to Solid Surfaces
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2007
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Radek Erban
S. Jonathan Chapman
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+
PDF
Chat
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Reactive boundary conditions for stochastic simulations of reaction–diffusion processes
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2007
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Radek Erban
S. Jonathan Chapman
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+
PDF
Chat
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Projective and coarse projective integration for problems with continuous symmetries
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2007
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Michail E. Kavousanakis
Radek Erban
Andreas G. Boudouvis
C. W. Gear
I.G. Kevrekidis
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+
PDF
Chat
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Taxis equations for amoeboid cells
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2007
|
Radek Erban
Hans G. Othmer
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+
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A practical guide to stochastic simulations of reaction-diffusion processes
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2007
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Radek Erban
Jonathan Chapman
Philip K. Maini
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+
PDF
Chat
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Variable-free exploration of stochastic models: A gene regulatory network example
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2007
|
Radek Erban
Thomas A. Frewen
Xiao Wang
Timothy C. Elston
Ronald R. Coifman
Boaz Nadler
Ioannis G. Kevrekidis
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+
PDF
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Spatially distributed stochastic systems: Equation-free and equation-assisted preconditioned computations
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2006
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Liang Qiao
Radek Erban
C. T. Kelley
Ioannis G. Kevrekidis
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Spatially Distributed Stochastic Systems: equation-free and equation-assisted bifurcation analysis
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2006
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Liang Qiao
Radek Erban
C. T. Kelley
Ioannis G. Kevrekidis
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PDF
Chat
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An equation-free computational approach for extracting population-level behavior from individual-based models of biological dispersal
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2006
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Radek Erban
Ioannis G. Kevrekidis
Hans G. Othmer
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PDF
Chat
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Gene regulatory networks: A coarse-grained, equation-free approach to multiscale computation
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2006
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Radek Erban
Ioannis G. Kevrekidis
David Adalsteinsson
Timothy C. Elston
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+
PDF
Chat
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Global existence results for complex hyperbolic models of bacterial chemotaxis
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2006
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Radek Erban
Hyung Ju Hwang
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Dynamics of polydisperse irreversible adsorption: a pharmacological example
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2006
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Radek Erban
Jonathan Chapman
Kerry Fisher
Ioannis G. Kevrekidis
Leonard W. Seymour
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+
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Global existence results for complex hyperbolic models of bacterial chemotaxis
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2006
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Radek Erban
Hyung Ju Hwang
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+
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Taxis Equations for Amoeboid Cells
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2006
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Radek Erban
Hans G. Othmer
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+
PDF
Chat
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Gene regulatory networks: A coarse-grained, equation-free approach to multiscale computation
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2006
|
Radek Erban
Ioannis G. Kevrekidis
David Adalsteinsson
Timothy C. Elston
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PDF
Chat
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From Signal Transduction to Spatial Pattern Formation in<i>E. coli</i>: A Paradigm for Multiscale Modeling in Biology
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2005
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Radek Erban
Hans G. Othmer
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+
PDF
Chat
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From Individual to Collective Behavior in Bacterial Chemotaxis
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2004
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Radek Erban
Hans G. Othmer
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+
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On the existence of solutions to the Navier–Stokes equations of a two‐dimensional compressible flow
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2003
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Radek Erban
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On the Static-Limit Solutions to the Navier—Stokes Equations of Compressible Flow
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2001
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Radek Erban
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