we created a simple cellular automata (ca) model for hepatitis b infection dynamics associated with spatial structure performed under various ages of liver tissue correspond to different immune responses in order to study the effect of spatial heterogeneities on the dynamical evolution of a viral infection. the results of the simulations show biphasic nature of viral load decreases, as observed...

Dynamical process upscaling for deriving catchment scale state variables and constitutive relations for meso-scale process models E. Zehe, H. Lee, and M. Sivapalan Institute of Geoecology, University of Potsdam, Germany Centre of Water Research, University of Western Australia, Crawley, Australia Departments of Geography and of Civil & Environmental Engineering, University of Illinois at Urbana...

This paper introduces Gaussian Process Dynamical Models (GPDM) for nonlinear time series analysis. A GPDM comprises a low-dimensional latent space with associated dynamics, and a map from the latent space to an observation space. We marginalize out the model parameters in closed-form, which amounts to using Gaussian Process (GP) priors for both the dynamics and the observation mappings. This re...

The recently proposed Gaussian process dynamical models (GPDMs) have been successfully applied to time series modeling. There are four learning algorithms for GPDMs: maximizing a posterior (MAP), fixing the kernel hyperparameters ᾱ (Fix.ᾱ), balanced GPDM (B-GPDM) and twostage MAP (T.MAP), which are designed for model training with complete data. When data are incomplete, GPDMs reconstruct the m...

High dimensional time series are endemic in applications of machine learning such as robotics (sensor data), computational biology (gene expression data), vision (video sequences) and graphics (motion capture data). Practical nonlinear probabilistic approaches to this data are required. In this paper we introduce the variational Gaussian process dynamical system. Our work builds on recent varia...