Inverse Modelling, Sensitivity and Monte Carlo Analysis in R Using Package FME

Mathematical simulation models are commonly applied to analyze experimental or environmental data and eventually to acquire predictive capabilities. Typically these models depend on poorly defined, unmeasurable parameters that need to be given a value. Fitting a model to data, so-called inverse modelling, is often the sole way of finding reasonable values for these parameters. There are many challenges involved in inverse model applications, e.g., the existence of non-identifiable parameters, the estimation of parameter uncertainties and the quantification of the implications of these uncertainties on model predictions. The R package FME is a modeling package designed to confront a mathematical model with data. It includes algorithms for sensitivity and Monte Carlo analysis, parameter identifiability, model fitting and provides a Markov-chain based method to estimate parameter confidence intervals. Although its main focus is on mathematical systems that consist of differential equations, FME can deal with other types of models. In this paper, FME is applied to a model describing the dynamics of the HIV virus.

Introduction to the Special Volume on "Ecology and Ecological Modeling in R"

The third special volume in the "Foometrics in R" series of the Journal of Statistical Software collects a number of contributions describing statistical methodology and corresponding implementations related to ecology and ecological modelling. The scope of the papers ranges from theoretical ecology and ecological modelling to statistical methodology relevant for data analyses in ecological applications.

simecol: An Object-Oriented Framework for Ecological Modeling in R

The simecol package provides an open structure to implement, simulate and share ecological models. A generalized object-oriented architecture improves readability and potential code re-use of models and makes simecol-models freely extendable and simple to use. The simecol package was implemented in the S4 class system of the programming language R. Reference applications, e.g. predator-prey models or grid models are provided which can be used as a starting point for own developments. Compact example applications and the complete code of an individual-based model of the water flea Daphnia document the efficient usage of simecol for various purposes in ecological modeling, e.g. scenario analysis, stochastic simulations and individual based population dynamics. Ecologists are encouraged to exploit the abilities of simecol to structure their work and to use R and object-oriented programming as a suitable medium for the distribution and share of ecological modeling code.

Regularity results for interface problems in 2D

We investigate the regularity of solutions of interface problems in 2D. Our objective are regularity results which are independent of global bounds of the data (the diffusion). Therefore we introduce a criterion on the data,the quasi-monotonicity condition, which we show to be sufficient and necessary to provide regularity better then H1. In the proof we use estimates of eigenvalues of a related Sturm-Liouville eigenvalue problem. This approach allows to derive sharp regularity results for quite a large class of configurations. Additionally we give a regularity result depending on the global bounds of the data

Presynaptic Precursor Vesicles - Cargo, Biogenesis, and Kinesin-Based Transport across Species

The faithful formation and, consequently, function of a synapse requires continuous and tightly controlled delivery of synaptic material. At the presynapse, a variety of proteins with unequal molecular properties are indispensable to compose and control the molecular machinery concerting neurotransmitter release through synaptic vesicle fusion with the presynaptic membrane. As presynaptic proteins are produced mainly in the neuronal soma, they are obliged to traffic along microtubules through the axon to reach the consuming presynapse. This anterograde transport is performed by highly specialised and diverse presynaptic precursor vesicles, membranous organelles able to transport as different proteins such as synaptic vesicle membrane and membrane-associated proteins, cytosolic active zone proteins, ion-channels, and presynaptic membrane proteins, coordinating synaptic vesicle exo- and endocytosis. This review aims to summarise and categorise the diverse and numerous findings describing presynaptic precursor cargo, mode of trafficking, kinesin-based axonal transport and the molecular mechanisms of presynaptic precursor vesicles biogenesis in both vertebrate and invertebrate model systems

Solving Differential Equations in R: Package deSolve

In this paper we present the R package deSolve to solve initial value problems (IVP) written as ordinary differential equations (ODE), differential algebraic equations (DAE) of index 0 or 1 and partial differential equations (PDE), the latter solved using the method of lines approach. The differential equations can be represented in R code or as compiled code. In the latter case, R is used as a tool to trigger the integration and post-process the results, which facilitates model development and application, whilst the compiled code significantly increases simulation speed. The methods implemented are efficient, robust, and well documented public-domain Fortran routines. They include four integrators from the ODEPACK package (LSODE, LSODES, LSODA, LSODAR), DVODE and DASPK2.0. In addition, a suite of Runge-Kutta integrators and special-purpose solvers to efficiently integrate 1-, 2- and 3-dimensional partial differential equations are available. The routines solve both stiff and non-stiff systems, and include many options, e.g., to deal in an efficient way with the sparsity of the Jacobian matrix, or finding the root of equations. In this article, our objectives are threefold: (1) to demonstrate the potential of using R for dynamic modeling, (2) to highlight typical uses of the different methods implemented and (3) to compare the performance of models specified in R code and in compiled code for a number of test cases. These comparisons demonstrate that, if the use of loops is avoided, R code can efficiently integrate problems comprising several thousands of state variables. Nevertheless, the same problem may be solved from 2 to more than 50 times faster by using compiled code compared to an implementation using only R code. Still, amongst the benefits of R are a more flexible and interactive implementation, better readability of the code, and access to RâÂÂs high-level procedures. deSolve is the successor of package odesolve which will be deprecated in the future; it is free software and distributed under the GNU General Public License, as part of the R software project.

The role of dynamics in total ozone deviations from their long-term mean over the Northern Hemisphere

International audienceTotal ozone anomalies (deviation from the long-term mean) are created by anomalous circulation patterns. The dynamically produced ozone anomalies can be estimated from known circulation parameters in the layer between the tropopause and the middle stratosphere by means of statistics. Satellite observations of ozone anomalies can be compared with those expected from dynamics. Residual negative anomalies may be due to chemical ozone destruction. The statistics are derived from a 14 year data set of TOMS (Total Ozone Mapping Spectrometer January 1979-Dec. 1992) and corresponding 300 hPa geopotential (for the tropopause height) together with 30 hPa temperature (for stratospheric waves) at 60°N. The correlation coefficient for the linear multiple regression between total ozone (dependent variable) and the dynamical parameters (independent variables) is 0.88 for the zonal deviations in the winter of the Northern Hemisphere. Zonal means are also significantly dependent on circulation parameters, besides showing the known negative trend function of total ozone observed by TOMS. The significant linear trend for 60°N is \sim3 DU/year in the winter months taking into account the dependence on the dynamics between the tropopause region and the mid-stratosphere. The highest correlation coefficient for the monthly mean total ozone anomalies is reached in November with 0.94