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A Monte Carlo model checker for probabilistic LTL with numerical constraints
We define the syntax and semantics of a new temporal logic called probabilistic LTL with numerical constraints (PLTLc).
We introduce an efficient model checker for PLTLc properties. The efficiency of the model checker is through approximation
using Monte Carlo sampling of finite paths through the model’s state space (simulation outputs) and parallel model checking
of the paths. Our model checking method can be applied to any model producing quantitative output – continuous or
stochastic, including those with complex dynamics and those with an infinite state space. Furthermore, our offline approach
allows the analysis of observed (real-life) behaviour traces. We find in this paper that PLTLc properties with constraints
over free variables can replace full model checking experiments, resulting in a significant gain in efficiency. This overcomes
one disadvantage of model checking experiments which is that the complexity depends on system granularity and number of
variables, and quickly becomes infeasible. We focus on models of biochemical networks, and specifically in this paper on
intracellular signalling pathways; however our method can be applied to a wide range of biological as well as technical
systems and their models. Our work contributes to the emerging field of synthetic biology by proposing a rigourous approach
for the structured formal engineering of biological systems
The relationship between eddy-transport and second-order closure models for stratified media and for vortices
The question is considered of how complex a model should be used for the calculation of turbulent shear flows. At the present time there are models varying in complexity from very simple eddy-transport models to models in which all the equations for the nonzero second-order correlations are solved simultaneously with the equations for the mean variables. A discussion is presented of the relationship between these two models of turbulent shear flow. Two types of motion are discussed: first, turbulent shear flow in a stratified medium and, second, the motion in a turbulent line vortex. These two cases are instructive because in the first example eddy-transport methods have proven reasonably effective, whereas in the second, they have led to erroneous conclusions. It is not generally appreciated that the simplest form of eddy-transport theory can be derived from second-order closure models of turbulent flow by a suitably limiting process. This limiting process and the suitability of eddy-transport modeling for stratified media and line vortices are discussed
Petri nets for systems and synthetic biology
We give a description of a Petri net-based framework for
modelling and analysing biochemical pathways, which uni¯es the qualita-
tive, stochastic and continuous paradigms. Each perspective adds its con-
tribution to the understanding of the system, thus the three approaches
do not compete, but complement each other. We illustrate our approach
by applying it to an extended model of the three stage cascade, which
forms the core of the ERK signal transduction pathway. Consequently
our focus is on transient behaviour analysis. We demonstrate how quali-
tative descriptions are abstractions over stochastic or continuous descrip-
tions, and show that the stochastic and continuous models approximate
each other. Although our framework is based on Petri nets, it can be
applied more widely to other formalisms which are used to model and
analyse biochemical networks
An invariant second-order closure model of the compressible turbulent boundary layer on a flat plate
The development of an invariant model designed expressly for the computation of shear flows is discussed. The model for incompressible layers seeks a second-order closure of the equations for the mean and fluctuating fields. The development of a method for computing the behavior of shear layers in compressible forces is described. The complexity of the analysis is restrained by limiting the consideration to a flat plate boundary layer where the mean pressure can be taken to be constant
Discrete Geometric Structures in Homogenization and Inverse Homogenization with application to EIT
We introduce a new geometric approach for the homogenization and inverse
homogenization of the divergence form elliptic operator with rough conductivity
coefficients in dimension two. We show that conductivity
coefficients are in one-to-one correspondence with divergence-free matrices and
convex functions over the domain . Although homogenization is a
non-linear and non-injective operator when applied directly to conductivity
coefficients, homogenization becomes a linear interpolation operator over
triangulations of when re-expressed using convex functions, and is a
volume averaging operator when re-expressed with divergence-free matrices.
Using optimal weighted Delaunay triangulations for linearly interpolating
convex functions, we obtain an optimally robust homogenization algorithm for
arbitrary rough coefficients. Next, we consider inverse homogenization and show
how to decompose it into a linear ill-posed problem and a well-posed non-linear
problem. We apply this new geometric approach to Electrical Impedance
Tomography (EIT). It is known that the EIT problem admits at most one isotropic
solution. If an isotropic solution exists, we show how to compute it from any
conductivity having the same boundary Dirichlet-to-Neumann map. It is known
that the EIT problem admits a unique (stable with respect to -convergence)
solution in the space of divergence-free matrices. As such we suggest that the
space of convex functions is the natural space in which to parameterize
solutions of the EIT problem
At Short Telomeres Tel1 Directs Early Replication and Phosphorylates Rif1
Funding AS was supported by a Cancer Research UK PhD studentship and ORSAS. SK is supported by a Scottish Universities Life Sciences Alliance PhD studentship. This work was supported by Cancer Research UK grant A13356 to ADD (http://www.cancerresearchuk.org). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Peer reviewedPublisher PD
Is PCNA unloading the central function of the Elg1/ATAD5 replication factor C-like complex?
This is an open-access article licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License. The article may be redistributed, reproduced, and reused for non-commercial purposes, provided the original source is properly cited.Peer reviewedPublisher PD
Constitutive Models for Tumour Classification
The aim of this paper is to formulate new mathematical models that will be able to differentiate not only between normal and abnormal tissues, but, more importantly, between benign and malignant tumours. We present preliminary results of a tri-phasic model and numerical simulations of the effect of cellular adhesion forces on the mechanical properties of biological tissues.
We pursued the following three approaches:
(i) the simulation of the time-harmonic linear elastic models to examine coarse scale effects and adhesion properties,
(ii) the investigation of a tri-phasic model, with the intent of upscaling this model to determine effects of electro-mechanical coupling between cells,
and (iii) the upscaling of a simple cell model as a framework for studying interface conditions at malignant cells.
Each of these approaches has opened exciting new directions of research that we plan to study in the future
Development of a second order closure model for computation of turbulent diffusion flames
A typical eddy box model for the second-order closure of turbulent, multispecies, reacting flows developed. The model structure was quite general and was valid for an arbitrary number of species. For the case of a reaction involving three species, the nine model parameters were determined from equations for nine independent first- and second-order correlations. The model enabled calculation of any higher-order correlation involving mass fractions, temperatures, and reaction rates in terms of first- and second-order correlations. Model predictions for the reaction rate were in very good agreement with exact solutions of the reaction rate equations for a number of assumed flow distributions
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