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

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 $\sigma(x)$ in dimension two. We show that conductivity coefficients are in one-to-one correspondence with divergence-free matrices and convex functions $s(x)$ over the domain $\Omega$. 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 $\Omega$ 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 $G$-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

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

The effect of heavy rain on an airfoil at high lift

No serious studies of the relationship of heavy rain to aircraft safety were made until 1981 when it was suggested that the torrential rain which often occurs at the time of severe wind shear might substantially increase the danger to aircraft operating at slow speeds and high lift in the vicinity of airports. While these data were not published until early 1983, appropriate measures were taken by NASA to study the effect of heavy rain on the lift of wings typical of commercial aircraft. One of the aspects of these tests that seemed confirmed by the data was the existence of a velocity effect on the lift data. The data seemed to indicate that when all the normal non-dimensional aerodynamic parameters were used to sort out the data, the effect of velocity was not accounted for, as it usually is, by the effect of dynamic pressure. Indeed, the measured lift coefficients at high lift indicated a dropoff in lift coefficient for the same free-stream water content as velocity was increased. indicated a drop-off in lift coefficient for the same free-stream water content as velocity was increased