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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 modelās state space (simulation outputs) and parallel model checking
of the paths. Our model checking method can be applied to any model producing quantitative output ā 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 uniĀÆes 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
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An introduction to Biomodel engineering, illustrated for signal transduction pathways
BioModel Engineering is the science of designing, constructing
and analyzing computational models of biological systems. It is inspired
by concepts from software engineering and computing science.
This paper illustrates a major theme in BioModel Engineering, namely
that identifying a quantitative model of a dynamic system means building
the structure, finding an initial state, and parameter fitting. In our
approach, the structure is obtained by piecewise construction of models
from modular parts, the initial state is obtained by analysis of the structure
and parameter fitting comprises determining the rate parameters of
the kinetic equations. We illustrate this with an example in the area of
intracellular signalling pathways
Computing dispersal of atmospheric pollutants near airports
Computing dispersal of atmospheric pollutants near airports by use of mean wind and temperature profile
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
Some analyses of the chemistry and diffusion of SST exhaust materials during phase 3 of the wake period
In the generally stably stratified lower stratosphere, SST exhaust plumes could spend a significant length of time in a relatively undispersed state. This effort has utilized invariant modeling techniques to simulate the separate and combined effects of atmospheric turbulence, turbulent diffusion, and chemical reactions of SST exhaust materials in the lower stratosphere. The primary results to date are: (1) The combination of relatively slow diffusive mixing and rapid chemical reactions during the Phase III wake period minimizes the effect of SST exhausts on O3 depletion by the so-called NOx catalytic cycle. While the SST-produced NO is substantially above background concentrations, it appears diffusive mixing of NO and O3 is simply too slow to produce the O3 depletions originally proposed. (2) The time required to dilute the SST exhaust plume may be a significant fraction of the total time these materials are resident in the lower stratosphere. If this is the case, then prior estimates of the environmental impact of these materials must be revised significantly downward
Nondispersive infrared analyzer for specific gases in complex mixtures
Analyzer identifies and measures particular diatomic or polyatomic gases in complex gas mixtures. Mixing of absorption effects on light energy passing through gases to photodetector produces a signal component that is related to the absorption caused by reference-gas component in unknown gas mixture
Improvement of Terminal Area Capacity in the New York Airspace
The New York airspace is the most congested in the U.S. air transportation network.
Increasing capacity in this area is critical to ensure the balanced growth of traffic across the U.S. This study compares the total measured runway capacity at the New York airports with the achieved throughput of the New York airspace. The comparison is performed for six airspace configurations representing operations under different wind conditions, visibility and relative arrival and departure demand. The comparison shows that in all cases the capacity of the system of airports is lower than the total capacity of the airports considered individually by approximately 20%. This finding suggests that air traffic throughput in the New York area is constrained by shared airspace resources. If these constraints could be removed, these funding suggest that capacity could be increased approximately 20% without any airport infrastructure or procedure changes.
An examination of procedures close to the airports is performed to identify fixed constraints. The impact of these constraints is not captured by the empirical analysis because these constraints are always present. This analysis identifies cases where new navigation technologies could be used to reduce the interactions between airports. The greatest potential for improvement is found to be in the lower performing configurations. Therefore procedural changes close to the airports may provide more benefit in reducing the variability of capacity between different configurations, rather than providing large increases in maximum capacity.This research was supported by both NASA and the FAA through agreement
number NNA06CN24A and contract DTFA01-C-00030
On complex surfaces diffeomorphic to rational surfaces
In this paper we prove that no complex surface of general type is
diffeomorphic to a rational surface, thereby completing the smooth
classification of rational surfaces and the proof of the Van de Ven conjecture
on the smooth invariance of Kodaira dimension.Comment: 34 pages, AMS-Te
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