6,515 research outputs found
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
The Hardness of Finding Linear Ranking Functions for Lasso Programs
Finding whether a linear-constraint loop has a linear ranking function is an
important key to understanding the loop behavior, proving its termination and
establishing iteration bounds. If no preconditions are provided, the decision
problem is known to be in coNP when variables range over the integers and in
PTIME for the rational numbers, or real numbers. Here we show that deciding
whether a linear-constraint loop with a precondition, specifically with
partially-specified input, has a linear ranking function is EXPSPACE-hard over
the integers, and PSPACE-hard over the rationals. The precise complexity of
these decision problems is yet unknown. The EXPSPACE lower bound is derived
from the reachability problem for Petri nets (equivalently, Vector Addition
Systems), and possibly indicates an even stronger lower bound (subject to open
problems in VAS theory). The lower bound for the rationals follows from a novel
simulation of Boolean programs. Lower bounds are also given for the problem of
deciding if a linear ranking-function supported by a particular form of
inductive invariant exists. For loops over integers, the problem is PSPACE-hard
for convex polyhedral invariants and EXPSPACE-hard for downward-closed sets of
natural numbers as invariants.Comment: In Proceedings GandALF 2014, arXiv:1408.5560. I thank the organizers
of the Dagstuhl Seminar 14141, "Reachability Problems for Infinite-State
Systems", for the opportunity to present an early draft of this wor
ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra
Background: Many biological systems are modeled qualitatively with discrete
models, such as probabilistic Boolean networks, logical models, Petri nets, and
agent-based models, with the goal to gain a better understanding of the system.
The computational complexity to analyze the complete dynamics of these models
grows exponentially in the number of variables, which impedes working with
complex models. Although there exist sophisticated algorithms to determine the
dynamics of discrete models, their implementations usually require
labor-intensive formatting of the model formulation, and they are oftentimes
not accessible to users without programming skills. Efficient analysis methods
are needed that are accessible to modelers and easy to use. Method: By
converting discrete models into algebraic models, tools from computational
algebra can be used to analyze their dynamics. Specifically, we propose a
method to identify attractors of a discrete model that is equivalent to solving
a system of polynomial equations, a long-studied problem in computer algebra.
Results: A method for efficiently identifying attractors, and the web-based
tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other
analysis methods for discrete models. ADAM converts several discrete model
types automatically into polynomial dynamical systems and analyzes their
dynamics using tools from computer algebra. Based on extensive experimentation
with both discrete models arising in systems biology and randomly generated
networks, we found that the algebraic algorithms presented in this manuscript
are fast for systems with the structure maintained by most biological systems,
namely sparseness, i.e., while the number of nodes in a biological network may
be quite large, each node is affected only by a small number of other nodes,
and robustness, i.e., small number of attractors
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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
Lifted structural invariant analysis of Petri net product lines
Petri nets are commonly used to represent concurrent systems. However, they lack support
for modelling and analysing system families, like variants of controllers, different variations
of a process model, or the possible configurations of a flexible assembly line.
To facilitate modelling potentially large collections of similar systems, in this paper, we
enrich Petri nets with variability mechanisms based on product line engineering. Moreover,
we present methods for the efficient analysis of the place and transition invariants in
all defined versions of a Petri net. Efficiency is achieved by analysing the system family
as a whole, instead of analysing each possible net variant separately. For this purpose,
we lift the notion of incidence matrix to the product line level, and rely on constraint
solving techniques. We present tool support and evaluate the benefits of our techniques
on synthetic and realistic examples, achieving in some cases speed-ups of two orders of
magnitude with respect to analysing each net variant separatelyThis work has been funded by the Spanish Ministry of Science (PID2021-122270OB-I00) and the R&D
programme of Madrid (P2018/TCS-4314
Representations of nets of C*-algebras over S^1
In recent times a new kind of representations has been used to describe
superselection sectors of the observable net over a curved spacetime, taking
into account of the effects of the fundamental group of the spacetime. Using
this notion of representation, we prove that any net of C*-algebras over S^1
admits faithful representations, and when the net is covariant under Diff(S^1),
it admits representations covariant under any amenable subgroup of Diff(S^1)
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