1,098 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 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
Analysis of Petri Nets and Transition Systems
This paper describes a stand-alone, no-frills tool supporting the analysis of
(labelled) place/transition Petri nets and the synthesis of labelled transition
systems into Petri nets. It is implemented as a collection of independent,
dedicated algorithms which have been designed to operate modularly, portably,
extensibly, and efficiently.Comment: In Proceedings ICE 2015, arXiv:1508.0459
Computational Processes and Incompleteness
We introduce a formal definition of Wolfram's notion of computational process
based on cellular automata, a physics-like model of computation. There is a
natural classification of these processes into decidable, intermediate and
complete. It is shown that in the context of standard finite injury priority
arguments one cannot establish the existence of an intermediate computational
process
Computational Complexity of Atomic Chemical Reaction Networks
Informally, a chemical reaction network is "atomic" if each reaction may be
interpreted as the rearrangement of indivisible units of matter. There are
several reasonable definitions formalizing this idea. We investigate the
computational complexity of deciding whether a given network is atomic
according to each of these definitions.
Our first definition, primitive atomic, which requires each reaction to
preserve the total number of atoms, is to shown to be equivalent to mass
conservation. Since it is known that it can be decided in polynomial time
whether a given chemical reaction network is mass-conserving, the equivalence
gives an efficient algorithm to decide primitive atomicity.
Another definition, subset atomic, further requires that all atoms are
species. We show that deciding whether a given network is subset atomic is in
, and the problem "is a network subset atomic with respect to a
given atom set" is strongly -.
A third definition, reachably atomic, studied by Adleman, Gopalkrishnan et
al., further requires that each species has a sequence of reactions splitting
it into its constituent atoms. We show that there is a to decide whether a given network is reachably atomic, improving
upon the result of Adleman et al. that the problem is . We
show that the reachability problem for reachably atomic networks is
-.
Finally, we demonstrate equivalence relationships between our definitions and
some special cases of another existing definition of atomicity due to Gnacadja
A recursive paradigm for aligning observed behavior of large structured process models
The alignment of observed and modeled behavior is a crucial problem in process mining, since it opens the door for conformance checking and enhancement of process models. The state of the art techniques for the computation of alignments rely on a full exploration of the combination of the model state space and the observed behavior (an event log), which hampers their applicability for large instances. This paper presents a fresh view to the alignment problem: the computation of alignments is casted as the resolution of Integer Linear Programming models, where the user can decide the granularity of the alignment steps. Moreover, a novel recursive strategy is used to split
the problem into small pieces, exponentially reducing the complexity of the ILP models to be solved. The contributions of this paper represent a promising alternative to fight the inherent complexity of computing alignments for large instances.Peer ReviewedPostprint (author's final draft
Security-sensitive tackling of obstructed workflow executions
Imposing access control onto workflows considerably reduces the set of users authorized to execute the workflow tasks. Further constraints (e.g. Separation of Duties) as well as unexpected unavailabilty of users may finally obstruct the successful workflow execution. To still complete the execution of an obstructed workflow, we envisage a hybrid
approach. If a log is provided, we partition its traces into “successful” and “obstructed” ones by analysing the given workflow and its authorizations. An obstruction should then be solved by finding its nearest match from the list of successful traces. If no log is provided, we flatten the workflow and its authorizations into a Petri net and encode the obstruction with a corresponding “obstruction marking”. The structural theory of Petri nets shall then be tweaked to provide a minimized Parikh vector, that may violate given firing rules, however reach a complete marking and by that, complete the workflow.Peer ReviewedPostprint (published version
Ergodicity of the zigzag process
The zigzag process is a Piecewise Deterministic Markov Process which can be
used in a MCMC framework to sample from a given target distribution. We prove
the convergence of this process to its target under very weak assumptions, and
establish a central limit theorem for empirical averages under stronger
assumptions on the decay of the target measure. We use the classical
"Meyn-Tweedie" approach. The main difficulty turns out to be the proof that the
process can indeed reach all the points in the space, even if we consider the
minimal switching rates
Synthesis of Bounded Choice-Free Petri Nets
This paper describes a synthesis algorithm tailored to the construction of choice-free Petri nets from finite persistent transition systems. With this goal in mind, a minimised set of simplified systems of linear inequalities is distilled from a general region-theoretic approach, leading to algorithmic improvements as well as to a partial characterisation of the class of persistent transition systems that have a choice-free Petri net realisation
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