scholarly journals From Petri Nets to Differential Equations – An Integrative Approach for Biochemical Network Analysis

2006 ◽  
pp. 181-200 ◽  
Author(s):  
David Gilbert ◽  
Monika Heiner
Keyword(s):  
Network Analysis ◽  
Differential Equations ◽  
Petri Nets ◽  
Biochemical Network ◽  
Integrative Approach

scholarly journals CONTINUOUS PETRI NETS: EXPRESSIVE POWER AND DECIDABILITY ISSUES

2010 ◽  
Vol 21 (02) ◽  
pp. 235-256 ◽  
Author(s):  
LAURA RECALDE ◽  
SERGE HADDAD ◽  
MANUEL SILVA
Keyword(s):  
Differential Equations ◽  
Petri Nets ◽  
Fundamental Problem ◽  
Discrete Event ◽  
Expressive Power ◽  
Timed Petri Nets ◽  
Analysis And Synthesis ◽  
Continuous Petri Nets ◽  
Linear Differential ◽  
The One

State explosion is a fundamental problem in the analysis and synthesis of discrete event systems. Continuous Petri nets can be seen as a relaxation of the corresponding discrete model. The expected gains are twofold: improvements in complexity and in decidability. In the case of autonomous nets we prove that liveness or deadlock-freeness remain decidable and can be checked more efficiently than in Petri nets. Then we introduce time in the model which now behaves as a dynamical system driven by differential equations and we study it w.r.t. expressiveness and decidability issues. On the one hand, we prove that this model is equivalent to timed differential Petri nets which are a slight extension of systems driven by linear differential equations (LDE). On the other hand, (contrary to the systems driven by LDEs) we show that continuous timed Petri nets are able to simulate Turing machines and thus that basic properties become undecidable.

scholarly journals Modeling biological gradient formation: combining partial differential equations and Petri nets

2015 ◽  
Vol 15 (4) ◽  
pp. 665-675 ◽  
Author(s):  
Laura M. F. Bertens ◽  
Jetty Kleijn ◽  
Sander C. Hille ◽  
Monika Heiner ◽  
Maciej Koutny ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Petri Nets ◽  
Partial Differential ◽  
Gradient Formation

Network Analysis: An Integrative Approach to the Structure of Psychopathology

2013 ◽  
Vol 9 (1) ◽  
pp. 91-121 ◽  
Author(s):  
Denny Borsboom ◽  
Angélique O.J. Cramer
Keyword(s):  
Network Analysis ◽  
Integrative Approach

scholarly journals Bisimulation Relations Between Automata, Stochastic Differential Equations and Petri Nets

2010 ◽  
Vol 20 ◽  
pp. 1-15 ◽  
Author(s):  
Mariken H.C. Everdij ◽  
Henk A.P. Blom
Keyword(s):  
Differential Equations ◽  
Petri Nets ◽  
Stochastic Differential Equations

scholarly journals Graph models and mathematical programming in biochemical network analysis and metabolic engineering design

2008 ◽  
Vol 55 (5) ◽  
pp. 970-983 ◽  
Author(s):  
Stefano Lanzeni ◽  
Enza Messina ◽  
Francesco Archetti
Keyword(s):  
Metabolic Engineering ◽  
Network Analysis ◽  
Mathematical Programming ◽  
Engineering Design ◽  
Biochemical Network ◽  
Graph Models

scholarly journals An integrative approach to develop computational pipeline for drug-target interaction network analysis

2018 ◽  
Vol 8 (1) ◽  
Author(s):  
Ankush Bansal ◽  
Pulkit Anupam Srivastava ◽  
Tiratha Raj Singh
Keyword(s):  
Network Analysis ◽  
Drug Target ◽  
Interaction Network ◽  
Integrative Approach ◽  
Computational Pipeline ◽  
Target Interaction
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