Bio-PEPAd: A non-Markovian extension of Bio-PEPA

Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed, or to provide abstraction of some behavior of the system resulting in more compact models. In this paper, we enrich the stochastic process algebra Bio-PEPA, with the possibility o...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Theoretical computer science Jg. 419; S. 26 - 49
Hauptverfasser: Caravagna, Giulio, Hillston, Jane
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 17.02.2012
Schlagworte:
ISSN:0304-3975, 1879-2294
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Abstract Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed, or to provide abstraction of some behavior of the system resulting in more compact models. In this paper, we enrich the stochastic process algebra Bio-PEPA, with the possibility of assigning delays to actions, yielding a new non-Markovian stochastic process algebra: Bio-PEPAd. This is a conservative extension meaning that the original syntax of Bio-PEPA is retained and the delay specification which can now be associated with actions may be added to existing Bio-PEPA models. The semantics of the firing of the actions with delays is the delay-as-duration approach, earlier presented in papers on the stochastic simulation of biological systems with delays. This semantics of the algebra is given in the Starting–Terminating style, meaning that the state and the completion of an action are observed as two separate events, as required by delays. We formally define the encoding of Bio-PEPAd systems in Generalized Semi-Markov Processes (GSMPs), as input for a Delay Stochastic Simulation Algorithm (DSSA) and as sets of Delay Differential Equations (DDEs), the deterministic framework for modeling of biological systems with delays. Finally, we prove theorems stating the relation between Bio-PEPA and Bio-PEPAd models. We end the paper with an example model of biological systems with delays to illustrate the approach.
AbstractList Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed, or to provide abstraction of some behavior of the system resulting in more compact models. In this paper, we enrich the stochastic process algebra Bio-PEPA, with the possibility of assigning delays to actions, yielding a new non-Markovian stochastic process algebra: Bio-PEPAd. This is a conservative extension meaning that the original syntax of Bio-PEPA is retained and the delay specification which can now be associated with actions may be added to existing Bio-PEPA models. The semantics of the firing of the actions with delays is the delay-as-duration approach, earlier presented in papers on the stochastic simulation of biological systems with delays. This semantics of the algebra is given in the Starting–Terminating style, meaning that the state and the completion of an action are observed as two separate events, as required by delays. We formally define the encoding of Bio-PEPAd systems in Generalized Semi-Markov Processes (GSMPs), as input for a Delay Stochastic Simulation Algorithm (DSSA) and as sets of Delay Differential Equations (DDEs), the deterministic framework for modeling of biological systems with delays. Finally, we prove theorems stating the relation between Bio-PEPA and Bio-PEPAd models. We end the paper with an example model of biological systems with delays to illustrate the approach.
Author Hillston, Jane
Caravagna, Giulio
Author_xml – sequence: 1
  givenname: Giulio
  surname: Caravagna
  fullname: Caravagna, Giulio
  email: caravagn@di.unipi.it
  organization: Dipartimento di Informatica, Università di Pisa, Largo Bruno Pontecorvo 3, 56127 Pisa, Italy
– sequence: 2
  givenname: Jane
  surname: Hillston
  fullname: Hillston, Jane
  email: jane.hillston@ed.ac.uk
  organization: Laboratory for Foundations of Computer Science, The University of Edinburgh, Edinburgh EH8 9AB, Scotland, United Kingdom
BookMark eNp9j01LAzEQhoMo2FZ_gLf9A1kz2a-snmqpH1CxBz2HJDuB1LqRJBT996ZULx46DDMMzPPCMyWnox-RkCtgJTBorzdlMrHkDKDMzbg4IRMQXU857-tTMmEVq2nVd805mca4Ybmarp0Qduc8XS_X8-GmmBc5lD6r8O53To0FfiUco_Nj4W3x93dBzqzaRrz83TPydr98XTzS1cvD02K-oob3XaJaY2XbAYRhPXCBoretRoX50ornYbVhjR56XQOCsJzbRtQVNEIhb0FVMwKHXBN8jAGt_AzuQ4VvCUzuleVGZmW5V5a5s3Jmun-McUmlbJCCctuj5O2BxKy0cxhkNA5Hg4MLaJIcvDtC_wBPCHEj
CitedBy_id crossref_primary_10_1016_j_entcs_2013_02_016
crossref_primary_10_1088_1478_3975_abc2ab
crossref_primary_10_1016_j_peva_2016_09_001
crossref_primary_10_1016_j_ic_2014_01_010
crossref_primary_10_1016_j_tcs_2015_03_051
crossref_primary_10_1186_1752_0509_9_S3_S8
crossref_primary_10_1016_j_ic_2014_01_016
crossref_primary_10_1080_17445760_2025_2527713
Cites_doi 10.4204/EPTCS.6.2
10.1017/S0305004100030437
10.1016/j.tcs.2007.11.013
10.1007/978-3-642-11712-1_3
10.1007/978-3-642-19748-2_4
10.1016/S0020-0190(01)00214-9
10.1016/j.tcs.2011.01.007
10.4204/EPTCS.40.7
10.1016/S0304-3975(01)00043-3
10.1145/1364644.1364653
10.1371/journal.pcbi.0020117
10.1016/j.ic.2005.07.002
10.1016/j.jlap.2004.03.009
10.1016/S0025-5564(00)00006-7
10.1073/pnas.0503858102
10.1007/3-540-45605-8_14
10.1145/1839764.1839771
10.1016/j.amc.2007.09.053
10.1093/comjnl/38.7.578
10.1021/j100540a008
10.1016/j.tcs.2004.03.061
10.1007/s00285-003-0211-0
10.1016/j.tcs.2009.02.037
ContentType Journal Article
Copyright 2011 Elsevier B.V.
Copyright_xml – notice: 2011 Elsevier B.V.
DBID 6I.
AAFTH
AAYXX
CITATION
DOI 10.1016/j.tcs.2011.11.028
DatabaseName ScienceDirect Open Access Titles
Elsevier:ScienceDirect:Open Access
CrossRef
DatabaseTitle CrossRef
DatabaseTitleList
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
Computer Science
EISSN 1879-2294
EndPage 49
ExternalDocumentID 10_1016_j_tcs_2011_11_028
S0304397511009479
GroupedDBID --K
--M
-~X
.DC
.~1
0R~
123
1B1
1RT
1~.
1~5
29Q
4.4
457
4G.
5VS
6I.
7-5
71M
8P~
9JN
AABNK
AACTN
AAEDT
AAEDW
AAFTH
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAQXK
AAXUO
AAYFN
ABAOU
ABBOA
ABEFU
ABFNM
ABJNI
ABMAC
ABTAH
ABVKL
ABXDB
ABYKQ
ACAZW
ACDAQ
ACGFS
ACNNM
ACRLP
ACZNC
ADBBV
ADEZE
ADMUD
AEBSH
AEKER
AENEX
AEXQZ
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AHZHX
AIALX
AIEXJ
AIKHN
AITUG
AJBFU
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
AOUOD
ARUGR
ASPBG
AVWKF
AXJTR
AZFZN
BKOJK
BLXMC
CS3
DU5
EBS
EFJIC
EFLBG
EJD
EO8
EO9
EP2
EP3
F5P
FDB
FEDTE
FGOYB
FIRID
FNPLU
FYGXN
G-2
G-Q
G8K
GBLVA
GBOLZ
HVGLF
HZ~
IHE
IXB
J1W
KOM
LG9
M26
M41
MHUIS
MO0
N9A
NCXOZ
O-L
O9-
OAUVE
OK1
OZT
P-8
P-9
P2P
PC.
Q38
R2-
RIG
ROL
RPZ
SCC
SDF
SDG
SES
SEW
SPC
SPCBC
SSV
SSW
SSZ
T5K
TAE
TN5
WH7
WUQ
XJT
YNT
ZMT
ZY4
~G-
9DU
AATTM
AAXKI
AAYWO
AAYXX
ABDPE
ABWVN
ACLOT
ACRPL
ACVFH
ADCNI
ADNMO
ADVLN
AEIPS
AEUPX
AFJKZ
AFPUW
AGQPQ
AIGII
AIIUN
AKBMS
AKRWK
AKYEP
ANKPU
APXCP
CITATION
EFKBS
~HD
ID FETCH-LOGICAL-c297t-bbe3f6d18c09128e89f6beae091ba291bfbc05bd9b41e18f22f5843158ae261a3
ISICitedReferencesCount 13
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000300534900004&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 0304-3975
IngestDate Sat Nov 29 05:15:08 EST 2025
Tue Nov 18 21:56:45 EST 2025
Fri Feb 23 02:16:40 EST 2024
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Keywords DDEs
Delay-as-duration
GSMPs
Non-Markovian process algebra
DSSA
Bio-PEPA
Language English
License http://www.elsevier.com/open-access/userlicense/1.0
https://www.elsevier.com/tdm/userlicense/1.0
https://www.elsevier.com/open-access/userlicense/1.0
LinkModel OpenURL
MergedId FETCHMERGED-LOGICAL-c297t-bbe3f6d18c09128e89f6beae091ba291bfbc05bd9b41e18f22f5843158ae261a3
OpenAccessLink https://dx.doi.org/10.1016/j.tcs.2011.11.028
PageCount 24
ParticipantIDs crossref_primary_10_1016_j_tcs_2011_11_028
crossref_citationtrail_10_1016_j_tcs_2011_11_028
elsevier_sciencedirect_doi_10_1016_j_tcs_2011_11_028
PublicationCentury 2000
PublicationDate 2012-02-17
PublicationDateYYYYMMDD 2012-02-17
PublicationDate_xml – month: 02
  year: 2012
  text: 2012-02-17
  day: 17
PublicationDecade 2010
PublicationTitle Theoretical computer science
PublicationYear 2012
Publisher Elsevier B.V
Publisher_xml – name: Elsevier B.V
References Beretta, Hara, Ma, Takeuchi (br000030) 2002; 54
German (br000115) 2000
Pedersen, Plotkin (br000175) 2010; 5945
Priami (br000185) 1995; 38
Caravagna, Hillston (br000065) 2010; vol. 40
Bravetti, Bernardo, Gorrieri (br000055) 1998; vol. 1466
Priami, Regev, Shapiro, Silverman (br000190) 2001; 80
M. Bravetti, Specification and analysis of stochastic real-time systems, Ph.D. Thesis, Università di Bologna, 2002.
Zhanga, Lia, Zhangc (br000215) 2008; 199
Heath, Kwiatkowska, Norman, Parker, Tymchyshyn (br000140) 2008; 391
Ciocchetta, Hillston (br000070) 2009; 410
Bratsun, Volfson, Tsimring, Hasty (br000040) 2005; 102
P.W. Glynn, On the role of generalized semi-markov processes in simulation output analysis, in: Proc. of the 15th Conference on Winter Simulation, Volume 1, 1983, pp. 39–44.
Barbuti, Caravagna, Maggiolo-Schettini, Milazzo, Pardini (br000015) 2008; vol. 5016
J. Markovski, Real and stochastic time in process algebras for performance evaluation, Ph.D. Thesis, University of Eindhoven, 2008.
Barbuti, Caravagna, Maggiolo-Schettini, Milazzo (br000005) 2009; vol. 6
Milner, Toft, Harper (br000160) 1990
Bravetti, Gorrieri (br000050) 2002; 282
Barbuti, Caravagna, Maggiolo-Schettini, Milazzo (br000010) 2011; 6575
Bio-PEPA web site
Regev, Panina, Silverman, Cardelli, Shapiro (br000195) 2004; 325
Villasana, Radunskaya (br000210) 2003; 47
G. Caravagna, Formal modeling and simulation of biological systems with delays, Ph.D. Thesis, Università di Pisa, 2011.
Lopez, Nunez (br000145) 2000
Danos, Feret, Fontana, Harmer, Krivine (br000100) 2007; vol. 4703
L. Paulevé, S. Youssef, M.R. Lakin, A. Phillips, A generic abstract machine for stochastic process calculi, in: Proceedings of the 8th International Conference on Computational Methods in Systems Biology CMSB vol. 10, 2010, pp. 43–54.
Mura, Prandi, Priami, Romanel (br000165) 2009; 253
D’Argenio, Katoen (br000090) 2005; 203
Barbuti, Maggiolo-Schettini, Milazzo, Pardini (br000020) 2008; 229
van Glabbeek, Vaandrager (br000125) 1987; 259
Dematté, Priami, Romanel (br000105) 2008; 35
Culshaw, Ruan (br000085) 2000; 165
Plotkin (br000180) 2004; 60–61
.
Galpin, Hillston (br000110) 2011; 412
Hillston (br000135) 1996
Barrio, Burrage, Leier, Tian (br000025) 2006; 2
Cox (br000080) 1955; 51
Regev, Silverman, Shapiro (br000200) 2001
Gillespie (br000120) 1977; 81
Prism web site
P. Milazzo, Qualitative and quantitative formal modeling of biological systems, Ph.D. Thesis, Università di Pisa, 2007.
P.R. D’Argenio, J.-P. Katoen, E. Brinksma, A stochastic automata model and its algebraic approach, in: Proc. 5th Int. Workshop on Process Algebra and Performance Modeling, PAPM’97, CTIT technical reports series 97–14, University of Twente, 1997, pp. 1–16.
Ciocchetta, Hillston (br000075) 2008; vol. 5016
10.1016/j.tcs.2011.11.028_br000035
Danos (10.1016/j.tcs.2011.11.028_br000100) 2007; vol. 4703
10.1016/j.tcs.2011.11.028_br000155
Beretta (10.1016/j.tcs.2011.11.028_br000030) 2002; 54
Barbuti (10.1016/j.tcs.2011.11.028_br000020) 2008; 229
Priami (10.1016/j.tcs.2011.11.028_br000185) 1995; 38
Milner (10.1016/j.tcs.2011.11.028_br000160) 1990
Barbuti (10.1016/j.tcs.2011.11.028_br000015) 2008; vol. 5016
Regev (10.1016/j.tcs.2011.11.028_br000195) 2004; 325
Zhanga (10.1016/j.tcs.2011.11.028_br000215) 2008; 199
Ciocchetta (10.1016/j.tcs.2011.11.028_br000075) 2008; vol. 5016
Culshaw (10.1016/j.tcs.2011.11.028_br000085) 2000; 165
Cox (10.1016/j.tcs.2011.11.028_br000080) 1955; 51
Priami (10.1016/j.tcs.2011.11.028_br000190) 2001; 80
Barbuti (10.1016/j.tcs.2011.11.028_br000005) 2009; vol. 6
Plotkin (10.1016/j.tcs.2011.11.028_br000180) 2004; 60–61
Mura (10.1016/j.tcs.2011.11.028_br000165) 2009; 253
Ciocchetta (10.1016/j.tcs.2011.11.028_br000070) 2009; 410
Barbuti (10.1016/j.tcs.2011.11.028_br000010) 2011; 6575
10.1016/j.tcs.2011.11.028_br000060
Bratsun (10.1016/j.tcs.2011.11.028_br000040) 2005; 102
German (10.1016/j.tcs.2011.11.028_br000115) 2000
Bravetti (10.1016/j.tcs.2011.11.028_br000055) 1998; vol. 1466
Hillston (10.1016/j.tcs.2011.11.028_br000135) 1996
10.1016/j.tcs.2011.11.028_br000045
Pedersen (10.1016/j.tcs.2011.11.028_br000175) 2010; 5945
Barrio (10.1016/j.tcs.2011.11.028_br000025) 2006; 2
Gillespie (10.1016/j.tcs.2011.11.028_br000120) 1977; 81
Caravagna (10.1016/j.tcs.2011.11.028_br000065) 2010; vol. 40
Galpin (10.1016/j.tcs.2011.11.028_br000110) 2011; 412
10.1016/j.tcs.2011.11.028_br000205
Bravetti (10.1016/j.tcs.2011.11.028_br000050) 2002; 282
Villasana (10.1016/j.tcs.2011.11.028_br000210) 2003; 47
D’Argenio (10.1016/j.tcs.2011.11.028_br000090) 2005; 203
Heath (10.1016/j.tcs.2011.11.028_br000140) 2008; 391
Lopez (10.1016/j.tcs.2011.11.028_br000145) 2000
Dematté (10.1016/j.tcs.2011.11.028_br000105) 2008; 35
10.1016/j.tcs.2011.11.028_br000170
10.1016/j.tcs.2011.11.028_br000095
10.1016/j.tcs.2011.11.028_br000150
Regev (10.1016/j.tcs.2011.11.028_br000200) 2001
10.1016/j.tcs.2011.11.028_br000130
van Glabbeek (10.1016/j.tcs.2011.11.028_br000125) 1987; 259
References_xml – reference: J. Markovski, Real and stochastic time in process algebras for performance evaluation, Ph.D. Thesis, University of Eindhoven, 2008.
– start-page: 33
  year: 2000
  end-page: 40
  ident: br000145
  article-title: NMSPA: a non-Markovian model for stochastic processes
  publication-title: Proc. of ICDS 2000
– volume: 325
  start-page: 141
  year: 2004
  end-page: 167
  ident: br000195
  article-title: Bioambients: an abstraction for biological compartments
  publication-title: Theoret. Comput. Sci.
– reference: L. Paulevé, S. Youssef, M.R. Lakin, A. Phillips, A generic abstract machine for stochastic process calculi, in: Proceedings of the 8th International Conference on Computational Methods in Systems Biology CMSB vol. 10, 2010, pp. 43–54.
– volume: 259
  start-page: 224
  year: 1987
  end-page: 242
  ident: br000125
  article-title: Petri net models for algebraic theories of concurrency
  publication-title: LNCS
– volume: 2
  year: 2006
  ident: br000025
  article-title: Oscillatory regulation of Hes1: discrete stochastic delay modelling and simulation
  publication-title: PLoS Comp. Bio.
– reference: M. Bravetti, Specification and analysis of stochastic real-time systems, Ph.D. Thesis, Università di Bologna, 2002.
– volume: 60–61
  start-page: 3
  year: 2004
  end-page: 15
  ident: br000180
  article-title: The origins of structural operational semantics
  publication-title: J. Log. Alg. Progr.
– reference: Bio-PEPA web site
– volume: 391
  start-page: 239
  year: 2008
  end-page: 257
  ident: br000140
  article-title: Probabilistic model checking of complex biological pathways
  publication-title: Theoret. Comput. Sci.
– volume: 199
  start-page: 285
  year: 2008
  end-page: 291
  ident: br000215
  article-title: Global stability of an SIR epidemic model with constant infectious period
  publication-title: Appl. Math. Comp.
– volume: 6575
  start-page: 61
  year: 2011
  end-page: 84
  ident: br000010
  article-title: Delay stochastic simulation of biological systems: a purely delayed approach
  publication-title: Trans. Comp. Sys. Bio. XIII
– volume: vol. 1466
  start-page: 405
  year: 1998
  end-page: 422
  ident: br000055
  article-title: Towards performance evaluation with general distributions in process algebras
  publication-title: Proc. of CONCUR’98
– volume: vol. 40
  start-page: 85
  year: 2010
  end-page: 101
  ident: br000065
  article-title: Modeling biological systems with delays in Bio-PEPA
  publication-title: Proc. of the 4-th Workshop on Membrane Computing and Biologically Inspired Process Calculi, MeCBIC 2010
– volume: vol. 5016
  start-page: 265
  year: 2008
  end-page: 312
  ident: br000075
  article-title: Calculi for biological systems
  publication-title: Formal Methods for Computational Systems Biology, SFM 2008
– year: 1996
  ident: br000135
  article-title: A Compositional Approach to Performance Modelling
– volume: 80
  start-page: 25
  year: 2001
  end-page: 31
  ident: br000190
  article-title: Application of a stochastic name-passing calculus to representation and simulation of molecular processes
  publication-title: Inform. Process. Lett.
– volume: 54
  start-page: 581
  year: 2002
  end-page: 591
  ident: br000030
  article-title: Permanence of an SIR epidemic model with distributed time delays
  publication-title: Tohoku Math. J.
– volume: vol. 4703
  start-page: 17
  year: 2007
  end-page: 41
  ident: br000100
  article-title: Rule-based modelling of cellular signalling
  publication-title: Proc. of CONCUR’07
– reference: P.W. Glynn, On the role of generalized semi-markov processes in simulation output analysis, in: Proc. of the 15th Conference on Winter Simulation, Volume 1, 1983, pp. 39–44.
– volume: vol. 5016
  start-page: 387
  year: 2008
  end-page: 423
  ident: br000015
  article-title: The Calculus of Looping Sequences
  publication-title: Formal Methods for Computational Systems Biology, SFM 2008
– volume: 51
  start-page: 433
  year: 1955
  end-page: 440
  ident: br000080
  article-title: The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables
  publication-title: Proc. Cambridge Phil. Soc.
– volume: 253
  start-page: 83
  year: 2009
  end-page: 98
  ident: br000165
  article-title: Exploiting non-Markovian bio-processes
  publication-title: ENTCS
– volume: 5945
  start-page: 77
  year: 2010
  end-page: 145
  ident: br000175
  article-title: A language for biochemical systems: design and formal specification
  publication-title: Trans. Comp. Sys. Bio. XII
– reference: Prism web site
– volume: 165
  start-page: 27
  year: 2000
  end-page: 39
  ident: br000085
  article-title: A Delay-differential equation model of HIV infection of CD4+ T-cells
  publication-title: Math. Biosci.
– year: 2000
  ident: br000115
  article-title: Performance Analysis of Communication Systems with Non–Markovian Stochastic Petri Nets
– reference: P. Milazzo, Qualitative and quantitative formal modeling of biological systems, Ph.D. Thesis, Università di Pisa, 2007.
– year: 1990
  ident: br000160
  article-title: The Definition of Standard ML
– volume: 81
  start-page: 2340
  year: 1977
  ident: br000120
  article-title: Exact stochastic simulation of coupled chemical reactions
  publication-title: J. Phys. Chem.
– volume: 102
  start-page: 14593
  year: 2005
  end-page: 14598
  ident: br000040
  article-title: Delay-induced stochastic oscillations in gene regulation
  publication-title: PNAS
– volume: 282
  start-page: 5
  year: 2002
  end-page: 32
  ident: br000050
  article-title: The theory of interactive generalized semi-Markov processes
  publication-title: Theoret. Comput. Sci.
– volume: 203
  start-page: 39
  year: 2005
  end-page: 74
  ident: br000090
  article-title: A theory of stochastic systems, part II: process algebra
  publication-title: Inf. and Comp.
– volume: vol. 6
  start-page: 17
  year: 2009
  end-page: 29
  ident: br000005
  article-title: On the interpretation of delays in delay stochastic simulation of biological systems
  publication-title: Proceedings of the 2nd Int. Workshop on Computational Models for Cell Processes, CompMod’09
– volume: 412
  start-page: 2142
  year: 2011
  end-page: 2161
  ident: br000110
  article-title: A semantic equivalence for Bio-PEPA based on discretisation of continuous values
  publication-title: Theoret. Comput. Sci.
– volume: 47
  start-page: 270
  year: 2003
  end-page: 294
  ident: br000210
  article-title: A delay differential equation model for tumor growth
  publication-title: J. Math. Biol.
– start-page: 459
  year: 2001
  end-page: 470
  ident: br000200
  article-title: Representation and simulation of biochemical processes using the pi-calculus process algebra
  publication-title: Pacific Symposium on Biocomputing, vol. 6
– reference: P.R. D’Argenio, J.-P. Katoen, E. Brinksma, A stochastic automata model and its algebraic approach, in: Proc. 5th Int. Workshop on Process Algebra and Performance Modeling, PAPM’97, CTIT technical reports series 97–14, University of Twente, 1997, pp. 1–16.
– volume: 38
  start-page: 578
  year: 1995
  end-page: 589
  ident: br000185
  article-title: Stochastic
  publication-title: The Comp. J.
– volume: 229
  start-page: 21
  year: 2008
  end-page: 39
  ident: br000020
  article-title: Spatial calculus of looping sequences
  publication-title: Int. Workshop From Biology to Concurrency and Back, FBTC’08
– reference: .
– volume: 35
  start-page: 32
  year: 2008
  end-page: 39
  ident: br000105
  article-title: Modelling and simulation of biological processes in BlenX
  publication-title: SIGMETRICS Perform. Eval. Rev.
– reference: G. Caravagna, Formal modeling and simulation of biological systems with delays, Ph.D. Thesis, Università di Pisa, 2011.
– volume: 410
  start-page: 3065
  year: 2009
  end-page: 3084
  ident: br000070
  article-title: Bio-PEPA: a framework for the modelling and analysis of biochemical networks
  publication-title: Theoret. Comput. Sci.
– volume: vol. 6
  start-page: 17
  year: 2009
  ident: 10.1016/j.tcs.2011.11.028_br000005
  article-title: On the interpretation of delays in delay stochastic simulation of biological systems
  publication-title: EPTCS
  doi: 10.4204/EPTCS.6.2
– ident: 10.1016/j.tcs.2011.11.028_br000035
– ident: 10.1016/j.tcs.2011.11.028_br000060
– volume: 51
  start-page: 433
  year: 1955
  ident: 10.1016/j.tcs.2011.11.028_br000080
  article-title: The analysis of non-Markovian stochastic processes by the inclusion of supplementary variables
  publication-title: Proc. Cambridge Phil. Soc.
  doi: 10.1017/S0305004100030437
– year: 2000
  ident: 10.1016/j.tcs.2011.11.028_br000115
– volume: 391
  start-page: 239
  year: 2008
  ident: 10.1016/j.tcs.2011.11.028_br000140
  article-title: Probabilistic model checking of complex biological pathways
  publication-title: Theoret. Comput. Sci.
  doi: 10.1016/j.tcs.2007.11.013
– ident: 10.1016/j.tcs.2011.11.028_br000150
– volume: 5945
  start-page: 77
  issue: 3
  year: 2010
  ident: 10.1016/j.tcs.2011.11.028_br000175
  article-title: A language for biochemical systems: design and formal specification
  publication-title: Trans. Comp. Sys. Bio. XII
  doi: 10.1007/978-3-642-11712-1_3
– volume: 6575
  start-page: 61
  year: 2011
  ident: 10.1016/j.tcs.2011.11.028_br000010
  article-title: Delay stochastic simulation of biological systems: a purely delayed approach
  publication-title: Trans. Comp. Sys. Bio. XIII
  doi: 10.1007/978-3-642-19748-2_4
– start-page: 33
  year: 2000
  ident: 10.1016/j.tcs.2011.11.028_br000145
  article-title: NMSPA: a non-Markovian model for stochastic processes
– ident: 10.1016/j.tcs.2011.11.028_br000205
– volume: vol. 5016
  start-page: 387
  year: 2008
  ident: 10.1016/j.tcs.2011.11.028_br000015
  article-title: The Calculus of Looping Sequences
  publication-title: LNCS
– volume: 80
  start-page: 25
  year: 2001
  ident: 10.1016/j.tcs.2011.11.028_br000190
  article-title: Application of a stochastic name-passing calculus to representation and simulation of molecular processes
  publication-title: Inform. Process. Lett.
  doi: 10.1016/S0020-0190(01)00214-9
– volume: 412
  start-page: 2142
  issue: 21
  year: 2011
  ident: 10.1016/j.tcs.2011.11.028_br000110
  article-title: A semantic equivalence for Bio-PEPA based on discretisation of continuous values
  publication-title: Theoret. Comput. Sci.
  doi: 10.1016/j.tcs.2011.01.007
– volume: vol. 40
  start-page: 85
  year: 2010
  ident: 10.1016/j.tcs.2011.11.028_br000065
  article-title: Modeling biological systems with delays in Bio-PEPA
  publication-title: EPTCS
  doi: 10.4204/EPTCS.40.7
– volume: 282
  start-page: 5
  issue: 1
  year: 2002
  ident: 10.1016/j.tcs.2011.11.028_br000050
  article-title: The theory of interactive generalized semi-Markov processes
  publication-title: Theoret. Comput. Sci.
  doi: 10.1016/S0304-3975(01)00043-3
– volume: vol. 4703
  start-page: 17
  year: 2007
  ident: 10.1016/j.tcs.2011.11.028_br000100
  article-title: Rule-based modelling of cellular signalling
  publication-title: LNCS
– volume: 35
  start-page: 32
  issue: 4
  year: 2008
  ident: 10.1016/j.tcs.2011.11.028_br000105
  article-title: Modelling and simulation of biological processes in BlenX
  publication-title: SIGMETRICS Perform. Eval. Rev.
  doi: 10.1145/1364644.1364653
– volume: 2
  issue: 9
  year: 2006
  ident: 10.1016/j.tcs.2011.11.028_br000025
  article-title: Oscillatory regulation of Hes1: discrete stochastic delay modelling and simulation
  publication-title: PLoS Comp. Bio.
  doi: 10.1371/journal.pcbi.0020117
– volume: 203
  start-page: 39
  issue: 1
  year: 2005
  ident: 10.1016/j.tcs.2011.11.028_br000090
  article-title: A theory of stochastic systems, part II: process algebra
  publication-title: Inf. and Comp.
  doi: 10.1016/j.ic.2005.07.002
– volume: 60–61
  start-page: 3
  year: 2004
  ident: 10.1016/j.tcs.2011.11.028_br000180
  article-title: The origins of structural operational semantics
  publication-title: J. Log. Alg. Progr.
  doi: 10.1016/j.jlap.2004.03.009
– volume: 54
  start-page: 581
  issue: 2
  year: 2002
  ident: 10.1016/j.tcs.2011.11.028_br000030
  article-title: Permanence of an SIR epidemic model with distributed time delays
  publication-title: Tohoku Math. J.
– volume: 165
  start-page: 27
  year: 2000
  ident: 10.1016/j.tcs.2011.11.028_br000085
  article-title: A Delay-differential equation model of HIV infection of CD4+ T-cells
  publication-title: Math. Biosci.
  doi: 10.1016/S0025-5564(00)00006-7
– volume: 253
  start-page: 83
  issue: 3
  year: 2009
  ident: 10.1016/j.tcs.2011.11.028_br000165
  article-title: Exploiting non-Markovian bio-processes
  publication-title: ENTCS
– volume: 102
  start-page: 14593
  issue: 41
  year: 2005
  ident: 10.1016/j.tcs.2011.11.028_br000040
  article-title: Delay-induced stochastic oscillations in gene regulation
  publication-title: PNAS
  doi: 10.1073/pnas.0503858102
– ident: 10.1016/j.tcs.2011.11.028_br000045
  doi: 10.1007/3-540-45605-8_14
– year: 1996
  ident: 10.1016/j.tcs.2011.11.028_br000135
– volume: 259
  start-page: 224
  year: 1987
  ident: 10.1016/j.tcs.2011.11.028_br000125
  article-title: Petri net models for algebraic theories of concurrency
  publication-title: LNCS
– ident: 10.1016/j.tcs.2011.11.028_br000170
  doi: 10.1145/1839764.1839771
– volume: 199
  start-page: 285
  issue: 1
  year: 2008
  ident: 10.1016/j.tcs.2011.11.028_br000215
  article-title: Global stability of an SIR epidemic model with constant infectious period
  publication-title: Appl. Math. Comp.
  doi: 10.1016/j.amc.2007.09.053
– volume: 38
  start-page: 578
  issue: 7
  year: 1995
  ident: 10.1016/j.tcs.2011.11.028_br000185
  article-title: Stochastic π-calculus
  publication-title: The Comp. J.
  doi: 10.1093/comjnl/38.7.578
– volume: 81
  start-page: 2340
  year: 1977
  ident: 10.1016/j.tcs.2011.11.028_br000120
  article-title: Exact stochastic simulation of coupled chemical reactions
  publication-title: J. Phys. Chem.
  doi: 10.1021/j100540a008
– volume: 325
  start-page: 141
  issue: 1
  year: 2004
  ident: 10.1016/j.tcs.2011.11.028_br000195
  article-title: Bioambients: an abstraction for biological compartments
  publication-title: Theoret. Comput. Sci.
  doi: 10.1016/j.tcs.2004.03.061
– volume: 47
  start-page: 270
  year: 2003
  ident: 10.1016/j.tcs.2011.11.028_br000210
  article-title: A delay differential equation model for tumor growth
  publication-title: J. Math. Biol.
  doi: 10.1007/s00285-003-0211-0
– volume: 229
  start-page: 21
  issue: 1
  year: 2008
  ident: 10.1016/j.tcs.2011.11.028_br000020
  article-title: Spatial calculus of looping sequences
  publication-title: ENTCS
– start-page: 459
  year: 2001
  ident: 10.1016/j.tcs.2011.11.028_br000200
  article-title: Representation and simulation of biochemical processes using the pi-calculus process algebra
– ident: 10.1016/j.tcs.2011.11.028_br000095
– ident: 10.1016/j.tcs.2011.11.028_br000130
– year: 1990
  ident: 10.1016/j.tcs.2011.11.028_br000160
– ident: 10.1016/j.tcs.2011.11.028_br000155
– volume: vol. 1466
  start-page: 405
  year: 1998
  ident: 10.1016/j.tcs.2011.11.028_br000055
  article-title: Towards performance evaluation with general distributions in process algebras
  publication-title: LNCS
– volume: 410
  start-page: 3065
  issue: 33–34
  year: 2009
  ident: 10.1016/j.tcs.2011.11.028_br000070
  article-title: Bio-PEPA: a framework for the modelling and analysis of biochemical networks
  publication-title: Theoret. Comput. Sci.
  doi: 10.1016/j.tcs.2009.02.037
– volume: vol. 5016
  start-page: 265
  year: 2008
  ident: 10.1016/j.tcs.2011.11.028_br000075
  article-title: Calculi for biological systems
  publication-title: LNCS
SSID ssj0000576
Score 2.0633001
Snippet Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed, or to provide abstraction of some...
SourceID crossref
elsevier
SourceType Enrichment Source
Index Database
Publisher
StartPage 26
SubjectTerms Bio-PEPA
DDEs
Delay-as-duration
DSSA
GSMPs
Non-Markovian process algebra
Title Bio-PEPAd: A non-Markovian extension of Bio-PEPA
URI https://dx.doi.org/10.1016/j.tcs.2011.11.028
Volume 419
WOSCitedRecordID wos000300534900004&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVESC
  databaseName: Elsevier SD Freedom Collection Journals 2021
  customDbUrl:
  eissn: 1879-2294
  dateEnd: 20180131
  omitProxy: false
  ssIdentifier: ssj0000576
  issn: 0304-3975
  databaseCode: AIEXJ
  dateStart: 19950109
  isFulltext: true
  titleUrlDefault: https://www.sciencedirect.com
  providerName: Elsevier
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3NT9swFH_ayg7bYTC2aeVLOewEyuQ4SePsVlCBoQ31UKbeIju1p6KqRU2p-ufzXD-nhcEEh12sxPJHkp_z3rPfF8BXbhQzecxsPG0sZEuFQqU6ROaWGJ3GRi1TJ_z-mV1ein4_71ISxGqZTiAbj8Vikd_8V6ixDsG2rrMvgLseFCvwGkHHEmHH8lnAHw8nYbfTbQ-c0zlu70PrkDOZ2195eeZdkZDoW64LqL01x8aSMj4cEZtc6Sumci7_OG-ys-HtyNlyuRPs0agii_wLSSp7OlSw1hk8dD6U3pnKKkxyl9TEE8qEiBuRutYa03RhR_8ix-5k4PrbrKxctFQbMJWcwe-Fvn7AkmpDQW-Ddl3gEIUdArcsBQ7xGjZ4luaiARvtH53-xYr7ppnTT9MLeE320qbvwXM8LousyRe9LXhPG4Og7QD9AK_0eBs2fdKNgGjwNrz7VQfarT4Cq9H-HrSDe1gHNdbBxAS-3Se4Ou30Ts5DSoIRljzPZqFSOjatQSRKlOy40CI3LaWlxjslORZGlSxVg1wlkY6E4dygTBlHqZAad8cy_gwNnF1_gYBFkmHPUnE-SCR2TSLGjImEiG191ATmP0dRUoR4m6hkVDwJQxMO6y43LjzKvxon_hsXtHCd3Fbgenm6285L5tiFt6v1vAeN2fRW78Obcj4bVtMDWix3kORrdw
linkProvider Elsevier
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Bio-PEPAd%3A+A+non-Markovian+extension+of+Bio-PEPA&rft.jtitle=Theoretical+computer+science&rft.au=Caravagna%2C+Giulio&rft.au=Hillston%2C+Jane&rft.date=2012-02-17&rft.issn=0304-3975&rft.volume=419&rft.spage=26&rft.epage=49&rft_id=info:doi/10.1016%2Fj.tcs.2011.11.028&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_tcs_2011_11_028
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0304-3975&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0304-3975&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0304-3975&client=summon