SlideShare uma empresa Scribd logo
1 de 26
Baixar para ler offline
Computer Science Large Practical:
                       More Stochastic Simulation Examples

                                               Stephen Gilmore

                                               School of Informatics


                                          Friday 2nd November, 2012




Stephen Gilmore (School of Informatics)       Stochastic simulation examples   Friday 2nd November, 2012   1 / 26
A reaction network: the cascade



         Often one chemical species transforms into another, which transforms
         into a third, which transforms into a fourth, and so on.
         Events such as these are the basis of signalling processes which occur
         within living organisms.
         A series of reactions such as A becoming B, B becoming C , and so
         forth is called a cascade.
         The reactions in the cascade may occur at different rates. This will
         affect the dynamics of the process.




Stephen Gilmore (School of Informatics)   Stochastic simulation examples   Friday 2nd November, 2012   2 / 26
A simulation script, cascade.txt (1/3)



   # The simulation stop time (t) is 100 seconds
   t = 100

   #    The kinetic real-number rate constants of the four
   #    reactions: a, b, c, d
   a    = 0.5
   b    = 0.25
   c    = 0.125
   d    = 0.0625




Stephen Gilmore (School of Informatics)   Stochastic simulation examples   Friday 2nd November, 2012   3 / 26
A simulation script, cascade.txt (2/3)



   #    The initial integer molecule counts of the five species,
   #    A, B, C, D, and E. Only A is present initially.
   #    (A, B, C, D, E) = (1000, 0, 0, 0, 0)
   A    = 1000
   B    = 0
   C    = 0
   D    = 0
   E    = 0




Stephen Gilmore (School of Informatics)   Stochastic simulation examples   Friday 2nd November, 2012   4 / 26
A simulation script, cascade.txt (3/3)

   #    The four reactions. The reaction ‘a’ transforms
   #    A into B. The reaction ’b’ transforms B into C, and
   #    so on through the cascade. The cascade stops
   #    with E.

   # A has a special role because it is only consumed,
   # never produced. E has a special role because it
   # is only produced, never consumed.

   a    :     A   ->    B
   b    :     B   ->    C
   c    :     C   ->    D
   d    :     D   ->    E


Stephen Gilmore (School of Informatics)   Stochastic simulation examples   Friday 2nd November, 2012   5 / 26
A simulation of the first second of the cascade example

 The columns are time, and the molecule counts of A, B, C, D, E.
                                0.0,      1000,       0,           0,       0,     0
                                0.1,      949,        51,          0,       0,     0
                                0.2,      888,        112,         0,       0,     0
                                0.3,      843,        154,         3,       0,     0
                                0.4,      791,        203,         6,       0,     0
                                0.5,      756,        232,         12,      0,     0
                                0.6,      707,        273,         20,      0,     0
                                0.7,      674,        302,         22,      2,     0
                                0.8,      644,        322,         32,      2,     0
                                0.9,      615,        339,         44,      2,     0

 From this we can see (as expected) that A decreases and B increases, then
 later C increases, and later still D increases. No molecules of E were
 produced during the first second of this simulation.
Stephen Gilmore (School of Informatics)    Stochastic simulation examples        Friday 2nd November, 2012   6 / 26
Visualising the results using GNUplot
Store as “cascade.gnu”, plot using “gnuplot cascade.gnu” if results are in “cascade.csv”


   set terminal postscript color
   set output "cascade.ps"

   set key right center
   set xlabel "time"
   set ylabel "molecule count"

   set datafile separator ","

   plot 
       "cascade.csv"                 using   1:2     with     linespoints     title     "A",     
       "cascade.csv"                 using   1:3     with     linespoints     title     "B",     
       "cascade.csv"                 using   1:4     with     linespoints     title     "C",     
       "cascade.csv"                 using   1:5     with     linespoints     title     "D",     
       "cascade.csv"                 using   1:6     with     linespoints     title     "E"


Stephen Gilmore (School of Informatics)      Stochastic simulation examples   Friday 2nd November, 2012   7 / 26
Visualising the results of a cascade simulation
                            1000




                             800




                             600
           molecule count




                                                                                        A
                                                                                        B
                                                                                        C
                                                                                        D
                                                                                        E
                             400




                             200




                               0
                                   0   20           40                 60        80              100
                                                            time


Stephen Gilmore (School of Informatics)     Stochastic simulation examples   Friday 2nd November, 2012   8 / 26
Adding a reaction: allowing E to decay




         Now we make a slight change to the model, adding a reaction which
         decays E.
         We need a new reaction constant for this new reaction. We have
         assigned reaction e the slowest rate.
         Our intuition should be that this does not make much difference to
         the profile of chemical species A, B, C and D in the output, but it
         should affect the profile of species E .




Stephen Gilmore (School of Informatics)   Stochastic simulation examples   Friday 2nd November, 2012   9 / 26
A simulation script, cascade-decay.txt (1/3)


   # The simulation stop time (t) is 100 seconds
   t = 100

   #    The kinetic real-number rate constants of the five
   #    reactions: a, b, c, d, e
   a    = 0.5
   b    = 0.25
   c    = 0.125
   d    = 0.0625
   e    = 0.03125




Stephen Gilmore (School of Informatics)   Stochastic simulation examples   Friday 2nd November, 2012   10 / 26
A simulation script, cascade-decay.txt (2/3)
This part is exactly the same as cascade.txt




   #    The initial integer molecule counts of the five species,
   #    A, B, C, D, and E. Only A is present initially.
   #    (A, B, C, D, E) = (1000, 0, 0, 0, 0)
   A    = 1000
   B    = 0
   C    = 0
   D    = 0
   E    = 0




Stephen Gilmore (School of Informatics)   Stochastic simulation examples   Friday 2nd November, 2012   11 / 26
A simulation script, cascade-decay.txt (3/3)

   #    The five reactions. The reaction ‘a’ transforms
   #    A into B. The reaction ’b’ transforms B into C, and
   #    so on through the cascade. The cascade stops
   #    with E.

   # A has a special role because it is only consumed,
   # never produced. E has a special role because it
   # decays without producing another output.

   a    :     A   ->    B
   b    :     B   ->    C
   c    :     C   ->    D
   d    :     D   ->    E
   e    :     E   ->

Stephen Gilmore (School of Informatics)   Stochastic simulation examples   Friday 2nd November, 2012   12 / 26
Visualising the results of a cascade-decay simulation
                            1000




                             800




                             600
           molecule count




                                                                                         A
                                                                                         B
                                                                                         C
                                                                                         D
                                                                                         E
                             400




                             200




                               0
                                   0   20           40                 60         80               100
                                                            time


Stephen Gilmore (School of Informatics)     Stochastic simulation examples   Friday 2nd November, 2012   13 / 26
About the cascade-decay simulation



         Our intuition was correct. The profiles of A, B, C , and D are very
         similar to previously.
                 Because this is a stochastic simulation which involves pseudo-random
                 number generation the results will not be exactly the same but they
                 will be very similar.
         We can see that reactions are still occurring right up to the stop-time
         of this simulation (t = 100 seconds).
         That is perfectly OK in the results. We simulate up to the stop-time
         and no further.




Stephen Gilmore (School of Informatics)   Stochastic simulation examples   Friday 2nd November, 2012   14 / 26
Changing a rate in the model




         We set the new reaction, e, to be the slowest reaction in the model,
         but what if we had chosen it to be the fastest reaction instead?
         We can find out how this would affect the results by changing the
         rate of reaction e.
         Our intuition should be that this again does not make much
         difference to the profile of chemical species A, B, C and D in the
         output, but it should affect the profile of species E .




Stephen Gilmore (School of Informatics)   Stochastic simulation examples   Friday 2nd November, 2012   15 / 26
A simulation script, cascade-decay-fast.txt (1/3)


   # The simulation stop time (t) is 100 seconds
   t = 100

   #    The kinetic             real-number rate constants of the five
   #    reactions:              a, b, c, d, e
   a    = 0.5
   b    = 0.25
   c    = 0.125
   d    = 0.0625
   e    = 1.0
   #    The fastest             reaction is e, the decay reaction for E.
   #    The slowest             reaction here is d.



Stephen Gilmore (School of Informatics)   Stochastic simulation examples   Friday 2nd November, 2012   16 / 26
A simulation script, cascade-decay-fast.txt (2/3)
This part is exactly the same as cascade-decay.txt




   #    The initial integer molecule counts of the five species,
   #    A, B, C, D, and E. Only A is present initially.
   #    (A, B, C, D, E) = (1000, 0, 0, 0, 0)
   A    = 1000
   B    = 0
   C    = 0
   D    = 0
   E    = 0




Stephen Gilmore (School of Informatics)   Stochastic simulation examples   Friday 2nd November, 2012   17 / 26
A simulation script, cascade-decay-fast.txt (3/3)
This part is exactly the same as cascade-decay.txt

   #    The five reactions. The reaction ‘a’ transforms
   #    A into B. The reaction ’b’ transforms B into C, and
   #    so on through the cascade. The cascade stops
   #    with E.

   # A has a special role because it is only consumed,
   # never produced. E has a special role because it
   # decays without producing another output.

   a    :     A   ->    B
   b    :     B   ->    C
   c    :     C   ->    D
   d    :     D   ->    E
   e    :     E   ->

Stephen Gilmore (School of Informatics)   Stochastic simulation examples   Friday 2nd November, 2012   18 / 26
Visualising the results of a cascade-decay-fast simulation
                            1000




                             800




                             600
           molecule count




                                                                                         A
                                                                                         B
                                                                                         C
                                                                                         D
                                                                                         E
                             400




                             200




                               0
                                   0   20           40                 60         80               100
                                                            time


Stephen Gilmore (School of Informatics)     Stochastic simulation examples   Friday 2nd November, 2012   19 / 26
About the cascade-decay-fast simulation




         Our intuition was correct again. The profiles of A, B, C , and D are
         very similar to previously.
         We can see that very little E builds up in the system (because it
         decays away much faster than it is produced).
         The profile for E hovers around zero throughout the simulation run.




Stephen Gilmore (School of Informatics)   Stochastic simulation examples   Friday 2nd November, 2012   20 / 26
A dimerisation example




         We saw earlier that dimerisation is a special case for the Gillespie
         simulation algorithm.
         Let’s consider an example which uses dimerisation and also includes a
         decay reaction.




Stephen Gilmore (School of Informatics)   Stochastic simulation examples   Friday 2nd November, 2012   21 / 26
A simulation script, dimer-decay.txt (1/3)



   # The simulation stop time (t) is 20 seconds
   t = 20

   #    The kinetic real-number rate constants of the four
   #    reactions: d, x, y, z
   d    = 1.0
   x    = 0.002
   y    = 0.5
   z    = 0.04




Stephen Gilmore (School of Informatics)   Stochastic simulation examples   Friday 2nd November, 2012   22 / 26
A simulation script, dimer-decay.txt (2/3)




   #    The initial integer molecule counts of the three
   #    species, X, Y, and Z. Only X is present initially.
   #    (X, Y, Z) = (10000, 0, 0)
   X    = 10000
   Y    = 0
   Z    = 0




Stephen Gilmore (School of Informatics)   Stochastic simulation examples   Friday 2nd November, 2012   23 / 26
A simulation script, dimer-decay.txt (3/3)


   #    The four reactions:
   #    (d), X can decay to nothing;
   #    (x), two molecules of X can bind to form Y;
   #    (y), Y can unbind to give two molecules of X; and
   #    (z), a molecule of Y can produce a molecule of Z.

   d    :     X   ->
   x    :     X   + X -> Y
   y    :     Y   -> X + X
   z    :     Y   -> Z




Stephen Gilmore (School of Informatics)   Stochastic simulation examples   Friday 2nd November, 2012   24 / 26
Visualising the results of a dimer-decay simulation
                            10000




                             8000




                             6000
           molecule count




                                                                                            X
                                                                                            Y
                                                                                            Z

                             4000




                             2000




                                0
                                    0     5                      10             15                   20
                                                               time


Stephen Gilmore (School of Informatics)       Stochastic simulation examples   Friday 2nd November, 2012   25 / 26
Summary




         We have seen some examples of simulation scripts involving cascades
         and dimerisation.
         Try creating some of your own. For example:
                 A cascade which involves more species.
                 A cascade where every species can decay, not just the last one.
                 A dimerisation example without a decay reaction.




Stephen Gilmore (School of Informatics)   Stochastic simulation examples   Friday 2nd November, 2012   26 / 26

Mais conteúdo relacionado

Mais de Stephen Gilmore

Common Java problems when developing with Android
Common Java problems when developing with AndroidCommon Java problems when developing with Android
Common Java problems when developing with AndroidStephen Gilmore
 
Quick quiz on Objective-C
Quick quiz on Objective-CQuick quiz on Objective-C
Quick quiz on Objective-CStephen Gilmore
 
Getting started with Xcode
Getting started with XcodeGetting started with Xcode
Getting started with XcodeStephen Gilmore
 
Working with databases in Android
Working with databases in AndroidWorking with databases in Android
Working with databases in AndroidStephen Gilmore
 
Crash Course in Objective-C
Crash Course in Objective-CCrash Course in Objective-C
Crash Course in Objective-CStephen Gilmore
 
SELP: Debugging, AVDs and Manifests
SELP: Debugging, AVDs and ManifestsSELP: Debugging, AVDs and Manifests
SELP: Debugging, AVDs and ManifestsStephen Gilmore
 
The Stochastic Simulation Algorithm
The Stochastic Simulation AlgorithmThe Stochastic Simulation Algorithm
The Stochastic Simulation AlgorithmStephen Gilmore
 
Beginning Android Development
Beginning Android DevelopmentBeginning Android Development
Beginning Android DevelopmentStephen Gilmore
 
Computer Science Large Practical coursework
Computer Science Large Practical courseworkComputer Science Large Practical coursework
Computer Science Large Practical courseworkStephen Gilmore
 
Software Engineering Large Practical coursework
Software Engineering Large Practical courseworkSoftware Engineering Large Practical coursework
Software Engineering Large Practical courseworkStephen Gilmore
 
Introduction to the CSLP and the SELP
Introduction to the CSLP and the SELPIntroduction to the CSLP and the SELP
Introduction to the CSLP and the SELPStephen Gilmore
 
Fixing errors in Android Java applications
Fixing errors in Android Java applicationsFixing errors in Android Java applications
Fixing errors in Android Java applicationsStephen Gilmore
 
Feedback on Part 1 of the Individual Practical
Feedback on Part 1 of the Individual PracticalFeedback on Part 1 of the Individual Practical
Feedback on Part 1 of the Individual PracticalStephen Gilmore
 
Creating and working with databases in Android
Creating and working with databases in AndroidCreating and working with databases in Android
Creating and working with databases in AndroidStephen Gilmore
 
Continuing Android development
Continuing Android developmentContinuing Android development
Continuing Android developmentStephen Gilmore
 
Project management for the individual practical
Project management for the individual practicalProject management for the individual practical
Project management for the individual practicalStephen Gilmore
 
Beginning Android development
Beginning Android developmentBeginning Android development
Beginning Android developmentStephen Gilmore
 
CS/SE Individual practical - DDMS and AVD
CS/SE Individual practical - DDMS and AVDCS/SE Individual practical - DDMS and AVD
CS/SE Individual practical - DDMS and AVDStephen Gilmore
 

Mais de Stephen Gilmore (18)

Common Java problems when developing with Android
Common Java problems when developing with AndroidCommon Java problems when developing with Android
Common Java problems when developing with Android
 
Quick quiz on Objective-C
Quick quiz on Objective-CQuick quiz on Objective-C
Quick quiz on Objective-C
 
Getting started with Xcode
Getting started with XcodeGetting started with Xcode
Getting started with Xcode
 
Working with databases in Android
Working with databases in AndroidWorking with databases in Android
Working with databases in Android
 
Crash Course in Objective-C
Crash Course in Objective-CCrash Course in Objective-C
Crash Course in Objective-C
 
SELP: Debugging, AVDs and Manifests
SELP: Debugging, AVDs and ManifestsSELP: Debugging, AVDs and Manifests
SELP: Debugging, AVDs and Manifests
 
The Stochastic Simulation Algorithm
The Stochastic Simulation AlgorithmThe Stochastic Simulation Algorithm
The Stochastic Simulation Algorithm
 
Beginning Android Development
Beginning Android DevelopmentBeginning Android Development
Beginning Android Development
 
Computer Science Large Practical coursework
Computer Science Large Practical courseworkComputer Science Large Practical coursework
Computer Science Large Practical coursework
 
Software Engineering Large Practical coursework
Software Engineering Large Practical courseworkSoftware Engineering Large Practical coursework
Software Engineering Large Practical coursework
 
Introduction to the CSLP and the SELP
Introduction to the CSLP and the SELPIntroduction to the CSLP and the SELP
Introduction to the CSLP and the SELP
 
Fixing errors in Android Java applications
Fixing errors in Android Java applicationsFixing errors in Android Java applications
Fixing errors in Android Java applications
 
Feedback on Part 1 of the Individual Practical
Feedback on Part 1 of the Individual PracticalFeedback on Part 1 of the Individual Practical
Feedback on Part 1 of the Individual Practical
 
Creating and working with databases in Android
Creating and working with databases in AndroidCreating and working with databases in Android
Creating and working with databases in Android
 
Continuing Android development
Continuing Android developmentContinuing Android development
Continuing Android development
 
Project management for the individual practical
Project management for the individual practicalProject management for the individual practical
Project management for the individual practical
 
Beginning Android development
Beginning Android developmentBeginning Android development
Beginning Android development
 
CS/SE Individual practical - DDMS and AVD
CS/SE Individual practical - DDMS and AVDCS/SE Individual practical - DDMS and AVD
CS/SE Individual practical - DDMS and AVD
 

Último

The Singapore Teaching Practice document
The Singapore Teaching Practice documentThe Singapore Teaching Practice document
The Singapore Teaching Practice documentXsasf Sfdfasd
 
Quality Assurance_GOOD LABORATORY PRACTICE
Quality Assurance_GOOD LABORATORY PRACTICEQuality Assurance_GOOD LABORATORY PRACTICE
Quality Assurance_GOOD LABORATORY PRACTICESayali Powar
 
How to Add Existing Field in One2Many Tree View in Odoo 17
How to Add Existing Field in One2Many Tree View in Odoo 17How to Add Existing Field in One2Many Tree View in Odoo 17
How to Add Existing Field in One2Many Tree View in Odoo 17Celine George
 
Practical Research 1 Lesson 9 Scope and delimitation.pptx
Practical Research 1 Lesson 9 Scope and delimitation.pptxPractical Research 1 Lesson 9 Scope and delimitation.pptx
Practical Research 1 Lesson 9 Scope and delimitation.pptxKatherine Villaluna
 
How to Add a New Field in Existing Kanban View in Odoo 17
How to Add a New Field in Existing Kanban View in Odoo 17How to Add a New Field in Existing Kanban View in Odoo 17
How to Add a New Field in Existing Kanban View in Odoo 17Celine George
 
Presentation on the Basics of Writing. Writing a Paragraph
Presentation on the Basics of Writing. Writing a ParagraphPresentation on the Basics of Writing. Writing a Paragraph
Presentation on the Basics of Writing. Writing a ParagraphNetziValdelomar1
 
3.21.24 The Origins of Black Power.pptx
3.21.24  The Origins of Black Power.pptx3.21.24  The Origins of Black Power.pptx
3.21.24 The Origins of Black Power.pptxmary850239
 
AUDIENCE THEORY -- FANDOM -- JENKINS.pptx
AUDIENCE THEORY -- FANDOM -- JENKINS.pptxAUDIENCE THEORY -- FANDOM -- JENKINS.pptx
AUDIENCE THEORY -- FANDOM -- JENKINS.pptxiammrhaywood
 
How to Add a many2many Relational Field in Odoo 17
How to Add a many2many Relational Field in Odoo 17How to Add a many2many Relational Field in Odoo 17
How to Add a many2many Relational Field in Odoo 17Celine George
 
CHUYÊN ĐỀ DẠY THÊM TIẾNG ANH LỚP 11 - GLOBAL SUCCESS - NĂM HỌC 2023-2024 - HK...
CHUYÊN ĐỀ DẠY THÊM TIẾNG ANH LỚP 11 - GLOBAL SUCCESS - NĂM HỌC 2023-2024 - HK...CHUYÊN ĐỀ DẠY THÊM TIẾNG ANH LỚP 11 - GLOBAL SUCCESS - NĂM HỌC 2023-2024 - HK...
CHUYÊN ĐỀ DẠY THÊM TIẾNG ANH LỚP 11 - GLOBAL SUCCESS - NĂM HỌC 2023-2024 - HK...Nguyen Thanh Tu Collection
 
Easter in the USA presentation by Chloe.
Easter in the USA presentation by Chloe.Easter in the USA presentation by Chloe.
Easter in the USA presentation by Chloe.EnglishCEIPdeSigeiro
 
CapTechU Doctoral Presentation -March 2024 slides.pptx
CapTechU Doctoral Presentation -March 2024 slides.pptxCapTechU Doctoral Presentation -March 2024 slides.pptx
CapTechU Doctoral Presentation -March 2024 slides.pptxCapitolTechU
 
How to Manage Cross-Selling in Odoo 17 Sales
How to Manage Cross-Selling in Odoo 17 SalesHow to Manage Cross-Selling in Odoo 17 Sales
How to Manage Cross-Selling in Odoo 17 SalesCeline George
 
Practical Research 1: Lesson 8 Writing the Thesis Statement.pptx
Practical Research 1: Lesson 8 Writing the Thesis Statement.pptxPractical Research 1: Lesson 8 Writing the Thesis Statement.pptx
Practical Research 1: Lesson 8 Writing the Thesis Statement.pptxKatherine Villaluna
 
Education and training program in the hospital APR.pptx
Education and training program in the hospital APR.pptxEducation and training program in the hospital APR.pptx
Education and training program in the hospital APR.pptxraviapr7
 
How to Make a Field read-only in Odoo 17
How to Make a Field read-only in Odoo 17How to Make a Field read-only in Odoo 17
How to Make a Field read-only in Odoo 17Celine George
 
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdf
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdfMaximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdf
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdfTechSoup
 
Patterns of Written Texts Across Disciplines.pptx
Patterns of Written Texts Across Disciplines.pptxPatterns of Written Texts Across Disciplines.pptx
Patterns of Written Texts Across Disciplines.pptxMYDA ANGELICA SUAN
 
M-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptxM-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptxDr. Santhosh Kumar. N
 

Último (20)

The Singapore Teaching Practice document
The Singapore Teaching Practice documentThe Singapore Teaching Practice document
The Singapore Teaching Practice document
 
Quality Assurance_GOOD LABORATORY PRACTICE
Quality Assurance_GOOD LABORATORY PRACTICEQuality Assurance_GOOD LABORATORY PRACTICE
Quality Assurance_GOOD LABORATORY PRACTICE
 
How to Add Existing Field in One2Many Tree View in Odoo 17
How to Add Existing Field in One2Many Tree View in Odoo 17How to Add Existing Field in One2Many Tree View in Odoo 17
How to Add Existing Field in One2Many Tree View in Odoo 17
 
Practical Research 1 Lesson 9 Scope and delimitation.pptx
Practical Research 1 Lesson 9 Scope and delimitation.pptxPractical Research 1 Lesson 9 Scope and delimitation.pptx
Practical Research 1 Lesson 9 Scope and delimitation.pptx
 
How to Add a New Field in Existing Kanban View in Odoo 17
How to Add a New Field in Existing Kanban View in Odoo 17How to Add a New Field in Existing Kanban View in Odoo 17
How to Add a New Field in Existing Kanban View in Odoo 17
 
Presentation on the Basics of Writing. Writing a Paragraph
Presentation on the Basics of Writing. Writing a ParagraphPresentation on the Basics of Writing. Writing a Paragraph
Presentation on the Basics of Writing. Writing a Paragraph
 
3.21.24 The Origins of Black Power.pptx
3.21.24  The Origins of Black Power.pptx3.21.24  The Origins of Black Power.pptx
3.21.24 The Origins of Black Power.pptx
 
AUDIENCE THEORY -- FANDOM -- JENKINS.pptx
AUDIENCE THEORY -- FANDOM -- JENKINS.pptxAUDIENCE THEORY -- FANDOM -- JENKINS.pptx
AUDIENCE THEORY -- FANDOM -- JENKINS.pptx
 
How to Add a many2many Relational Field in Odoo 17
How to Add a many2many Relational Field in Odoo 17How to Add a many2many Relational Field in Odoo 17
How to Add a many2many Relational Field in Odoo 17
 
CHUYÊN ĐỀ DẠY THÊM TIẾNG ANH LỚP 11 - GLOBAL SUCCESS - NĂM HỌC 2023-2024 - HK...
CHUYÊN ĐỀ DẠY THÊM TIẾNG ANH LỚP 11 - GLOBAL SUCCESS - NĂM HỌC 2023-2024 - HK...CHUYÊN ĐỀ DẠY THÊM TIẾNG ANH LỚP 11 - GLOBAL SUCCESS - NĂM HỌC 2023-2024 - HK...
CHUYÊN ĐỀ DẠY THÊM TIẾNG ANH LỚP 11 - GLOBAL SUCCESS - NĂM HỌC 2023-2024 - HK...
 
Easter in the USA presentation by Chloe.
Easter in the USA presentation by Chloe.Easter in the USA presentation by Chloe.
Easter in the USA presentation by Chloe.
 
Personal Resilience in Project Management 2 - TV Edit 1a.pdf
Personal Resilience in Project Management 2 - TV Edit 1a.pdfPersonal Resilience in Project Management 2 - TV Edit 1a.pdf
Personal Resilience in Project Management 2 - TV Edit 1a.pdf
 
CapTechU Doctoral Presentation -March 2024 slides.pptx
CapTechU Doctoral Presentation -March 2024 slides.pptxCapTechU Doctoral Presentation -March 2024 slides.pptx
CapTechU Doctoral Presentation -March 2024 slides.pptx
 
How to Manage Cross-Selling in Odoo 17 Sales
How to Manage Cross-Selling in Odoo 17 SalesHow to Manage Cross-Selling in Odoo 17 Sales
How to Manage Cross-Selling in Odoo 17 Sales
 
Practical Research 1: Lesson 8 Writing the Thesis Statement.pptx
Practical Research 1: Lesson 8 Writing the Thesis Statement.pptxPractical Research 1: Lesson 8 Writing the Thesis Statement.pptx
Practical Research 1: Lesson 8 Writing the Thesis Statement.pptx
 
Education and training program in the hospital APR.pptx
Education and training program in the hospital APR.pptxEducation and training program in the hospital APR.pptx
Education and training program in the hospital APR.pptx
 
How to Make a Field read-only in Odoo 17
How to Make a Field read-only in Odoo 17How to Make a Field read-only in Odoo 17
How to Make a Field read-only in Odoo 17
 
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdf
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdfMaximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdf
Maximizing Impact_ Nonprofit Website Planning, Budgeting, and Design.pdf
 
Patterns of Written Texts Across Disciplines.pptx
Patterns of Written Texts Across Disciplines.pptxPatterns of Written Texts Across Disciplines.pptx
Patterns of Written Texts Across Disciplines.pptx
 
M-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptxM-2- General Reactions of amino acids.pptx
M-2- General Reactions of amino acids.pptx
 

More Stochastic Simulation Examples

  • 1. Computer Science Large Practical: More Stochastic Simulation Examples Stephen Gilmore School of Informatics Friday 2nd November, 2012 Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 1 / 26
  • 2. A reaction network: the cascade Often one chemical species transforms into another, which transforms into a third, which transforms into a fourth, and so on. Events such as these are the basis of signalling processes which occur within living organisms. A series of reactions such as A becoming B, B becoming C , and so forth is called a cascade. The reactions in the cascade may occur at different rates. This will affect the dynamics of the process. Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 2 / 26
  • 3. A simulation script, cascade.txt (1/3) # The simulation stop time (t) is 100 seconds t = 100 # The kinetic real-number rate constants of the four # reactions: a, b, c, d a = 0.5 b = 0.25 c = 0.125 d = 0.0625 Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 3 / 26
  • 4. A simulation script, cascade.txt (2/3) # The initial integer molecule counts of the five species, # A, B, C, D, and E. Only A is present initially. # (A, B, C, D, E) = (1000, 0, 0, 0, 0) A = 1000 B = 0 C = 0 D = 0 E = 0 Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 4 / 26
  • 5. A simulation script, cascade.txt (3/3) # The four reactions. The reaction ‘a’ transforms # A into B. The reaction ’b’ transforms B into C, and # so on through the cascade. The cascade stops # with E. # A has a special role because it is only consumed, # never produced. E has a special role because it # is only produced, never consumed. a : A -> B b : B -> C c : C -> D d : D -> E Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 5 / 26
  • 6. A simulation of the first second of the cascade example The columns are time, and the molecule counts of A, B, C, D, E. 0.0, 1000, 0, 0, 0, 0 0.1, 949, 51, 0, 0, 0 0.2, 888, 112, 0, 0, 0 0.3, 843, 154, 3, 0, 0 0.4, 791, 203, 6, 0, 0 0.5, 756, 232, 12, 0, 0 0.6, 707, 273, 20, 0, 0 0.7, 674, 302, 22, 2, 0 0.8, 644, 322, 32, 2, 0 0.9, 615, 339, 44, 2, 0 From this we can see (as expected) that A decreases and B increases, then later C increases, and later still D increases. No molecules of E were produced during the first second of this simulation. Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 6 / 26
  • 7. Visualising the results using GNUplot Store as “cascade.gnu”, plot using “gnuplot cascade.gnu” if results are in “cascade.csv” set terminal postscript color set output "cascade.ps" set key right center set xlabel "time" set ylabel "molecule count" set datafile separator "," plot "cascade.csv" using 1:2 with linespoints title "A", "cascade.csv" using 1:3 with linespoints title "B", "cascade.csv" using 1:4 with linespoints title "C", "cascade.csv" using 1:5 with linespoints title "D", "cascade.csv" using 1:6 with linespoints title "E" Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 7 / 26
  • 8. Visualising the results of a cascade simulation 1000 800 600 molecule count A B C D E 400 200 0 0 20 40 60 80 100 time Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 8 / 26
  • 9. Adding a reaction: allowing E to decay Now we make a slight change to the model, adding a reaction which decays E. We need a new reaction constant for this new reaction. We have assigned reaction e the slowest rate. Our intuition should be that this does not make much difference to the profile of chemical species A, B, C and D in the output, but it should affect the profile of species E . Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 9 / 26
  • 10. A simulation script, cascade-decay.txt (1/3) # The simulation stop time (t) is 100 seconds t = 100 # The kinetic real-number rate constants of the five # reactions: a, b, c, d, e a = 0.5 b = 0.25 c = 0.125 d = 0.0625 e = 0.03125 Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 10 / 26
  • 11. A simulation script, cascade-decay.txt (2/3) This part is exactly the same as cascade.txt # The initial integer molecule counts of the five species, # A, B, C, D, and E. Only A is present initially. # (A, B, C, D, E) = (1000, 0, 0, 0, 0) A = 1000 B = 0 C = 0 D = 0 E = 0 Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 11 / 26
  • 12. A simulation script, cascade-decay.txt (3/3) # The five reactions. The reaction ‘a’ transforms # A into B. The reaction ’b’ transforms B into C, and # so on through the cascade. The cascade stops # with E. # A has a special role because it is only consumed, # never produced. E has a special role because it # decays without producing another output. a : A -> B b : B -> C c : C -> D d : D -> E e : E -> Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 12 / 26
  • 13. Visualising the results of a cascade-decay simulation 1000 800 600 molecule count A B C D E 400 200 0 0 20 40 60 80 100 time Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 13 / 26
  • 14. About the cascade-decay simulation Our intuition was correct. The profiles of A, B, C , and D are very similar to previously. Because this is a stochastic simulation which involves pseudo-random number generation the results will not be exactly the same but they will be very similar. We can see that reactions are still occurring right up to the stop-time of this simulation (t = 100 seconds). That is perfectly OK in the results. We simulate up to the stop-time and no further. Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 14 / 26
  • 15. Changing a rate in the model We set the new reaction, e, to be the slowest reaction in the model, but what if we had chosen it to be the fastest reaction instead? We can find out how this would affect the results by changing the rate of reaction e. Our intuition should be that this again does not make much difference to the profile of chemical species A, B, C and D in the output, but it should affect the profile of species E . Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 15 / 26
  • 16. A simulation script, cascade-decay-fast.txt (1/3) # The simulation stop time (t) is 100 seconds t = 100 # The kinetic real-number rate constants of the five # reactions: a, b, c, d, e a = 0.5 b = 0.25 c = 0.125 d = 0.0625 e = 1.0 # The fastest reaction is e, the decay reaction for E. # The slowest reaction here is d. Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 16 / 26
  • 17. A simulation script, cascade-decay-fast.txt (2/3) This part is exactly the same as cascade-decay.txt # The initial integer molecule counts of the five species, # A, B, C, D, and E. Only A is present initially. # (A, B, C, D, E) = (1000, 0, 0, 0, 0) A = 1000 B = 0 C = 0 D = 0 E = 0 Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 17 / 26
  • 18. A simulation script, cascade-decay-fast.txt (3/3) This part is exactly the same as cascade-decay.txt # The five reactions. The reaction ‘a’ transforms # A into B. The reaction ’b’ transforms B into C, and # so on through the cascade. The cascade stops # with E. # A has a special role because it is only consumed, # never produced. E has a special role because it # decays without producing another output. a : A -> B b : B -> C c : C -> D d : D -> E e : E -> Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 18 / 26
  • 19. Visualising the results of a cascade-decay-fast simulation 1000 800 600 molecule count A B C D E 400 200 0 0 20 40 60 80 100 time Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 19 / 26
  • 20. About the cascade-decay-fast simulation Our intuition was correct again. The profiles of A, B, C , and D are very similar to previously. We can see that very little E builds up in the system (because it decays away much faster than it is produced). The profile for E hovers around zero throughout the simulation run. Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 20 / 26
  • 21. A dimerisation example We saw earlier that dimerisation is a special case for the Gillespie simulation algorithm. Let’s consider an example which uses dimerisation and also includes a decay reaction. Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 21 / 26
  • 22. A simulation script, dimer-decay.txt (1/3) # The simulation stop time (t) is 20 seconds t = 20 # The kinetic real-number rate constants of the four # reactions: d, x, y, z d = 1.0 x = 0.002 y = 0.5 z = 0.04 Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 22 / 26
  • 23. A simulation script, dimer-decay.txt (2/3) # The initial integer molecule counts of the three # species, X, Y, and Z. Only X is present initially. # (X, Y, Z) = (10000, 0, 0) X = 10000 Y = 0 Z = 0 Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 23 / 26
  • 24. A simulation script, dimer-decay.txt (3/3) # The four reactions: # (d), X can decay to nothing; # (x), two molecules of X can bind to form Y; # (y), Y can unbind to give two molecules of X; and # (z), a molecule of Y can produce a molecule of Z. d : X -> x : X + X -> Y y : Y -> X + X z : Y -> Z Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 24 / 26
  • 25. Visualising the results of a dimer-decay simulation 10000 8000 6000 molecule count X Y Z 4000 2000 0 0 5 10 15 20 time Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 25 / 26
  • 26. Summary We have seen some examples of simulation scripts involving cascades and dimerisation. Try creating some of your own. For example: A cascade which involves more species. A cascade where every species can decay, not just the last one. A dimerisation example without a decay reaction. Stephen Gilmore (School of Informatics) Stochastic simulation examples Friday 2nd November, 2012 26 / 26