Mathematical modeling of molecular motors:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
2012
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | II, 116 S. graph. Darst. |
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MARC
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| 245 | 1 | 0 | |a Mathematical modeling of molecular motors |c von Peter Keller |
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Record in the Search Index
| _version_ | 1804149738824531968 |
|---|---|
| adam_text | IMAGE 1
C O N T E N T S
INTRODUCTION 1
1 M A R K O V C H A I N S IN D I S C R E T E A N D C O N T I N U O U S T
I M E W I T H C O U N T A B L E S T A T E S P A C E 5
1.1 O N NOTATION 5
1.2 BASIC FACTS 6
1.2.1 MARKOV CHAINS IN DISCRETE TIME 6
1.2.2 CONTINUOUS TIME 9
1.3 REVERSIBILITY, PERMUTED BALANCE AND EXTENDED KOLMOGOROFF CRITERION
11
1.4 LOCAL TIME 21
1.5 P A T T E R N MATCHING 22
2 A B S O R P T I O N I N M A R K O V C H A I N S 2 5
2.1 P H A S E T Y P E DISTRIBUTIONS 25
2.1.1 PH-TYPE DISTRIBUTION AS ABSORPTION TIME DISTRIBUTION 25
2.1.2 BASIC PROPERTIES 27
2.1.3 TYPICAL EXAMPLES OF P H - T Y P E DISTRIBUTIONS 28
2.1.4 EXAMPLES FOR DISCRETE DISTRIBUTIONS 28
2.1.4.1 T H E GEOMETRIC DISTRIBUTION 28
2.1.4.2 GENERALIZED GEOMETRIC DISTRIBUTIONS 29
2.1.5 EXAMPLES FOR CONTINUOUS DISTRIBUTIONS 30
2.1.5.1 EXPONENTIAL DISTRIBUTION 30
2.1.5.2 ERLANG DISTRIBUTION 30
2.1.5.3 HYPO EXPONENTIAL O R GENERALIZED ERLANG DISTRIBUTION 31
2.1.5.4 COX DISTRIBUTION 32
2.2 EXTENSIONS TO SEVERAL ABSORBING STATES 32
2.2.1 ABSORPTION IN A GIVEN SUBSET OF ABSORBING STATES 33
2.2.2 ABSORPTION LAW AS MIXTURE OF P H - T Y P E DISTRIBUTIONS 3 8
2.2.3 ROLE OF PSEUDO INVERSES AND CONDITIONAL ABSORBING STATES 40
3 T I M E D U A L I T Y I N M A R K O V C H A I N S 4 3
3.1 DEFINITIONS A N D PRELIMINARIES 43
3.2 SUFFICIENT CONDITIONS FOR T I M E DUALITY IN CASE OF SIMPLE
NEIGHBOURHOOD 4 8
3.2.1 A CONDITION BASED ON M O M E N T GENERATING FUNCTIONS 4 8
3.2.2 T I M E DUALITY VIA PERMUTED BALANCE 49
3.2.3 FURTHER RESULTS BASED ON THE S T R U C T U R E OF T H E TRANSITION
G R A P H 50
3.3 EXTENSION TO NON-SIMPLE B O U N D A R Y 55
3.4 SOME EXAMPLES 57
3.4.1 T I M E DUALITY WITHOUT P E R M U T E D BALANCE 57
HTTP://D-NB.INFO/1030278458
IMAGE 2
C O N T E N T S
3.4.2 BIRTH-AND-DEATH PROCESSES WITH REFLECTING B O U N D A R Y A N D
PROCESSES ON TREES 59
4 K I L L E D Q U A S I - R A N D O M - W A L K 6 1
4.1 DEFINITIONS A N D PRELIMINARIES 6 1
4.2 LIFETIME 6 5
4.3 T H E NOTION OF FORWARD A N D BACKWARD STEPS A N D THEIR
DISTRIBUTION 66
4.4 T H E LAST VISITED LEVEL A N D T H E MINIMAL A N D MAXIMAL LEVEL
ATTAINED BEFORE KILLING . 73
5 M O D E L L I N G O F M O L E C U L A R M O T O R S A N D A P P L I C
A T I O N S T O K I N E S I N V 7 7
5.1 LIFETIME 79
5.2 T H E STEP-PROCESS AND DERIVED QUANTITIES 80
6 P E R S P E C T I V E S A N D O U T L O O K 8 7
6.1 TIME DUALITY IN SEMI-MARKOV CHAINS 87
6.2 EXTENSION TO COUPLING OF KILLED QUASI RANDOM-WALKS IN T H E MODELING
OF MOLECULAR MOTORS 89
A M A T R I X T H E O R Y 9 1
A . L O N T H E INVERTIBILITY OF SUBGENERATORS A N D SUBSTOCHASTIC MAT
RICES 91
A.2 T H E FROBENIUS FORMULA FOR BLOCK MATRICES 92
B O N P H - T Y P E D I S T R I B U T I O N S 9 3
B . L DISCRETE TIME 93
B . L . L DISTRIBUTION A N D DISTRIBUTION FUNCTION 93
B . L . 2 GENERATING FUNCTION A N D FACTORIAL MOMENTS 95
B.2 CONTINUOUS TIME 96
B.2.1 DISTRIBUTION A N D DISTRIBUTION FUNCTION 96
B.2.2 CHARACTERISTIC A N D M O M E N T GENERATING FUNCTION, MOMENTS 97
C T H E S I M P L E KILLED R A N D O M W A L K 9 9
N O M E N C L A T U R E 1 0 7
E I D E S S T A T T L I C H E E R K L A R U N G 1 1 1
B I B L I O G R A P H Y 1 1 3
I I
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| dewey-ones | 571 - Physiology & related subjects |
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| dewey-search | 571.65401519233 |
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| dewey-tens | 570 - Biology |
| discipline | Biologie |
| format | Thesis Book |
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| indexdate | 2024-07-10T00:27:48Z |
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| language | English |
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| physical | II, 116 S. graph. Darst. |
| publishDate | 2012 |
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| spelling | Keller, Peter Verfasser aut Mathematical modeling of molecular motors von Peter Keller 2012 II, 116 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Potsdam, Univ., Diss., 2012 (DE-588)4113937-9 Hochschulschrift gnd-content DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025456172&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Keller, Peter Mathematical modeling of molecular motors |
| subject_GND | (DE-588)4113937-9 |
| title | Mathematical modeling of molecular motors |
| title_auth | Mathematical modeling of molecular motors |
| title_exact_search | Mathematical modeling of molecular motors |
| title_full | Mathematical modeling of molecular motors von Peter Keller |
| title_fullStr | Mathematical modeling of molecular motors von Peter Keller |
| title_full_unstemmed | Mathematical modeling of molecular motors von Peter Keller |
| title_short | Mathematical modeling of molecular motors |
| title_sort | mathematical modeling of molecular motors |
| topic_facet | Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025456172&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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