Mathematical models of biological systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford University Press
2011
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 236 S. Ill., graph. Darst. |
| ISBN: | 9780199582181 |
Internformat
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| 245 | 1 | 0 | |a Mathematical models of biological systems |c Hugo van den Berg |
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| 264 | 1 | |a Oxford [u.a.] |b Oxford University Press |c 2011 | |
| 300 | |a XIII, 236 S. |b Ill., graph. Darst. | ||
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| 650 | 4 | |a Mathematisches Modell | |
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Datensatz im Suchindex
| _version_ | 1804143785702064128 |
|---|---|
| adam_text | IMAGE 1
MATHEMATICAL MODELS
OF BIOLOGICAL SYSTEMS
HUGO VAN DEN BERG
UNIVERSIIATS- AND LANDAS- BIBMOTHSK DARMSTADT .BIBFIOTJIEK B I O ! O G I
3
OXJORD
UNIVERSITY PRESS
IMAGE 2
CONTENTS
WHAT MODELS CAN DO FOR THE LIFE SCIENCES 1 1.1 DONKEY AND DIPLODOCUS
11.2 WHAT IS A MATHEMATICAL MODEL? 31.3 WHY USE DIFFERENTIAL EQUATIONS?
* 4 1.4 A MODELLING RECIPE 61.5 DEFINING BIOLOGICAL SYSTEMS * , 8
FURTHER READING 9EXERCISES . 10 BASIC MODELLING CONCEPTS AND
TECHNIQUES 11 2.1 ALCOHOL METABOLISM 112.2 THE FOOD INTAKE RATE OF A
PREDATOR 142.3 AN ENZYME WITH A MODULATING LIGAND 15 2.4 MINERAL
DYNAMICS OF A MUSSEL IN A TIDAL ZONE 17 2.5 THE SALT BALANCE IN A POND
SNAIL 182.6 FLUXES AND FLOWS BETWEEN COMPARTMENTS . 20 2.6.1 BLOOD
VOLUMES IN A POND SNAIL 212.6.2 CIRCULATION OF LYMPHOCYTES 232.6.3
CLOSED, CONNECTED COMPARTMENTAL SYSTEMS 25 2.7 SUBCELLULAR DYNAMICS
272.7.1 DYNAMICS OF A METABOLITE AND, AN ENZYME 27 2.7.2 A GENETIC
SWITCH 292.7.3 A GENETIC CLOCK - 31FURTHER READING 32EXERCISES ^ 33
WORKING WITH ORDINARY DIFFERENTIAL EQUATIONS 41 3.1 SOLUTIONS AND HOW TO
AVOID CALCULATING THEM 41 3.2 ELEMENTARY TECHNIQUES FOR SOLVING SCALAR
FIRST-ORDER ODES 42 3.2.1 SEPARATION OF VARIABLES 433.2.2 VARIATIONS ON
THE THEME OF YO EXP{A} 43 3.3 LINEAR SYSTEMS 453.3.1 THE BASIC IDEA:
Y(I) = E * Z(T) 453.3.2 OTHER BUILDING BLOCKS; COMPLEX EIGENVALUES 47
3.3.3 WHEN THERE ARE FEWER THAN N DISTINCT EIGENVALUES 48 3.3.4
STABILITY OF A LINEAR SYSTEM WITH N = 2; ROUTH-HURWITZ CRITERIA 493.3.5
CARVING UP PHASE SPACE 50* 3.4 NON-LINEAR SYSTEMS 52
IMAGE 3
X CONTENTS
3.4.1 EQUILIBRIUM POINTS IN NON-LINEAR SYSTEMS 3.4.2 PHASE PLANE
ANALYSIS 3.5 MODEL SIMULATIONS FURTHER READING EXERCISES
MODELS AND DATA ANALYSIS 4.1 MEASUREMENT * 4.1.1 EMPIRICAL DIMENSION
4.1.2 MEASUREMENT UNITS
4.1.3 DIMENSIONAL ANALYSIS 4.1.4 UNITS AND SCALES OF MEASUREMENT 4.2
PARAMETER ESTIMATION AND STATISTICS 4.2.1 LEAST SUM-OF-SQUARES FITTING
4.2.2 SIMULTANEOUS FITTING 4.2.3 STEP-WISE PARAMETER FITTING: THE
PEELING METHOD 4.2.4 SUPPORT FROM PARAMETER ESTIMATES: NUMERICAL VERSUS
STRUCTURAL CONFIDENCE
4.2.5 TESTING WHETHER THE MODEL FITS THE DATA 4.2.6 CONFIDENCE REGIONS
4.3 PARAMETER VALUES FOR EXTENSIVE MODELS FURTHER READING EXERCISES
MODELLING PRINCIPLES 5.1 MODEL STRUCTURE 5.2 MODEL ASSUMPTIONS 5.2.1
COUNTING ASSUMPTIONS
5.2.2 IMPLICIT AND EXPLICIT ASSUMPTIONS 5.2.3 STRONG AND WEAK
ASSUMPTIONS 5.2.4 STRINGENT AND RELAXED ASSUMPTIONS 5.3 APPLICATIONS OF
MODELS 5.4 GOOD MODELLING PRACTICE
5.4.1 SIMPLIFYING A MODEL 5.4.2 CONSISTENCY AND COHERENCY 5.4.3 PETITIO
PRINCIPII OR BEGGING THE QUESTION 5.4.4 SALIENCY AND RELEVANCE 5.4.5
TAILORING ASSUMPTIONS TO ATTRACTIVE EQUATIONS 5.4.6 NAMING THE
QUANTITIES IN THE MODEL
5.4.7 ADOPTING AN ENGINEER S POINT OF VIEW 5.5 FROM MODELS TO THEORIES
5.5.1 NEUTRAL ANALOGIES MAKE MODELS USEFUL 5.5.2 HOW TO JUDGE SUCCESSFUL
PREDICTIONS, OR FAILED ONES EXERCISES
GROWTH OF POPULATIONS AND OF INDIVIDUALS 6.1 BASIC MODELS OF POPULATION
GROWTH 6.1.1 LIMITS ON GROWTH
IMAGE 4
CONTENTS XI
6.1.2 INTERFERENCE: LOGISTIC GROWTH AND VARIATIONS 95 6.1.3 POSITIVE
INTERFERENCE : * , 96
6.1.4 HARVESTING 96
6.2 TROPHIC CASCADES AND FOOD WEBS - 98
6.3 MICROBIAL GROWTH IN A CHEMOSTAT 101
6.3.1 BASIC CHEMOSTAT EQUATIONS 102
6.3.2 LOGISTIC GROWTH IN- THE CHEMOSTAT 103
6.3.3 TOWARDS A MODEL FOR THE RELATIVE GROWTH RATE 104 6.4 GROWTH OF
INDIVIDUALS 107
6.4.1 THE BERTALANFFY-LIEBIG MODEL 108
6.4.2 BEYOND BERTALANFFY-LIEBIG 110
6.4.3 THE STOICHIOMETRIC PERSPECTIVE 111
FURTHER READING - - , 113
EXERCISES 113
INFECTION AND IMMUNITY 119
7.1 INFECTION DYNAMICS IN A POPULATION 119
7.1.1 EPIDEMICS - * _ * 120
7.1.2 IMPERFECT IMMUNITY 121
7.1.3 LATENCY * , 122
7.2 INFECTION AND IMMUNITY WITHIN THE HOST ORGANISM 123 7.2.1 IMMUNE
CONTROL AND VIRAL RUNAWAY 123
7.2.2 THE VIRAL QUASI-SPECIES 124
7.2.3 THE T CELL RESPONSE . 125
7.2.4 THE T CELL REPERTOIRE - 129
FURTHER READING 131
EXERCISES 132
(^PHYSIOLOGY 137
F V 8.1 THE CARDIOVASCULAR SYSTEM 137
8.1.1 CONTROL OF BLOOD PRESSURE AND BLOOD VOLUME 138 8.1.2 BEAT-TO-BEAT
VARIATIONS IN THE HEART 139
8.1.3 ARTERIAL PULSE WAVES 142
|. 8.2 RENAL PHYSIOLOGY 144
8.3 HYDROMINERAL PHYSIOLOGY 147
8.3.1 CELLULAR HOMEOSTASIS 147
; 8.3.2 EXCITABILITY 150
8.4 GLUCOSE HOMEOSTASIS 153
8.4.1 TOWARDS THE SIMPLEST POSSIBLE MODEL 154
8.4.2 CONTROL OF INSULIN SECRETION 155
|JFURTHER READING . 158
|T EXERCISES * 158
FESTOCHASTIC MODELS 167
J P .L BUTTERFLIES, AGAIN 167
9.1.1 TIME OF DEATH AND TIME OF EXTINCTION 168
9.1.2 THE HAZARD RATE 169
9.1.3 PROBABILITY DYNAMICS 171
IMAGE 5
XII CONTENTS
9.2 ERADICATION OF CANCER 9.3 THE REPRODUCTIVE NUMBER 9.4 SIGNALLING
FIDELITY 9.4.1 INTRINSIC STOCHASTIC NOISE
9.4.2 ADDING EXTRINSIC NOISE 9.5 SPATIAL FLUCTUATIONS 9.5.1.
ADAPTOR-MEDIATED RECEPTOR SIGNALLING * 9.5.2 PAIR DYNAMICS FURTHER
READING EXERCISES
A MATHS MISCELLANY A.I SETS A.2 RELATIONS AND FUNCTIONS A.3 DERIVATIVES
AND INTEGRALS
A.4 TAYLOR SERIES A.5 USEFUL TECHNIQUES A.5.1 SOME STANDARD SOLUTIONS
A.5.2 COMMONLY USED TAYLOR SERIES
A.5.3 STIRLING S FORMULA A.5.4 L HOPITAL S RULE A.5.5 PARTIAL FRACTION
DECOMPOSITION A.5.6 LAGRANGE MULTIPLIERS A.5.7 SOME SUMS A.6 COMPLEX
NUMBERS A.7 VECTORS AND MATRICES A.8 PROBABILITY
A.8.1 FUNDAMENTAL LAWS OF PROBABILITY A.8.2 RANDOM VARIABLES AND THEIR
DISTRIBUTIONS A.8.3 EXPECTATION AND VARIANCE A.8.4 SOME DISTRIBUTIONS
OFTEN ENCOUNTERED IN PRACTICE A.9 PROBLEM SOLVING
FURTHER READING
B FROM BOLTZMANN TO NERNST B.I BOLTZMANN B.2 WORK, HEAT, TEMPERATURE,
AND ENTROPY B.3 NERNST FURTHER READING
C ULTIMATE BEHAVIOUR OF A CLOSED, CONNECTED, COMPARTMENTAL SYSTEM
FURTHER READING
D BUCKINGHAM S THEOREM FURTHER READING
E MINIMIZING THE SUM OF SQUARES WITH RESPECT TO THE PARAMETERS FURTHER
READING
|
| any_adam_object | 1 |
| author | Berg, Hugo van den 1968- |
| author_GND | (DE-588)143085387 |
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| classification_rvk | SK 950 WC 7000 |
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| dewey-ones | 570 - Biology |
| dewey-raw | 570.1/5118 |
| dewey-search | 570.1/5118 |
| dewey-sort | 3570.1 45118 |
| dewey-tens | 570 - Biology |
| discipline | Biologie Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV037198327 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:53:11Z |
| institution | BVB |
| isbn | 9780199582181 |
| language | English |
| lccn | 2010029642 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021112626 |
| oclc_num | 699900419 |
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| owner | DE-19 DE-BY-UBM DE-11 DE-20 DE-83 |
| owner_facet | DE-19 DE-BY-UBM DE-11 DE-20 DE-83 |
| physical | XIII, 236 S. Ill., graph. Darst. |
| publishDate | 2011 |
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| publisher | Oxford University Press |
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| spelling | Berg, Hugo van den 1968- Verfasser (DE-588)143085387 aut Mathematical models of biological systems Hugo van den Berg 1. publ. Oxford [u.a.] Oxford University Press 2011 XIII, 236 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematisches Modell Biology Mathematical models Biological systems Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Biologisches System (DE-588)4122930-7 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 s Biologisches System (DE-588)4122930-7 s DE-604 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021112626&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Berg, Hugo van den 1968- Mathematical models of biological systems Mathematisches Modell Biology Mathematical models Biological systems Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Biologisches System (DE-588)4122930-7 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4122930-7 |
| title | Mathematical models of biological systems |
| title_auth | Mathematical models of biological systems |
| title_exact_search | Mathematical models of biological systems |
| title_full | Mathematical models of biological systems Hugo van den Berg |
| title_fullStr | Mathematical models of biological systems Hugo van den Berg |
| title_full_unstemmed | Mathematical models of biological systems Hugo van den Berg |
| title_short | Mathematical models of biological systems |
| title_sort | mathematical models of biological systems |
| topic | Mathematisches Modell Biology Mathematical models Biological systems Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Biologisches System (DE-588)4122930-7 gnd |
| topic_facet | Mathematisches Modell Biology Mathematical models Biological systems Mathematical models Biologisches System |
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