Multiscale problems in the life sciences: from microscopic to macroscopic ; lectures given at the Banach Center and C.I.M.E. joint summer school held in Będlewo, Poland, September 4 - 9, 2006
Gespeichert in:
| Weitere Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2008
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| Schriftenreihe: | Lecture notes in mathematics
1940 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 321 S. graph. Darst. |
| ISBN: | 9783540783602 3540783601 9783540783626 |
Internformat
MARC
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| 245 | 1 | 0 | |a Multiscale problems in the life sciences |b from microscopic to macroscopic ; lectures given at the Banach Center and C.I.M.E. joint summer school held in Będlewo, Poland, September 4 - 9, 2006 |c Jacek Banasiak ... Ed.: Vincenzo Capasso ... |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a XII, 321 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1940 | |
| 650 | 0 | 7 | |a Mehrskalenmodell |0 (DE-588)7600619-0 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Capasso, Vincenzo |d 1945- |0 (DE-588)110728556 |4 edt | |
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| 830 | 0 | |a Lecture notes in mathematics |v 1940 |w (DE-604)BV000676446 |9 1940 | |
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Datensatz im Suchindex
| _version_ | 1804137778553815040 |
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| adam_text | Contents
Positivity
in
Natural
Sciences
Jacek Bnnasiak
.................................................. 1
1
Introduction
................................................. 1
1.1
What can go Wrong?
..................................... 3
1.2
And if Everything Seems to be Fine?
....................... 3
2
Spectral Properties of Operators
............................... 4
2.1
Operators
............................................... 5
2.2
Spectral Properties of a Single Operator
.................... 7
3
Banach Lattices and Positive Operators
......................... 13
3.1
Defining Order
.......................................... 13
3.2
Banach Lattices
......................................... 15
3.3
Positive Operators
....................................... 19
3.4
Relation Between Order and Norm
......................... 20
3.5
Complexification
......................................... 23
3.6
Spectral Radius of Positive Operators
...................... 24
4
First Semigroups
............................................. 25
4.1
Around the Hille-Yosida Theorem
......................... 27
4.2
Dissipative Operators
.................................... 28
4.3
Long Time Behaviour of Semigroups
....................... 29
4.4
Positive Semigroups
...................................... 37
4.5
Generation Through Perturbation
.......................... 39
4.6
Positive Perturbations of Positive Semigroups
............... 42
5
What can go Wrong?
......................................... 45
5.1
Applications to Birth-and-Death Type Problems
............. 52
5.2
Chaos in Population Theory
.............................. 59
6
Asynchronous Growth
........................................ 61
6.1
Essential Growth Bound
.................................. 61
6.2
Peripheral Spectrum of Positive Semigroups
................. 63
6.3
Compactness,
Positivity
and Irreducibility of Perturbed
Semigroups
............................................. 67
X
Contents
7
Asymptotic Analysis of Singularly Perturbed Dynamical Systems
... 75
7.1
Compressed Expansion
................................... 77
References
...................................................... 87
Rescaling Stochastic Processes: Asymptotics
V. Capasso and D. Morale
........................................ 91
1
Introduction
................................................. 91
1.1
First Examples of Rescaling
............................... 95
2
Stochastic Processes
.......................................... 97
2.1
Processes with Independent Increments
.....................100
2.2
Martingales
.............................................100
2.3
Markov Processes
........................................103
2.4
Brownian Motion and the Wiener Process
..................109
3
Ito
Calculus
.................................................110
3.1
The
Ito
Integral
.........................................110
3.2
The Stochastic Differential
................................112
3.3
Stochastic Differential Equations
...........................113
3.4
Kolmogorov and Fokker-Planck Equations
..................115
3.5
The Multidimensional Case
...............................117
4
Deterministic Approximation of Stochastic Systems
...............118
4.1
Continuous Approximation of Jump Population Processes
.....118
4.2
Continuous Approximation of Stochastic Interacting
Particle Systems
.........................................120
4.3
Convergence of the Empirical Measure
......................122
5
A Specific Model for Interacting Particles
........................128
5.1
Asymptotic Behavior of the System for Large Populations:
A Heuristic Derivation
...................................130
5.2
Asymptotic Behavior of the System for Large Populations:
A Rigorous Derivation
....................................134
6
Long Time Behavior: Invariant Measure
.........................137
A Proof of the Identification of the Limit
ρ
........................141
References
......................................................144
Modelling Aspects of Cancer Growth: Insight
from Mathematical and Numerical Analysis
and Computational Simulation
Mark A.J. Chaplain
..............................................147
1
Introduction
.................................................147
1.1
Macroscopic Modelling
...................................148
1.2
Cancer Growth and Development
..........................149
2
Modelling Avascular Solid Tumour Growth
......................
I50
2.1
Introduction
............................................150
2.2
Linearised Stability Theory
...............................151
2.3
The Role of Pre-Pattern Theory in Solid Tumour Growth
and Invasion
............................................153
Contents
XI
2.4 Model
Extension:
Application
to a Growing
Spherical Tumour
........................................156
2.5
Discussion and Conclusions
...............................157
3
Mathematical Modelling of T-Lymphocyte Response
to a Solid Tumour
............................................160
3.1
Introduction
............................................160
3.2
The Mathematical Model
.................................161
3.3
Travelling Wave Analysis
.................................173
3.4
Discussion
..............................................178
4
Mathematical Modelling of Cancer Invasion
......................180
4.1
Introduction
............................................180
4.2
Cancer Invasion of Tissue and Metastasis
...................182
4.3
Proteolysis and Extracellular Matrix Degradation
............182
4.4
The Mathematical Model of Proteolysis and Cancer Cell
Invasion of Tissue
........................................184
4.5
Nondimensionalisation of the Model Equations
..............187
4.6
Model Analysis
..........................................188
4.7
Spatially Uniform Steady States
...........................188
4.8
Taxis-Driven Instability and Dispersion Curves
..............188
4.9
Numerical Results
.......................................189
4.10
Numerical Technique
.....................................190
4.11
Computational Simulation Results
.........................191
4.12
Discussion and Conclusions
...............................191
5
Summary
....................................................195
References
......................................................195
Lins
Between Microscopic and Macroscopic Descriptions
Mirosław Lachowicz
..............................................201
1
Introduction
.................................................201
2
Microscopic (Stochastic) Systems
...............................205
3
Generalized Kinetic Models
....................................213
4
Diffusive Limit
...............................................227
5
Links in the Space-Homogeneous Case
..........................231
6
Coagulation-Fragmentation Equations
..........................243
7
The Space-Inhomogeneous Case: Reaction-Diffusion Equations
.... 245
8
Reaction-Diffusion-Chemotaxis Equations
.......................252
References
......................................................262
Evolutionary Game Theory and Population Dynamics
Jacek
Miçkisz....................................................
269
1
Short Overview
..............................................269
2
Introduction
.................................................270
3
A Crash Course in Game Theory
...............................273
4
Replicator Dynamics
..........................................277
5
Replicator Dynamics with Migration
............................280
XII Contents
6
Replicator
Dynamics with Time Delay
..........................285
6.1
Social-Type Time Delay
..................................285
6.2
Biological-Type Time Delay
...............................288
7
Stochastic Dynamics of Finite Populations
.......................290
8
Stochastic Dynamics of Well-Mixed Populations
..................292
9
Spatial Games with Local Interactions
..........................298
9.1
Nash Configurations and Stochastic Dynamics
...............298
9.2
Ground States and Nash Configurations
....................300
9.3
Ensemble Stability
.......................................303
9.4
Stochastic Stability in
Non-
Potential Games
.................306
9.5
Dominated Strategies
....................................310
10
Review of Other Results
......................................311
References
......................................................312
List of Participants
............................................317
Index
..........................................................319
|
| adam_txt |
Contents
Positivity
in
Natural
Sciences
Jacek Bnnasiak
. 1
1
Introduction
. 1
1.1
What can go Wrong?
. 3
1.2
And if Everything Seems to be Fine?
. 3
2
Spectral Properties of Operators
. 4
2.1
Operators
. 5
2.2
Spectral Properties of a Single Operator
. 7
3
Banach Lattices and Positive Operators
. 13
3.1
Defining Order
. 13
3.2
Banach Lattices
. 15
3.3
Positive Operators
. 19
3.4
Relation Between Order and Norm
. 20
3.5
Complexification
. 23
3.6
Spectral Radius of Positive Operators
. 24
4
First Semigroups
. 25
4.1
Around the Hille-Yosida Theorem
. 27
4.2
Dissipative Operators
. 28
4.3
Long Time Behaviour of Semigroups
. 29
4.4
Positive Semigroups
. 37
4.5
Generation Through Perturbation
. 39
4.6
Positive Perturbations of Positive Semigroups
. 42
5
What can go Wrong?
. 45
5.1
Applications to Birth-and-Death Type Problems
. 52
5.2
Chaos in Population Theory
. 59
6
Asynchronous Growth
. 61
6.1
Essential Growth Bound
. 61
6.2
Peripheral Spectrum of Positive Semigroups
. 63
6.3
Compactness,
Positivity
and Irreducibility of Perturbed
Semigroups
. 67
X
Contents
7
Asymptotic Analysis of Singularly Perturbed Dynamical Systems
. 75
7.1
Compressed Expansion
. 77
References
. 87
Rescaling Stochastic Processes: Asymptotics
V. Capasso and D. Morale
. 91
1
Introduction
. 91
1.1
First Examples of Rescaling
. 95
2
Stochastic Processes
. 97
2.1
Processes with Independent Increments
.100
2.2
Martingales
.100
2.3
Markov Processes
.103
2.4
Brownian Motion and the Wiener Process
.109
3
Ito
Calculus
.110
3.1
The
Ito
Integral
.110
3.2
The Stochastic Differential
.112
3.3
Stochastic Differential Equations
.113
3.4
Kolmogorov and Fokker-Planck Equations
.115
3.5
The Multidimensional Case
.117
4
Deterministic Approximation of Stochastic Systems
.118
4.1
Continuous Approximation of Jump Population Processes
.118
4.2
Continuous Approximation of Stochastic Interacting
Particle Systems
.120
4.3
Convergence of the Empirical Measure
.122
5
A Specific Model for Interacting Particles
.128
5.1
Asymptotic Behavior of the System for Large Populations:
A Heuristic Derivation
.130
5.2
Asymptotic Behavior of the System for Large Populations:
A Rigorous Derivation
.134
6
Long Time Behavior: Invariant Measure
.137
A Proof of the Identification of the Limit
ρ
.141
References
.144
Modelling Aspects of Cancer Growth: Insight
from Mathematical and Numerical Analysis
and Computational Simulation
Mark A.J. Chaplain
.147
1
Introduction
.147
1.1
Macroscopic Modelling
.148
1.2
Cancer Growth and Development
.149
2
Modelling Avascular Solid Tumour Growth
.
I50
2.1
Introduction
.150
2.2
Linearised Stability Theory
.151
2.3
The Role of Pre-Pattern Theory in Solid Tumour Growth
and Invasion
.153
Contents
XI
2.4 Model
Extension:
Application
to a Growing
Spherical Tumour
.156
2.5
Discussion and Conclusions
.157
3
Mathematical Modelling of T-Lymphocyte Response
to a Solid Tumour
.160
3.1
Introduction
.160
3.2
The Mathematical Model
.161
3.3
Travelling Wave Analysis
.173
3.4
Discussion
.178
4
Mathematical Modelling of Cancer Invasion
.180
4.1
Introduction
.180
4.2
Cancer Invasion of Tissue and Metastasis
.182
4.3
Proteolysis and Extracellular Matrix Degradation
.182
4.4
The Mathematical Model of Proteolysis and Cancer Cell
Invasion of Tissue
.184
4.5
Nondimensionalisation of the Model Equations
.187
4.6
Model Analysis
.188
4.7
Spatially Uniform Steady States
.188
4.8
Taxis-Driven Instability and Dispersion Curves
.188
4.9
Numerical Results
.189
4.10
Numerical Technique
.190
4.11
Computational Simulation Results
.191
4.12
Discussion and Conclusions
.191
5
Summary
.195
References
.195
Lins
Between Microscopic and Macroscopic Descriptions
Mirosław Lachowicz
.201
1
Introduction
.201
2
Microscopic (Stochastic) Systems
.205
3
Generalized Kinetic Models
.213
4
Diffusive Limit
.227
5
Links in the Space-Homogeneous Case
.231
6
Coagulation-Fragmentation Equations
.243
7
The Space-Inhomogeneous Case: Reaction-Diffusion Equations
. 245
8
Reaction-Diffusion-Chemotaxis Equations
.252
References
.262
Evolutionary Game Theory and Population Dynamics
Jacek
Miçkisz.
269
1
Short Overview
.269
2
Introduction
.270
3
A Crash Course in Game Theory
.273
4
Replicator Dynamics
.277
5
Replicator Dynamics with Migration
.280
XII Contents
6
Replicator
Dynamics with Time Delay
.285
6.1
Social-Type Time Delay
.285
6.2
Biological-Type Time Delay
.288
7
Stochastic Dynamics of Finite Populations
.290
8
Stochastic Dynamics of Well-Mixed Populations
.292
9
Spatial Games with Local Interactions
.298
9.1
Nash Configurations and Stochastic Dynamics
.298
9.2
Ground States and Nash Configurations
.300
9.3
Ensemble Stability
.303
9.4
Stochastic Stability in
Non-
Potential Games
.306
9.5
Dominated Strategies
.310
10
Review of Other Results
.311
References
.312
List of Participants
.317
Index
.319 |
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| discipline | Biologie Mathematik Medizin |
| discipline_str_mv | Biologie Mathematik Medizin |
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| genre | (DE-588)1071861417 Konferenzschrift 2006 Będlewo gnd-content |
| genre_facet | Konferenzschrift 2006 Będlewo |
| id | DE-604.BV023397527 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:22:29Z |
| indexdate | 2024-07-09T21:17:42Z |
| institution | BVB |
| institution_GND | (DE-588)114568-X |
| isbn | 9783540783602 3540783601 9783540783626 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016580366 |
| oclc_num | 244626851 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-824 DE-29T DE-83 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-824 DE-29T DE-83 DE-188 |
| physical | XII, 321 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Multiscale problems in the life sciences from microscopic to macroscopic ; lectures given at the Banach Center and C.I.M.E. joint summer school held in Będlewo, Poland, September 4 - 9, 2006 Jacek Banasiak ... Ed.: Vincenzo Capasso ... Berlin [u.a.] Springer 2008 XII, 321 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1940 Mehrskalenmodell (DE-588)7600619-0 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2006 Będlewo gnd-content Mehrskalenmodell (DE-588)7600619-0 s DE-604 Banasiak, Jacek Sonstige oth Capasso, Vincenzo 1945- (DE-588)110728556 edt Międzynarodowe Centrum Matematyczne im. Stefana Banacha Sonstige (DE-588)114568-X oth Lecture notes in mathematics 1940 (DE-604)BV000676446 1940 Digitalisierung TU Muenchen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016580366&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Multiscale problems in the life sciences from microscopic to macroscopic ; lectures given at the Banach Center and C.I.M.E. joint summer school held in Będlewo, Poland, September 4 - 9, 2006 Lecture notes in mathematics Mehrskalenmodell (DE-588)7600619-0 gnd |
| subject_GND | (DE-588)7600619-0 (DE-588)1071861417 |
| title | Multiscale problems in the life sciences from microscopic to macroscopic ; lectures given at the Banach Center and C.I.M.E. joint summer school held in Będlewo, Poland, September 4 - 9, 2006 |
| title_auth | Multiscale problems in the life sciences from microscopic to macroscopic ; lectures given at the Banach Center and C.I.M.E. joint summer school held in Będlewo, Poland, September 4 - 9, 2006 |
| title_exact_search | Multiscale problems in the life sciences from microscopic to macroscopic ; lectures given at the Banach Center and C.I.M.E. joint summer school held in Będlewo, Poland, September 4 - 9, 2006 |
| title_exact_search_txtP | Multiscale problems in the life sciences from microscopic to macroscopic ; lectures given at the Banach Center and C.I.M.E. joint summer school held in Będlewo, Poland, September 4 - 9, 2006 |
| title_full | Multiscale problems in the life sciences from microscopic to macroscopic ; lectures given at the Banach Center and C.I.M.E. joint summer school held in Będlewo, Poland, September 4 - 9, 2006 Jacek Banasiak ... Ed.: Vincenzo Capasso ... |
| title_fullStr | Multiscale problems in the life sciences from microscopic to macroscopic ; lectures given at the Banach Center and C.I.M.E. joint summer school held in Będlewo, Poland, September 4 - 9, 2006 Jacek Banasiak ... Ed.: Vincenzo Capasso ... |
| title_full_unstemmed | Multiscale problems in the life sciences from microscopic to macroscopic ; lectures given at the Banach Center and C.I.M.E. joint summer school held in Będlewo, Poland, September 4 - 9, 2006 Jacek Banasiak ... Ed.: Vincenzo Capasso ... |
| title_short | Multiscale problems in the life sciences |
| title_sort | multiscale problems in the life sciences from microscopic to macroscopic lectures given at the banach center and c i m e joint summer school held in bedlewo poland september 4 9 2006 |
| title_sub | from microscopic to macroscopic ; lectures given at the Banach Center and C.I.M.E. joint summer school held in Będlewo, Poland, September 4 - 9, 2006 |
| topic | Mehrskalenmodell (DE-588)7600619-0 gnd |
| topic_facet | Mehrskalenmodell Konferenzschrift 2006 Będlewo |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016580366&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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