Mathematics as a laboratory tool: dynamics, delays and noise
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
Springer
2014
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XXV, 500 S. Ill., graph. Darst. |
| ISBN: | 9781461490951 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV042168815 | ||
| 003 | DE-604 | ||
| 005 | 20191001 | ||
| 007 | t| | ||
| 008 | 141105s2014 xx ad|| |||| 00||| eng d | ||
| 020 | |a 9781461490951 |c Print |9 978-1-4614-9095-1 | ||
| 035 | |a (OCoLC)897148019 | ||
| 035 | |a (DE-599)BVBBV042168815 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 |a DE-91G |a DE-188 |a DE-11 | ||
| 084 | |a SK 950 |0 (DE-625)143273: |2 rvk | ||
| 084 | |a MAT 022f |2 stub | ||
| 084 | |a 510 |2 sdnb | ||
| 084 | |a BIO 105f |2 stub | ||
| 100 | 1 | |a Milton, John |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematics as a laboratory tool |b dynamics, delays and noise |c John Milton ; Toru Ohira |
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 2014 | |
| 300 | |a XXV, 500 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Neurologie |0 (DE-588)4041888-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Biowissenschaftlerin |0 (DE-588)4698137-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Cytologie |0 (DE-588)4070177-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Mathematik |0 (DE-588)4037944-9 |D s |
| 689 | 0 | 1 | |a Neurologie |0 (DE-588)4041888-1 |D s |
| 689 | 0 | 2 | |a Cytologie |0 (DE-588)4070177-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Mathematik |0 (DE-588)4037944-9 |D s |
| 689 | 1 | 1 | |a Biowissenschaftlerin |0 (DE-588)4698137-8 |D s |
| 689 | 1 | |8 1\p |5 DE-604 | |
| 700 | 1 | |a Ohira, Toru |d 1963- |e Verfasser |0 (DE-588)1059084139 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4614-9096-8 |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027608287&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027608287&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-027608287 | |
Record in the Search Index
| _version_ | 1825638369629044736 |
|---|---|
| adam_text |
Contents
Preface
.
vii
Notation. xv
Tools.xvii
1 Science
and the Mathematics of
Black
Boxes
. 1
1.1
The Scientific Method
. 3
1.2
Dynamical Systems
. 3
1.2.1
Variables
. 4
1.2.2
Measurements
. 6
1.2.3
Units
. 7
1.3
Input-Output Relationships
. 8
1.3.1
Linear Versus Nonlinear Black Boxes
. 9
1.3.2
The Neuron as a Dynamical System
. 10
1.4
Interactions Between System and Surroundings
. 13
1.5
What Have We Learned?
. 14
1.6
Exercises for Practice and Insight
. 15
2
The Mathematics of Change
. 17
2.1
Differentiation
. 18
2.2
Differential Equations
. 19
2.2.Î
Population Growth
. 20
2.2.2
Time Scale of Change
. 22
2.2.3
Linear ODEs with Constant Coefficients
. 23
2.3
Black Boxes
. 25
2.3.
1
Nonlinear Differential Equations
. 27
2.4
Existence and Uniqueness
. 29
2.5
What Have We Learned?
. 30
2.6
Exercises for Practice and Insight
. 30
SIX
xx Contents
3
Equilibria and Steady States
. 33
3.1
Law of Mass Action
. 34
3.2
Closed Dynamical Systems
. 36
3.2.1
Equilibria: Drag Binding
. 36
3.2.2
Transient Steady States: Enzyme Kinetics
. 39
3.3
Open Dynamical Systems
. 42
3.3.1
Water Fountains
. 43
3.4
The "Steady-State Approximation'*
. 45
3.4.1
Steady State: Enzyme-Substrate Reactions
. 45
3.4.2
Steady State: Consecutive Reactions
. 48
3.5
Existence of Fixed Points
. 52
3.6
What Have We learned?
. 54
3.7
Exercises for Practice and Insight
. 55
'c'
Stability
. 57
4.1
Landscapes in Stability
. 58
4.1.1
Postural Stability
. 62
4.1.2
Perception of Ambiguous Figures
. 62
4.1.3
Stopping Epileptic Seizures
. 63
4.2
Fixed-Point Stability
. 64
4.3
Stability of Second-Order ODEs
. 66
4.3.1
Real Eigenvalues
. 68
4.3.2
Complex Eigenvalues
. 70
4.3.3
Phase-Plane Representation
. 72
4.4
Illustrative Examples
. 74
4.4.1
The
Lotka-
Volterra Equation
. 74
4.4.2
The van
der Pol
Oscillator
. 78
4.4.3
Computer: Friend or Foe?
. 80
4.5
Lyapunov's Insight
. 81
4.5.1
Conservative Dynamical Systems
. 81
4.5.2
Lyapunov's Direct Method
. 83
4.6
What Have We Learned?
. 85
4.7
Exercises for Practice and Insight
. 86
Fixed Points: Creation and Destruction
. 91
5.1
Saddle-Node Bifurcation
. 93
5.1.1
Neuron Bistability
. 94
5.2
Transcritical Bifurcation
. 96
5.2.1
Postponement of Instability
. 98
5.3
Pitchfork Bifurcation
.100
5.3.1
Finger-Spring Compressions
.101
5.4
Near the Bifurcation Point
.104
5.4.1
The Slowing-Down Phenomenon
.105
5.4.2
Critical Phenomena
.106
5.5
Bifurcations at the Benchtop
.107
Contents xxi
5.6
What Have We Learned?
.108
5.7
Exercises for Practice and Insight
.109
6
Transient Dynamics
.
Ill
6.1
Step Functions
.113
6.2
Ramp Functions
.115
6.3
Impulse Responses
.116
6.3.1
Measuring the Impulse Response
.119
6.4
The Convolution Integral
.120
6.4.1
Summing
Neuronal
Inputs
.123
6.5
Transients in Nonlinear Dynamical Systems
.126
6.5.
і
Excitability
.
1
27
6.5.2
Bounded
Ті
me-Dependent States
.129
6.6
What Have We Learned?
.131
6.7
Exercises for Practice and Insight
.132
7
Frequency Oomain I: Bode Plots and Transfer Functions
.137
7.1
Low-Pass Filters
.138
7.2
Laplace Transform Toolbox
.142
7.2.1
Tool
8:
Eulers
Formula
.142
7.2.2
Tool
9:
The Laplace Transform
.146
7.3
Transfer Functions
.149
7.4
Biological Filters
.153
7.4.1
Crayfish Photoreceptor
.154
7.4.2
Osmoregulation in Yeast
.156
7.5
Bode-Plot
Cookbook
.157
7.5.1
Constant Term (Gain)
.158
7.5.2
Integral or Derivative Term
.159
7.5.3
Lags and Leads
.161
7.5.4
Time Delays
.163
7.5.5
Complex Pair: Amplification
.163
7.6
Interpreting Biological Bode Plots
.166
7.6.1
Crayfish Photoreceptor Transfer Function
.166
7.6.2
Yeast Osmotic Stress Transfer Function
.
Î
67
7.7
What Have We Learned?
.169
7.8
Exercises for Practice and Insight
.169
8
Frequency Domain II: Fourier Analysis and Power Spectra
.175
8.1
Laboratory Applications
.177
8.1.1
Creating Sinusoidal Inputs
.177
8.
і
.2
Electrical Interference
.
J
79
8.1.3
The Electrical World
.180
8.2
Fourier Analysis Toolbox
.181
8.2.1
Tool
10:
Fourier Series
.182
8.2.2
Tool
1
1
:
The Fourier Transform
.185
\xiî
Contents
8.3 Applications
of Fourier Analysis
.189
8.3.1
Uncertainties in Fourier Analysis
.189
8.3.2
Approximating a Square Wave
.
1
92
8.3.3
Power Spectrum
.194
8.3.4
Fractal Heartbeats
.196
8.4
Digital Signals
.198
8.4Л
Low-Pass Filtering
.198
8.4.2
introducing the FFT
.201
8.4.3
Power Spectrum: Discrete Time Signals
.204
8.4.4
Using FFTs in the Laboratory
.209
8.4.5
Power Spectral Density Recipe
.213
8.5
What Have We Learned?
.215
8.6
Exercises for Practice and Insight
.216
9
Feedback and Control Systems
.219
9.1
Feedback Control
.221
9.2
Pupil Light Reflex (PLR)
.223
9.3
"Linear^Feedback
.225
9.3.1
Proportional-Integral-Derivative
(PID)
Controllers
.227
9.4
Delayed Feedback
.229
9.4.1
Example: Wright's Equation
.232
9.5
Production-Destruction
.235
9.5.1
Negative Feedback: PLR
.236
9.5.2
Negative Feedback: Gene Regulatory Systems
.241
9.5.3
Stability: General Forms
.243
9.5.4
Positive Feedback: Cheyne-Stokes Respiration
.244
9.6
Electronic Feedback
.247
9.6.1
The Clamped PLR
.247
9.7
intermittent Control
.250
9.7.1
Virtual Balancing
.250
9.8
Integrating DDEs
.252
9.9
What Have We Learned?
.252
9.10
Exercises for Practice and insight
.253
10
Oscillations
.259
10. !
Neural Oscillations
.260
JO.
1
.1
Hodgkin-Huxley Neuron Model
.260
10.2 Hopf
Bifurcations
.269
10.2.1
PLR: Supercritical
Hopf
Bifurcation
.271
10.2.2
HH Equation:
Hopf
Bifurcations .
272
10.3
Analyzing Oscillations
.273
10.4
Poincaré
Sections
.274
10.4.
1 Gait Stride Variability
.275
10.5
Phase Resetting
.276
10.5.1
Stumbling
.281
Contents xxiii
10.6
Interacting Oscillators
.282
10.6.1
Periodic Forcing
.283
10.6.2
Coupled Oscillators
.290
10.7
What Have We Learned?
.291
10.8
Exercises for Practice and Insight
.292
11
Beyond Limit Cycles
.295
11.1
Chaos and Parameters
.296
11.2
Dynamical Diseases and Parameters
.301
11.3
Chaos in the Laboratory
.304
11.3.1
Flour Beetle Cannibalism
.304
11.3.2
Clamped PLR with "Mixed Feedback"
.307
11.4
Complex Dynamics: The Human Brain
.310
1
1.4.І
Reduced Hodgkin-Huxley Models
.310
11.4.2
Delay-Induced Transient Oscillations
.314
11.5
What Have We Learned?
.316
11.6
Exercises for Practice and Insight
.317
12
Random Perturbations
.321
12.1
Noise and Dynamics
.322
12.1.1
Stick Balancing at the Fingertip
.323
12.1.2
Noise and Thresholds
.324
12.1.3
Stochastic Gene Expression
.324
12.2
Stochastic Processes Toolbox
.325
12.2.1
Random Variables and Their Properties
.325
12.2.2
Stochastic Processes
.329
12.2.3
Statistical Averages
.332
12.3
Laboratory Evaluations
.336
12.3.1
Intensity
.336
12.3.2
Estimation of the Probability Density Function
.336
12.3.3
Estimation of Moments
.339
12.3.4
Broad-Shouldered Probability Density Functions
.340
12.4
Correlation Functions
.342
1
2.4.1
Estimating Autocorrelation
.344
12.5
Power Spectrum of Stochastic Signals
.347
12.6
Examples of Noise
.350
12.7
Cross-Correlation Function
.351
12.7.1
Impulse Response
.353
12.7.2
Measuring Time Delays
.353
12.7.3
Coherence
.355
12.8
What Have We Learned?
.355
12.9
Problems for Practice and Insight
.356
xxiv
Contents
13
Noisy Dynamical Systems
.359
1
3.1
The
Langevin
Equation: Additive Noise
.360
13.1.1
The Retina As a Recording Device
.364
13.1.2
Time-Delayed
Langevin
Fquation
.367
13.1.3
Skill Acquisition
.368
13.1.4
Stochastic Gene Expression
.369
13.1.5
Numerical Integration of
Langevin
Equations
.372
13.2
Noise and Thresholds
.373
13.2.1
Linearization
.373
13.2.2
Dithering
.375
13.2.3
Stochastic Resonance
.376
13.3
Parametric Noise
.379
13.3.1
On-Off Intermittency: Quadratic Map
.380
13.3.2
Langevin
Equation with Parametric Noise
.382
13.3.3
Stick Balancing at the Fingertip
.383
13.4
What Have We Learned?
.384
13.5
Problems for Practice and Insight
.385
14
Random Walks
.389
14.1
A Simple Random Walk
.391
14.1.1
Walking Molecules as Cellular Probes
.395
14.2
Anomalous Random Walks
.397
14.3
Correlated Random Walks
.397
14.3. 1
Random Walking While Standing Still
.398
14.3.2
Gait Stride Variability:
DPA.401
14.3.3
Walking on the
DNA
Sequence
.402
14.4
Delayed Random Walks
.402
14.5
Portraits in Diffusion
.404
14.5.1
Finding a Mate
.405
14.5.2
Facilitated Diffusion on the Double Helix
.407
14.6
Optimal Search Patterns: Levy Flights
.408
14.7
Probability Density Functions
.410
14.7.1
Master Equation
.411
14.8
Tool 1
2:
Generating Functions
.412
14.8.1
Approaches Using the Characteristic Function
.416
14.9
What Have We Learned?
.420
14.10
Problems for Practice and Insight
.421
15
Thermodynamic Perspectives
.425
15.1
Equilibrium
.427
15.1.1
Mathematical Background
.427
15.1.2
First and Second Laws of Thermodynamics
.430
15.1.3
Spontaneity
.432
15.2
Nonequilibrmm
.,.434
Contents xxv
1
5.3 Dynamics
and Temperature
.436
15.3.1
Near Equilibrium
.438
15.3.2
Principle of Detailed Balancing
.441
15.4
Entropy Production
.443
15.4.1
Minimum Entropy Production
.443
15.4.2
Microscopic Entropy Production
.444
15.5
Far from Equilibrium
.447
15.5.1
The Sandpile Paradigm
.447
15.5.2
Power Laws
.449
15.5.3
Measuring Power Laws
.451
15.5.4
Epileptic Quakes
.452
15.6
What Have We Learned?
.454
15.7
Exercises for Practice and Insight
.456
16
Concluding Remarks
.459
References
.461
Index
.489
John Milton·
ToruOhira
Mathematics as a Laboratory Tool
Dynamics, Delays and Noise
The importance of mathematics in the undergraduate biology curriculum is ever
increasing, as is the importance of biology within the undergraduate applied
mathematics curriculum. This ambitious forward thinking book strives to make
concrete connections between the two fields at the undergraduate level, bringing
in a wide variety of mathematical methods such as signal processing, systems
identification, and stochastic differential equations to an undergraduate audience
interested in biological dynamics. The presentation stresses a practical hands-on
approach: important concepts are introduced using linear first- or second-order
differential equations that can be solved using "pencil and paper"; next, these are
extended to "real world" applications through the use of computer algorithms written
in Scientific Python or similar software.
This book developed from a course taught by Professor John Milton at the University
of Chicago and developed and continued over many years with Professor
Toru
Ohira at
the Claremont Colleges. The tone of the book is pedagogical, engaging, accessible, with
lots of examples and exercises. The authors attempt to tread a line between accessibility
of the text and mathematical exposition. Online laboratories are provided as a teaching
aid. At the beginning of each chapter a number of questions are posed to the reader,
and then answered at the conclusion of the chapter.
Milton and Ohiras book is aimed at an undergraduate audience, makes close ties to
the laboratory, and includes a range of biological applications, favoring physiology.
This makes it a unique contribution to the literature. This book will be of interest to
quantitatively inclined undergraduate biologists, biophysicists and bioengineers and
in addition through its focus on techniques actually used by biologists, the authors
hope this text will help shape curricula in biomathematics education going forward. |
| any_adam_object | 1 |
| author | Milton, John Ohira, Toru 1963- |
| author_GND | (DE-588)1059084139 |
| author_facet | Milton, John Ohira, Toru 1963- |
| author_role | aut aut |
| author_sort | Milton, John |
| author_variant | j m jm t o to |
| building | Verbundindex |
| bvnumber | BV042168815 |
| classification_rvk | SK 950 |
| classification_tum | MAT 022f BIO 105f |
| ctrlnum | (OCoLC)897148019 (DE-599)BVBBV042168815 |
| discipline | Biologie Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 c 4500</leader><controlfield tag="001">BV042168815</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20191001</controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">141105s2014 xx ad|| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781461490951</subfield><subfield code="c">Print</subfield><subfield code="9">978-1-4614-9095-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)897148019</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042168815</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 950</subfield><subfield code="0">(DE-625)143273:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 022f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">510</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">BIO 105f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Milton, John</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Mathematics as a laboratory tool</subfield><subfield code="b">dynamics, delays and noise</subfield><subfield code="c">John Milton ; Toru Ohira</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York, NY [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2014</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XXV, 500 S.</subfield><subfield code="b">Ill., graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Neurologie</subfield><subfield code="0">(DE-588)4041888-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Biowissenschaftlerin</subfield><subfield code="0">(DE-588)4698137-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Cytologie</subfield><subfield code="0">(DE-588)4070177-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Neurologie</subfield><subfield code="0">(DE-588)4041888-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Cytologie</subfield><subfield code="0">(DE-588)4070177-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Biowissenschaftlerin</subfield><subfield code="0">(DE-588)4698137-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Ohira, Toru</subfield><subfield code="d">1963-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)1059084139</subfield><subfield code="4">aut</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-1-4614-9096-8</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg - ADAM Catalogue Enrichment</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027608287&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg - ADAM Catalogue Enrichment</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027608287&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Klappentext</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027608287</subfield></datafield></record></collection> |
| id | DE-604.BV042168815 |
| illustrated | Illustrated |
| indexdate | 2025-03-04T05:00:23Z |
| institution | BVB |
| isbn | 9781461490951 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027608287 |
| oclc_num | 897148019 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-188 DE-11 |
| owner_facet | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-188 DE-11 |
| physical | XXV, 500 S. Ill., graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Springer |
| record_format | marc |
| spelling | Milton, John Verfasser aut Mathematics as a laboratory tool dynamics, delays and noise John Milton ; Toru Ohira New York, NY [u.a.] Springer 2014 XXV, 500 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Neurologie (DE-588)4041888-1 gnd rswk-swf Biowissenschaftlerin (DE-588)4698137-8 gnd rswk-swf Cytologie (DE-588)4070177-3 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematik (DE-588)4037944-9 s Neurologie (DE-588)4041888-1 s Cytologie (DE-588)4070177-3 s DE-604 Biowissenschaftlerin (DE-588)4698137-8 s 1\p DE-604 Ohira, Toru 1963- Verfasser (DE-588)1059084139 aut Erscheint auch als Online-Ausgabe 978-1-4614-9096-8 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027608287&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027608287&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Milton, John Ohira, Toru 1963- Mathematics as a laboratory tool dynamics, delays and noise Neurologie (DE-588)4041888-1 gnd Biowissenschaftlerin (DE-588)4698137-8 gnd Cytologie (DE-588)4070177-3 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4041888-1 (DE-588)4698137-8 (DE-588)4070177-3 (DE-588)4037944-9 |
| title | Mathematics as a laboratory tool dynamics, delays and noise |
| title_auth | Mathematics as a laboratory tool dynamics, delays and noise |
| title_exact_search | Mathematics as a laboratory tool dynamics, delays and noise |
| title_full | Mathematics as a laboratory tool dynamics, delays and noise John Milton ; Toru Ohira |
| title_fullStr | Mathematics as a laboratory tool dynamics, delays and noise John Milton ; Toru Ohira |
| title_full_unstemmed | Mathematics as a laboratory tool dynamics, delays and noise John Milton ; Toru Ohira |
| title_short | Mathematics as a laboratory tool |
| title_sort | mathematics as a laboratory tool dynamics delays and noise |
| title_sub | dynamics, delays and noise |
| topic | Neurologie (DE-588)4041888-1 gnd Biowissenschaftlerin (DE-588)4698137-8 gnd Cytologie (DE-588)4070177-3 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Neurologie Biowissenschaftlerin Cytologie Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027608287&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027608287&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT miltonjohn mathematicsasalaboratorytooldynamicsdelaysandnoise AT ohiratoru mathematicsasalaboratorytooldynamicsdelaysandnoise |