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1. The Mathematics of Darwin’s Legacy
edited by Fabio A. C. C. Chalub, José Francisco Rodrigues
出版情報: Basel : Springer Basel AG, 2011
シリーズ名: Mathematics and Biosciences in Interaction ;
オンライン: http://dx.doi.org/10.1007/978-3-0348-0122-5
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2. An Introduction to Continuous-Time Stochastic Processes : Theory, Models, and Applications to Finance, Biology, and Medicine. 2nd ed. 2012
by Vincenzo Capasso, David Bakstein
出版情報: Boston : Birkhäuser Boston : Imprint: Birkhäuser, 2012
シリーズ名: Modeling and Simulation in Science, Engineering and Technology ;
オンライン: http://dx.doi.org/10.1007/978-0-8176-8346-7
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Part I. The Theory of Stochastic Processes
Fundamentals of Probability
Stochastic Processes
The Itô Integral
Stochastic Differential Equations
Part II. The Applications of Stochastic Processes
Applications to Finance and Insurance
Applications to Biology and Medicine
Part III. Appendices
Measure and Integration
Convergence of Probability Measures on Metric Spaces
Elliptic and Parabolic Operators
D Semigroups and Linear Operators.- E Stability of Ordinary Differential Equations
References
Part I. The Theory of Stochastic Processes
Fundamentals of Probability
Stochastic Processes
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3. Excursions in Harmonic Analysis, Volume 1 : The February Fourier Talks at the Norbert Wiener Center
edited by Travis D. Andrews, Radu Balan, John J. Benedetto, Wojciech Czaja, Kasso A. Okoudjou
出版情報: Boston : Birkhäuser Boston : Imprint: Birkhäuser, 2013
シリーズ名: Applied and Numerical Harmonic Analysis ;
オンライン: http://dx.doi.org/10.1007/978-0-8176-8376-4
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Part 1 Sampling Theory
Unions of Subspaces for Data Modeling and Subspace Clustering
Fusion frames and Unbiased Basic Sequences
Sampling in Spaces of Bandlimited Functions on Commutative Spaces
Smooth Interpolation of Data by Efficient Algorithms
An Overview of Time and Multiband Limiting
A Panorama of Sampling Theory
Part II Remote Sensing
Multistatic Radar Waveforms for Imaging of Moving Targets
Exploitation Performance and Characterization of a Prototype Compressive Sensing Imaging Spectrometer
An Introduction to Hyperspectral Image Data Modeling
Hyperspectral Demixing: Sparse Recovery of Highly Correlated Endmembers
Theory of Passive Synthetic Aperture Imaging
Part III Mathematics of Data Processing
Golay-Rudin-Shapiro Polynomials and Phased Arrays
Multi-Resolution Geometric Analysis for Data in High Dimensions
On the Fourth-Order Structure Function of a Fractal
Harmonic Analysis of Databases and Matrices
The Structure of Sidelobe-Preserving Operator Groups
Zeros of some Self-Reciprocal Polynomials
Part IV Applications of Data Processing
Generalized Mutual Interdependence Analysis of Noisy Channels
Approximation Methods for the Recovery of Shapes and Images from Gradients
FM Perturbations due to Near-Identity Linear Systems
Eddy Current Sensor Signal Processing for Stall Detection
State Dependent Channels: Strong Converse and Bounds on Reliability Function
Part 1 Sampling Theory
Unions of Subspaces for Data Modeling and Subspace Clustering
Fusion frames and Unbiased Basic Sequences
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4. Excursions in Harmonic Analysis, Volume 2 : The February Fourier Talks at the Norbert Wiener Center
edited by Travis D. Andrews, Radu Balan, John J. Benedetto, Wojciech Czaja, Kasso A. Okoudjou
出版情報: Boston : Birkhäuser Boston : Imprint: Birkhäuser, 2013
シリーズ名: Applied and Numerical Harmonic Analysis ;
オンライン: http://dx.doi.org/10.1007/978-0-8176-8379-5
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Part V Measure Theory
Absolute Continuity and Singularity of Measures Without Measure Theory
Visible and Invisible Cantor Sets
Convolution Inequalities for Positive Borel Measures on R^d and Beurling Density
Positive Operator-Valued Measures: A General Setting for Frames
Part VI Filtering
Extending Wavelet Filters, Infinite Dimensions, the Non-Rational Case, and Indefinite-Inner Product Spaces
On the Group-Theoretic Structure of Lifted Filter Banks
Parametric Optimization of Biorthogonal Wavelets and Filterbanks via Pseudoframes for Subspaces
On the Convergence of Iterative Filtering Empirical Mode Decomposition
Wavelet Transforms by Nearest Neighbor Lifting
Part VII Operator Theory
On the Heat Kernel of a Left Invariant Elliptic Operator
Mixed-Norm Estimates for the k-Plane Transform
Representation of Linear Operators by Gabor Multipliers
Extensions of Berezin-Lieb Inequalities
Bilinear Calderon-Zygmund Operators
Weighted Inequalities and Dyadic Harmonic Analysis
Part VIII Biomathematics
Enhancement and Recovery in Atomic Force Micosopy Images
Numerical Harmonic Analysis and Diffusions on the 3D-Motion Group
Quantification of Retinal Chromophores Through Autofluorescence Imaging to Identify Precursors of Age-Related Macular
Simple Harmonic Oscillator Based Reconstruction and Estimation for One-Dimensional q-Space Magnetic Resonance (1D-SHORE)
Fourier Blues: Structural Coloration of Biological Tissues
A Harmonic Analysis View On Neuroscience Imaging
Part V Measure Theory
Absolute Continuity and Singularity of Measures Without Measure Theory
Visible and Invisible Cantor Sets
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5. Advances in Applied Mathematics, Modeling, and Computational Science
edited by Roderick Melnik, Ilias S. Kotsireas
出版情報: Boston, MA : Springer US : Imprint: Springer, 2013
シリーズ名: Fields Institute Communications ; 66
オンライン: http://dx.doi.org/10.1007/978-1-4614-5389-5
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6. Modeling in Computational Biology and Biomedicine : A Multidisciplinary Endeavor
edited by Frédéric Cazals, Pierre Kornprobst
出版情報: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013
オンライン: http://dx.doi.org/10.1007/978-3-642-31208-3
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Foreword by Olivier Faugeras
Foreword by Joël Janin
Preface
Part I Bioinformatics
1.Modeling Macro-molecular Complexes: a Journey Across Scales. F.Cazals, T.Dreyfus, and C.H. Robert
1.1.Introduction
1.2.Modeling Atomic Resolution
1.3.Modeling Large Assemblies
1.4.Outlook
1.5.Online Resources
References
2.Modeling and Analysis of Gene Regulatory Networks. G.Bernot, J-P.Comet, A.Richard, M.Chaves, J-L.Gouzé, and F.Dayan
2.1.Introduction
2.2.Continuous and Hybrid Models of Genetic Regulatory Networks
2.3.Discrete Models of GRN
2.4.Outlook
2.5.Online Resources
2.6.Acknowledgments
Part II Biomedical Signal and Image Analysis
3.Noninvasive Cardiac Signal Analysis Using Data Decomposition Techniques. V.Zarzoso, O.Meste, P.Comon, D.G.Latcu, and N.Saoudi
3.1.Preliminaries and Motivation
3.2.T-Wave Alternans Detection via Principal Component Analysis
3.3.Atrial Activity Extraction via Independent Component Analysis
3.4.Conclusion and Outlook
3.5.Online Resources
4.Deconvolution and Denoising for Confocal Microscopy. P.Pankajakshan, G.Engler, L.Blanc-Féraud, and J.Zerubia
4.1.Introduction
4.2.Development of the Auxiliary Computational Lens
4.3.Outlook
4.4.Selected Online Resources
5.Statistical Shape Analysis of Surfaces in Medical Images Applied to the Tetralogy of Fallot Heart. K.McLeod, T.Mansi, M.Sermesant, G.Pongiglione, and X.Pennec
5.1.Introduction
5.2.Statistical Shape Analysis
5.3.Shape Analysis of ToF Data
5.4.Conclusion
5.5.Online Resources
6.From Diffusion MRI to Brain Connectomics. A.Ghosh and R.Deriche
6.1.Introduction
6.2.A Brief History of NMR and MRI
6.3.Nuclear Magnetic Resonance and Diffusion
6.4.From Diffusion MRI to Tissue Microstructure
6.5.Computational Framework for Processing Diffusion MR Images
6.6.Tractography: Inferring the Connectivity
6.7.Clinical Applications 6.8.Conclusion
6.9.Online Resources
Part III Modeling in neuroscience
7.Single-Trial Analysis of Bioelectromagnetic Signals: The Quest for Hidden Information. M.Clerc, T.Papadopoulo, and C.Bénar
7.1.Introduction
7.2.Data-driven Approaches: Non-linear Dimensionality Reduction
7.3.Model-Driven Approaches: Matching Pursuit and its Extensions
7.4.Success Stories
7.5.Conclusion
7.6.Selected Online Resources
8 Spike Train Statistics from Empirical Facts to Theory: The Case of the Retina. B.Cessac and A.Palacios
8.1.Introduction
8.2.Unraveling the Neural Code in the Retina via Spike Train Statistics Analysis
8.3.Spike Train Statistics from a Theoretical Perspective
8.4.Using Gibbs Distributions to Analysing Spike Trains Statistics
8.5.Conclusion
8.6.Outlook
8.7.Online Resources
Biology, Medicine and Biophysics
Mathematics and Computer Science
Index
Foreword by Olivier Faugeras
Foreword by Joël Janin
Preface
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7. An Introduction to Mathematical Population Dynamics : Along the trail of Volterra and Lotka
by Mimmo Iannelli, Andrea Pugliese
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2014
シリーズ名: UNITEXT ; 79
オンライン: http://dx.doi.org/10.1007/978-3-319-03026-5
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1 Malthus, Verhulst and all that
2 Delayed population models
3 Models of discrete-time population growth
4 Stochastic modeling of population growth
5 Spatial spread of a population
6 Prey-predator models
7 Competition among species
8 Mathematical modeling of epidemics
9 Models with several species and trophic levels
10 Appendices: A Basic theory of Ordinary Differential Equations; B Delay Equations; C Discrete dynamics; D Continuous-time Markov chains
1 Malthus, Verhulst and all that
2 Delayed population models
3 Models of discrete-time population growth
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8. Molecular Dynamics : With Deterministic and Stochastic Numerical Methods
by Ben Leimkuhler, Charles Matthews
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2015
シリーズ名: Interdisciplinary Applied Mathematics ; 39
オンライン: http://dx.doi.org/10.1007/978-3-319-16375-8
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1.Introduction
2.Numerical Integrators
3.Analyzing Geometric Integrators
4.The Stability Threshold
5.Phase Space Distributions and Microcanonical Averages
6. The Canonical Distribution and Stochastic Differential Equations
7. Numerical Methods for Stochastic Molecular Dynamics
8. Extended Variable Methods
References
Index
1.Introduction
2.Numerical Integrators
3.Analyzing Geometric Integrators
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9. Parabolic Equations in Biology : Growth, reaction, movement and diffusion
by Benoît Perthame
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2015
シリーズ名: Lecture Notes on Mathematical Modelling in the Life Sciences ;
オンライン: http://dx.doi.org/10.1007/978-3-319-19500-1
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1.Parabolic Equations in Biology
2.Relaxation, Perturbation and Entropy Methods
3.Weak Solutions of Parabolic Equations in whole Space
4.Traveling Waves
5.Spikes, Spots and Pulses
6.Blow-up and Extinction of Solutions
7.Linear Instability, Turing Instability and Pattern Formation
8.The Fokker-Planck Equation
9.From Jumps and Scattering to the Fokker-Planck Equation
10.Fast Reactions and the Stefan free Boundary Problem
1.Parabolic Equations in Biology
2.Relaxation, Perturbation and Entropy Methods
3.Weak Solutions of Parabolic Equations in whole Space
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10. Dispersal, Individual Movement and Spatial Ecology : A Mathematical Perspective
edited by Mark A. Lewis, Philip K. Maini, Sergei V. Petrovskii
出版情報: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013
シリーズ名: Lecture Notes in Mathematics ; 2071
オンライン: http://dx.doi.org/10.1007/978-3-642-35497-7
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Part I: Individual Animal Movement
1. Stochas-tic optimal foraging theory
2. Levy or not? Analysing positional data from animal movement paths
3. Beyond optimal searching: Recent developments in the modelling of animal movement patterns as Levy walks
Part II: From Individuals to Populations
4. The mathematical analysis of biological aggregation and dispersal: progress, problems and perspectives
5. Hybrid modelling of individual movement and collective behaviour
6. From individual movement rules to population level patterns: the case of central-place foragers
7. Transport and anisotropic diffusion models for movement in oriented habitats
8. Incorporating complex foraging of zooplankton in models: role of micro- and mesoscale processes in macroscale patterns
Part III: Populations, Communities and Ecosystems
9. Life on the move: modeling the effects of climate-driven range shifts with integrodifference equations
10. Control of competitive bioinvasion
11. Destruction and diversity: effects of habitat loss on ecological communities
12. Emergence and propagation of patterns in nonlocal reaction-diffusion equations arising in the theory of speciation
13. Numerical study of pest population size at various diffusion rates
Part I: Individual Animal Movement
1. Stochas-tic optimal foraging theory
2. Levy or not? Analysing positional data from animal movement paths