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E-raamat: Hamiltonian Partial Differential Equations and Applications

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This book is a unique selection of work by world-class experts exploring the latest developments in Hamiltonian partial differential equations and their applications. Topics covered within are representative of the field’s wide scope, including KAM and normal form theories, perturbation and variational methods, integrable systems, stability of nonlinear solutions as well as applications to cosmology, fluid mechanics and water waves.

The volume contains both surveys and original research papers and gives a concise overview of the above topics, with results ranging from mathematical modeling to rigorous analysis and numerical simulation. It will be of particular interest to graduate students as well as researchers in mathematics and physics, who wish to learn more about the powerful and elegant analytical techniques for Hamiltonian partial differential equations.

Part I Introduction
1 An Introduction to Uncertainty in the Development of Computational Models of Biological Processes
3(12)
Liesbet Geris
David Gomez-Cabrero
Part II Modeling Establishment Under Uncertainty
2 Reverse Engineering Under Uncertainty
15(18)
Paul Kirk
Daniel Silk
Michael P.H. Stumpf
3 Probabilistic Computational Causal Discovery for Systems Biology
33(42)
Vincenzo Lagani
Sofia Triantafillou
Gordon Ball
Jesper Tegner
Ioannis Tsamardinos
4 Stochastic Modeling and Simulation Methods for Biological Processes: Overview
75(52)
Annelies Lejon
Giovanni Samaey
Part III Model Selection and Parameter Fitting
5 The Experimental Side of Parameter Estimation
127(28)
Monica Schliemann-Bullinger
Dirk Fey
Thierry Bastogne
Rolf Findeisen
Peter Scheurich
Eric Bullinger
6 Statistical Data Analysis and Modeling
155(22)
Millie Shah
Zeinab Chitforoushzadeh
Kevin A. Janes
7 Optimization in Biology Parameter Estimation and the Associated Optimization Problem
177(22)
Gunnar Cedersund
Oscar Samuelsson
Gordon Ball
Jesper Tegner
David Gomez-Cabrero
8 Interval Methods
199(14)
Warwick Tucker
9 Model Extension and Model Selection
213(30)
Mikael Sunnaker
Joerg Stelling
10 Bayesian Model Selection Methods and Their Application to Biological ODE Systems
243(28)
Sabine Hug
Daniel Schmidl
Wei Bo Li
Matthias B. Greiter
Fabian J. Theis
Part IV Sensitivity Analysis and Model Adaptation
11 Sloppiness and the Geometry of Parameter Space
271(30)
Brian K. Mannakee
Aaron P. Ragsdale
Mark K. Transtrum
Ryan N. Gutenkunst
12 Modeling and Model Simplification to Facilitate Biological Insights and Predictions
301(26)
Olivia Eriksson
Jesper Tegner
13 Sensitivity Analysis by Design of Experiments
327(40)
An Van Schepdael
Aurelie Carlier
Liesbet Geris
14 Waves in Spatially-Disordered Neural Fields: A Case Study in Uncertainty Quantification
367(26)
Carlo R. Laing
15 In-Silico Models of Trabecular Bone: A Sensitivity Analysis Perspective
393(34)
Marlene Mengoni
Sebastien Sikora
Vinciane D'Otreppe
Ruth Karen Wilcox
Alison Claire Jones
Part V Model Predictions Under Uncertainty
16 Neuroswarm: A Methodology to Explore the Constraints that Function Imposes on Simulation Parameters in Large-Scale Networks of Biological Neurons
427(22)
David Gomez-Cabrero
Salva Ardid
Maria Cano-Colino
Jesper Tegner
Albert Compte
17 Prediction Uncertainty Estimation Despite Unidentifiability: An Overview of Recent Developments
449(18)
Gunnar Cedersund
18 Computational Modeling Under Uncertainty: Challenges and Opportunities
467(10)
David Gomez-Cabrero
Jesper Tegner
Liesbet Geris
Author Index 477