Math for biologists

This page is the start of a project to develop math modules to be inserted into biology courses.

General References

• Pacific Symposium on Biocomputing
• International society for computational biology
• Journal of Comp Bio
• InSilico Biology
• UCSC Bioinformatics
• USC comp bio
• University of Minnesota Comp Bio center
• UPenn comp bio and informatics
• W.M. Keck Center for Computational and Structural Biology
• Comp molecular bio at NIH
• Laboratory of Experimental and Computational Biology (NIC)
• General Sources of Information on Mathematical and Computational Biology.
• computational biology list
• Artificial Life "Games"
• alife.org
• Zooland: "The Artificial Life Resource"
• Google - Artificial Life
• Google - Artificial worlds
• FRAMSTICKS. Artificial Life
• Mathworld
• DALi - distributed artifical life
• Vortex Physics Simulator
• breve - 3D simulator
• Open Dynamics Engine
• havoc physics engine
• Hardware physics engine
• Database of biomodels
• BioModels.net
• Gallery of Mathematical Models
• AgentCell E.Coli simulator
• Special Section on Math in Biology (Science,303,6Feb2004,p781)

Teaching

• Biocomputing for schools
• Why Biologists Should Not Treat Software as a Black Box
• Bioinformatics Educational Resource
• Computational Molecular Biology (stanford)
• A LIST OF BIOINFORMATICS COURSES
• Biocomputing Course Resource List
• University Bioinformatics Programs
• The Geometers Sketchpad and 101 ideas and Sketchpad Links
• Standards for School math
• Case Studies in Mathematical Modeling---Ecology, Physiology, and Cell Biology
• Just-In-Time teaching:
• Sample JiTT Materials
• WebScience
• Math in Biology
• Interactive Differential Equations
• Teaching in a Research Context (Science,302,28Nov2003,p1510)
• Mathematical Sciences Digital Library
• Introductory Science and Math Education for 21st Century Biologists (Science,303,6Feb2004,p788)
• Special Section on Math in Biology (Science,303,6Feb2004,p781)

Possible topics:

• Statistics/Probability
  • Mathworld
  • Probability/Bayes Theorum
    • Bayes Net Toolbox for Matlab
  • Markov models
    • hidden Markov model
    • Hidden Markov Model (HMM) Toolbox for Matlab
    • Markov software
  • MonteCarlo
    • MCell
    • Molecular Monte Carlo
  • Fisher information
    • Fisher information and the Cramer-Rao bound
• Differential equations
  • Cellerator
  • Neuron
  • Genesis
  • numerical methods
    • Numerical Recipes, Ch 16
  • signal processing
    • Transform methods
      • Designing Texture Filters with Genetic Algorithms
      • Sonograms
      • FFT image synthesis
    • Time Domain Filtering
  • dynamic systems/chaos
    • Xmorphia
    • Reaction-Diffusion Texture Synthesis
    • Dynamical Systems data base
    • dynamical-systems.org
    • Pattern Formation in Nonequilibrium Systems (CalTech)
  • linear feedback/control
    • Feedback Control Theory and Postgenomic Mol Bio
    • Control of Circulation
    • A fixation and viewpoint measure for object-based gaze control
  • optimum tracking filters
    • Tracking objects in video microscopy
    • Is the hippocampus a Kalman filter?
• Graphics/Visualization/Sound
  • 3D visualization
    • The Visible human
    • 3D Reconstruction of Optically Sectioned Images
    • Stereo Displays
  • Sound
    • Using Sound to Extract Meaning From Complex Data
  • High dimensional approaches
    • Visualizing the Behavior of Higher Dimensional Dynamical Systems
    • Interactive Hierarchical Dimension Ordering, Spacing and Filtering for
      Exploration of High Dimensional Datasets
    • 30 Years of Multidimensional Multivariate Visualization
    • Parallel coordinate schemes
      • Parallel coordinate graphics using MATLAB
      • Representing Protein and Peptide Structures with Parallel-Coordinates
      • Hyperdimensional data analysis using parallel coordinates, EJ Wegman,
        Journal of the American Statistical Association, Vol. 411(85), p. 664-675, 1990.
      • Navigating Hierarchies with Structure-Based Brushes
      • Parallel Coordinates for Exploratory Modelling Analysis
    • embedded world schemes
      • Worlds within Worlds, Metaphors for Exploring n-Dimensional Virtual Worlds
    • projection pursuit
      • What is projection pursuit, M.C. Jones & R. Sibson (1987),
        Journal of the Royal Statistical Society, Ser. A, 150, p. 1-36.
      • A review of dimension reduction techniques
      • A strategy for analysis of (molecular) equilibrium simulations:
        configuration space density estimation, clustering and visualization
  • imaging methods
• Graph theory
  • Exploring the repertoire of RNA secondary motifs using graph theory
  • Graph Theory in Practice: Part I
  • Graph Theory in Practice: Part II
  • Graph Theory Lessons
  • Practical Graph Theory
  • Graph Theory Links
  • Links and Intro
  • Generating Network Topologies That Obey Power Laws
  • The large-scale structure of metabolic networks
• Data fitting
  • regression
    • Least Squares Applet
    • Least Squares applet
    • Least Squares Fitting (Regression)
    • Mathworld
    • Nonlinear Least Squares Curve Fitter
  • multidimensional scaling
    • A strategy for analysis of (molecular) equilibrium simulations:
      configuration space density estimation, clustering and visualization
    • Metric-space analysis of spike trains: theory, algorithms, and application
  • principal components
    • A review of dimension reduction techniques
• Recursive systems
  • L-systems
    • L-systems in Matlab
    • Evolving L-systems to generate virtual creatures
• Vector Analysis/Complex numbers
• Automata
  • Finite State machine
    • A graphical tool for building logical representations of genetic regulatory networks
  • Turing Machine
  • Cellular Automata
    • CA in Matlab
    • Primordial soup kitchen
    • Rudy Rucker's Home Page
    • Mathworld
• optimization
  • mathworld
  • genetic algorithms
    • Gene Pool simulation
    • OPTIMIZATION OF AN INTEGRATE-AND-FIRE NETWORK
    • Processing of auditory midbrain interspike intervals by model neurons
    • Designing Texture Filters with Genetic Algorithms
    • Genetic and Evolutionary Algorithm Toolbox (for Matlab)
    • Evolutionary Algorithms for MATLAB
    • Genetic Algorithm Toolbox
      
  • gradient methods
  • simulated annealing
  • dynamic programming
    • A Tutorial on Dynamic Programming
• Searching and sorting
• Game theory
  • game theory.net
  • game theory society
  • mathworld
• Information Theory
  • Information theory and molecular biology
  • Evolution of Biological Information
  • mathworld
  • Entropy estimation
    • Metric-space analysis of spike trains: theory, algorithms, and application
    • Binless strategies for estimation of information from neural data

Possible application areas:

• Neurobiology
  • Computational morphology
  • Compartmental modeling
    • Neuron
    • Genesis
    • MCell
  • spike train analysis
    • Cost-based metrics for spike trains
    • Metric-space analysis of spike trains: theory, algorithms, and application
• Cell Metabolism
  • CENTER FOR COMPUTATIONAL BIOLOGY
  • Fast Evaluation of the Likelihood of an HMM: Ion Channel Currents with Filtering and Colored Noise
  • Cellerator
  • MCell
  • The large-scale structure of metabolic networks
• Molecular biology
  • Introduction to computational molecular biology, ISBN: 0-534-95262-3
  • Representing Protein and Peptide Structures with Parallel-Coordinates
  • A strategy for analysis of (molecular) equilibrium simulations:
    configuration space density estimation, clustering and visualization
  • INFERRING GENE REGULATORY NETWORKS FROM
    TIME-ORDERED GENE EXPRESSION DATA OF BACILLUS
    SUBTILIS USING DIFFERENTIAL EQUATIONS
  • Biocomputing and Drug Design
• Physiology
  • Control of Circulation
  • Electrophysiological heterogeneity and stability of reentry in simulated cardiac tissue
  • Mathematical Physiology
• Ecology
  • GEOSPOD
  • Game Theory and Animal Behavior, by Lee Alan Dugatkin (Editor), Hudson Kern Reeve (Editor), Kern Hudson ,
    Publisher: Oxford University Press; Reprint edition (May 2000) ISBN: 0195137906
• Evolution
  • Evolution of Biological Information
  • Gene Pool simulation and details
  • Biomorph
  • Biomorph viewer
  • Evolution of Morphology and Behaviour for Physically Modelled Creatures
• Medical/imaging
  • An introduction to Multiway Methods for Multi-Subject fMRI experiment
  • Sequential annealing–gradient Gamma-Knife radiosurgery optimization
  • A First Course in Pharmacokinetics and Biopharmaceutics
• Genomics/genetics
  • Flexible Information Visualization of Multivariate Data from Biological Sequence Similarity Searches
  • DNA sequence analysis
  • A Hidden Markov Model that finds genes in E. coli DNA
  • Exploring the repertoire of RNA secondary motifs using graph theory; implications for RNA design
  • Gene Network Inference from Large-Scale Gene Expression Data
  • Feedback Control Theory and Postgenomic Mol Bio
• Development
  • Visual models of Morphogensis
  • Reaction Diffusion Equations and Animal Coat Patterns
  • Zebra Stripes
  • Evolving L-systems to generate virtual creatures
  • Recent Developments in the Evolution of Morphologies and
    Controllers for Physically Simulated Creatures*
• Epidemiology
  • Parallel Coordinates for Exploratory Modelling Analysis
  • Algorithmic and computational procedures for a Markov model in survival analysis
• Paleontology
  • Computational Paleontology