Quantifying life : a sympiosis of computational, mathematics, and biology (Book, 2016) [WorldCat.org]
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Quantifying life : a sympiosis of computational, mathematics, and biology

Author: Dmitry A Kondrashov
Publisher: Chicago : University Of Chicago Press, [2016]
Edition/Format:   Print book : EnglishView all editions and formats
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Document Type: Book
All Authors / Contributors: Dmitry A Kondrashov
ISBN: 9780226371627 022637162X 9780226371764 022637176X
OCLC Number: 1031875159
Description: xvi, 417 pages ; 24 cm
Contents: 0.1. What is mathematical modeling? --
0.2. Purpose of this book --
0.3. Organization of the book --
1. Arithmetic and variables: The lifeblood of modeling --
1.1. Blood circulation and mathematical modeling --
1.2. Parameters and variables in models --
1.2.1. Discrete state variables: genetics --
1.2.2. Continuous state variables: concentration --
1.3. First steps in R programming --
1.3.1. Numbers and arithmetic operations --
1.3.2. Variable assignment --
1.4. Computational projects --
2. Functions and their graphs --
2.1. Dimensions of quantities --
2.2. Functions and their graphs --
2.2.1. Linear and exponential functions --
2.2.2. Rational and logistic functions --
2.3. Scripts, functions, and plotting in R --
2.3.1. Writing scripts and calling functions --
2.3.2. Vector variables --
2.3.3. Arithmetic with vector variables --
2.3.4. Plotting graphs --
2.4. Rates of biochemical reactions --
2.5. Computational projects --
3. Describing data sets --
3.1. Mutations and their rates --
3.2. Describing data sets --
3.2.1. Central value of a data set --
3.2.2. Spread of a data set --
3.2.3. Graphical representation of data sets --
3.3. Working with data in R --
3.4. Computational projects --
3.4.1. Data description --
3.4.2. Plotting data and fitting by eye --
4. Random variables and distributions --
4.1. Probability distributions --
4.1.1. Axioms of probability --
4.1.2. Random variables --
4.1.3. Expectation (mean) of random variables --
4.1.4. Variance of random variables --
4.2. Examples of distributions --
4.2.1. Uniform distribution --
4.2.2. Binomial distribution --
4.3. Testing for mutants --
4.4. Random numbers and iteration in R --
4.4.1. Random numbers --
4.4.2. For loops --
4.5. Computational projects --
4.5.1. uniform distribution --
4.5.2. Binomial distribution --
5. Estimation from a random sample --
5.1. Law of Large Numbers --
5.1.1. Sample mean --
5.1.2. Sample size and standard error --
5.2. Central Limit Theorem --
5.2.1. Normal distribution --
5.2.2. Confidence intervals --
5.3. Relative risk --
5.4. Sampling in R --
5.4.1. simulated sampling --
5.4.2. computing confidence intervals --
5.5. Computational projects --
6. Independence of random variables --
6.1. Categorical data sets with two variables --
6.2. Mathematics of independence --
6.2.1. Conditional probability and information --
6.2.2. Independence of events --
6.2.3. Calculation of expected frequencies --
6.3. Testing for independence --
6.3.1. Hypothesis testing --
6.3.2. Rejecting the null hypothesis --
6.3.3. The chi-squared statistic --
6.4. Hypothesis testing in R --
6.5. Independence in data sets --
6.5.1. Maternal age and Down syndrome --
6.5.2. Stop-and-frisk and race --
6.6. Computational projects --
6.6.1. Thumb-on-top preference and sex --
6.6.2. Relationship between species and habitat --
6.6.3. Independence testing of simulated data --
7. Bayes' amazing formula --
7.1. Prior knowledge --
7.2. Bayes' formula --
7.2.1. Positive and negative predictive values --
7.3. Applications of Bayesian thinking --
7.3.1. When too much testing is bad --
7.3.2. Reliability of scientific studies --
7.4. Random simulations --
7.5. Computational project --
8. Linear regression and correlation --
8.1. Linear relationship between two variables --
8.2. Linear least-squares fitting --
8.2.1. Sum of squared errors --
8.2.2. Best-fit slope and intercept --
8.2.3. Correlation and goodness of fit --
8.3. Linear regression using R --
8.4. Regression to the mean --
8.5. Computational projects --
8.5.1. parental age and new mutations --
8.5.2. heart rates on two different days --
9. Nonlinear data fitting --
9.1. Nonlinear relationships between variables --
9.2. Fitting using log transforms --
9.3. Generalized linear fitting in R --
9.3.1. Logarithmic transforms --
9.3.2. Polynomial regression --
9.4. Allometry and power law scaling --
9.5. Computational projects --
10. Markov models with discrete states --
10.1. Building Markov models --
10.2. Markov property --
10.2.1. Transition matrices --
10.2.2. Probability of a string of states --
10.3. Simulation of Markov models --
10.4. Markov models of medical treatment --
10.5. Computational projects --
10.5.1. State strings for a two-state model --
10.5.2. State strings for a three-state model --
11. Probability distributions of Markov chains --
11.1. Distributions evolve over time --
11.1.1. Markov chains --
11.1.2. matrix multiplication --
11.1.3. Propagation of probability vectors --
11.2. Matrix multiplication in R --
11.3. Mutations in evolution --
11.4. Computational projects --
11.4.1. Pobability vectors of a two-state model --
11.4.2. Probability vectors of a three-state model --
12. Stationary distributions of Markov chains --
12.1. The origins of Markov chains: A feud and a poem --
12.2. Stationary distributions --
12.2.1. Definition of stationary distribution --
12.2.2. Condition for unique stationary distribution --
12.3. Multiple random simulations in R --
12.4. Bioinformatics and Markov models --
12.5. Computational projects --
12.5.1. Multiple two-state model simulations --
12.5.2. Multiple three-state model simulations --
13. Dynamics of Markov models --
13.1. Phylogenetic trees --
13.2. Eigenvalues of Markov models --
13.2.1. Basic linear algebra terminology --
13.2.2. Calculation of eigenvalues on paper --
13.2.3. Calculation of eigenvectors on paper --
13.2.4. Rate of convergence --
13.3. Matrix diagonalization in R --
13.4. Molecular evolution --
13.4.1. Jukes-Cantor model --
13.4.2. Time since divergence --
13.4.3. Calculation of phylogenetic distance --
13.4.4. Divergence of human and chimp genomes --
13.5. Computational projects --
13.5.1. Eigenvalues of a two-state model --
13.5.2. Eigenvalues of a three-state model --
13.5.3. Analysis of the Jukes-Cantor model --
14. Linear difference equations --
14.1. Discrete-time population models --
14.1.1. Static population --
14.1.2. Exponential population growth --
14.1.3. Example with birth and death --
14.1.4. Dimensions of birth and death rates --
14.2. Solutions of linear difference models --
14.2.1. Simple linear models --
14.2.2. Models with a constant term --
14.3. Population growth and decline --
14.4. Numerical solutions in R --
14.4.1. Functions in R --
14.4.2. Solving difference equations --
14.5. Computational project --
15. Linear ordinary differential equations --
15.1. From discrete time to smooth change --
15.1.1. Bacteria that divide at arbitrary times --
15.1.2. Growth proportional to population size --
15.1.3. Chemical kinetics --
15.2. Solutions of ordinary differential equations --
15.2.1. Separate-and-integrate method --
15.2.2. Solution of inhomogeneous ODES --
15.2.3. Forward Euler method --
15.3. Numerical solutions of ODEs --
15.3.1. Implementation of Forward Euler --
15.3.2. error in Forward Euler solutions --
15.4. Applications of linear ODE models --
15.4.1. model of pharmacokinetics --
15.4.2. Cole's membrane potential model --
15.5. Computational projects --
15.5.1. Error and time step --
15.5.2. Pharmacokinetics model --
16. Graphical analysis of ordinary differential equations --
16.1. ODEs with nonlinear terms --
16.2. Qualitative analysis of ODEs --
16.2.1. Graphical analysis of the defining function --
16.2.2. Fixed points and stability --
16.3. Modeling infectious disease spread --
16.4. Computational projects --
16.4.1. Logistic population growth model --
16.4.2. SIS epidemic model --
17. Chaos and bifuractions in difference equations --
17.1. Logistic model in discrete time --
17.2. Qualitative analysis of difference --
17.2.1. Fixed points or equilibria --
17.2.2. Stability of fixed points --
17.3. Graphical analysis --
17.3.1. Graphical analysis using R --
17.3.2. Cobweb plots --
17.4. Discrete-time logistic model and chaos --
17.5. Computational projects --
17.5.1. Graphical stability analysis --
17.5.2. Investigation of chaotic dynamics.
Responsibility: Dimitry A. Kondrashov.

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