The art of the pfug

OpenStax

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How to compose a pfug

Algebraic geometry

Vigre 2009: algebraic geometry

0.1 Introduction

0.2 Definitions

0.3 Continued fractions

0.4 Proof of theorem

1 A brief introduction to computational algebraic geometry

1.1 Plane curve singularities

1.2 Multiplicity and the tangent cone

1.3 Rational curves

1.4 Ideals and monomial orders

1.5 The division algorithm

1.6 Buchberger's algorithm for computing gröbner bases

1.7 Reduced gröbner bases

1.9 Resultants and symmetric polynomials

1.10 Quotient rings and the tjurina number

Legendrian knots and links

Dynamical systems

Arithmetic sums of cantor sets

Calculus of variations

Rice university vigre: edge length minimizing polyhedra

1 Michell trusses

1.1 Introduction

1.3 Existence of equilibrating trusses

1.4 Some economical trusses

1.5 Some global properties

1.6 Some local properties: cutting corners

1.7 Other deformations

2 Minimizing the energy of vector fields on surfaces of revolution

2.1 Introduction

2.2 Defining energy

2.3 Initial remarks

2.4 Some special cases

2.6 Minimizing energy

2.7 Calculus of variations: an interlude

2.8 Our application: the unit cylinder

2.9 Uniqueness of solutions

2.10 Non-unit length minimizers on the cylinder

2.11 Limiting results on the cylinder

2.12 Some results on general surfaces

2.13 The euler-lagrange equation

2.14 θ -independent vector fields

2.15 Non-uniqueness

2.16 Computer approximations

2.17 Polynomal interpolation and runge's phenomenon

2.18 Chebyshev points, fourier matrices, and plots

2.19 Limitations and future work

2.20 Numerical plots

2.22 Acknowledgements

3 Minimizing the energy of vector fields on surfaces of revolution, part

4 Surfaces minimizing boundary-weighted area

4.1 Introduction

4.3 Boundary-value weighted energy & Area

4.4 Minimal surface equation

4.5 Future work

4.6 Acknowledgements

5 Geometric calculus of variations: vigre summer 2011

Combinatorial optimization

A combinatorial algorithm for finding maximum cuts

1 Vizing's conjecture and related graph properties

2 Using markov random fields for election prediction

Computational biology

Statistical analysis of cancer

1 Analysis of mirna and mrna associated with epithelial mesenchymal

Computational finance

An application of model-based clustering in market segmentation

0.1 Introduction

0.2 Time series of counts data in marketing

0.3 Current market segmentation methods

0.4 Model-based clustering

0.5 Outline for remainder of the discussion

0.6 Methodology

0.7 Modeling tsc

0.8 Clustering of tsc models

0.10 Finding relevant data

0.11 Data simulation

0.12 Ongoing work

0.13 Modeling consumer purchases

0.14 Next steps

0.15 Implications of mbc

0.16 Directions for future research

0.17 Acknowledgements

1 The coordinated max-median rule for portfolio selection

2 Modeling time series of return-based rankings of currencies

Computational neuroscience

Dynamics of a network of single compartmental cells

1 Dynamics of the firing rate of single compartmental cells

1.1 Introduction

1.2 Dynamics of a single-compartment cell

1.3 Active ionic currents,

1.4 Implementing the single-cell model

1.5 Simulation results

1.7 Acknowledgements

2 Cell assemblies: a binary integer programming problem

2.1 Module goal

2.2 Introduction

2.3 Mathematics of cell assemblies

2.4 Adjacency matrix ( A d )

2.5 Threshold ( k )

2.6 The excitation map, e(x,k)

2.7 Graph theory and cell assemblies

2.9 Algorithms for finding a k -assembly

2.10 Finding minimal k -cores:

2.11 Algorithm examples

2.12 bintprog Example

2.13 Closure example

2.14 Finding k -assemblies

2.15 Future work for finding cell assemblies

2.16 Conclusion

2.17 Acknowledgements

2.18 References

3 A model of a grid cell

4 Modeling cell assemblies

5 Cell assembly enumeration in random graphs

5.1 Introduction

5.3 Definitions

5.5 Finding k-assemblies

5.6 K-core enumeration

5.8 Assembly enumeration

5.9 Experimentation

5.10 Random graph generation

5.12 Future work

5.13 Conclusion

6 Mathematical models of hippocampal spatial memory

7 Mathematical modeling of hippocampal spatial memory with place cells

8 Exploring the biochemical and mechanical effects of intestinal edema on

8.1 Introduction

8.3 Hypothesis 1

8.4 Hypothesis 2

8.5 Mathematical model

8.6 Biochemical model

8.7 Ach simulation

8.8 Calcium control

8.9 Myosin activation

8.10 Force generation

8.11 Mechanical model

8.13 Discussion

Image denoising via the redundant wavelet transform

1 A class of fast algorithms for total variation image restoration

1.1 Introduction

1.2 Total variation for image restoration

1.3 Discretization and notation

1.4 Existing methods

1.5 A new alternating minimization algorithm

1.6 Basic algorithm

1.7 Optimality conditions and convergence results

1.8 Extensions to multichannel images and tv/l

1.9 Multichannel image deconvolution

1.10 Deconvolution with impulsive noise

1.11 Experiments

1.12 Practical implementation

1.13 Recovered results

1.14 Concluding remarks

1.15 Acknowledgements

Physics of strings

The network wave equation

0.1 Introduction

0.2 The wave equation

0.3 Eigenvalues, eigenfunctions, and their significance

0.4 Finite element solution method

0.6 Networks of strings

0.7 Network wave equation

0.8 Finite element discretization of the network wave equation

0.9 The tritar example case

0.10 Generalized numbering scheme and -adaptivity

0.11 Assembling the And Matrices

0.13 Matlab gui

0.14 Setting up the web

0.15 Solving for the solution with fem

0.16 Solving the eigenvalue problem with fem

0.17 Other approaches

0.18 Interpretation of results

0.19 Numerical results

0.20 Closed form solutions

0.21 Acknowledgments

1 Experiments with the three-spectral inverse problem for a beaded string

2 The fhp lattice gas cellular automaton for simulating fluid flows

3 The physics of springs

4 Optimizing transient finger damping on a driven string

4.1 Introduction

4.2 Finite difference methods

4.3 Optimization

4.5 Acknowledgments

5 There and back again - an exploration of the liouville transformation

5.1 Introduction

5.2 Problem setup

5.3 The forward problem

5.4 The inverse problem

5.5 The transformations

5.6 Changing from mass density to sturm-liouville potential

5.7 Changing from potential to density

5.8 Numerical results

5.9 Error analysis: recovering eigenvalues

5.10 Corresponding q ( t ) And ρ ( x ) Functions in closed form

5.11 q and ρ that satisfy the Liouville Transformation

5.12 Example from Euler

5.13 Numerical methods

5.14 Spectral discretization

5.16 Acknowledgments

6 Networks of uniform strings

Exact sampling of skew young diagrams

An exploratory data analysis of the us housing crisis

1 A theoretical model for the data analysis process based on cognitive

Mean, variance, and histograms

1 An introduction to the analysis of brain waves

1.1 Table of contents

1.2 Background: brain waves and the eeg

1.3 Sine and cosine waves

1.5 Characteristics of the sine wave

1.9 Hearing sine waves

1.10 Adding sine waves

1.14 Equations:

1.15 Trapezoid rule for estimating area (integration)

1.16 Basic method

1.17 Coding the trapezoid rule

1.18 Integration and the trapezoid rule

1.20 Fourier method for decomposing signals

1.21 Building the tools

1.22 Numerical implementation

1.23 Estimating other functions

1.25 Spectrogram applications to eeg

1.26 Short-time fourier transform and the spectrogram

1.27 Testing the spectrogram

1.28 Application to eeg data

1.29 Application: driving a car

1.30 Conclusion

1.32 Code for mytrapz.m

1.33 Code for myfreq.m

1.34 Code for myfourier.m

1.35 Code for mysgram.m

Latex template for vigre modules: general guidelines

0.1 Introduction

0.2 Purpose of this template

0.3 General instructions for conversion

0.4 Rules for converting latex source

0.5 Future editing

0.6 Importing equations

0.7 A sample figure

0.8 A sample table

0.9 Incorporating code

0.10 Adding a bibliography

0.11 Acknowledgements

1 Latex template for vigre modules: importing hyperlinks into connexions

Source: OpenStax, The art of the pfug. OpenStax CNX. Jun 05, 2013 Download for free at http://cnx.org/content/col10523/1.34

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