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Scipy Lecture NotesP
One document to learn numerics, science, and data with PythonP
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Tutorials on the scientific Python ecosystem: a quick introduction to
central tools and techniques. The different chapters each correspond
to a 1 to 2 hours course with increasing level of expertise, from
beginner to expert.
Release: 2020.2
* About the scipy lecture notes
+ Authors
+ What's new
+ License
+ Contributing
* 1. Getting started with Python for science
+ 1.1. Python scientific computing ecosystem
o 1.1.1. Why Python?
# 1.1.1.1. The scientist's needs
# 1.1.1.2. Python's strengths
# 1.1.1.3. How does Python compare to other solutions?
@ Compiled languages: C, C++, Fortran...
@ Matlab scripting language
@ Julia
@ Other scripting languages: Scilab, Octave, R,
IDL, etc.
@ Python
o 1.1.2. The Scientific Python ecosystem
o 1.1.3. Before starting: Installing a working environment
o 1.1.4. The workflow: interactive environments and text
editors
# 1.1.4.1. Interactive work
# 1.1.4.2. Elaboration of the work in an editor
# 1.1.4.3. IPython and Jupyter Tips and Tricks
+ 1.2. The Python language
o 1.2.1. First steps
o 1.2.2. Basic types
# 1.2.2.1. Numerical types
# 1.2.2.2. Containers
@ Lists
@ Strings
@ Dictionaries
@ More container types
# 1.2.2.3. Assignment operator
o 1.2.3. Control Flow
# 1.2.3.1. if/elif/else
# 1.2.3.2. for/range
# 1.2.3.3. while/break/continue
# 1.2.3.4. Conditional Expressions
# 1.2.3.5. Advanced iteration
@ Iterate over any sequence
@ Keeping track of enumeration number
@ Looping over a dictionary
# 1.2.3.6. List Comprehensions
o 1.2.4. Defining functions
# 1.2.4.1. Function definition
# 1.2.4.2. Return statement
# 1.2.4.3. Parameters
# 1.2.4.4. Passing by value
# 1.2.4.5. Global variables
# 1.2.4.6. Variable number of parameters
# 1.2.4.7. Docstrings
# 1.2.4.8. Functions are objects
# 1.2.4.9. Methods
# 1.2.4.10. Exercises
o 1.2.5. Reusing code: scripts and modules
# 1.2.5.1. Scripts
# 1.2.5.2. Importing objects from modules
# 1.2.5.3. Creating modules
# 1.2.5.4. '__main__' and module loading
# 1.2.5.5. Scripts or modules? How to organize your
code
@ How modules are found and imported
# 1.2.5.6. Packages
# 1.2.5.7. Good practices
o 1.2.6. Input and Output
# 1.2.6.1. Iterating over a file
@ File modes
o 1.2.7. Standard Library
# 1.2.7.1. os module: operating system functionality
@ Directory and file manipulation
@ os.path: path manipulations
@ Running an external command
@ Walking a directory
@ Environment variables:
# 1.2.7.2. shutil: high-level file operations
# 1.2.7.3. glob: Pattern matching on files
# 1.2.7.4. sys module: system-specific information
# 1.2.7.5. pickle: easy persistence
o 1.2.8. Exception handling in Python
# 1.2.8.1. Exceptions
# 1.2.8.2. Catching exceptions
@ try/except
@ try/finally
@ Easier to ask for forgiveness than for permission
# 1.2.8.3. Raising exceptions
o 1.2.9. Object-oriented programming (OOP)
+ 1.3. Python 2 and Python 3
o 1.3.1. A very short summary
o 1.3.2. Breaking changes between Python 2 and Python 3
# 1.3.2.1. Print function
# 1.3.2.2. Division
o 1.3.3. Some new features in Python 3
+ 1.4. NumPy: creating and manipulating numerical data
o 1.4.1. The NumPy array object
# 1.4.1.1. What are NumPy and NumPy arrays?
@ NumPy arrays
@ NumPy Reference documentation
@ Import conventions
# 1.4.1.2. Creating arrays
@ Manual construction of arrays
@ Functions for creating arrays
# 1.4.1.3. Basic data types
# 1.4.1.4. Basic visualization
# 1.4.1.5. Indexing and slicing
# 1.4.1.6. Copies and views
# 1.4.1.7. Fancy indexing
@ Using boolean masks
@ Indexing with an array of integers
o 1.4.2. Numerical operations on arrays
# 1.4.2.1. Elementwise operations
@ Basic operations
@ Other operations
# 1.4.2.2. Basic reductions
@ Computing sums
@ Other reductions
# 1.4.2.3. Broadcasting
# 1.4.2.4. Array shape manipulation
@ Flattening
@ Reshaping
@ Adding a dimension
@ Dimension shuffling
@ Resizing
# 1.4.2.5. Sorting data
# 1.4.2.6. Summary
o 1.4.3. More elaborate arrays
# 1.4.3.1. More data types
@ Casting
@ Different data type sizes
# 1.4.3.2. Structured data types
# 1.4.3.3. maskedarray: dealing with (propagation of)
missing data
o 1.4.4. Advanced operations
# 1.4.4.1. Polynomials
@ More polynomials (with more bases)
# 1.4.4.2. Loading data files
@ Text files
@ Images
@ NumPy's own format
@ Well-known (& more obscure) file formats
o 1.4.5. Some exercises
# 1.4.5.1. Array manipulations
# 1.4.5.2. Picture manipulation: Framing a Face
# 1.4.5.3. Data statistics
# 1.4.5.4. Crude integral approximations
# 1.4.5.5. Mandelbrot set
# 1.4.5.6. Markov chain
o 1.4.6. Full code examples
# 1.4.6.1. Full code examples for the numpy chapter
+ 1.5. Matplotlib: plotting
o 1.5.1. Introduction
# 1.5.1.1. IPython, Jupyter, and matplotlib modes
# 1.5.1.2. pyplot
o 1.5.2. Simple plot
# 1.5.2.1. Plotting with default settings
# 1.5.2.2. Instantiating defaults
# 1.5.2.3. Changing colors and line widths
# 1.5.2.4. Setting limits
# 1.5.2.5. Setting ticks
# 1.5.2.6. Setting tick labels
# 1.5.2.7. Moving spines
# 1.5.2.8. Adding a legend
# 1.5.2.9. Annotate some points
# 1.5.2.10. Devil is in the details
o 1.5.3. Figures, Subplots, Axes and Ticks
# 1.5.3.1. Figures
# 1.5.3.2. Subplots
# 1.5.3.3. Axes
# 1.5.3.4. Ticks
@ Tick Locators
o 1.5.4. Other Types of Plots: examples and exercises
# 1.5.4.1. Regular Plots
# 1.5.4.2. Scatter Plots
# 1.5.4.3. Bar Plots
# 1.5.4.4. Contour Plots
# 1.5.4.5. Imshow
# 1.5.4.6. Pie Charts
# 1.5.4.7. Quiver Plots
# 1.5.4.8. Grids
# 1.5.4.9. Multi Plots
# 1.5.4.10. Polar Axis
# 1.5.4.11. 3D Plots
# 1.5.4.12. Text
o 1.5.5. Beyond this tutorial
# 1.5.5.1. Tutorials
# 1.5.5.2. Matplotlib documentation
# 1.5.5.3. Code documentation
# 1.5.5.4. Galleries
# 1.5.5.5. Mailing lists
o 1.5.6. Quick references
# 1.5.6.1. Line properties
# 1.5.6.2. Line styles
# 1.5.6.3. Markers
# 1.5.6.4. Colormaps
o 1.5.7. Full code examples
# 1.5.7.1. Code samples for Matplotlib
# 1.5.7.2. Code for the chapter's exercises
# 1.5.7.3. Example demoing choices for an option
# 1.5.7.4. Code generating the summary figures with a
title
+ 1.6. Scipy : high-level scientific computing
o 1.6.1. File input/output: scipy.io
o 1.6.2. Special functions: scipy.special
o 1.6.3. Linear algebra operations: scipy.linalg
o 1.6.4. Interpolation: scipy.interpolate
o 1.6.5. Optimization and fit: scipy.optimize
# 1.6.5.1. Curve fitting
# 1.6.5.2. Finding the minimum of a scalar function
# 1.6.5.3. Finding the roots of a scalar function
o 1.6.6. Statistics and random numbers: scipy.stats
# 1.6.6.1. Distributions: histogram and probability
density function
# 1.6.6.2. Mean, median and percentiles
# 1.6.6.3. Statistical tests
o 1.6.7. Numerical integration: scipy.integrate
# 1.6.7.1. Function integrals
# 1.6.7.2. Integrating differential equations
o 1.6.8. Fast Fourier transforms: scipy.fftpack
o 1.6.9. Signal processing: scipy.signal
o 1.6.10. Image manipulation: scipy.ndimage
# 1.6.10.1. Geometrical transformations on images
# 1.6.10.2. Image filtering
# 1.6.10.3. Mathematical morphology
# 1.6.10.4. Connected components and measurements on
images
o 1.6.11. Summary exercises on scientific computing
# 1.6.11.1. Maximum wind speed prediction at the Sprogo
station
@ Statistical approach
@ Computing the cumulative probabilities
@ Prediction with UnivariateSpline
@ Exercise with the Gumbell distribution
# 1.6.11.2. Non linear least squares curve fitting:
application to point extraction in topographical
lidar data
@ Introduction
@ Loading and visualization
@ Fitting a waveform with a simple Gaussian model
- Model
- Initial solution
- Fit
@ Going further
# 1.6.11.3. Image processing application: counting
bubbles and unmolten grains
@ Statement of the problem
# 1.6.11.4. Example of solution for the image
processing exercise: unmolten grains in glass
o 1.6.12. Full code examples for the scipy chapter
# 1.6.12.18. Solutions of the exercises for scipy
+ 1.7. Getting help and finding documentation
* 2. Advanced topics
+ 2.1. Advanced Python Constructs
o 2.1.1. Iterators, generator expressions and generators
# 2.1.1.1. Iterators
# 2.1.1.2. Generator expressions
# 2.1.1.3. Generators
# 2.1.1.4. Bidirectional communication
# 2.1.1.5. Chaining generators
o 2.1.2. Decorators
# 2.1.2.1. Replacing or tweaking the original object
# 2.1.2.2. Decorators implemented as classes and as
functions
# 2.1.2.3. Copying the docstring and other attributes
of the original function
# 2.1.2.4. Examples in the standard library
# 2.1.2.5. Deprecation of functions
# 2.1.2.6. A while-loop removing decorator
# 2.1.2.7. A plugin registration system
o 2.1.3. Context managers
# 2.1.3.1. Catching exceptions
# 2.1.3.2. Using generators to define context managers
+ 2.2. Advanced NumPy
o 2.2.1. Life of ndarray
# 2.2.1.1. It's...
# 2.2.1.2. Block of memory
# 2.2.1.3. Data types
@ The descriptor
@ Example: reading .wav files
@ Casting and re-interpretation/views
- Casting
- Re-interpretation / viewing
# 2.2.1.4. Indexing scheme: strides
@ Main point
- C and Fortran order
- Slicing with integers
@ Example: fake dimensions with strides
@ Broadcasting
@ More tricks: diagonals
@ CPU cache effects
# 2.2.1.5. Findings in dissection
o 2.2.2. Universal functions
# 2.2.2.1. What they are?
@ Parts of an Ufunc
@ Making it easier
# 2.2.2.2. Exercise: building an ufunc from scratch
# 2.2.2.3. Solution: building an ufunc from scratch
# 2.2.2.4. Generalized ufuncs
o 2.2.3. Interoperability features
# 2.2.3.1. Sharing multidimensional, typed data
# 2.2.3.2. The old buffer protocol
# 2.2.3.3. The old buffer protocol
# 2.2.3.4. Array interface protocol
o 2.2.4. Array siblings: chararray, maskedarray, matrix
# 2.2.4.1. chararray: vectorized string operations
# 2.2.4.2. masked_array missing data
@ The mask
@ Domain-aware functions
# 2.2.4.3. recarray: purely convenience
# 2.2.4.4. matrix: convenience?
o 2.2.5. Summary
o 2.2.6. Contributing to NumPy/Scipy
# 2.2.6.1. Why
# 2.2.6.2. Reporting bugs
@ Good bug report
# 2.2.6.3. Contributing to documentation
# 2.2.6.4. Contributing features
# 2.2.6.5. How to help, in general
+ 2.3. Debugging code
o 2.3.1. Avoiding bugs
# 2.3.1.1. Coding best practices to avoid getting in
trouble
# 2.3.1.2. pyflakes: fast static analysis
@ Running pyflakes on the current edited file
@ A type-as-go spell-checker like integration
o 2.3.2. Debugging workflow
o 2.3.3. Using the Python debugger
# 2.3.3.1. Invoking the debugger
@ Postmortem
@ Step-by-step execution
@ Other ways of starting a debugger
# 2.3.3.2. Debugger commands and interaction
@ Getting help when in the debugger
o 2.3.4. Debugging segmentation faults using gdb
+ 2.4. Optimizing code
o 2.4.1. Optimization workflow
o 2.4.2. Profiling Python code
# 2.4.2.1. Timeit
# 2.4.2.2. Profiler
# 2.4.2.3. Line-profiler
o 2.4.3. Making code go faster
# 2.4.3.1. Algorithmic optimization
@ Example of the SVD
o 2.4.4. Writing faster numerical code
# 2.4.4.1. Additional Links
+ 2.5. Sparse Matrices in SciPy
o 2.5.1. Introduction
# 2.5.1.1. Why Sparse Matrices?
# 2.5.1.2. Sparse Matrices vs. Sparse Matrix Storage
Schemes
# 2.5.1.3. Typical Applications
# 2.5.1.4. Prerequisites
# 2.5.1.5. Sparsity Structure Visualization
o 2.5.2. Storage Schemes
# 2.5.2.1. Common Methods
# 2.5.2.2. Sparse Matrix Classes
@ Diagonal Format (DIA)
- Examples
@ List of Lists Format (LIL)
- Examples
@ Dictionary of Keys Format (DOK)
- Examples
@ Coordinate Format (COO)
- Examples
@ Compressed Sparse Row Format (CSR)
- Examples
@ Compressed Sparse Column Format (CSC)
- Examples
@ Block Compressed Row Format (BSR)
- Examples
# 2.5.2.3. Summary
o 2.5.3. Linear System Solvers
# 2.5.3.1. Sparse Direct Solvers
@ Examples
# 2.5.3.2. Iterative Solvers
@ Common Parameters
@ LinearOperator Class
@ A Few Notes on Preconditioning
# 2.5.3.3. Eigenvalue Problem Solvers
@ The eigen module
o 2.5.4. Other Interesting Packages
+ 2.6. Image manipulation and processing using Numpy and Scipy
o 2.6.1. Opening and writing to image files
o 2.6.2. Displaying images
o 2.6.3. Basic manipulations
# 2.6.3.1. Statistical information
# 2.6.3.2. Geometrical transformations
o 2.6.4. Image filtering
# 2.6.4.1. Blurring/smoothing
# 2.6.4.2. Sharpening
# 2.6.4.3. Denoising
# 2.6.4.4. Mathematical morphology
o 2.6.5. Feature extraction
# 2.6.5.1. Edge detection
# 2.6.5.2. Segmentation
o 2.6.6. Measuring objects properties: ndimage.measurements
o 2.6.7. Full code examples
o 2.6.8. Examples for the image processing chapter
+ 2.7. Mathematical optimization: finding minima of functions
o 2.7.1. Knowing your problem
# 2.7.1.1. Convex versus non-convex optimization
# 2.7.1.2. Smooth and non-smooth problems
# 2.7.1.3. Noisy versus exact cost functions
# 2.7.1.4. Constraints
o 2.7.2. A review of the different optimizers
# 2.7.2.1. Getting started: 1D optimization
# 2.7.2.2. Gradient based methods
@ Some intuitions about gradient descent
@ Conjugate gradient descent
# 2.7.2.3. Newton and quasi-newton methods
@ Newton methods: using the Hessian (2nd
differential)
@ Quasi-Newton methods: approximating the Hessian
on the fly
o 2.7.3. Full code examples
o 2.7.4. Examples for the mathematical optimization chapter
# 2.7.4.12. Gradient-less methods
@ A shooting method: the Powell algorithm
@ Simplex method: the Nelder-Mead
# 2.7.4.13. Global optimizers
@ Brute force: a grid search
o 2.7.5. Practical guide to optimization with scipy
# 2.7.5.1. Choosing a method
# 2.7.5.2. Making your optimizer faster
# 2.7.5.3. Computing gradients
# 2.7.5.4. Synthetic exercices
o 2.7.6. Special case: non-linear least-squares
# 2.7.6.1. Minimizing the norm of a vector function
# 2.7.6.2. Curve fitting
o 2.7.7. Optimization with constraints
# 2.7.7.1. Box bounds
# 2.7.7.2. General constraints
o 2.7.8. Full code examples
o 2.7.9. Examples for the mathematical optimization chapter
+ 2.8. Interfacing with C
o 2.8.1. Introduction
o 2.8.2. Python-C-Api
# 2.8.2.1. Example
# 2.8.2.2. Numpy Support
o 2.8.3. Ctypes
# 2.8.3.1. Example
# 2.8.3.2. Numpy Support
o 2.8.4. SWIG
# 2.8.4.1. Example
# 2.8.4.2. Numpy Support
o 2.8.5. Cython
# 2.8.5.1. Example
# 2.8.5.2. Numpy Support
o 2.8.6. Summary
o 2.8.7. Further Reading and References
o 2.8.8. Exercises
# 2.8.8.1. Python-C-API
# 2.8.8.2. Ctypes
# 2.8.8.3. SWIG
# 2.8.8.4. Cython
* 3. Packages and applications
+ 3.1. Statistics in Python
o 3.1.1. Data representation and interaction
# 3.1.1.1. Data as a table
# 3.1.1.2. The pandas data-frame
@ Creating dataframes: reading data files or
converting arrays
@ Manipulating data
@ Plotting data
o 3.1.2. Hypothesis testing: comparing two groups
# 3.1.2.1. Student's t-test: the simplest statistical
test
@ 1-sample t-test: testing the value of a
population mean
@ 2-sample t-test: testing for difference across
populations
# 3.1.2.2. Paired tests: repeated measurements on the
same individuals
o 3.1.3. Linear models, multiple factors, and analysis of
variance
# 3.1.3.1. "formulas" to specify statistical models in
Python
@ A simple linear regression
@ Categorical variables: comparing groups or
multiple categories
# 3.1.3.2. Multiple Regression: including multiple
factors
# 3.1.3.3. Post-hoc hypothesis testing: analysis of
variance (ANOVA)
o 3.1.4. More visualization: seaborn for statistical
exploration
# 3.1.4.1. Pairplot: scatter matrices
# 3.1.4.2. lmplot: plotting a univariate regression
o 3.1.5. Testing for interactions
o 3.1.6. Full code for the figures
o 3.1.7. Solutions to this chapter's exercises
+ 3.2. Sympy : Symbolic Mathematics in Python
o 3.2.1. First Steps with SymPy
# 3.2.1.1. Using SymPy as a calculator
# 3.2.1.2. Symbols
o 3.2.2. Algebraic manipulations
# 3.2.2.1. Expand
# 3.2.2.2. Simplify
o 3.2.3. Calculus
# 3.2.3.1. Limits
# 3.2.3.2. Differentiation
# 3.2.3.3. Series expansion
# 3.2.3.4. Integration
o 3.2.4. Equation solving
o 3.2.5. Linear Algebra
# 3.2.5.1. Matrices
# 3.2.5.2. Differential Equations
+ 3.3. Scikit-image: image processing
o 3.3.1. Introduction and concepts
# 3.3.1.1. scikit-image and the SciPy ecosystem
# 3.3.1.2. What's to be found in scikit-image
o 3.3.2. Input/output, data types and colorspaces
# 3.3.2.1. Data types
# 3.3.2.2. Colorspaces
o 3.3.3. Image preprocessing / enhancement
# 3.3.3.1. Local filters
# 3.3.3.2. Non-local filters
# 3.3.3.3. Mathematical morphology
o 3.3.4. Image segmentation
# 3.3.4.1. Binary segmentation: foreground + background
@ Histogram-based method: Otsu thresholding
@ Labeling connected components of a discrete image
# 3.3.4.2. Marker based methods
@ Watershed segmentation
@ Random walker segmentation
o 3.3.5. Measuring regions' properties
o 3.3.6. Data visualization and interaction
o 3.3.7. Feature extraction for computer vision
o 3.3.8. Full code examples
o 3.3.9. Examples for the scikit-image chapter
+ 3.4. Traits: building interactive dialogs
o 3.4.1. Introduction
o 3.4.2. Example
o 3.4.3. What are Traits
# 3.4.3.1. Initialisation
# 3.4.3.2. Validation
# 3.4.3.3. Documentation
# 3.4.3.4. Visualization: opening a dialog
# 3.4.3.5. Deferral
# 3.4.3.6. Notification
# 3.4.3.7. Some more advanced traits
+ 3.5. 3D plotting with Mayavi
o 3.5.1. Mlab: the scripting interface
# 3.5.1.1. 3D plotting functions
@ Points
@ Lines
@ Elevation surface
@ Arbitrary regular mesh
@ Volumetric data
# 3.5.1.2. Figures and decorations
@ Figure management
@ Changing plot properties
@ Decorations
o 3.5.2. Interactive work
# 3.5.2.1. The "pipeline dialog"
# 3.5.2.2. The script recording button
o 3.5.3. Slicing and dicing data: sources, modules and
filters
# 3.5.3.1. An example: inspecting magnetic fields
# 3.5.3.2. Different views on data: sources and modules
@ Different sources: scatters and fields
@ Transforming data: filters
@ mlab.pipeline: the scripting layer
o 3.5.4. Animating the data
o 3.5.5. Making interactive dialogs
# 3.5.5.1. A simple dialog
# 3.5.5.2. Making it interactive
o 3.5.6. Putting it together
+ 3.6. scikit-learn: machine learning in Python
o 3.6.1. Introduction: problem settings
# 3.6.1.1. What is machine learning?
# 3.6.1.2. Data in scikit-learn
@ The data matrix
@ A Simple Example: the Iris Dataset
- The application problem
- Loading the Iris Data with Scikit-learn
o 3.6.2. Basic principles of machine learning with
scikit-learn
# 3.6.2.1. Introducing the scikit-learn estimator
object
@ Fitting on data
# 3.6.2.2. Supervised Learning: Classification and
regression
# 3.6.2.3. A recap on Scikit-learn's estimator
interface
# 3.6.2.4. Regularization: what it is and why it is
necessary
@ Prefering simpler models
@ Simple versus complex models for classification
o 3.6.3. Supervised Learning: Classification of Handwritten
Digits
# 3.6.3.1. The nature of the data
# 3.6.3.2. Visualizing the Data on its principal
components
# 3.6.3.3. Gaussian Naive Bayes Classification
# 3.6.3.4. Quantitative Measurement of Performance
o 3.6.4. Supervised Learning: Regression of Housing Data
# 3.6.4.1. A quick look at the data
# 3.6.4.2. Predicting Home Prices: a Simple Linear
Regression
o 3.6.5. Measuring prediction performance
# 3.6.5.1. A quick test on the K-neighbors classifier
# 3.6.5.2. A correct approach: Using a validation set
# 3.6.5.3. Model Selection via Validation
# 3.6.5.4. Cross-validation
# 3.6.5.5. Hyperparameter optimization with
cross-validation
@ Basic Hyperparameter Optimization
@ Automatically Performing Grid Search
@ Built-in Hyperparameter Search
@ Nested cross-validation
o 3.6.6. Unsupervised Learning: Dimensionality Reduction
and Visualization
# 3.6.6.1. Dimensionality Reduction: PCA
# 3.6.6.2. Visualization with a non-linear embedding:
tSNE
o 3.6.7. The eigenfaces example: chaining PCA and SVMs
o 3.6.8. The eigenfaces example: chaining PCA and SVMs
# 3.6.8.1. Preprocessing: Principal Component Analysis
# 3.6.8.2. Doing the Learning: Support Vector Machines
# 3.6.8.3. Pipelining
o 3.6.9. Parameter selection, Validation, and Testing
# 3.6.9.1. Hyperparameters, Over-fitting, and
Under-fitting
@ Bias-variance trade-off: illustration on a simple
regression problem
# 3.6.9.2. Visualizing the Bias/Variance Tradeoff
@ Validation Curves
@ Learning Curves
# 3.6.9.3. Summary on model selection
@ High Bias
@ High Variance
# 3.6.9.4. A last word of caution: separate validation
and test set
o 3.6.10. Examples for the scikit-learn chapter
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