https://paul-st-young.github.io/algorithms/ 2023-09-11T02:06:20+00:00 Founded by a group of physics graduate students at UIUC, this archival site will aid us in our practice of physics through algorithmic developments and hopefully *vice versa*. Yubo "Paul" Yang yyang173@illinois.edu https://paul-st-young.github.io/ Jekyll https://paul-st-young.github.io/algorithms/algorithm/Inference-on-Growing-Trees-Kevin-Ly/ 2021-05-10T00:00:00+00:00 kevin

<!-- Page Content Starts Here --> <h2 id="presentation-summary">Presentation Summary</h2> <p>In <a href="https://paul-st-young.github.io/algorithms/assets/slides/growing_trees.pdf">these slides</a>, I present:</p> <ul> <li>A new algorithm for calculating probabilities of growing trees.</li> </ul> <h2 id="examples">Examples</h2> <ul> <li><a href="https://paul-st-young.github.io/algorithms/assets/notebooks/growing_trees/example.ipynb">Randomly growing trees</a></li> </ul> <h2 id="references">References</h2> <ul> <li><a href="https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.126.038301">[1] <code class="language-plaintext highlighter-rouge">PRL 126, 038301 (2021)</code></a></li> </ul> 2021-05-10T00:00:00+00:00 https://paul-st-young.github.io/algorithms/algorithm/Huffman-Encoding-Chad-Germany/ 2021-04-12T00:00:00+00:00 Yubo "Paul" Yang yyang173@illinois.edu https://paul-st-young.github.io/

Huffman Encoding is a technique of compressing data to reduce its size without losing any of the details. Huffman Coding is generally useful to compress the data in which there are frequently occurring characters. The most frequent character gets the smallest code and the least frequent character gets the largest code.

<!-- Page Content Starts Here --> <h2 id="presentation-summary">Presentation Summary</h2> <p>In <a href="https://paul-st-young.github.io/algorithms/assets/slides/huffman_encoding.pdf">these slides</a>, I present:</p> <ul> <li>Basic idea behind the Huffman encoding algorithm.</li> <li>Implementation of the algorithm on a text document.</li> </ul> <h2 id="examples">Examples</h2> <ul> <li><a href="https://paul-st-young.github.io/algorithms/assets/notebooks/huffman_encoding.ipynb">huffman_encoding.ipynb</a>: I created a text file and wrote a message that the code reads and encodes that message to huffman.txt. It can then be read and and written to decode.txt(<a href="https://paul-st-young.github.io/algorithms/assets/notebooks/huffman_encoding.html">html</a>)</li> </ul> <h3 class="t60" id="all-compression">All Compression</h3> <ul class="side-nav"> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/Huffman-Encoding-Chad-Germany/">by Chad Germany &middot; <strong>Huffman Encoding</strong></a></li> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/Audio-Compression-Benji-Villalonga/">by Benjamin Villalonga Correa &middot; <strong>Audio Compression</strong></a></li> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/Fractal-Compression-Alex-Munoz/">by Alex Munoz &middot; <strong>Fractal Compression</strong></a></li> </ul> 2021-04-12T00:00:00+00:00 https://paul-st-young.github.io/algorithms/algorithm/Stochastic_Gradient-Descent-Kevin-Kleiner/ 2021-03-22T00:00:00+00:00 Kevin Kleiner

Introducing SGD optimization: the bread and butter of model fitting problems

<!-- Page Content Starts Here --> <h2 id="presentation-summary">Presentation Summary</h2> <p>In <a href="https://paul-st-young.github.io/algorithms/assets/slides/SGD_Slides.pdf">these slides</a>, I present:</p> <ul> <li>Context and conceptual overview <a href="https://arxiv.org/pdf/1609.04747.pdf">2</a> of gradient descent and stochastic gradient descent</li> <li>Brief descriptions of modifications to SGD with visual comparisons <a href="http://www.denizyuret.com/2015/03/alec-radfords-animations-for.html">3</a></li> </ul> <h2 id="examples">Examples</h2> <ul> <li><a href="https://paul-st-young.github.io/algorithms/assets/notebooks/SGD_Demos.ipynb">SGD_Demos.ipynb</a> using Kaggle height-weight data <a href="https://www.kaggle.com/mustafaali96/weight-height">5</a></li> </ul> <h3 class="t60" id="references">References</h3> <ul class="side-nav"> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/Stochastic_Gradient-Descent-Kevin-Kleiner/">Kevin Kleiner: Algorithm Interest Group on March 22, 2021 &middot; <strong>Exploring Stochastic Gradient Descent and its Modifications</strong></a></li> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/Linear-Sum-Assignment-Yubo-Paul-Yang/">by Yubo "Paul" Yang &middot; <strong>Linear Sum Assignment</strong></a></li> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/PSLQ-Kevin-Ly/">by Kevin Ly &middot; <strong>PSLQ</strong></a></li> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/Simulated-Annealing-Chad-Germany/">by Chad Germany &middot; <strong>Simulated Annealing</strong></a></li> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/BK-Tree-Brian-Busemeyer/">by Brian Busemeyer &middot; <strong>BK-Tree</strong></a></li> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/Simulated-Annealing/">by Brian Busemeyer &middot; <strong>Simulated annealing</strong></a></li> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/Cellular-Automaton-Brian-Busemeyer/">by Brian Busemeyer &middot; <strong>Cellular Automaton</strong></a></li> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/Autofocus-Juha-Tiihonen/">by Juha Tiihonen &middot; <strong>Automatic focusing of cameras</strong></a></li> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/Particle-Swarm-Optimization-Yubo-Paul-Yang/">by Yubo "Paul" Yang &middot; <strong>Particle Swarm Optimization</strong></a></li> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/Evolutionary-Brian-Busemeyer/">by Brian Busemeyer &middot; <strong>Evolutionary algorithms</strong></a></li> </ul> 2021-03-22T00:00:00+00:00 https://paul-st-young.github.io/algorithms/algorithm/RANSAC-Ryan-Levy/ 2021-02-22T00:00:00+00:00 Ryan Levy yyang173@illinois.edu https://ryanlevy.github.io/

Fitting models with outlier detection

<!-- Page Content Starts Here --> <h2 id="presentation-summary">Presentation Summary</h2> <p>In <a href="https://paul-st-young.github.io/algorithms/assets/slides/RANSAC.pdf">these slides</a>, I present:</p> <ul> <li>RANSAC - Random Sample Consensus</li> <li>Brief extensions (the RANSAC family of algorithms)</li> </ul> <h2 id="examples">Examples</h2> <ul> <li><a href="https://paul-st-young.github.io/algorithms/assets/notebooks/RANSAC.ipynb">RANSAC.ipynb</a></li> </ul> <h2 id="references">References</h2> <ul> <li><a href="https://pjreddie.com/courses/computer-vision/">Ancient Secrets of Computer Vision</a></li> <li><a href="http://dx.doi.org/10.1561/0600000009 ">doi:10.1561/0600000009</a> | <a href="https://link.springer.com/chapter/10.1007/978-3-540-88688-4_37">doi:10.1007/978-3-540-88688-4_37</a></li> </ul> <h3 class="t60" id="all-fitting">All Fitting</h3> <ul class="side-nav"> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/RANSAC-Ryan-Levy/">by Ryan Levy &middot; <strong>RANSAC</strong></a></li> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/Expectation-Maximization-Eli-Chertkov/">by Eli Chertkov &middot; <strong>Expectation Maximization</strong></a></li> </ul> 2021-02-22T00:00:00+00:00 https://paul-st-young.github.io/algorithms/algorithm/Expectation-Maximization-Eli-Chertkov/ 2021-02-08T00:00:00+00:00 eli

Parameter estimation via maximum likelihood

<!-- Page Content Starts Here --> <h2 id="presentation-summary">Presentation Summary</h2> <p>In <a href="https://paul-st-young.github.io/algorithms/assets/slides/EMTalk.pdf">these slides</a>, I present:</p> <ul> <li>Expectation Maximization algorithm using Gaussian Mixture Models</li> </ul> <h2 id="examples">Examples</h2> <ul> <li><a href="https://paul-st-young.github.io/algorithms/assets/codes/em/em.py">em.py</a></li> <li><a href="https://paul-st-young.github.io/algorithms/assets/codes/em/test_em.py">test_em.py</a></li> <li><a href="https://paul-st-young.github.io/algorithms/assets/codes/em/test_em1.py">test_em1.py</a></li> <li><a href="https://paul-st-young.github.io/algorithms/assets/codes/em/test_em2.py">test_em2.py</a></li> <li><a href="https://paul-st-young.github.io/algorithms/assets/codes/em/test_em3.py">test_em3.py</a></li> </ul> <h2 id="references">References</h2> <ul> <li><a href="https://see.stanford.edu/materials/aimlcs229/cs229-notes8.pdf">Andrew Ng’s Stanford CS 229 Lectures</a></li> <li><a href="https://www.ics.uci.edu/~smyth/courses/cs274/notes/EMnotes.pdf">Padhraic Smyth’s UCI CS 274 Lecture notes</a></li> </ul> <h3 class="t60" id="all-fitting">All Fitting</h3> <ul class="side-nav"> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/RANSAC-Ryan-Levy/">by Ryan Levy &middot; <strong>RANSAC</strong></a></li> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/Expectation-Maximization-Eli-Chertkov/">by Eli Chertkov &middot; <strong>Expectation Maximization</strong></a></li> </ul> 2021-02-08T00:00:00+00:00 https://paul-st-young.github.io/algorithms/algorithm/Magic-Of-NUTS-Ryan-Levy/ 2020-12-14T00:00:00+00:00 Ryan Levy yyang173@illinois.edu https://ryanlevy.github.io/

The No U-Turn Sampler is a powerful Monte Carlo Technique

<!-- Page Content Starts Here --> <h2 id="presentation-summary">Presentation Summary</h2> <p>In <a href="https://paul-st-young.github.io/algorithms/assets/slides/The_Magic_of_NUTS.pdf">these slides</a>, I present:</p> <ul> <li>Hamiltonian Monte Carlo</li> <li>The No U-Turn Sampler (NUTS)</li> </ul> <h2 id="examples">Examples</h2> <ul> <li><a href="https://paul-st-young.github.io/algorithms/assets/notebooks/HMC_noan.ipynb">HMC_noan.ipynb</a></li> </ul> <h2 id="references">References</h2> <ul> <li><a href="https://elevanth.org/blog/2017/11/28/build-a-better-markov-chain/">Build a Better Markov Chain</a></li> <li><a href="https://chi-feng.github.io/mcmc-demo/">MCMC Demo</a></li> <li><a href="https://arxiv.org/abs/1111.4246">arXiv:1111.4246</a> | <a href="https://arxiv.org/abs/1304.1920">arXiv:1304.1920</a> | <a href="https://arxiv.org/abs/1701.02434">arxiv1701.02434</a> | <a href="https://doi.org/10.1111/2041-210X.12681">doi:10.1111/2041-210X.12681</a></li> </ul> <h3 class="t60" id="all-monte-carlo">All Monte Carlo</h3> <ul class="side-nav"> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/Magic-Of-NUTS-Ryan-Levy/">by Ryan Levy &middot; <strong>The Magic of NUTS</strong></a></li> </ul> 2020-12-14T00:00:00+00:00 https://paul-st-young.github.io/algorithms/algorithm/Persistent-Homology-Greg-Hamilton/ 2020-11-30T00:00:00+00:00 Yubo "Paul" Yang yyang173@illinois.edu https://paul-st-young.github.io/

An intro to topological data analysis

<!-- Page Content Starts Here --> <h2 id="presentation-summary">Presentation Summary</h2> <p>In <a href="https://paul-st-young.github.io/algorithms/assets/slides/PersHomAIG.pdf">these slides</a>, I present:</p> <ul> <li>How persistent homology can be used as a central tool of topological data analysis</li> </ul> <h2 id="exapmples">Exapmples</h2> <ul> <li><a href="https://paul-st-young.github.io/algorithms/assets/notebooks/AIGExample.ipynb">jupyter-notebook</a></li> </ul> <h3 class="t60" id="all-dataanalysis">All DataAnalysis</h3> <ul class="side-nav"> </ul> 2020-11-30T00:00:00+00:00 https://paul-st-young.github.io/algorithms/algorithm/Graphing-Connectivitiy-FMRI-Mayisha-Nakib/ 2020-11-09T00:00:00+00:00 Yubo "Paul" Yang yyang173@illinois.edu https://paul-st-young.github.io/

Understanding FMRI Data through PageRank

<!-- Page Content Starts Here --> <h2 id="presentation-summary">Presentation Summary</h2> <p>In <a href="https://paul-st-young.github.io/algorithms/assets/slides/Graphing_Directional_Connectivity_in_FMRI.pdf">these slides</a>, I present:</p> <ul> <li>How FMRI data can be used for modeling</li> <li>How one can use the PageRank algorithm to identify important relationships in the BOLD signals w/ the rbeta algorithm</li> </ul> <h2 id="references">References</h2> <ul> <li><a href="https://github.com/gdbassett/rbeta">rbeta algorithm</a></li> <li><a href="https://graph-tool.skewed.de/">graph-tool</a></li> <li><a href="https://crcns.org/data-sets/vc/vim-1/about-vim-1">vim-1 BOLD fMRI dataset</a></li> </ul> <h3 class="t60" id="all-pagerank">All PageRank</h3> <ul class="side-nav"> </ul> 2020-11-09T00:00:00+00:00 https://paul-st-young.github.io/algorithms/algorithm/Linear-Sum-Assignment-Yubo-Paul-Yang/ 2020-10-19T00:00:00+00:00 Yubo "Paul" Yang yyang173@illinois.edu https://paul-st-young.github.io/

The Linear Sum Assignment Problem (LSAP) is a combinatoric optimization problem with many practical applications. An elegant solution was proposed in 1955 by Kuhn and lovingly dubbed "The Hungarian algorithm". This polynomial-scaling algorithm is sometimes credited as the predecessor to primal-dual linear programming approaches.

<!-- Page Content Starts Here --> <h2 id="presentation-summary">Presentation Summary</h2> <p>In <a href="https://paul-st-young.github.io/algorithms/assets/slides/lsap-kuhn-hungarian.pdf">these slides</a>, I present:</p> <ul> <li>Definition and examples of the linear assignment problem.</li> <li>A polynomial-scaling solution: the Hungarian algorithm.</li> </ul> <h2 id="examples">Examples</h2> <ul> <li><a href="https://paul-st-young.github.io/algorithms/assets/codes/lsap-kuhn-hung.tgz">lsap-kuhn-hung.tgz</a>: “a_dev” contains a simple implementation of the Hungarian algorithm along with visualization. “b_time” is a snakemake folder that measures execution time.</li> </ul> <h2 id="references">References</h2> <ul> <li><a href="https://www.springer.com/gp/book/9783540102670">Burkard and Derigs 1980</a></li> <li><a href="http://www.assignmentproblems.com">Burkard et al. 2009</a></li> </ul> <h3 class="t60" id="all-linear-programming">All Linear Programming</h3> <ul class="side-nav"> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/Linear-Sum-Assignment-Yubo-Paul-Yang/">by Yubo "Paul" Yang &middot; <strong>Linear Sum Assignment</strong></a></li> </ul> 2020-10-19T00:00:00+00:00 https://paul-st-young.github.io/algorithms/algorithm/PSLQ-Kevin-Ly/ 2020-10-05T00:00:00+00:00 Yubo "Paul" Yang yyang173@illinois.edu https://paul-st-young.github.io/

Finding Integer Relations

<!-- Page Content Starts Here --> <h2 id="presentation-summary">Presentation Summary</h2> <p>In <a href="https://paul-st-young.github.io/algorithms/assets/slides/PSLQ.pdf">these slides</a>, I present:</p> <ul> <li>Definition and examples of finding integer relations.</li> <li>One solution via the PSLQ algogithm.</li> </ul> <h2 id="examples">Examples</h2> <ul> <li><a href="https://paul-st-young.github.io/algorithms/assets/notebooks/PSLQ/demo1.ipynb">demo1.ipynb</a>: A demo on the basics of mpmath’s PSLQ function</li> <li><a href="https://paul-st-young.github.io/algorithms/assets/notebooks/PSLQ/demo2.ipynb">demo2.ipynb</a>: A demo trying (and failing) to find a finite series form of the Euler-Mascheroni constant</li> <li><a href="https://paul-st-young.github.io/algorithms/assets/notebooks/PSLQ/demo3.ipynb">demo3.ipynb</a>: A demo showing how to use PSLQ to find a formula for Pi</li> </ul> <h2 id="references">References</h2> <ul> <li><a href="http://mpmath.org">mpmath library</a></li> <li><a href="http://www.cecm.sfu.ca/organics/papers/bailey/paper/html/node3.html">Pseudocode (Bailey)</a></li> </ul> <h3 class="t60" id="all-optimization">All Optimization</h3> <ul class="side-nav"> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/Stochastic_Gradient-Descent-Kevin-Kleiner/">Kevin Kleiner: Algorithm Interest Group on March 22, 2021 &middot; <strong>Exploring Stochastic Gradient Descent and its Modifications</strong></a></li> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/Linear-Sum-Assignment-Yubo-Paul-Yang/">by Yubo "Paul" Yang &middot; <strong>Linear Sum Assignment</strong></a></li> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/PSLQ-Kevin-Ly/">by Kevin Ly &middot; <strong>PSLQ</strong></a></li> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/Simulated-Annealing-Chad-Germany/">by Chad Germany &middot; <strong>Simulated Annealing</strong></a></li> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/BK-Tree-Brian-Busemeyer/">by Brian Busemeyer &middot; <strong>BK-Tree</strong></a></li> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/Simulated-Annealing/">by Brian Busemeyer &middot; <strong>Simulated annealing</strong></a></li> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/Cellular-Automaton-Brian-Busemeyer/">by Brian Busemeyer &middot; <strong>Cellular Automaton</strong></a></li> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/Autofocus-Juha-Tiihonen/">by Juha Tiihonen &middot; <strong>Automatic focusing of cameras</strong></a></li> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/Particle-Swarm-Optimization-Yubo-Paul-Yang/">by Yubo "Paul" Yang &middot; <strong>Particle Swarm Optimization</strong></a></li> <li><a href="https://paul-st-young.github.io/algorithms/algorithm/Evolutionary-Brian-Busemeyer/">by Brian Busemeyer &middot; <strong>Evolutionary algorithms</strong></a></li> </ul> 2020-10-05T00:00:00+00:00