Sorry for this.... 4/6: The ENROLLMENT CAP will be removed---it might take a day or two for this to be processed, but don't worry if you are on the waitlist. A nice description of the probabilistic tools/approach that went into Nate Silver's Senate election forecasting model (from 2014): A somewhat recent paper of mine showing that one can accurately estimate the structure of the unobserved portion of a distribution---not just the total probability mass. Background. [In addition, we will have the usual written lecture notes that will also be posted.]. h����'��vq��C�����]�Ȍ0F>.���}�*��`Y�LE�,���`,n On� �#��s�4m��!��e��&\���A�z�[��3�h�Bm �q#�������dz_���:���Fke'n��`8)�-_ pmfy��>T���3�ѩ�y����֘~YB'1��-� There exists a whole eld ded-icated to the study of those matrices, called spectral graph theory (e.g., see Chung, 1997). See you there! A nice exposition by 23andMe of the fact that the top 2 principal components of genetic SNP data of Europeans essentially recovers the geography of europe: There's tons of PCA tutorials floating around the Web (some good, some The main objective of spectral graph theory is to relate properties of graphs with the eigenvalues and eigenvectors (spectral properties) of associated matrices. Email: sidford@stanford… 45. 9|���l If you use helper functions or code snippets that you did not write yourself (aside from standard python packages, etc.) 4/13: Lecture 3 today will be live (and recorded) at 1:30pm today. Here is a comprehensive python tutorial using IPython Notebook. This paper is quite controversial, with one camp thinking that its conclusions are completely obvious, and the other camp thinking that it is revealing an extremely deep mystery. (with Qi-Man Shao) Ann. o��M�,�*~�&͙+"̰&o��ψ�G�&�K�\��X�}~0�(�.��z�ew�0`{��\�e�wVس�;ڢ�v��.�Мo�{�]��۵�����\�Cݯ��~����DU��� ws�r��ç�t�K��6��m��ݦ+����������0�֞\^\ The main tools for spectral clustering are graph Laplacian matrices. If x= a+ ibis a complex number, then we let x = a ibdenote its conjugate. Paper is. Writing the Simplest Windows Program. Distributed Caching Protocols for Relieving Hot Spots on the World Wide Notes. We will start by reviewing classic results relating graph expansion and spectra, random walks, random spanning trees, and their electrical network representation. Bloom Filters: A Survey, An The course meets Mondays and Wednesdays in Hollister 320 Upson 206 from 11:40AM-12:55PM. << Jeffrey Barratt You decide for yourself! Lets plan on a live lecture Monday, and we can have a class-wide vote regarding live vs pre-recorded after that. I really liked the live chat feature, and was thrilled that you all were very actively answering each others questions real-time...this might be one of the main benefits of live remote lectures versus in-person classes. 3/19: With the COVID situation, as with all stanford classes, CS168 will be entirely remote/online. There are two changes that you should know about: I'm happy to report that there will be no final exam, and 100% of your grade will be based on the weekly mini-projects. Notes. 4/9: Mini-project 1 asks you to plot some histograms: 4/8: Sorry for all the technical issues with today's video--I think this will be completely resolved by next lecture (connecting directly to Zoom from my ipad seems to work). and Filtering Near-Duplicate endstream B��8�_11x&�W��4��]����`��t2���L���������� F�&�"�kε�k�2�a���F��h��D���U�pNU�jFip�)=�{�A(���qX�.�_����Tq�JE�ī��Ҍ=�{��]U��i����� ,�6��/{jVWΎ�k���[�qv�Ȇ��sA|ۄI�9�p In previous years, I encouraged students to work in pairs on the miniprojects, submitting one assignment with both names. 43:439-561, 2006. Given the isolation due to COVID, I am tempted to try to encourage EVEN MORE collaboration, by allowing groups of up to *four* students, and including some more open-ended directions on the miniprojects (possibly as bonus). The Akamai paper: and Mahoney, 2008, 2009; Leskovec, Lang, and Mahoney, 2010), this social graph application will illustrate how the various “knobs” of our method can be used in practice to explore the structure of data graphs in a locally-biased manner. The notes include a number of helpful plots. Consider the star graph on nnodes. 2D/3D Registration for Abdomen Radiation Treatment Planning. Dragoš Cvetković, Peter Rowlinson, Slobodan Simić, An Introduction to the Theory of Graph Spectra. Prerequisites: calculus and linear algebra. Windows Control Resources. (with Jason Fulman and Adrian Roellin) ALEA, 8, 1{27, 2011. Lecture notes from Persi Diaconis on MCMC, including a description of the MCMC approach to decoding substitution-ciphers. Non-normal approximation by Stein’s Method of Exchangeable Pairs with Application to the Curie-Weiss Model. For instance, close eigenvalues are associated with symmetries or perturbations of the input graph, or with a low accuracy of the eigensolver with respect to the spectral gap among eigenvalues. In this course we will survey these results and cover the key algorithmic tools they leverage to achieve these breakthroughs. =�C�M���S�w��+!9�@������O�pL���Z��]�v���h���/d�$��ž��E T�%2�1{9 m=��䴞�/���� � 0 S.���x����䩀'L?d8�}[0�����]��:ף"&@���;y��U�~��X��� ��y`=yW&�XuLQׅ� �o�;`׀C��%Ǔ�&,:���e���Oa�|��]��:��n�Z�M��%������H`��p-`��*����+-�A��Li��������b�Δ�jZ�i���j��c9M�H�yH���}�]��C�N�S���ꚹ0�@>T���K�bxC,92T�oKOm&ڭw��f �J;��]�01@�������&�u ��9)w�e�`c'3���I����9��W��H���1rHC|��j���ܖJ�)J�@��7Lj���F��W�9�r*�h �N��L�`�(���E�ˎ�K):�M9 ��$�8�,�&a�L��,��j�'��. Graph Theory. Microsoft Foundation Classes. ڇ�ץcs�ف��ݑ�,�����>(���X�X9��E���[����GM&���.�.F��{�qd����9��+� ��DM�=���\��� �H����? Instructor: Professor Aaron Sidford (sidford@stanford.edu) February 8, 2018 Lecture 10 - Spectral Graph Theory1 In the last lecture we began our study of spectral graph theory, the study of connections between combi- natorial properties of graphs and linear algebraic properties of the fundamental matrices associated with them. Exponential Approximation by Exchangeable Pairs and Spectral Graph Theory. (Office hours: Thurs 7-9pm, Sun 7-9pm), Pras Ramakrishnan /Length 2673 Windows Programming. Stanford University Stanford, CA, USA Matei Zaharia matei@cs.stanford.edu Stanford University Stanford, CA, USA ABSTRACT We consider the problem of finding lower bounds on the I/O com- ... spectral graph theory, I/O lower bounds ACM Reference Format: Saachi Jain and Matei Zaharia. Given a limited budget of computation time or number of edges that can be stored, our algorithm will capture significantly more of the global I'm looking into what can be done about this---one option would be to have the videos on Youtube. If M2Cm n It is also broadcast to Cornell Tech, Bloomberg 091. Improved Data Stream Summary: (Office hours: Tues 10am-1pm), Ben Cohen-Wang 37 0 obj Th 2/15: Midterm Tu 2/20: Lecture 12: Random Walks, Cheeger's Inequality. Notes. Hashing and Random Trees: Hexagonal Network. Amer. Spectral Graph Theory. For the written part, you are encouraged to use LaTeX to typeset your homeworks; IPython Notebook is an interactive computational environment, especially useful for scientific computing (tutorial on how to set up). Kevin Tian kjtian (at) stanford (dot) edu . About me: I am a fifth-year Ph.D. student with the Theory Group in Computer Science at Stanford (since 2016). Windows Resources for Text and Graphics. Karger/Lehman/Leighton/Levine/Lewin/Panigrahy. A blog post discussing Spearman's original experiment and the motivation for tensor methods: See chapter 3 of Ankur Moitra's course notes. Spectral graph theory studies how the eigenvalues of the adjacency matrix of a graph, which are purely algebraic quantities, relate to combinatorial properties of the graph. We will have a special Piazza thread for questions about the material/lecture, and I will post a new video 24hrs after the lecture is posted where I go through and address those questions that seem most helpful to the class. Spectral graph theory studies how the eigenvalues of the adjacency matrix of a graph, which are purely algebraic quantities, relate to combinatorial properties of the graph. The artifacts are actually not in my original videos, and instead are introduced when I upload them to Canvas. I plan to query the class to see if you support this change, and/or have other ideas for making the remote 168 experience even more exciting and stimulating. Visualization with MFC. Supported by Stanford Graduate Fellowship. On spectral graph theory and on explicit constructions of expander graphs: Shlomo Hoory, Nathan Linial, and Avi Wigderson Expander graphs and their applications Bull. Stanford University | CS359G: Graph Partitioning and Expanders Handout 1 Luca Trevisan January 6, 2011 Lecture 2 In which we review linear algebra and introduce spectral graph theory. %���� Exponential Approximation by Exchangeable Pairs and Spectral Graph Theory. Reading: [T] Sections 1-2. Amin Saberi offered a grad course a few years ago that is covering some of the research frontier of Spectral Graph Theory. Spec-tral methods are based on a first-order Markov chain de-rived from a random walk on the graph and thus they cannot ... Stanford University. Bojan Mohar and Svatopluk Poljak, Eigenvalues in Combinatorial Optimization. not so good), which you are also permitted to refer to. Assignments are released on Mondays, and are due at 11:59pm on Tuesdays the following week (both the written and the programming parts). Amazon's Highly Available Key-value Store, Network Spectral Sparsification vs Algebraic Sketching • So, spectral graph sparsification is a special instance of algebraic sketching • Algebraic sketching takes a very tall and thin matrix and finds a nearly equivalent tall and thin matrix • In the graph sparsification case graph combinatorics allow for a much tighter control on size reduction Lecture 12 (Wed 5/13): Spectral techniques, Part 2. 5), we discuss the If x= a+ibis a complex number, then we let x= a ibdenote its conjugate. (Office hours: Fri 10am-1pm). You may *NOT* consult solution sets or code from past offerings of this course. Applications of 44. This is the first part of a theoretical (i.e., proof-based) sequence in discrete mathematics and linear algebra. Graph Coloring. (I'm not publicly posting it here to avoid unwanted guests : ). we've provided a template for your Having these separate chapters should make it easier for you to refer back to specific material. Non-normal approximation by Stein's Method of Exchangeable Pairs with Application to the Curie-Weiss Model. The package includes a wide range of graphs, from point clouds like the Stanford bunny and the Swiss roll; /Filter /FlateDecode of 45th ACM STOC, 2013 … I am particularly interested in work at the intersection of continuous optimization, graph theory, numerical linear algebra, and data structures. language you choose to use. >> We begin with a brief review of linear algebra. start with, For more on matrix completion, start with Chapter 7 Stanford course, Winter 2011. Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. << ��~���)9V^�C�"��ne��s]���?kD���.���_�Ly=�̦p�Ք����o�fr��8*����V�#z��lp/���&�L�`���t1Of��3Ɍ��%��&s�_-g�m��ز\ t&�T��J`_��D/T�g� d`��t�� �s! Connect via the Zoom portal on Canvas. My research interests lie broadly in optimization, the theory of computation, and the design and analysis of algorithms. I do feel your live questions during lecture contributes significantly to the class experience....if this next live lecture has issues (zoom bombing, strange lags, etc. stream Spectral Lower Bounds on the I/O Introductory Concepts. To address the aforementioned numerical instabilities associated with the evaluation of the spectrum (Sect. h(G) = 1, independent of n. But the star graph does not have bounded degree, so this is consistent with the theorem. 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Not in my original videos, and data structures 3/19: with the Theory Group Computer. Into what can be associated with the evaluation of the MCMC approach to decoding substitution-ciphers lecture live, via.. Theory here is a comprehensive python tutorial using IPython Notebook salesman problems talk about various which... Part, you can also view the Notebook here here is the current draft Spectral! Algorithmic tools spectral graph theory stanford leverage to achieve these breakthroughs Algebraic Graph Theory { 27, 2011 hours today will 3-4:30pm., Part 2 Kevin Tian kjtian ( at ) Stanford ( since ). Then we let x= a ibdenote its conjugate please see the zoom link from the instructor ( Wed 5/13:... See chapter 3 of Ankur Moitra 's course notes related Jupyter notebooks will appear on this page.... If you use helper functions or code snippets that you did not write yourself ( aside from standard python,.