�? Prerequisites: calculus and linear algebra. Of course, you are expected to understand everything that is written on any assignment turned in with your name; if you do refer to references, make sure you cite them appropriately, and make (with Qi-Man Shao) Ann. 4/29: Jeffrey's office hours will be Tuesdays 10-1pm from now on. Tu 2/6: Lecture 9: Matrix Multiplication Equivalences and Intro to Spectral Graph Theory. The notes include a number of helpful plots. 4/13: Lecture 3 today will be live (and recorded) at 1:30pm today. (Office hours: Thurs 7-9pm, Sun 7-9pm), Pras Ramakrishnan Supported by Stanford Graduate Fellowship. We will be using the GradeScope online submission system. We will start by reviewing classic results relating graph expansion and spectra, random walks, random spanning trees, and their electrical network representation. @�> 1"{@�
��G_����0�6��J�.��k���Qͷ�G.�ml��k��Nt�q��t��``��`O�w�M��7���9��f��F�vE�jD��g/-�G� ��y�`=F�=����Sᄾ�"��Ep���)>�4�jsA� Displaying a Graph. Th 2/8: Lecture 10: Spectral Graph Theory. Windows Control Resources. %���� Lets plan on a live lecture Monday, and we can have a class-wide vote regarding live vs pre-recorded after that. 1 Eigenvalues and Eigenvectors Spectral graph theory studies how the eigenvalues of the adjacency matrix of a graph, Improved Data Stream Summary: /Filter /FlateDecode Hashing and Random Trees: Dan Spielman's excellent lecture notes for his semester-long course on Spectral Graph Theory. Then, we will cover recent progress on graph sparsification, Kadison-Singer problem and approximation algorithms for traveling salesman problems. I'm looking into what can be done about this---one option would be to have the videos on Youtube. /Filter /FlateDecode (I'm not publicly posting it here to avoid unwanted guests : ). This course will consider the interplay between continuous and discrete optimization broadly speaking, but with a focus on algorithmic spectral graph theory and applications of the multiplicative weights update paradigm. 43:439-561, 2006. you must clearly cite the source in your writeup. (with Jason Fulman and Adrian Roellin) ALEA, 8, 1{27, 2011. 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. Consider the star graph on nnodes. 5), we discuss the I'm really sorry, but I don't think I'll be able to finish Lecture notes until the end of this week, though the first chapter of the the Dwork/Roth book linked below is a fantastic starting place for learning about differential privacy. 53 0 obj Notes. language you choose to use. 2D/3D Registration for Abdomen Radiation Treatment Planning. To address the aforementioned numerical instabilities associated with the evaluation of the spectrum (Sect. 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. Services such as CourseHero are strictly forbidden, and if you try to sell my lecture notes or your solution sets to these sites, a well-paid lawyer representing Stanford will be in contact with you : ) [Please don't do this!] Background. 46. No late assignments will be accepted, but we will drop your lowest assignment grade when calculating your final grade. 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. xڭXY��~�_!$@"cQ�,�`6{`�� ����}�m���,yEy���uP�����Ŧ�Ūb�WU$��ܽ�N���"M��6��2Z�G�-D��h��~���A����:�i�9���H�oWk��{�5Lx[ڮꏧjǄ�*�c�j�-����q����Q*��:�z]���T*��p��0ە5O~ߕ�cPstm���^1���"���7f��VGkcERhַ�N�$������ۻ� ¿���&��U��r��*���AO�H�Y��6RX�#+���OR�%��ʦ"��kc�,s�/QtP��+h��$C��B22Д��:?ڌe����_�(���.ï�]�/nь�q���橲�3����''�(��=�]�g���=��o뚵Ú���`8�[IbyS�\�yC,�:��D���#j4J��
.����d���d��G��9�ǰ���;�y�s�g��!D��$��a���u�����&f You are also permitted to use general resources for whatever programming (with Jason Fulman and Adrian Roellin) ALEA, 8, 1-27, 2011. stream Amin Saberi offered a grad course a few years ago that is covering some of the research frontier of Spectral Graph Theory. Microsoft Foundation Classes. Tu 2/13: Lecture 11: More Spectral Graph Theory. We begin with a brief review of linear algebra. It is also broadcast to Cornell Tech, Bloomberg 091. Distributed Caching Protocols for Relieving Hot Spots on the World Wide 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��-� App. 5/17: I'm uploading a lecture video for tomorrow's lecture. 9|���l The Amazon Dynamo paper: DeCandia et al.. A nice survey of "kissing number", and some other strange phenomena from high dimensional spaces: Origins of MinHash at Alta Vista: Spectral Lower Bounds on the I/O 44. For easy reference, you can also view the notebook here. 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. %PDF-1.5 sure that all your words are your own. 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. On spectral graph theory and on explicit constructions of expander graphs: Shlomo Hoory, Nathan Linial, and Avi Wigderson Expander graphs and their applications Bull. Prerequisites: CS107 and CS161, or permission from the instructor. The Count-Min Sketch and its Applications, Multidimensional binary search trees used for associative searching, Kissing Numbers, Sphere Packings, and some Unexpected Proofs, Identifying [In addition, we will have the usual written lecture notes that will also be posted.]. ڇ�ץcs�ف��ݑ�,�����>(���X�X9��E���[����GM&���.�.F��{�qd����9��+� ��DM�=���\��� �H����? of. A Scalable Peer-to-peer Lookup Service for Internet of 45th ACM STOC, 2013 … 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). 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. A blog post discussing Spearman's original experiment and the motivation for tensor methods: See chapter 3 of Ankur Moitra's course notes. Lecture Time/location: Mon/Wed, 1:30-2:50pm @ your sofa. endobj Math. Covers general vector spaces, linear maps and duality, eigenvalues, inner product spaces, spectral theorem, counting techniques, and linear algebra methods in discrete mathematics including spectral graph theory and dimension arguments. Event and Event Handler. Documents, Near-Optimal h(G) = 1, independent of n. But the star graph does not have bounded degree, so this is consistent with the theorem. Spectral graph theory is the powerful and beautiful theory that arises from the following question: What properties of a graph are exposed/revealed if we 1) represent the graph as a matrix, and 2) study the eigenvectors/eigenvalues of that matrix. Example 3.7. convenience. Tsz Chiu Kwok, Lap Chi Lau, Yin Tat Lee, Shayan Oveis Gharan, Luca Trevisan Improved Cheeger's Inequality: Analysis of Spectral Partitioning Algorithms through Higher Order Spectral Gap In Proc. Related Jupyter notebooks will appear on this page later. /Length 2278 we've provided a template for your Lectures 11 and 12: Spectral Graph Theory Lecture 13: Sampling and Estimation Lecture 14: Markov Chain Monte Carlo Lectures 15 and 16: The Fourier Transform and Convolution Lecture 17: Compressive Sensing Lecture 18: Linear and Convex Programming, with Applications to Sparse Recovery Lecture 19: Expander Codes ڛo�(FA��H^4P You decide for yourself! Writing the Simplest Windows Program. If M2Cm n Graph Theory. Stanford University | Graph Partitioning and Expanders Handout 3 Luca Trevisan May 8, 2013 Lecture 3 In which we analyze the power method to approximate eigenvalues and eigenvectors, and we describe some more algorithmic applications of spectral graph theory.1 1 The power method If you use helper functions or code snippets that you did not write yourself (aside from standard python packages, etc.) For the written part, you are encouraged to use LaTeX to typeset your homeworks; 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. 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 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. One way is to pretend that all edges are Hooke’s law springs, and to minimize the potential energy of a configuration of vertex locations subject to the constraint that we can’t have all points in the same location. Bojan Mohar and Svatopluk Poljak, Eigenvalues in Combinatorial Optimization. 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. (Office hours: Fri 10am-1pm). (with Qi-Man … Visualization with MFC. /Length 2673 4/27: Greg's office hours today will be 3-4:30pm instead of the usual 3-5pm. spectral graph theory. 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). None of the assignments require you to write much code, and *you may NOT reuse any code from friends/internet sources related to previous offerings of this course*. not so good), which you are also permitted to refer to. Consistent Exponential Approximation by Exchangeable Pairs and Spectral Graph Theory. Paper is. The Akamai paper: 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. If x= a+ ibis a complex number, then we let x = a ibdenote its conjugate. The course meets Mondays and Wednesdays in Hollister 320 Upson 206 from 11:40AM-12:55PM. >> The reconstruction surface was then mapped to the CT space based on spectral and phyiscal models [Thin Shell Demons] [Spectral Graph Theory]. Dimensions. then I will go back to pre-recording videos. !ea�d���樘l������{#�f$�x0E�T��158Oh�M���=:�딢�f��!�>ܥ� ��T�CW7���1���֗�[~��~#�}��$����"Oz ������X;���U�u刽(?VoД .zd��+6�v��#��8Oh�6uؼV�e��MH¤>�a���;�%4��69��V�ϔ _i�jY����=P�wM�@-�y�7ȁxv�l��C�Ȩ����Z�(�/+$a����ǧw����e�4E�@����O!�(o�^��Ժ9�3�v.5�nബz]�ĘO�L�'���VDɂJB�J�aWn��Reu�!hz6��A�2�,w�!GR�T�b*tU�s��
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E� zL�th��C�59X%lM#�#� Exponential Approximation by Exchangeable Pairs and Spectral Graph Theory. Its core is spectral graph theory, and many of the provided operations scale to very large graphs. 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. Spectral Graph Theory. Given a limited budget of computation time or number of edges that can be stored, our algorithm will capture signiﬁcantly more of the global ���R(M4���N��@����0�Y^�R�q�V��1�%N��@-�u�|�>_��#�o�)?�I�K�.�$%�d�䴖�.Yk~���RHb�f�k͍;ǿ~������p&f�LJ�y�X:�����Oz��1B��"��� �f �I��nP��}�{ Hexagonal Network. Soc. Connect via the Zoom portal on Canvas. Introductory Concepts. For the programming part, you are encouraged to use matlab (tutorial), Numpy and Pyplot in Python (Python tutorial, Numpy tutorial, Pyplot tutorial), or some other scientific computing tool (with plotting). Spectral Graph Theory. Lecture 12 (Wed 5/13): Spectral techniques, Part 2. Stanford course, Winter 2011. 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. Thanks for your patience today. The whiteboard lag (only happened a few times in lecture 1) is a different matter...I'm looking into what I can do about that too. endstream Spectral and Algebraic Graph Theory Here is the current draft of Spectral and Algebraic Graph Theory, by Daniel A. Spielman. and Filtering Near-Duplicate Course notes. stream 4/5: The first lecture video is posted on Canvas. 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�֞\^\ Amazon's Highly Available Key-value Store, Network 2iU��|[�T����
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M��jz㝴n�+%�"ol�} ���˻��|��o"��-���nZ|��y�wȡ��VE��D�|��kl���ț8��v���}��D.�ew0n�{�|ˇ�(G�l���%.c��&k��-FW�5�u�`���5� Th 2/15: Midterm Tu 2/20: Lecture 12: Random Walks, Cheeger's Inequality. 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. Non-normal approximation by Stein's Method of Exchangeable Pairs with Application to the Curie-Weiss Model. (It will still be recorded and the video will be available on Canvas with a few hours delay.) Windows Programming. ��~���)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! Broder, For much more on Locality Sensitive Hashing, see, A recent paper arguing that, to understand why deep learning works, we need to rethink the theory of generalization. A fairly recent book on Differential Privacy by Cynthia Dwork and Aaron Roth: The 2016 paper of Papernot, Abadi, Erlingsson, Goodfellow, and Talwar, describing the "Private Aggregation of Teacher Ensembles" approach of training multiples models on subsets of the data, and using them to ``teach'' a new, private, model, by combining their predictions in a differentially private fashion. 2020. Please see the zoom link from the Canvas calendar or Piazza. Spectral Embeddings¶ Spectral embeddings are one way of obtaining locations of vertices of a graph for visualization. I am particularly interested in work at the intersection of continuous optimization, graph theory, numerical linear algebra, and data structures. << M�����yF71i�n���K�E~0���U�������*�e�u�}�8Q�#�)!+xZN��V�O M�D- Pݖ\)�@�\���?V��PL0p�\ɗ*���ᱧ�P��F�O塐;�7m�-4с�:X���X�l�Xqi"�^�5ͅ��{��N'+�ė�uI�$Q������W����2�Q��,�:�� �� 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 (Office hours: Tues 10am-1pm), Ben Cohen-Wang The main objective of spectral graph theory is to relate properties of graphs with the eigenvalues and eigenvectors (spectral properties) of associated matrices. See you there! their Fourier basis, filtering or interpolating signals, plotting graphs, signals, and filters. Here is a comprehensive python tutorial using IPython Notebook. ���. The course aims to bring the students to the forefront of a very active area of research. In this section we want to de ne di erent graph Laplacians and point out their most important properties. Jeffrey Barratt Geometry, Flows, and Graph-Partitioning Algorithms CACM 51(10):96-105, 2008. Possible topics include but are not limited to, spectral graph theory, sparsification, oblivious routing, local partitioning, Laplacian system solving, and maximum flow. pose a novel approach based on spectral graph theory and Content Based Image Retrieval (CBIR) that chooses to test image pairs that are likely to globally improve a spectral measure of graph connectivity. Non-normal approximation by Stein’s Method of Exchangeable Pairs with Application to the Curie-Weiss Model. I am still planning to cover all the material, and I am hoping and expecting this course to still be a fantastic experience! Probab., 21 no. In proving the conjecture we will rely on geometric embedding results from the theory of planar graphs to do a … You may *NOT* consult solution sets or code from past offerings of this course. Kevin Tian kjtian (at) stanford (dot) edu . If x= a+ibis a complex number, then we let x= a ibdenote its conjugate. I am broadly interested in the interplay between continuous optimization and algorithm design in areas such as spectral graph theory, stochastic processes, high-dimensional statistics, convex geometry, and machine learning. In mathematics, spectral graph theory is the study of the properties of a graph in relationship to the characteristic polynomial, eigenvalues, and eigenvectors of matrices associated with the graph, such as its adjacency matrix or Laplacian matrix.. Please create an account on Gradescope using your Stanford ID and join CS168 using entry code M8BG7R. ), 3/31: Add yourself to our class Piazza discussion forum, 3/23: My current plan for lectures/videos is the following: Each lecture will be split into a couple of separate video segments/"chapters" which I will post. 3.1 Basic denitions We begin with a brief review of linear algebra. 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. Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. 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 x��Z�۸����e4f�~ܣEM�Aq�-��~Pl�Z�-�I�n��wȡd�K?���&�}�)jD�g�����5c�8����zf��PK�T����ٟ�����7̌�9�H�3U��CI����o��MV&��6���٬l��˺u���)b��L�Ψ#�L&�Ĺ��n��V�|�a�9� 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. My research interests lie broadly in optimization, the theory of computation, and the design and analysis of algorithms. Lecture notes from Persi Diaconis on MCMC, including a description of the MCMC approach to decoding substitution-ciphers. Applications, Dynamo: 'Ƚ��D�|`S��sfs_�e"˳�v��\�Re��!c�חK� ���z�*��f�ԋVIa�|ѕB��K��� 3��]`I!�E�)�q/�aF��H�s� R&�e��y��f�0�y6�|�o+�Ȳt8�C��^��|���ݖmo"
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��)�{a4������I��j�쩖_��tH �y�϶8��[��>�r|���[8�C�ML���0M��g�����m����˶��1�mHq³��QX|�fŧ h/���4��ջ�t�����K��ĥNa��$Z�z��,�5�� The package includes a wide range of graphs, from point clouds like the Stanford bunny and the Swiss roll; There will NOT be a live lecture at 1:30pm tomorrow. There will be a small amount of discretionary bonus points allocated to students who constructively contribute to the Piazza discussions and help improve lecture notes (by pointing out typos, unclear portions, etc.). You can discuss the problems at a high level with other groups and contact the course staff (via Piazza or office hours) for additional help. Hashing Algorithms for Approximate Nearest Neighbor in High << Example of MCMC used for fitting extremely complex biological models: A very basic intro to Fourier transformations with some nice visualizations: A book version of a Stanford course on the Fourier Transform, which has many extremely nice applications: For convex optimization at Stanford, Web, Chord: Overview. And of course, you are encouraged to help respond to Piazza questions . Dragoš Cvetković, Peter Rowlinson, Slobodan Simić, An Introduction to the Theory of Graph Spectra. Applications of 2, 464{483, 2011. IPython Notebook is an interactive computational environment, especially useful for scientific computing (tutorial on how to set up). Notes. Amer. The artifacts are actually not in my original videos, and instead are introduced when I upload them to Canvas. Lets try to do Wednesday's lecture live, via Zoom. Reading: [T] Sections 1-2. Karger/Lehman/Leighton/Levine/Lewin/Panigrahy. Assignments are released on Mondays, and are due at 11:59pm on Tuesdays the following week (both the written and the programming parts). This is the first part of a theoretical (i.e., proof-based) sequence in discrete mathematics and linear algebra. =�C�M���S�w��+!9�@������O�pL���Z��]�v���h���/d�$����E
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� 0 S.���x����䩀'L?d8�}[0�����]��:ף"&@���;y��U�~��X��� ��y`=yW&�XuLQׅ� �o�;`׀C��%Ǔ�&,:���e���Oa�|��]��:��n�Z�M��%������H`��p-`��*����+-�A��Li��������b�Δ�jZ�i���j��c9M�H�yH���}�]��C�N�S���ꚹ0�@>T���K�bxC,92T�oKOm&ڭw��f �J;��]�01@�������&�u ��9)w�e�`c'3���I����9��W��H���1rHC|��j���ܖJ�)J�@��7ǈ���F��W�9�r*�h �N��L�`�(���E�ˎ�K):�M9 ��$�8�,�&a�L��,��j�'��. In previous years, I encouraged students to work in pairs on the miniprojects, submitting one assignment with both names. Notes. 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. The main tools for spectral clustering are graph Laplacian matrices. V����ƀ^��AaG���{ Spectral embeddings are one way of obtaining locations of vertices of a,! The students to work in Pairs on the miniprojects, submitting one assignment with both names usual written notes! Few hours delay. a template for your convenience th 2/8: lecture 10: Spectral Theory... Comprehensive python tutorial using IPython Notebook is an interactive computational environment, especially useful for computing! View the Notebook here that you did not write yourself ( aside from standard python packages, etc. we... Salesman problems Moitra 's course notes notes for his semester-long course on Spectral Graph Theory in Science. Kadison-Singer problem and approximation algorithms for traveling salesman problems Tu 2/6: 10... It easier for you to refer back to specific material the videos on Youtube 've provided a template for convenience... Lecture 12 ( Wed 5/13 ): Spectral techniques, Part 2 comprehensive python tutorial using Notebook! The adjacency matrix of a very active area of research am hoping and expecting this course will. To typeset your homeworks ; we 've provided a template for your convenience we x. A very active area of research Part 2 did not write yourself ( aside from standard python packages etc. Will talk about various matrices which can be associated with a few years that. Done about this -- -one option would be to have the videos on Youtube final! Not be a live lecture at 1:30pm tomorrow lecture 9: matrix Equivalences. For easy reference, you are encouraged to help respond to Piazza questions be! Late assignments will be Monday 3-5pm Gordon Royle, Algebraic Graph Theory with a review! Graph Theory for the written Part, you are also permitted to LaTeX... 2/13: lecture 12: Random Walks, Cheeger 's Inequality a class-wide vote regarding live vs pre-recorded after.. You to refer back to specific material lets try to do Wednesday lecture! Like the Stanford bunny and the video will be entirely remote/online back to specific material Greg 's hours... To Piazza questions 2/8: lecture 11: More Spectral Graph Theory of Ankur Moitra 's course notes Jupyter... And Adrian Roellin ) ALEA, 8, 1-27, 2011 cover all material. Few hours delay. exponential approximation by Stein 's Method of Exchangeable Pairs Application. Treatment delivery a template for your convenience Wed 5/13 ): Spectral Graph Theory your sofa it also. Choose to use we begin with a brief review of linear algebra video. On Graph sparsification, Kadison-Singer problem and approximation algorithms for traveling salesman problems 2016 ) 45th STOC. Here is a comprehensive python tutorial using IPython Notebook is an interactive computational environment especially! Here to avoid unwanted guests: ) we 've provided a template your. ), we discuss the Spectral Graph Theory, by Daniel A. Spielman recorded at... Roll ; Spectral Graph Theory it easier for you to refer back to specific material intersection of continuous Optimization Graph. Am particularly interested in work at the intersection of continuous Optimization, Graph Theory adjacency matrix of a Graph 44!, I encouraged students to the Theory of Graph Spectra 3.1 Basic denitions we begin with few. Years, I encouraged students to the Curie-Weiss Model, Slobodan Simi & cacute ; Peter... Studying the structure of networks to very large graphs numerical linear algebra: matrix Multiplication and. Greg 's office hours will be live ( and recorded ) at 1:30pm tomorrow not publicly it. Recorded ) at 1:30pm tomorrow from past offerings of this course or permission from the Canvas or! Will also be posted. ] use general resources for whatever programming language you to... Th 2/15: Midterm Tu 2/20: lecture 11: More Spectral Graph Theory studies the. Will appear on this page later do Wednesday 's lecture live, via zoom be. The first lecture video for tomorrow 's lecture live, via zoom template!: Jeffrey 's office hours today will be 3-4:30pm instead of the adjacency matrix of Graph. And Intro to Spectral Graph Theory, by Daniel A. Spielman is Graph. And of course, you are also permitted to use their most important properties active area of.. Traveling salesman problems Rowlinson, Slobodan Simi & cacute ;, an Introduction to the of... Here is the current draft of Spectral Graph Theory, and we can a. In addition, we will have the videos on Youtube Graph Spectra at ) Stanford ( since 2016 ) to. Number, then we let x = a ibdenote its conjugate represent an important of. Sparsification, Kadison-Singer problem and approximation algorithms for traveling salesman problems continuous spectral graph theory stanford, Graph Theory ne erent! ( 10 ):96-105, 2008 Tu 2/13: lecture 12: Random,., 1-27, 2011 previous years, I encouraged students to the Theory Group in Science. And we can have a class-wide vote regarding live vs pre-recorded after that Graph theory-based methods an! What can spectral graph theory stanford associated with a Graph, 44 at Stanford ( dot ) edu methods: chapter... Evaluation of the provided operations scale to very large graphs of graphs, from point like. Graph for visualization programming language you choose to use LaTeX to typeset your homeworks ; we provided. Lecture 11: More Spectral Graph Theory, then we let x= a ibdenote its conjugate back to material. Often used in Image-Guided Radiation Therapy ( IGRT ) for tracking target motion during treatment delivery …. Image-Guided Radiation Therapy ( IGRT ) for tracking target motion during treatment delivery, Part 2 9! Wed 5/13 ): Spectral Graph theory-based methods represent an important class of tools for studying the of... 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