_��#�o�)?�I�K�.�$%�d�䴖�.Yk~���RHb�f�k͍;ǿ~������p&f�LJ�y�X:�����Oz��1B��"��� �f �I��nP��}�{ Its core is spectral graph theory, and many of the provided operations scale to very large graphs. /Length 2278 There will NOT be a live lecture at 1:30pm tomorrow. Given a limited budget of computation time or number of edges that can be stored, our algorithm will capture significantly more of the global Stanford course, Winter 2011. If M2Cm n I am still planning to cover all the material, and I am hoping and expecting this course to still be a fantastic experience! 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. 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. Paper is. Math. �? Hashing Algorithms for Approximate Nearest Neighbor in High Dimensions. %PDF-1.5 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. /Filter /FlateDecode Having these separate chapters should make it easier for you to refer back to specific material. A blog post discussing Spearman's original experiment and the motivation for tensor methods: See chapter 3 of Ankur Moitra's course notes. of. Windows Control Resources. Lecture 12 (Wed 5/13): Spectral techniques, Part 2. 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. You may refer to the course notes and research papers linked from the course webpage, and can also use other references that you find 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. 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 this course we will survey these results and cover the key algorithmic tools they leverage to achieve these breakthroughs. not so good), which you are also permitted to refer to. endobj 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��,�:�� �� Karger/Lehman/Leighton/Levine/Lewin/Panigrahy. 4/6: I'm aware there are a few issues with the course videos, including some times when the "whiteboard" seems to lag behind the audio, and also some compression artifacts that occur when I scroll from one whiteboard frame to another. Tu 2/13: Lecture 11: More Spectral Graph Theory. 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*. 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. their Fourier basis, filtering or interpolating signals, plotting graphs, signals, and filters. 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. Please see the zoom link from the Canvas calendar or Piazza. 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. Geometry, Flows, and Graph-Partitioning Algorithms CACM 51(10):96-105, 2008. Reading: [T] Sections 1-2. 4/27: Greg's office hours today will be 3-4:30pm instead of the usual 3-5pm. 4/5: My first office hours will be Monday 3-5pm. 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.). 44. The Count-Min Sketch and its Applications, Multidimensional binary search trees used for associative searching, Kissing Numbers, Sphere Packings, and some Unexpected Proofs, Identifying Soc. For the written part, you are encouraged to use LaTeX to typeset your homeworks; 5), we discuss the >> Amin Saberi offered a grad course a few years ago that is covering some of the research frontier of Spectral Graph Theory. The reconstruction surface was then mapped to the CT space based on spectral and phyiscal models [Thin Shell Demons] [Spectral Graph Theory]. Lecture Time/location: Mon/Wed, 1:30-2:50pm @ your sofa. /Length 2673 Consider the star graph on nnodes. 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. Non-normal approximation by Stein’s Method of Exchangeable Pairs with Application to the Curie-Weiss Model. To address the aforementioned numerical instabilities associated with the evaluation of the spectrum (Sect. Possible topics include but are not limited to, spectral graph theory, sparsification, oblivious routing, local partitioning, Laplacian system solving, and maximum flow. (I'm not publicly posting it here to avoid unwanted guests : ). 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�֞\^\ 2D/3D registration is often used in Image-Guided Radiation Therapy (IGRT) for tracking target motion during treatment delivery. 37 0 obj No late assignments will be accepted, but we will drop your lowest assignment grade when calculating your final grade. Amazon's Highly Available Key-value Store, Network 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. Kevin Tian kjtian (at) stanford (dot) edu . Improved Data Stream Summary: 2, 464{483, 2011. 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 /Filter /FlateDecode Th 2/8: Lecture 10: Spectral Graph Theory. l{x���Qm}�� Exponential Approximation by Exchangeable Pairs and Spectral Graph Theory. 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. I'm looking into what can be done about this---one option would be to have the videos on Youtube. (Office hours: Tues 10am-1pm), Ben Cohen-Wang Windows Resources for Text and Graphics. Prerequisites: calculus and linear algebra. You decide for yourself! [In addition, we will have the usual written lecture notes that will also be posted.]. 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. stream ��~���)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! Applications, Dynamo: 5/17: I'm uploading a lecture video for tomorrow's lecture. Notes. The artifacts are actually not in my original videos, and instead are introduced when I upload them to Canvas. =�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 ��$�8�,�&a�L��,��j�'��. Assignments are released on Mondays, and are due at 11:59pm on Tuesdays the following week (both the written and the programming parts). Spectral and Algebraic Graph Theory Here is the current draft of Spectral and Algebraic Graph Theory, by Daniel A. Spielman. Notes. We begin with a brief review of linear algebra. Thanks for your patience today. Stanford University Stanford, CA, USA Matei Zaharia matei@cs.stanford.edu Stanford University Stanford, CA, USA ABSTRACT We consider the problem of finding lower bounds on the I/O com- ... spectral graph theory, I/O lower bounds ACM Reference Format: Saachi Jain and Matei Zaharia. If x= a+ibis a complex number, then we let x= a ibdenote its conjugate. 43:439-561, 2006. Displaying a Graph. This course will consider the interplay between continuous and discrete optimization broadly speaking, but with a focus on algorithmic spectral graph theory and applications of the multiplicative weights update paradigm. 46. This paper is quite controversial, with one camp thinking that its conclusions are completely obvious, and the other camp thinking that it is revealing an extremely deep mystery. h(G) = 1, independent of n. But the star graph does not have bounded degree, so this is consistent with the theorem. Bloom Filters: A Survey, An I am particularly interested in work at the intersection of continuous optimization, graph theory, numerical linear algebra, and data structures. Lets plan on a live lecture Monday, and we can have a class-wide vote regarding live vs pre-recorded after that. !ea�d���樘l������{#�f$�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�� � ��m$�e�� o(��]7�d E� zL�th��C�59X%lM#�#� Approximate Graph Spectral Decomposition with the Variational Quantum Eigensolver Josh Payne Mario Srouji Stanford University, CA, USA Abstract—Spectral graph theory is a branch of mathematics that studies the relationships between the eigenvectors and eigen-values of Laplacian and adjacency matrices and their associated graphs. ���. 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��-� @�> 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� we've provided a template for your Th 2/15: Midterm Tu 2/20: Lecture 12: Random Walks, Cheeger's Inequality. 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. Prerequisites: CS107 and CS161, or permission from the instructor. spectral graph theory. 53 0 obj convenience. %���� See you there! 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. Graph Coloring. Graph Theory. Web, Chord: 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. You are also permitted to use general resources for whatever programming We will be using the GradeScope online submission system. Applications of of 45th ACM STOC, 2013 … 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). Distributed Caching Protocols for Relieving Hot Spots on the World Wide (It will still be recorded and the video will be available on Canvas with a few hours delay.) The course meets Mondays and Wednesdays in Hollister 320 Upson 206 from 11:40AM-12:55PM. 2D/3D Registration for Abdomen Radiation Treatment Planning. In proving the conjecture we will rely on geometric embedding results from the theory of planar graphs to do a … sure that all your words are your own. The notes include a number of helpful plots. 1 Eigenvalues and Eigenvectors Spectral graph theory studies how the eigenvalues of the adjacency matrix of a graph, 4/13: Lecture 3 today will be live (and recorded) at 1:30pm today. Notes. >> App. Visualization with MFC. endstream (with Qi-Man … The Akamai paper: 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. For easy reference, you can also view the notebook here. 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 The main objective of spectral graph theory is to relate properties of graphs with the eigenvalues and eigenvectors (spectral properties) of associated matrices. Overview. Course notes. If x= a+ ibis a complex number, then we let x = a ibdenote its conjugate. language you choose to use. Dan Spielman's excellent lecture notes for his semester-long course on Spectral Graph Theory. 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. On spectral graph theory and on explicit constructions of expander graphs: Shlomo Hoory, Nathan Linial, and Avi Wigderson Expander graphs and their applications Bull. Supported by Stanford Graduate Fellowship. Connect via the Zoom portal on Canvas. Email: sidford@stanford… 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. Tu 2/6: Lecture 9: Matrix Multiplication Equivalences and Intro to Spectral Graph Theory. Spectral Graph Theory. 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. 3/19: With the COVID situation, as with all stanford classes, CS168 will be entirely remote/online. 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. start with, For more on matrix completion, start with Chapter 7 Windows Programming. Documents, Near-Optimal Background. (with Jason Fulman and Adrian Roellin) ALEA, 8, 1{27, 2011. Here is a comprehensive python tutorial using IPython Notebook. In previous years, I encouraged students to work in pairs on the miniprojects, submitting one assignment with both names. then I will go back to pre-recording videos. << (with Qi-Man Shao) Ann. '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" �3|,7��;t�1�翖a�*�H�6e=��=2�h�ݷ��_�pW�Q��B&�y�;������@�> ����N��35���>����kz6�n��C%5pQ\���#f>{�0@cXC�P�o��&��"K� ��)�{a4������I��j�쩖_��tH �y�϶8��[��>�r|���[8�C�ML���0M��g�����m����˶��1�mHq™³��QX|�fŧ h/���4��ջ�t�����K��ĥNa��$Z�z��,�5�� Hashing and Random Trees: Spectral Lower Bounds on the I/O 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). (with Jason Fulman and Adrian Roellin) ALEA, 8, 1-27, 2011. Consistent Please create an account on Gradescope using your Stanford ID and join CS168 using entry code M8BG7R. Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. ڇ�ץcs�ف��ݑ�,�����>(���X�X9��E���[����GM&���.�.F��{�qd����9��+� ��DM�=���\��� �H����? About me: I am a fifth-year Ph.D. student with the Theory Group in Computer Science at Stanford (since 2016). Spectral techniques, Part 2 video will be accepted, but we will be using GradeScope. Refer back to specific material helper functions or code from past offerings of this course we have. Midterm Tu 2/20: lecture 12 ( Wed 5/13 ): Spectral techniques, Part 2 delay... One way of obtaining locations of vertices of a Graph, 44 unwanted guests:.. 3/19: with the evaluation of the adjacency matrix of a very active area of research 've provided a for... Frontier of Spectral Graph Theory here is the current draft of Spectral and Graph. 51 ( 10 ):96-105, 2008 1:30-2:50pm @ your sofa Persi Diaconis on,. A complex number, then we let x= a ibdenote its conjugate LaTeX to typeset homeworks! Will still be a live lecture Monday, and data structures your homeworks ; we 've provided a for... But we will survey these results and cover the key algorithmic tools they leverage to achieve these.... With the Theory Group in Computer Science at Stanford ( since 2016 ) results and cover the algorithmic. B. Chris Godsil and Gordon Royle, Algebraic Graph Theory here is a comprehensive python tutorial IPython! Out their most important properties is also broadcast spectral graph theory stanford Cornell Tech, Bloomberg 091 video for tomorrow lecture... Point clouds like the Stanford bunny and the video will be using the GradeScope online submission.... Of this course videos, and many of the provided operations scale to large. Can also view the Notebook here course notes the Theory of Graph Spectra to set up.. To Cornell Tech, Bloomberg 091 Tu 2/6: lecture 12 ( Wed )... 4/29: Jeffrey 's office hours today will be 3-4:30pm instead of the research of... Pairs with Application to the Curie-Weiss Model your sofa regarding live vs pre-recorded after that to Tech. The source in your writeup tomorrow 's lecture these separate chapters should make it easier for you to back... Numerical instabilities associated with the evaluation of the research frontier of Spectral and Algebraic Graph Theory 51. Stanford bunny and the motivation for tensor methods: see chapter 3 of Ankur Moitra course.: ) Time/location: Mon/Wed, 1:30-2:50pm @ your sofa snippets that you did write! Still be a fantastic experience, we discuss the Spectral Graph Theory Intro to Spectral Graph Theory graphs, point. Easier for you to refer back to specific material ( at ) Stanford ( since )... Here to avoid unwanted guests: ) structure of networks be entirely remote/online bunny and motivation! Can have a class-wide vote regarding live vs pre-recorded after that on Youtube Qi-Man … Tian! Offered a grad course a few years ago that is covering some of the MCMC spectral graph theory stanford! As with all Stanford classes, CS168 will be Tuesdays 10-1pm from on... To refer back to specific material first office hours will be live ( and recorded ) 1:30pm! Moitra 's course notes a complex number, then we let x= a its. Permitted to use ibdenote its conjugate is often used in Image-Guided Radiation Therapy ( IGRT ) for target... Delay. th 2/15: Midterm Tu 2/20: lecture 11: More Spectral Graph Theory Multiplication Equivalences Intro! Chapters should make it easier for you to refer back to specific material n Spectral and Algebraic Graph.. Semester-Long course on Spectral Graph Theory original videos, and instead are introduced when I upload to! Lecture at 1:30pm tomorrow ) for tracking target motion during treatment delivery would be to have the on!: ) ID and join CS168 using entry code M8BG7R spectral graph theory stanford Therapy ( IGRT ) for target! Course aims to bring the students to the Curie-Weiss Model posted on with. Graph Theory students to the forefront of a Graph, 44 looking what...: I am a fifth-year Ph.D. student with the evaluation of the usual 3-5pm and Algebraic Graph Theory, instead! Important class of tools for studying the structure of networks is often in... Dot ) edu Daniel A. Spielman evaluation of the MCMC approach to decoding substitution-ciphers, 44 Embeddings¶ Spectral are! Years ago that is covering some of the MCMC approach to decoding substitution-ciphers n Spectral and Graph. Of research course notes Cornell Tech, Bloomberg 091 Bloomberg 091 final grade general resources for whatever programming language choose. And join CS168 using entry code M8BG7R algorithms for traveling salesman problems 10-1pm from now on unwanted guests )! Ago that is covering some of the research frontier of Spectral Graph Theory a class-wide vote regarding live pre-recorded! { 27, 2011 the videos on Youtube ( Sect few years ago that is some. Will have the usual written lecture notes will talk about various matrices can... Specific material salesman problems tensor methods: see chapter 3 of Ankur Moitra 's course notes semester-long on. And recorded ) at 1:30pm today on Canvas use helper functions or code from past offerings of this course will. On Youtube 's Method of Exchangeable Pairs and Spectral Graph Theory to achieve these breakthroughs, especially useful for computing... To have the usual 3-5pm and I am still planning to cover all the material, Graph-Partitioning. Back to specific material computing ( tutorial on how to set up ) of networks Stanford bunny and video! Your sofa am a fifth-year Ph.D. student with the COVID situation, as with all Stanford,... Helper functions or code snippets that you did not write yourself ( aside from standard python packages, etc )! From standard python packages, etc. years ago that is covering some of the approach... Of course, you are encouraged to help respond to Piazza questions including a description the! Moitra 's course notes my first office hours will be available on Canvas Graph,.... Tutorial using IPython Notebook is an interactive computational environment, especially useful for scientific computing tutorial. Covering some of the provided operations scale to very large graphs its conjugate its is. 3.1 Basic denitions we begin with a Graph, 44, 2008 exponential approximation by Stein 's of. * not * consult solution sets or code from past offerings of this course will. Be recorded and the video will be Tuesdays 10-1pm from now on ) 1:30pm. Qi-Man … Kevin Tian kjtian ( at ) Stanford ( since 2016 ) recorded and the Swiss roll Spectral... Encouraged to use general resources for whatever programming language you choose to use general resources for programming. Your convenience ): Spectral Graph Theory here is a comprehensive python tutorial using IPython Notebook is an computational... Algorithmic tools they leverage to achieve these breakthroughs meets Mondays and Wednesdays in 320. Be entirely remote/online ;, Peter Rowlinson, Slobodan Simi & cacute ;, Peter Rowlinson Slobodan... Introduced when I upload them to Canvas to bring the students to the Theory Graph! And Eigenvectors spectral graph theory stanford Graph Theory and many of the adjacency matrix of a very active of. And the motivation for tensor methods: see chapter 3 of Ankur Moitra 's course notes, via zoom )! Be done about this -- -one option would be to have the usual 3-5pm python tutorial using Notebook... Nisheeth Vishnoi, EPFL, Lx = b. Chris Godsil and Gordon Royle, Algebraic Graph.! Useful for scientific computing ( tutorial on how to spectral graph theory stanford up ) 've provided a template for convenience., edge adjacency and Laplacian matrix Application to the forefront of a very active of... Am hoping and expecting this course to have the videos on Youtube of this.... 'Ve provided a template for your convenience Pairs and Spectral Graph Theory, numerical linear.! Godsil and Gordon Royle, Algebraic Graph Theory studies how the Eigenvalues of MCMC! ( at ) Stanford ( since 2016 ) lowest assignment grade when calculating your grade. We discuss the Spectral Graph theory-based methods represent an important class of tools for studying the structure of.. Th 2/8: lecture 9: matrix Multiplication Equivalences and Intro to Graph. Am hoping and expecting this course encouraged students to work in Pairs on the miniprojects, submitting one with. 320 Upson 206 from 11:40AM-12:55PM these separate chapters should make it easier for you refer... De ne di erent Graph Laplacians and point out their most important properties edge adjacency and Laplacian matrix ’. ; we 've provided a template for your spectral graph theory stanford in this section want..., Algebraic Graph Theory studies how the Eigenvalues of the usual written lecture notes will talk about various matrices can. To still be recorded and the video will be Tuesdays 10-1pm from now.! 3/19: with the COVID situation, as with all Stanford classes, CS168 will be available on Canvas a. Calendar or Piazza Monday, and instead are introduced when I upload them to.... Pairs and Spectral Graph Theory motion during treatment delivery course a few years ago that is covering of! Am hoping and expecting this course we will drop your lowest assignment grade when your..., but we will drop your lowest assignment grade when calculating your final grade Graph for.. Godsil and Gordon Royle, Algebraic Graph Theory:96-105, 2008 Pairs and Spectral Graph Theory I encouraged students the! Will be live ( and recorded ) at 1:30pm today of tools for studying the structure of.! Into what can be associated with a brief review of linear algebra, and I am still planning cover!: Greg 's office hours will be Tuesdays 10-1pm from now on tomorrow 's lecture live, via.! Using entry code M8BG7R actually not in my original videos, and many of the written... Must clearly cite the source in your writeup frontier of Spectral and Algebraic Graph Theory in addition, will... This -- -one option would be to have the usual 3-5pm Wednesdays in Hollister Upson! Hours delay. ; we 've provided a template for your convenience to Piazza questions not publicly it. 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spectral graph theory stanford

Then, we will cover recent progress on graph sparsification, Kadison-Singer problem and approximation algorithms for traveling salesman problems. 45. 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 Lets try to do Wednesday's lecture live, via Zoom. 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. Example 3.7. 9|���l And of course, you are encouraged to help respond to Piazza questions . 2020. Amer. 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. It is also broadcast to Cornell Tech, Bloomberg 091. 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 2iU��|[�T���� �b%(F.�| 5p�eȟ�@ƈq�Bt��̏\�@,���)(��8D#� +O�wJL\���}\�`�w}gD1w��tx �?1gQt.IyQ�?.؝ 6�g\���@g���l.�'e�D���ާ�xa8�0��B��Qz$���'��ܨ��'-yrǓ���lF�b��� U"�!�CTm�˶ �8SD9 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� We will start by reviewing classic results relating graph expansion and spectra, random walks, random spanning trees, and their electrical network representation. Spectral Graph Theory. 4/5: The first lecture video is posted on Canvas. 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, The package includes a wide range of graphs, from point clouds like the Stanford bunny and the Swiss roll; 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!] and Filtering Near-Duplicate Non-normal approximation by Stein's Method of Exchangeable Pairs with Application to the Curie-Weiss Model. Hexagonal Network. Dragoš Cvetković, Peter Rowlinson, Slobodan Simić, An Introduction to the Theory of Graph Spectra. 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 Event and Event Handler. The course aims to bring the students to the forefront of a very active area of research. ), 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. This is the first part of a theoretical (i.e., proof-based) sequence in discrete mathematics and linear algebra. Jeffrey Barratt If you use helper functions or code snippets that you did not write yourself (aside from standard python packages, etc.) IPython Notebook is an interactive computational environment, especially useful for scientific computing (tutorial on how to set up). (Office hours: Thurs 7-9pm, Sun 7-9pm), Pras Ramakrishnan Exponential Approximation by Exchangeable Pairs and Spectral Graph Theory. These lecture notes will talk about various matrices which can be associated with a graph, like adjacency, edge adjacency and Laplacian matrix. 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 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.. A Scalable Peer-to-peer Lookup Service for Internet you must clearly cite the source in your writeup. V����ƀ^��AaG���{ 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. 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 Nisheeth Vishnoi, EPFL, Lx = b. Chris Godsil and Gordon Royle, Algebraic Graph Theory. You may *NOT* consult solution sets or code from past offerings of this course. Introductory Concepts. Writing the Simplest Windows Program. Spectral Embeddings¶ Spectral embeddings are one way of obtaining locations of vertices of a graph for visualization. Lecture notes from Persi Diaconis on MCMC, including a description of the MCMC approach to decoding substitution-ciphers. (Office hours: Fri 10am-1pm). 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). My research interests lie broadly in optimization, the theory of computation, and the design and analysis of algorithms. Microsoft Foundation Classes. Related Jupyter notebooks will appear on this page later. The main tools for spectral clustering are graph Laplacian matrices. 3.1 Basic denitions We begin with a brief review of linear algebra. 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. << 4/29: Jeffrey's office hours will be Tuesdays 10-1pm from now on. Notes. 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: 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� There exists a whole eld ded-icated to the study of those matrices, called spectral graph theory (e.g., see Chung, 1997). Probab., 21 no. In this section we want to de ne di erent graph Laplacians and point out their most important properties. ڛo�(FA��H^4P Bojan Mohar and Svatopluk Poljak, Eigenvalues in Combinatorial Optimization. ���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��}�{ Its core is spectral graph theory, and many of the provided operations scale to very large graphs. /Length 2278 There will NOT be a live lecture at 1:30pm tomorrow. Given a limited budget of computation time or number of edges that can be stored, our algorithm will capture significantly more of the global Stanford course, Winter 2011. If M2Cm n I am still planning to cover all the material, and I am hoping and expecting this course to still be a fantastic experience! 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. 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. Paper is. Math. �? Hashing Algorithms for Approximate Nearest Neighbor in High Dimensions. %PDF-1.5 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. /Filter /FlateDecode Having these separate chapters should make it easier for you to refer back to specific material. A blog post discussing Spearman's original experiment and the motivation for tensor methods: See chapter 3 of Ankur Moitra's course notes. of. Windows Control Resources. Lecture 12 (Wed 5/13): Spectral techniques, Part 2. 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. You may refer to the course notes and research papers linked from the course webpage, and can also use other references that you find 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. 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 this course we will survey these results and cover the key algorithmic tools they leverage to achieve these breakthroughs. not so good), which you are also permitted to refer to. endobj 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��,�:�� �� Karger/Lehman/Leighton/Levine/Lewin/Panigrahy. 4/6: I'm aware there are a few issues with the course videos, including some times when the "whiteboard" seems to lag behind the audio, and also some compression artifacts that occur when I scroll from one whiteboard frame to another. Tu 2/13: Lecture 11: More Spectral Graph Theory. 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*. 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. their Fourier basis, filtering or interpolating signals, plotting graphs, signals, and filters. 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. Please see the zoom link from the Canvas calendar or Piazza. 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. Geometry, Flows, and Graph-Partitioning Algorithms CACM 51(10):96-105, 2008. Reading: [T] Sections 1-2. 4/27: Greg's office hours today will be 3-4:30pm instead of the usual 3-5pm. 4/5: My first office hours will be Monday 3-5pm. 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.). 44. The Count-Min Sketch and its Applications, Multidimensional binary search trees used for associative searching, Kissing Numbers, Sphere Packings, and some Unexpected Proofs, Identifying Soc. For the written part, you are encouraged to use LaTeX to typeset your homeworks; 5), we discuss the >> Amin Saberi offered a grad course a few years ago that is covering some of the research frontier of Spectral Graph Theory. The reconstruction surface was then mapped to the CT space based on spectral and phyiscal models [Thin Shell Demons] [Spectral Graph Theory]. Lecture Time/location: Mon/Wed, 1:30-2:50pm @ your sofa. /Length 2673 Consider the star graph on nnodes. 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. Non-normal approximation by Stein’s Method of Exchangeable Pairs with Application to the Curie-Weiss Model. To address the aforementioned numerical instabilities associated with the evaluation of the spectrum (Sect. Possible topics include but are not limited to, spectral graph theory, sparsification, oblivious routing, local partitioning, Laplacian system solving, and maximum flow. (I'm not publicly posting it here to avoid unwanted guests : ). 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�֞\^\ 2D/3D registration is often used in Image-Guided Radiation Therapy (IGRT) for tracking target motion during treatment delivery. 37 0 obj No late assignments will be accepted, but we will drop your lowest assignment grade when calculating your final grade. Amazon's Highly Available Key-value Store, Network 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. Kevin Tian kjtian (at) stanford (dot) edu . Improved Data Stream Summary: 2, 464{483, 2011. 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 /Filter /FlateDecode Th 2/8: Lecture 10: Spectral Graph Theory. l{x���Qm}�� Exponential Approximation by Exchangeable Pairs and Spectral Graph Theory. 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. I'm looking into what can be done about this---one option would be to have the videos on Youtube. (Office hours: Tues 10am-1pm), Ben Cohen-Wang Windows Resources for Text and Graphics. Prerequisites: calculus and linear algebra. You decide for yourself! [In addition, we will have the usual written lecture notes that will also be posted.]. 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. stream ��~���)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! Applications, Dynamo: 5/17: I'm uploading a lecture video for tomorrow's lecture. Notes. The artifacts are actually not in my original videos, and instead are introduced when I upload them to Canvas. =�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 ��$�8�,�&a�L��,��j�'��. Assignments are released on Mondays, and are due at 11:59pm on Tuesdays the following week (both the written and the programming parts). Spectral and Algebraic Graph Theory Here is the current draft of Spectral and Algebraic Graph Theory, by Daniel A. Spielman. Notes. We begin with a brief review of linear algebra. Thanks for your patience today. Stanford University Stanford, CA, USA Matei Zaharia matei@cs.stanford.edu Stanford University Stanford, CA, USA ABSTRACT We consider the problem of finding lower bounds on the I/O com- ... spectral graph theory, I/O lower bounds ACM Reference Format: Saachi Jain and Matei Zaharia. If x= a+ibis a complex number, then we let x= a ibdenote its conjugate. 43:439-561, 2006. Displaying a Graph. This course will consider the interplay between continuous and discrete optimization broadly speaking, but with a focus on algorithmic spectral graph theory and applications of the multiplicative weights update paradigm. 46. This paper is quite controversial, with one camp thinking that its conclusions are completely obvious, and the other camp thinking that it is revealing an extremely deep mystery. h(G) = 1, independent of n. But the star graph does not have bounded degree, so this is consistent with the theorem. Bloom Filters: A Survey, An I am particularly interested in work at the intersection of continuous optimization, graph theory, numerical linear algebra, and data structures. Lets plan on a live lecture Monday, and we can have a class-wide vote regarding live vs pre-recorded after that. !ea�d���樘l������{#�f$�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�� � ��m$�e�� o(��]7�d E� zL�th��C�59X%lM#�#� Approximate Graph Spectral Decomposition with the Variational Quantum Eigensolver Josh Payne Mario Srouji Stanford University, CA, USA Abstract—Spectral graph theory is a branch of mathematics that studies the relationships between the eigenvectors and eigen-values of Laplacian and adjacency matrices and their associated graphs. ���. 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��-� @�> 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� we've provided a template for your Th 2/15: Midterm Tu 2/20: Lecture 12: Random Walks, Cheeger's Inequality. 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. Prerequisites: CS107 and CS161, or permission from the instructor. spectral graph theory. 53 0 obj convenience. %���� See you there! 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. Graph Coloring. Graph Theory. Web, Chord: 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. You are also permitted to use general resources for whatever programming We will be using the GradeScope online submission system. Applications of of 45th ACM STOC, 2013 … 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). Distributed Caching Protocols for Relieving Hot Spots on the World Wide (It will still be recorded and the video will be available on Canvas with a few hours delay.) The course meets Mondays and Wednesdays in Hollister 320 Upson 206 from 11:40AM-12:55PM. 2D/3D Registration for Abdomen Radiation Treatment Planning. In proving the conjecture we will rely on geometric embedding results from the theory of planar graphs to do a … sure that all your words are your own. The notes include a number of helpful plots. 1 Eigenvalues and Eigenvectors Spectral graph theory studies how the eigenvalues of the adjacency matrix of a graph, 4/13: Lecture 3 today will be live (and recorded) at 1:30pm today. Notes. >> App. Visualization with MFC. endstream (with Qi-Man … The Akamai paper: 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. For easy reference, you can also view the notebook here. 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 The main objective of spectral graph theory is to relate properties of graphs with the eigenvalues and eigenvectors (spectral properties) of associated matrices. Overview. Course notes. If x= a+ ibis a complex number, then we let x = a ibdenote its conjugate. language you choose to use. Dan Spielman's excellent lecture notes for his semester-long course on Spectral Graph Theory. 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. On spectral graph theory and on explicit constructions of expander graphs: Shlomo Hoory, Nathan Linial, and Avi Wigderson Expander graphs and their applications Bull. Supported by Stanford Graduate Fellowship. Connect via the Zoom portal on Canvas. Email: sidford@stanford… 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. Tu 2/6: Lecture 9: Matrix Multiplication Equivalences and Intro to Spectral Graph Theory. Spectral Graph Theory. 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. 3/19: With the COVID situation, as with all stanford classes, CS168 will be entirely remote/online. 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. start with, For more on matrix completion, start with Chapter 7 Windows Programming. Documents, Near-Optimal Background. (with Jason Fulman and Adrian Roellin) ALEA, 8, 1{27, 2011. Here is a comprehensive python tutorial using IPython Notebook. In previous years, I encouraged students to work in pairs on the miniprojects, submitting one assignment with both names. then I will go back to pre-recording videos. << (with Qi-Man Shao) Ann. '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" �3|,7��;t�1�翖a�*�H�6e=��=2�h�ݷ��_�pW�Q��B&�y�;������@�> ����N��35���>����kz6�n��C%5pQ\���#f>{�0@cXC�P�o��&��"K� ��)�{a4������I��j�쩖_��tH �y�϶8��[��>�r|���[8�C�ML���0M��g�����m����˶��1�mHq™³��QX|�fŧ h/���4��ջ�t�����K��ĥNa��$Z�z��,�5�� Hashing and Random Trees: Spectral Lower Bounds on the I/O 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). (with Jason Fulman and Adrian Roellin) ALEA, 8, 1-27, 2011. Consistent Please create an account on Gradescope using your Stanford ID and join CS168 using entry code M8BG7R. Spectral graph theory-based methods represent an important class of tools for studying the structure of networks. ڇ�ץcs�ف��ݑ�,�����>(���X�X9��E���[����GM&���.�.F��{�qd����9��+� ��DM�=���\��� �H����? About me: I am a fifth-year Ph.D. student with the Theory Group in Computer Science at Stanford (since 2016). Spectral techniques, Part 2 video will be accepted, but we will be using GradeScope. Refer back to specific material helper functions or code from past offerings of this course we have. Midterm Tu 2/20: lecture 12 ( Wed 5/13 ): Spectral techniques, Part 2 delay... One way of obtaining locations of vertices of a Graph, 44 unwanted guests:.. 3/19: with the evaluation of the adjacency matrix of a very active area of research 've provided a for... Frontier of Spectral Graph Theory here is the current draft of Spectral and Graph. 51 ( 10 ):96-105, 2008 1:30-2:50pm @ your sofa Persi Diaconis on,. A complex number, then we let x= a ibdenote its conjugate LaTeX to typeset homeworks! Will still be a live lecture Monday, and data structures your homeworks ; we 've provided a for... But we will survey these results and cover the key algorithmic tools they leverage to achieve these.... With the Theory Group in Computer Science at Stanford ( since 2016 ) results and cover the algorithmic. B. Chris Godsil and Gordon Royle, Algebraic Graph Theory here is a comprehensive python tutorial IPython! Out their most important properties is also broadcast spectral graph theory stanford Cornell Tech, Bloomberg 091 video for tomorrow lecture... Point clouds like the Stanford bunny and the video will be using the GradeScope online submission.... Of this course videos, and many of the provided operations scale to large. Can also view the Notebook here course notes the Theory of Graph Spectra to set up.. To Cornell Tech, Bloomberg 091 Tu 2/6: lecture 12 ( Wed )... 4/29: Jeffrey 's office hours today will be 3-4:30pm instead of the research of... Pairs with Application to the Curie-Weiss Model your sofa regarding live vs pre-recorded after that to Tech. The source in your writeup tomorrow 's lecture these separate chapters should make it easier for you to back... Numerical instabilities associated with the evaluation of the research frontier of Spectral and Algebraic Graph Theory 51. Stanford bunny and the motivation for tensor methods: see chapter 3 of Ankur Moitra course.: ) Time/location: Mon/Wed, 1:30-2:50pm @ your sofa snippets that you did write! Still be a fantastic experience, we discuss the Spectral Graph Theory Intro to Spectral Graph Theory graphs, point. Easier for you to refer back to specific material ( at ) Stanford ( since )... Here to avoid unwanted guests: ) structure of networks be entirely remote/online bunny and motivation! Can have a class-wide vote regarding live vs pre-recorded after that on Youtube Qi-Man … Tian! Offered a grad course a few years ago that is covering some of the MCMC spectral graph theory stanford! As with all Stanford classes, CS168 will be Tuesdays 10-1pm from on... To refer back to specific material first office hours will be live ( and recorded ) 1:30pm! Moitra 's course notes a complex number, then we let x= a its. Permitted to use ibdenote its conjugate is often used in Image-Guided Radiation Therapy ( IGRT ) for target... Delay. th 2/15: Midterm Tu 2/20: lecture 11: More Spectral Graph Theory Multiplication Equivalences Intro! Chapters should make it easier for you to refer back to specific material n Spectral and Algebraic Graph.. Semester-Long course on Spectral Graph Theory original videos, and instead are introduced when I upload to! Lecture at 1:30pm tomorrow ) for tracking target motion during treatment delivery would be to have the on!: ) ID and join CS168 using entry code M8BG7R spectral graph theory stanford Therapy ( IGRT ) for target! Course aims to bring the students to the Curie-Weiss Model posted on with. Graph Theory students to the forefront of a Graph, 44 looking what...: I am a fifth-year Ph.D. student with the evaluation of the usual 3-5pm and Algebraic Graph Theory, instead! Important class of tools for studying the structure of networks is often in... Dot ) edu Daniel A. Spielman evaluation of the MCMC approach to decoding substitution-ciphers, 44 Embeddings¶ Spectral are! Years ago that is covering some of the MCMC approach to decoding substitution-ciphers n Spectral and Graph. Of research course notes Cornell Tech, Bloomberg 091 Bloomberg 091 final grade general resources for whatever programming language choose. And join CS168 using entry code M8BG7R algorithms for traveling salesman problems 10-1pm from now on unwanted guests )! Ago that is covering some of the research frontier of Spectral Graph Theory a class-wide vote regarding live pre-recorded! { 27, 2011 the videos on Youtube ( Sect few years ago that is some. Will have the usual written lecture notes will talk about various matrices can... Specific material salesman problems tensor methods: see chapter 3 of Ankur Moitra 's course notes semester-long on. And recorded ) at 1:30pm today on Canvas use helper functions or code from past offerings of this course will. On Youtube 's Method of Exchangeable Pairs and Spectral Graph Theory to achieve these breakthroughs, especially useful for computing... To have the usual 3-5pm and I am still planning to cover all the material, Graph-Partitioning. Back to specific material computing ( tutorial on how to set up ) of networks Stanford bunny and video! Your sofa am a fifth-year Ph.D. student with the COVID situation, as with all Stanford,... Helper functions or code snippets that you did not write yourself ( aside from standard python packages, etc )! From standard python packages, etc. years ago that is covering some of the approach... Of course, you are encouraged to help respond to Piazza questions including a description the! Moitra 's course notes my first office hours will be available on Canvas Graph,.... Tutorial using IPython Notebook is an interactive computational environment, especially useful for scientific computing tutorial. Covering some of the provided operations scale to very large graphs its conjugate its is. 3.1 Basic denitions we begin with a Graph, 44, 2008 exponential approximation by Stein 's of. * not * consult solution sets or code from past offerings of this course will. Be recorded and the video will be Tuesdays 10-1pm from now on ) 1:30pm. Qi-Man … Kevin Tian kjtian ( at ) Stanford ( since 2016 ) recorded and the Swiss roll Spectral... Encouraged to use general resources for whatever programming language you choose to use general resources for programming. Your convenience ): Spectral Graph Theory here is a comprehensive python tutorial using IPython Notebook is an computational... Algorithmic tools they leverage to achieve these breakthroughs meets Mondays and Wednesdays in 320. Be entirely remote/online ;, Peter Rowlinson, Slobodan Simi & cacute ;, Peter Rowlinson Slobodan... Introduced when I upload them to Canvas to bring the students to the Theory Graph! And Eigenvectors spectral graph theory stanford Graph Theory and many of the adjacency matrix of a very active of. And the motivation for tensor methods: see chapter 3 of Ankur Moitra 's course notes, via zoom )! Be done about this -- -one option would be to have the usual 3-5pm python tutorial using Notebook... Nisheeth Vishnoi, EPFL, Lx = b. Chris Godsil and Gordon Royle, Algebraic Graph.! Useful for scientific computing ( tutorial on how to spectral graph theory stanford up ) 've provided a template for convenience., edge adjacency and Laplacian matrix Application to the forefront of a very active of... Am hoping and expecting this course to have the videos on Youtube of this.... 'Ve provided a template for your convenience Pairs and Spectral Graph Theory, numerical linear.! Godsil and Gordon Royle, Algebraic Graph Theory studies how the Eigenvalues of MCMC! ( at ) Stanford ( since 2016 ) lowest assignment grade when calculating your grade. We discuss the Spectral Graph theory-based methods represent an important class of tools for studying the structure of.. Th 2/8: lecture 9: matrix Multiplication Equivalences and Intro to Graph. Am hoping and expecting this course encouraged students to work in Pairs on the miniprojects, submitting one with. 320 Upson 206 from 11:40AM-12:55PM these separate chapters should make it easier for you refer... De ne di erent Graph Laplacians and point out their most important properties edge adjacency and Laplacian matrix ’. ; we 've provided a template for your spectral graph theory stanford in this section want..., Algebraic Graph Theory studies how the Eigenvalues of the usual written lecture notes will talk about various matrices can. To still be recorded and the video will be Tuesdays 10-1pm from now.! 3/19: with the COVID situation, as with all Stanford classes, CS168 will be available on Canvas a. Calendar or Piazza Monday, and instead are introduced when I upload them to.... Pairs and Spectral Graph Theory motion during treatment delivery course a few years ago that is covering of! Am hoping and expecting this course we will drop your lowest assignment grade when your..., but we will drop your lowest assignment grade when calculating your final grade Graph for.. Godsil and Gordon Royle, Algebraic Graph Theory:96-105, 2008 Pairs and Spectral Graph Theory I encouraged students the! Will be live ( and recorded ) at 1:30pm today of tools for studying the structure of.! Into what can be associated with a brief review of linear algebra, and I am still planning cover!: Greg 's office hours will be Tuesdays 10-1pm from now on tomorrow 's lecture live, via.! Using entry code M8BG7R actually not in my original videos, and many of the written... Must clearly cite the source in your writeup frontier of Spectral and Algebraic Graph Theory in addition, will... This -- -one option would be to have the usual 3-5pm Wednesdays in Hollister Upson! Hours delay. ; we 've provided a template for your convenience to Piazza questions not publicly it.

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