PPT-Lossless Dimension Expanders via Linearized Polynomials and Subspace Designs

Venkat Guruswami Nicolas Resch and Chaoping Xing Algebraic Pseudorandomness Traditional pseudorandom objects eg expander graphs randomness extractors pseudorandom generators. Ohanes. . Dadian. , Danny . Luong. , Yu Lu. Contents. 7.1 Presentation Formatting. 7.1.1 Taxonomy. 7.1.2 Examples. 7.1.3 Markup Languages. 7.2 Multimedia Data. 7.2.1 Lossless Compression Techniques. Tali Kaufman. Joint work with Irit Dinur. Codes as CSPs . A constraint satisfaction problem (CSP) is a sequence of constraints over variables:. f. 1 . (x. 1. ,x. 2. ,x. 5. ), f. 2 . (x. 5. ,x. 1. ,x. M. Soltanolkotabi E.Elhamifar E.J. Candes. 报告. 人：万晟、元玉慧. 、. 张. 驰. 昱. 信息科学与技术学院. 智. 能科学系. 1. Main Contribution. Existing work. Subspace Clustering. Tali Kaufman. Joint work with Irit Dinur. Codes as CSPs . A constraint satisfaction problem (CSP) is a sequence of constraints over variables:. f. 1 . (x. 1. ,x. 2. ,x. 5. ), f. 2 . (x. 5. ,x. 1. ,x. Normal Forms. Given . a design, how do we know it is good or not? . What is the . best. design?. Can a bad design be transformed into a good one? . Conceptual design. Schemas. ICs. Normalization. A relation is said to be in a particular normal form if it satisfies a certain set of constraints.. Zeev . Dvir. (Princeton). Shachar. Lovett (IAS). STOC 2012. Subspace evasive sets. is . (. k,c. ) subspace evasive. if for any k-dimensional linear subspace V, . Motivation. is . Yining Wang. , Yu-Xiang Wang, . Aarti. Singh. Machine Learning Department. Carnegie . mellon. university. 1. Subspace Clustering. 2. Subspace Clustering Applications. Motion Trajectories tracking. 1. Moritz . Hardt. , David P. Woodruff. IBM Research . Almaden. Two Aspects of Coping with Big Data. Efficiency. Handle. enormous inputs. Robustness. Handle . adverse conditions. Big Question: Can we have both?. René Vidal. Center for Imaging Science. Institute for Computational Medicine. Johns Hopkins University. Data segmentation and clustering. Given a set of points, separate them into multiple groups. Discriminative methods: learn boundary. René Vidal. Center for Imaging Science. Institute for Computational Medicine. Johns Hopkins University. Manifold Clustering with Applications to Computer Vision and Diffusion Imaging. René Vidal. Center for Imaging Science. Lesson Objective: NCSCOS 1.01 – Write the equivalent forms of algebraic expressions to solve problems. Students will know the terms for polynomials.. Students will know how to arrange polynomials in ascending and descending order.. Definitions. Coefficient. : the numerical factor of each term.. Constant. : the term without a variable.. Term. : a number or a product of a number and variables raised . to a power.. Polynomial. : a finite sum of terms of the form . HW ANS: Day 3 . pg. 170-171 #’s 3,9,11,15,17,19,27,29,35,37,41 . . SWBAT: Divide Polynomials using Long Division Page 13. Do by hand. Factor First. SWBAT: Divide Polynomials using Long Division . Ryan . LeFebre. Terminated Lossless Line. The ratio of voltage to current at z=0 must be Z. L. , to satisfy this waves may be reflected. Terminated Lossless Line. Total voltage on the line:. Total current on the line:.