PPT-Sketching and Embedding

are Equivalent for Norms Alexandr Andoni Simons Inst Columbia Robert Krauthgamer Weizmann Inst Ilya Razenshteyn MIT now at IBM Almaden 1 Sketching n d When is sketching possible. 3D . printer. Jacob . Bayless. Mo Chen. Bing Dai. Outline. Introduction to the . Replicating Rapid . Prototyper. . (. RepRap. ). Project goals and motivation. RepRap. Details. Our contribution:. Wire embedding module. Non-normed spaces. Alexandr. . Andoni. (MSR). Embedding / Sketching. Definition. : an embedding . is a map . f:M. . H. . of a metric . (M, . d. M. ). into a host metric . (H, . . H. ). such that for any . Alexandr. . Andoni. (MSR). Definition by example. Problem. : Compute the diameter of a set . S. , of size . n. , living in . d. -dimensional . ℓ. 1. d. Trivial solution: . O(d * n. 2. ) . time. Will see solution in . Alexandr. . Andoni. . (Simons Institute). Robert . Krauthgamer. . (. Weizmann. . Institute). Ilya Razenshteyn . (CSAIL MIT). 1. Sketching. Compress a massive object to a . small. . sketch. Rich theories: . Sublinear. Algorithms:. Euclidean space: . dimension reduction and NNS. Alex Andoni. (MSR SVC). A Sketching Problem. 2. Sketching:. :objects . short bit-strings. given . . and . . should be able to deduce if . Purposes of Sketching. Think through a design. Convey your ideas. Uses lines and symbols to describe a design. Common Uses of Sketching . Brainstorm. Communicate. Document Measurements. Advantages of Sketching. Sketching. for streaming. Alexandr. . Andoni. (MSR). Application: Streaming. IP. Frequency. 131.107.65.14. 3. 18.0.1.12. 2. 80.97.56.20. 2. 131.107.65.14. 131.107.65.14. 131.107.65.14. 18.0.1.12. 18.0.1.12. © 2012 Project Lead The Way, Inc.. Introduction to Engineering Design. Sketching an Isometric Circle. Circular features and cylindrical forms are common in engineering designs, and appear as . ellipses. Explain the importance of sketching in the engineering design process. Make simple sketches of basic shapes such as lines, circles, and ellipses. Use 3-D coordinate systems, particularly right-handed systems. Design and Modeling. Common Uses of Sketching . Brainstorm. Communicate. Document. Advantages of Hand Sketching. Convenient. Inexpensive. Sketching Techniques. Lines. Vertical Line. Horizontal Line. English II. What is embedding? . Embedding involves selecting only the most important words in your text evidence. In other words, you will never use an entire sentence from the text verbatim (that means word-for- word). . © 2012 Project Lead The Way, Inc.. Introduction to Engineering Design. Sketching an Isometric Circle. Circular features and cylindrical forms are common in engineering designs, and appear as . ellipses. by: R. Yang. ,. . J. Shi. ,. . X. Xiao. ,. . Y. Yang. ,. . J. Liu. ,. . and . S. . Bhowmick. Basic data analytics is easy.. Stock. Profit. Revenue. Market share. Overvalued?. Buy?. TSLA. $721m. $31B. Robert Krauthgamer, . Weizmann Institute of Science. Bertinoro. . workshop, May . 2014. Joint work with . Alexandr. . Andoni. and David Woodruff. TexPoint. fonts used in EMF. . Read the . TexPoint.