PPT-Convex Independent Subsets

Problems in Ramsey theory typically ask a question of the form how many elements of some structure must there be to guarantee that a particular property will hold Here we consider geometric Ramseytype results about finite point sets in the plane. Consider all possible pairs of points in the set and consider the line segment connecting any such pair. All such line segments must lie entirely within the set.. Convex Set of Points. Convex –vs- Nonconvex. Point Set. Sandip. . Das (. sandipdas@isical.ac.in. ). Indian Statistical Institute. Convex Set. A set . C . . . . . d. is convex if for every two points . a, b . . . C, . the line segment joining . Problems in Ramsey theory typically ask a question of the form: "how many elements of some structure must there be to guarantee that a particular property will hold?“. Here we consider geometric Ramsey-type results about finite point sets in the plane.. Lenses. A . convex lens. (or a . converging lens. ) converges parallel light rays passing through it.. Various shapes of convex lenses. Terms for describing lenses. Optical centre. is the centre of a lens.. Reading Materials:. Ch. . 3.6 . of . [SG]. Contents. :. Incrementing a Binary Counter. How many subsets, Representation. Printing All Subsets Problem. Exponential Time Algorithms. Four seemingly unrelated problems. Tandy . Warnow. Topics for today. Reminder about . Examlet. on . Tuesday. My office hours next week:. Tuesday . 2-3 PM and Thursday 3-4 . PM. Office hours after next week will be based on response to poll sent . ICS 6D. Sandy . Irani. Two Different Counting Problems. Student council has 15 members. Must select officers (. Pres. , VP, Treasurer, Secretary. ). Sample selection: (Sally, Frank, Margaret, George). for Sequential Game Solving. Overview. Sequence-form transformation. Bilinear saddle-point problems. EGT/Mirror . prox. Smoothing techniques for sequential games. Sampling techniques. Some experimental results. A set is a well defined collection of objects. A collection of beanie babies. A collection of hats. An . Element (∈. ) is one of the objects in a set. A = {1, 2, 3}. 1 ∈ A. 2 ∈ A. 3 ∈ A. 4 ∉ A. http://. www.robots.ox.ac.uk. /~oval/. Slides available online http://. mpawankumar.info. Convex Sets. Convex Functions. Convex Program. Outline. Convex Set. x. 1. x. 2. λ. . x. 1. (1 - . λ. ) . machine learning. Yuchen Zhang. Stanford University. Non-convexity . in . modern machine learning. 2. State-of-the-art AI models are learnt by minimizing (often non-convex) loss functions.. T. raditional . Nicholas . Ruozzi. University of Texas at Dallas. Where We’re Going. Multivariable calculus tells us where to look for global optima, but our goal is to design algorithms that can actually find one!. Lecture 2 . Convex Set. CK Cheng. Dept. of Computer Science and Engineering. University of California, San Diego. Convex Optimization Problem:. 2. . is a convex function. For . , .  .  . Subject to. Xinyuan Wang. 01/. 17. /20. 20. 1. Contents. Affine. . and. . convex. . sets. Example. . of. . convex. . sets. Key. . properties. . of. . convex. . sets. Proper . cone, dual cone and . generalized .