PPT-Lecture 6: Creating a simplicial complex from data

in a series of preparatory lectures for the Fall 2013 online course MATH7450 22M305 Topics in Topology Scientific and Engineering Applications of Algebraic Topology Target Audience Anyone interested in . MATTHEW KAHLE & ELIZABETH MECKE. Presented by Ariel Szapiro. INTRODUCTION : . betti. numbers. Informally, the . k. th. Betti number refers to the number of unconnected . k. -dimensional surfaces. The first few Betti numbers have the following intuitive definitions:. Arvind . Computer Science & Artificial Intelligence Lab. Massachusetts Institute of Technology. February 21, 2012. L04-. 1. http://csg.csail.mit.edu/6.S078. Combinational IFFT. in0. …. in1. in2. Step 0.) Start by adding 0-dimensional vertices . (0-simplices). Creating a simplicial complex. 1. .) . A. dding . 1. -dimensional edges (1-simplices). Add an edge between data points that are “close”. (and cell complexes). . in a series of preparatory lectures for the Fall 2013 online course MATH:7450 (22M:305) Topics in Topology: Scientific and Engineering Applications of Algebraic Topology. Target Audience: Anyone interested in . Applications I. ©2008 I.K. Darcy. All rights reserved. This work was partially supported by  the Joint DMS/NIGMS Initiative to Support Research in the Area of Mathematical Biology (NSF 0800285).. Isabel K. Darcy. MATTHEW KAHLE & ELIZABETH MECKE. Presented by Ariel Szapiro. INTRODUCTION : . betti. numbers. Informally, the . k. th. Betti number refers to the number of unconnected . k. -dimensional surfaces. The first few Betti numbers have the following intuitive definitions:. Station 4. Directions: Each slide will present a sentence. . Write the sentence on your paper.. Identify if the sentence is complex or compound-complex.. After EVERYONE in the group has written the sentence & made a selection, check your answer by pressing the space bar.. complex = CW . complex. Building block: n-cells = { x in . R. n. : || x || ≤ 1 } . 2-cell = open disk = { x in R. 2. : ||x || < 1 }. Examples: . 0-cell = { x in R. 0. : ||x || < 1 }. Applications II. This work was partially supported by  the Joint DMS/NIGMS Initiative to Support Research in the Area of Mathematical Biology (NSF 0800285).. Isabel K. Darcy. Mathematics Department . .. . Once a student knows the difference between the three sentence types (simple, compound, and complex), it is possible to write with sentence variety. Sentence variety helps make your writing more interesting.. MATTHEW KAHLE & ELIZABETH MECKE. Presented by Ariel Szapiro. INTRODUCTION : . betti. numbers. Informally, the . k. th. Betti number refers to the number of unconnected . k. -dimensional surfaces. The first few Betti numbers have the following intuitive definitions:. Starting up the Program. 2. Creating a Data Visualization . Using Tableau Public. Try 1. Creating a Data Visualization . Using Tableau Public. 3. Open Data. Creating a Data Visualization . Using Tableau Public. Sept 4, 2013. Clustering Via Persistent Homology. Creating a simplicial complex. Step 0.) Start by adding 0-dimensional vertices . (0-simplices). Creating a simplicial complex. 1. .) . A. dding . 1. How can coaching strategies help us to solve student problems?. Creating a Coaching Culture. 1. Outline and objectives of session. To share our current experiences of student support in this and other schools..