Outline Formulation of the . . . Out of Eden Walk . . . This Project Has . . . How Knowledge Propagates? Out of Eden Walk . . . A Fractal Model Justified Power Law Model . . . How We Compare: . . . on the Example of the Comparison Results Conclusions Out of Eden Walk Home Page Octavio Lerma 1 , 2 , Leobardo Valera 2 , Title Page Deana Pennington 2 , and Vladik Kreinovich 1 , 2 ◭◭ ◮◮ 1 Computational Science Program 2 Cyber-ShARE Center ◭ ◮ University of Texas at El Paso, El Paso, TX 79968, USA Page 1 of 15 lolerma@episd.org, leobardovalera@gmail.com, ddpennington@utep.edu, vladik@utep.edu Go Back Full Screen Close Quit
Outline Formulation of the . . . 1. Outline Out of Eden Walk . . . • Most quantitative models of knowledge propagation This Project Has . . . use a system of differential equations. Out of Eden Walk . . . Power Law Model . . . • In such models, after a certain period of time: How We Compare: . . . – the number of new people getting a certain knowl- Comparison Results edge (or acquiring a certain skill) Conclusions – decreases exponentially with time. Home Page • Experiments show that sometime, a slower “fractal” Title Page power law describes knowledge propagation better. ◭◭ ◮◮ • In this talk, we analyze which model is better. ◭ ◮ • As an example, we use responses to Out of Eden Walk Page 2 of 15 dispatches. Go Back • In this project, a Pulitzer Prize-winning journalist Paul Salopek reports from different locations. Full Screen • This example confirms the fractal model. Close Quit
Outline Formulation of the . . . 2. Formulation of the Problem Out of Eden Walk . . . • To improve teaching and learning, it is important to This Project Has . . . understand how knowledge propagates. Out of Eden Walk . . . Power Law Model . . . • Traditional knowledge propagation models are based How We Compare: . . . on diff, equations – similar to epidemics propagation. Comparison Results • In these models, for large times t , the number of new Conclusions learners decreases as r ( t ) ≈ A · exp( − α · t ). Home Page • Some empirical data suggests that this decrease follows Title Page the power law: r ( t ) ≈ A · t − α . ◭◭ ◮◮ • Power laws are ubiquitous in real life. ◭ ◮ • These laws underlie fractal techniques pioneered by Page 3 of 15 B. Mandelbrot. Go Back • In this talk, we check which model is better. Full Screen Close Quit
Outline Formulation of the . . . 3. Out of Eden Walk Project: A Description Out of Eden Walk . . . • Commenced on January 10th, 2013 in Ethiopia. This Project Has . . . Out of Eden Walk . . . • The Out of Eden Walk is a 7-year, 21,000 mile long, Power Law Model . . . storytelling journey created by Paul Salopek. How We Compare: . . . • Paul Salopek is a two-time Pulitzer Prize winning jour- Comparison Results nalist. Conclusions Home Page • This project is sponsored by the National Geographic Society. Title Page • Reports from this journey regularly appear: ◭◭ ◮◮ – in the National Geographic magazine; ◭ ◮ – in leading newspapers: NY Times, Washington Page 4 of 15 Post, Chicago Tribune, Los Angeles Times, etc.; Go Back – on the US National Public Radio (NPR). Full Screen Close Quit
Outline Formulation of the . . . 4. The Journey Starts in Ethiopia Out of Eden Walk . . . This Project Has . . . Out of Eden Walk . . . Power Law Model . . . How We Compare: . . . Comparison Results Conclusions Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 5 of 15 Go Back Full Screen Close Quit
Outline Formulation of the . . . 5. The Journey Starts in Ethiopia (cont-d) Out of Eden Walk . . . This Project Has . . . Out of Eden Walk . . . Power Law Model . . . How We Compare: . . . Comparison Results Conclusions Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 6 of 15 Go Back Full Screen Close Quit
Outline Formulation of the . . . 6. Walking Through Jerusalem Out of Eden Walk . . . This Project Has . . . Out of Eden Walk . . . Power Law Model . . . How We Compare: . . . Comparison Results Conclusions Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 7 of 15 Go Back Full Screen Close Quit
Outline Formulation of the . . . 7. It Is Not Only About Beauty of the Faraway Out of Eden Walk . . . Lands: Refugees This Project Has . . . Out of Eden Walk . . . Power Law Model . . . How We Compare: . . . Comparison Results Conclusions Home Page Title Page ◭◭ ◮◮ ◭ ◮ Page 8 of 15 Go Back Full Screen Close Quit
Outline Formulation of the . . . 8. This Project Has Important Educational and Out of Eden Walk . . . Knowledge Propagation Goals This Project Has . . . • Main objective: to enhance education and knowledge Out of Eden Walk . . . propagation as main features of journalism. Power Law Model . . . How We Compare: . . . • Main idea: slow journalism – revealing human stories Comparison Results and world events from the ground, at a walking pace. Conclusions • The project has largely succeeded in this goal: Home Page – the website has thousands of followers worldwide, Title Page – there are also many Facebook and Twitter follow- ◭◭ ◮◮ ers; ◭ ◮ – over 200 schools worldwide regularly use Salopek’s Page 9 of 15 reports to teach about world’s cultures. Go Back Full Screen Close Quit
Outline Formulation of the . . . 9. Out of Eden Walk Project: Technical Details Out of Eden Walk . . . • After visiting an area, Paul Salopek publishes a dis- This Project Has . . . patch describing his impressions and thoughts. Out of Eden Walk . . . Power Law Model . . . • As of now, there are more than 100 dispatches. How We Compare: . . . • Followers are welcome to add comments after each dis- Comparison Results patch. Conclusions Home Page • After two weeks, each dispatch gathers from 15 to more than 250 comments. Title Page • These comments are part of the knowledge propagation ◭◭ ◮◮ process. ◭ ◮ • We trace how the number of comments made by the Page 10 of 15 readers changes with time. Go Back • This number reflects how the knowledge contained in Full Screen a dispatch propagates with time. Close Quit
Outline Formulation of the . . . 10. Power Law Model vs. Traditional Approach Out of Eden Walk . . . • In the power law model, the number of comments r ( t ) This Project Has . . . decreases with t as r ( t ) = A · t − α . Out of Eden Walk . . . Power Law Model . . . • This model has two parameters: A and α > 0. How We Compare: . . . • Traditional models use differential equations: Comparison Results dr Conclusions dt = − f ( r ) . Home Page Title Page • When r = 0, we have f ( r ) = 0. ◭◭ ◮◮ • The simplest function f ( r ) with f (0) = 0 is linear: f ( r ) = α · r . ◭ ◮ • For this f ( r ), we already get a 2-parametric family of Page 11 of 15 solutions r ( t ) = A · exp( − α · t ). Go Back • So, we compare power law with this exponential model. Full Screen Close Quit
Outline Formulation of the . . . 11. How We Compare: Technical Details Out of Eden Walk . . . • How the number of comments r ( t ) depends on time t ? This Project Has . . . Out of Eden Walk . . . – exponential model: r ( t ) ≈ r 0 ( t ) = A · exp( − α · t ); Power Law Model . . . – power law model: r ( t ) ≈ r 0 ( t ) = A · t − α . How We Compare: . . . • To check which model is more adequate, we use the Comparison Results chi-square criterion Conclusions ( r ( t ) − r 0 ( t )) 2 Home Page χ 2 def � = . r 0 ( t ) Title Page t • To estimate A and α , we use both Least Squares ◭◭ ◮◮ e 2 i → min and robust ( ℓ 1 ) estimation � � | e i | → min. ◭ ◮ i i • Result: the power law is more adequate: Page 12 of 15 – for exponential model H 0 , p ≪ 0 . 05, so H 0 is re- Go Back jected; Full Screen – for power law model H 0 , p ≫ 0 . 05, so H 0 is not Close rejected. Quit
Outline Formulation of the . . . 12. Comparison Results Out of Eden Walk . . . This Project Has . . . χ 2 χ 2 χ 2 Dispatch Title N c p p p p, 1 p e p, 1 Out of Eden Walk . . . p e Let’s Walk 271 30.6 30.0 31,360 0 . 33 0 . 37 0.00 Power Law Model . . . Sole Brothers 61 22.1 22.8 83 0 . 76 0 . 74 0.00 How We Compare: . . . The Glorious Comparison Results Boneyard 59 16.3 18.6 262 0.96 0.91 0.00 Conclusions The Self-Love Home Page Boat 67 63.1 60.0 124 0.00 0.00 0.00 Title Page Go Slowly–Work ◭◭ ◮◮ Slowly 91 33.0 31.5 821 0 . 24 0 . 29 0.00 The Camel and ◭ ◮ the Gyrocopter 52 28.4 24.6 72 0 . 45 0 . 65 0.00 Page 13 of 15 Lines in Sand 69 21.4 18.3 89 0.81 0 . 92 0.00 Go Back Full Screen Close Quit
Recommend
More recommend
