1 1 1 1 1 1 1 1 1 1 1 1 1 1
play

1 1 1 1 1 1 1 1 1 1 1 1 1 1 Jerome F riedman T rev - PowerPoint PPT Presentation

Jul 25, 2023 •480 likes •675 views

Stanford Univ ersit y Decem b er Bo osting Stanford Univ ersit y Decem b er Bo osting Classication Problem Additiv e Logistic Regression a

  1. � � � � Stanford Univ ersit y Decem b er �� ���� Bo osting� � Stanford Univ ersit y Decem b er �� ���� Bo osting� � Classi�cation Problem Additiv e Logistic Regression a Statistical View of Bo osting 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Jerome F riedman� T rev or Hastie� Rob Tibshirani 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1 0 1 1 0 0 1 0 1 1 1 0 0 0 1 0 1 0 0 1 1 1 1 0 0 0 0 1 0 1 Stanford Univ ersit y 1 1 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0 1 1 1 0 0 1 1 0 0 0 0 0 1 0 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 0 0 1 0 1 0 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 00 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 1 1 1 1 1 0 1 0 1 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 0 1 0 0 1 0 1 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 1 1 00 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 0 1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 0 0 1 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 0 0 1 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Thanks to Bogdan P op escu for helpful and v ery liv ely 1 1 discussions on the history of b o osting� and for help in preparing that part of this talk p Data � X � Y � � R � f � � � g � X is predictor� feature� Y is class lab el� resp onse� � X � Y � ha v e join t probabilit y distribution D � Email� trevor�stat�stanford �ed u Goal� Based on N training pairs � X � Y � dra wn Ftp� stat�stanford�edu� pub�hastie i i � from D pro duce a classi�er C � X � � f � � � g WWW� http���www�stat�sta nfo rd� edu �� tre vor � Goal� c ho ose C to ha v e lo w generalization error � � R � C � � P � C � X � � � Y � D These transparencies are a v ailable via ftp� � E �� � D � ftp���stat�stanford �e du� pub �ha sti e� boo st� ��p s � � X � � � Y � C � � � �

  2. � � � � Stanford Univ ersit y Decem b er �� ���� Bo osting� � Stanford Univ ersit y Decem b er �� ���� Bo osting� � Deterministic Concepts Classi�cation T rees 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 94/200 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 x.2<-1.06711 1 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 x.2>-1.06711 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 11 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 1 0/34 72/166 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 x.2<1.14988 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 x.2>1.14988 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 40/134 0/32 x.1<1.13632 x.1>1.13632 0 1 p X � R has distribution D � 23/117 0/17 x.1<-0.900735 x.1>-0.900735 C � X � is deterministic function � concept class� 1 0 Goal� Based on N training pairs 5/26 2/91 x.1<-1.1668 x.2<-0.823968 x.1>-1.1668 x.2>-0.823968 � X � Y � C � X �� dra wn from D pro duce a i i i � 1 1 0 0 classi�er C � X � � f � � � g 0/12 5/14 2/8 0/83 x.1<-1.07831 � x.1>-1.07831 Goal� c ho ose C to ha v e lo w generalization error 1 1 � � R � C � � P � C � X � � � C � X �� 1/5 4/9 D � E �� � D � � � X � � � C � X �� C � � � �

  3. � � � � Stanford Univ ersit y Decem b er �� ���� Bo osting� � Stanford Univ ersit y Decem b er �� ���� Bo osting� � Decision Boundary� T ree Bagging and Bo osting Classi�cation trees can b e simple� but often pro duce noisy �bush y� or w eak �stun ted� classi�ers� 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 � Bagging �Breiman� ������ Fit man y large 1 0 1 1 1 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 trees to b o otstrap�resampled v ersions of the 0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 training data� and classify b y ma jorit y v ote� 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 � Bo osting �F reund � Shapire� ������ Fit man y 1 1 1 1 1 1 1 1 1 1 1 1 large or small trees to rew eigh ted v ersions of 1 1 the training data� Classify b y w eigh ted ma jorit y v ote� In general Bo osting � Bagging � Single T ree� �� TM When the nested spheres are in R � CAR T �AdaBo ost � � � b est o��the�shelf classi�er in the pro duces a rather noisy and inaccurate rule � w orld� � Leo Breiman� NIPS w orkshop� ����� C � X �� with error rates around ���� � � � �

  4. � � � � Stanford Univ ersit y Decem b er �� ���� Bo osting� � Stanford Univ ersit y Decem b er �� ���� Bo osting� � Bagging and Bo osting Final classifier sign[ Σα b f b (x)] weighted sample f B (x) weighted sample f 3 (x) f 2 (x) weighted sample �� ���� p oin ts from Nested Spheres in R � Ba y es training sample f 1 (x) error rate is ��� The w eigh ting in b o osting can b e ac hiev ed b y T rees are gro wn Best First without pruning� w eigh ted imp ortance sampling� Leftmost iteration is a single tree� � � � �

Download Presentation
Download Policy: The content available on the website is offered to you 'AS IS' for your personal information and use only. It cannot be commercialized, licensed, or distributed on other websites without prior consent from the author. To download a presentation, simply click this link. If you encounter any difficulties during the download process, it's possible that the publisher has removed the file from their server.

Recommend

CONTRACT DRAFTING PRACTICAL GUIDANCE &amp; BEST PRACTICE PRACTICE John Bennett John Bennett

CONTRACT DRAFTING PRACTICAL GUIDANCE &amp; BEST PRACTICE PRACTICE John Bennett John Bennett

1 CONTRACT DRAFTING PRACTICAL GUIDANCE &amp; BEST PRACTICE PRACTICE John Bennett John Bennett Eversheds www.mblseminars.co.uk 0161 793 0984 2 What you will learn (1) What you will learn (1) Why it is important to start with an open

542 views • 43 slides
Plannin ing Law U Update by Killian an G Garvey ey Covid-19 a and P d Plann nning i. a

Plannin ing Law U Update by Killian an G Garvey ey Covid-19 a and P d Plann nning i. a

Plannin ing Law U Update by Killian an G Garvey ey Covid-19 a and P d Plann nning i. a appea eals ls ii. p planning c commit ittees ees iii. co court w work iv. keep epin ing p permissio ions a alive v. Ne . New PD R

912 views • 66 slides
Tracking Illiquidities in Daily and Intradaily Characteristics 1 Gulten MERO 2 co-authors: Serge

Tracking Illiquidities in Daily and Intradaily Characteristics 1 Gulten MERO 2 co-authors: Serge

Introduction Our framework The estimation methodology Empirical applications Concluding remarks Tracking Illiquidities in Daily and Intradaily Characteristics 1 Gulten MERO 2 co-authors: Serge Darolles 3 and Ga elle Le Fol 4 November 25,

721 views • 34 slides
#2: Does Four Seasons really treat the rectification of pension schemes differently? James

#2: Does Four Seasons really treat the rectification of pension schemes differently? James

Follow us: @WilberforceCh The Nugee Pensions Lectures #2: Does Four Seasons really treat the rectification of pension schemes differently? James McCreath and Jonathan Chew wilberforce.co.uk How have we got here? Chartbrook v Persimmon

876 views • 19 slides
Improving Data Access Performance of Applications in IT Infrastructure Hao Wen Advisor: David

Improving Data Access Performance of Applications in IT Infrastructure Hao Wen Advisor: David

Improving Data Access Performance of Applications in IT Infrastructure Hao Wen Advisor: David Du April 24 th , 2019 Department of Computer Science and Engineering, University of Minnesota, USA C enter for R esearch in I ntelligent S torage

1.1k views • 66 slides
PADS/ML A Functional Data Description Language Yitzhak Mandelbaum Princeton University, AT&amp;T

PADS/ML A Functional Data Description Language Yitzhak Mandelbaum Princeton University, AT&amp;T

PADS/ML A Functional Data Description Language Yitzhak Mandelbaum Princeton University, AT&amp;T With: Kathleen Fisher, David Walker, Mary Fernandez, Artem Gleyzer Meet Stan Stan works for a large networking company, managing their routers.

731 views • 33 slides
Efficient Parameter Estimation for ODE Models from Relative Data Using Hierarchical

Efficient Parameter Estimation for ODE Models from Relative Data Using Hierarchical

MASAMB 2016 Efficient Parameter Estimation for ODE Models from Relative Data Using Hierarchical Optimization Sabrina Krause, Carolin Loos, Jan Hasenauer Helmholtz Zentrum Mnchen Institute of Computational Biology Data-driven

1.03k views • 43 slides
Complexity of automatic verification of cryptographic protocols Clermont Ferrand 02/02/2017

Complexity of automatic verification of cryptographic protocols Clermont Ferrand 02/02/2017

Complexity of automatic verification of cryptographic protocols Clermont Ferrand 02/02/2017 Vincent Cheval Equipe Pesto, INRIA, Nancy 1 Cryptographic protocols Communication on public network Cryptographic protocols: Concurrent programs

946 views • 69 slides
Surfaces/Meshes Well stick to triangles Working with Meshes CS 176 Winter 2011 CS 176 Winter

Surfaces/Meshes Well stick to triangles Working with Meshes CS 176 Winter 2011 CS 176 Winter

Surfaces/Meshes Well stick to triangles Working with Meshes CS 176 Winter 2011 CS 176 Winter 2011 1 2 Discrete Surfaces Whats a Mesh? Setup Formally pointers floats topology &amp; geometry abstract simplicial

532 views • 4 slides
CSSE 220 Interfaces and Polymorphism Check out Interfaces from SVN Interfaces What, When,

CSSE 220 Interfaces and Polymorphism Check out Interfaces from SVN Interfaces What, When,

CSSE 220 Interfaces and Polymorphism Check out Interfaces from SVN Interfaces What, When, Why, How? What: Code Structure used to express operations that multiple class have in common No method implementations No fields

611 views • 12 slides
Time-regularized versus framewise reconstruction (a) A = 2 . 8 cps (c) A = 5 . 7 cps (e) A = 5 . 7

Time-regularized versus framewise reconstruction (a) A = 2 . 8 cps (c) A = 5 . 7 cps (e) A = 5 . 7

Time-regularized versus framewise reconstruction (a) A = 2 . 8 cps (c) A = 5 . 7 cps (e) A = 5 . 7 cps t y x (b) A = 4 . 3 cps (d) A = 8 . 3 cps (f) A = 8 . 3 cps Tuning of scattering/regularization parameters p , 7 1 . 0 12 A = 2 . 8 cps A

401 views • 3 slides
1 Peter Series Lesson #143 September 6, 2018 Dean Bible Ministries www.deanbibleministries.org Dr.

1 Peter Series Lesson #143 September 6, 2018 Dean Bible Ministries www.deanbibleministries.org Dr.

1 Peter Series Lesson #143 September 6, 2018 Dean Bible Ministries www.deanbibleministries.org Dr. Robert L. Dean, Jr. Leading the Church: The Beginnings 1 Peter 5:14 1 Pet. 5:1, The elders who are among you I exhort, I who am a fellow

605 views • 33 slides
LECTURE 5 Advanced Functions and OOP FUNCTIONS Before we start, lets talk about how name

LECTURE 5 Advanced Functions and OOP FUNCTIONS Before we start, lets talk about how name

LECTURE 5 Advanced Functions and OOP FUNCTIONS Before we start, lets talk about how name resolution is done in Python: When a function executes, a new namespace is created (locals). New namespaces can also be created by modules, classes,

868 views • 67 slides
Curb Your Dogs Enthusiasm Kate Naito, CPDT-KA Doggie Academy SEQUENCE FOR TRAINING 1 . Mark:

Curb Your Dogs Enthusiasm Kate Naito, CPDT-KA Doggie Academy SEQUENCE FOR TRAINING 1 . Mark:

Curb Your Dogs Enthusiasm Kate Naito, CPDT-KA Doggie Academy SEQUENCE FOR TRAINING 1 . Mark: Good dog! 2. Reward 3. Release: Okay. 4. No Reward Marker (NRM): Oops! FOUR for FOUR When teaching any new behavior,

528 views • 13 slides
1 Peter Series Lesson #115 December 21, 2017 Dean Bible Ministries www.deanbibleministries.org Dr.

1 Peter Series Lesson #115 December 21, 2017 Dean Bible Ministries www.deanbibleministries.org Dr.

1 Peter Series Lesson #115 December 21, 2017 Dean Bible Ministries www.deanbibleministries.org Dr. Robert L. Dean, Jr. Christs Example of Unjust Suffering: The Power of the Resurrection 1 Peter 3:1922 What the Bible Teaches About

892 views • 30 slides
Plasma models physically consistent from kinetic scale to hydrodynamic scale Thierry Magin

Plasma models physically consistent from kinetic scale to hydrodynamic scale Thierry Magin

Plasma models physically consistent from kinetic scale to hydrodynamic scale Thierry Magin Aeronautics and Aerospace Department von Karman Institute for Fluid Dynamics, Belgium Workshop on Moment Methods in Kinetic Theory II Fields Institute,

1.08k views • 73 slides
Imp mpro roving Search rch Thro rough Effici cient A/ A/B Test sting: : A A Ca Case se

Imp mpro roving Search rch Thro rough Effici cient A/ A/B Test sting: : A A Ca Case se

Imp mpro roving Search rch Thro rough Effici cient A/ A/B Test sting: : A A Ca Case se Study Nokia Maps Place Discovery Team, Berlin: Hannes Kruppa, Steffen Bickel, Mark Waldaukat, Felix Weigel, Ross Turner, Peter Siemen Nokia

323 views • 30 slides
PROPNEX LIMITED AGM 25 April 2019 1 Disclaimer This presentation does not constitute or form

PROPNEX LIMITED AGM 25 April 2019 1 Disclaimer This presentation does not constitute or form

PROPNEX LIMITED AGM 25 April 2019 1 Disclaimer This presentation does not constitute or form part of any opinion on any advice to sell, or any solicitation of any offer to subscribe for any shares nor shall it or any part of it nor the fact of

808 views • 44 slides
Evaluation of State and Local Education Programs and Policies (84.305E) Allen Ruby Associate

Evaluation of State and Local Education Programs and Policies (84.305E) Allen Ruby Associate

Evaluation of State and Local Education Programs and Policies (84.305E) Allen Ruby Associate Commissioner Policy and Systems Division National Center for Education Research Agenda Background on the Institute of Education Sciences and its

870 views • 38 slides
DARTEP NOVEMBER 30, 2018 WAYNE STATE UNIVERSITY WELCOME DARTEP ATTENDEES Julie Sinkovitz, Chair

DARTEP NOVEMBER 30, 2018 WAYNE STATE UNIVERSITY WELCOME DARTEP ATTENDEES Julie Sinkovitz, Chair

DARTEP NOVEMBER 30, 2018 WAYNE STATE UNIVERSITY WELCOME DARTEP ATTENDEES Julie Sinkovitz, Chair of DARTEP Mike MacDonald, Vice-Chair of DARTEP DARTEP REPORTS DARTEP REPORTS Michigan Michigan Association of DARTEP Association of

663 views • 32 slides
CS6220: DATA MINING TECHNIQUES Chapter 1: Introduction Instructor: Yizhou Sun yzsun@ccs.neu.edu

CS6220: DATA MINING TECHNIQUES Chapter 1: Introduction Instructor: Yizhou Sun yzsun@ccs.neu.edu

CS6220: DATA MINING TECHNIQUES Chapter 1: Introduction Instructor: Yizhou Sun yzsun@ccs.neu.edu January 8, 2013 Course Information Class homepage: http://www.ccs.neu.edu/home/yzsun/classes/2013Spring _CS6220/index.htm Class schedule

853 views • 42 slides
Heterogeneity and the Business Cycle Advances in Macroeconomic Modelling Vincent Sterk UCL , CfM ,

Heterogeneity and the Business Cycle Advances in Macroeconomic Modelling Vincent Sterk UCL , CfM ,

Heterogeneity and the Business Cycle Advances in Macroeconomic Modelling Vincent Sterk UCL , CfM , CEPR Tinbergen Today: Challenges for Macroeconomic Modelling DNB, November 2019 Heterogeneity &amp; Business Cycle Models Since 1980s: strong

816 views • 81 slides
Volet data-centers de SILECS (A.K.A. Grid5000) Prsentation et exemples dexpriences

Volet data-centers de SILECS (A.K.A. Grid5000) Prsentation et exemples dexpriences

Volet data-centers de SILECS (A.K.A. Grid5000) Prsentation et exemples dexpriences Frdric Desprez &amp; Lucas Nussbaum Grid5000 Scientific &amp; Technical Directors Visite du comit TGIR du CNRS 2019-04-19 F. Desprez &amp;

464 views • 42 slides
Passive scalar decay in bounded and unbounded fluid flows Jacques Vanneste School of Mathematics

Passive scalar decay in bounded and unbounded fluid flows Jacques Vanneste School of Mathematics

S CALAR DECAY B OUNDED DOMAINS U NBOUNDED DOMAINS C ONCLUSIONS Passive scalar decay in bounded and unbounded fluid flows Jacques Vanneste School of Mathematics and Maxwell Institute University of Edinburgh, UK www.maths.ed.ac.uk/vanneste

373 views • 25 slides

More recommend