exact reasoning
play

Exact Reasoning: AND/OR Search and Hybrids COMPSCI 276, Fall 2009 - PowerPoint PPT Presentation

Nov 03, 2022 •305 likes •772 views

Exact Reasoning: AND/OR Search and Hybrids COMPSCI 276, Fall 2009 Set 8, Rina dechter Approximation Techniques bounded inference COMPSCI 276, Fall 2009 Set 6: Rina Dechter eading: Primary: Class Notes (7) econdary: , Darwiche chapters 14)

  1. Exact Reasoning: AND/OR Search and Hybrids COMPSCI 276, Fall 2009 Set 8, Rina dechter

  2. Approximation Techniques bounded inference COMPSCI 276, Fall 2009 Set 6: Rina Dechter eading: Primary: Class Notes (7) econdary: , Darwiche chapters 14)

  3. Probabilistic Inference Tasks  Belief updating:   BEL(X ) P(X x | evidence) i i i  Finding most probable explanation (MPE)  x * arg max P( x , e) x  Finding maximum a-posteriory hypothesis A   : X  * * (a ,..., a ) arg max P( x , e) 1 k hypothesis variables a X/A  Finding maximum-expected-utility (MEU) decision D   : X decision variables  * * (d ,..., d ) arg max P( x , e) U( x ) 1 k ( ) : U x utility function d X/D CS 276 3

  4. Belief Updating Smoking Bronchitis lung Cancer X-ray Dyspnoea P (lung cancer=yes | smoking=no, dyspnoea=yes ) = ? CS 276 4

  5. Conditioning generates the probability tree       ( , 0 ) ( ) ( | ) ( | ) ( | , ) ( | , ) P a e P a P b a P c a P d a b P e b c  b c b e 0 Complexity of conditioning: exponential time, linear space CS 276 5

  6. Conditioning+Elimination       ( , 0 ) ( ) ( | ) ( | ) ( | , ) ( | , ) P a e P a P b a P c a P d a b P e b c  0 b c d e Idea: conditioning until of a (sub)problem gets small * w CS 276 6

  7. Loop-cutset decomposition  You condition until you get a polytree A=1 A=0 A A=0 A=0 A=1 A=1 A=0 A=1 C B C B C B B B B F F F P(B|F=0) = P(B, A=0|F=0)+P(B,A=1|F=0) Loop-cutset method is time exp in loop-cutset size And linear space CS 276 7

  8. OR search space A F Ordering: A B E C D F B C E D A 0 1 B 0 1 0 1 E 0 1 0 1 0 1 0 1 C 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 D 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 F 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 CS 276 8

  9. AND/OR search space A A A A F F F B B B C C B C E C E E D D E D D F Primal graph DFS tree OR A AND 0 1 OR B B AND 0 1 0 1 OR E C E C E C E C AND 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 OR D F D F D F D F D F D F D F D F AND 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 CS 276 9

  10. A A F B B C OR vs AND/OR E C E D D F OR A AND 0 1 AND/OR OR B B AND 0 1 0 1 OR E C E C E C E C AND 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 OR D F D F D F D F D F D F D F D F AND 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 A A 0 0 0 1 1 OR B B 0 0 1 1 1 0 0 1 1 E E 0 0 1 1 0 0 1 1 1 0 0 1 1 0 0 1 1 C C 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 D D 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 F F 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 CS 276 10

  11. A A F B AND/OR vs. OR B C E C E D D F OR A AND 0 1 AND/OR OR B B AND 0 1 0 1 OR E C E C E C E C AND 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 OR D F D F D F D F D F D F D F D F AND 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 AND/OR size: exp(4), OR size exp(6) A A A 0 0 0 1 1 1 OR B B B 0 0 0 1 1 1 0 0 0 1 1 1 E E E 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 C C C 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 D D D 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 CS 276 11 F F F 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

  12. No-goods A A (A=1,B=1) F B (B=0,C=0) B C E C AND/OR vs. OR E D D F OR A AND 0 1 AND/OR OR B B AND 0 1 0 1 OR E C E C E C E C AND 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 OR D F D F D F D F D F D F D F D F AND 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 A A A 0 0 0 1 1 1 OR B B B 0 0 0 1 1 1 0 0 0 1 1 1 E E E 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 C C C 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 D D D 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 CS 276 12 F F F 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

  13. (A=1,B=1) A A (B=0,C=0) F B B C E C AND/OR vs. OR E D D F OR A AND 0 1 AND/OR OR B B AND 0 1 0 OR E C E C E C AND 0 1 1 0 1 0 1 0 1 1 OR D F D F D F D F AND 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 A A A 0 0 0 1 1 1 OR B B B 0 0 0 1 1 1 0 0 0 E E E 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 C C C 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 1 D D D 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 CS 276 13 F F F 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1

  14. OR space vs. AND/OR space OR space AND/OR space width height time(sec.) nodes backtracks time(sec.) AND nodes OR nodes 5 10 3.154 2,097,150 1,048,575 0.03 10,494 5,247 4 9 3.135 2,097,150 1,048,575 0.01 5,102 2,551 5 10 3.124 2,097,150 1,048,575 0.03 8,926 4,463 4 10 3.125 2,097,150 1,048,575 0.02 7,806 3,903 5 13 3.104 2,097,150 1,048,575 0.1 36,510 18,255 5 10 3.125 2,097,150 1,048,575 0.02 8,254 4,127 6 9 3.124 2,097,150 1,048,575 0.02 6,318 3,159 5 10 3.125 2,097,150 1,048,575 0.02 7,134 3,567 5 13 3.114 2,097,150 1,048,575 0.121 37,374 18,687 5 10 3.114 2,097,150 1,048,575 0.02 7,326 3,663 CS 276 14

  15. AND/OR search tree for graphical models The AND/OR search tree of R relative to a spanning-tree, T, has:  Alternating levels of: OR nodes (variables) and AND nodes (values)  Successor function: A  The successors of OR nodes X are all its consistent values along its path F  The successors of AND <X,v> are all X child variables in T B C  E D A solution is a consistent subtree  Task: compute the value of the root node  A B E C OR A D F AND 0 1 OR B B AND 0 1 0 1 OR E C E C E C E C AND 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 OR D F D F D F D F D F D F D F D F AND 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 CS 276 15

  16. From DFS trees to pseudo-trees (Freuder 85, Bayardo 95) 1 4 1 6 2 3 2 7 5 3 (a) Graph 4 7 1 1 2 7 5 3 5 3 5 4 2 7 6 6 4 6 (b) DFS tree (c) pseudo- tree (d) Chain depth=3 depth=2 depth=6 CS 276 16

  17. From DFS trees to Pseudo-trees OR 1 AND a b c OR 2 7 AND a b c a b c DFS tree OR 3 3 3 5 5 5 AND a b c a b c a b c a b c a b c a b c depth = 3 OR 4 4 4 4 4 4 4 4 4 6 6 6 6 6 6 6 6 6 AND a b c a b c a b c a b c a b c a b c a b c a b c a b c a b c a b c a b c a b c a b c a b c a b c a b c a b c OR 1 AND a b c OR 3 5 AND a b c a b c pseudo- tree OR 4 4 4 7 7 7 2 2 2 6 6 6 depth = 2 AND a b c a b c a b c a b c a b c a b c a b c a b c a b c a b c a b c a b c CS 276 17

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

Process and thread answers 1. There is no exact answer, but from reasoning you should be able to

Process and thread answers 1. There is no exact answer, but from reasoning you should be able to

Linkping University 2011-03-28 Department of Computer and Information Science (IDA) Concurrent programming, Operating systems and Real-time operating systems (TDDI04) Process and thread answers 1. There is no exact answer, but from reasoning

642 views • 16 slides
Exact Reasoning: AND/ OR Search and Hybrids COMPSCI 276, Fall 2014 Set 8, Rina dechter

Exact Reasoning: AND/ OR Search and Hybrids COMPSCI 276, Fall 2014 Set 8, Rina dechter

Exact Reasoning: AND/ OR Search and Hybrids COMPSCI 276, Fall 2014 Set 8, Rina dechter Probabilistic Inference Tasks Belief updating: = = BEL(X ) P(X x | evidence) i i i Finding most probable explanation (MPE) = x * arg

901 views • 64 slides
Exact Inference for Hidden Markov Models Michael Gutmann Probabilistic Modelling and Reasoning

Exact Inference for Hidden Markov Models Michael Gutmann Probabilistic Modelling and Reasoning

Exact Inference for Hidden Markov Models Michael Gutmann Probabilistic Modelling and Reasoning (INFR11134) School of Informatics, University of Edinburgh Spring Semester 2020 Recap Assuming a factorisation / set of statistical

535 views • 32 slides
Core Claim Formal Methods in Software Development Computer programs/systems are subject to exact

Core Claim Formal Methods in Software Development Computer programs/systems are subject to exact

Core Claim Formal Methods in Software Development Computer programs/systems are subject to exact reasoning. Computer programming is an exact science in that all the properties Wolfgang Schreiner of a program and all the consequences of

399 views • 5 slides
CHAPTER-4 1 LOGIC AND REASONING ! Knowledge and ! Reasoning in Knowledge- Reasoning Based

CHAPTER-4 1 LOGIC AND REASONING ! Knowledge and ! Reasoning in Knowledge- Reasoning Based

CHAPTER-4 1 LOGIC AND REASONING ! Knowledge and ! Reasoning in Knowledge- Reasoning Based Systems ! syntax and semantics ! shallow and deep reasoning ! validity and satisfiability ! forward and backward ! logic languages chaining ! alternative

616 views • 23 slides
BEST OF EXACT GLOBE Jos Suijkens Michiel Beek Best of Exact Globe 2 Agenda 1. A fresh look for

BEST OF EXACT GLOBE Jos Suijkens Michiel Beek Best of Exact Globe 2 Agenda 1. A fresh look for

BEST OF EXACT GLOBE Jos Suijkens Michiel Beek Best of Exact Globe 2 Agenda 1. A fresh look for Exact Globe 2. Increased efficiency with Analytical Accounting 3. High level to detail 4. Pivot analyses, flexible reporting 5. ExactA: Auditing made

626 views • 36 slides
Probabilistic Reasoning; Probabilistic Reasoning; Network-based reasoning Network-based

Probabilistic Reasoning; Probabilistic Reasoning; Network-based reasoning Network-based

Probabilistic Reasoning; Probabilistic Reasoning; Network-based reasoning Network-based reasoning COMPSCI 276, Fall 2014 Set 1: Introduction and Background Rina Dechter (Reading: Pearl chapter 1-2, Darwiche chapters 1,3) 1 Why/What/How

700 views • 45 slides
Evidential and Causal Reasoning Much reasoning in AI can be seen as evidential reasoning ,

Evidential and Causal Reasoning Much reasoning in AI can be seen as evidential reasoning ,

Evidential and Causal Reasoning Much reasoning in AI can be seen as evidential reasoning , (observations to a theory) followed by causal reasoning (theory to predictions). Diagnosis Given symptoms, evidential reasoning leads to hypotheses about

243 views • 8 slides
Informatics 2D Reasoning and Agents Semester 2, 20192020 Alex Lascarides

Informatics 2D Reasoning and Agents Semester 2, 20192020 Alex Lascarides

Introduction Inference by enumeration The variable elimination algorithm Summary Informatics 2D Reasoning and Agents Semester 2, 20192020 Alex Lascarides alex@inf.ed.ac.uk Lecture 24 Exact Inference in Bayesian Networks 13th

159 views • 13 slides
SECTION 1: Introductions Code Reasoning Forward Reasoning CODE REASONING +

SECTION 1: Introductions Code Reasoning Forward Reasoning CODE REASONING +

OUTLINE SECTION 1: Introductions Code Reasoning Forward Reasoning CODE REASONING + Backward Reasoning Weaker vs. Stronger statements Version control VERSION CONTROL CSE 331 Summer 2018 slides borrowed and

763 views • 11 slides
Reasoning and Meta-reasoning Sonia Marin IT-University of Copenhagen, Denmark 85-211

Reasoning and Meta-reasoning Sonia Marin IT-University of Copenhagen, Denmark 85-211

Reasoning and Meta-reasoning Sonia Marin IT-University of Copenhagen, Denmark 85-211 Cognitive Psychology, Guest lecture CMU Qatar November 28, 2018 1 / 15 What is reasoning? Reasoning is the process of drawing conclusions from

911 views • 59 slides
Exact constructions with inexact diagrams John Mumma Division of Logic, Methodology, and

Exact constructions with inexact diagrams John Mumma Division of Logic, Methodology, and

Exact constructions with inexact diagrams John Mumma Division of Logic, Methodology, and Philosophy of Science in the Suppes Center for History and Philosophy of Science, Stanford University Symposium on Constructive Geometric Reasoning

642 views • 52 slides
Algebraic Tools for Exact Geometric Computing I - Exact Arithmetic and Filtering Michael Hemmer

Algebraic Tools for Exact Geometric Computing I - Exact Arithmetic and Filtering Michael Hemmer

Algebraic Tools for Exact Geometric Computing I - Exact Arithmetic and Filtering Michael Hemmer School of Computer Science - University of Tel Aviv 2010, Tel Aviv Michael Hemmer Exact Arithmetic and Filtering Outline Motivate Exact

1.37k views • 71 slides
Automated Reasoning Course Presentation Summary Automated Reasoning Motivations Course Plan

Automated Reasoning Course Presentation Summary Automated Reasoning Motivations Course Plan

Automated Reasoning Automated Reasoning Course Presentation Summary Automated Reasoning Motivations Course Plan Resources Exam Methods Motivations Automated Reasoning Automated reasoning mechanising the reasoning process. reasoning :

159 views • 14 slides
Automated Reasoning: Some Successes and New Challenges Predrag Jani ci c

Automated Reasoning: Some Successes and New Challenges Predrag Jani ci c

What is this talk about? What is automated reasoning? Automated reasoning in propositional logic Automated reasoning in first-order logic Automated reasoning in higher-order logic Automated reasoning in geometry Conclusions Automated

806 views • 52 slides
Models for Inexact Reasoning Reasoning with Subjective Pseudo Reasoning with Subjective Pseudo

Models for Inexact Reasoning Reasoning with Subjective Pseudo Reasoning with Subjective Pseudo

Models for Inexact Reasoning Reasoning with Subjective Pseudo Reasoning with Subjective Pseudo Probabilities: The PROSPECTOR Approach Miguel Garca Remesal Department of Artificial Intelligence mgremesal@fi.upm.es The PROSPECTOR System The

276 views • 17 slides
Mineral and Mining Research at UAF Mark Myers, Vice Chancellor for Research University of Alaska

Mineral and Mining Research at UAF Mark Myers, Vice Chancellor for Research University of Alaska

Mineral and Mining Research at UAF Mark Myers, Vice Chancellor for Research University of Alaska Fairbanks UAF Has Research Expertise That Spans the Mining Cycle UAF Mining and Mineral Expertise Mining Engineering Resource Estimation

518 views • 18 slides
The interval branch-and-prune algorithm for the protein structure determination by NMR Th er`

The interval branch-and-prune algorithm for the protein structure determination by NMR Th er`

Introduction Global optimisation The interval branch-and-prune algorithm for the protein structure determination by NMR Th er` ese E Malliavin Unit e de Bioinformatique Structurale Institut Pasteur and UMR CNRS 3528 Paris, France

603 views • 38 slides
CS 4495 Computer Vision Calibration and Projective Geometry (1) Aaron Bobick School of

CS 4495 Computer Vision Calibration and Projective Geometry (1) Aaron Bobick School of

Calibration and Projective Geometry 1 CS 4495 Computer Vision A. Bobick CS 4495 Computer Vision Calibration and Projective Geometry (1) Aaron Bobick School of Interactive Computing Calibration and Projective Geometry 1 CS 4495 Computer

603 views • 48 slides
Principles &amp; implementation of automatic exposure control systems in CT Maria Lewis ImPACT

Principles &amp; implementation of automatic exposure control systems in CT Maria Lewis ImPACT

Principles &amp; implementation of automatic exposure control systems in CT Maria Lewis ImPACT UKRC June 07 Overview Why AEC in CT? Principles of AEC in CT Implementation of AEC in CT UKRC June 07 Why AEC in CT? Cruise Control

2.89k views • 41 slides
APPLICATIONS OF MICROLOCAL ANALYSIS TO INVERSE PROBLEMS MIKKO SALO Abstract. These are lecture

APPLICATIONS OF MICROLOCAL ANALYSIS TO INVERSE PROBLEMS MIKKO SALO Abstract. These are lecture

APPLICATIONS OF MICROLOCAL ANALYSIS TO INVERSE PROBLEMS MIKKO SALO Abstract. These are lecture notes for a minicourse on applications of microlocal analysis in inverse problems, to be given in Helsinki and Shanghai in June 2019. Preface

256 views • 24 slides
Running Probabilistic Running Probabilistic Running Probabilistic Programs Backwards Programs

Running Probabilistic Running Probabilistic Running Probabilistic Programs Backwards Programs

Running Probabilistic Running Probabilistic Running Probabilistic Programs Backwards Programs Backwards Programs Backwards Neil Toronto * Jay McCarthy David Van Horn * * University of Maryland Vassar College ESOP 2015 2015/04/14

1.69k views • 145 slides
The Indispensable Role of Visualization In Obtaining Insight from Astrophysical Simulation

The Indispensable Role of Visualization In Obtaining Insight from Astrophysical Simulation

The Indispensable Role of Visualization In Obtaining Insight from Astrophysical Simulation Bronson Messer Oak Ridge Leadership Computing Facility Oak Ridge National Laboratory &amp; Department of Physics &amp; Astronomy University of

590 views • 35 slides
CAST Search for Solar Axions The CAST Collaboration Athens, CERN, Chicago, Darmstadt, Frankfurt,

CAST Search for Solar Axions The CAST Collaboration Athens, CERN, Chicago, Darmstadt, Frankfurt,

CAST Search for Solar Axions The CAST Collaboration Athens, CERN, Chicago, Darmstadt, Frankfurt, Freiburg, Gainesville, Istanbul, Katlenburg-Lindau, Livermore, Moscow (INR), Munich ( MPE-MPP ), Patras, Pisa, Saclay, Thessaloniki, Trieste,

456 views • 17 slides

More recommend