running probabilistic running probabilistic running
play

Running Probabilistic Running Probabilistic Running Probabilistic - PowerPoint PPT Presentation

Nov 20, 2023 •219 likes •1.69k views

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. Simpler Example Simpler Example Simpler Example • Assume (random) returns a value uniformly in for value of (max 0.5 (random)) : Density function 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 p ₘ (x) = ??? p ₘ (x) = ??? p ₘ (x) = ??? p ₘ (x) = ??? p ₘ (x) = ??? p ₘ (x) = ??? p ₘ (x) = ??? p ₘ (x) = ??? p ₘ (x) = ??? 1 1 1 1 1 1 1 1 1 .75 .75 .75 .75 .75 .75 .75 .75 .75 p ₘ (x) p ₘ (x) p ₘ (x) p ₘ (x) p ₘ (x) p ₘ (x) p ₘ (x) p ₘ (x) p ₘ (x) .5 .5 .5 .5 .5 .5 .5 .5 .5 .25 .25 .25 .25 .25 .25 .25 .25 .25 0 0 0 0 0 0 0 0 0 0 0 0 .25 .25 .25 .5 .5 .5 .75 .75 .75 1 1 1 1.25 1.25 1.25 0 0 0 .25 .25 .25 .5 .5 .5 .75 .75 .75 1 1 1 1.25 1.25 1.25 0 0 0 .25 .25 .25 .5 .5 .5 .75 .75 .75 1 1 1 1.25 1.25 1.25 x x x x x x x x x 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

  2. Simpler Example Simpler Example Simpler Example • Assume (random) returns a value uniformly in for value of (max 0.5 (random)) : Density function 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 p ₘ (x) = ??? p ₘ (x) = ??? p ₘ (x) = ??? p ₘ (x) = ??? p ₘ (x) = ??? p ₘ (x) = ??? p ₘ (x) = ??? p ₘ (x) = ??? p ₘ (x) = ??? 1 1 1 1 1 1 1 1 1 .75 .75 .75 .75 .75 .75 .75 .75 .75 p ₘ (x) p ₘ (x) p ₘ (x) p ₘ (x) p ₘ (x) p ₘ (x) p ₘ (x) p ₘ (x) p ₘ (x) .5 .5 .5 .5 .5 .5 .5 .5 .5 .25 .25 .25 .25 .25 .25 .25 .25 .25 0 0 0 0 0 0 0 0 0 0 0 0 .25 .25 .25 .5 .5 .5 .75 .75 .75 1 1 1 1.25 1.25 1.25 0 0 0 .25 .25 .25 .5 .5 .5 .75 .75 .75 1 1 1 1.25 1.25 1.25 0 0 0 .25 .25 .25 .5 .5 .5 .75 .75 .75 1 1 1 1.25 1.25 1.25 x x x x x x x x x 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

  3. Simpler Example Simpler Example Simpler Example • Assume (random) returns a value uniformly in for value of (max 0.5 (random)) : Density function 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 p ₘ (x) = ??? p ₘ (x) = ??? p ₘ (x) = ??? p ₘ (x) = ??? p ₘ (x) = ??? p ₘ (x) = ??? p ₘ (x) = ??? p ₘ (x) = ??? p ₘ (x) = ??? 1 1 1 1 1 1 1 1 1 .75 .75 .75 .75 .75 .75 .75 .75 .75 p ₘ (x) p ₘ (x) p ₘ (x) p ₘ (x) p ₘ (x) p ₘ (x) p ₘ (x) p ₘ (x) p ₘ (x) .5 .5 .5 .5 .5 .5 .5 .5 .5 .25 .25 .25 .25 .25 .25 .25 .25 .25 0 0 0 0 0 0 0 0 0 0 0 0 .25 .25 .25 .5 .5 .5 .75 .75 .75 1 1 1 1.25 1.25 1.25 0 0 0 .25 .25 .25 .5 .5 .5 .75 .75 .75 1 1 1 1.25 1.25 1.25 0 0 0 .25 .25 .25 .5 .5 .5 .75 .75 .75 1 1 1 1.25 1.25 1.25 x x x x x x x x x 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

  4. Simpler Example Simpler Example Simpler Example • Assume (random) returns a value uniformly in for value of (max 0.5 (random)) : Density function 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 p ₘ (x) doesn't exist p ₘ (x) doesn't exist p ₘ (x) doesn't exist p ₘ (x) doesn't exist p ₘ (x) doesn't exist p ₘ (x) doesn't exist p ₘ (x) doesn't exist p ₘ (x) doesn't exist p ₘ (x) doesn't exist 1 1 1 1 1 1 1 1 1 .75 .75 .75 .75 .75 .75 .75 .75 .75 p ₘ (x) p ₘ (x) p ₘ (x) p ₘ (x) p ₘ (x) p ₘ (x) p ₘ (x) p ₘ (x) p ₘ (x) .5 .5 .5 .5 .5 .5 .5 .5 .5 .25 .25 .25 .25 .25 .25 .25 .25 .25 0 0 0 0 0 0 0 0 0 0 0 0 .25 .25 .25 .5 .5 .5 .75 .75 .75 1 1 1 1.25 1.25 1.25 0 0 0 .25 .25 .25 .5 .5 .5 .75 .75 .75 1 1 1 1.25 1.25 1.25 0 0 0 .25 .25 .25 .5 .5 .5 .75 .75 .75 1 1 1 1.25 1.25 1.25 x x x x x x x x x 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

  5. What Can’t Densities Model? What Can’t Densities Model? What Can’t Densities Model? 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

  6. What Can’t Densities Model? What Can’t Densities Model? What Can’t Densities Model? • Results of discontinuous functions (bounded measuring devices) (let ([temperature (normal 99 1)]) (min 100 temperature)) 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

  7. What Can’t Densities Model? What Can’t Densities Model? What Can’t Densities Model? • Results of discontinuous functions (bounded measuring devices) (let ([temperature (normal 99 1)]) (min 100 temperature)) • Variable-dimensional things (union types) (if test? none (just x)) 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

  8. What Can’t Densities Model? What Can’t Densities Model? What Can’t Densities Model? • Results of discontinuous functions (bounded measuring devices) (let ([temperature (normal 99 1)]) (min 100 temperature)) • Variable-dimensional things (union types) (if test? none (just x)) • In fi nite-dimensional things (recursion) 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

  9. What Can’t Densities Model? What Can’t Densities Model? What Can’t Densities Model? • Results of discontinuous functions (bounded measuring devices) (let ([temperature (normal 99 1)]) (min 100 temperature)) • Variable-dimensional things (union types) (if test? none (just x)) • In fi nite-dimensional things (recursion) • In general: the distributions of program values 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

  10. Probability Measures Probability Measures Probability Measures • Like already-integrated densities, but a primitive concept 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

  11. Probability Measures Probability Measures Probability Measures • Like already-integrated densities, but a primitive concept • Measure of (random) is , de fi ned by 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

  12. Probability Measures Probability Measures Probability Measures • Like already-integrated densities, but a primitive concept • Measure of (random) is , de fi ned by 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

  13. Probability Measures Probability Measures Probability Measures • Like already-integrated densities, but a primitive concept • Measure of (random) is , de fi ned by • Measure of (max 0.5 (random)) de fi ned by 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

  14. Probability Measures Probability Measures Probability Measures • Like already-integrated densities, but a primitive concept • Measure of (random) is , de fi ned by • Measure of (max 0.5 (random)) de fi ned by This term assigns probability 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

  15. Probability Measures Probability Measures Probability Measures • Like already-integrated densities, but a primitive concept • Measure of (random) is , de fi ned by • Measure of (max 0.5 (random)) de fi ned by This term assigns probability • Need a way to derive measures from code 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

  16. Probability Measures Via Preimages Probability Measures Via Preimages Probability Measures Via Preimages • Interpret (max 0.5 (random)) as , de fi ned 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6

  17. Probability Measures Via Preimages Probability Measures Via Preimages Probability Measures Via Preimages • Interpret (max 0.5 (random)) as , de fi ned • Derive measure of (max 0.5 (random)) as 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6

  18. Probability Measures Via Preimages Probability Measures Via Preimages Probability Measures Via Preimages • Interpret (max 0.5 (random)) as , de fi ned • Derive measure of (max 0.5 (random)) as where 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6

  19. Probability Measures Via Preimages Probability Measures Via Preimages Probability Measures Via Preimages • Interpret (max 0.5 (random)) as , de fi ned • Derive measure of (max 0.5 (random)) as where • Factored into random and deterministic parts: 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6

  20. Probability Measures Via Preimages Probability Measures Via Preimages Probability Measures Via Preimages • Interpret (max 0.5 (random)) as , de fi ned • Derive measure of (max 0.5 (random)) as where • Factored into random and deterministic parts: • In other words, compute measures of expressions by running them backwards 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6

  21. Crazy Idea is Feasible If... Crazy Idea is Feasible If... Crazy Idea is Feasible If... • Seems like we need: 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7

  22. Crazy Idea is Feasible If... Crazy Idea is Feasible If... Crazy Idea is Feasible If... • Seems like we need: Standard interpretation of programs as pure functions from a random source 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7

  23. Crazy Idea is Feasible If... Crazy Idea is Feasible If... Crazy Idea is Feasible If... • Seems like we need: Standard interpretation of programs as pure functions from a random source E ffi cient way to compute preimage sets 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7

  24. Crazy Idea is Feasible If... Crazy Idea is Feasible If... Crazy Idea is Feasible If... • Seems like we need: Standard interpretation of programs as pure functions from a random source E ffi cient way to compute preimage sets E ffi cient representation of arbitrary sets 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7

  25. Crazy Idea is Feasible If... Crazy Idea is Feasible If... Crazy Idea is Feasible If... • Seems like we need: Standard interpretation of programs as pure functions from a random source E ffi cient way to compute preimage sets E ffi cient representation of arbitrary sets E ffi cient way to compute areas of preimage sets 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7

  26. Crazy Idea is Feasible If... Crazy Idea is Feasible If... Crazy Idea is Feasible If... • Seems like we need: Standard interpretation of programs as pure functions from a random source E ffi cient way to compute preimage sets E ffi cient representation of arbitrary sets E ffi cient way to compute areas of preimage sets Proof of correctness w.r.t. standard interpretation 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7

  27. Crazy Idea is Feasible If... Crazy Idea is Feasible If... Crazy Idea is Feasible If... • Seems like we need: Standard interpretation of programs as pure functions from a random source E ffi cient way to compute preimage sets E ffi cient representation of arbitrary sets E ffi cient way to compute areas of preimage sets Proof of correctness w.r.t. standard interpretation • WAT 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7

  28. What About Approximating? What About Approximating? What About Approximating? Conservative approximation with rectangles: 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8

  29. What About Approximating? What About Approximating? What About Approximating? Conservative approximation with rectangles: 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8

  30. What About Approximating? What About Approximating? What About Approximating? Restricting preimages to rectangular subdomains: 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9

  31. What About Approximating? What About Approximating? What About Approximating? Restricting preimages to rectangular subdomains: 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9

  32. What About Approximating? What About Approximating? What About Approximating? Restricting preimages to rectangular subdomains: 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9

  33. What About Approximating? What About Approximating? What About Approximating? Restricting preimages to rectangular subdomains: 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9

  34. What About Approximating? What About Approximating? What About Approximating? Restricting preimages to rectangular subdomains: 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9

  35. What About Approximating? What About Approximating? What About Approximating? Restricting preimages to rectangular subdomains: 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9

  36. What About Approximating? What About Approximating? What About Approximating? Restricting preimages to rectangular subdomains: 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9

  37. What About Approximating? What About Approximating? What About Approximating? Restricting preimages to rectangular subdomains: 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9

  38. What About Approximating? What About Approximating? What About Approximating? Restricting preimages to rectangular subdomains: 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9

  39. What About Approximating? What About Approximating? What About Approximating? Restricting preimages to rectangular subdomains: 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9

  40. What About Approximating? What About Approximating? What About Approximating? Restricting preimages to rectangular subdomains: 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9

  41. What About Approximating? What About Approximating? What About Approximating? Restricting preimages to rectangular subdomains: 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9

  42. What About Approximating? What About Approximating? What About Approximating? Sampling: exponential to quadratic (e.g. days to minutes) 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

  43. What About Approximating? What About Approximating? What About Approximating? Sampling: exponential to quadratic (e.g. days to minutes) 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10

  44. Contribution: Making This Crazy Idea Feasible Contribution: Making This Crazy Idea Feasible Contribution: Making This Crazy Idea Feasible • Standard interpretation of programs as pure functions from a random source • E ffi cient way to compute preimage sets • E ffi cient representation of arbitrary sets • E ffi cient way to compute volumes of preimage sets • Proof of correctness w.r.t. standard interpretation 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

  45. Contribution: Making This Crazy Idea Feasible Contribution: Making This Crazy Idea Feasible Contribution: Making This Crazy Idea Feasible • Standard interpretation of programs as pure functions from a random source • E ffi cient way to compute abstract preimage subsets • E ffi cient representation of arbitrary sets • E ffi cient way to compute volumes of preimage sets • Proof of correctness w.r.t. standard interpretation 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

  46. Contribution: Making This Crazy Idea Feasible Contribution: Making This Crazy Idea Feasible Contribution: Making This Crazy Idea Feasible • Standard interpretation of programs as pure functions from a random source • E ffi cient way to compute abstract preimage subsets • E ffi cient representation of abstract sets • E ffi cient way to compute volumes of preimage sets • Proof of correctness w.r.t. standard interpretation 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

  47. Contribution: Making This Crazy Idea Feasible Contribution: Making This Crazy Idea Feasible Contribution: Making This Crazy Idea Feasible • Standard interpretation of programs as pure functions from a random source • E ffi cient way to compute abstract preimage subsets • E ffi cient representation of abstract sets • E ffi cient way to sample uniformly in preimage sets • Proof of correctness w.r.t. standard interpretation 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

  48. Contribution: Making This Crazy Idea Feasible Contribution: Making This Crazy Idea Feasible Contribution: Making This Crazy Idea Feasible • Standard interpretation of programs as pure functions from a random source • E ffi cient way to compute abstract preimage subsets • E ffi cient representation of abstract sets • E ffi cient way to sample uniformly in preimage sets E ffi cient domain partition sampling • Proof of correctness w.r.t. standard interpretation 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

  49. Contribution: Making This Crazy Idea Feasible Contribution: Making This Crazy Idea Feasible Contribution: Making This Crazy Idea Feasible • Standard interpretation of programs as pure functions from a random source • E ffi cient way to compute abstract preimage subsets • E ffi cient representation of abstract sets • E ffi cient way to sample uniformly in preimage sets E ffi cient domain partition sampling E ffi cient way to determine whether a domain sample is actually in the preimage (just use standard interpretation) • Proof of correctness w.r.t. standard interpretation 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

  50. How Many Meanings? How Many Meanings? How Many Meanings? • Start with pure programs, then lift by threading a random store 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

  51. How Many Meanings? How Many Meanings? How Many Meanings? • Start with pure programs, then lift by threading a random store • Nonrecursive, nonprobabilistic programs: , , 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

  52. How Many Meanings? How Many Meanings? How Many Meanings? • Start with pure programs, then lift by threading a random store • Nonrecursive, nonprobabilistic programs: , , • Add 3 semantic functions for recursion and probabilistic choice 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

  53. How Many Meanings? How Many Meanings? How Many Meanings? • Start with pure programs, then lift by threading a random store • Nonrecursive, nonprobabilistic programs: , , • Add 3 semantic functions for recursion and probabilistic choice • Full development needs 2 more to transfer theorems from measure theory... 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

  54. How Many Meanings? How Many Meanings? How Many Meanings? • Start with pure programs, then lift by threading a random store • Nonrecursive, nonprobabilistic programs: , , • Add 3 semantic functions for recursion and probabilistic choice • Full development needs 2 more to transfer theorems from measure theory... • ... oh, and 1 more to collect information for Monte Carlo integration 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

  55. How Many Meanings? How Many Meanings? How Many Meanings? • Start with pure programs, then lift by threading a random store • Nonrecursive, nonprobabilistic programs: , , • Add 3 semantic functions for recursion and probabilistic choice • Full development needs 2 more to transfer theorems from measure theory... • ... oh, and 1 more to collect information for Monte Carlo integration Tally: 3+3+2+1 = 9 semantic functions, 11 or 12 rules each 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

  56. Enter Category Theory Enter Category Theory Enter Category Theory • Moggi (1989): Introduces monads for interpreting e ff ects 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

  57. Enter Category Theory Enter Category Theory Enter Category Theory • Moggi (1989): Introduces monads for interpreting e ff ects • Other kinds of categories: idioms, arrows 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

  58. Enter Category Theory Enter Category Theory Enter Category Theory • Moggi (1989): Introduces monads for interpreting e ff ects • Other kinds of categories: idioms, arrows • Arrow de fi ned by type constructor and these combinators: 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

  59. Enter Category Theory Enter Category Theory Enter Category Theory • Moggi (1989): Introduces monads for interpreting e ff ects • Other kinds of categories: idioms, arrows • Arrow de fi ned by type constructor and these combinators: • Arrows are always function-like 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

  60. Reducing Complexity Reducing Complexity Reducing Complexity Function arrow: is just 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

  61. Reducing Complexity Reducing Complexity Reducing Complexity Function arrow: is just 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

  62. Reducing Complexity Reducing Complexity Reducing Complexity Function arrow: is just 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

  63. Reducing Complexity Reducing Complexity Reducing Complexity Function arrow: is just 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

  64. Reducing Complexity Reducing Complexity Reducing Complexity Function arrow: is just 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

  65. Reducing Complexity Reducing Complexity Reducing Complexity Function arrow: is just 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

  66. Reducing Complexity Reducing Complexity Reducing Complexity Function arrow: is just 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

  67. Reducing Complexity Reducing Complexity Reducing Complexity Function arrow: is just 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

  68. Reducing Complexity Reducing Complexity Reducing Complexity Function arrow: is just 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

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

Formalising Semantics for Expected Running Time of Probabilistic Programs (Rough Diamond)

Formalising Semantics for Expected Running Time of Probabilistic Programs (Rough Diamond)

Johannes Hlzl TU Mnchen, Germany Formalising Semantics for Expected Running Time of Probabilistic Programs (Rough Diamond) Kaminski, Katoen, Matheja, and Olmedo [ESOP 2016] Denotational: Operational: Correspondence: Denotational 2

954 views • 84 slides
Formalising Semantics for Expected Running Time of Probabilistic Programs (Rough Diamond)

Formalising Semantics for Expected Running Time of Probabilistic Programs (Rough Diamond)

Johannes Hlzl TU Mnchen, Germany Formalising Semantics for Expected Running Time of Probabilistic Programs (Rough Diamond) Kaminski, Katoen, Matheja, and Olmedo [ESOP 2016] Denotational: Operational: Correspondence: Denotational 2

1.36k views • 89 slides
Deep Water Running Richard Lucas What is it? Mimicking running action while in the water

Deep Water Running Richard Lucas What is it? Mimicking running action while in the water

Deep Water Running Richard Lucas What is it? Mimicking running action while in the water Suspended in the water (not touching the bottom) Comparison to Land Running No impact Same techniques Same workouts (avg 30st/100m) Greater

744 views • 11 slides
D7: Front-running Race conditions #7: Front ont-running running A form of a race condition

D7: Front-running Race conditions #7: Front ont-running running A form of a race condition

D7: Front-running Race conditions #7: Front ont-running running A form of a race condition time-of-check vs time-of-use (TOCTOU) race conditions and transaction ordering dependence (TOD) A classic problem in operating systems 15.8%

467 views • 31 slides
Hybrid Indexes Huanchen Zhang You are running out of memory 2 You are running out of memory 2

Hybrid Indexes Huanchen Zhang You are running out of memory 2 You are running out of memory 2

Reducing the Storage Overhead of Main-Memory OLTP Databases with Hybrid Indexes Huanchen Zhang You are running out of memory 2 You are running out of memory 2 ? Buy more You are running out of memory 2 TPC-C on -Store Memory Limit =

632 views • 35 slides
Welcome to the running start information session. This presentation will give an overview of the

Welcome to the running start information session. This presentation will give an overview of the

Welcome to the running start information session. This presentation will give an overview of the running start program, other options for earning college credit while in high school, and how students can access the running start program. Running

416 views • 23 slides
Running Time Why do we need to analyze the running Algorithm/Running Time Analysis time of a

Running Time Why do we need to analyze the running Algorithm/Running Time Analysis time of a

Running Time Why do we need to analyze the running Algorithm/Running Time Analysis time of a program? Option 1: Run the program and time it Why is this option bad? What can we do about it? Pseudo-Code Math Review Used

329 views • 3 slides
Running Footwear: What the Rehab Professional Needs to Know Dr. Matthew Klein PT DPT KAISER

Running Footwear: What the Rehab Professional Needs to Know Dr. Matthew Klein PT DPT KAISER

Running Footwear: What the Rehab Professional Needs to Know Dr. Matthew Klein PT DPT KAISER PERMANENTE SOUTHERN CALIFORNIA ORTHOPAEDIC SPORTS FELLOWSHIP Running Footwear Development Consultant Goals of This The Anatomy of Running Shoes

782 views • 33 slides
Running 'me of algorithms How can we measure the running

Running 'me of algorithms How can we measure the running

Running 'me of algorithms How can we measure the running 'me of algorithms? Idea: Use a stopwatch. What if we run the algorithm on a

569 views • 25 slides
- Running in Muon g-2 Chris Polly 4 April 2017 Running - BNL experiment was able to run

- Running in Muon g-2 Chris Polly 4 April 2017 Running - BNL experiment was able to run

- Running in Muon g-2 Chris Polly 4 April 2017 Running - BNL experiment was able to run - with a matched sensitivity to + FNAL experiment only approved to run + Complicated by x2.5 reduction in p - relative to p +

398 views • 10 slides
BASE RUNNING PRESENTATION NOTES BOB HARROW, AUSTRAILIAN MENS NATIONAL TEAM HEAD COACH

BASE RUNNING PRESENTATION NOTES BOB HARROW, AUSTRAILIAN MENS NATIONAL TEAM HEAD COACH

BASE RUNNING PRESENTATION NOTES BOB HARROW, AUSTRAILIAN MENS NATIONAL TEAM HEAD COACH Extracts from the Softball Australia Base running manual BASE RUNNING PHILOSOPHY The art of base running is, and will continue to be, an integral and

422 views • 21 slides
Gravity and running coupling constants 1) Motivation and history 2) Brief review of running

Gravity and running coupling constants 1) Motivation and history 2) Brief review of running

Gravity and running coupling constants 1) Motivation and history 2) Brief review of running couplings 3) Gravity as an effective field theory 4) Running couplings in effective field theory 5) Summary 6) If time incomplete comments on pure

615 views • 50 slides
Where we are going Where we have been Where we are now PUSD Running ning Ef Efficiently

Where we are going Where we have been Where we are now PUSD Running ning Ef Efficiently

Where we are going Where we have been Where we are now PUSD Running ning Ef Efficiently iently Running efficiently despite our obstacles Desp spit ite e our Obsta tacles cles Miller Valley Elementary School Washington Elementary

341 views • 18 slides
Running and Jumping PE | Year 1 | Outdoor | Running and Jumping | Changing Gears | Lesson 1 Aim

Running and Jumping PE | Year 1 | Outdoor | Running and Jumping | Changing Gears | Lesson 1 Aim

Running and Jumping PE | Year 1 | Outdoor | Running and Jumping | Changing Gears | Lesson 1 Aim Aim To move at different speeds. Success Criteria Success Criteria Statement 1 Lorem ipsum dolor sit amet, consectetur adipiscing elit. I

539 views • 18 slides
Running time of algorithms How can we measure the running time of algorithms? Idea: Use a

Running time of algorithms How can we measure the running time of algorithms? Idea: Use a

Running time of algorithms How can we measure the running time of algorithms? Idea: Use a stopwatch. What if we run the algorithm on a different computer? What if we code the algorithm in a different programming language? Timing

601 views • 34 slides
RUNNING 1 Kenny Krotzer | Brooks Running Associate Footwear Developer Sam Green | Stratasys

RUNNING 1 Kenny Krotzer | Brooks Running Associate Footwear Developer Sam Green | Stratasys

3D PRINTING AT BROOKS RUNNING 1 Kenny Krotzer | Brooks Running Associate Footwear Developer Sam Green | Stratasys Product Marketing Lead, Rapid Prototyping 2 STRATASYS / A GLOBAL LEADER IN APPLIED ADDITIVE TECHNOLOGY SOLUTIONS 3D PRINTING

388 views • 21 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
Exact Reasoning: AND/OR Search and Hybrids COMPSCI 276, Fall 2009 Set 8, Rina dechter

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

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)

772 views • 46 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
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 & Department of Physics & 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
Les Pulsars gamma The GeV Gamma Gamma- -ray ray The GeV avec GLAST Sky with the Large Large

Les Pulsars gamma The GeV Gamma Gamma- -ray ray The GeV avec GLAST Sky with the Large Large

Les Pulsars gamma The GeV Gamma Gamma- -ray ray The GeV avec GLAST Sky with the Large Large Area Area Sky with the Fermi on Fermi Telescope on Telescope (formerly GLAST) with an accent on pulsars an accent on pulsars with David

770 views • 35 slides
Light Dark Matter Kenji Kadota IBS Center for Theoretical Physics of the Universe (CTPU)

Light Dark Matter Kenji Kadota IBS Center for Theoretical Physics of the Universe (CTPU)

Light Dark Matter Kenji Kadota IBS Center for Theoretical Physics of the Universe (CTPU) Institute for Basic Science, Korea Two concrete examples Sterile neutrino DM Production mechanism Axion(-like) Particle Radio (SKA-like) survey

243 views • 13 slides

More recommend