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http://fredrikj.net/blog/2018/07/interesting-interference-integrals/

Diffraction catastrophe integrals describe complex wave interference phenomena. This post is about a simple test implementation in Arb. Scroll to the end for a note on T. Pearcey's remarkable hand-drawn plots from 1946!

Diffraction catastrophe integrals describe complex wave interference phenomena. This post is about a simple test implementation in Arb. Scroll to the end for a note on T. Pearcey's remarkable hand-drawn plots from 1946!

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http://fredrikj.net/blog/2018/07/the-arb-matrix-revolutions/

The previous post on linear algebra in Arb ended with the cliffhanger that the improvements for multiplication and linear solving had yet to be adapted for computing determinants and for complex matrices. That is now done.

The previous post on linear algebra in Arb ended with the cliffhanger that the improvements for multiplication and linear solving had yet to be adapted for computing determinants and for complex matrices. That is now done.

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http://fredrikj.net/blog/2018/06/the-arb-matrix-reloaded/

Basic linear algebra in Arb is getting a significant upgrade in Arb 2.14 which is due to be released within a few weeks. The main improvements are more accurate linear solving and faster matrix multiplication.

Basic linear algebra in Arb is getting a significant upgrade in Arb 2.14 which is due to be released within a few weeks. The main improvements are more accurate linear solving and faster matrix multiplication.

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https://arxiv.org/abs/1806.06725

This is a chapter hopefully going into a forthcoming LNCS conference proceedings volume . Any corrections or other comments before the final version is due in a couple of weeks would be welcome!

This is a chapter hopefully going into a forthcoming LNCS conference proceedings volume . Any corrections or other comments before the final version is due in a couple of weeks would be welcome!

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Spektrum der Wissenschaft (the German edition of Scientific American) recently asked me if they could use one of my renders of the j-function for an illustration. The article is now available in the May issue: https://www.spektrum.de/magazin/mondschein-verbindung-fuer-eine-paria-gruppe/1555490

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+Fredrik Johansson has a new paper out

/Computing Stieltjes constants using complex integration/

https://arxiv.org/abs/1804.01679

/Computing Stieltjes constants using complex integration/

https://arxiv.org/abs/1804.01679

**The Stieltjes constants γ_n are the coefficients appearing in the Laurent series of the Riemann zeta function at s=1. We give a simple and efficient method to compute a p-bit approximation of γ_n with rigorous error bounds. Starting from an integral representation due to Blagouchine, we shift the contour to eliminate cancellation. The integral is then evaluated numerically in ball arithmetic using the Petras algorithm, with the use of a Taylor expansion for bounds near the saddle point. This appears to be the first algorithm for Stieltjes constants with uniformly low complexity with respect to both n and p. An implementation is provided in the Arb library. We can, for example, compute γ_n to 1000 digits in a minute for any n≤10100.**Add a comment...

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LCZero (http://lczero.org/) is an open source neural network chess engine trained from scratch in the spirit of AlphaZero. The training is done as a distributed computing project. It seems to be making slow but steady progress, and could be competitive with top chess engines in a few months. It would be nice if more people with fast GPUs volunteered to speed up the process. (Caution: the progress graph on the front page shows Elo rating measured by self-play games, which is not calibrated against human players.)

You can play against the most recent version of the network at http://play.lczero.org/. It's currently at a level where it's fun to play against as a total chess novice. I played it a few times on fast mode and won two games when I didn't blunder (one game below). Just so I can tell people "I once beat LCZero" in the future when this will sound much more impressive.

1. e4 h5

2. Nc3 c6

3. Nf3 d5

4. d3 dxe4

5. Nxe4 Nd7

6. Be2 e5

7. O-O Be7

8. d4 exd4

9. Nxd4 Ngf6

10. Nxf6+ Nxf6

11. Bg5 O-O

12. Re1 c5

13. Nf3 Bd7

14. Qd2 Ne4

15. Bxe7 Nxd2

16. Bxd8 Raxd8

17. Nxd2 Rfe8

18. Nb3 Bc6

19. Nxc5 Rc8

20. Bxh5 Rxe1+

21. Rxe1 g6

22. Bg4 Rc7

23. b4 Bd5

24. a3 g5

25. c3 b6

26. Nd7 Bb3

27. Nf6+ Kg7

28. Nh5+ Kg6

29. h3 Rxc3

30. Re7 f5

31. Bf3 a6

32. Rg7+ Kh6

33. Ra7 Kg6

34. Rxa6 Rc2

35. Rxb6+ Kf7

36. Rb7+ Kg6

37. Rb5 Rb2

38. g4 Ba2

39. gxf5+ Kf7

40. Bd5+ Ke7

41. f6+ Kd6

42. f7 Ke7

43. Rb7+ Kf8

44. Bxa2 Rxa2

45. Ra7 Rc2

46. Nf6 Rc1+

47. Kg2 Rb1

48. Rb7 Rd1

49. Nh7+ Kg7

50. Nxg5 Kf8

51. h4 Rd2

52. h5 Rd4

53. h6 Rxb4

54. Rxb4 Ke7

55. Re4+ Kf8

56. Re8#

You can play against the most recent version of the network at http://play.lczero.org/. It's currently at a level where it's fun to play against as a total chess novice. I played it a few times on fast mode and won two games when I didn't blunder (one game below). Just so I can tell people "I once beat LCZero" in the future when this will sound much more impressive.

1. e4 h5

2. Nc3 c6

3. Nf3 d5

4. d3 dxe4

5. Nxe4 Nd7

6. Be2 e5

7. O-O Be7

8. d4 exd4

9. Nxd4 Ngf6

10. Nxf6+ Nxf6

11. Bg5 O-O

12. Re1 c5

13. Nf3 Bd7

14. Qd2 Ne4

15. Bxe7 Nxd2

16. Bxd8 Raxd8

17. Nxd2 Rfe8

18. Nb3 Bc6

19. Nxc5 Rc8

20. Bxh5 Rxe1+

21. Rxe1 g6

22. Bg4 Rc7

23. b4 Bd5

24. a3 g5

25. c3 b6

26. Nd7 Bb3

27. Nf6+ Kg7

28. Nh5+ Kg6

29. h3 Rxc3

30. Re7 f5

31. Bf3 a6

32. Rg7+ Kh6

33. Ra7 Kg6

34. Rxa6 Rc2

35. Rxb6+ Kf7

36. Rb7+ Kg6

37. Rb5 Rb2

38. g4 Ba2

39. gxf5+ Kf7

40. Bd5+ Ke7

41. f6+ Kd6

42. f7 Ke7

43. Rb7+ Kf8

44. Bxa2 Rxa2

45. Ra7 Rc2

46. Nf6 Rc1+

47. Kg2 Rb1

48. Rb7 Rd1

49. Nh7+ Kg7

50. Nxg5 Kf8

51. h4 Rd2

52. h5 Rd4

53. h6 Rxb4

54. Rxb4 Ke7

55. Re4+ Kf8

56. Re8#

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