MATHEMATICAL SETI

Statistics, Signal Processing, Space Missions

Claudio Maccone

MATHEMATICAL SETI: Statistics, Signal Processing, Space Missions This book introduces the Statistical Drake Equation where, from a simple product of seven positive numbers, the Drake Equation is turned into the product of seven positive random variables. The mathematical consequences of this transformation are demonstrated and it is proven that the new random variable N for the number of communicating civilizations in the Galaxy must follow the lognormal probability distribution when the number of factors in the Drake Equation is allowed to increase at will.

Mathematical SETI also studies the proposal FOCAL (Fast Outgoing Cyclopean Astronomical Lens) space mission to the nearest Sun Focal Sphere at 550 AU and describes its consequences for future interstellar precursor missions and truly interstellar missions. In addition the author shows how SETI signal processing may be dramatically improved by use of the Karhumen-Loève Transform (KLT) rather than Fast Fourier Transform (FFT). Finally, he describes the efforts made to persuade the United Nations to make the central part of the Moon Far Side a UN-protected zone, in order to preserve the unique radio-noise-free environment for future scientific use.


Table of Contents

Preface
Acknowledgments and dedication
Foreword by Frank Drake
Foreword by Giovanni Bignami
List of figures
List of tables
List of abbreviations and acronyms


PART I SETI STATISTICS
1. The statistical Drake equation
2. Letting Maxima do the calculations
3. How many planets for man and aliens?
4. Statistical Fermi paradox and Galactic travels
5. How long does a civilization live?
6. Life-span modeling by finite b-lognormals
7. Civilizations as finite b-lognormals: Mathematical history
8. Darwinian exponential growth and cladistics
9. Societal statistics by the statistical Drake equation
10. Cubics of historical recovery
11. Exponential evolution in time as a geometric Brownian motion

PART II SPACE MISSIONS TO EXPLOIT GRAVITATIONAL LENSING
12. So much to gain at 550 AU
13. FOCAL mission to 1,000 AU as an interstellar precursor
14. Belt of focal spheres between 550 and 17,000 AU
15. Galactic Internet by star gravitational lensing
16. Extragalactic Internet by black hole gravitational lensing

PART III KLT FOR OPTIMAL SIGNAL PROCESSING
17. A simple introduction to the KLT and BAM-KLT
18. KLT of radio signals from relativistic spaceships in uniform and decelerated motion
19. KLT of radio signals from relativistic spaceships in hyperbolic motion
20. KLT of radio signals from relativistic spaceships in arbitrary motion
21. Brownian motion and its time rescaling
22. Maccone first KLT theorem: KLT of all time-rescaled Brownian motions
23. KLT of the B(t2H)
24. Maccone second KLT theorem: KLT of all time-rescaled square Brownian motions
25. KLT of the B2(t2H) time-rescaled quare Brownian motion
26. Maccone third KLT theorem: Asymptotic KLT of GBM
27. A Matlab code for KLT simulations
28. KLT applications and a Fortran code (Stephane Dumas)

PART IV THE UNITED NATIONS AND PROTECTION OF THE MOON'S FARSIDE
29. The United Nations and protection of the Moon's farside

PART V EPILOGUE
30. Epilogue: Evolution, progress, and SETI

Index



Extent: 760 pages, Black and white/colour images integrated with text
Binding: Hardback
Published: 2012
ISBN: 978-3-642-27436-7



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