Papers by claudio maccone
HAL (Le Centre pour la Communication Scientifique Directe), 1985
Monthly Notices of the Royal Astronomical Society, Mar 13, 2020
In this work, we propose a new method of computing the Karhunen-Loève Transform (KLT) applied to ... more In this work, we propose a new method of computing the Karhunen-Loève Transform (KLT) applied to complex voltage data for the detection and noise level reduction in astronomical signals. We compared this method with the standard KLT techniques based on the Toeplitz correlation matrix and we conducted a performance analysis for the detection and extraction of astrophysical and artificial signals via Monte Carlo (MC) simulations. We applied our novel method to a real data study-case: the Voyager 1 telemetry signal. We evaluated the KLT performance in an astrophysical context: our technique provides a remarkable improvement in computation time and MC simulations show significant reconstruction results for signalto-noise ratio (SNR) down to −10 dB and comparable results with standard signal detection techniques. The application to artificial signals, such as the Voyager 1 data, shows a notable gain in SNR after the KLT.
Acta Astronautica, 2018
Consider two great scientists of the past: Kepler (1571-1630) and Newton (1642-1727). Kepler disc... more Consider two great scientists of the past: Kepler (1571-1630) and Newton (1642-1727). Kepler discovered his three laws of planetary motion by observing Mars: he knew experimentally that his three laws were correct, but he didn't even suspect that all three mathematical laws could be derived as purely mathematical consequences by a "superior" mathematical law. The latter was the Law of Gravitation that Newton gave the world together with his supreme mathematical discovery of the Calculus, necessary for that mathematical derivation. We think we did the same for the "molecular clock", the experimental law of genetics discovered in 1962 by Émile Zuckerkandl (1922-2013) and Linus Pauling (1901-1994) and derived by us as a purely mathematical consequence of our mathematical Evo-SETI Theory. Let us now summarize how this mathematical derivation was achieved. Darwinian evolution over the last 3.5 billion years was an increase in the number of living species from one (RNA ?) to the current (say) 50 million. This increasing trend in time looks like being exponential, but one may not assume an exact exponential curve since many species went extinct in the past, especially in the five, big mass extinctions. Thus, the simple exponential curve must be replaced by a stochastic process having an exponential mean value. Borrowing from financial mathematics (the "Black-Sholes models"), this "exponential" stochastic process is called Geometric Brownian Motion (GBM). Its probability density function (pdf) is a lognormal (and not a Gaussian) (Proof: see ref. [3], Chapter 30, and ref. [4]). Lognormal also is the pdf of the statistical number of communicating ExtraTerrestrial (ET) civilizations in the Galaxy at a certain fixed time, like a snapshot: this result was obtained in 2008 by this author as his solution to the Statistical Drake Equation of SETI (Proof: see ref. [1]). Thus, the GBM of Darwinian evolution may also be regarded as the extension in time of the Statistical Drake equation (Proof: see ref. [4]). But the key step ahead made by this author in his Evo-SETI (Evolution and SETI) mathematical theory was to realize that life also is just a b-lognormal in time: every living organism (a cell, a human, a civilization, even an ET civilization) is born at a certain time b ("birth"), grows up to a peak p (with an ascending inflexion point in between, a for adolescence), then declines from p to s (senility, i.e. descending inflexion point) and finally declines linearly and dies at a final instant d (death). In other words, the infinite tail of the b-lognormal was cut away and replaced by just a straight line between s and d, leading to simple mathematical formulae ("History Formulae") allowing one to find this "finite b-lognormal" when the three instants b, s, and d are assigned. Next our crucial Peak-Locus Theorem comes. It means that the GBM exponential may be regarded as the geometric locus of all the peaks of a one-parameter (i.e. the peak time p) family of b-lognormals. Since b-lognormals are pdf-s, the area under each of them always equals 1 (normalization condition) and so, going from left to right on the time axis, the b-lognormals become more and more "peaky", and so they last less and less in time. This is precisely what happened in Human History: civilizations that lasted a millennium each (like Ancient Greece and Rome) lasted just a few centuries in later times (like the Italian Renaissance and Portuguese, Spanish, French, British and USA Empires) but they were more and more advanced in the "level of civilization". This "level of civilization" is what physicists call entropy. Also, in refs. [3] and [4], this author proved that, for all GBMs, the (Shannon) Entropy of the b-lognormals in his Peak-Locus Theorem grows linearly in time. The Molecular Clock (refs. [6] through [11]), well known to geneticists since 1962, shows that the DNA base-substitutions occur linearly in time since they are neutral with respect to Darwinian selection. This is Kimura's neutral theory of molecular evolution. The conclusion is that the Molecular Clock and the linear increase of EvoEntropy in time are just the same thing! In other words, we derived the Molecular Clock mathematically as a part of our Evo-SETI Theory. In addition, our EvoEntropy, i.e. the Shannon Entropy of the b-lognormal (with the minus sign reversed and starting at zero at the time of the origin of Life on Earth) is just the new EvoSETI Scale to measure the evolution of life on Exoplanets (measured in bits). That was the situation prior to the present paper, firstly presented at the SETI II Session of the Adelaide IAC in October 2017. In fact, just as classical thermodynamics entails both energy and entropy, so our Evo-SETI Theory needs entailing the energy used by a living Species or Civilization along its whole lifetime in addition to its entropy (i.e. Molecular Clock). In other words still, while the Molecular Clock is a measure of the advancement in evolution, the energy required to get that advancement is another topic not faced by this author prior to 2017. However, in the present paper we were able to add the consideration of energy in addition to entropy by replacing the b-lognormal probability densities previously used by a new curve, finite in the time, that we call "logpar". This logpar is made up by an ascending b-lognormal in the time between the birth and the peak of the living organism, followed by a descending parabola in the time between its peak and death. The logpar curve is not normalized to one: the area under the logpar curve may be any positive number since it represents the energy requested by the organism to live over its entire lifetime "birth-to-death". In other words still, we mathematically demonstrate in this paper that just three instants (birth b, peak p and death d) must be assigned in order to make the mathematical logpar curve perfectly described.
56th International Astronautical Congress of the International Astronautical Federation, the International Academy of Astronautics, and the International Institute of Space Law, 2005
Assume that the history of Astronomy and SETI is the leading proof of the evolution of human inte... more Assume that the history of Astronomy and SETI is the leading proof of the evolution of human intelligence on Earth over the last 3000 years. Then, human intelligence has increased a lot, although not at a uniform pace. A mathematical description of how much has human intelligence increased, however, is difficult to achieve. In this paper, we cast a mathematical model the evolution of human intelligence over the last three thousand years that seems to reflect reasonably well both what is known from past and might be extrapolated into the future. Our model is based on two seminal books: 1) “Cosmos” by Carl Sagan (1980), widely known to millions of people all over the western world because of the corresponding TV series, and 2) “Interstellar Migration and the Human Experience” (by Ben Finney and Eric Jones, Editors, University of California Press, 1983). Our model is based on the use of two cubic curves, representing the evolution of Astronomy and of SETI, respectively. We conclude by extrapolating these curves into the future and reach the conclusion that the ”Star Trek” age of humankind might possibly begin by the end of this century.
Acta Astronautica, 2017
Abstract Ray Kurzweil's famous 2006 book “The Singularity Is Near” predicted that the Singula... more Abstract Ray Kurzweil's famous 2006 book “The Singularity Is Near” predicted that the Singularity (i.e. computers taking over humans) would occur around the year 2045. In this paper we prove that Kurzweil's prediction is in agreement with the “Evo-SETI” (Evolution and SETI)” mathematical model that this author has developed over the last five years in a series of mathematical papers published in both Acta Astronautica and the International Journal of Astrobiology. The key ideas of Evo-SETI are: 1) Evolution of life on Earth over the last 3.5 billion years is a stochastic process in the number of living Species called Geometric Brownian Motion (GBM). It increases exponentially in time and is in agreement with the Statistical Drake Equation of SETI (see ref. [1] ). 2) The level of advancement of each living Species is the (Shannon) ENTROPY of the b-lognormal probability density (i.e. a lognormal starting at the positive time b (birth)) corresponding to that Species. (Peak-Locus Theorem of Evo-SETI Theory). 3) Humanity is now very close to the point of minimum radius of curvature of the GBM exponential, called “GBM knee”. We claim that this knee is precisely Kurzweil's Singularity, in that before the Singularity the exponential growth was very slow (these are animal and human Species made of meat and reproducing sexually over millions of years), whereas, after the Singularity, the exponential growth will be extremely rapid (computers reproducing technologically faster and faster in time). But how is this paper structured in detail? Well, first of all (Part 1) we describe what the GBM is, and why it reflects the stochastic exponential increase that occurred in Darwinian Evolution for over 3.5 billion years. Please notice that the denomination “Geometric Brownian Motion” (taken from Financial Mathematics) is incorrect since the GBM is NOT a Brownian motion as understood by physicists (i.e. a stochastic process whose probability density function (pdf) is a Gaussian). On the contrary, the GBM is a lognormal process, i.e. a process whose pdf is a lognormal pdf. Next (Part 2) we compute the time when the GBM knee occurs (i.e. the time of minimum radius of curvature) and find what we call the knee equation, i.e. the relationship between t_knee, ts (the time of the origin of life on Earth) and B (the rate of growth of the GBM exponential. This equation holds good for any time assumed to be the Singularity time, either in the past, or now, or in the future. Then (Part 3) Ray Kurzweil's claim that the Singularity is near becomes part of our Evo-SETI Theory in that t_knee is set to zero (i.e. approximately nowadays, when compared to the 3.5 billions of years of past Darwinian Evolution of life on Earth). This leads to a very easy form of the GBM exponential as well as to the discovery of a pair of important new equations: 1) The inverse proportionality between the average number of Species living NOW on Earth and B, the pace of evolution. In other words, it would be possible to find B were the biologists able to tell us “fairly precisely” how many Species live on Earth nowadays. Unfortunately, this is not the case since, when it comes to insects and so on, the number of Species is so huge that it is not even known if it ranges in the millions or even in the billions. 2) More promising appears to be another new equation, that we discovered, relating the time of the origin of life on Earth, ts (that is known fairly precisely to range between 3.5 and 3.8 billion years ago) and the average number of living Species NOW. Finally, the mathematical machinery typical of the Evo-SETI Theory is called into action: 1) The Peak-Locus Theorem stating that the GBM exponential is where ALL PEAKS of the b-lognormals running left-to-right are located, so that the b-lognormals become higher and higher and narrower and narrower (with area =1 as the normalization). 2) The Shannon ENTROPY as EVOLUTION MEASURE of the b-lognormals, more correctly with the sign reversed and starting at the time of the origin of life on Earth, that is rather called EvoEntropy. 3) After this point, one more paper should be written to describe… how the b-lognormal's “width” would correctly describe the “average duration in time” of each Species (before the Singularity) and of each COMPUTER Species (after the Singularity)… 4) …but this is “too much to be done now”, and so we leave it to a new, forthcoming paper.
The international scientific community, and especially the IAA (International Academy of As-trona... more The international scientific community, and especially the IAA (International Academy of As-tronautics) have long been discussing the need to keep the Farside of the Moon free of man-made RFI (radio frequency interference). In fact, the center of the Farside, specifically crater Daedalus, is ideal to set up a future radiotelescope (or phased array) to detect radio waves of all kinds that it is impossible to detect on Earth because of both the ever-growing RFI and of the intervening ionosphere. Nobody, however, seems to have established a precise border for the circular region around the antipode of the Earth (i.e. zero latitude and 180o longitude both East and West) that should be Protected from wild human exploitation when several nations will have reached the capability of easy travel to the Moon. In this paper we propose the cre-ation of PAC, the Protected Antipode Circle, centered around the antipode on the Farside and spanning an angle of 30o in longitude, in latitude and in all radial directions from the antipode. There are sound scientific reasons for this definition: 1) PAC is the most shielded area of the Farside, with an expected attenuation of man-made RFI of 100 dB or higher; 2) PAC is the only area of the Farside that will never be reached by the radiation emitted by future human space bases located at the L4 and L5 Lagrangian points of the Earth-Moon system; 3) PAC does not overlap with other areas of interest to human activity except for possibly a minor common area with the Aitken Basin, the southern depression supposed to have been created 3.8 billion years ago during the "big wham" between the Earth and the Moon. In view of these unique features, we propose PAC to be officially recognized by the United Nations as an Internationally Protected Area where no radio contamination by humans will possibly take place now and in the future for the benefit of all Humankind.
COSPAR Colloquia Series, 2001
... And FOCAL (an acronym for Fast Outgoing Craft for Astrophysical Lensing), will not just b... more ... And FOCAL (an acronym for Fast Outgoing Craft for Astrophysical Lensing), will not just be looking at a point, but rather at a small line segment in the sky, enormously enlarged. SunLensing the Cosmic Microwave Background from 763 AU Claudio Maccone a "G. Colombo ...
Nonlinear Stochastic Problems, 1983
The nonlinear time dependent Brownian motion, B(g(t)), is the object of the present paper. The ti... more The nonlinear time dependent Brownian motion, B(g(t)), is the object of the present paper. The time-rescaling function, g(t), may be any function continuous over a finite positive time interval ranging from O to a fixed T, and such that g(0)=0. We firstly prove B(g(t)) to be equivalent to a white—noise integral having zero mean and a time—dependent variance. Secondly we find the eigenfunction (Karhunen — Loeve) expansion of B(g(t)). The eigenfunctions are Bessel functions of the first kind, with a suitable time function for argument, and they are multiplied by another time function. The eigenvalues virtually are determined by the zeros of the Bessel functions.
Mathematical SETI, 2012
Just as Chapter 23 showed the application of the general results obtained in Chapter 22 to the pa... more Just as Chapter 23 showed the application of the general results obtained in Chapter 22 to the particular time-rescaled stochastic process \( {B}(t^{2H})\), the present appendix investigates the application of the general results obtained in Chapter 24 about the square time-rescaled process B2(...) to the particular process \( {B^2}(t^{2H})\).
Mathematical SETI, 2012
In two recent papers [1, 2] the author proved that radio communications between any pair of stars... more In two recent papers [1, 2] the author proved that radio communications between any pair of stars within our Galaxy are feasible with modest transmitted powers if the gravitational lenses of both stars are exploited. In this chapter we extend those innovative results to the case of radio communications between nearby galaxies. We show that radio communications between galaxies may become feasible if supermassive black holes, usually located at the center of galaxies, are exploited as gravitational lenses. In other words, a massive black hole may be regarded as a huge focusing device for radio waves being transmitted out of that galaxy and/or being received from another galaxy.
Mathematical SETI, 2012
Since the 1990s the international scientific community—especially the IAA (International Academy ... more Since the 1990s the international scientific community—especially the IAA (International Academy of Astronautics)—have been discussing the need to keep the farside of the Moon free from man-made radio frequency interference (RFI). In fact, the center of the farside, specifically the Daedalus crater, is an ideal site to set up a future radio telescope (or, more realistically, a phased array) to detect radiowaves of all kinds, which are impossible to detect on Earth because of the ever-growing RFI.
Mathematical SETI, 2012
Let us now change topics completely! Rather than looking for ETs in the Galaxy, we now seek habit... more Let us now change topics completely! Rather than looking for ETs in the Galaxy, we now seek habitable planets for man in the Galaxy. How many are there and how far from us is the nearest such habitable planet?
Mathematical SETI, 2012
It is well known that the probability density function(pdf) \( f_{aX+b} (x) \)of the random varia... more It is well known that the probability density function(pdf) \( f_{aX+b} (x) \)of the random variable \( {aX+b}\)where a and b are arbitrary real constants with respect to the independent variable x, is related to the pdf \( f_{\rm{X}}(x)\)of the random variable X by the linear transformation formula for random variables that reads: $$ f_{aX+b}(x)=\frac{1}{\mid a \mid} f_X \left(\frac{x-b}{\mid a \mid}\right).$$ (5.1)
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Papers by claudio maccone