scholarly journals SETI, Evolution and Human History Merged into a Mathematical Model

2013 ◽  
Vol 12 (3) ◽  
pp. 218-245 ◽  
Author(s):  
Claudio Maccone
Keyword(s):  
Mathematical Model ◽  
Exponential Growth ◽  
Numerical Estimate ◽  
Mean Value ◽  
Darwinian Evolution ◽  
Human History ◽  
The Galaxy ◽  
Positive Time ◽  
A Cell ◽  
Geometric Locus

AbstractIn this paper we propose a new mathematical model capable of merging Darwinian Evolution, Human History and SETI into a single mathematical scheme:(1) Darwinian Evolution over the last 3.5 billion years is defined as one particular realization of a certain stochastic process called Geometric Brownian Motion (GBM). This GBM yields the fluctuations in time of the number of species living on Earth. Its mean value curve is an increasing exponential curve, i.e. the exponential growth of Evolution.(2) In 2008 this author provided the statistical generalization of the Drake equation yielding the number N of communicating ET civilizations in the Galaxy. N was shown to follow the lognormal probability distribution.(3) We call “b-lognormals” those lognormals starting at any positive time b (“birth”) larger than zero. Then the exponential growth curve becomes the geometric locus of the peaks of a one-parameter family of b-lognormals: this is our way to re-define Cladistics.(4) b-lognormals may be also be interpreted as the lifespan of any living being (a cell, or an animal, a plant, a human, or even the historic lifetime of any civilization). Applying this new mathematical apparatus to Human History, leads to the discovery of the exponential progress between Ancient Greece and the current USA as the envelope of all b-lognormals of Western Civilizations over a period of 2500 years.(5) We then invoke Shannon's Information Theory. The b-lognormals' entropy turns out to be the index of “development level” reached by each historic civilization. We thus get a numerical estimate of the entropy difference between any two civilizations, like the Aztec-Spaniard difference in 1519.(6) In conclusion, we have derived a mathematical scheme capable of estimating how much more advanced than Humans an Alien Civilization will be when the SETI scientists will detect the first hints about ETs.

scholarly journals Evolution and mass extinctions as lognormal stochastic processes

2014 ◽  
Vol 13 (4) ◽  
pp. 290-309 ◽  
Author(s):  
Claudio Maccone
Keyword(s):  
Mathematical Model ◽  
Stochastic Process ◽  
Molecular Evolution ◽  
Stochastic Processes ◽  
Neutral Theory ◽  
Mean Value ◽  
Darwinian Evolution ◽  
List Type ◽  
Mass Extinctions ◽  
Human History

AbstractIn a series of recent papers and in a book, this author put forward a mathematical model capable of embracing the search for extra-terrestrial intelligence (SETI), Darwinian Evolution and Human History into a single, unified statistical picture, concisely calledEvo-SETI. The relevant mathematical tools are:(1)Geometric Brownian motion (GBM), the stochastic process representing evolution as the stochastic increase of the number of species living on Earth over the last 3.5 billion years. This GBM is well known in the mathematics of finances (Black–Sholes models). Its main features are that its probability density function (pdf) is a lognormal pdf, and its mean value is either an increasing or, more rarely, decreasing exponential function of the time.(2)The probability distributions known asb-lognormals, i.e. lognormals starting at a certain positive instantb>0 rather than at the origin. Theseb-lognormals were then forced by us to have their peak value located on the exponential mean-value curve of the GBM (Peak-Locus theorem). In the framework of Darwinian Evolution, the resulting mathematical construction was shown to be what evolutionary biologists callCladistics.(3)The (Shannon)entropyof suchb-lognormals is then seen to represent the ‘degree of progress’ reached by each living organism or by each big set of living organisms, like historic human civilizations. Having understood this fact, human history may then be cast into the language ofb-lognormals that are more and more organized in time (i.e. having smaller and smaller entropy, or smaller and smaller ‘chaos’), and have their peaks on the increasing GBM exponential. This exponential is thus the ‘trend of progress’ in human history.(4)All these results also match with SETI in that the statistical Drake equation (generalization of the ordinary Drake equation to encompass statistics) leads just to the lognormal distribution as the probability distribution for the number of extra-terrestrial civilizations existing in the Galaxy (as a consequence of the central limit theorem of statistics).(5)But the most striking new result is that the well-known ‘Molecular Clock of Evolution’, namely the ‘constant rate of Evolution at the molecular level’ as shown by Kimura's Neutral Theory of Molecular Evolution,identifieswith growth rate of the entropy of our Evo-SETI model, because they both grewlinearlyin time since the origin of life.(6)Furthermore, we apply our Evo-SETI model to lognormal stochastic processesother than GBMs.For instance, we provide two models for the mass extinctions that occurred in the past: (a) one based on GBMs and (b) the other based on aparabolicmean value capable of covering both the extinction and the subsequent recovery of life forms.(7)Finally, we show that the Markov & Korotayev (2007, 2008) model for Darwinian Evolution identifies with an Evo-SETI model for which the mean value of the underlying lognormal stochastic process is acubicfunction of the time.In conclusion: we have provided a new mathematical model capable of embracing molecular evolution, SETI and entropy into a simple set of statistical equations based uponb-lognormals and lognormal stochastic processes with arbitrary mean, of which the GBMs are theparticular case of exponential growth.

scholarly journals The Chemical Abundances of the Halo Clusters of the Galaxy

1978 ◽  
Vol 80 ◽  
pp. 177-182
Author(s):  
R. Canterna ◽  
R. A. Schommer
Keyword(s):  
Globular Clusters ◽  
Broad Band ◽  
Mean Value ◽  
Red Giants ◽  
Galactocentric Distance ◽  
Chemical Abundances ◽  
Dwarf Spheroidal Galaxies ◽  
The Galaxy ◽  
Ursa Minor ◽  
Metal Abundances

Photometric metal abundances of individual red giants in eight extremely distant halo globular clusters and the Draco and Ursa Minor dwarf spheroidal galaxies have been obtained using the Washington broad-band system, C, M, T1, T2(Canterna 1976). Observations were made at the KPNO 2.1-m and CTIO 1.5-m telescopes. In Table I we list for each system the mean value of [Fe/H], the number of stars observed in each system, n, the Galactocentric distance, RGC, the intrinsic color of the giant branch at the level of the horizontal branch (HB), (B-V)o,g, and the fraction of HB stars bluer than the RR Lyrae gap, fB. Sources for unpublished color-magnitude diagram (CMD) data are: Pal 11 (Canterna and Schommer), Pal 12 (Canterna and Harris), and Ursa Minor (Schommer, Olszewski and Kunkel).

The expected population size in a cell-size-dependent branching process

1981 ◽  
Vol 18 (01) ◽  
pp. 65-75 ◽  
Author(s):  
Aidan Sudbury
Keyword(s):  
Cell Size ◽  
Exponential Growth ◽  
Branching Process ◽  
Expected Number ◽  
Size Dependent ◽  
Daughter Cells ◽  
Rate Of Increase ◽  
A Cell ◽  
Dependent Growth ◽  
Number Of Cells

In cell-size-dependent growth the probabilistic rate of division of a cell into daughter-cells and the rate of increase of its size depend on its size. In this paper the expected number of cells in the population at time t is calculated for a variety of models, and it is shown that population growths slower and faster than exponential are both possible. When the cell sizes are bounded conditions are given for exponential growth.

First Principle-Based Control Oriented Model of a Gasoline Engine

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Ahmed Yar ◽  
A. I. Bhatti ◽  
Qadeer Ahmed
Keyword(s):  
Mathematical Model ◽  
Gasoline Engine ◽  
Mean Value ◽  
First Principle ◽  
Unified Framework ◽  
Engine Model ◽  
Proposed Model ◽  
Suitable Form ◽  
Speed Fluctuations ◽  
The Mathematical Model

A first principle based-control oriented gasoline engine model is proposed that is based on the mathematical model of the actual piston and crankshaft mechanism. Unlike conventional mean value engine models (MVEMs), which involve approximating the torque production mechanism with a volumetric pump, the proposed model obviates this rather over-simplistic assumption. The alleviation of this assumption leads to the additional features in the model such as crankshaft speed fluctuations and tension in bodies forming the mechanism. The torque production dynamics are derived through Lagrangian mechanics. The derived equations are reduced to a suitable form that can be easily used in the control-oriented model. As a result, the abstraction level is greatly reduced between the engine system and the mathematical model. The proposed model is validated successfully against a commercially available 1.3 L gasoline engine. Being a transparent and more capable model, the proposed model can offer better insight into the engine dynamics, improved control design and diagnosis solutions, and that too, in a unified framework.

scholarly journals Determination of the C/M5+ Ratio in the Galactic Disk

1995 ◽  
Vol 148 ◽  
pp. 276-279
Author(s):  
Francisco J. Fuenmayor
Keyword(s):  
Near Infrared ◽  
Galactic Center ◽  
Galactic Disk ◽  
Mean Value ◽  
Galactocentric Distance ◽  
The Galaxy ◽  
Metal Abundance ◽  
Objective Prism ◽  
M Stars

AbstractA determination of the C/M5+ ratio, as a function of the galactocentric distance, in the galactic disk is presented. These results are based upon previous determinations of the space density for cool carbon stars and for late giant M stars in the Milky Way. Most of these results were obtained from objective-prism surveys in the near infrared using mainly Schmidt-type telescopes. The ratio C/M5+ appears to increase from 0.05 to 0.25 in the galactic disk, from the galactic center outwards. A mean value of 0.15 of this ratio for the Galaxy is suggested. Correlations between the C/M5+ ratio and currently known metal abundance gradients in the galactic disk are discussed.

scholarly journals (In)validating experimentally derived knowledge about influenza A defective interfering particles

2016 ◽  
Vol 13 (124) ◽  
pp. 20160412 ◽  
Author(s):  
Laura E. Liao ◽  
Shingo Iwami ◽  
Catherine A. A. Beauchemin
Keyword(s):  
Mathematical Model ◽  
Experimental Method ◽  
Influenza A Virus ◽  
Influenza A ◽  
Infectious Virus ◽  
Full Length ◽  
Prior Work ◽  
Defective Interfering Particles ◽  
A Cell ◽  
Eclipse Phase

A defective interfering particle (DIP) in the context of influenza A virus is a virion with a significantly shortened RNA segment substituting one of eight full-length parent RNA segments, such that it is preferentially amplified. Hence, a cell co-infected with DIPs will produce mainly DIPs, suppressing infectious virus yields and affecting infection kinetics. Unfortunately, the quantification of DIPs contained in a sample is difficult because they are indistinguishable from standard virus (STV). Using a mathematical model, we investigated the standard experimental method for counting DIPs based on the reduction in STV yield (Bellett & Cooper, 1959, Journal of General Microbiology 21 , 498–509 ( doi:10.1099/00221287-21-3-498 )). We found the method is valid for counting DIPs provided that: (i) an STV-infected cell's co-infection window is approximately half its eclipse phase (it blocks infection by other virions before it begins producing progeny virions), (ii) a cell co-infected by STV and DIP produces less than 1 STV per 1000 DIPs and (iii) a high MOI of STV stock (more than 4 PFU per cell) is added to perform the assay. Prior work makes no mention of these criteria such that the method has been applied incorrectly in several publications discussed herein. We determined influenza A virus meets these criteria, making the method suitable for counting influenza A DIPs.

scholarly journals Mathematical Model of a Cell Size Checkpoint

2010 ◽  
Vol 6 (12) ◽  
pp. e1001036 ◽  
Author(s):  
Marco Vilela ◽  
Jeffrey J. Morgan ◽  
Paul A. Lindahl
Keyword(s):  
Mathematical Model ◽  
Cell Size ◽  
A Cell

scholarly journals New Spectral Observations of the Variable Galaxy Kaz 163

2013 ◽  
Vol 9 (S304) ◽  
pp. 39-40
Author(s):  
Emilia L. Karapetyan
Keyword(s):  
Elliptical Galaxy ◽  
Short Wave ◽  
Mean Value ◽  
Emission Lines ◽  
Byurakan Astrophysical Observatory ◽  
X Ray ◽  
Long Wave ◽  
The Galaxy ◽  
The Mean ◽  
Active Processes

AbstractKaz 163 is a close double galaxy. Its southern component S is compact, with a very blue nucleus, in which heated active processes take place. From time to time gas formations are ejected from it, which behave themselves like emission components around the main emission lines Hα and Hβ, around both from their long-wave and short-wave sides. This paper presents the spectral data of new observations, which were carried out with the 2.6m telescope at the Byurakan Astrophysical Observatory in September 2011. During the former observation in October 1981, lines [NII] λλ 6584,6548 were not visible in the spectrum of the component S. In 2001 they were already visible on the spectrum, and on the spectrum obtained in 2011 they already surpassed the intensity of Hα. The magnitude of the component S is also changing: its nucleus is very blue and its U-B = −0m.63. In the soft X-ray spectral range (0.1–2 keV) the flux of the radiation changed by 45% during 55,000 sec, and in the hard one (2–10keV) it changed up to 3.4 times. Photoindices Γ for the soft and hard ranges in the spectrum of galaxy S, unlike other objects, do not so much differ from each other. The mean value for the first interval is approximately 2.5 and is equal −2.0 for the second one. On the histogram of redshifts Kaz 163 corresponds to the first big peak of the distribution. It is concluded that the component S of the galaxy Kaz 163 is a NLS1 galaxy, with the development of their evolution, is in the preliminary stage. Component N is a normal elliptical galaxy with no activity.

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