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We consider training probabilistic classifiers in the case of a large number of classes. The number of classes is assumed too large to perform exact normalisation over all classes. To account for this we consider a simple approach that…

Machine Learning · Statistics 2016-07-08 David Barber , Aleksandar Botev

(l) I have enough evidence to render the sentence S probable. (la) So, relative to what I know, it is rational of me to believe S. (2) Now that I have more evidence, S may no longer be probable. (2a) So now, relative to what I know, it is…

Artificial Intelligence · Computer Science 2016-11-26 Henry E. Kyburg

Starting with a likelihood or preference order on worlds, we extend it to a likelihood ordering on sets of worlds in a natural way, and examine the resulting logic. Lewis (1973) earlier considered such a notion of relative likelihood in the…

Artificial Intelligence · Computer Science 2014-07-29 Joseph Y. Halpern

Well protected human and laboratory animal populations with abundant resources are evolutionary unprecedented. Physical approach, which takes advantage of their extensively quantified mortality, establishes that its dominant fraction yields…

Quantitative Methods · Quantitative Biology 2007-05-23 Mark Ya. Azbel'

The puzzling idea that the combination of independent estimates of the magnitude of a quantity results in a very accurate prediction, which is superior to any or, at least, to most of the individual estimates is known as the wisdom of…

Applications · Statistics 2021-05-26 Sandro M. Reia , José F. Fontanari

We find that the hypothesis made by Jan, Stauffer and Moseley [Theory in Biosc., 119, 166 (2000)] for the evolution of sex, namely a strategy devised to escape extinction due to too many deleterious mutations, is sufficient but not…

Soft Condensed Matter · Physics 2009-11-07 Erkan Tuzel , Volkan Sevim , Ayse Erzan

Gompertz's law tells us that for humans above the age of 35 the death rate increases exponentially with a doubling time of about 10 years. Here, we show that the same law continues to hold even for ages over 100. Beyond 106 there is so far…

Physics and Society · Physics 2016-02-17 Peter Richmond , Bertrand M. Roehner

A wide range of stochastic processes that model the growth and decline of populations exhibit a curious dichotomy: with certainty either the population goes extinct or its size tends to infinity. There is a elegant and classical theorem…

Populations and Evolution · Quantitative Biology 2014-09-17 Mike Steel

Recent developments in cosmology indicate that every history having a nonzero probability is realized in infinitely many distinct regions of spacetime. Thus, it appears that the universe contains infinitely many civilizations exactly like…

Physics and Society · Physics 2010-12-06 Joshua Knobe , Ken D. Olum , Alexander Vilenkin

Contrary to common belief, both the Earth's human population and its economic output have grown faster than exponential, i.e., in a super-Malthusian mode, for most of the known history. These growth rates are compatible with a spontaneous…

Condensed Matter · Physics 2009-10-31 Anders Johansen , Didier Sornette

This paper shows that differentiating the lifetimes of two phenotypes independently from their fertility can lead to a qualitative change in the equilibrium of a population: since survival and reproduction are distinct functional aspects of…

Populations and Evolution · Quantitative Biology 2013-05-22 Ignacio Gallo

There are many randomness notions. On the classical account, many of them are about whether a given infinite binary sequence is random for some given probability. If so, this probability turns out to be the same for all these notions, so…

Probability · Mathematics 2021-07-19 Floris Persiau , Jasper De Bock , Gert de Cooman

Theoretical analysis proves that human survivability is dominated by an unusual physical, rather than biological, mechanism, which yields an exact law. The law agrees with all experimental data, but, contrary to existing theories, it is the…

Biological Physics · Physics 2009-11-07 Mark Ya. Azbel'

Why did the emergence of our species require a timescale similar to the entire habitable period of our planet? Our late appearance has previously been interpreted by Carter (2008) as evidence that observers typically require a very long…

Earth and Planetary Astrophysics · Physics 2016-09-01 Fergus Simpson

Human populations have a complex history of introgression and of changing population size. Human genetic variation has been affected by both these processes, so that inference of past population size depends upon the pattern of gene flow…

Populations and Evolution · Quantitative Biology 2017-03-29 John Hawks

In a recent paper [1] Lineweaver and Davis performed a statistical analysis to claim that the rapidity of biogenesis on Earth indicates high probability of biogenesis on terrestrial- type planets. We argue that the rapid appearance of life…

Astrophysics · Physics 2007-05-23 V. V. Flambaum

Well protected human and laboratory animal populations with abundant resources are evolutionary unprecedented, and their survival far beyond reproductive age may be a byproduct rather than tool of evolution. Physical approach, which takes…

Populations and Evolution · Quantitative Biology 2015-06-26 Mark Ya. Azbel'

We studied two probabilistic models of the distribution of primes in the natural number [1].The paper considers the third probabilistic model of the distribution of primes in the natural number. The author proved that the results obtained…

Number Theory · Mathematics 2015-09-30 Victor Volfson

We consider a stochastic model for an evolving population. We show that in the presence of genotype extinctions the population dies out for a low mutation probability but may survive for a high mutation probability. This turns upside down…

Populations and Evolution · Quantitative Biology 2014-10-24 Rinaldo B. Schinazi

Is it a good idea to use the frequency of events in the past, as a guide to their frequency in the future (as we all do anyway)? In this paper the question is attacked from the perspective of universal prediction of individual sequences. It…

Information Theory · Computer Science 2013-01-29 Yuval Lomnitz , Meir Feder