Related papers: Supercentenarian paradox
To determine whether a number is congruent or not is an old and difficult topic and progress is slow. The paper presents a new theorem when a prime number is a congruent number or not. The proof is not necessarily any simpler or shorter…
One of the important questions in statistical mechanics is how irreversibility (time's arrow) occurs when Newton equations of motion are time reversal invariant. One objection to irreversibility is based on Poincar\'e's recursion theorem: a…
Current observations of the fraction of dark energy and a lower limit on its tension, coupled with an assumption of the non-convexity of the dark energy potential, are used to derive a lower limit of 26 billion years for the future age of…
We consider a large population of asexually reproducing individuals in absence of selective pressure. The population size is maintained constant by the environment. We find out that distances between individuals (time from the last common…
We consider the diffusion approximation of branching processes in random environment (BPREs). This diffusion approximation is similar to and mathematically more tractable than BPREs. We obtain the exact asymptotic behavior of the survival…
It is demonstrated that the statistical method of the famous Aspect - Bell experiment requires negative probability densities and negative probabilities from "the thing" researched, else that thing doesn't exist. The thing refers here to…
Throughout history, for reasons of health, well known personalities have opted not to eat to satiety - to under-eat - with known benefits. Here, for the benefits of under-eating a very simple explanation is offered and discussed in some…
Heritability is a central concept in the long-standing debate about nature versus nurture in biological and social sciences. However, existing notions of heritability are based on strong assumptions and do not use explicit causal models. We…
A family of non-equilibrium statistical operators is introduced which differ by the system age distribution over which the quasi-equilibrium (relevant) distribution is averaged. To describe the nonequilibrium states of a system we introduce…
We revisit classic balancing problems for linear extensions of a partially ordered set $P$, proving results that go far beyond many of the best earlier results on this topic. For example, with $p(x\prec y)$ the probability that $x$ precedes…
We propose a complete proof of the Born rule using an additional postulate stating that for a short enough time {\Delta}t between two measurements, a property of a particle will keep its values fixed. This dynamical postulate allows us to…
Biological organisms have to cope with stochastic variations in both the external environment and the internal population dynamics. Theoretical studies and laboratory experiments suggest that population diversification could be an effective…
We study how much data a Bayesian observer needs to correctly infer the relative likelihoods of two events when both events are arbitrarily rare. Each period, either a blue die or a red die is tossed. The two dice land on side $1$ with…
The data recently accumulated by the Kepler mission have demonstrated that small planets are quite common and that a significant fraction of all stars may have an Earth-like planet within their Habitable Zone. These results are combined…
This paper suggests that a universal solution to the Fermi paradox exists and can be derived directly from the definition of life and/or intelligence, therefore eliminating the need for any questionable assumptions and even for the…
Probability models are only useful at explaining the uncertainty of what we do not know, and should never be used to say what we already know. Probability and statistical models are useless at discerning cause. Classical statistical…
We study approximation in the unit interval by rational numbers whose numerators are selected randomly with certain probabilities. Previous work showed that an analogue of Khintchine's Theorem holds in a similar random model and raised the…
The "obesity paradox" has been reported in several observational studies, where obesity was shown to be associated to a decreased mortality in individuals suffering from a chronic disease, such as diabetes or heart failure. Causal arguments…
In this paper we argue that biological fitness is a multi-objective concept hence the statement "fittest" is inappropriate. The following statement is proposed "Survival is mostly for those with non-dominated fitness". Also we use some TV…
Longevity of a taxonomic group is an important issue in understanding the dynamics of evolution. In this respect a key observation is that genera, families or orders can each be assigned a characteristic average lifetime [Van Valen, L.,…