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Stop calling Bernoulli’s law of large numbers his "Golden Theorem" (Please?)
Revista Brasileira de História da MatemáticaJakob Bernoulli (1655 - 1705) proved the first form of the law of large numbers before 1690 and realized the range of applications of probability calculus would be largely widened by the result.
Marcio Alves Diniz
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The Essence of the Law of Large Numbers [PDF]
, 1995 The law of large numbers, not really a law but a mathematical theorem, is at the same time a justification for application of statistics and an essential tool for the mathematical theory of probability. As such, it must be taught to many students. The traditional method for this, using independent and identically distributed random variables, was ...
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The Shewanella oneidensis Fic enzyme SoFic targets the switch‐I region of EF‐Tu for AMPylation
FEBS Letters, EarlyView.Fic enzymes mediate diverse post‐translational modifications across all domains of life, including AMPylation. Prokaryotic EF‐Tu can be AMPylated and deAMPylated by the conserved Fic enzyme SoFic. Structural and biochemical approaches were used to characterize the effect of AMPylation on EF‐Tu, SoFic's enzymatic activities, and the enzyme‐target ...
Svenja Runge +6 more
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Uniform strong law of large numbers for random signed measures
, 2018 We prove a strong law of large numbers for random signed measures on Euclidean space that holds uniformly over a family of arguments (sets) scaled by diagonal matrices.
Klesov, Oleg I. +4 more
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A Conditional Law of Large Numbers
The Annals of Probability, 1980 It is shown that, when conditional on a set of given average values, the frequency distribution of a series of independent random variables with a common finite distribution converges in probability to the distribution which has the maximum relative entropy for the given mean values.
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Artificial molecular machines and motors—Design and control of nanoscale motion
FEBS Letters, EarlyView.Molecules are constantly moving because of thermal fluctuations, but random motion alone cannot be exploited to perform directional tasks. Artificial molecular machines use chemical, electrical, or light energy to bias this motion. Molecular shuttles, rotary motors, and supramolecular pumps illustrate how nanoscale movement can be controlled and ...
Leonardo Andreoni, Alberto Credi
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Characterization of risk: a sharp law of large numbers [PDF]
, 2007 An extensive literature in economics uses a continuum of random variables to model individual random shocks imposed on a large population. Let H denote the Hilbert space of square-integrable random variables.
Sun, Yeneng, Hammond, Peter J.
core
AxiomsWe show how the Brooks–Chacon Biting Lemma can be combined with the Castaing–Saadoune procedure to provide the complete rate of convergence along subsequences when the uniformly boundedness condition is violated.
George Stoica, Deli Li, Liping Liu
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Inequalities for the Law of Large Numbers
The Annals of Mathematical Statistics, 1972 Let $X_1, X_2, X_3, \cdots$ be independent random variables and $a_1, a_2, a_3, \cdots$ positive real numbers. Define $F(t) = \sup_k P\{|X_k| > t\}$ and $S_m = \sum^m_{k=1} a_k X_k.$ Inequalities of the form $P\{\sup_m|S_m| > \delta\} \leqq C \sum_k \int^1_0 \varphi'(u)F(u/a_k) du$ are given for a large class of functions $\varphi$, as well as ...
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Molecular Oncology, EarlyView.In this explorative study, the abundance of circular RNA molecules in bone marrow stem cells was found to be elevated in patients with high‐risk myelodysplastic neoplasms, and to be associated with an increased risk of progression to acute myeloid leukemia.
Eileen Wedge +17 more
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