Random Sequences, Series, and Averages

AbstractIn this paper, we investigate the asymptotic behavior of the multivariate record values by using the Reduced Ordering Principle (R-ordering). Necessary and sufficient conditions for weak convergence of the multivariate record values based on sup-norm are determined. Some illustrative examples are given.

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Pseudo-random sequences with non-maximal length realized according to the Galois scheme based on the primitive polynomial in degree

Journal of Physics Conference Series ◽

10.1088/1742-6596/1658/1/012036 ◽

2020 ◽

Vol 1658 ◽

pp. 012036

Author(s):

V A Pesoshin ◽

V M Kuznetsov ◽

A S Kuznetsova

Keyword(s):

Maximal Length ◽

Random Sequences ◽

Primitive Polynomial

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Sampling multidimensional signals by a new class of quasi-random sequences

Multidimensional Systems and Signal Processing ◽

10.1007/s11045-010-0120-5 ◽

2010 ◽

Vol 23 (1-2) ◽

pp. 237-253 ◽

Cited By ~ 4

Author(s):

Ewa Skublska-Rafajłowicz ◽

Ewaryst Rafajłowicz

Keyword(s):

Random Sequences ◽

New Class ◽

Multidimensional Signals

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Asymptotic properties of a certain class of Bush–Mosteller learning models

Advances in Applied Probability ◽

10.2307/1426749 ◽

1980 ◽

Vol 12 (4) ◽

pp. 922-941

Author(s):

Peter Findeisen

Keyword(s):

Necessary Conditions ◽

Asymptotic Properties ◽

Response Sequence ◽

Positive Probability ◽

Learning Models ◽

Random Sequences ◽

Learning Experiment ◽

Sufficient And Necessary Conditions

One general and three specialized models of the Bush–Mosteller type are presented to describe the kind of learning experiment where the response of the learner is always reinforced. Inhomogeneity is admitted. The random sequences of response probabilities and of responses associated with the different models are considered. Information about the existence and the distribution of asymptotic response probabilities is provided. The stress is on sufficient and necessary conditions for convergence (a.s. or with positive probability) of the response sequence, which is what ‘learning' means.

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Efficiency and diversity of protein localization by random signal sequences

Molecular and Cellular Biology ◽

10.1128/mcb.10.6.3163-3173.1990 ◽

1990 ◽

Vol 10 (6) ◽

pp. 3163-3173

Author(s):

C A Kaiser ◽

D Botstein

Keyword(s):

Saccharomyces Cerevisiae ◽

Endoplasmic Reticulum ◽

Signal Peptide ◽

Signal Sequence ◽

Protein Localization ◽

Random Signal ◽

Perinuclear Region ◽

Hybrid Protein ◽

Random Sequences ◽

Beta Galactosidase

Three randomly derived sequences that can substitute for the signal peptide of Saccharomyces cerevisiae invertase were tested for the efficiency with which they can translocate invertase or beta-galactosidase into the endoplasmic reticulum. The rate of translocation, as measured by glycosylation, was estimated in pulse-chase experiments to be less than 6 min. When fused to beta-galactosidase, these peptides, like the normal invertase signal sequence, direct the hybrid protein to a perinuclear region, consistent with localization to the endoplasmic reticulum. The diversity of function of random peptides was studied further by immunofluorescence localization of proteins fused to 28 random sequences: 4 directed the hybrid to the endoplasmic reticulum, 3 directed it to the mitochondria, and 1 directed it to the nucleus.

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Foldamer hypothesis for the growth and sequence differentiation of prebiotic polymers

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1620179114 ◽

2017 ◽

Vol 114 (36) ◽

pp. E7460-E7468 ◽

Cited By ~ 17

Author(s):

Elizaveta Guseva ◽

Ronald N. Zuckermann ◽

Ken A. Dill

Keyword(s):

Computational Model ◽

Short Chain ◽

Attractive Feature ◽

Hydrophobic Surfaces ◽

Random Sequences ◽

Chain Molecules ◽

Single Solution ◽

Specific Sequences

It is not known how life originated. It is thought that prebiotic processes were able to synthesize short random polymers. However, then, how do short-chain molecules spontaneously grow longer? Also, how would random chains grow more informational and become autocatalytic (i.e., increasing their own concentrations)? We study the folding and binding of random sequences of hydrophobic (H) and polar (P) monomers in a computational model. We find that even short hydrophobic polar (HP) chains can collapse into relatively compact structures, exposing hydrophobic surfaces. In this way, they act as primitive versions of today’s protein catalysts, elongating other such HP polymers as ribosomes would now do. Such foldamer catalysts are shown to form an autocatalytic set, through which short chains grow into longer chains that have particular sequences. An attractive feature of this model is that it does not overconverge to a single solution; it gives ensembles that could further evolve under selection. This mechanism describes how specific sequences and conformations could contribute to the chemistry-to-biology (CTB) transition.

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