scholarly journals Nonconventional limits of random sequences related to partitions of integers

2020 ◽  
Vol 148 (4) ◽  
pp. 1791-1804
Author(s):  
Jordan M. Stoyanov ◽  
Christophe Vignat
Keyword(s):  
Random Sequences ◽  
Partitions Of Integers

Asymptotic behavior of the records of multivariate random sequences in a norm sense

2020 ◽  
Vol 70 (6) ◽  
pp. 1457-1468
Author(s):  
Haroon M. Barakat ◽  
M. H. Harpy
Keyword(s):  
Asymptotic Behavior ◽  
Weak Convergence ◽  
Sufficient Conditions ◽  
Record Values ◽  
Necessary And Sufficient Conditions ◽  
Random Sequences ◽  
Necessary And Sufficient

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.

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

2010 ◽  
Vol 23 (1-2) ◽  
pp. 237-253 ◽  
Author(s):  
Ewa Skublska-Rafajłowicz ◽  
Ewaryst Rafajłowicz
Keyword(s):  
Random Sequences ◽  
New Class ◽  
Multidimensional Signals

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

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.

An Invitation to Combinatorics

2021 ◽  
Author(s):  
Shahriar Shahriari
Keyword(s):  
Stirling Numbers ◽  
Exclusion Principle ◽  
Open Problems ◽  
Warm Up ◽  
Calculus Sequence ◽  
Award Winning ◽  
Self Study ◽  
Conversational Style ◽  
The Subject ◽  
Partitions Of Integers

Active student engagement is key to this classroom-tested combinatorics text, boasting 1200+ carefully designed problems, ten mini-projects, section warm-up problems, and chapter opening problems. The author – an award-winning teacher – writes in a conversational style, keeping the reader in mind on every page. Students will stay motivated through glimpses into current research trends and open problems as well as the history and global origins of the subject. All essential topics are covered, including Ramsey theory, enumerative combinatorics including Stirling numbers, partitions of integers, the inclusion-exclusion principle, generating functions, introductory graph theory, and partially ordered sets. Some significant results are presented as sets of guided problems, leading readers to discover them on their own. More than 140 problems have complete solutions and over 250 have hints in the back, making this book ideal for self-study. Ideal for a one semester upper undergraduate course, prerequisites include the calculus sequence and familiarity with proofs.

Efficiency and diversity of protein localization by random signal sequences

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.

scholarly journals Foldamer hypothesis for the growth and sequence differentiation of prebiotic polymers

2017 ◽  
Vol 114 (36) ◽  
pp. E7460-E7468 ◽  
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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