scholarly journals Random graphs, weak coarse embeddings, and higher index theory

2015 ◽  
Vol 07 (03) ◽  
pp. 361-388 ◽  
Author(s):  
Rufus Willett
Keyword(s):  
Geometric Property ◽  
Random Sequence ◽  
Index Theory ◽  
Weak Form ◽  
Bounded Degree ◽  
Random Sequences ◽  
Finite Graphs ◽  
Coarse Embedding ◽  
Property T ◽  
Assembly Map

This paper studies higher index theory for a random sequence of bounded degree, finite graphs with diameter tending to infinity. We show that in a natural model for such random sequences the following hold almost surely: the coarse Baum–Connes assembly map is injective; the coarse Baum–Connes assembly map is not surjective; the maximal coarse Baum–Connes assembly map is an isomorphism. These results are closely tied to issues of expansion in graphs: in particular, we also show that such random sequences almost surely do not have geometric property (T), a strong form of expansion.The key geometric ingredients in the proof are due to Mendel and Naor: in our context, their results imply that a random sequence of graphs almost surely admits a weak form of coarse embedding into Hilbert space.

scholarly journals Von Mises' definition of random sequences reconsidered

1987 ◽  
Vol 52 (3) ◽  
pp. 725-755 ◽  
Author(s):  
Michiel van Lambalgen
Keyword(s):  
Statistical Tests ◽  
Random Sequence ◽  
The Other ◽  
Selection Procedures ◽  
Random Sequences ◽  
Definition Of ◽  
Von Mises ◽  
The Relationship

AbstractWe review briefly the attempts to define random sequences (§0). These attempts suggest two theorems: one concerning the number of subsequence selection procedures that transform a random sequence into a random sequence (§§1–3 and 5); the other concerning the relationship between definitions of randomness based on subsequence selection and those based on statistical tests (§4).

scholarly journals RECYCLE OF RANDOM SEQUENCES

1993 ◽  
Vol 04 (03) ◽  
pp. 569-590 ◽  
Author(s):  
NOBUYASU ITO ◽  
MACOTO KIKUCHI ◽  
YUTAKA OKABE
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Random Sequence ◽  
Random Sequences

The correlation between a random sequence and its transformed sequences is studied. In the case of a permutation operation or, in other words, the shuffling operation, it is shown that the correlation can be so small that the sequences can be regarded as independent random sequences. The applications to the Monte Carlo simulations are also given. This method is especially useful in the Ising Monte Carlo simulation.

scholarly journals Lowness for effective Hausdorff dimension

2014 ◽  
Vol 14 (02) ◽  
pp. 1450011 ◽  
Author(s):  
Steffen Lempp ◽  
Joseph S. Miller ◽  
Keng Meng Ng ◽  
Daniel D. Turetsky ◽  
Rebecca Weber
Keyword(s):  
Hausdorff Dimension ◽  
Random Sequence ◽  
Effective Dimension ◽  
Random Sequences ◽  
Central Notion

We examine the sequences A that are low for dimension, i.e. those for which the effective (Hausdorff) dimension relative to A is the same as the unrelativized effective dimension. Lowness for dimension is a weakening of lowness for randomness, a central notion in effective randomness. By considering analogues of characterizations of lowness for randomness, we show that lowness for dimension can be characterized in several ways. It is equivalent to lowishness for randomness, namely, that every Martin-Löf random sequence has effective dimension 1 relative to A, and lowishness for K, namely, that the limit of KA(n)/K(n) is 1. We show that there is a perfect [Formula: see text]-class of low for dimension sequences. Since there are only countably many low for random sequences, many more sequences are low for dimension. Finally, we prove that every low for dimension is jump-traceable in order nε, for any ε > 0.

scholarly journals The analytical assembly map and index theory

2015 ◽  
Vol 9 (2) ◽  
pp. 603-619 ◽  
Author(s):  
Markus Land
Keyword(s):  
Index Theory ◽  
Assembly Map

scholarly journals Unimodular random trees

2013 ◽  
Vol 35 (2) ◽  
pp. 359-373 ◽  
Author(s):  
ITAI BENJAMINI ◽  
RUSSELL LYONS ◽  
ODED SCHRAMM
Keyword(s):  
Weak Convergence ◽  
Degree Distribution ◽  
Local Convergence ◽  
Hyperbolic Plane ◽  
Random Trees ◽  
Uniform Integrability ◽  
Ideal Boundary ◽  
Bounded Degree ◽  
Regular Tree ◽  
Finite Graphs

AbstractWe consider unimodular random rooted trees (URTs) and invariant forests in Cayley graphs. We show that URTs of bounded degree are the same as the law of the component of the root in an invariant percolation on a regular tree. We use this to give a new proof that URTs are sofic, a result of Elek. We show that ends of invariant forests in the hyperbolic plane converge to ideal boundary points. We also note that uniform integrability of the degree distribution of a family of finite graphs implies tightness of that family for local convergence, also known as random weak convergence.

Goodness-of-fit tests for random sequences incorporating several components

2017 ◽  
Vol 25 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Tetiana O. Ianevych ◽  
Yuriy V. Kozachenko ◽  
Viktor B. Troshki
Keyword(s):  
Covariance Function ◽  
Goodness Of Fit ◽  
Random Sequence ◽  
Random Variables ◽  
Gaussian Random Variables ◽  
Random Sequences ◽  
Goodness Of Fit Tests

AbstractIn this paper we have constructed the goodness-of-fit tests incorporating several components, like expectation and covariance function for identification of a non-centered univariate random sequence or auto-covariances and cross-covariances for identification of a centered multivariate random sequence. For the construction of the corresponding estimators and investigation of their properties we utilized the theory of square Gaussian random variables.

scholarly journals Group approximation in Cayley topology and coarse geometry, III: Geometric property (T)

2015 ◽  
Vol 15 (2) ◽  
pp. 1067-1091 ◽  
Author(s):  
Masato Mimura ◽  
Narutaka Ozawa ◽  
Hiroki Sako ◽  
Yuhei Suzuki
Keyword(s):  
Geometric Property ◽  
Coarse Geometry ◽  
Property T

scholarly journals Random Sequences Rapidly Evolve into de novo Promoters

2017 ◽  
Author(s):  
Avihu H. Yona ◽  
Eric J. Alm ◽  
Jeff Gore
Keyword(s):  
Protein Interactions ◽  
De Novo ◽  
Random Sequence ◽  
Lac Operon ◽  
Protein Protein Interactions ◽  
Random Sequences ◽  
E Coli ◽  
Promoter Recognition ◽  
Motif Recognition ◽  
Active Promoter

AbstractHow do new promoters evolve? To follow evolution of de novo promoters, we put various random sequences upstream to the lac operon in Escherichia coli and evolved the cells in the presence of lactose. We found that a typical random sequence of ~100 bases requires only one mutation in order to enable growth on lactose by increasing resemblance to the canonical promoter motifs. We further found that ~10% of random sequences could serve as active promoters even without any period of evolutionary adaptation. Such a short mutational distance from a random sequence to an active promoter may improve evolvability yet may also lead to undesirable accidental expression. We found that across the E. coli genome accidental expression is minimized by avoiding codon combinations that resemble promoter motifs. Our results suggest that the promoter recognition machinery has been tuned to allow high accessibility to new promoters, and similar findings might also be observed in higher organisms or in other motif recognition machineries, like transcription factor binding sites or protein-protein interactions.

scholarly journals Upper bound of probability of receiving error of aperiodic pseudo-random sequence at jamming

2020 ◽  
Vol 2020 (1) ◽  
pp. 64-72
Author(s):  
Iscandar Maratovich Azhmukhamedov ◽  
Evgeny Melnikov
Keyword(s):  
Communication Systems ◽  
Communication Channel ◽  
Random Sequence ◽  
Upper Bounds ◽  
Error Distribution ◽  
Reliable Operation ◽  
Broadband Communication ◽  
Worst Case ◽  
Random Sequences ◽  
Synchronizing Sequence

The article discusses the obtained estimate of the upper bounds for the probable receiving error of the synchronizing sequence during sensor phasing of aperiodic pseudo-random sequences (CRR) in broadband communication systems in the channels of low quality with strong disturbances of natural and organized structure. The obtained results allow to design synchronization systems of pseudo-random sequences for the worst case, which guarantees their reliable operation in low-quality channels, and, unlike the well-known methods, the estimation of synchronization of aperiodic pseudo-random sequence sensors doesn’t depend on the error distribution in the communication channel and the period of sequence. The appointed differences simplify the evaluation of synchronization in the operation of broadband communication systems in low-quality channels.

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