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 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 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.

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 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.

scholarly journals Yield of Indeterminate, Small-vine Cowpea Cultivars Unaffected by Uniformity of Within-row Spacing

HortScience ◽  
1995 ◽  
Vol 30 (5) ◽  
pp. 994-996 ◽  
Author(s):  
Brian A. Kahn ◽  
Peter J. Stoffella ◽  
Daniel I. Leskovar ◽  
James R. Cooksey
Keyword(s):  
Seed Yield ◽  
Vigna Unguiculata ◽  
Harvest Index ◽  
Random Sequence ◽  
Dry Weight ◽  
Row Spacing ◽  
Random Sequences ◽  
Cowpea Cultivars ◽  
Seed Spacing ◽  
Precision Planting

Cowpea [Vigna unguiculata (L.) Walp.] planters can produce variable within-row seed spacing. We determined whether precision planting of cowpea would produce a yield advantage over more random planting at the same rate. Studies were conducted from May 1992 to Feb. 1993 at three locations: Uvalde, Texas; Bixby, Okla.; and Fort Pierce, Fla. Seeds of the indeterminate, small-vine cowpea cultivars Mississippi Silver and Pinkeye Purplehull BVR were hand-planted at 42 per 3.15 m of row. Seeds within rows were either spaced uniformly at 7.5 cm [control, with sd = 0] or in one of two random sequences (sd = 4.8). At harvest, in Oklahoma and Florida, mean within-row spacings were similar, but sd values of random-sequence plots remained greater than those of control plots. Control plots averaged four more plants at harvest than random-sequence plots in Texas. However, seed yield (seed dry weight per hectare) and harvest index were unaffected by uniformity of within-row spacing at all three locations. Thus, precision seeding of indeterminate, small-vine cowpea cultivars seems unlikely to produce a yield advantage over more random planting at the same rate.

Shift-complex sequences

2013 ◽  
Vol 19 (2) ◽  
pp. 199-215 ◽  
Author(s):  
Mushfeq Khan
Keyword(s):  
Kolmogorov Complexity ◽  
Initial Segment ◽  
Random Sequence ◽  
Binary Sequence ◽  
Low Complexity ◽  
Constant Number ◽  
Random Sequences ◽  
Halting Problem ◽  
Complex Sequences ◽  
Do So

AbstractA Martin-Löf random sequence is an infinite binary sequence with the property that every initial segment σ has prefix-free Kolmogorov complexity K(σ) at least ∣σ∣ − c, for some constant c ϵ ω. Informally, initial segments of Martin-Löf randoms are highly complex in the sense that they are not compressible by more than a constant number of bits. However, all Martin-Löf randoms necessarily have contiguous substrings of arbitrarily low complexity. If we demand that all substrings of a sequence be uniformly complex, then we arrive at the notion of shift-complex sequences. In this paper, we collect some of the existing results on these sequences and contribute two new ones. Rumyantsev showed that the measure of oracles that compute shift-complex sequences is zero. We strengthen this result by proving that the Martin-Löf random sequences that do not compute shift-complex sequences are exactly the incomplete ones, in other words, the ones that do not compute the halting problem. In order to do so, we make use of the characterization by Franklin and Ng of the class of incomplete Martin-Löf randoms via a notion of randomness called difference randomness. Turning to the power of shift-complex sequences as oracles, we show that there are shift-complex sequences that do not compute Martin-Löf random (or even Kurtz random) sequences.

On Producing Random Responses

1964 ◽  
Vol 14 (3) ◽  
pp. 931-941 ◽  
Author(s):  
Robert L. Weiss
Keyword(s):  
Individual Differences ◽  
Psychiatric Patients ◽  
Random Sequence ◽  
New Method ◽  
Random Sequences ◽  
Marked Individual ◽  
Binary Choices ◽  
Response Patterning ◽  
Random Responses ◽  
Do So

This paper has surveyed studies of response patterning in an attempt to illustrate the various ways in which this fact of behavior has been used in psychology. The view is expressed that response biasing takes on significance as an important dependent variable when we note that human Ss are unable to generate binary choices in a random sequence even when instructed to do so. Production of random sequences may be intimately related to processes of set and attention; success in generating responses randomly indicates ability to maintain an appropriate set for randomness. Techniques for measuring response patterning, or variability, were reviewed, and a new method was described. Data were presented to illustrate the difficulties encountered by students and psychiatric patients when instructed to generate a random sequence of binary choices. Almost nothing is known about the correlates of ability to maintain a set for randomness, yet there are marked individual differences in this ability. Generating random choices is basically a very non-stimulating task, so that differences in arousal may be of particular importance, when studying this particular kind of set.

scholarly journals Construction of some Chowla sequences

2020 ◽  
Author(s):  
Ruxi Shi
Keyword(s):  
Dynamical Systems ◽  
Differentiable Function ◽  
Random Sequence ◽  
Complex Numbers ◽  
Random Sequences ◽  
Zero Entropy ◽  
Topological Dynamical Systems

AbstractIn this paper, we show that for a twice differentiable function g having countable zeros and for Lebesgue almost every $$\beta >1$$ β > 1 , the sequence $$(e^{2\pi i \beta ^ng(\beta )})_{n\in {\mathbb {N}}}$$ ( e 2 π i β n g ( β ) ) n ∈ N is orthogonal to all topological dynamical systems of zero entropy. To this end, we define the Chowla property and the Sarnak property for numerical sequences taking values 0 or complex numbers of modulus 1. We prove that the Chowla property implies the Sarnak property and show that for Lebesgue almost every $$\beta >1$$ β > 1 , the sequence $$(e^{2\pi i \beta ^n})_{n\in {\mathbb {N}}}$$ ( e 2 π i β n ) n ∈ N shares the Chowla property. It is also discussed whether the samples of a given random sequence have the Chowla property almost surely. Some dependent random sequences having almost surely the Chowla property are constructed.

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