scholarly journals Uniform Endomorphisms Which Are Isomorphic to a Bernoulli Shift

2002 ◽  
Vol 156 (1) ◽  
pp. 79 ◽  
Author(s):  
Christopher Hoffman ◽  
Daniel Rudolph
Keyword(s):  
Bernoulli Shift

scholarly journals Probing bacterial cell wall growth by tracing wall-anchored protein complexes

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Yi-Jen Sun ◽  
Fan Bai ◽  
An-Chi Luo ◽  
Xiang-Yu Zhuang ◽  
Tsai-Shun Lin ◽  
...  
Keyword(s):  
Cell Wall ◽  
Cell Shape ◽  
Bernoulli Shift ◽  
Protein Complexes ◽  
Axial Direction ◽  
Cell Wall Growth ◽  
Flagellar Motors ◽  
Shift Map ◽  
Dynamic Assembly ◽  
Wall Growth

AbstractThe dynamic assembly of the cell wall is key to the maintenance of cell shape during bacterial growth. Here, we present a method for the analysis of Escherichia coli cell wall growth at high spatial and temporal resolution, which is achieved by tracing the movement of fluorescently labeled cell wall-anchored flagellar motors. Using this method, we clearly identify the active and inert zones of cell wall growth during bacterial elongation. Within the active zone, the insertion of newly synthesized peptidoglycan occurs homogeneously in the axial direction without twisting of the cell body. Based on the measured parameters, we formulate a Bernoulli shift map model to predict the partitioning of cell wall-anchored proteins following cell division.

Efficient JPEG Encoding Using Bernoulli Shift Map for Secure Communication

2021 ◽  
Author(s):  
Nisar Ahmad ◽  
Muhammad Usman Younus ◽  
Muhammad Rizwan Anjum ◽  
Gulshan Saleem ◽  
Zaheer Ahmed Gondal ◽  
...  
Keyword(s):  
Secure Communication ◽  
Communication Systems ◽  
Bernoulli Shift ◽  
Random Number Generator ◽  
Lossless Compression ◽  
Jpeg Compression ◽  
Digital Data ◽  
Compression Scheme ◽  
Encrypt Data ◽  
Shift Map

Abstract Digital data must be compressed and encrypted to maintain confidentiality and efficient bandwidth usage. These two parameters are essential for information processing in most communication systems. Image compression and encryption may result in reduced restoration quality and degraded performance. This study attempts to provide a compression and encryption scheme for digital data named as Secure-JPEG. This scheme is built on the JPEG compression format, the most widely used lossy compression scheme. It extends the standard JPEG compression algorithm to encrypt data during compression. Secure-JPEG scheme provides encryption along with the process of compression, and it could be altered easily to provide lossless compression. On the other hand, the lossless compression provides less compression ratio and is suitable only in specific scenarios. The paper address the problem of security lacks due to the use of a simple random number generator which can not be cryptographically secure. The improved security characteristics are provided through Generalized Bernoulli Shift Map, which has a chaotic system with demonstrated security. The algorithm's security is tested by several cryptographic tests and the chaotic system’s behavior is also analyzed.

scholarly journals Chaotic Behavior of One-Dimensional Cellular Automata Rule 24

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zujie Bie ◽  
Qi Han ◽  
Chao Liu ◽  
Junjian Huang ◽  
Lepeng Song ◽  
...  
Keyword(s):  
Cellular Automata ◽  
Characteristic Function ◽  
Symbolic Dynamics ◽  
Bernoulli Shift ◽  
Chaotic Behavior ◽  
Class Ii ◽  
Chaotic Attractors ◽  
One Dimensional ◽  
Dynamical Behaviors ◽  
Shift Map

Wolfram divided the 256 elementary cellular automata rules informally into four classes using dynamical concepts like periodicity, stability, and chaos. Rule 24, which is Bernoulliστ-shift rule and is member of Wolfram’s class II, is said to be simple as periodic before. Therefore, it is worthwhile studying dynamical behaviors of four rules, whether they possess chaotic attractors or not. In this paper, the complex dynamical behaviors of rule 24 of one-dimensional cellular automata are investigated from the viewpoint of symbolic dynamics. We find that rule 24 is chaotic in the sense of both Li-Yorke and Devaney on its attractor. Furthermore, we prove that four rules of global equivalenceε52of cellular automata are topologically conjugate. Then, we use diagrams to explain the attractor of rule 24, where characteristic function is used to describe the fact that all points fall into Bernoulli-shift map after two iterations under rule 24.

scholarly journals Aperiodic sequences and aperiodic geodesics

2013 ◽  
Vol 34 (5) ◽  
pp. 1699-1723
Author(s):  
VIKTOR SCHROEDER ◽  
STEFFEN WEIL
Keyword(s):  
Dynamical Systems ◽  
Bernoulli Shift ◽  
Hyperbolic Manifolds ◽  
Quantitative Condition

AbstractWe introduce a quantitative condition on orbits of dynamical systems, which measures their aperiodicity. We show the existence of sequences in the Bernoulli shift and geodesics on closed hyperbolic manifolds which are as aperiodic as possible with respect to this condition.

scholarly journals Projective Stochastic Equations and Nonlinear Long Memory

2014 ◽  
Vol 46 (4) ◽  
pp. 1084-1105
Author(s):  
Ieva Grublytė ◽  
Donatas Surgailis
Keyword(s):  
Long Memory ◽  
Volterra Series ◽  
Bernoulli Shift ◽  
Moving Average ◽  
Stochastic Equations ◽  
Partial Sums ◽  
Martingale Transform ◽  
New Class ◽  
Moving Average Processes ◽  
Nonlinear Stochastic Equations

A projective moving average {Xt, t ∈ ℤ} is a Bernoulli shift written as a backward martingale transform of the innovation sequence. We introduce a new class of nonlinear stochastic equations for projective moving averages, termed projective equations, involving a (nonlinear) kernel Q and a linear combination of projections of Xt on ‘intermediate’ lagged innovation subspaces with given coefficients αi and βi,j. The class of such equations includes usual moving average processes and the Volterra series of the LARCH model. Solvability of projective equations is obtained using a recursive equality for projections of the solution Xt. We show that, under certain conditions on Q, αi, and βi,j, this solution exhibits covariance and distributional long memory, with fractional Brownian motion as the limit of the corresponding partial sums process.

scholarly journals K-property for Maharam extensions of non-singular Bernoulli and Markov shifts

2018 ◽  
Vol 39 (12) ◽  
pp. 3292-3321
Author(s):  
ALEXANDRE I. DANILENKO ◽  
MARIUSZ LEMAŃCZYK
Keyword(s):  
Bernoulli Shift ◽  
Markov Shifts

It is shown that each conservative non-singular Bernoulli shift is either of type $\mathit{II}_{1}$ or $\mathit{III}_{1}$. Moreover, in the latter case the corresponding Maharam extension of the shift is a $K$-automorphism. This extends earlier results obtained by Kosloff for equilibrial shifts. Non-equilibrial shifts of type $\mathit{III}_{1}$ are constructed. We further generalize (partly) the main results to non-singular Markov shifts.

scholarly journals Chaos and shadowing around a homoclinic tube

2003 ◽  
Vol 2003 (16) ◽  
pp. 923-931 ◽  
Author(s):  
Yanguang (Charles) Li
Keyword(s):  
Banach Space ◽  
Invariant Manifold ◽  
Bernoulli Shift ◽  
Current Work ◽  
Shadowing Lemma ◽  
Shift Dynamics

LetFbe aC3diffeomorphism on a Banach spaceB.Fhas a homoclinic tube asymptotic to an invariant manifold. Around the homoclinic tube, Bernoulli shift dynamics of submanifolds is established through a shadowing lemma. This work removes an uncheckable condition of Silnikov (1968). Also, the result of Silnikov does not imply Bernoulli shift dynamics of a single map, but rather only provides a labeling of all invariant tubes around the homoclinic tube. The work of Silnikov was done inℝnand the current work is done in a Banach space.

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