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 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.

On C*-Algebras Associated with Subshifts

1997 ◽  
Vol 08 (03) ◽  
pp. 357-374 ◽  
Author(s):  
Kengo Matsumoto
Keyword(s):  
Symbolic Dynamics ◽  
Markov Shift ◽  
C Algebra ◽  
C Algebras ◽  
Markov Shifts ◽  
Universal Properties

We construct and study C*-algebras associated with subshifts in symbolic dynamics as a generalization of Cuntz–Krieger algebras for topological Markov shifts. We prove some universal properties for the C*-algebras and give a criterion for them to be simple and purely infinite. We also present an example of a C*-algebra coming from a subshift which is not conjugate to a Markov shift.

scholarly journals Irreducible complexity of iterated symmetric bimodal maps

2005 ◽  
Vol 2005 (1) ◽  
pp. 69-85 ◽  
Author(s):  
J. P. Lampreia ◽  
R. Severino ◽  
J. Sousa Ramos
Keyword(s):  
Tree Structure ◽  
Unimodal Maps ◽  
Markov Shifts ◽  
Irreducible Complexity ◽  
The Family

We introduce a tree structure for the iterates of symmetric bimodal maps and identify a subset which we prove to be isomorphic to the family of unimodal maps. This subset is used as a second factor for a∗-product that we define in the space of bimodal kneading sequences. Finally, we give some properties for this product and study the∗-product induced on the associated Markov shifts.

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 A class of Markov shifts which are Bernoulli shifts

1971 ◽  
Vol 6 (3) ◽  
pp. 323-328 ◽  
Author(s):  
Robert McCabe ◽  
Paul Shields
Keyword(s):  
Bernoulli Shifts ◽  
Markov Shifts

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.

Sign in / Sign up

Export Citation Format

Share Document