scholarly journals Chaotic Features of the Forward Shift Map on the Generalized m-Symbol Space

2020 ◽  
Vol 4 (3) ◽  
pp. 104-112
Author(s):  
Hena Rani Biswas ◽  
Md. Shahidul Islam
Keyword(s):  
Symbol Space ◽  
Shift Map

SYMBOLIC DYNAMICS FROM HOMOCLINIC TANGLES

2002 ◽  
Vol 12 (03) ◽  
pp. 605-617 ◽  
Author(s):  
PIETER COLLINS
Keyword(s):  
Lower Bound ◽  
Symbolic Dynamics ◽  
Numerical Techniques ◽  
Symbol Space ◽  
Stable And Unstable Manifolds ◽  
Subshift Of Finite Type ◽  
Homoclinic Tangle ◽  
Shift Map ◽  
Homoclinic Tangles ◽  
Unstable Manifolds

We present a method for finding symbolic dynamics for a planar diffeomorphism with a homoclinic tangle. The method only requires a finite piece of tangle, which can be computed with available numerical techniques. The symbol space is naturally given by components of the complement of the stable and unstable manifolds. The shift map defining the dynamics is a factor of a subshift of finite type, and is obtained from a graph related to the tangle. The entropy of this shift map is a lower bound for the topological entropy of the planar diffeomorphism. We give examples arising from the Hénon family.

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.

Gear shift map design methodology for automotive transmissions

2013 ◽  
Vol 228 (1) ◽  
pp. 50-72 ◽  
Author(s):  
Viet Dac Ngo ◽  
Theo Hofman ◽  
Maarten Steinbuch ◽  
Alex Serrarens
Keyword(s):  
Design Methodology ◽  
Gear Shift ◽  
Shift Map ◽  
Map Design

scholarly journals The Research of Sequence Shadowing Property and Regularly Recurrent Point on the Double Inverse Limit Space

2022 ◽  
Vol 2022 ◽  
pp. 1-6
Author(s):  
Zhan jiang Ji
Keyword(s):  
Inverse Limit ◽  
Point Sets ◽  
Recurrent Point ◽  
Shadowing Property ◽  
Limit Space ◽  
Shift Map ◽  
Dynamical Properties ◽  
Definition Of ◽  
Inverse Limit Space

According to the definition of sequence shadowing property and regularly recurrent point in the inverse limit space, we introduce the concept of sequence shadowing property and regularly recurrent point in the double inverse limit space and study their dynamical properties. The following results are obtained: (1) Regularly recurrent point sets of the double shift map σ f ∘ σ g are equal to the double inverse limit space of the double self-map f ∘ g in the regularly recurrent point sets. (2) The double self-map f ∘ g has sequence shadowing property if and only if the double shift map σ f ∘ σ g has sequence shadowing property. Thus, the conclusions of sequence shadowing property and regularly recurrent point are generalized to the double inverse limit space.

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.

On Computable Numbers: Corrections and Critiques

2004 ◽  
Author(s):  
Alan Turing ◽  
Emil Post
Keyword(s):  
Short Note ◽  
Degree Theory ◽  
London Mathematical Society ◽  
Problem Solver ◽  
Symbolic Logic ◽  
Present Position ◽  
Symbol Space ◽  
Important Field ◽  
Formed Part ◽  
The Right

As is not uncommon in work of such complexity, there are a number of mistakes in ‘On Computable Numbers’. Turing corrected some of these in his short note 2.1, published in the Proceedings of the London Mathematical Society a few months after the original paper had appeared. The mathematician Emil L. Post’s critique of ‘On Computable Numbers’ was published in 1947 and formed part of Post’s paper ‘Recursive Unsolvability of a Problem of Thue’. Post is one of the major figures in the development of mathematical logic in the twentieth century, although his work did not gainwide recognition until after his death. (Born in 1897, Post died in the same year as Turing.) By 1936 Post had arrived independently at an analysis of computability substantially similar to Turing’s. Post’s ‘problem solver’ operated in a ‘symbol space’ consisting of ‘a two way infinite sequence of spaces or boxes’. A box admitted ‘of but two possible conditions, i.e., being empty or unmarked, and having a single mark in it, say a vertical stroke’. The problem solver worked in accordance with ‘a fixed unalterable set of directions’ and could perform the following ‘primitive acts’: determine whether the box at present occupied is marked or not; erase any mark in the box that is at present occupied; mark the box that is at present occupied if it is unmarked; move to the box to the right of the present position; move to the box to the left of the present position. Later, Post considerably extended certain of the ideas in Turing’s ‘Systems of Logic Based on Ordinals’, developing the important field now called degree theory. In his draft letter to Church, Turing responded to Post’s remarks concerning ‘Turing convention-machines’. It is doubtful whether Turing ever sent the letter. The approximate time of writing can be inferred from Turing’s opening remarks: Kleene’s review appeared in the issue of the Journal of Symbolic Logic dated September 1947 (12: 90–1) and Turing’s ‘Practical Forms of Type Theory’ appeared in the same journal in June 1948.

Backward Continued Fractions and their Invariant Measures

1996 ◽  
Vol 39 (2) ◽  
pp. 186-198 ◽  
Author(s):  
Karlheinz Gröchenig ◽  
Andrew Haas
Keyword(s):  
Nonnegative Integer ◽  
Continued Fractions ◽  
Invariant Measures ◽  
Specific Class ◽  
Integer Sequences ◽  
New Family ◽  
Shift Map ◽  
Shift Invariant Spaces ◽  
Invariant Spaces

AbstractThis paper continues our investigation of backward continued fractions, associated with the generalized Renyi maps on [0,1). We first show that the dynamics of the shift map on a specific class of shift invariant spaces of nonnegative integer sequences exactly models the maps Tu for u € (0,4). In the second part we construct a new family of explicit invariant measures for certain values of the parameter u.

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