scholarly journals Stochastic Gene Expression Revisited

Genes ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 648
Author(s):  
Andrzej Tomski ◽  
Maciej Zakarczemny
Keyword(s):  
Gene Expression ◽  
Continuous Time ◽  
Iterated Function System ◽  
Main Idea ◽  
Stochastic Gene Expression ◽  
Limit Measure ◽  
Piecewise Deterministic Markov Process ◽  
Probabilistic Description ◽  
Iterated Function ◽  
Random Jump

We investigate the model of gene expression in the form of Iterated Function System (IFS), where the probability of choice of any iterated map depends on the state of the phase space. Random jump times of the process mark activation periods of the gene when pre-mRNA molecules are produced before mRNA and protein processing phases occur. The main idea is inspired by the continuous-time piecewise deterministic Markov process describing stochastic gene expression. We show that for our system there exists a unique invariant limit measure. We provide full probabilistic description of the process with a comparison of our results to those obtained for the model with continuous time.

Fractional fractals

2020 ◽  
Vol 23 (5) ◽  
pp. 1329-1348
Author(s):  
J.A. Tenreiro Machado ◽  
Daniel Cao Labora
Keyword(s):  
Fractional Derivative ◽  
Iterated Function System ◽  
Main Idea ◽  
Higher Order ◽  
Numerical Calculations ◽  
Function System ◽  
Limit Sets ◽  
First Order ◽  
Iterated Function

Abstract This paper introduces the notion of “fractional fractals”. The main idea is to establish a connection between the classical iterated function system and the first order truncation of the Gründwald-Letnikov fractional derivative. This allows us to consider higher order truncations, and also to study the limit sets for these higher order systems. We prove several results involving the existence and dimension of such limit sets, that will be called “fractional fractals”. Some numerical calculations and representations illustrate relevant examples.

scholarly journals Graph directed Markov systems on Hilbert spaces

2009 ◽  
Vol 147 (2) ◽  
pp. 455-488 ◽  
Author(s):  
R. D. MAULDIN ◽  
T. SZAREK ◽  
M. URBAŃSKI
Keyword(s):  
Hausdorff Measure ◽  
Iterated Function System ◽  
Sufficient Conditions ◽  
Topological Pressure ◽  
Limit Set ◽  
Covering Theorem ◽  
Limit Sets ◽  
Markov Systems ◽  
Polish Spaces ◽  
Iterated Function

AbstractWe deal with contracting finite and countably infinite iterated function systems acting on Polish spaces, and we introduce conformal Graph Directed Markov Systems on Polish spaces. Sufficient conditions are provided for the closure of limit sets to be compact, connected, or locally connected. Conformal measures, topological pressure, and Bowen's formula (determining the Hausdorff dimension of limit sets in dynamical terms) are introduced and established. We show that, unlike the Euclidean case, the Hausdorff measure of the limit set of a finite iterated function system may vanish. Investigating this issue in greater detail, we introduce the concept of geometrically perfect measures and provide sufficient conditions for geometric perfectness. Geometrical perfectness guarantees the Hausdorff measure of the limit set to be positive. As a by–product of the mainstream of our investigations we prove a 4r–covering theorem for all metric spaces. It enables us to establish appropriate co–Frostman type theorems.

ARCLENGTH AS THE INVARIANT MEASURE FOR AN IFS WITH PROBABILITIES

Fractals ◽  
2015 ◽  
Vol 23 (04) ◽  
pp. 1550046
Author(s):  
D. LA TORRE ◽  
F. MENDIVIL
Keyword(s):  
Invariant Measure ◽  
Iterated Function System ◽  
Function System ◽  
Iterated Function

Given a continuous rectifiable function [Formula: see text], we present a simple Iterated Function System (IFS) with probabilities whose invariant measure is the normalized arclength measure on the graph of [Formula: see text].

Stochastic Fractal Modeling and Process Planning for Machining Using Two-Dimensional Iterated Function System

2008 ◽  
Vol 392-394 ◽  
pp. 575-579
Author(s):  
Yu Hao Li ◽  
Jing Chun Feng ◽  
Y. Li ◽  
Yu Han Wang
Keyword(s):  
Path Planning ◽  
Tool Path ◽  
Iterated Function System ◽  
Numerical Control ◽  
Function System ◽  
Tool Path Planning ◽  
Ongoing Research ◽  
Iterated Function ◽  
Planning Algorithm ◽  
Path Planning Algorithm

Self-affine and stochastic affine transforms of R2 Iterated Function System (IFS) are investigated in this paper for manufacturing non-continuous objects in nature that exhibit fractal nature. A method for modeling and fabricating fractal bio-shapes using machining is presented. Tool path planning algorithm for numerical control machining is presented for the geometries generated by our fractal generation function. The tool path planning algorithm is implemented on a CNC machine, through executing limited number of iteration. This paper describes part of our ongoing research that attempts to break through the limitation of current CAD/CAM and CNC systems that are oriented to Euclidean geometry objects.

scholarly journals Quantifying the contribution of chromatin dynamics to stochastic gene expression reveals long, locus-dependent periods between transcriptional bursts

BMC Biology ◽  
2013 ◽  
Vol 11 (1) ◽  
pp. 15 ◽  
Author(s):  
José Viñuelas ◽  
Gaël Kaneko ◽  
Antoine Coulon ◽  
Elodie Vallin ◽  
Valérie Morin ◽  
...  
Keyword(s):  
Gene Expression ◽  
Stochastic Gene Expression ◽  
Chromatin Dynamics

A Novel Iterated Function System-Based Model for Coloured Image Encryption

2021 ◽  
Vol 12 (2) ◽  
pp. 1-10
Author(s):  
Amine Rahmani
Keyword(s):  
Image Encryption ◽  
Iterated Function System ◽  
Mathematical Concept ◽  
Logistic Equation ◽  
Encryption Scheme ◽  
Symmetric Encryption ◽  
New Model ◽  
Proposed Model ◽  
Iterated Function ◽  
Chaotic Cryptography

Chaotic cryptography has been a well-studied domain over the last few years. Many works have been done, and the researchers are still getting benefit from this incredible mathematical concept. This paper proposes a new model for coloured image encryption using simple but efficient chaotic equations. The proposed model consists of a symmetric encryption scheme in which it uses the logistic equation to generate secrete keys then an affine recursive transformation to encrypt pixels' values. The experimentations show good results, and theoretic discussion proves the efficiency of the proposed model.

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