FRACTAL DIMENSION OF THE DROSOPHILA CIRCADIAN CLOCK

Fractals ◽  
2011 ◽  
Vol 19 (04) ◽  
pp. 423-430 ◽  
Author(s):  
HASSAN M. FATHALLAH-SHAYKH
Keyword(s):  
Fractal Dimension ◽  
Circadian Clock ◽  
Lyapunov Exponents ◽  
Fractal Geometry ◽  
Target Genes ◽  
Transcriptional Repressor ◽  
High Dimensional ◽  
Counting Procedure ◽  
Box Counting ◽  
Direct Target

Fractal geometry can adequately represent many complex and irregular objects in nature. The fractal dimension is typically computed by the box-counting procedure. Here I compute the box-counting and the Kaplan-Yorke dimensions of the 14-dimensional models of the Drosophila circadian clock. Clockwork Orange (CWO) is transcriptional repressor of direct target genes that appears to play a key role in controlling the dynamics of the clock. The findings identify these models as strange attractors and highlight the complexity of the time-keeping actions of CWO in light-day cycles. These fractals are high-dimensional counterexamples of the Kaplan-Yorke conjecture that uses the spectrum of the Lyapunov exponents.

The Interpretation of Vernacular Architecture through Fractal Models

2016 ◽  
pp. 55-77
Author(s):  
Ehsan Reza ◽  
Ozgur Dincyurek
Keyword(s):  
Twentieth Century ◽  
Fractal Dimension ◽  
Fractal Geometry ◽  
Vernacular Architecture ◽  
Decision Makers ◽  
Housing Developments ◽  
Mathematical Algorithm ◽  
Fractal Models ◽  
Box Counting ◽  
Box Counting Method

Mathematical algorithm and nonlinear theories were used in order to study the establishment and development of traditional settlements since the second half of twentieth century. In order to interrogate vernacular architecture, fractal geometry is one of the most advanced methodologies in this study. Vernacular architecture is an organic architecture, which is formed in response to environmental, cultural, economical factors. There are plenty of variations in topography; climate and geographical issues among the mountainous areas in Iran. Therefor, there are many useful thought, which can be learnt from the existing vernacular architecture. This study is going to investigate fractal pattern of housing in Masouleh village, Iran. By referring to the fractal dimension calculated with box counting method, different type of information will be collected and this attempt will help decision makers, planners, architects and designers, especially in new housing developments.

A MODIFIED BOX-COUNTING METHOD

Fractals ◽  
1994 ◽  
Vol 02 (02) ◽  
pp. 321-324 ◽  
Author(s):  
S. KYRIACOS ◽  
S. BUCZKOWSKI ◽  
F. NEKKA ◽  
L. CARTILIER
Keyword(s):  
Fractal Dimension ◽  
Biomedical Research ◽  
Fractal Geometry ◽  
Traditional Method ◽  
Counting Method ◽  
Standard Methods ◽  
Box Counting ◽  
Irregular Structures ◽  
Proposed Modification ◽  
Box Counting Method

Fractal geometry has been widely used to characterize irregular structures. Our interest in applying this concept in biomedical research leads us to the conclusion that there are no standard methods. In order to objectively set parameters involved in the estimation of fractal dimension, a significantly more accurate and efficient box-counting method based on a new algorithm was developed. Measurements of mathematical objects with known fractal dimension was performed using the traditional method and the proposed modification. The latter always yields results with less than 1% difference from the theoretical value, which represents a significant improvement.

An Image Segmentation Calculation Based on Differential Box-Counting of Fractal Geometry

2015 ◽  
Vol 719-720 ◽  
pp. 964-968 ◽  
Author(s):  
Tao He ◽  
Long Fei Cheng ◽  
Qing Hua Wu ◽  
Zheng Jia Wang ◽  
Lian Gen Yang ◽  
...  
Keyword(s):  
Image Segmentation ◽  
Fractal Dimension ◽  
Fractal Geometry ◽  
Computer Image ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Counting Method ◽  
Box Counting ◽  
Box Counting Method ◽  
Important Significance

Differential box-counting of fractal geometry has been widely used in image processing.A method which uses the differential box-counting to segment the gathered images is discussed in this paper . It is to construct a three-dimensional gray space and use the same size boxes to contain the three dimensional space.The number of boxes needed to cover the entire image are calculated .Different sizes of boxes can receive different number of boxes, so least squares method is used to calculate the fractal dimension. According to the fractal dimension parameters, appropriate threshold is chose to segment the image by using binarization .From the handle case of bearing pictures can be seen that image segmentation based on differential box-counting method can get clear image segmentation .This method is easy to understand, to operate, and has important significance on computer image segmentation .

Fractal Geometry Based Mathematical Model and Simulation of Permeability of Dehulled Rapeseed Cake

2010 ◽  
Vol 29-32 ◽  
pp. 269-274
Author(s):  
Xiao Zheng ◽  
Jing Zhou Wang ◽  
Guo Xiang Lin ◽  
Nong Wan ◽  
Don Ping He
Keyword(s):  
Fractal Dimension ◽  
Fractal Geometry ◽  
Fractal Dimensions ◽  
Image Analyzer ◽  
Rapeseed Cake ◽  
Box Counting ◽  
Model And Simulation ◽  
Pore Size Distributions ◽  
Cold Condition ◽  
Box Counting Method

In view of the fact that dehulled rapeseed cake formed under cold pressing condition is a fractal structure, the relation between the permeability and the pore fractal dimension of dehulled rapeseed cake has been investigated using fractal geometry. The microstructures of dehulled rapeseed cake under six pressing pressures are measured by using scanning electronic microscope and Image-pro image analyzer. The fractal dimensions of pore size distributions are measured by the box-counting method. Combining Hagen-Poiseulle equation with Darcy’s law for flow of fluid through porous media, the relational expression of fractal dimension and permeability has been developed to predicate the permeability of compressed dehulled rapeseed cake under cold condition. The permeability experiments of dehulled rapeseed cake are also carried out in order to validate the predication model proposed in this study. The value of mean relative error is 15.5%. A fairly good agreement is obtained in the case of high pressing pressures.

BIFURCATION TO HIGH-DIMENSIONAL CHAOS

2000 ◽  
Vol 10 (06) ◽  
pp. 1471-1483 ◽  
Author(s):  
MARY ANN HARRISON ◽  
YING-CHENG LAI
Keyword(s):  
Fractal Dimension ◽  
Lyapunov Exponent ◽  
Characteristic Feature ◽  
Lyapunov Exponents ◽  
High Dimensional ◽  
Numerical Examples ◽  
System A ◽  
Characteristic Features ◽  
Pass Through ◽  
Low Dimensional

High-dimensional chaos has been an area of growing recent investigation. The questions of how dynamical systems become high-dimensionally chaotic with multiple positive Lyapunov exponents, and what the characteristic features associated with the transition are, remain less investigated. In this paper, we present one possible route to high-dimensional chaos. By this route, a subsystem becomes chaotic with one positive Lyapunov exponent via one of the known routes to low-dimensional chaos, after which the complementary subsystem becomes chaotic, leading to additional positive Lyapunov exponents for the whole system. A characteristic feature of this route is that the additional Lyapunov exponents pass through zero smoothly. As a consequence, the fractal dimension of the chaotic attractor changes continuously through the transition, in contrast to the transition to low-dimensional chaos at which the fractal dimension changes abruptly. We present a heuristic theory and numerical examples to illustrate this route to high-dimensional chaos.

Fractal Research of Pore-Structure in Porous Titanium Fibers

2014 ◽  
Vol 804 ◽  
pp. 259-262 ◽  
Author(s):  
Shi Feng Liu ◽  
Hui Ping Tang ◽  
Xin Yang ◽  
Zhao Hui Zhang
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Fractal Geometry ◽  
Three Dimensional ◽  
Quantitative Relationship ◽  
Porous Titanium ◽  
Spatial Network ◽  
Vacuum Sintering ◽  
Box Counting ◽  
Box Counting Dimension

This paper adopted the vacuum sintering technology to prepare titanium fiber porous material with a three-dimensional spatial network fiber backbone and connectivity pore structure. With the help of fractal geometry theory and scanning and digitizing the image, the fractal research of pore-structure in porous titanium fibers is executed and we studied the influence of adopting the box-counting dimension method to calculate the fractal dimension. Additionally, we determined the quantitative relationship between fractal dimension and the porosity of the porous in titanium fiber, while described the physical meaning of the fractal dimension.

Optimal Density Determination of Bouguer Anomaly Using Fractal Analysis (Case of study: Charak area,IRAN)

2005 ◽  
Vol 1 (1) ◽  
pp. 21-24
Author(s):  
Hamid Reza Samadi
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Fractal Analysis ◽  
Fractal Geometry ◽  
Host Rock ◽  
Bouguer Anomaly ◽  
Research Area ◽  
Density Difference ◽  
Optimal Density

In exploration geophysics the main and initial aim is to determine density of under-research goals which have certain density difference with the host rock. Therefore, we state a method in this paper to determine the density of bouguer plate, the so-called variogram method based on fractal geometry. This method is based on minimizing surface roughness of bouguer anomaly. The fractal dimension of surface has been used as surface roughness of bouguer anomaly. Using this method, the optimal density of Charak area insouth of Hormozgan province can be determined which is 2/7 g/cfor the under-research area. This determined density has been used to correct and investigate its results about the isostasy of the studied area and results well-coincided with the geology of the area and dug exploratory holes in the text area

3D box-counting algorithm for calculating fractal dimension of cities

2010 ◽  
Vol 30 (8) ◽  
pp. 2070-2072
Author(s):  
Le-shan ZHANG ◽  
Ge CHEN ◽  
Yong HAN ◽  
Tao ZHANG
Keyword(s):  
Fractal Dimension ◽  
Box Counting ◽  
Counting Algorithm

MiRNA-145 and Its Direct Downstream Targets in Digestive System Cancers: A Promising Therapeutic Target

2020 ◽  
Vol 26 ◽  
Author(s):  
Yini Ma ◽  
Xiu Cao ◽  
Guojuan Shi ◽  
Tianlu Shi
Keyword(s):  
Digestive System ◽  
Target Genes ◽  
Malignant Neoplasm ◽  
Vital Role ◽  
Diagnostic Biomarkers ◽  
Cellular Processes ◽  
Promising Therapeutic Target ◽  
Direct Target ◽  
Potential Strategy

: MicroRNAs (miRNAs) play a vital role in the onset and development of many diseases, including cancers. Emerging evidence shows that numerous miRNAs have the potential to be used as diagnostic biomarkers for cancers, and miRNA-based therapy may be a promising therapy for the treatment of malignant neoplasm. MicroRNA-145 (miR-145) has been considered to play certain roles in various cellular processes, such as proliferation, differentiation and apoptosis, via modulating expression of direct target genes. Recent reports show that miR-145 participates in the progression of digestive system cancers, and plays crucial and novel roles for cancer treatment. In this review, we summarize the recent knowledge concerning the function of miR-145 and its direct targets in digestive system cancers. We discuss the potential role of miR-145 as valuable biomarkers for digestive system cancers and how miR-145 regulates these digestive system cancers via different targets to explore the potential strategy of targeting miR-145.

scholarly journals Supramolecular Fractal Growth of Self-Assembled Fibrillar Networks

Gels ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 46
Author(s):  
Pedram Nasr ◽  
Hannah Leung ◽  
France-Isabelle Auzanneau ◽  
Michael A. Rogers
Keyword(s):  
Fractal Dimension ◽  
Crystallization Temperature ◽  
Cayley Tree ◽  
Fractal Dimensions ◽  
Self Similarity ◽  
Avrami Model ◽  
Cluster Aggregation ◽  
Box Counting ◽  
Self Assembled ◽  
Limited Diffusion

Complex morphologies, as is the case in self-assembled fibrillar networks (SAFiNs) of 1,3:2,4-Dibenzylidene sorbitol (DBS), are often characterized by their Fractal dimension and not Euclidean. Self-similarity presents for DBS-polyethylene glycol (PEG) SAFiNs in the Cayley Tree branching pattern, similar box-counting fractal dimensions across length scales, and fractals derived from the Avrami model. Irrespective of the crystallization temperature, fractal values corresponded to limited diffusion aggregation and not ballistic particle–cluster aggregation. Additionally, the fractal dimension of the SAFiN was affected more by changes in solvent viscosity (e.g., PEG200 compared to PEG600) than crystallization temperature. Most surprising was the evidence of Cayley branching not only for the radial fibers within the spherulitic but also on the fiber surfaces.

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