scholarly journals Genome-level parameters describe the pan-nuclear fractal nature of eukaryotic interphase chromosomal arrangement

2016 ◽  
Author(s):  
Sarosh N. Fatakia ◽  
Basuthkar J. Rao
Keyword(s):  
Fractal Dimension ◽  
Large Scale ◽  
Fractal Dimensions ◽  
Rod Photoreceptor ◽  
Fractal Nature ◽  
Scaling Effects ◽  
Closely Related Species ◽  
Chromosomal Arrangement ◽  
Genome Level ◽  
Regulatory Functions

AbstractLong-range inter-chromosomal interactions in the interphase nucleus subsume critical genome-level regulatory functions such as transcription and gene expression. To decipher a physical basis of diverse pan-nuclear inter-chromosomal arrangement that facilitates these processes, we investigate the scaling effects as obtained from disparate eukaryotic genomes and compare their total number of genes with chromosome size. First, we derived the pan-nuclear average fractal dimension of inter-chromosomal arrangement in interphase nuclei of different species and corroborated our predictions with independently reported results. Then, we described the different patterns across disparate unicellular and multicellular eukaryotes. We report that, unicellular lower eukaryotes have inter-chromosomal fractal dimension ≈ 1 at pan-nuclear dimensions, which is analogous to the multi-polymer crumpled globule model. Multi-fractal dimensions, corresponding to different inter-chromosomal arrangements emerged from multicellular eukaryotes, such that closely related species have relatively similar patterns. Using this theoretical approach, we computed that the average fractal dimension from human acrocentric versus metacentric chromosomes was distinct, implying that a multi-fractal nature of inter-chromosomal geometry may facilitate viable large-scale chromosomal aberrations, such as Robertsonian translocation. Next, based on inter-chromosomal geometry, we also report that this average multi-fractal dimension in nocturnal mammals is distinct from diurnal ones, and our result seems to corroborate the plasticity of the inter-chromosomal arrangement reported among nocturnal species. (For example, the arrangement of heterochromatin versus euchromatin in rod photoreceptor and fibroblast cells of Mus musculus is inverted.) Altogether, our results substantiate that genome-level constraints have also co-evolved with the average pan-nuclear fractal dimension of inter-chromosomal folding during eukaryotic evolution.

Fractal behavior and detectibility limits of geophysical surveys

Geophysics ◽  
1998 ◽  
Vol 63 (6) ◽  
pp. 1943-1946 ◽  
Author(s):  
V. P. Dimri
Keyword(s):  
Fractal Dimension ◽  
Seismic Hazard ◽  
Large Scale ◽  
Seismic Hazard Assessment ◽  
Fractal Nature ◽  
Seismic Profiling ◽  
Geophysical Surveys ◽  
Nonrandom Distribution ◽  
Measuring Network ◽  
The Difference

The detectibility limits of a large‐scale geophysical measuring network (such as arrays of seismometers for seismic hazard assessment, arrays of air guns and vibrators in seismic profiling, and station spacing in gravity, magnetic, magnetotelluric, and other geophysical surveys for exploration of oil, minerals, and groundwater) depends on the fractal dimension of the network and the anomaly (Lovejoy et al., 1986; Korvin, 1992). The geophysical anomaly resulting from the fractal nature of sources (Turcotte, 1992) [such as length of fault (Okubo and Aki, 1987; Robertson et al., 1995), velocity inhomogeneities (Sato, 1988), nonrandom distribution of density (Thorarinsson and Magnusson, 1990) and susceptibility (Pilkington and Todoeschuck, 1993; Pilkington et al., 1994; Maus and Dimri, 1994, 1995, 1996), reflectivity (Todoeschuck et al., 1990; Dimri, 1992), etc.] cannot be accurately measured unless its fractal dimension does not exceed the difference of the 2-D Euclidean and fractal dimension of the network (Lovejoy et al., 1986; Korvin, 1992).

CONFORMAL INVARIANCE OF CONTOUR LINES ON THE (2 + 1)-DIMENSIONAL RESTRICTED SOLID-ON-SOLID SURFACE

2011 ◽  
Vol 25 (04) ◽  
pp. 255-264 ◽  
Author(s):  
WEI ZHOU ◽  
GANG TANG ◽  
KUI HAN ◽  
HUI XIA ◽  
DA-PENG HAO ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Solid Surface ◽  
Large Scale ◽  
Fractal Dimensions ◽  
Universality Class ◽  
Invariant Curves ◽  
Conformal Invariant ◽  
Contour Lines ◽  
Loewner Evolution ◽  
Scale Limit

The contour lines of the saturated surface of the (2 + 1)-dimensional restricted solid-on-solid (RSOS) growth model are investigated by numerical method. It is shown that the calculated contour lines are conformal invariant curves with fractal dimension df = 1.34, and they belong to the universality class at large-scale limit, called the Schramm–Loewner evolution with diffusivity κ = 4. This is identical to the value obtained from the inverse cascade of surface quasigeostrophic (SQG) turbulence [Phys. Rev. Lett.98 (2007) 024501]. We also found that the measured fractal dimensions of contours on the (2 + 1)-dimensional RSOS saturated surfaces do not coincide well with that of SLE4 df = 1 + κ/8.

IMPACT OF FRACTAL DIMENSION IN THE DESIGN OF MULTI-RESONANT FRACTAL ANTENNAS

Fractals ◽  
2004 ◽  
Vol 12 (01) ◽  
pp. 55-66 ◽  
Author(s):  
K. J. VINOY ◽  
JOSE K. ABRAHAM ◽  
V. K. VARADAN
Keyword(s):  
Fractal Dimension ◽  
Resonant Frequency ◽  
Numerical Simulations ◽  
Fractal Dimensions ◽  
Input Resistance ◽  
Direct Influence ◽  
Fractal Nature ◽  
Science And Engineering ◽  
Resonant Frequencies ◽  
Atmospheric Sciences

During the last few decades, fractal geometries have found numerous applications in several fields of science and engineering such as geology, atmospheric sciences, forest sciences, physiology and electromagnetics. Although the very fractal nature of these geometries have been the impetus for their application in many of these areas, a direct quantifiable link between a fractal property such as dimension and antenna characteristics has been elusive thus far. In this paper, the variations in the input characteristics of multi-resonant antennas based on generalizations of Koch curves and fractal trees are examined by numerical simulations. Schemes for such generalizations of these geometries to vary their fractal dimensions are presented. These variations are found to have a direct influence on the primary resonant frequency, the input resistance at this resonance, and ratios resonant frequencies of these antennas. It is expected that these findings would further enhance the popularity of the study of fractals.

Fractal Structure of Au Geochemical Field for Shuikoushan Orefield in Hunan Province, China and its Application to Mineralization

2015 ◽  
Vol 1092-1093 ◽  
pp. 1398-1401 ◽  
Author(s):  
Yan Shi Xie ◽  
Jian Wen Yin ◽  
Kai Xuan Tan ◽  
Liang Chen ◽  
Yang Hu ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Large Scale ◽  
Fractal Structure ◽  
Fractal Dimensions ◽  
Hunan Province ◽  
Small Scale ◽  
Fractal Measure ◽  
Mafic Magmatism ◽  
Covering Method ◽  
Polymetallic Ore

The fractal measure on Au geochemical field of Mawangtang and Xinmengshan in Shuikoushan Pb-Zn-Au polymetallic ore field, Hunan, China was achieved by projective covering method in this paper. The results show a bifractal relation for Au Geochemical field which includes a textural fractal dimension (D1) at small scale and a structural fractal dimension (D2) at large scale with average breakpoint 86.0m which may be look as the movement scale of ore-forming fluid. All of fractal dimensions were between 2 to 3, D1 was 2.0011 and D2 was 2.0001 at Mawangtang as well as D1 was 2.4466 and D2 was 2.0408 at Xinmengshan respectively. The fractal dimensions appear the textural fractal dimensions were larger than their structural fractal dimensions indicate that the evolution of ore-forming fluid more complex than background value of this ore field. And what’s more, the fractal values of Mawangtang were larger than Xinmengshan may result from the mineralization with the former not only control by the overthrust structure and fold the same as the latter but also had a closed relationship with the acid to mafic magmatism.

FRACTAL DIMENSION, PRIMES, AND THE PERSISTENCE OF MEMORY

2003 ◽  
Vol 06 (02) ◽  
pp. 241-249
Author(s):  
JOSEPH L. PE
Keyword(s):  
Number Theory ◽  
Fractal Dimension ◽  
Fractal Dimensions ◽  
Distinguishing Characteristic ◽  
Local Behavior ◽  
Remarkable Similarity ◽  
Recursive Procedures

Many sequences from number theory, such as the primes, are defined by recursive procedures, often leading to complex local behavior, but also to graphical similarity on different scales — a property that can be analyzed by fractal dimension. This paper computes sample fractal dimensions from the graphs of some number-theoretic functions. It argues for the usefulness of empirical fractal dimension as a distinguishing characteristic of the graph. Also, it notes a remarkable similarity between two apparently unrelated sequences: the persistence of a number, and the memory of a prime. This similarity is quantified using fractal dimension.

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.

scholarly journals Dynamic characteristics and fractal representations of crack propagation of rock with different fissures under multiple impact loadings

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bing Sun ◽  
Shun Liu ◽  
Sheng Zeng ◽  
Shanyong Wang ◽  
Shaoping Wang
Keyword(s):  
Fractal Dimension ◽  
Crack Propagation ◽  
Crack Growth ◽  
Impact Test ◽  
Fractal Theory ◽  
Dynamic Change ◽  
Fractal Dimensions ◽  
Peak Stress ◽  
Dynamic Mechanical Properties ◽  
Gravitational Potential Energy

AbstractTo investigate the influence of the fissure morphology on the dynamic mechanical properties of the rock and the crack propagation, a drop hammer impact test device was used to conduct impact failure tests on sandstones with different fissure numbers and fissure dips, simultaneously recorded the crack growth after each impact. The box fractal dimension is used to quantitatively analyze the dynamic change in the sandstone cracks and a fractal model of crack growth over time is established based on fractal theory. The results demonstrate that under impact test conditions of the same mass and different heights, the energy absorbed by sandstone accounts for about 26.7% of the gravitational potential energy. But at the same height and different mass, the energy absorbed by the sandstone accounts for about 68.6% of the total energy. As the fissure dip increases and the number of fissures increases, the dynamic peak stress and dynamic elastic modulus of the fractured sandstone gradually decrease. The fractal dimensions of crack evolution tend to increase with time as a whole and assume as a parabolic. Except for one fissure, 60° and 90° specimens, with the extension of time, the increase rate of fractal dimension is decreasing correspondingly.

LATTICE DYNAMICS OF THE BINARY APERIODIC CHAINS OF ATOMS I: FRACTAL DIMENSION OF PHONON SPECTRA

1995 ◽  
Vol 09 (12) ◽  
pp. 1429-1451 ◽  
Author(s):  
WŁODZIMIERZ SALEJDA
Keyword(s):  
Fractal Dimension ◽  
Lattice Dynamics ◽  
Nearest Neighbor ◽  
Average Distance ◽  
Local Maximum ◽  
Fractal Dimensions ◽  
Dimension Formula ◽  
Phonon Spectra ◽  
Wide Range ◽  
Silver Mean

The microscopic harmonic model of lattice dynamics of the binary chains of atoms is formulated and studied numerically. The dependence of spring constants of the nearest-neighbor (NN) interactions on the average distance between atoms are taken into account. The covering fractal dimensions [Formula: see text] of the Cantor-set-like phonon spec-tra (PS) of generalized Fibonacci and non-Fibonaccian aperiodic chains containing of 16384≤N≤33461 atoms are determined numerically. The dependence of [Formula: see text] on the strength Q of NN interactions and on R=mH/mL, where mH and mL denotes the mass of heavy and light atoms, respectively, are calculated for a wide range of Q and R. In particular we found: (1) The fractal dimension [Formula: see text] of the PS for the so-called goldenmean, silver-mean, bronze-mean, dodecagonal and Severin chain shows a local maximum at increasing magnitude of Q and R>1; (2) At sufficiently large Q we observe power-like diminishing of [Formula: see text] i.e. [Formula: see text], where α=−0.14±0.02 and α=−0.10±0.02 for the above specified chains and so-called octagonal, copper-mean, nickel-mean, Thue-Morse, Rudin-Shapiro chain, respectively.

Fractal dimension based features are useful descriptors of leaf complexity and shape

1999 ◽  
Vol 29 (9) ◽  
pp. 1301-1310 ◽  
Author(s):  
Wojciech Borkowski
Keyword(s):  
Fractal Dimension ◽  
Tree Species ◽  
Fractal Dimensions ◽  
Plant Identification ◽  
Simple Method ◽  
Mass Dimension ◽  
Scale Range ◽  
Computer Identification

An application of fractal dimensions as measures of leaf complexity to morphometric studies and automated plant identification is presented. Detailed algorithms for the calculation of compass dimension and averaged mass dimension together with a simple method of grasping the scale range related variability are given. An analysis of complexity of more than 300 leaves from 10 tree species is reported. Several classical biometric descriptors as well as 16 fractal dimension features were computed on digitized leaf silhouettes. It is demonstrated that properly defined fractal dimension based features may be used to discriminate between species with more than 90% accuracy, especially when used together with other measures. It seems, therefore, that they can be utilized in computer identification systems and for purely taxonomical purposes.

scholarly journals Development of Back-calculation Model for Aggregate Gradation Determination Using Fractal Theory

2018 ◽  
Vol 159 ◽  
pp. 01006
Author(s):  
Bagus Hario Setiadji ◽  
Supriyono ◽  
Djoko Purwanto
Keyword(s):  
Fractal Dimension ◽  
Fractal Theory ◽  
Asphalt Mixture ◽  
Fractal Dimensions ◽  
Calculation Model ◽  
Careful Consideration ◽  
Upper And Lower Bounds ◽  
Aggregate Gradation ◽  
Fractal Characteristic ◽  
Fractal Characteristics

Several studies have shown that fractal theory can be used to analyze the morphology of aggregate materials in designing the gradation. However, the question arises whether a fractal dimension can actually represent a single aggregate gradation. This study, which is a part of a grand research to determine aggregate gradation based on known asphalt mixture specifications, is performed to clarify the aforementioned question. To do so, two steps of methodology were proposed in this study, that is, step 1 is to determine the fractal characteristics using 3 aggregate gradations (i.e. gradations near upper and lower bounds, and middle gradation); and step 2 is to back-calculate aggregate gradation based on fractal characteristics obtained using 2 scenarios, one-and multi-fractal dimension scenarios. The results of this study indicate that the multi-fractal dimension scenario provides a better prediction of aggregate gradation due to the ability of this scenario to better represent the shape of the original aggregate gradation. However, careful consideration must be observed when using more than two fractal dimensions in predicting aggregate gradation as it will increase the difficulty in developing the fractal characteristic equations.

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